Transcriber's note: A few typographical errors have been corrected: theyare listed at the end of the text. * * * * * BY AUGUSTUS DE MORGAN A BUDGET OFPARADOXES REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM SECOND EDITION EDITED BY DAVID EUGENE SMITH WITH A NEW INTRODUCTION BY ERNEST NAGEL PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE Volume I DOVER PUBLICATIONS, INC. , NEW YORK * * * * * PREFACE TO THE FIRST EDITION. (1872) It is not without hesitation that I have taken upon myself the editorshipof a work left avowedly imperfect by the author, and, from itsmiscellaneous and discursive character, difficult of completion with dueregard to editorial limitations by a less able hand. Had the author lived to carry out his purpose he would have looked throughhis Budget again, amplifying and probably rearranging some of its contents. He had collected materials for further illustration of Paradox of the kindtreated of in this book; and he meant to write a second part, in which thecontradictions and inconsistencies of orthodox learning would have beensubjected to the same scrutiny and castigation as heterodox ignorance hadalready received. It will be seen that the present volume contains more than the _Athenæum_Budget. Some of the additions formed a Supplement to the original articles. These supplementary paragraphs were, by the author, placed after those towhich they respectively referred, being distinguished from the rest of thetext by brackets. I have omitted these brackets as useless, except wherethey were needed to indicate subsequent writing. Another and a larger portion of the work consists of discussion of mattersof contemporary interest, for the Budget was in some degree a receptaclefor the author's thoughts on any literary, scientific, or social question. Having grown thus gradually to its present size, the book as it was leftwas not quite in a fit condition for publication, but the alterations whichhave been made are slight and few, being in most cases verbal, and such asthe sense absolutely required, or transpositions of sentences to securecoherence with the rest, in places where the author, in his more recentinsertion of them, had overlooked the connection in which they stood. In nocase has the meaning been in any degree modified or interfered with. One rather large omission must be mentioned here. It is an account of thequarrel between Sir James South and Mr. Troughton on the mounting, etc. Ofthe equatorial telescope at Campden Hill. At some future time when theaffair has passed entirely out of the memory of living Astronomers, theappreciative sketch, which is omitted in this edition of the Budget, willbe an interesting piece of history and study of character. [1] A very small portion of Mr. James Smith's circle-squaring has been leftout, with a still smaller portion of Mr. De Morgan's answers to thatCyclometrical Paradoxer. In more than one place repetitions, which would have disappeared under theauthor's revision, have been allowed to remain, because they could not havebeen taken away without leaving a hiatus, not easy to fill up withoutdamage to the author's meaning. I give these explanations in obedience to the rules laid down for theguidance of editors at page 15. [2] If any apology for the fragmentarycharacter of the book be thought necessary, it may be found in the author'sown words at page 281 of the second volume. [3] The publication of the Budget could not have been delayed without lesseningthe interest attaching to the writer's thoughts upon questions of our ownday. I trust that, incomplete as the work is compared with what it mighthave been, I shall not be held mistaken in giving it to the world. Ratherlet me hope that it will be welcomed as an old friend returning under greatdisadvantages, but bringing a pleasant remembrance of the amusement whichits weekly appearance in the _Athenæum_ gave to both writer and reader. The Paradoxes are dealt with in chronological order. This will be a guideto the reader, and with the alphabetical Index of Names, etc. , will, Itrust, obviate all difficulty of reference. SOPHIA DE MORGAN. 6 MERTON ROAD, PRIMROSE HILL. * * * * * PREFACE TO THE SECOND EDITION. If Mrs. De Morgan felt called upon to confess her hesitation at taking uponherself the labor of editing these Paradoxes, much more should one who wasborn two generations later, who lives in another land and who was rearedamid different influences, confess to the same feeling when undertaking torevise this curious medley. But when we consider the nature of the work, the fact that its present rarity deprives so many readers of the enjoymentof its delicious satire, and the further fact that allusions that werecommonplace a half century ago are now forgotten, it is evident that someone should take up the work and perform it _con amore_. Having long been an admirer of De Morgan, having continued his work in thebibliography of early arithmetics, and having worked in his library amongthe books of which he was so fond, it is possible that the present editor, whatever may be his other shortcomings, may undertake the labor with asmuch of sympathy as any one who is in a position to perform it. With thisthought in mind, two definite rules were laid down at the beginning of thetask: (1) That no alteration in the text should be made, save in slightlymodernizing spelling and punctuation and in the case of manifesttypographical errors; (2) That whenever a note appeared it should show atonce its authorship, to the end that the material of the original editionmight appear intact. In considering, however, the unbroken sequence of items that form theBudget, it seems clear that readers would be greatly aided if the variousleading topics were separated in some convenient manner. After considerablethought it was decided to insert brief captions from time to time thatmight aid the eye in selecting the larger subjects of the text. In someparts of the work these could easily be taken from the original folioheads, but usually they had to be written anew. While, therefore, thepresent editor accepts the responsibility for the captions of the varioussubdivisions, he has endeavored to insert them in harmony with the originaltext. As to the footnotes, the first edition had only a few, some due to DeMorgan himself and others to Mrs. De Morgan. In the present edition thosedue to the former are signed A. De M. , and those due to Mrs. De Morganappear with her initials, S. E. De M. For all other footnotes the presenteditor is responsible. In preparing them the effort has been made toelucidate the text by supplying such information as the casual reader mightwish as he passes over the pages. Hundreds of names are referred to in thetext that were more or less known in England half a century ago, but arenow forgotten there and were never familiar elsewhere. Many books that werethen current have now passed out of memory, and much that agitated Englandin De Morgan's prime seems now like ancient history. Even with respect towell-known names, a little information as to dates and publications willoften be welcome, although the editor recognizes that it will quite asoften be superfluous. In order, therefore, to derive the pleasure thatshould come from reading the Budget, the reader should have easy access tothe information that the notes are intended to supply. That they furnishtoo much here and too little there is to be expected. They are a humanproduct, and if they fail to serve their purpose in all respects it ishoped that this failure will not seriously interfere with the reader'spleasure. In general the present editor has refrained from expressing any opinionsthat would strike a discordant note in the reading of the text as De Morganleft it. The temptation is great to add to the discussion at variouspoints, but it is a temptation to be resisted. To furnish such informationas shall make the reading more pleasant, rather than to attempt to improveupon one of the most delicious bits of satire of the nineteenth century, has been the editor's wish. It would have been an agreeable task to reviewthe history of circle squaring, of the trisection problem, and of theduplication of the cube. This, however, would be to go too far afield. Forthe benefit of those who wish to investigate the subject the editor canonly refer to such works and articles as the following: F. Rudio, _Archimedes, Huygens, Lambert, Legendre, --mit einer Uebersicht über dieGeschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;Thomas Muir, "Circle, " in the eleventh edition of the _EncyclopædiaBritannica_; the various histories of mathematics; and to his own articleon "The Incommensurability of [pi]" in Prof. J. W. A. Young's _Monographson Topics of Modern Mathematics_, New York, 1911. The editor wishes to express his appreciation and thanks to Dr. Paul Carus, editor of _The Monist_ and _The Open Court_ for the opportunity ofundertaking this work; to James Earl Russell, LL. D. , Dean of TeachersCollege, Columbia University, for his encouragement in its prosecution; toMiss Caroline Eustis Seely for her intelligent and painstaking assistancein securing material for the notes; and to Miss Lydia G. Robinson and MissAnna A. Kugler for their aid and helpful suggestions in connection with theproof-sheets. Without the generous help of all five this work would havebeen impossible. DAVID EUGENE SMITH. TEACHERS COLLEGE, COLUMBIA UNIVERSITY. * * * * * A BUDGET OF PARADOXES {1} INTRODUCTORY. If I had before me a fly and an elephant, having never seen more than onesuch magnitude of either kind; and if the fly were to endeavor to persuademe that he was larger than the elephant, I might by possibility be placedin a difficulty. The apparently little creature might use such argumentsabout the effect of distance, and might appeal to such laws of sight andhearing as I, if unlearned in those things, might be unable wholly toreject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different andfrequently contradictory reasons; and each one despising and opposing thereasons of the others--I should feel quite at my ease. I should certainlysay, My little friends, the case of each one of you is destroyed by therest. I intend to show flies in the swarm, with a few larger animals, forreasons to be given. In every age of the world there has been an established system, which hasbeen opposed from time to time by isolated and dissentient reformers. Theestablished system has sometimes fallen, slowly and gradually: it haseither been upset by the rising influence of some one man, or it has beensapped by gradual change of opinion in the many. I have insisted on the isolated character of the dissentients, as anelement of the _a priori_ probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; butan {2} organized opposition, supported by the efforts of many acting inconcert, appealing to common arguments and experience, with perpetualsuccession and a common seal, as the Queen says in the charter, is, be themerit of the schism what it may, a thing wholly different from the case ofthe isolated opponent in the mode of opposition to it which reason pointsout. During the last two centuries and a half, physical knowledge has beengradually made to rest upon a basis which it had not before. It has become_mathematical_. The question now is, not whether this or that hypothesis isbetter or worse to the pure thought, but whether it accords with observedphenomena in those consequences which can be shown necessarily to followfrom it, if it be true. Even in those sciences which are not yet under thedominion of mathematics, and perhaps never will be, a working copy of themathematical process has been made. This is not known to the followers ofthose sciences who are not themselves mathematicians and who very oftenexalt their horns against the mathematics in consequence. They might aswell be squaring the circle, for any sense they show in this particular. A great many individuals, ever since the rise of the mathematical method, have, each for himself, attacked its direct and indirect consequences. Ishall not here stop to point out how the very accuracy of exact sciencegives better aim than the preceding state of things could give. I shallcall each of these persons a _paradoxer_, and his system a _paradox_. I usethe word in the old sense: a paradox is something which is apart fromgeneral opinion, either in subject-matter, method, or conclusion. Many of the things brought forward would now be called _crotchets_, whichis the nearest word we have to old _paradox_. But there is this difference, that by calling a thing a _crotchet_ we mean to speak lightly of it; whichwas not the necessary sense of _paradox_. Thus in the sixteenth centurymany spoke of the earth's motion as the _paradox of {3} Copernicus_, whoheld the ingenuity of that theory in very high esteem, and some, I think, who even inclined towards it. In the seventeenth century, the depravationof meaning took place, in England at least. Phillips says _paradox_ is "athing which seemeth strange"--here is the old meaning: after a colon heproceeds--"and absurd, and is contrary to common opinion, " which is anaddition due to his own time. Some of my readers are hardly inclined to think that the word _paradox_could once have had no disparagement in its meaning; still less thatpersons could have applied it to themselves. I chance to have met with acase in point against them. It is Spinoza's _Philosophia ScripturæInterpres, Exercitatio Paradoxa_, printed anonymously at Eleutheropolis, in1666. This place was one of several cities in the clouds, to which thecuckoos resorted who were driven away by the other birds; that is, afeigned place of printing, adopted by those who would have caught it iforthodoxy could have caught them. Thus, in 1656, the works of Socinus couldonly be printed at Irenopolis. The author deserves his self-imposed title, as in the following:[4] "Quanto sane satius fuisset illam [Trinitatem] pro mysterio non habuisse, et Philosophiæ ope, antequam quod esset statuerent, secundum veræ logicespræcepta quid esset cum Cl. Kleckermanno investigasse; tanto fervore aclabore in profundissimas speluncas et obscurissimos metaphysicarumspeculationum atque fictionum recessus se recipere ut ab adversariorumtelis sententiam suam in tuto collocarent. {4} Profecto magnus ille vir ... Dogma illud, quamvis apud theologos eo nomine non multum gratiæ iniverit, ita ex immotis Philosophiæ fundamentis explicat ac demonstrat, ut paucistantum immutatis, atque additis, nihil amplius animus veritate sincerededitus desiderare possit. " This is properly paradox, though also heterodox. It supposes, contrary toall opinion, orthodox and heterodox, that philosophy can, with slightchanges, explain the Athanasian doctrine so as to be at least compatiblewith orthodoxy. The author would stand almost alone, if not quite; and thisis what he meant. I have met with the counter-paradox. I have heard itmaintained that the doctrine as it stands, in all its mystery is _a priori_more likely than any other to have been Revelation, if such a thing were tobe; and that it might almost have been predicted. After looking into books of paradoxes for more than thirty years, andholding conversation with many persons who have written them, and many whomight have done so, there is one point on which my mind is fully made up. The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has notmade a sufficient knowledge of what has been done by others, _especially asto the mode of doing it_, a preliminary to inventing knowledge for himself. That a little knowledge is a dangerous thing is one of the most fallaciousof proverbs. A person of small knowledge is in danger of trying to make his_little_ do the work of _more_; but a person without any is in more dangerof making his _no_ knowledge do the work of _some_. Take the speculationson the tides as an instance. Persons with nothing but a little geometryhave certainly exposed themselves in their modes of objecting to resultswhich require the higher mathematics to be known before an independentopinion can be formed on sufficient grounds. But persons with no geometryat all have done the same thing much more completely. {5} There is a line to be drawn which is constantly put aside in the argumentsheld by paradoxers in favor of their right to instruct the world. Mostpersons must, or at least will, like the lady in Cadogan Place, [5] form andexpress an immense variety of opinions on an immense variety of subjects;and all persons must be their own guides in many things. So far all iswell. But there are many who, in carrying the expression of their ownopinions beyond the usual tone of private conversation, whether they go nofurther than attempts at oral proselytism, or whether they committhemselves to the press, do not reflect that they have ceased to stand uponthe ground on which their process is defensible. Aspiring to lead _others_, they have never given themselves the fair chance of being first led by_other_ others into something better than they can start for themselves;and that they should first do this is what both those classes of othershave a fair right to expect. New knowledge, when to any purpose, must comeby contemplation of old knowledge in every matter which concerns thought;mechanical contrivance sometimes, not very often, escapes this rule. Allthe men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned inwhat had been before them. There is not one exception. I do not say thatevery man has made direct acquaintance with the whole of his mentalancestry; many have, as I may say, only known their grandfathers by thereport of their fathers. But even on this point it is remarkable how manyof the greatest names in all departments of knowledge have been realantiquaries in their several subjects. I may cite, among those who have wrought strongly upon opinion or practicein science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahé, Galileo, Napier, Descartes, Leibnitz, Newton, Locke. I take none but names known out of their {6}fields of work; and all were learned as well as sagacious. I have chosen myinstances: if any one will undertake to show a person of little or noknowledge who has established himself in a great matter of pure thought, let him bring forward his man, and we shall see. This is the true way of putting off those who plague others with theirgreat discoveries. The first demand made should be--Mr. Moses, before Iallow you to lead me over the Red Sea, I must have you show that you arelearned in all the wisdom of the Egyptians upon your own subject. The pleathat it is unlikely that this or that unknown person should succeed whereNewton, etc. Have failed, or should show Newton, etc. To be wrong, isutterly null and void. It was worthily versified by Sylvanus Morgan (thegreat herald who in his _Sphere of Gentry_ gave coat armor to "GentlemanJesus, " as he said), who sang of Copernicus as follows (1652): "If Tellus winged be, The earth a motion round; Then much deceived are they Who nere before it found. Solomon was the wisest, His wit nere this attained; Cease, then, Copernicus, Thy hypothesis is vain. " Newton, etc. Were once unknown; but they made themselves known by what theyknew, and then brought forward what they could do; which I see is as goodverse as that of Herald Sylvanus. The demand for previous knowledgedisposes of twenty-nine cases out of thirty, and the thirtieth is worthlistening to. I have not set down Copernicus, Galileo, etc. Among the paradoxers, merelybecause everybody knows them; if my list were quite complete, they wouldhave been in it. But the reader will find Gilbert, the great precursor ofsound magnetical theory; and several others on whom no censure can be cast, though some of their paradoxes are inadmissible, {7} some unprovoked, andsome capital jokes, true or false: the author of _Vestiges of Creation_ isan instance. I expect that my old correspondent, General Perronet Thompson, will admit that his geometry is part and parcel of my plan; and also that, if that plan embraced politics, he would claim a place for his _Catechismon the Corn Laws_, a work at one time paradoxical, but which had more to dowith the abolition of the bread-tax than Sir Robert Peel. My intention in publishing this Budget in the _Athenæum_ is _to enablethose who have been puzzled by one or two discoverers to see how they lookin a lump_. The only question is, has the selection been fairly made? Tothis my answer is, that no selection at all has been made. The books are, without exception, those which I have in my own library; and I have taken_all_--I mean all of the kind: Heaven forbid that I should be supposed tohave no other books! But I may have been a collector, influenced in choiceby bias? I answer that I never have collected books of this sort--that is, I have never searched for them, never made up my mind to look out for thisbook or that. I have bought what happened to come in my way at show orauction; I have retained what came in as part of the _undescribed_ portionof miscellaneous auction lots; I have received a few from friends who foundthem among what they called their rubbish; and I have preserved books sentto me for review. In not a few instances the books have been bound up withothers, unmentioned at the back; and for years I knew no more I had themthan I knew I had Lord Macclesfield's speech on moving the change of Style, which, after I had searched shops, etc. For it in vain, I found had beenreposing on my own shelves for many years, at the end of a summary ofLeibnitz's philosophy. Consequently, I may positively affirm that thefollowing list is formed by accident and circumstance alone, and that ittruly represents the casualties of about a third of a century. Forinstance, the large proportion of works {8} on the quadrature of the circleis not my doing: it is the natural share of this subject in the actual runof events. [I keep to my plan of inserting only such books as I possessed in 1863, except by casual notice in aid of my remarks. I have found several books onmy shelves which ought to have been inserted. These have their titles setout at the commencement of their articles, in leading paragraphs; thecasuals are without this formality. [6]] Before proceeding to open the Budget, I say something on my personalknowledge of the class of discoverers who square the circle, upset Newton, etc. I suspect I know more of the English class than any man in Britain. Inever kept any reckoning; but I know that one year with another--and lessof late years than in earlier time--I have talked to more than five in eachyear, giving more than a hundred and fifty specimens. Of this I am sure, that it is my own fault if they have not been a thousand. Nobody knows howthey swarm, except those to whom they naturally resort. They are in allranks and occupations, of all ages and characters. They are very earnestpeople, and their purpose is _bona fide_ the dissemination of theirparadoxes. A great many--the mass, indeed--are illiterate, and a great manywaste their means, and are in or approaching penury. But I must say thatnever, in any one instance, has the quadrature of the circle, or the like, been made a pretext for begging; even to be asked to purchase a book is ofthe very rarest occurrence--it has happened, and that is all. These discoverers despise one another: if there were the concert among themwhich there is among foreign mendicants, a man who admitted one to aconference would be plagued to death. I once gave something to a verygenteel French applicant, who overtook me in the street, at my own door, saying he had picked up my handkerchief: whether he picked it up in mypocket for an introduction, I know not. {9} But that day week came anotherFrenchman to my house, and that day fortnight a French lady; both failed, and I had no more trouble. The same thing happened with Poles. It is not sowith circle-squarers, etc. : they know nothing of each other. Some will readthis list, and will say I am right enough, generally speaking, but thatthere _is_ an exception, if I could but see it. I do not mean, by my confession of the manner in which I have sinnedagainst the twenty-four hours, to hold myself out as accessible to personalexplanation of new plans. Quite the contrary: I consider myself as havingmade my report, and being discharged from further attendance on thesubject. I will not, from henceforward, talk to any squarer of the circle, trisector of the angle, duplicator of the cube, constructor of perpetualmotion, subverter of gravitation, stagnator of the earth, builder of theuniverse, etc. I will receive any writings or books which require noanswer, and read them when I please: I will certainly preserve them--thislist may be enlarged at some future time. There are three subjects which I have hardly anything upon; astrology, mechanism, and the infallible way of winning at play. I have never cared topreserve astrology. The mechanists make models, and not books. Theinfallible winners--though I have seen a few--think their secret toovaluable, and prefer _mutare quadrata rotundis_--to turn dice into coin--atthe gaming-house: verily they have their reward. I shall now select, to the mystic number seven, instances of my personalknowledge of those who think they have discovered, in illustration of asmany misconceptions. 1. _Attempt by help of the old philosophy, the discoverer not being inpossession of modern knowledge. _ A poor schoolmaster, in rags, introducedhimself to a scientific friend with whom I was talking, and announced thathe had found out the composition of the sun. "How was that done?"--"Byconsideration of the four elements. "--"What are {10} they?"--"Of course, fire, air, earth, and water. "--"Did you not know that air, earth, andwater, have long been known to be no elements at all, butcompounds?"--"What do you mean, sir? Who ever heard of such a thing?" 2. _The notion that difficulties are enigmas, to be overcome in a moment bya lucky thought. _ A nobleman of very high rank, now long dead, read anarticle by me on the quadrature, in an early number of the _PennyMagazine_. He had, I suppose, school recollections of geometry. He putpencil to paper, drew a circle, and constructed what seemed likely toanswer, and, indeed, was--as he said--certain, if only this bit were equalto that; which of course it was not. He forwarded his diagram to theSecretary of the Diffusion Society, to be handed to the author of thearticle, in case the difficulty should happen to be therein overcome. 3. _Discovery at all hazards, to get on in the world. _ Thirty years ago, anofficer of rank, just come from foreign service, and trying for adecoration from the Crown, found that his claims were of doubtful amount, and was told by a friend that so and so, who had got the order, had theadditional claim of scientific distinction. Now this officer, while abroad, had bethought himself one day, that there really could be no difficulty infinding the circumference of a circle: if a circle were rolled upon astraight line until the undermost point came undermost again, there wouldbe the straight line equal to the circle. He came to me, saying that he didnot feel equal to the statement of his claim in this respect, but that ifsome clever fellow would put the thing in a proper light, he thought hisaffair might be managed. I was clever enough to put the thing in a properlight to himself, to this extent at least, that, though perhaps they werewrong, the advisers of the Crown would never put the letters K. C. B. To sucha circle as his. 4. _The notion that mathematicians cannot find the circle for commonpurposes. _ A working man measured the altitude of a cylinder accurately, and--I think the process of {11} Archimedes was one of hisproceedings--found its bulk. He then calculated the ratio of thecircumference to the diameter, and found it answered very well on othermodes of trial. His result was about 3. 14. He came to London, and somebodysent him to me. Like many others of his pursuit, he seemed to have turnedthe whole force of his mind upon one of his points, on which alone he wouldbe open to refutation. He had read some of Kater's experiments, and had gotthe Act of 1825 on weights and measures. Say what I would, he had for along time but one answer--"Sir! I go upon Captain Kater and the Act ofParliament. " But I fixed him at last. I happened to have on the table aproof-sheet of the _Astronomical Memoirs_, in which were a large number ofobserved places of the planets compared with prediction, and asked himwhether it could be possible that persons who did not know the circlebetter than he had found it could make the calculations, of which I gavehim a notion, so accurately? He was perfectly astonished, and took thetitles of some books which he said he would read. 5. _Application for the reward from abroad. _ Many years ago, abouttwenty-eight, I think, a Jesuit came from South America, with a quadrature, and a cutting from a newspaper announcing that a reward was ready for thediscovery in England. On this evidence he came over. After satisfying himthat nothing had ever been offered here, I discussed his quadrature, whichwas of no use. I succeeded better when I told him of Richard White, also aJesuit, and author of a quadrature published before 1648, under the name of_Chrysæspis_, of which I can give no account, having never seen it. ThisWhite (_Albius_) is the only quadrator who was ever convinced of his error. My Jesuit was struck by the instance, and promised to read moregeometry--he was no Clavius--before he published his book. He relapsed, however, for I saw his book advertised in a few days. I may say, assufficient proof of my being no collector, that I had not the curiosity tobuy his book; and my friend the {12} Jesuit did not send me a copy, whichhe ought to have done, after the hour I had given him. 6. _Application for the reward at home. _ An agricultural laborer squaredthe circle, and brought the proceeds to London. He left his papers with me, one of which was the copy of a letter to the Lord Chancellor, desiring hisLordship to hand over forthwith 100, 000 pounds, the amount of the allegedoffer of reward. He did not go quite so far as M. De Vausenville, who, Ithink in 1778, brought an action against the Academy of Sciences to recovera reward to which he held himself entitled. I returned the papers, with anote, stating that he had not the knowledge requisite to see in what theproblem consisted. I got for answer a letter in which I was told that aperson who could not see that he had done the thing should "change hisbusiness, and appropriate his time and attention to a Sunday-school, tolearn what he could, and keep the _litle_ children from _durting_ their_close_. " I also received a letter from a friend of the quadrator, informing me that I knew his friend had succeeded, and had been heard tosay so. These letters were printed--without the names of the writers--forthe amusement of the readers of _Notes and Queries_, First Series, xii. 57, and they will appear again in the sequel. [There are many who have such a deep respect for any attempt at thoughtthat they are shocked at ridicule even of those who have made themselvesconspicuous by pretending to lead the world in matters which they have notstudied. Among my anonyms is a gentleman who is angry at my treatment ofthe "poor but thoughtful" man who is described in my introduction asrecommending me to go to a Sunday-school because I informed him that he didnot know in what the difficulty of quadrature consisted. My impugner quiteforgets that this man's "thoughtfulness" chiefly consisted in his demandinga hundred thousand pounds from the Lord Chancellor for his discovery; and Imay add, that his greatest stretch of invention was finding out that "theclergy" {13} were the means of his modest request being unnoticed. Imention this letter because it affords occasion to note a very commonerror, namely, that men unread in their subjects have, by natural wisdom, been great benefactors of mankind. My critic says, "Shakspeare, whom thePro^r (_sic_) may admit to be a wisish man, though an object of contempt asto learning ... " Shakespeare an object of contempt as to learning! Thoughnot myself a thoroughgoing Shakespearean--and adopting the first half ofthe opinion given by George III, "What! is there not sad stuff? only onemust not say so"--I am strongly of opinion that he throws out the masonicsigns of learning in almost every scene, to all who know what they are. Andthis over and above every kind of direct evidence. First, foremost, andenough, the evidence of Ben Jonson that he had "little Latin and lessGreek"; then Shakespeare had as much Greek as Jonson would call _some_, even when he was depreciating. To have any Greek at all was in those daysexceptional. In Shakespeare's youth St. Paul's and Merchant Taylor'sschools were to have masters learned in good and clean Latin literature, _and also in Greek if such may be gotten_. When Jonson spoke as above, heintended to put Shakespeare low among the learned, but not out of theirpale; and he spoke as a rival dramatist, who was proud of his own learnedsock; and it may be a subject of inquiry how much Latin _he_ would call_little_. If Shakespeare's learning on certain points be very much lessvisible than Jonson's, it is partly because Shakespeare's writings hold itin chemical combination, Jonson's in mechanical aggregation. ] 7. An elderly man came to me to show me how the universe was created. Therewas one molecule, which by vibration became--Heaven knows how!--the Sun. Further vibration produced Mercury, and so on. I suspect the nebularhypothesis had got into the poor man's head by reading, in some singularmixture with what it found there. Some modifications of vibration gaveheat, electricity, etc. I {14} listened until my informant ceased tovibrate--which is always the shortest way--and then said, "Our knowledge ofelastic fluids is imperfect. " "Sir!" said he, "I see you perceive the truthof what I have said, and I will reward your attention by telling you what Iseldom disclose, never, except to those who can receive my theory--thelittle molecule whose vibrations have given rise to our solar system is theLogos of St. John's Gospel!" He went away to Dr. Lardner, who would not gointo the solar system at all--the first molecule settled the question. Sohard upon poor discoverers are men of science who are not antiquaries intheir subject! On leaving, he said, "Sir, Mr. De Morgan received me in avery different way! he heard me attentively, and I left him perfectlysatisfied of the truth of my system. " I have had much reason to think thatmany discoverers, of all classes, believe they have convinced every one whois not peremptory to the verge of incivility. My list is given in chronological order. My readers will understand that mygeneral expressions, where slighting or contemptuous, refer to theignorant, who teach before they have learned. In every instance, those ofwhom I am able to speak with respect, whether as right or wrong, havesought knowledge in the subject they were to handle before they completedtheir speculations. I shall further illustrate this at the conclusion of mylist. Before I begin the list, I give prominence to the following letter, addressed by me to the _Correspondent_ of October 28, 1865. Some of myparadoxers attribute to me articles in this or that journal; and others maythink--I know some do think--they know me as the writer of reviews of someof the very books noticed here. The following remarks will explain the wayin which they may be right, and in which they may be wrong. {15} * * * * * THE EDITORIAL SYSTEM. "Sir, --I have reason to think that many persons have a very inaccuratenotion of the _Editorial System_. What I call by this name has grown up inthe last _centenary_--a word I may use to signify the hundred years nowending, and to avoid the ambiguity of _century_. It cannot conveniently beexplained by editors themselves, and _edited_ journals generally do notlike to say much about it. In _your_ paper perhaps, in which editorialduties differ somewhat from those of ordinary journals, the common systemmay be freely spoken of. "When a reviewed author, as very often happens, writes to the editor of thereviewing journal to complain of what has been said of him, hefrequently--even more often than not--complains of 'your reviewer. ' Hesometimes presumes that 'you' have, 'through inadvertence' in thisinstance, 'allowed some incompetent person to lower the character of yourusually accurate pages. ' Sometimes he talks of 'your scribe, ' and, inextreme cases, even of 'your hack. ' All this shows perfect ignorance of thejournal system, except where it is done under the notion of letting theeditor down easy. But the editor never accepts the mercy. "All that is in a journal, except what is marked as from a correspondent, either by the editor himself or by the correspondent's real or fictitioussignature, is published entirely on editorial responsibility, as much as ifthe editor had written it himself. The editor, therefore, may claim, anddoes claim and exercise, unlimited right of omission, addition, andalteration. This is so well understood that the editor performs his lastfunction on the last revise without the 'contributor' knowing what is done. The word _contributor_ is the proper one; it implies that he furnishesmaterials without stating what he furnishes or how much of it is accepted, or whether he be the only contributor. All this applies both to politicaland literary journals. No editor acknowledges {16} the right of acontributor to withdraw an article, if he should find alterations in theproof sent to him for correction which would make him wish that the articleshould not appear. If the _demand_ for suppression were made--I say nothingabout what might be granted to _request_--the answer would be, 'It is notyour article, but mine; I have all the responsibility; if it should containa libel, I could not give you up, even at your own desire. You havefurnished me with materials, on the known and common understanding that Iwas to use them at my discretion, and you have no right to impede myoperations by making the appearance of the article depend on yourapprobation of my use of your materials. ' "There is something to be said for this system, and something against it--Imean simply on its own merits. But the all-conquering argument in its favoris, that the only practicable alternative is the modern French plan of noarticles without the signature of the writers. I need not discuss thisplan; there is no collective party in favor of it. Some may think it is notthe only alternative; they have not produced any intermediate proposal inwhich any dozen of persons have concurred. Many will say, Is not all this, though perfectly correct, well known to be matter of form? Is it notpractically the course of events that an engaged contributor writes thearticle, and sends it to the editor, who admits it aswritten--substantially, at least? And is it not often very well known, bystyle and in other ways, who it was wrote the article? This system ismatter of form just as much as loaded pistols are matter of form so long asthe wearer is not assailed; but matter of form takes the form of matter inthe pulling of a trigger, so soon as the need arises. Editors andcontributors who can work together find each other out by electiveaffinity, so that the common run of events settles down into most articlesappearing much as they are written. And there are two safety-valves; thatis, when judicious persons come together. In the first place, the editorhimself, when he has selected his contributor, feels that {17} thecontributor is likely to know his business better than an editor can teachhim; in fact, it is on that principle that the selection is made. But hefeels that he is more competent than the writer to judge questions ofstrength and of tone, especially when the general purpose of the journal isconsidered, of which the editor is the judge without appeal. An editor whomeddles with substantive matter is likely to be wrong, even when he knowsthe subject; but one who prunes what he deems excess, is likely to beright, even when he does not know the subject. In the second place, acontributor knows that he is supplying an editor, and learns, withoutsuppressing truth or suggesting falsehood, to make the tone of hiscommunications suit the periodical in which they are to appear. Hence itvery often arises that a reviewed author, who thinks he knows the name ofhis reviewer, and proclaims it with expressions of dissatisfaction, is onlywrong in supposing that his critic has given all his mind. It has happenedto myself more than once, to be announced as the author of articles which Icould not have signed, because they did not go far enough to warrant myaffixing my name to them as to a sufficient expression of my own opinion. "There are two other ways in which a reviewed author may be wrong about hiscritic. An editor frequently makes slight insertions or omissions--I meanslight in quantity of type--as he goes over the last proof; this he does ina comparative hurry, and it may chance that he does not know the full stingof his little alteration. The very bit which the writer of the book mostcomplains of may not have been seen by the person who is called the writerof the article until after the appearance of the journal; nay, if he be oneof those--few, I daresay--who do not read their own articles, may neverhave been seen by him at all. Possibly, the insertion or omission would nothave been made if the editor could have had one minute's conversation withhis contributor. Sometimes it actually contradicts something which is {18}allowed to remain in another part of the article; and sometimes, especiallyin the case of omission, it renders other parts of the articleunintelligible. These are disadvantages of the system, and a judiciouseditor is not very free with his _unus et alter pannus_. Next, readers ingeneral, when they see the pages of a journal with the articles so nicelyfitting, and so many ending with the page or column, have very littlenotion of the cutting and carving which goes to the process. At the verylast moment arises the necessity of some trimming of this kind; and theeditor, who would gladly call the writer to counsel if he could, is obligedto strike out ten or twelve lines. He must do his best, but it may chancethat the omission selected would take from the writer the power of owningthe article. A few years ago, an able opponent of mine wrote to a journalsome criticisms upon an article which he expressly attributed to me. Ireplied as if I were the writer, which, in a sense, I was. But if any onehad required of me an unmodified 'Yes' or 'No' to the question whether Iwrote the article, I must, of two falsehoods, have chosen 'No': for certainomissions, dictated by the necessities of space and time, would haveamounted, had my signature been affixed, to a silent surrender of pointswhich, in my own character, I must have strongly insisted on, unless I hadchosen to admit certain inferences against what I had previously publishedin my own name. I may here add that the forms of journalism obliged me inthis case to remind my opponent that it could not be permitted to me, _inthat journal_, either to acknowledge or deny the authorship of thearticles. The cautions derived from the above remarks are particularlywanted with reference to the editorial comments upon letters of complaint. There is often no time to send these letters to the contributor, and evenwhen this can be done, an editor is--and very properly--never of soeditorial a mind as when he is revising the comments of a contributor uponan assailant of the article. He is then in a better position as toinformation, and a more {19} critical position as to responsibility. Ofcourse, an editor never meddles, except under notice, with the letter of acorrespondent, whether of a complainant, of a casual informant, or of acontributor who sees reason to become a correspondent. Omissions mustsometimes be made when a grievance is too highly spiced. It did once happento me that a waggish editor made an insertion without notice in a lettersigned by me with some fiction, which insertion contained the name of afriend of mine, with a satire which I did not believe, and should not havewritten if I had. To my strong rebuke, he replied--'I know it was verywrong; but human nature could not resist. ' But this was the only occasionon which such a thing ever happened to me. "I daresay what I have written may give some of your readers to understandsome of the _pericula et commoda_ of modern journalism. I have known men ofdeep learning and science as ignorant of the prevailing system as anyuneducated reader of a newspaper in a country town. I may perhaps inducesome writers not to be too sure about this, that, or the other person. Theymay detect their reviewer, and they may be safe in attributing to him thegeneral matter and tone of the article. But about one and another point, especially if it be a short and stinging point, they may very easily chanceto be wrong. It has happened to myself, and within a few weeks topublication, to be wrong in two ways in reading a past article--toattribute to editorial insertion what was really my own, and to attributeto myself what was really editorial insertion. " What is a man to do who is asked whether he wrote an article? He may, ofcourse, refuse to answer; which is regarded as an admission. He may say, asSwift did to Serjeant Bettesworth, "Sir, when I was a young man, a friendof mine advised me, whenever I was asked whether I had written a certainpaper, to deny it; and I accordingly tell that I did _not_ write it. " Hemay say, as I often do, {20} when charged with having invented a joke, story, or epigram, "I want all the credit I can get, and therefore I alwaysacknowledge all that is attributed to me, truly or not; the story, etc. _is_ mine. " But for serious earnest, in the matter of imputed criticism, the answer may be, "The article was of my material, but the editor has notlet it stand as I gave it; I cannot own it as a whole. " He may then refuseto be particular as to the amount of the editor's interference. Of thisthere are two extreme cases. The editor may have expunged nothing but aqualifying adverb. Or he may have done as follows. We all remember theaccount of Adam which satirizes woman, but eulogizes her if every secondand third line be transposed. As in: "Adam could find no solid peace When Eve was given him for a mate, Till he beheld a woman's face, Adam was in a happy state. " If this had been the article, and a gallant editor had made thetranspositions, the author could not with truth acknowledge. If thealteration were only an omitted adverb, or a few things of the sort, theauthor could not with truth deny. In all that comes between, every man mustbe his own casuist. I stared, when I was a boy, to hear grave personsapprove of Sir Walter Scott's downright denial that he was the author ofWaverley, in answer to the Prince Regent's downright question. If Iremember rightly, Samuel Johnson would have approved of the same course. It is known that, whatever the law gives, it also gives all that isnecessary to full possession; thus a man whose land is environed by land ofothers has a right of way over the land of these others. By analogy, it isargued that when a man has a right to his secret, he has a right to allthat is necessary to keep it, and that is not unlawful. If, then, he canonly keep his secret by denial, he has a right to denial. This I admit tobe an answer against all men except the denier himself; if conscience andself-respect will allow {21} it, no one can impeach it. But the questioncannot be solved on a case. That question is, A lie, is it _malum in se_, without reference to meaning and circumstances? This is a question with twosides to it. Cases may be invented in which a lie is the only way ofpreventing a murder, or in which a lie may otherwise save a life. In thesecases it is difficult to acquit, and almost impossible to blame; discretionintroduced, the line becomes very hard to draw. I know but one work which has precisely--as at first appears--the characterand object of my Budget. It is the _Review of the Works of the RoyalSociety of London_, by Sir John Hill, M. D. (1751 and 1780, 4to. ). This manoffended many: the Royal Society, by his work, the medical profession, byinventing and selling extra-pharmacopoeian doses; Garrick, by resenting therejection of a play. So Garrick wrote: "For physic and farces his equal there scarce is; His farces are physic; his physic a farce is. " I have fired at the Royal Society and at the medical profession, but I havegiven a wide berth to the drama and its wits; so there is no epigram outagainst me, as yet. He was very able and very eccentric. Dr. Thomson(_Hist. Roy. Soc. _) says he has no humor, but Dr. Thomson was a man whonever would have discovered humor. Mr. Weld (_Hist. Roy. Soc. _) backs Dr. Thomson, but with a remarkableaddition. Having followed his predecessor in observing that the_Transactions_ in Martin Folkes's time have an unusual proportion oftrifling and puerile papers, he says that Hill's book is a poor attempt athumor, and glaringly exhibits the feelings of a disappointed man. It isprobable, he adds, that the points told with some effect on the Society;for shortly after its publication the _Transactions_ possess a much higherscientific value. I copy an account which I gave elsewhere. When the Royal Society was founded, the Fellows set {22} to work to proveall things, that they might hold fast that which was good. They bentthemselves to the question whether sprats were young herrings. They made acircle of the powder of a unicorn's horn, and set a spider in the middle ofit; "but it immediately ran out. " They tried several times, and the spider"once made some stay in the powder. " They inquired into Kenelm Digby'ssympathetic powder. "Magnetic cures being discoursed of, Sir Gilbert Talbotpromised to communicate what he knew of sympathetical cures; and thosemembers who had any of the powder of sympathy, were desired to bring someof it at the next meeting. " June 21, 1661, certain gentlemen were appointed "curators of the proposalof tormenting a man with the sympathetic powder"; I cannot find any recordof the result. And so they went on until the time of Sir John Hill'ssatire, in 1751. This once well-known work is, in my judgment, the greatestcompliment the Royal Society ever received. It brought forward a number ofwhat are now feeble and childish researches in the PhilosophicalTransactions. It showed that the inquirers had actually been inquiring; andthat they did not pronounce decision about "natural _knowledge_" by help of"_natural_ knowledge. " But for this, Hill would neither have known what toassail, nor how. Matters are now entirely changed. The scientific bodiesare far too well established to risk themselves. _Ibit qui zonam perdidit:_ "Let him take castles who has ne'er a groat. " These great institutions are now without any collective purpose, exceptthat of promoting individual energy; they print for their contributors, andguard themselves by a general declaration that they will not be answerablefor the things they print. Of course they will not put forward anything foreverybody; but a writer of a certain reputation, or matter of a certainlook of plausibility and safety, {23} will find admission. This is as itshould be; the pasturer of flocks and herds and the hunters of wild beastsare two very different bodies, with very different policies. The scientificacademies are what a spiritualist might call "publishing mediums, " and_their_ spirits fall occasionally into writing which looks as if minds inthe higher state were not always impervious to nonsense. The following joke is attributed to Sir John Hill. I cannot honestly say Ibelieve it; but it shows that his contemporaries did not believe he had nohumor. Good stories are always in some sort of keeping with the characterson which they are fastened. Sir John Hill contrived a communication to theRoyal Society from Portsmouth, to the effect that a sailor had broken hisleg in a fall from the mast-head; that bandages and a plentiful applicationof tarwater had made him, in three days, able to use his leg as well asever. While this communication was under grave discussion--it must beremembered that many then thought tarwater had extraordinary remedialproperties--the joker contrived that a second letter should be delivered, which stated that the writer had forgotten, in his previous communication, to mention that the leg was a wooden leg! Horace Walpole told this story, Isuppose for the first time; he is good authority for the fact ofcirculation, but for nothing more. Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec. RoyalSociety) wrote thus of it in the _Journal Britannique_ (Feb. 1751), ofwhich he was editor: "Il est fâcheux que cet ingénieux Naturaliste, qui nous a déjà donné et quinous prépare encore des ouvrages plus utiles, emploie à cette odieuse tâcheune plume qu'il trempe dans le fiel et dans l'absinthe. Il est vrai queplusieurs de ses remarques sont fondées, et qu'à l'erreur qu'il indique, iljoint en même tems la correction. Mais il n'est pas toujours équitable, etne manque jamais d'insulter. Que peut {24} après tout prouver son livre, sice n'est que la quarante-cinquième partie d'un très-ample et très-utileRecueil n'est pas exempte d'erreurs? Devoit-il confondre avec des Ecrivainssuperficiels, dont la Liberté du Corps ne permet pas de restreindre lafertilité, cette foule de savans du Premier ordre, dont les Ecrits ont ornéet ornent encore les Transactions? A-t-il oublié qu'on y a vu fréquemmentles noms des Boyle, des Newton, des Halley, des De Moivres, des HansSloane, etc. ? Et qu'on y trouve encore ceux des Ward, des Bradley, desGraham, des Ellicot, des Watson, et d'un Auteur que Mr. Hill préfère à tousles autres, je veux dire de Mr. Hill lui-même?"[7] This was the only answer; but it was no answer at all. Hill's object was toexpose the absurdities; he therefore collected the absurdities. I feel surethat Hill was a benefactor of the Royal Society; and much more than hewould have been if he had softened their errors and enhanced their praises. No reviewer will object to me that I have omitted Young, Laplace, etc. Butthen my book has a true title. Hill should not have called his a review ofthe "Works. " It was charged against Sir John Hill that he had tried to become a Fellowof the Royal Society and had failed. This he denied, and challenged theproduction of the certificate which a candidate always sends in, and whichis preserved. {25} But perhaps he could not get so far as acertificate--that is, could not find any one to recommend him; he was alikely man to be in such a predicament. As I have myself run foul of theSociety on some little points, I conceive it possible that I may fall undera like suspicion. Whether I could have been a Fellow, I cannot know; as thegentleman said who was asked if he could play the violin, I never tried. Ihave always had a high opinion of the Society upon its whole history. Aperson used to historical inquiry learns to look at wholes; theUniversities of Oxford and Cambridge, the College of Physicians, etc. Aretaken in all their duration. But those who are not historians--I mean notpossessed of the habit of history--hold a mass of opinions about currentthings which lead them into all kinds of confusion when they try to lookback. Not to give an instance which will offend any set of existingmen--this merely because I can do without it--let us take the country atlarge. Magna Charta for ever! glorious safeguard of our liberties! _Nullusliber homo capiatur aut imprisonetur ... Aut aliquo modo destruatur, nisiper judicium parium_ .... [8] _Liber homo: frank home_; a capital thing forhim--but how about the _villeins_? Oh, there are none _now_! But therewere. Who cares for villains, or barbarians, or helots? And so England, andAthens, and Sparta, were free States; all the freemen in them were free. Long after Magna Charta, villains were sold with their "chattels andoffspring, " named in that order. Long after Magna Charta, it was law that"Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt, salve que il ne poit luy maim. "[9] The Royal Society was founded as a co-operative body, and co-operation wasits purpose. The early charters, etc. Do not contain a trace of theintention to create a _scientific distinction_, a kind of Legion of Honor. It is clear that the {26} qualification was ability and willingness to dogood work for the promotion of natural knowledge, no matter in how manypersons, nor of what position in society. Charles II gave a smart rebukefor exclusiveness, as elsewhere mentioned. In time arose, almost of course, the idea of distinction attaching to the title; and when I first began toknow the Society, it was in this state. Gentlemen of good social positionwere freely elected if they were really educated men; but the moment aclaimant was announced as resting on his science, there was a dispositionto inquire whether he was scientific enough. The maxim of the poet wasadopted; and the Fellows were practically divided into _Drink-deeps_ and_Taste-nots_. I was, in early life, much repelled by the tone taken by the Fellows of theSociety with respect to their very mixed body. A man high in science--somethirty-seven years ago (about 1830)--gave me some encouragement, as hethought. "We shall have you a Fellow of the Royal Society in time, " saidhe. Umph! thought I: for I had that day heard of some recent elections, theunited science of which would not have demonstrated I. 1, nor explained theaction of a pump. Truly an elevation to look up at! It came, further, to myknowledge that the Royal Society--if I might judge by the claims made byvery influential Fellows--considered itself as entitled to the best ofeverything: second-best being left for the newer bodies. A secretary, inreturning thanks for the Royal at an anniversary of the Astronomical, gaverather a lecture to the company on the positive duty of all present to sendthe very best to the old body, and the absolute right of the old body toexpect it. An old friend of mine, on a similar occasion, stated as a factthat the thing was always done, as well as that it ought to be done. Of late years this pretension has been made by a President of the Society. In 1855, Lord Rosse presented a confidential memorandum to the Council onthe expediency of enlarging their number. He says, "In a Council so smallit {27} is impossible to secure a satisfactory representation of theleading scientific Societies, and it is scarcely to be expected that, undersuch circumstances, they will continue to publish inferior papers whilethey send the best to our _Transactions_. " And, again, with all the Societies represented on the Council, "even ifevery Science had its Society, and if they published everything, withholding their best papers [i. E. , from the Royal Society], which theywould not be likely to do, still there would remain to the Royal Society.... " Lord Rosse seems to imagine that the minor Societies themselvestransfer their best papers to the Royal Society; that if, for instance, theAstronomical Society were to receive from A. B. A paper of unusual merit, the Society would transfer it to the Royal Society. This is quite wrong:any preference of the Royal to another Society is the work of thecontributor himself. But it shows how well hafted is the Royal Society'sclaim, that a President should acquire the notion that it is acknowledgedand acted upon by the other Societies, in their joint and corporatecapacities. To the pretension thus made I never could give any sympathy. When I first heard Mr. Christie, Sec. R. S. , set it forth at theanniversary dinner of the Astronomical Society, I remembered the Baron inWalter Scott: "Of Gilbert the Galliard a heriot he sought, Saying, Give thy best steed as a vassal ought. " And I remembered the answer: "Lord and Earl though thou be, I trow I can rein Buck's-foot better than thou. " Fully conceding that the Royal Society is entitled to preeminent rank andall the respect due to age and services, I could not, nor can I now, seeany more obligation in a contributor to send his best to that Society thanhe can make out to be due to himself. This pretension, in my mind, washooked on, by my historical mode of viewing things already mentioned, to myknowledge of the fact that the Royal {28} Society--the chief fault, perhaps, lying with its President, Sir Joseph Banks--had sternly set itselfagainst the formation of other societies; the Geological and Astronomical, for instance, though it must be added that the chief rebels came out of theSociety itself. And so a certain not very defined dislike was generated inmy mind--an anti-aristocratic affair--to the body which seemed to me alittle too uplifted. This would, I daresay, have worn off; but a moreformidable objection arose. My views of physical science gradually arrangedthemselves into a form which would have rendered F. R. S. , as attached to myname, a false representation symbol. The Royal Society is the greatfortress of general physics: and in the philosophy of our day, as togeneral physics, there is something which makes the banner of the R. S. Oneunder which I cannot march. Everybody who saw the three letters after myname would infer certain things as to my mode of thought which would not betrue inference. It would take much space to explain this in full. I mayhereafter, perhaps, write a budget of collected results of the _a prioriphilosophy_, the nibbling at the small end of omniscience, and the effectit has had on common life, from the family parlor to the jury-box, from thegirls'-school to the vestry-meeting. There are in the Society those whowould, were there no others, prevent my criticism, be its conclusions trueor false, from having any basis; but they are in the minority. There is no objection to be made to the principles of philosophy in vogueat the Society, when they are stated as principles; but there is anomniscience in daily practice which the principles repudiate. In likemanner, the most retaliatory Christians have a perfect form of round wordsabout behavior to those who injure them; none of them are as candid as alittle boy I knew, who, to his mother's admonition, You should love yourenemies, answered--Catch me at it! Years ago, a change took place which would alone have {29} put a sufficientdifficulty in the way. The co-operative body got tired of getting fundsfrom and lending name to persons who had little or no science, and wantedF. R. S. To be in every case a Fellow Really Scientific. Accordingly, thenumber of yearly elections was limited to fifteen recommended by theCouncil, unless the general body should choose to elect more; which it doesnot do. The election is now a competitive examination: it is no longer--Areyou able and willing to promote natural knowledge; it is--Are you one ofthe upper fifteen of those who make such claim. In the list ofcandidates--a list rapidly growing in number--each year shows from thirtyto forty of those whom Newton and Boyle would have gladly welcomed asfellow-laborers. And though the rejected of one year may be the accepted ofthe next--or of the next but one, or but two, if self-respect will permitthe candidate to hang on--yet the time is clearly coming when many of thosewho ought to be welcomed will be excluded for life, or else shelved atlast, when past work, with a scientific peerage. Coupled with this attemptto create a kind of order of knighthood is an absurdity so glaring that itshould always be kept before the general eye. This distinction, this markset by science upon successful investigation, is of necessity aclass-distinction. Rowan Hamilton, one of the greatest names of our day inmathematical science, never could attach F. R. S. To his name--_he could notafford it_. There is a condition precedent--Four Red Sovereigns. It is fourpounds a year, or--to those who have contributed to the Transactions--fortypounds down. This is as it should be: the Society must be supported. But itis not as it should be that a kind of title of honor should be forged, thata body should take upon itself to confer distinctions _for science_, whenit is in the background--and kept there when the distinction istrumpeted--that the wearer is a man who can spare four pounds a year. I amwell aware that in England a person who is not gifted either by nature orart, with this amount of money power, {30} is, with the mass, a verysecond-rate sort of Newton, whatever he may be in the field ofinvestigation. Even men of science, so called, have this feeling. I knowthat the _scientific advisers_ of the Admiralty, who, years ago, received100 pounds a year each for his trouble, were sneered at by a wealthypretender as "fellows to whom a hundred a year is an object. " Dr. ThomasYoung was one of them. To a bookish man--I mean a man who can manage tocollect books--there is no tax. To myself, for example, 40 pounds worth ofbooks deducted from my shelves, and the life-use of the Society's splendidlibrary instead, would have been a capital exchange. But there may be, andare, men who want books, and cannot pay the Society's price. The Councilwould be very liberal in allowing books to be consulted. I have no doubtthat if a known investigator were to call and ask to look at certain books, the Assistant-Secretary would forthwith seat him with the books before him, absence of F. R. S. Not in any wise withstanding. But this is not like havingthe right to consult any book on any day, and to take it away, if fartherwanted. So much for the Royal Society as concerns myself. I must add that there isnot a spark of party feeling against those who wilfully remain outside. Thebetter minds of course know better; and the smaller _savants_ lookcomplacently on the idea of an outer world which makes _élite_ of them. Ihave done such a thing as serve on a committee of the Society, and reporton a paper: they had the sense to ask, and I had the sense to see that noneof my opinions were compromised by compliance. And I will be of any usewhich does not involve the status of _homo trium literarum_; as I haveelsewhere explained, I would gladly be _Fautor Realis Scientiæ_, but Iwould not be taken for _Falsæ Rationis Sacerdos_. Nothing worse will ever happen to me than the smile which individualsbestow on a man who does not _groove_. Wisdom, like religion, belongs tomajorities; who can {31} wonder that it should be so thought, when it is soclearly pictured in the New Testament from one end to the other? The counterpart of _paradox_, the isolated opinion of one or of few, is thegeneral opinion held by all the rest; and the counterpart of false andabsurd paradox is what is called the "vulgar error, " the _pseudodox_. Thereis one great work on this last subject, the _Pseudodoxia Epidemica_ of SirThomas Browne, the famous author of the _Religio Medici_; it usually goesby the name of Browne "On Vulgar Errors" (1st ed. 1646; 6th, 1672). Acareful analysis of this work would show that vulgar errors are frequentlyopposed by scientific errors; but good sense is always good sense, andBrowne's book has a vast quantity of it. As an example of bad philosophy brought against bad observation. TheAmphisbæna serpent was supposed to have two heads, one at each end; partlyfrom its shape, partly because it runs backwards as well as forwards. Onthis Sir Thomas Browne makes the following remarks: "And were there any such species or natural kind of animal, it would behard to make good those six positions of body which, according to the threedimensions, are ascribed unto every Animal; that is, _infra_, _supra_, _ante_, _retro_, _dextrosum_, _sinistrosum_: for if (as it is determined)that be the anterior and upper part wherein the senses are placed, and thatthe posterior and lower part which is opposite thereunto, there is noinferior or former part in this Animal; for the senses, being placed atboth extreams, doth make both ends anterior, which is impossible; the termsbeing Relative, which mutually subsist, and are not without each other. Andtherefore this duplicity was ill contrived to place one head at bothextreams, and had been more tolerable to have settled three or four at one. And therefore also Poets have been more reasonable than Philosophers, and_Geryon_ or _Cerberus_ less monstrous than _Amphisbæna_. " {32} There may be paradox upon paradox: and there is a good instance in theeighth century in the case of Virgil, an Irishman, Bishop of Salzburg andafterwards Saint, and his quarrels with Boniface, an Englishman, Archbishopof Mentz, also afterwards Saint. All we know about the matter is, thatthere exists a letter of 748 from Pope Zachary, citing Virgil--then, itseems, at most a simple priest, though the Pope was not sure even ofthat--to Rome to answer the charge of maintaining that there is anotherworld (_mundus_) under our earth (_terra_), with another sun and anothermoon. Nothing more is known: the letter contains threats in the event ofthe charge being true; and there history drops the matter. Since Virgil wasafterwards a Bishop and a Saint, we may fairly conclude that he died in thefull flower of his orthodox reputation. It has been supposed--and it seemsprobable--that Virgil maintained that the earth is peopled all the wayround, so that under some spots there are antipodes; that hiscontemporaries, with very dim ideas about the roundness of the earth, andmost of them with none at all, interpreted him as putting another earthunder ours--turned the other way, probably, like the second piece ofbread-and-butter in a sandwich, with a sun and moon of its own. In theeighth century this would infallibly have led to an underground Gospel, anunderground Pope, and an underground Avignon for him to live in. When, inlater times, the idea of inhabitants for the planets was started, it wasimmediately asked whether they had sinned, whether Jesus Christ died for_them_, whether their wine and their water could be lawfully used in thesacraments, etc. On so small a basis as the above has been constructed a companion case tothe persecution of Galileo. On one side the positive assertion, withindignant comment, that Virgil was deposed for antipodal heresy, on theother, serious attempts at justification, palliation, or mystification. Some writers say that Virgil was found guilty; others that he gavesatisfactory explanation, and became very good friends with {33} Boniface:for all which see Bayle. Some have maintained that the antipodist was adifferent person from the canonized bishop: there is a second Virgil, madeto order. When your shoes pinch, and will not stretch, always throw themaway and get another pair: the same with your facts. Baronius was not up tothe plan of a substitute: his commentator Pagi (probably writing about1690) argues for it in a manner which I think Baronius would not haveapproved. This Virgil was perhaps a slippery fellow. The Pope says he hearsthat Virgil pretended licence from him to claim one of some new bishoprics:this he declares is totally false. It is part of the argument that such aman as this could not have been created a Bishop and a Saint: on this pointthere will be opinions and opinions. [10] Lactantius, four centuries before, had laughed at the antipodes in a mannerwhich seems to be ridicule thrown on the idea of the earth's roundness. Ptolemy, without reference to the antipodes, describes the extent of theinhabited part of the globe in a way which shows that he could have had noobjection to men turned opposite ways. Probably, in the eighth century, theroundness of the earth was matter of thought only to astronomers. It shouldalways be remembered, especially by those who affirm persecution of a trueopinion, that but for our knowing from Lactantius that the antipodal notionhad been matter of assertion and denial among theologians, we could neverhave had any great confidence in Virgil really having maintained the simpletheory of the existence of antipodes. And even now we are not entitled toaffirm it as having historical proof: the evidence {34} goes to Virgilhaving been charged with very absurd notions, which it seems more likelythan not were the absurd constructions which ignorant contemporaries putupon sensible opinions of his. One curious part of this discussion is that neither side has allowed PopeZachary to produce evidence to character. He shall have been an Urban, saythe astronomers; an Urban he ought to have been, say the theologians. Whatsort of man was Zachary? He was eminently sensible and conciliatory; hecontrived to make northern barbarians hear reason in a way which puts himhigh among that section of the early popes who had the knack of managinguneducated swordsmen. He kept the peace in Italy to an extent whichhistorians mention with admiration. Even Bale, that Maharajah ofpope-haters, allows himself to quote in favor of Zachary, that "multaPapalem dignitatem decentia, eademque præclara (scilicet) operaconfecit. "[11] And this, though so willing to find fault that, speaking ofZachary putting a little geographical description of the earth on theportico of the Lateran Church, he insinuates that it was intended to affirmthat the Pope was lord of the whole. Nor can he say how long Zachary heldthe see, except by announcing his death in 752, "cum decem annispestilentiæ sedi præfuisset. "[12] There was another quarrel between Virgil and Boniface which is anillustration. An ignorant priest had baptized "in nomine Patri_a_, etFili_a_ et Spiritu_a_ Sancta. " Boniface declared the rite null and void:Virgil maintained the contrary; and Zachary decided in favor of Virgil, onthe ground that the absurd form was only ignorance of Latin, and notheresy. It is hard to believe that this man deposed a priest for assertingthe whole globe to be inhabited. To me the little information that we haveseems {35} to indicate--but not with certainty--that Virgil maintained theantipodes: that his ignorant contemporaries travestied his theory into thatof an underground cosmos; that the Pope cited him to Rome to explain hissystem, which, as reported, looked like what all would then have affirmedto be heresy; that he gave satisfactory explanations, and was dismissedwith honor. It may be that the educated Greek monk, Zachary, knew hisPtolemy well enough to guess what the asserted heretic would say; we haveseen that he seems to have patronized geography. The _description_ of theearth, according to historians, was a _map_; this Pope may have been moreready than another to prick up his ears at any rumor of geographicalheresy, from hope of information. And Virgil, who may have entered thesacred presence as frightened as Jacquard, when Napoleon I sent for him andsaid, with a stern voice and threatening gesture, "You are the man who cantie a knot in a stretched string, " may have departed as well pleased asJacquard with the riband and pension which the interview was worth to him. A word more about Baronius. If he had been pope, as he would have been butfor the opposition of the Spaniards, and if he had lived ten years longerthan he did, and if Clavius, who would have been his astronomical adviser, had lived five years longer than he did, it is probable, nay almostcertain, that the great exhibition, the proceeding against Galileo, wouldnot have furnished a joke against theology in all time to come. ForBaronius was sensible and witty enough to say that in the Scriptures theHoly Spirit intended to teach how to go to Heaven, not how Heaven goes; andClavius, in his last years, confessed that the whole system of the heavenshad broken down, and must be mended. The manner in which the Galileo case, a reality, and the Virgil case, afiction, have been hawked against the Roman see are enough to show that thePope and his adherents have not cared much about physical philosophy. Intruth, orthodoxy has always had other fish to fry. Physics, which {36} inmodern times has almost usurped the name _philosophy_, in England at least, has felt a little disposed to clothe herself with all the honors ofpersecution which belong to the real owner of the name. But the bishops, etc. Of the Middle Ages knew that the contest between nominalism andrealism, for instance, had a hundred times more bearing upon orthodoxy thananything in astronomy, etc. A wrong notion about _substance_ might play themischief with _transubstantiation_. The question of the earth's motion was the single point in which orthodoxycame into real contact with science. Many students of physics weresuspected of magic, many of atheism: but, stupid as the mistake may havebeen, it was _bona fide_ the magic or the atheism, not the physics, whichwas assailed. In the astronomical case it was the very doctrine, as adoctrine, independently of consequences, which was the _corpus delicti_:and this because it contradicted the Bible. And so it did; for thestability of the earth is as clearly assumed from one end of the OldTestament to the other as the solidity of iron. Those who take the Bible tobe _totidem verbis_ dictated by the God of Truth can refuse to believe it;and they make strange reasons. They undertake, _a priori_, to settle Divineintentions. The Holy Spirit did not _mean_ to teach natural philosophy:this they know beforehand; or else they infer it from finding that theearth does move, and the Bible says it does not. Of course, ignoranceapart, every word is truth, or the writer did not mean truth. But this putsthe whole book on its trial: for we never can find out what the writermeant, until we otherwise find out what is true. Those who like may, ofcourse, declare for an inspiration over which they are to be viceroys; butcommon sense will either accept verbal meaning or deny verbal inspiration. * * * * * {37} A BUDGET OF PARADOXES. VOLUME I. THE STORY OF BURIDAN'S ASS. Questiones Morales, folio, 1489 [Paris]. By T. Buridan. This is the title from the Hartwell Catalogue of Law Books. I suppose it iswhat is elsewhere called the "Commentary on the Ethics of Aristotle, "printed in 1489. [13] Buridan[14] (died about 1358) is the creator of thefamous ass which, as _Burdin's_[15] ass, was current in Burgundy, perhapsis, as a vulgar proverb. Spinoza[16] says it was a jenny ass, and that aman would not have been so foolish; but whether the compliment is paid tohuman or to masculine character does not appear--perhaps to both in one. The story _told_ about the famous paradox is very curious. The Queen ofFrance, Joanna or Jeanne, was in the habit of sewing her lovers up insacks, and throwing them into the Seine; not for blabbing, but that theymight not blab--certainly the safer plan. Buridan was exempted, and, ingratitude, invented the sophism. What it has to do with the matter {38} hasnever been explained. Assuredly _qui facit per alium facit per se_ willconvict Buridan of prating. The argument is as follows, and is seldom toldin full. Buridan was for free-will--that is, will which determines conduct, let motives be ever so evenly balanced. An ass is _equally_ pressed byhunger and by thirst; a bundle of hay is on one side, a pail of water onthe other. Surely, you will say, he will not be ass enough to die for wantof food or drink; he will then make a choice--that is, will choose betweenalternatives of equal force. The problem became famous in the schools; someallowed the poor donkey to die of indecision; some denied the possibilityof the balance, which was no answer at all. MICHAEL SCOTT'S DEVILS. The following question is more difficult, and involves free-will to all whoanswer--"Which you please. " If the northern hemisphere were land, and allthe southern hemisphere water, ought we to call the northern hemisphere anisland, or the southern hemisphere a lake? Both the questions would be goodexercises for paradoxers who must be kept employed, like MichaelScott's[17] devils. The wizard {39} knew nothing about squaring the circle, etc. , so he set them to make ropes out of sea sand, which puzzled them. Stupid devils; much of our glass is sea sand, and it makes beautifulthread. Had Michael set them to square the circle or to find a perpetualmotion, he would have done his work much better. But all this isconjecture: who knows that I have not hit on the very plan he adopted?Perhaps the whole race of paradoxers on hopeless subjects are Michael'ssubordinates, condemned to transmigration after transmigration, until theirtask is done. The above was not a bad guess. A little after the time when the famousPascal papers[18] were produced, I came into possession of a correspondencewhich, but for these papers, I should have held too incredible to be putbefore the world. But when one sheep leaps the ditch, another will follow:so I gave the following account in the _Athenæum_ of October 5, 1867: "The recorded story is that Michael Scott, being bound by contract toproduce perpetual employment for a number of young demons, was worried outof his life in inventing jobs for them, until at last he set them to makeropes out of sea sand, which they never could do. We have obtained a verycurious correspondence between the wizard Michael and his demon-slaves; butwe do not feel at liberty to say how it came into our hands. We much regretthat we did not receive it in time for the British Association. It appearsthat the story, true as far as it goes, was never finished. The demonseasily conquered the rope difficulty, by the simple process of making thesand into glass, and spinning the glass into thread, which they twisted. Michael, thoroughly disconcerted, hit upon the plan of setting some to {40}square the circle, others to find the perpetual motion, etc. He commandedeach of them to transmigrate from one human body into another, until theirtasks were done. This explains the whole succession of cyclometers, and allthe heroes of the Budget. Some of this correspondence is very recent; it ismuch blotted, and we are not quite sure of its meaning: it is full offigurative allusions to driving something illegible down a steep into thesea. It looks like a humble petition to be allowed some diversion in theintervals of transmigration; and the answer is-- Rumpat et serpens iter institutum, [19] --a line of Horace, which the demons interpret as a direction to comeathwart the proceedings of the Institute by a sly trick. Until we saw this, we were suspicious of M. Libri, [20] the unvarying blunders of thecorrespondence look like knowledge. To be always out of the road requires amap: genuine ignorance occasionally lapses into truth. We thought itpossible M. Libri might have played the trick to show how easily the Frenchare deceived; but with our present information, our minds are at rest onthe subject. We see M. Chasles does not like to avow the real source ofinformation: he will not confess himself a spiritualist. " PHILO OF GADARA. Philo of Gadara[21] is asserted by Montucla, [22] on the {41} authority ofEutocius, [23] the commentator on Archimedes, to have squared the circlewithin the _ten-thousandth_ part of a unit, that is, to _four_ places ofdecimals. A modern classical dictionary represents it as done by Philo to_ten thousand_ places of decimals. Lacroix comments on Montucla to theeffect that _myriad_ (in Greek _ten thousand_) is here used as we use it, vaguely, for an immense number. On looking into Eutocius, I find that notone definite word is said about the extent to which Philo carried thematter. I give a translation of the passage: "We ought to know that Apollonius Pergæus, in his Ocytocium [this work islost], demonstrated the same by other numbers, and came nearer, which seemsmore accurate, but has nothing to do with Archimedes; for, as before said, he aimed only at going near enough for the wants of life. Neither is Porusof Nicæa fair when he takes Archimedes to task for not giving a lineaccurately equal to the circumference. He says in his Cerii that histeacher, Philo of Gadara, had given a more accurate approximation ([Greek:eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to22. But all these [the rest as well as Philo] miss the intention. Theymultiply and divide by _tens of thousands_, which no one can easily do, unless he be versed in the logistics [fractional computation] of Magnus[now unknown]. " Montucla, or his source, ought not to have made this mistake. He had beenat the Greek to correct Philo _Gadetanus_, as he had often been called, andhe had brought away {42} and quoted [Greek: apo Gadarôn]. Had he read twosentences further, he would have found the mistake. We here detect a person quite unnoticed hitherto by the moderns, Magnus thearithmetician. The phrase is ironical; it is as if we should say, "To dothis a man must be deep in Cocker. "[24] Accordingly, Magnus, Baveme, [25]and Cocker, are three personifications of arithmetic; and there may bemore. ON SQUARING THE CIRCLE. Aristotle, treating of the category of relation, denies that the quadraturehas been found, but appears to assume that it can be done. Boethius, [26] inhis comment on the passage, says that it has been done since Aristotle, butthat the demonstration is too long for him to give. Those who have nonotion of the quadrature question may look at the _English Cyclopædia_, art. "Quadrature of the Circle. " Tetragonismus. Id est circuli quadratura per Campanum, Archimedem Syracusanum, atque Boetium mathematicæ perspicacissimos adinventa. --At the end, Impressum Venetiis per Ioan. Bapti. Sessa. Anno ab incarnatione Domini, 1503. Die 28 Augusti. {43} This book has never been noticed in the history of the subject, and Icannot find any mention of it. The quadrature of Campanus[27] takes theratio of Archimedes, [28] 7 to 22 to be absolutely correct; the accountgiven of Archimedes is not a translation of his book; and that of Boetiushas more than is in Boet_h_ius. This book must stand, with the next, as theearliest in print on the subject, until further showing: Murhard[29] andKastner[30] have nothing so early. It is edited by Lucas Gauricus, [31] whohas given a short preface. Luca Gaurico, Bishop of Civita Ducale, anastrologer of astrologers, published this work at about thirty years ofage, and lived to eighty-two. His works are collected in folios, but I donot know whether they contain this production. The poor fellow could nevertell his own fortune, because his father neglected to note the hour andminute of his birth. But if there had been anything in astrology, he couldhave worked back, as Adams[32] and Leverrier[33] did when they caught {44}Neptune: at sixty he could have examined every minute of his day of birth, by the events of his life, and so would have found the right minute. Hecould then have gone on, by rules of prophecy. Gauricus was themathematical teacher of Joseph Scaliger, [34] who did him no credit, as weshall see. BOVILLUS ON THE QUADRATURE PROBLEM. In hoc opere contenta Epitome.... Liber de quadratura Circuli.... Paris, 1503, folio. The quadrator is Charles Bovillus, [35] who adopted the views of CardinalCusa, [36] presently mentioned. Montucla is hard on his compatriot, who, hesays, was only saved from the laughter of geometers by his obscurity. Persons must guard against most historians of mathematics in one point:they frequently attribute to _his own_ age the obscurity which a writer hasin _their own_ time. This tract was printed by Henry Stephens, [37] at theinstigation of Faber Stapulensis, [38] {45} and is recorded by Dechales, [39]etc. It was also introduced into the _Margarita Philosophica_ of 1815, [40]in the same appendix with the new perspective from Viator. This is notextreme obscurity, by any means. The quadrature deserved it; but that isanother point. It is stated by Montucla that Bovillus makes [pi] = [root]10. But Montuclacites a work of 1507, _Introductorium Geometricum_, which I have neverseen. [41] He finds in it an account which Bovillus gives of the quadratureof the peasant laborer, and describes it as agreeing with his own. But thedescription makes [pi] = 3-1/8, which it thus appears Bovillus could notdistinguish from [root]10. It seems also that this 3-1/8, about which weshall see so much in the sequel, takes its rise in the thoughtful head of apoor laborer. It does him great honor, being so near the truth, and hehaving no means of instruction. In our day, when an ignorant person choosesto bring his fancy forward in opposition to demonstration which he will notstudy, he is deservedly laughed at. {46} THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE. Mr. James Smith, [42] of Liverpool--hereinafter notorified--attributes thefirst announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, ofwhom he gives the following account: "In the year 1836, at which time Lacomme could neither read nor write, hehad constructed a circular reservoir and wished to know the quantity ofstone that would be required to pave the bottom, and for this purposecalled on a professor of mathematics. On putting his question and givingthe diameter, he was surprised at getting the following answer from theProfessor: _'Qu'il lui était impossible de le lui dire au juste, attenduque personne n'avait encore pu trouver d'une manière exacte le rapport dela circonférence au diametre. '_[43] From this he was led to attempt thesolution of the problem. His first process was purely mechanical, and hewas so far convinced he had made the discovery that he took to educatinghimself, and became an expert arithmetician, and then found thatarithmetical results agreed with his mechanical experiments. He appears tohave eked out a bare existence for many years by teaching arithmetic, allthe time struggling to get a hearing from some of the learned societies, but without success. In the year 1855 he found his way to Paris, where, asif by accident, he made the acquaintance of a young gentleman, son of M. Winter, a commissioner of police, and taught him his peculiar methods ofcalculation. The young man was so enchanted that he strongly recommendedLacomme to his father, and {47} subsequently through M. Winter he obtainedan introduction to the President of the Society of Arts and Sciences ofParis. A committee of the society was appointed to examine and report uponhis discovery, and the society at its _séance_ of March 17, 1856, awarded asilver medal of the first class to M. Joseph Lacomme for his discovery ofthe true ratio of diameter to circumference in a circle. He subsequentlyreceived three other medals from other societies. While writing this I havehis likeness before me, with his medals on his breast, which stands as afrontispiece to a short biography of this extraordinary man, for which I amindebted to the gentleman who did me the honor to publish a Frenchtranslation of the pamphlet I distributed at the meeting of the BritishAssociation for the Advancement of Science, at Oxford, in1860. "--_Correspondent_, May 3, 1866. My inquiries show that the story of the medals is not incredible. There areat Paris little private societies which have not so much claim to beexponents of scientific opinion as our own Mechanics' Institutes. Some ofthem were intended to give a false lustre: as the "Institut Historique, "the members of which are "Membre de l'Institut Historique. " That M. Lacommeshould have got four medals from societies of this class is very possible:that he should have received one from any society at Paris which has theleast claim to give one is as yet simply incredible. NICOLAUS OF CUSA'S ATTEMPT. Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. Folio. The real title is "Hæc accurata recognitio trium voluminum operum clariss. P. Nicolai Cusæ ... Proxime sequens pagina monstrat. "[44] Cardinal Cusa, who died in 1464, is one of the earliest modern attempters. His quadratureis found in the second volume, and is now quite unreadable. {48} In these early days every quadrator found a geometrical opponent, whofinished him. Regimontanus[45] did this office for the Cardinal. HENRY CORNELIUS AGRIPPA. De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons, 1550, 8vo. De incertitudine et vanitate scientiarum. By the same. Cologne, 1531, 8vo. The first editions of these works were of 1530, as well as I can make out;but the first was in progress in 1510. [46] In the second work Agripparepents of having wasted time on the magic of the first; but all those whoactually deal with demons are destined to eternal fire with Jamnes andMambres and Simon Magus. This means, as is the fact, that his occultphilosophy did not actually enter upon _black_ magic, but confined itselfto the power of the stars, of numbers, etc. The fourth book, which appearedafter the death of Agrippa, and really concerns dealing with evil spirits, is undoubtedly spurious. It is very difficult to make out what Agrippareally believed on the subject. I have introduced his books as the mostmarked specimens of treatises on magic, a paradox of our day, though notfar from orthodoxy in his; and here I should have ended my notice, if I hadnot casually found something more interesting to the reader of our day. {49} WHICH LEADS TO WALTER SCOTT. Walter Scott, it is well known, was curious on all matters connected withmagic, and has used them very widely. But it is hardly known how much painshe has taken to be correct, and to give the real thing. The most decideddetail of a magical process which is found in his writings is that ofDousterswivel in _The Antiquary_; and it is obvious, by his accuracy ofprocess, that he does not intend the adept for a mere impostor, but for onewho had a lurking belief in the efficacy of his own processes, coupled withintent to make a fraudulent use of them. The materials for the process aretaken from Agrippa. I first quote Mr. Dousterswivel: "... I take a silver plate when she [the moon] is in her fifteenth mansion, which mansion is in de head of _Libra_, and I engrave upon one side deworts _Schedbarschemoth Scharta_ch_an_ [_ch_ should be _t_]--dat is, deIntelligence of de Intelligence of de moon--and I make his picture like aflying serpent with a turkey-cock's head--vary well--Then upon this side Imake de table of de moon, which is a square of nine, multiplied intoitself, with eighty-one numbers [nine] on every side and diameter nine.... " In the _De Occulta Philosophia_, p. 290, we find that the fifteenth mansionof the moon _incipit capite Libræ_, and is good _pro extrahendisthesauris_, the object being to discover hidden treasure. In p. 246, welearn that a _silver_ plate must be used with the moon. In p. 248, we havethe words which denote the Intelligence, etc. But, owing to the falling ofa number into a wrong line, or the misplacement of a line, one orother--which takes place in all the editions I have examined--Scott has, sad to say, got hold of the wrong words; he has written down the _demon ofthe demons_ of the moon. Instead of the gibberish above, it should havebeen _Malcha betarsisim hed beruah schenhakim_. In p. 253, we have themagic square of the moon, with eighty-one numbers, and the symbol for theIntelligence, which Scott likens to a flying {50} serpent with aturkey-cock's head. He was obliged to say something; but I will stake mycharacter--and so save a woodcut--on the scratches being more like a pairof legs, one shorter than the other, without a body, jumping over asix-barred gate placed side uppermost. Those who thought that Scott forgedhis own nonsense, will henceforth stand corrected. As to the spiritPeolphan, etc. , no doubt Scott got it from the authors he elsewherementions, Nicolaus Remigius[47] and Petrus Thyracus; but this last wordshould be Thyræus. The tendency of Scott's mind towards prophecy is very marked, and it isalways fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed isthe prince who barters justice for lust; he shall die in the gate by thesword of the stranger. " Tippoo was killed in a gateway at Seringapatam. [48] FINAEUS ON CIRCLE SQUARING. Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to. Orontius[49] squared the circle out of all comprehension; but he was killedby a feather from his own wing. His {51} former pupil, John Buteo, [50] thesame who--I believe for the first time--calculated the question of Noah'sark, as to its power to hold all the animals and stores, unsquared himcompletely. Orontius was the author of very many works, and died in 1555. Among the laudatory verses which, as was usual, precede this work, there isone of a rare character: a congratulatory ode to the wife of the author. The French now call this writer Oronce Finée; but there is much difficultyabout delatinization. Is this more correct than Oronce Fine, which thetranslator of De Thou uses? Or than Horonce Phine, which older writersgive? I cannot understand why M. De Viette[51] should be called Viète, because his Latin name is Vieta. It is difficult to restore Buteo; for notonly now is _butor_ a blockhead as well as a bird, but we really cannotknow what kind of bird Buteo stood for. We may be sure that Madame Fine wasDenise Blanche; for Dionysia Candida can mean nothing else. Let her shaderejoice in the fame which Hubertus Sussannæus has given her. I ought to add that the quadrature of Orontius, and solutions of all theother difficulties, were first published in _De Rebus Mathematicis HactenusDesideratis_, [52] of which I have not the date. {52} DUCHESNE, AND A DISQUISITION ON ETYMOLOGY. Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova doctrina sinuum et triangulorum.... Strasburg, 1588, 4to. [53] People choose the name of this astronomer for themselves: I take _Ursus_, because he _was_ a bear. This book gave the quadrature of SimonDuchesne, [54] or à Quercu, which excited Peter Metius, [55] as presentlynoticed. It also gave that unintelligible reference to Justus Byrgius whichhas been used in the discussion about the invention of logarithms. [56] The real name of Duchesne is Van der Eycke. I have met with a tract inDutch, _Letterkundige Aanteekeningen_, upon Van Eycke, Van Ceulen, [57]etc. , by J. J. Dodt van Flensburg, [58] which I make out to be since 1841 indate. I should {53} much like a translation of this tract to be printed, say in the _Phil. Mag. _ Dutch would be clear English if it were properlyspelt. For example, _learn-master_ would be seen at once to be _teacher_;but they will spell it _leermeester_. _Of these_ they write as _van deze_;_widow_ they make _weduwe_. All this is plain to me, who never saw a Dutchdictionary in my life; but many of their misspellings are quiteunconquerable. FALCO'S RARE TRACT. Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli quadraturam invenit. Antwerp, 1589, 4to. [59] The attempt is more than commonly worthless; but as Montucla and othershave referred to the verses at the end, and as the tract is of the rarest, I will quote them: _Circulus loquitur. _ Vocabar ante circulus Eramque curvus undique Ut alta solis orbita Et arcus ille nubium. Eram figura nobilis Carensque sola origine Carensque sola termino. Modo indecora prodeo Novisque foedor angulis. Nec hoc peregit Archytas[60] Neque Icari pater neque Tuus, Iapete, filius. Quis ergo casus aut Deus Meam quadravit aream? _Respondet auctor. _ Ad alta Turiæ ostia Lacumque limpidissimum Sita est beata civitas {54} Parum Saguntus abfuit Abestque Sucro plusculum. Hic est poeta quispiam Libenter astra consulens Sibique semper arrogans Negata doctioribus, Senex ubique cogitans Sui frequenter immemor Nec explicare circinum Nec exarare lineas Sciens ut ipse prædicat. Hic ergo bellus artifex Tuam quadravit aream. [61] Falco's verses are pretty, if the U-mysteries be correct; but of thesethings I have forgotten--what I knew. [One mistake has been pointed out tome: it is Arch[=y]tas]. As a specimen of the way in which history is written, I copy the accountwhich Montucla--who is accurate when he writes about what he hasseen--gives of these verses. He gives the date 1587; he places the versesat the beginning instead of the end; he says the circle thanks itsquadrator affectionately; and he says the good and modest chevalier givesall the glory to the patron saint of his order. All of little consequence, as it happens; but writing at second-hand makes as complete mistakes aboutmore important matters. {55} BUNGUS ON THE MYSTERY OF NUMBER. Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591, 4to. Second Edition. The first edition is said to be of 1585;[62] the third, Paris, 1618. Bungusis not for my purpose on his own score, but those who gave the numberstheir mysterious characters: he is but a collector. He quotes or uses 402authors, as we are informed by his list; this just beats Warburton, [63]whom some eulogist or satirist, I forget which, holds up as having used 400authors in some one work. Bungus goes through 1, 2, 3, etc. , and gives theaccount of everything remarkable in which each number occurs; his accountsnot being always mysterious. The numbers which have nothing to say forthemselves are omitted: thus there is a gap between 50 and 60. In treating666, Bungus, a good Catholic, could not compliment the Pope with it, but hefixes it on Martin Luther with a little forcing. If from A to I represent1-10, from K to S 10-90, and from T to Z 100-500, we see: M A R T I N L U T E R A 30 1 80 100 9 40 20 200 100 5 80 1 which gives 666. Again, in Hebrew, _Lulter_ does the same: [Hebrew: R T L W L] 200 400 30 6 30 And thus two can play at any game. The second is better than the first: toLatinize the surname and not the Christian {56} name is very unscholarlike. The last number mentioned is a thousand millions; all greater numbers aredismissed in half a page. Then follows an accurate distinction between_number_ and _multitude_--a thing much wanted both in arithmetic and logic. WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY. What may be the use of such a book as this? The last occasion on which itwas used was the following. Fifteen or sixteen years ago the Royal Societydetermined to restrict the number of yearly admissions to fifteen men ofscience, and noblemen _ad libitum_; the men of science being selected andrecommended by the Council, with a power, since practically surrendered, tothe Society to elect more. This plan appears to me to be directly againstthe spirit of their charter, the true intent of which is, that all who arefit should be allowed to promote natural knowledge in association, from andafter the time at which they are both fit and willing. It is also workingmore absurdly from year to year; the tariff of fifteen per annum will soonamount to the practical exclusion of many who would be very useful. Thisbegins to be felt already, I suspect. But, as appears above, the body ofthe Society has the remedy in its own hands. When the alteration wasdiscussed by the Council, my friend the late Mr. Galloway, [64] then one ofthe body, opposed it strongly, and inquired particularly into the reasonwhy _fifteen_, of all numbers, was the one to be selected. Was it becausefifteen is seven and eight, typifying the Old Testament Sabbath, and theNew Testament day of the resurrection following? Was it because Paul strovefifteen days against Peter, proving that he was a doctor both of the Oldand New Testament? Was it because the prophet Hosea bought a lady {57} forfifteen pieces of silver? Was it because, according to Micah, sevenshepherds and eight chiefs should waste the Assyrians? Was it becauseEcclesiastes commands equal reverence to be given to both Testaments--suchwas the interpretation--in the words "Give a portion to seven, and also toeight"? Was it because the waters of the Deluge rose fifteen cubits abovethe mountains?--or because they lasted fifteen decades of days? Was itbecause Ezekiel's temple had fifteen steps? Was it because Jacob's ladderhas been supposed to have had fifteen steps? Was it because fifteen yearswere added to the life of Hezekiah? Was it because the feast of unleavenedbread was on the fifteenth day of the month? Was it because the scene ofthe Ascension was fifteen stadia from Jerusalem? Was it because thestone-masons and porters employed in Solomon's temple amounted to fifteenmyriads? etc. The Council were amused and astounded by the volley offifteens which was fired at them; they knowing nothing about Bungus, ofwhich Mr. Galloway--who did not, as the French say, indicate hissources--possessed the copy now before me. In giving this anecdote I give aspecimen of the book, which is exceedingly rare. Should another editionever appear, which is not very probable, he would be but a bungling Bunguswho should forget the _fifteen_ of the Royal Society. AND ALSO TO A QUESTION OF EVIDENCE. [I make a remark on the different colors which the same person gives to onestory, according to the bias under which he tells it. My friend Gallowaytold me how he had quizzed the Council of the Royal Society, to my greatamusement. Whenever I am struck by the words of any one, I carry away avivid recollection of position, gestures, tones, etc. I do not know whetherthis be common or uncommon. I never recall this joke without seeing beforeme my friend, leaning against his bookcase, with Bungus open in his hand, and a certain half-depreciatory tone which he often used {58} when speakingof himself. Long after his death, an F. R. S. Who was present at thediscussion, told me the story. I did not say I had heard it, but I watchedhim, with Galloway at the bookcase before me. I wanted to see whether thetwo would agree as to the fact of an enormous budget of fifteens havingbeen fired at the Council, and they did agree perfectly. But when theparagraph of the Budget appeared in the _Athenæum_, my friend, who seemedrather to object to the _showing-up_, assured me that the thing was grosslyexaggerated; there was indeed a fifteen or two, but nothing like the numberI had given. I had, however, taken sharp note of the previous narration. AND TO ANOTHER QUESTION OF EVIDENCE. I will give another instance. An Indian officer gave me an account of anelephant, as follows. A detachment was on the march, and one of thegun-carriages got a wheel off the track, so that it was also off theground, and hanging over a precipice. If the bullocks had moved a step, carriages, bullocks, and all must have been precipitated. No one knew whatcould be done until some one proposed to bring up an elephant, and let himmanage it his own way. The elephant took a moment's survey of the fix, puthis trunk under the axle of the free wheel, and waited. The surrounders, who saw what he meant, moved the bullocks gently forward, the elephantfollowed, supporting the axle, until there was ground under the wheel, whenhe let it quietly down. From all I had heard of the elephant, this was nottoo much to believe. But when, years afterwards, I reminded my friend ofhis story, he assured me that I had misunderstood him, that the elephantwas _directed_ to put his trunk under the wheel, and saw in a moment why. This is reasonable sagacity, and very likely the correct account; but I amquite sure that, in the fit of elephant-worship under which the story wasfirst told, it was told as I have first stated it. ] {59} GIORDANO BRUNO AND HIS PARADOXES. [Jordani Bruni Nolani de Monade, Numero et Figura ... Item de Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo. [65] I cannot imagine how I came to omit a writer whom I have known so manyyears, unless the following story will explain it. The officer reproved theboatswain for perpetual swearing; the boatswain answered that he heard theofficers swear. "Only in an emergency, " said the officer. "That's just it, "replied the other; "a boatswain's life is a life of 'mergency. " GiordanoBruno was all paradox; and my mind was not alive to his paradoxes, just asmy ears might have become dead to the boatswain's oaths. He was, as hasbeen said, a vorticist before Descartes, [66] an optimist before Leibnitz, aCopernican before Galileo. It would be easy to collect a hundred strangeopinions of his. He was born about 1550, and was roasted alive at Rome, February 17, 1600, for the maintenance and defence of the holy Church, andthe rights and liberties of the same. These last words are from the writ ofour own good James I, under which Leggatt[67] was roasted at Smithfield, inMarch 1612; and if I had a copy of the instrument under which Wightman[68]was roasted at Lichfield, a month afterwards, I daresay I should {60} findsomething quite as edifying. I extract an account which I gave of Bruno inthe _Comp. Alm. _ for 1855: "He was first a Dominican priest, then a Calvinist; and was roasted aliveat Rome, in 1600, for as many heresies of opinion, religious andphilosophical, as ever lit one fire. Some defenders of the papal cause haveat least worded their accusations so to be understood as imputing to himvillainous actions. But it is positively certain that his death was due toopinions alone, and that retractation, even after sentence, would havesaved him. There exists a remarkable letter, written from Rome on the veryday of the murder, by Scioppius[69] (the celebrated scholar, a waspishconvert from Lutheranism, known by his hatred to Protestants and Jesuits)to Rittershusius, [70] a well-known Lutheran writer on civil and canon law, whose works are in the index of prohibited books. This letter has beenreprinted by Libri (vol. Iv. P. 407). The writer informs his friend (whomhe wished to convince that even a Lutheran would have burnt Bruno) that allRome would tell him that Bruno died for Lutheranism; but this is becausethe Italians do not know the difference between one heresy and another, inwhich simplicity (says the writer) may God preserve them. That is to say, they knew the difference between a live heretic and a roasted one by actualinspection, but had no idea of the difference between a Lutheran and aCalvinist. The countrymen of Boccaccio would have smiled at the idea whichthe German scholar entertained of them. They said Bruno was burnt forLutheranism, a name under which they classed all Protestants: and they arebetter witnesses than Schopp, or Scioppius. He then proceeds to describe tohis Protestant friend (to whom he would certainly not have omitted any actwhich both their churches would have condemned) the mass of opinions withwhich Bruno was charged; as that there {61} are innumerable worlds, thatsouls migrate, that Moses was a magician, that the Scriptures are a dream, that only the Hebrews descended from Adam and Eve, that the devils would besaved, that Christ was a magician and deservedly put to death, etc. Infact, says he, Bruno has advanced all that was ever brought forward by allheathen philosophers, and by all heretics, ancient and modern. A time forretractation was given, both before sentence and after, which should benoted, as well for the wretched palliation which it may afford, as for theadditional proof it gives that opinions, and opinions only, brought him tothe stake. In this medley of charges the Scriptures are a dream, whileAdam, Eve, devils, and salvation are truths, and the Saviour a deceiver. Wehave examined no work of Bruno except the _De Monade_, etc. , mentioned inthe text. A strong though strange _theism_ runs through the whole, andMoses, Christ, the Fathers, etc. , are cited in a manner which excites noremark either way. Among the versions of the cause of Bruno's death is_atheism_: but this word was very often used to denote rejection ofrevelation, not merely in the common course of dispute, but by suchwriters, for instance, as Brucker[71] and Morhof. [72] Thus Morhof says ofthe _De Monade, etc. _, that it exhibits no manifest signs of atheism. Whathe means by the word is clear enough, when he thus speaks of a work whichacknowledges God in hundreds of places, and rejects opinions as blasphemousin several. The work of Bruno in which his astronomical opinions arecontained is _De Monade, etc. _ (Frankfort, 1591, 8vo). He is the mostthorough-going Copernican possible, and throws out almost every opinion, true or false, which has ever been discussed by astronomers, from thetheory of innumerable inhabited worlds and systems to that {62} of theplanetary nature of comets. Libri (vol. Iv)[73] has reprinted the moststriking part of his expressions of Copernican opinion. " THIS LEADS TO THE CHURCH QUESTION. The Satanic doctrine that a church may employ force in aid of its dogma issupposed to be obsolete in England, except as an individual paradox; butthis is difficult to settle. Opinions are much divided as to what the RomanChurch would do in England, if she could: any one who doubts that sheclaims the right does not deserve an answer. When the hopes of theTractarian section of the High Church were in bloom, before the mostconspicuous intellects among them had _transgressed_ their ministry, thatthey might go to their own place, I had the curiosity to see how far itcould be ascertained whether they held the only doctrine which makes me thepersonal enemy of a sect. I found in one of their tracts the assumption ofa right to persecute, modified by an asserted conviction that force was notefficient. I cannot now say that this tract was one of the celebratedninety; and on looking at the collection I find it so poorly furnished withcontents, etc. , that nothing but searching through three thick volumeswould decide. In these volumes I find, augmenting as we go on, declarationsabout the character and power of "the Church" which have a suspiciousappearance. The suspicion is increased by that curious piece of sophistry, No. 87, on religious reserve. The queer paradoxes of that tract leave us indoubt as to everything but this, that the church(man) is not bound to givehis whole counsel in all things, and not bound to say what the things arein which he does not give it. It is likely enough that some of the "rightsand liberties" are but scantily described. There is now no fear; but thetime was when, if not fear, there might be a looking for of fear to come;nobody could then be so {63} sure as we now are that the lion was onlyasleep. There was every appearance of a harder fight at hand than wasreally found needful. Among other exquisite quirks of interpretation in the No. 87 abovementioned is the following. God himself employs reserve; he is said to bedecked with light as with a garment (the old or prayer-book version ofPsalm civ. 2). To an ordinary apprehension this would be a strong image ofdisplay, manifestation, revelation; but there is something more. "Does nota garment veil in some measure that which it clothes? Is not that verylight concealment?" This No. 87, admitted into a series, fixes upon the managers of the series, who permitted its introduction, a strong presumption of that underhandintent with which they were charged. At the same time it is honorable toour liberty that this series could be published: though its promoters weregreatly shocked when the Essayists and Bishop Colenso[74] took a swing onthe other side. When No. 90 was under discussion, Dr. Maitland, [75] thelibrarian at Lambeth, asked Archbishop Howley[76] a question about No. 89. "I did not so much as know there _was_ a No. 89, " was the answer. I amalmost sure I have seen this in print, and quite sure that Dr. Maitlandtold it to me. It is creditable that there was so much freedom; but No. 90was _too bad_, and was stopped. The Tractarian mania has now (October 1866) settled down into a chronicvestment disease, complicated with fits of transubstantiation, which hastaken the name of {64} _Ritualism_. The common sense of our nationalcharacter will not put up with a continuance of this grotesque folly;millinery in all its branches will at last be advertised only over theproper shops. I am told that the Ritualists give short and practicalsermons; if so, they may do good in the end. The English Establishment hasalways contained those who want an excitement; the New Testament, in itsplain meaning, can do little for them. Since the Revolution, Jacobitism, Wesleyanism, Evangelicism, Puseyism, [77] and Ritualism, have come on inturn, and have furnished hot water for those who could not wash without it. If the Ritualists should succeed in substituting short and practicalteaching for the high-spiced lectures of the doctrinalists, they will beremembered with praise. John the Baptist would perhaps not have brought allJerusalem out into the wilderness by his plain and good sermons: it was thecamel's hair and the locusts which got him a congregation, and which, perhaps, added force to his precepts. When at school I heard a dialogue, between an usher and the man who cleaned the shoes, about Mr. ----, aminister, a very corporate body with due area of waistcoat. "He is a man ofgreat erudition, " said the first. "Ah, yes sir, " said Joe; "any one can seethat who looks at that silk waistcoat. "] OF THOMAS GEPHYRANDER SALICETUS. [When I said at the outset that I had only taken books from my own store, Ishould have added that I did not make any search for information given as_part_ of a work. Had I looked _through_ all my books, I might have madesome curious additions. For instance, in Schott's _Magia Naturalis_[78]{65} (vol. Iii. Pp. 756-778) is an account of the quadrature ofGephyra_u_der, as he is misprinted in Montucla. He was Thomas GephyranderSalicetus; and he published two editions, in 1608 and 1609. [79] I nevereven heard of a copy of either. His work is of the extreme of absurdity: hemakes a distinction between geometrical and arithmetical fractions, andevolves theorems from it. More curious than his quadrature is his name;what are we to make of it? If a German, he is probably a German form of_Bridgeman_. And Salicetus refers him to _Weiden_. But _Thomas_ was hardlya German Christian name of his time; of 526 German philosophers, physicians, lawyers, and theologians who were biographed by MelchiorAdam, [80] only two are of this name. Of these one is Thomas Erastus, [81]the physician whose theological writings against the Church as a separatepower have given the name of Erastians to those who follow his doctrine, whether they have heard of him or not. Erastus is little known;accordingly, some have supposed that he must be Erastus, the friend of St. Paul and Timothy (Acts xix. 22; 2 Tim. Iv. 20; Rom. Xvi. 23), but what thisgentleman did to earn the character is not hinted at. Few words would havedone: Gaius (Rom. Xvi. 23) has an immortality which many more noted menhave missed, given by John Bunyan, out of seven words of St. Paul. I wasonce told that the Erastians got their name from _Blastus_, and I could notsolve _bl = er_: at last I remembered that Blastus was a _chamberlain_[82]as well as Erastus; hence the association which {66} caused the mistake. The real heresiarch was a physician who died in 1583; his heresy waspromulgated in a work, published immediately after his death by his widow, _De Excommunicatione Ecclesiastica_. He denied the power of excommunicationon the principle above stated; and was answered by Besa. [83] The work wastranslated by Dr. R. Lee[84] (Edinb. 1844, 8vo). The other is ThomasGrynæus, [85] a theologian, nephew of Simon, who first printed Euclid inGreek; of him Adam says that of works he published none, of learned sonsfour. If Gephyrander were a Frenchman, his name is not so easily guessedat; but he must have been of La Saussaye. The account given by Schott istaken from a certain Father Philip Colbinus, who wrote against him. In some manuscripts lately given to the Royal Society, David Gregory, [86]who seems to have seen Gephyrander's work, calls him Salicetus_Westphalus_, which is probably on the title-page. But the only Weiden Ican find is in Bavaria. Murhard has both editions in his Catalogue, but hadplainly never seen the books: he gives the author as Thomas Gep. Hyandrus, Salicettus Westphalus. Murhard is a very old referee of mine; but who the_non nominandus_ was to see Montucla's _Gephyrander_ in Murhard's _Gep. Hyandrus_, both writers being usually accurate?] NAPIER ON REVELATIONS. A plain discoverie of the whole Revelation of St. John ... Whereunto are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L. Of Marchiston. London, 1611, 4to. [87] {67} The first edition was Edinburgh, 1593, [88] 4to. Napier[89] always believedthat his great mission was to upset the Pope, and that logarithms, and suchthings, were merely episodes and relaxations. It is a pity that so manybooks have been written about this matter, while Napier, as good as any, isforgotten and unread. He is one of the first who gave us the six thousandyears. "There is a sentence of the house of Elias reserved in all ages, bearing these words: The world shall stand six thousand years, and then itshall be consumed by fire: two thousand yeares voide or without lawe, twothousand yeares under the law, and two thousand yeares shall be the daiesof the Messias.... " I give Napier's parting salute: it is a killing dilemma: "In summar conclusion, if thou o _Rome_ aledges thyselfe reformed, and tobeleeue true Christianisme, then beleeue Saint _John_ the Disciple, whomeChrist loued, publikely here in this Reuelation proclaiming thy wracke, butif thou remain Ethnick in thy priuate thoghts, beleeuing[90] the oldOracles of the _Sibyls_ reuerently keeped somtime in thy _Capitol_: thendoth here this _Sibyll_ proclame also thy wracke. Repent therefore alwayes, in this thy latter breath, as thou louest thine Eternall salvation. _Amen_. " --Strange that Napier should not have seen that this appeal could notsucceed, unless the prophecies of the Apocalypse were no true prophecies atall. {68} OF GILBERT'S DE MAGNETE. De Magnete magneticisque corporibus, et de magno magnete tellure. By William Gilbert. London, 1600, folio. --There is a second edition; and a third, according to Watt. [91] Of the great work on the magnet there is no need to speak, though it was aparadox in its day. The posthumous work of Gilbert, "De Mundo nostrosublunari philosophia nova" (Amsterdam, 1651, 4to)[92] is, as the titleindicates, confined to the physics of the globe and its atmosphere. It hasnever excited attention: I should hope it would be examined with ourpresent lights. OF GIOVANNI BATISTA PORTA. Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome, 1610, 4to. [93] This is a ridiculous attempt, which defies description, except that it isall about lunules. Porta was a voluminous writer. His printer announcesfourteen works printed, and four to come, besides thirteen plays printed, and eleven waiting. His name is, and will be, current in treatises onphysics for more reasons than one. {69} CATALDI ON THE QUADRATURE. Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi. Bologna, 1612, folio. [94] Rheticus, [95] Vieta, and Cataldi are the three untiring computers ofGermany, France, and Italy; Napier in Scotland, and Briggs[96] in England, come just after them. This work claims a place as beginning with thequadrature of Pellegrino Borello[97] of Reggio, who will have the circle tobe exactly 3 diameters and 69/484 of a diameter. Cataldi, taking VanCeulen's approximation, works hard at the finding of integers which nearlyrepresent the ratio. He had not then the _continued fraction_, a mode ofrepresentation which he gave the next year in his work on the square root. He has but twenty of Van Ceulen's thirty places, which he takes fromClavius[98]: and any one might be puzzled to know whence the Italians gotthe result; Van Ceulen, in 1612, not having been translated from Dutch. ButClavius names his comrade Gruenberger, and attributes the approximation tothem {70} jointly; "Lud. A Collen et Chr. Gruenbergerus[99] invenerunt, "which he had no right to do, unless, to his private knowledge, Gruenbergerhad verified Van Ceulen. And Gruenberger only handed over twenty of theplaces. But here is one instance, out of many, of the polyglot character ofthe Jesuit body, and its advantages in literature. OF LANSBERGIUS. Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616, 4to. [100] This is one of the legitimate quadratures, on which I shall here onlyremark that by candlelight it is quadrature under difficulties, for all thediagrams are in red ink. A TEXT LEADING TO REMARKS ON PRESTER JOHN. Recherches Curieuses des Mesures du Monde. By S. C. De V. Paris, 1626, 8vo (pp. 48). [101] It is written by some Count for his son; and if all the French nobilitywould have given their sons the same kind of instruction about rank, theold French aristocracy would have been as prosperous at this moment as theEnglish peerage and squireage. I sent the tract to Capt. Speke, [102]shortly after his arrival in England, thinking he might like {71} to seethe old names of the Ethiopian provinces. But I first made a copy of allthat relates to Prester John, [103] himself a paradox. The tract contains, _inter alia_, an account of the four empires; of the great Turk, the greatTartar, the great Sophy, and the great Prester John. This word _great_(_grand_), which was long used in the phrase "the great Turk, " is a genericadjunct to an emperor. Of the Tartars it is said that "c'est vne nationprophane et barbaresque, sale et vilaine, qui mangent la chair demie cruë, qui boiuent du laict de jument, et qui n'vsent de nappes et seruiettes quepour essuyer leurs bouches et leurs mains. "[104] Many persons have heard ofPrester John, and have a very indistinct idea of him. I give all that issaid about him, since the recent discussions about the Nile may give aninterest to the old notions of geography. "Le grand Prestre Jean qui est le quatriesme en rang, est Empereurd'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid, comme estant descendu de la Royne de Saba, Royne d'Ethiopie, laquelleestant venuë en Hierusalem pour voir la sagesse de Salomon, enuiron l'an dumonde 2952, s'en retourna grosse d'vn fils qu'ils nomment Moylech, duquelils disent estre descendus en ligne directe. Et ainsi il se glorified'estre le plus ancien Monarque de la terre, disant que son Empire a duréplus de trois mil ans, ce que nul autre Empire ne peut dire. Aussi met-ilen ses tiltres ce qui s'ensuit: Nous, N. Souuerain en mes Royaumes, vniquement aymé de Dieu, colomne de la foy, sorty de la race de Inda, etc. Les limites de cet Empire touchent à la mer Rouge, et aux montagnes d'Azumavers {72} l'Orient, et du costé de l'Occident, il est borné du fleuue duNil, qui le separe de la Nubie, vers le Septentrion il a l'Ægypte, et auMidy les Royaumes de Congo, et de Mozambique, sa longueur contenantquarante degré, qui font mille vingt cinq lieuës, et ce depuis Congo ouMozambique qui sont au Midy, iusqu'en Ægypte qui est au Septentrion, et salargeur contenant depuis le Nil qui est à l'Occident, iusqu'aux montagnesd'Azuma, qui sont à l'Orient, sept cens vingt cinq lieues, qui font vingtneuf degrez. Cét empire a sous soy trente grandes Prouinces, sçavoir, Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon(_sic_), Guegiera, Bally, Dobora et Macheda. Toutes ces Prouinces cy dessussont situées iustement sous la ligne equinoxiale, entres les Tropiques deCapricorne, et de Cancer. Mais elles s'approchent de nostre Tropique, dedeux cens cinquante lieuës plus qu'elles ne font de l'autre Tropique. Cemot de Prestre Jean signifie grand Seigneur, et n'est pas Prestre commeplusieurs pense, il a esté tousiours Chrestien, mais souuent Schismatique:maintenant il est Catholique, et reconnaist le Pape pour Souuerain Pontife. I'ay veu quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ayconferé souuent par le moyen de nostre trucheman: il estoit d'vn port graueet serieux, succiur (_sic_) en son parler, mais subtil à merueilles en toutce qu'il disoit. Il prenoit grand plaisir au recit que je luy faisais denos belles ceremonies, et de la grauité de nos Prelats en leurs habitsPontificaux, et autres choses que je laisse pour dire, que l'Ethiopien estioyoux et gaillard, ne ressemblant en rien a la saleté du Tartare, ny àl'affreux regard du miserable Arabe, mais ils sont fins et cauteleux, et nese fient en personne, soupçonneux à merueilles, et fort devotieux, ils nesont du tout noirs comme l'on croit, i'entens parler de ceux qui ne sontpas sous la ligne Equinoxiale, ny trop proches {73} d'icelle, car ceux quisont dessous sont les Mores que nous voyons. "[105] It will be observed that the author speaks of his conversation with anEthiopian bishop, about that bishop's sovereign. Something must have passedbetween the two which satisfied the writer that the bishop acknowledged hisown sovereign under some title answering to Prester John. {74} CONCERNING A TRACT BY FIENUS. De Cometa anni 1618 dissertationes Thomæ Fieni[106] et Liberti Fromondi[107] ... Equidem Thomæ Fieni epistolica quæstio, An verum sit Coelum moveri et Terram quiescere? London, 1670, 8vo. This tract of Fienus against the motion of the earth is a reprint of onepublished in 1619. [108] I have given an account of it as a good summary ofarguments of the time, in the _Companion to the Almanac_ for 1836. {75} ON SNELL'S WORK. Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to. This is a celebrated work on the approximative quadrature, which, havingthe suspicious word _cyclometricus_, must be noticed here fordistinction. [109] ON BACON'S NOVUM ORGANUM. 1620. In this year, Francis Bacon[110] published his _Novum Organum_, [111]which was long held in England--but not until the last century--to be thework which taught Newton and all his successors how to philosophize. ThatNewton never mentions Bacon, nor alludes in any way to his works, passedfor nothing. Here and there a paradoxer ventured not to find all thisteaching in Bacon, but he was pronounced blind. In our day it begins to beseen that, great as Bacon was, and great as his book really is, he is notthe philosophical father of modern discovery. But old prepossession will find reason for anything. A learned friend ofmine wrote to me that he had discovered proof that Newton owned Bacon forhis master: the proof was that Newton, in some of his earlier writings, used the {76} phrase _experimentum crucis_, which is Bacon's. Newton mayhave read some of Bacon, though no proof of it appears. I have a dim ideathat I once saw the two words attributed to the alchemists: if so, there isanother explanation; for Newton was deeply read in the alchemists. I subjoin a review which I wrote of the splendid edition of Bacon bySpedding, [112] Ellis, [113] and Heath. [114] All the opinions thereinexpressed had been formed by me long before: most of the materials werecollected for another purpose. The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis, and Douglas D. Heath. 5 vols. [115] No knowledge of nature without experiment and observation: so saidAristotle, so said Bacon, so acted Copernicus, Tycho Brahé, [116] Gilbert, Kepler, Galileo, Harvey, etc. , before Bacon wrote. [117] No derivedknowledge _until_ experiment and observation are concluded: so said Bacon, and no one else. We do not mean to say that he laid down his principle inthese words, or that he carried it to the utmost extreme: we mean thatBacon's ruling idea was the {77} collection of enormous masses of facts, and then digested processes of arrangement and elimination, so artisticallycontrived, that a man of common intelligence, without any unusual sagacity, should be able to announce the truth sought for. Let Bacon speak forhimself, in his editor's English: "But the course I propose for the discovery of sciences is such as leavesbut little to the acuteness and strength of wits, but places all wits andunderstandings nearly on a level. For, as in the drawing of a straight lineor a perfect circle, much depends on the steadiness and practice of thehand, if it be done by aim of hand only, but if with the aid of rule orcompass little or nothing, so it is exactly with my plan.... For my way ofdiscovering sciences goes far to level men's wits, and leaves but little toindividual excellence; because it performs everything by the surest rulesand demonstrations. " To show that we do not strain Bacon's meaning, we add what is said byHooke, [118] whom we have already mentioned as his professed disciple, and, we believe, his only disciple of the day of Newton. We must, however, remind the reader that Hooke was very little of a mathematician, and spokeof algebra from his own idea of what others had told him: "The intellect is not to be suffered to act without its helps, but iscontinually to be assisted by some method or engine, which shall be as aguide to regulate its actions, so as that it shall not be able to actamiss. Of this engine, no man except the incomparable Verulam hath had anythoughts and he indeed hath promoted it to a very good pitch; but there isyet somewhat more to be added, which he seemed to want time to complete. Bythis, as by that {78} art of algebra in geometry, 'twill be very easy toproceed in any natural inquiry, regularly and certainly.... For as 'tisvery hard for the most acute wit to find out any difficult problem ingeometry without the help of algebra ... And altogether as easy for themeanest capacity acting by that method to complete and perfect it, so willit be in the inquiry after natural knowledge. " Bacon did not live to mature the whole of this plan. Are we really tobelieve that if he had completed the _Instauratio_ we who write this--andwho feel ourselves growing bigger as we write it--should have been on alevel with Newton in physical discovery? Bacon asks this belief of us, anddoes not get it. But it may be said, Your business is with what he _did_leave, and with its consequences. Be it so. Mr. Ellis says: "That hismethod is impracticable cannot, I think, be denied, if we reflect not onlythat it never has produced any result, but also that the process by whichscientific truths have been established cannot be so presented as even toappear to be in accordance with it. " That this is very true is well knownto all who have studied the history of discovery: those who deny it arebound to establish either that some great discovery has been made byBacon's method--we mean by the part peculiar to Bacon--or, better still, toshow that some new discovery can be made, by actually making it. No generaltalk about _induction_: no reliance upon the mere fact that certainexperiments or observations have been made; let us see where _Bacon'sinduction_ has been actually used or can be used. Mere induction, _enumeratio simplex_, is spoken of by himself with contempt, as utterlyincompetent. For Bacon knew well that a thousand instances may becontradicted by the thousand and first: so that no enumeration ofinstances, however large, is "sure demonstration, " so long any are left. The immortal Harvey, who was _inventing_--we use the word in its oldsense--the circulation of the blood, while {79} Bacon was in the full flowof thought upon his system, may be trusted to say whether, when the systemappeared, he found any likeness in it to his own processes, or what wouldhave been any help to him, if he had waited for the _Novum Organum_. Hesaid of Bacon, "He writes philosophy like a Lord Chancellor. " This has beengenerally supposed to be only a sneer at the _sutor ultra crepidam_; but wecannot help suspecting that there was more intended by it. To us, Bacon iseminently the philosopher of _error prevented_, not of _progressfacilitated_. When we throw off the idea of being _led right_, and betakeourselves to that of being _kept from going wrong_, we read his writingswith a sense of their usefulness, his genius, and their probable effectupon purely experimental science, which we can be conscious of upon noother supposition. It amuses us to have to add that the part of Aristotle'slogic of which he saw the value was the book on _refutation of fallacies_. Now is this not the notion of things to which the bias of a practisedlawyer might lead him? In the case which is before the Court, generallyspeaking, truth lurks somewhere about the facts, and the elimination of allerror will show it in the residuum. The two senses of the word _law_ comein so as to look almost like a play upon words. The judge can apply the lawso soon as the facts are settled: the physical philosopher has to deducethe law from the facts. Wait, says the judge, until the facts aredetermined: did the prisoner take the goods with felonious intent? did thedefendant give what amounts to a warranty? or the like. Wait, says Bacon, until all the facts, or all the obtainable facts, are brought in: apply myrules of separation to the facts, and the result shall come out as easilyas by ruler and compasses. We think it possible that Harvey might allude tothe legal character of Bacon's notions: we can hardly conceive so acute aman, after seeing what manner of writer Bacon was, meaning only that he wasa lawyer and had better stick to his business. We do ourselves believe thatBacon's philosophy {80} more resembles the action of mind of a common-lawjudge--not a Chancellor--than that of the physical inquirers who have beensupposed to follow in his steps. It seems to us that Bacon's argument is, there can be nothing of law but what must be either perceptible, ormechanically deducible, when all the results of law, as exhibited inphenomena, are before us. Now the truth is, that the physical philosopherhas frequently to conceive law which never was in his previous thought--toeduce the unknown, not to choose among the known. Physical discovery wouldbe very easy work if the inquirer could lay down his this, his that, andhis t'other, and say, "Now, one of these it must be; let us proceed to trywhich. " Often has he done this, and failed; often has the truth turned outto be neither this, that, nor t'other. Bacon seems to us to think that thephilosopher is a judge who has to choose, upon ascertained facts, which ofknown statutes is to rule the decision: he appears to us more like a personwho is to write the statute-book, with no guide except the cases anddecisions presented in all their confusion and all their conflict. Let us take the well-known first aphorism of the _Novum Organum_: "Man being the servant and interpreter of nature, can do and understand somuch, and so much only, as he has observed in fact or in thought of thecourse of nature: beyond this he neither knows anything nor can doanything. " This aphorism is placed by Sir John Herschel[119] at the head of his_Discourse on the Study of Natural Philosophy_: a book containing notionsof discovery far beyond any of which Bacon ever dreamed; and this becauseit was written {81} after discovery, instead of before. Sir John Herschel, in his version, has avoided the translation of _re vel mente observaverit_, and gives us only "by his observation of the order of nature. " In makingthis the opening of an excellent sermon, he has imitated the theologians, who often employ the whole time of the discourse in stuffing matter intothe text, instead of drawing matter out of it. By _observation_ he(Herschel) means the whole course of discovery, observation, hypothesis, deduction, comparison, etc. The type of the Baconian philosopher as itstood in his mind, had been derived from a noble example, his own father, William Herschel, [120] an inquirer whose processes would have been held byBacon to have been vague, insufficient, compounded of chance work andsagacity, and too meagre of facts to deserve the name of induction. Inanother work, his treatise on Astronomy, [121] Sir John Herschel, afternoting that a popular account can only place the reader on the threshold, proceeds to speak as follows of all the higher departments of science. Theitalics are his own: "Admission to its sanctuary, and to the privileges and feelings of avotary, is only to be gained by one means--_sound and sufficient knowledgeof mathematics, the great instrument of all exact inquiry, without which noman can ever make such advances in this or any other of the higherdepartments of science as can entitle him to form an independent opinion onany subject of discussion within their range_. " How is this? Man can know no more than he gets from observation, and yetmathematics is the great instrument of all exact inquiry. Are the resultsof mathematical deduction results of observation? We think it likely that{82} Sir John Herschel would reply that Bacon, in coupling together_observare re_ and _observare mente_, has done what some wags said Newtonafterwards did in his study-door--cut a large hole of exit for the largecat, and a little hole for the little cat. [122] But Bacon did no suchthing: he never included any deduction under observation. To mathematics hehad a dislike. He averred that logic and mathematics should be thehandmaids, not the mistresses, of philosophy. He meant that they shouldplay a subordinate and subsequent part in the dressing of the vast mass offacts by which discovery was to be rendered equally accessible to Newtonand to us. Bacon himself was very ignorant of all that had been done bymathematics; and, strange to say, he especially objected to astronomy beinghanded over to the mathematicians. Leverrier and Adams, calculating anunknown planet into visible existence by enormous heaps of algebra, furnishthe last comment of note on this specimen of the goodness of Bacon's views. The following account of his knowledge of what had been done in his own dayor before it, is Mr. Spedding's collection of casual remarks in Mr. Ellis'sseveral prefaces: "Though he paid great attention to astronomy, discussed carefully themethods in which it ought to be studied, constructed for the satisfactionof his own mind an elaborate theory of the heavens, and listened eagerlyfor the news from the stars brought by Galileo's telescope, he appears tohave been utterly ignorant of the discoveries which had just been made byKepler's calculations. Though he complained in 1623 of the want ofcompendious methods for facilitating arithmetical computations, especiallywith regard to the doctrine of Series, and fully recognized the importanceof them as an aid to physical inquiries--he does not say a word aboutNapier's Logarithms, which had been published only nine years before andreprinted more than once in the {83} interval. He complained that noconsiderable advance had made in geometry beyond Euclid, without taking anynotice of what had been done by Archimedes and Apollonius. He saw theimportance of determining accurately the specific gravity of differentsubstances, and himself attempted to form a table of them by a rude processof his own, without knowing of the more scientific though still imperfectmethods previously employed by Archimedes, Ghetaldus, [123] and Porta. Hespeaks of the [Greek: heurêka] of Archimedes in a manner which implies thathe did not clearly apprehend either the nature of the problem to be solvedor the principles upon which the solution depended. In reviewing theprogress of mechanics, he makes no mention of Archimedes himself, or ofStevinus, [124] Galileo, Guldinus, [125] or Ghetaldus. He makes no allusionto the theory of equilibrium. He observes that a ball of one pound weightwill fall nearly as fast through the air as a ball of two, without alludingto the theory of the acceleration of falling bodies, which had been madeknown by Galileo more than thirty years before. He proposes an inquiry withregard to the lever--namely, whether in a balance with arms of differentlength but equal weight the distance from the fulcrum has any effect uponthe inclination, --though the theory of the lever was as well understood inhis own time as it is now. In making an experiment {84} of his own toascertain the cause of the motion of a windmill, he overlooks an obviouscircumstance which makes the experiment inconclusive, and an equallyobvious variation of the same experiment which would have shown him thathis theory was false. He speaks of the poles of the earth as fixed, in amanner which seems to imply that he was not acquainted with the precessionof the equinoxes; and in another place, of the north pole being above andthe south pole below, as a reason why in our hemisphere the north windspredominate over the south. " Much of this was known before, but such a summary of Bacon's want ofknowledge of the science of his own time was never yet collected in oneplace. We may add, that Bacon seems to have been as ignorant ofWright's[126] memorable addition to the resources of navigation as ofNapier's addition to the means of calculation. Mathematics was beginning tobe the great instrument of exact inquiry: Bacon threw the science aside, from ignorance, just at the time when his enormous sagacity, applied toknowledge, would have made him see the part it was to play. If Newton hadtaken Bacon for his master, not he, but somebody else, would have beenNewton. [127] ON METEOROLOGICAL OBSERVATORIES. There is an attempt at induction going on, which has yielded little or nofruit, the observations made in the meteorological observatories. Thisattempt is carried on in a manner which would have caused Bacon to dancefor joy; for he lived in times when Chancellors did dance. {85} Russia, says M. Biot, [128] is covered by an army of meteorographs, with generals, high officers, subalterns, and privates with fixed and defined duties ofobservation. Other countries have also their systematic observations. Andwhat has come of it? Nothing, says M. Biot, and nothing will ever come ofit; the veteran mathematician and experimental philosopher declares, asdoes Mr. Ellis, that no single branch of science has ever been fruitfullyexplored in this way. There is no _special object_, he says. Any one wouldsuppose that M. Biot's opinion, given to the French Government upon theproposal to construct meteorological observatories in Algeria (_ComptesRendus_, vol. Xli, Dec. 31, 1855), was written to support the mythicalBacon, modern physics, against the real Bacon of the _Novum Organum_. Thereis no _special object_. In these words lies the difference between the twomethods. [In the report to the Greenwich Board of Visitors for 1867 Mr. Airy, [129]speaking of the increase of meteorological observatories, remarks, "Whetherthe effect of this movement will be that millions of useless observationswill be added to the millions that already exist, or whether something maybe expected to result which will lead to a meteorological theory, I cannothazard a conjecture. " This _is_ a conjecture, and a very obvious one: ifMr. Airy would have given 2-3/4d. For the chance of a meteorological theoryformed by masses of observations, he would never have said what I havequoted. ] BASIS OF MODERN DISCOVERY. Modern discoveries have not been made by large collections of facts, withsubsequent discussion, separation, and {86} resulting deduction of a truththus rendered perceptible. A few facts have suggested an _hypothesis_, which means a _supposition_, proper to explain them. The necessary resultsof this supposition are worked out, and then, and not till then, otherfacts are examined to see if these ulterior results are found in nature. The trial of the hypothesis is the _special object_: prior to which, hypothesis must have been started, not by rule, but by that sagacity ofwhich no description can be given, precisely because the very owners of itdo not act under laws perceptible to themselves. [130] The inventor ofhypothesis, if pressed to explain his method, must answer as did ZerahColburn, [131] when asked for his mode of instantaneous calculation. Whenthe poor boy had been bothered for some time in this manner, he cried outin a huff, "God put it into my head, and I can't put it into yours. "[132]{87} Wrong hypotheses, rightly worked from, have produced more usefulresults than unguided observation. But this is not the Baconian plan. Charles the Second, when informed of the state of navigation, founded aBaconian observatory at Greenwich, to observe, observe, observe away at themoon, until her motions were known sufficiently well to render her usefulin guiding the seaman. And no doubt Flamsteed's[133] observations, twentyor thirty of them at least, were of signal use. But how? A somewhatfanciful thinker, one Kepler, had hit upon the approximate orbits of theplanets by trying one hypothesis after another: he found the _ellipse_, which the Platonists, well despised of Bacon, and who would have despisedhim as heartily if they had known him, had investigated and put ready tohand nearly 2000 years before. [134] The sun in the focus, the motions ofthe planet more and more rapid as they approach the sun, led Kepler--andBacon would have reproved him for his rashness--to imagine that a forceresiding in the sun might move the planets, a force inversely as thedistance. Bouillaud, [135] upon a fanciful analogy, rejected the inversedistance, {88} and, rejecting the force altogether, declared that if such athing there were, it would be as the inverse _square_ of the distance. Newton, ready prepared with the mathematics of the subject, tried the fallof the moon towards the earth, away from her tangent, and found that, ascompared with the fall of a stone, the law of the inverse square did holdfor the moon. He deduced the ellipse, he proceeded to deduce the effect ofthe disturbance of the sun upon the moon, upon the assumed theory of_universal_ gravitation. He found result after result of his theory inconformity with observed fact: and, by aid of Flamsteed's observations, which amended what mathematicians call his _constants_, he constructed hislunar theory. Had it not been for Newton, the whole dynasty of Greenwichastronomers, from Flamsteed of happy memory, to Airy whom Heavenpreserve, [136] might have worked away at nightly observation and dailyreduction, without any remarkable result: looking forward, as to amillennium, to the time when any man of moderate intelligence was to seethe whole explanation. What are large collections of facts for? To maketheories _from_, says Bacon: to try ready-made theories _by_, says thehistory of discovery: it's all the same, says the idolater: nonsense, saywe! Time and space run short: how odd it is that of the three leading ideas ofmechanics, time, space, and matter, the first two should always fail areviewer before the third. We might dwell upon many points, especially ifwe attempted a more descriptive account of the valuable edition before us. No one need imagine that the editors, by their uncompromising attack uponthe notion of Bacon's influence common even among mathematicians andexperimental philosophers, have lowered the glory of the great man whom itwas, many will think, their business to defend through thick and thin. Theyhave given a clearer notion of his {89} excellencies, and a better idea ofthe power of his mind, than ever we saw given before. Such a correction astheirs must have come, and soon, for as Hallam says--after noting that the_Novum Organum_ was _never published separately in England_, Bacon hasprobably been more read in the last thirty years--now forty--than in thetwo hundred years which preceded. He will now be more read than ever hewas. The history of the intellectual world is the history of the worship ofone idol after another. No sooner is it clear that a Hercules has appearedamong men, than all that imagination can conceive of strength is attributedto him, and his labors are recorded in the heavens. The time arrives when, as in the case of Aristotle, a new deity is found, and the old one isconsigned to shame and reproach. A reaction may afterwards take place, andthis is now happening in the case of the Greek philosopher. The end of theprocess is, that the opposing deities take their places, side by side, in aPantheon dedicated not to gods, but to heroes. THE REAL VALUE OF BACON'S WORKS. Passing over the success of Bacon's own endeavors to improve the details ofphysical science, which was next to nothing, and of his method as a whole, which has never been practised, we might say much of the good influence ofhis writings. Sound wisdom, set in sparkling wit, must instruct and amuseto the end of time: and, as against error, we repeat that Bacon is soundlywise, so far as he goes. There is hardly a form of human error within hisscope which he did not detect, expose, and attach to a satirical metaphorwhich never ceases to sting. He is largely indebted to a very extensivereading; but the thoughts of others fall into his text with such aclose-fitting compactness that he can make even the words of the SacredWriters pass for his own. A saying of the prophet Daniel, rather ahackneyed quotation in our day, _Multi pertransibunt, et augebiturscientia_, stands in the title-page of the first edition {90} of Montucla's_History of Mathematics_ as a quotation from Bacon--and it is not the onlyplace in which this mistake occurs. When the truth of the matter, as toBacon's system, is fully recognized, we have little fear that there will bea reaction against the man. First, because Bacon will always live to speakfor himself, for he will not cease to be read: secondly, because those whoseek the truth will find it in the best edition of his works, and will bemost ably led to know what Bacon was, in the very books which first showedat large what he _was not_. THE CONGREGATION OF THE INDEX, ON COPERNICUS. In this year (1620) appeared the corrections under which the Congregationof the Index--i. E. , the Committee of Cardinals which superintended the_Index_ of forbidden books--proposed to allow the work of Copernicus to beread. I insert these conditions in full, because they are often alluded to, and I know of no source of reference accessible to a twentieth part ofthose who take interest in the question. By a decree of the Congregation of the Index, dated March 5, 1616, the workof Copernicus, and another of Didacus Astunica, [137] are suspended _doneccorrigantur_, as teaching: "Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omninoadversantem, de mobilitate Terræ et immobilitate Solis. "[138] But a work of the Carmelite Foscarini[139] is: {91} "Omnino prohibendum atque damnandum, " because "ostendere conatur præfatamdoctrinam ... Consonam esse veritati et non adversari SacræScripturæ. "[140] Works which teach the false doctrine of the earth's motion are to becorrected; those which declare the doctrine conformable to Scripture are tobe utterly prohibited. In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, permissio, et correctio, " dated 1620 without the month or day, permission is given toreprint the work of Copernicus with certain alterations; and, byimplication, to read existing copies after correction in writing. In thepreamble the author is called _nobilis astrologus_; not a compliment to hisbirth, which was humble, but to his fame. The suspension was because: "Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi repugnantia(quod in homine Christiano minime tolerandum) non _per hypothesin_tractare, sed _ut verissima_ adstruere non dubitat!"[141] And the corrections relate: "Locis in quibus non _ex hypothesi_, sed _asserendo_ de situ et motu Terrædisputat. "[142] That is, the earth's motion may be an hypothesis for elucidation of theheavenly motions, but must not be asserted as a fact. (In Pref. Circa finem. ) "_Copernicus. _ Si fortasse erunt [Greek:mataiologoi], qui cum omnium Mathematum ignari sint, tamen de illisjudicium sibi summunt, propter aliquem locum scripturæ, male ad suumpropositum detortum, ausi fuerint meum {92} hoc institutum reprehendere acinsectari: illos nihil moror adeo ut etiam illorum judicium tanquamtemerarium contemnam. Non enim obscurum est Lactantium, celebrem alioquiscriptorem, sed Mathematicum parum, admodum pueriliter de forma terræloqui, cum deridet eos, qui terram globi formam habere prodiderunt. Itaquenon debet mirum videri studiosis, si qui tales nos etiam videbunt. Mathemata Mathematicis scribuntur, quibus et hi nostri labores, si me nonfallit opinio, videbuntur etiam Reipub. Ecclesiasticæ conducere aliquid.... _Emend. _ Ibi _si fortasse_ dele omnia, usque ad verbum _hi nostri labores_et sic accommoda--_Coeterum hi nostri labores_. "[143] All the allusion to Lactantius, who laughed at the notion of the earthbeing round, which was afterwards found true, is to be struck out. (Cap. 5. Lib. I. P. 3) "_Copernicus. _ Si tamen attentius rem consideremus, videbitur hæc quæstio nondum absoluta, et ideireo minime contemnenda. _Emend. _ Si tamen attentius rem consideremus, nihil refert an Terram inmedio Mundi, an extra Medium existere, quoad solvendas coelestium motuumapparentias existimemus. "[144] {93} We must not say the question is not yet settled, but only that it may besettled either way, so far as mere explanation of the celestial motions isconcerned. (Cap. 8. Lib. I. ) "Totum hoc caput potest expungi, quia ex professo tractatde veritate motus Terræ, dum solvit veterum rationes probantes ejusquietem. Cum tamen problematice videatur loqui; ut studiosis satisfiat, seriesque et ordo libri integer maneat; emendetur ut infra. "[145] A chapter which seems to assert the motion should perhaps be expunged; butit may perhaps be problematical; and, not to break up the book, must beamended as below. (p. 6. ) "_Copernicus. _ Cur ergo hesitamus adhuc, mobilitatem illi formæ suæa natura congruentem concedere, magisquam quod totus labatur mundus, cujusfinis ignoratur, scirique nequit, neque fateamur ipsius cotidianærevolutionis in coelo apparentiam esse, et in terra veritatem? Et hæcperinde se habere, ac si diceret Virgilianus Æneas: Provehimur portu ... _Emend. _ Cur ergo non possum mobilitatem illi formæ suæ concedere, magisquequod totus labatur mundus, cujus finis ignoratur scirique nequit, et quæapparent in coelo, perinde se habere ac si ... "[146] {94} "Why should we hesitate to allow the earth's motion, " must be altered into"I cannot concede the earth's motion. " (p. 7. ) "_Copernicus. _ Addo etiam, quod satis absurdum videretur, continenti sive locanti motum adscribi, et non potius contento et locato, quod est terra. _Emend. _ Addo etiam difficilius non esse contento etlocato, quod est Terra, motum adscribere, quam continenti. "[147] We must not say it is absurd to refuse motion to the _contained_ and_located_, and to give it to the containing and locating; say that neitheris more difficult than the other. (p. 7. ) "_Copernicus. _ Vides ergo quod ex his omnibus probabilior sitmobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione, tanquam terræ maxime propria. _Emend. _ _Vides_ ... Delendus est usque adfinem capitis. "[148] Strike out the whole of the chapter from this to the end; it says that themotion of the earth is the most probable hypothesis. (Cap. 9. Lib. I. P. 7. ) "_Copernicus. _ Cum igitur nihil prohibeatmobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motusconveniant, ut possit una errantium syderum existimari. _Emend. _ Cum igiturTerram moveri assumpserim, videndum nunc arbitror, an etiam illi plurespossint convenire motus. "[149] {95} We must not say that nothing prohibits the motion of the earth, only thathaving _assumed_ it, we may inquire whether our explanations requireseveral motions. (Cap. 10. Lib. I. P. 9. ) "_Copernicus. _ Non pudet nos fateri ... Hoc potiusin mobilitate terræ verificari. _Emend. _ Non pudet nos assumere ... Hocconsequenter in mobilitate verificari. "[150] (Cap. 10. Lib. I. P. 10. ) "_Copernicus. _ Tanta nimirum est divina hæc. Opt. Max. Fabrica. _Emend. _ Dele illa verba postrema. "[151] (Cap. Ii. Lib. I. [152]) "_Copernicus. _ De triplici motu tellurisdemonstratio. _Emend. _ De hypothesi triplicis motus Terræ, ejusquedemonstratione. "[153] (Cap. 10. Lib. Iv. P. 122. [154]) "_Copernicus. _ De magnitudine horum triumsiderum, Solis, Lunæ, et Terræ. _Emend. _ Dele verba _horum trium siderum_, quia terra non est sidus, ut facit eam Copernicus. "[155] We must not say we are not ashamed to _acknowledge_; _assume_ is the word. We must not call this assumption a _Divine work_. A chapter must not beheaded _demonstration_, but _hypothesis_. The earth must not be called a_star_; the word implies motion. It will be seen that it does not take much to reduce Copernicus to purehypothesis. No personal injury being done to the author--who indeed hadbeen 17 years out of {96} reach--the treatment of his book is now anexcellent joke. It is obvious that the Cardinals of the Index were a littleashamed of their position, and made a mere excuse of a few corrections. Their mode of dealing with chap. 8, this _problematice videtur loqui, utstudiosis satisfiat_, [156] is an excuse to avoid corrections. But theystruck out the stinging allusion to Lactantius[157] in the preface, littlethinking, honest men, for they really believed what they said--that thelight of Lactantius would grow dark before the brightness of their own. THE CONVOCATION AT OXFORD EQUALLY AT FAULT. 1622. I make no reference to the case of Galileo, except this. I havepointed out (_Penny Cycl. Suppl. _ "Galileo"; _Engl. Cycl. _ "Motion of theEarth") that it is clear the absurdity was the act of the _Italian_Inquisition--for the private and personal pleasure of the Pope, who _knew_that the course he took would not commit him as _Pope_--and not of the bodywhich calls itself the _Church_. Let the dirty proceeding have its rightname. The Jesuit Riccioli, [158] the stoutest and most learnedAnti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican andPope-hater, are equally positive that the Roman _Church_ never pronouncedany decision: and this in the time immediately following the ridiculousproceeding of the Inquisition. In like manner a decision of the Convocationof Oxford is not a law of the _English_ Church; which is fortunate, forthat Convocation, in 1622, came to a decision quite as absurd, and a greatdeal {97} more wicked than the declaration against the motion of the earth. The second was a foolish mistake; the first was a disgusting surrender ofright feeling. The story is told without disapprobation by Anthony Wood, who never exaggerated anything against the university of which he iswriting eulogistic history. In 1622, one William Knight[159] put forward in a sermon preached beforethe University certain theses which, looking at the state of the times, mayhave been improper and possibly of seditious intent. One of them was thatthe bishop might excommunicate the civil magistrate: this proposition theclerical body could not approve, and designated it by the term_erronea_, [160] the mildest going. But Knight also declared as follows: "Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in ipsosfaciat impetum, et ipsi nec potestatem ordinariam implorare, nec aliaratione effugere periculum possint, in presenti periculo se et suos contratyrannum, sicut contra privatum grassatorem, defendere licet. "[161] That is, a man may defend his purse or a woman her honor, against thepersonal attack of a king, as against that of a private person, if no othermeans of safety can be found. The Convocation sent Knight to prison, declared the proposition _"falsa_, periculosa, et _impia_, " and enactedthat all applicants for degrees should subscribe this censure, and makeoath that they would neither hold, teach, nor defend Knight's opinions. The thesis, in the form given, was unnecessary and improper. Though strongopinions of the king's rights were advanced at the time, yet no oneventured to say that, {98} ministers and advisers apart, the king might_personally_ break the law; and we know that the first and only attemptwhich his successor made brought on the crisis which cost him his throneand his head. But the declaration that the proposition was _false_ farexceeds in all that is disreputable the decision of the Inquisition againstthe earth's motion. We do not mention this little matter in England. Knightwas a Puritan, and Neal[162] gives a short account of his sermon. Fromcomparison with Wood, [163] I judge that the theses, as given, were notKnight's words, but the digest which it was customary to make in criminalproceedings against opinion. This heightens the joke, for it appears thatthe qualifiers of the Convocation took pains to present their condemnationof Knight in the terms which would most unequivocally make their censurecondemn themselves. This proceeding took place in the interval between thetwo proceedings against Galileo: it is left undetermined whether we mustsay pot-kettle-pot or kettle-pot-kettle. Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis. Antwerp, 1631, 8vo. [164] This book contains the evidence of an ardent opponent of Galileo to thefact, that Roman Catholics of the day did not consider the decree of the_Index_ or of the _Inquisition_ as a declaration of their _Church_. Fromondwould have been glad to say as much, and tries to come near it, butconfesses he must abstain. See _Penny Cyclop. Suppl. _ "Galileo, " and _Eng. Cycl. _ "Motion of the Earth. " The author of a celebrated article in the_Dublin Review_, in defence of the {99} Church of Rome, seeing thatDrinkwater Bethune[165] makes use of the authority of Fromondus, but foranother purpose, sneers at him for bringing up a "musty old Professor. " Ifhe had known Fromondus, and used him he would have helped his own case, which is very meagre for want of knowledge. [166] Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la Proposition faicte par le Sieur Morin pour l'invention des longitudes. Paris, 1634, 8vo. [167] This is the Official Report of the Commissioners appointed by the Cardinal, of whom Pascal is the one now best known, to consider Morin's plan. See thefull account in Delambre, _Hist. Astr. Mod. _ ii. 236, etc. THE METIUS APPROXIMATION. Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640, 4to. [168] This book contains the celebrated approximation _guessed at_ by his father, Peter Metius, [169] namely that the diameter is {100} to the circumferenceas 113 to 355. The error is at the rate of about a foot in 2, 000 miles. Peter Metius, having his attention called to the subject by the falsequadrature of Duchesne, found that the ratio lay between 333/106 and377/120. He then took the liberty of taking the mean of both numerators anddenominators, giving 355/113. He had no right to presume that this mean wasbetter than either of the extremes; nor does it appear positively that hedid so. He published nothing; but his son Adrian, [170] when Van Ceulen'swork showed how near his father's result came to the truth, first made itknown in the work above. (See _Eng. Cyclop. _, art. "Quadrature. ") ON INHABITABLE PLANETS. A discourse concerning a new world and another planet, in two books. London, 1640, 8vo. [171] Cosmotheoros: or conjectures concerning the planetary worlds and their inhabitants. Written in Latin, by Christianus Huyghens. This translation was first published in 1698. Glasgow, 1757, 8vo. [The original is also of 1698. ][172] The first work is by Bishop Wilkins, being the third edition, [first in1638] of the first book, "That the Moon may be a Planet"; and the firstedition of the second work, {101} "That the Earth may be a Planet. " [Seemore under the reprint of 1802. ] Whether other planets be inhabited or not, that is, crowded with organisations some of them having consciousness, isnot for me to decide; but I should be much surprised if, on going to one ofthem, I should find it otherwise. The whole dispute tacitly assumes that, if the stars and planets be inhabited, it must be by things of which we canform some idea. But for aught we know, what number of such bodies thereare, so many organisms may there be, of which we have no way of thinkingnor of speaking. This is seldom remembered. In like manner it is usuallyforgotten that the _matter_ of other planets may be of different chemistryfrom ours. There may be no oxygen and hydrogen in Jupiter, which may have_gens_ of its own. [173] But this must not be said: it would limit theomniscience of the _a priori_ school of physical inquirers, the larger halfof the whole, and would be very _unphilosophical_. Nine-tenths of my bestparadoxers come out from among this larger half, because they are just alittle more than of it at their entrance. There was a discussion on the subject some years ago, which began with The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm. Whewell, Master of Trinity College, Cambridge]. A dialogue on the plurality of worlds, being a supplement to the Essay on that subject. [First found in the second edition, 1854; removed to the end in subsequent editions, and separate copies issued. ][174] A work of skeptical character, insisting on analogies which prohibit thepositive conclusion that the planets, stars, etc. , are what we should call_inhabited_ worlds. It produced {102} several works and a large amount ofcontroversy in reviews. The last predecessor of whom I know was Plurality of Worlds.... By Alexander Maxwell. Second Edition. London, 1820, 8vo. This work is directed against the plurality by an author who does not admitmodern astronomy. It was occasioned by Dr. Chalmers's[175] celebrateddiscourses on religion in connection with astronomy. The notes contain manycitations on the gravity controversy, from authors now very little read:and this is its present value. I find no mention of Maxwell, not even inWatt. [176] He communicated with mankind without the medium of a publisher;and, from Vieta till now, this method has always been favorable to loss ofbooks. A correspondent informs me that Alex. Maxwell, who wrote on the pluralityof worlds, in 1820, was a law-bookseller and publisher (probably his ownpublisher) in Bell Yard. He had peculiar notions, which he was fond ofdiscussing with his customers. He was a bit of a Swedenborgian. INHABITED PLANETS IN FICTION. There is a class of hypothetical creations which do not belong to mysubject, because they are _acknowledged_ to be fictions, as those ofLucian, [177] Rabelais, [178] Swift, Francis {103} Godwin, [179] Voltaire, etc. All who have more positive notions as to either the composition ororganization of other worlds, than the reasonable conclusion that ourArchitect must be quite able to construct millions of other buildings onmillions of other plans, ought to rank with the writers just mentioned, inall but self-knowledge. Of every one of their systems I say, as the IrishBishop said of Gulliver's book, --I don't believe half of it. Huyghens hadbeen preceded by Fontenelle, [180] who attracted more attention. Huyghens isvery fanciful and very positive; but he gives a true account of his method. "But since there's no hopes of a Mercury to carry us such a journey, weshall e'en be contented with what's in our power: we shall supposeourselves there.... " And yet he says, "We have proved that they live insocieties, have hands and feet.... " Kircher[181] had gone to the starsbefore him, but would not find any life in them, either animal orvegetable. The question of the inhabitants of a particular planet is one which hastruth on one side or the other: either there are some inhabitants, or thereare none. Fortunately, it is of no consequence which is true. But there aremany cases where the balance is equally one of truth and falsehood, inwhich the choice is a matter of importance. My work selects, for the mostpart, sins against demonstration: but the world is full of questions offact or opinion, in which a struggling minority will become a majority, orelse will {104} be gradually annihilated: and each of the cases subdividesinto results of good, and results of evil. What is to be done? "Periculosum est credere et non credere; Hippolitus obiit quia novercæ creditum est; Cassandræ quia non creditum ruit Ilium: Ergo exploranda est veritas multum prius Quam stulta prove judicet sententia. "[182] Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to. [183] No magnetic body can move about its poles: the earth is a magnetic body, therefore, etc. The iron and its magnetism are typical of two natures inone person; so it is said, "Si exaltatus fuero à terra, omnia traham ad meipsum. "[184] A VENETIAN BUDGET OF PARADOXES. Le glorie degli incogniti, o vero gli huomini illustri dell' accademia de' signori incogniti di Venetia. Venice, 1647, 4to. This work is somewhat like a part of my own: it is a budget of Venetiannobodies who wished to be somebodies; but paradox is not the only meansemployed. It is of a serio-comic character, gives genuine portraits incopperplate, and grave lists of works; but satirical accounts. Theastrologer Andrew Argoli[185] is there, and his son; both of whom, withsome of the others, have place in modern works {105} on biography. Argoli'sdiscovery that logarithms facilitate easy processes, but increase the laborof difficult ones, is worth recording. Controversiæ de vera circuli mensura ... Inter ... C. S. Longomontanum et Jo. Pellium. [186] Amsterdam, 1647, 4to. Longomontanus, [187] a Danish astronomer of merit, squared the circle in1644: he found out that the diameter 43 gives the square root of 18252 forthe circumference; which gives 3. 14185... For the ratio. Pell answered him, and being a kind of circulating medium, managed to engage in thecontroversy names known and unknown, as Roberval, Hobbes, Carcavi, LordCharles Cavendish, Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri and Golius. [188] Among them, of course, Longomontanus was made{106} mincemeat: but he is said to have insisted on the discovery of hisepitaph. [189] {107} THE CIRCULATING MEDIA OF MATHEMATICS. The great circulating mediums, who wrote to everybody, heard fromeverybody, and sent extracts to everybody else, have been Father Mersenne, John Collins, and the late Professor Schumacher: all "late" no doubt, butonly the last recent enough to be so styled. If M. C. S. Should ever againstand for "Member of the Corresponding Society, " it should raise anacrostic thought of the three. There is an allusion to Mersenne'soccupation in Hobbes's reply to him. He wanted to give Hobbes, who was veryill at Paris, the Roman Eucharist: but Hobbes said, "I have settled allthat long ago; when did you hear from Gassendi?" We are reminded ofWilliam's answer to Burnet. John Collins disseminated Newton, among others. Schumacher ought to have been called the postmaster-general of astronomy, as Collins was called the attorney-general of mathematics. [190] {108} THE SYMPATHETIC POWDER. A late discourse ... By Sir Kenelme Digby.... Rendered into English by R. White. London, 1658, 12mo. On this work see _Notes and Queries_, 2d series, vii. 231, 299, 445, viii. 190. It contains the celebrated sympathetic powder. I am still in muchdoubt as to the connection of Digby with this tract. [191] Without enteringon the subject here, I observe that in Birch's _History of the RoyalSociety_, [192] to which both Digby and White belonged, Digby, though hebrought many things before the Society, never mentioned the powder, whichis connected only with the names of Evelyn[193] and Sir GilbertTalbot. [194] The sympathetic powder was that which cured by anointing theweapon with its salve instead of the wound. I have long been convinced thatit was efficacious. The directions were to keep the {109} wound clean andcool, and to take care of diet, rubbing the salve on the knife orsword. [195] If we remember the dreadful notions upon drugs which prevailed, both as to quantity and quality, we shall readily see that any way of _not_dressing the wound would have been useful. If the physicians had taken thehint, had been careful of diet etc. , and had poured the little barrels ofmedicine down the throat of a practicable doll, _they_ would have had theirmagical cures as well as the surgeons. [196] Matters are much improved now;the quantity of medicine given, even by orthodox physicians, would havebeen called infinitesimal by their professional ancestors. Accordingly, theCollege of Physicians has a right to abandon its motto, which is _Arslonga, vita brevis_, meaning _Practice is long, so life is short_. HOBBES AS A MATHEMATICIAN. Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. London, 1666, 4to. In six dialogues: the sixth contains a quadrature of the circle. [197] Butthere is another edition of this work, without place or date on thetitle-page, in which the quadrature is omitted. This seems to be connectedwith the publication {110} of another quadrature, without date, but about1670, as may be judged from its professing to answer a tract of Wallis, printed in 1669. [198] The title is "Quadratura circuli, cubatio sphæræ, duplicatio cubi, " 4to. [199] Hobbes, who began in 1655, was very wrong inhis quadrature; but, though not a Gregory St. Vincent, [200] he was not theignoramus in geometry that he is sometimes supposed. His writings, erroneous as they are in many things, contain acute remarks on points ofprinciple. He is wronged by being coupled with Joseph Scaliger, as the twogreat instances of men of letters who have come into geometry to help themathematicians out of their difficulty. I have never seen Scaliger'squadrature, [201] except in the answers of Adrianus Romanus, [202] Vieta andClavius, and in the extracts of Kastner. [203] Scaliger had no right to suchstrong opponents: Erasmus or Bentley might just as well have tried theproblem, and either would have done much better in any twenty minutes ofhis life. [204] AN ESTIMATE OF SCALIGER. Scaliger inspired some mathematicians with great respect for hisgeometrical knowledge. Vieta, the first man of his time, who answered him, had such regard for his opponent {111} as made him conceal Scaliger's name. Not that he is very respectful in his manner of proceeding: the followingdry quiz on his opponent's logic must have been very cutting, being true. "In grammaticis, dare navibus Austros, et dare naves Austris, sunt æquesignificantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD nonesse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majoratriginta sex segmenta BCDF. Illa adsumptiuncula vera est, hæc falsa. "[205]Isaac Casaubon, [206] in one of his letters to De Thou, [207] relates that, he and another paying a visit to Vieta, the conversation fell uponScaliger, of whom the host said that he believed Scaliger was the only manwho perfectly understood mathematical writers, especially the Greek ones:and that he thought more of Scaliger when wrong than of many others whenright; "pluris se Scaligerum vel errantem facere quam multos [Greek:katorthountas]. "[208] This must have been before Scaliger's quadrature(1594). There is an old story of some one saying, "Mallem cum Scaligeroerrare, quam cum Clavio recte sapere. "[209] This I cannot help suspectingto have been a version of Vieta's speech with Clavius satirically inserted, on account of the great hostility which Vieta showed towards Clavius in thelatter years of his life. Montucla could not have read with care either Scaliger's quadrature orClavius's refutation. He gives the first a wrong date: he assures the worldthat there is no question about Scaliger's quadrature being wrong, in theeyes of geometers at least: and he states that Clavius mortified him {112}extremely by showing that it made the circle less than its inscribeddodecagon, which is, of course, equivalent to asserting that a straightline is not always the shortest distance between two points. Did _Clavius_show this? No, it was Scaliger himself who showed it, boasted of it, anddeclared it to be a "noble paradox" that a theorem false in geometry istrue in arithmetic; a thing, he says with great triumph, not noticed byArchimedes himself! He says in so many words that the periphery of thedodecagon is greater than that of the circle; and that the more sides thereare to the inscribed figure, the more does it exceed the circle in which itis. And here _are_ the words, on the independent testimonies of Clavius andKastner: "Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum, tanto plus poterit ambitus polygoni quam ambitus circuli. "[210] There is much resemblance between Joseph Scaliger and WilliamHamilton, [211] in a certain impetuousity of character, and inaptitude tothink of quantity. Scaliger maintained that the arc of a circle is lessthan its chord in arithmetic, though greater in geometry; Hamilton arrivedat two quantities which are identical, but the greater the one the less theother. But, on the whole, I liken Hamilton rather to Julius than to Joseph. On this last hero of literature I repeat Thomas Edwards, [212] who says thata man is unlearned who, be his other knowledge what it may, does not {113}understand the subject he writes about. And now one of many instances inwhich literature gives to literature character in science. AnthonyTeissier, [213] the learned annotator of De Thou's biographies, says ofFinæus, "Il se vanta sans raison avoir trouvé la quadrature du cercle; lagloire de cette admirable découverte était réservée à Joseph Scalinger, comme l'a écrit Scévole de St. Marthe. "[214] JOHN GRAUNT AS A PARADOXER. Natural and Political Observations ... Upon the Bills of Mortality. By John Graunt, citizen of London. London, 1662, 4to. [215] This is a celebrated book, the first great work upon mortality. But theauthor, going _ultra crepidam_, has attributed to the motion of the moon inher orbit all the tremors which she gets from a shaky telescope. [216] Butthere is another paradox about this book: the above absurd opinion isattributed to that excellent mechanist, Sir William Petty, who passed hisdays among the astronomers. Graunt did not write his own book! AnthonyWood[217] hints that Petty "assisted, or put into a way" his oldbenefactor: no doubt the two friends talked the matter over many a time. Burnet and Pepys[218] state that Petty wrote the book. It is enough for methat {114} Graunt, whose honesty was never impeached, uses the plainestincidental professions of authorship throughout; that he was elected intothe Royal Society because he was the author; that Petty refers to him asauthor in scores of places, and published an edition, as editor, afterGraunt's death, with Graunt's name of course. The note on Graunt in the_Biographia Britannica_ may be consulted; it seems to me decisive. Mr. C. B. Hodge, an able actuary, has done the best that can be done on theother side in the _Assurance Magazine_, viii. 234. If I may say what is inmy mind, without imputation of disrespect, I suspect some actuaries have abias: they would rather have Petty the greater for their Coryphæus thanGraunt the less. [219] Pepys is an ordinary gossip: but Burnet's account has an animus which is ofa worse kind. He talks of "one Graunt, a Papist, under whose name SirWilliam Petty[220] published his observations on the bills of mortality. "He then gives the cock without a bull story of Graunt being a trustee ofthe New River Company, and shutting up the cocks and carrying off theirkeys, just before the fire of London, by which a supply of water wasdelayed. [221] It was one of the first objections made to Burnet's work, that Graunt was _not_ a trustee at the time; and Maitland, the historian ofLondon, ascertained from the books of the Company that he was not admitteduntil twenty-three days after the breaking out of the fire. Graunt's firstadmission {115} to the Company took place on the very day on which acommittee was appointed to inquire into the cause of the fire. So much forBurnet. I incline to the view that Graunt's setting London on fire stronglycorroborates his having written on the bills of mortality: every practicalman takes stock before he commences a grand operation in business. MANKIND A GULLIBLE LOT. De Cometis: or a discourse of the natures and effects of Comets, as they are philosophically, historically, and astrologically considered. With a brief (yet full) account of the III late Comets, or blazing stars, visible to all Europe. And what (in a natural way of judicature) they portend. Together with some observations on the nativity of the Grand Seignior. By John Gadbury, [Greek: Philomathêmatikos]. London, 1665, 4to. Gadbury, though his name descends only in astrology, was a well-informedastronomer. [222] D'Israeli[223] sets down Gadbury, Lilly, Wharton, Booker, etc. , as rank rogues: I think him quite wrong. The easy belief in rogueryand intentional imposture which prevails in educated society is, to mymind, a greater presumption against the honesty of mankind than all theroguery and imposture itself. Putting aside mere swindling for the sake ofgain, and looking at speculation and paradox, I find very little reason tosuspect wilful deceit. [224] My opinion of mankind is founded upon the {116}mournful fact that, so far as I can see, they find within themselves themeans of believing in a thousand times as much as there is to believe in, judging by experience. I do not say anything against Isaac D'Israeli fortalking his time. We are all in the team, and we all go the road, but we donot all draw. A FORERUNNER OF A WRITTEN ESPERANTO. An essay towards a real character and a philosophical language. By John Wilkins [Dean of Ripon, afterwards Bishop of Chester]. [225] London, 1668, folio. This work is celebrated, but little known. Its object gives it a right to aplace among paradoxes. It proposes a language--if that be the propername--in which _things_ and their relations shall be denoted by signs, not_words_: so that any person, whatever may be his mother tongue, may read itin his own words. This is an obvious possibility, and, I am afraid, anobvious impracticability. One man may construct such a system--BishopWilkins has done it--but where is the man who will learn it? The secondtongue makes a language, as the second blow makes a fray. There has beenvery little curiosity about his performance, the work is scarce; and I donot know where to refer the reader for any account of its details, except, to the partial reprint of Wilkins presently mentioned under 1802, in whichthere is an unsatisfactory abstract. There is nothing in the _BiographiaBritannica_, except discussion of Anthony Wood's statement that the hintwas derived from Dalgarno's book, {117} _De Signis_, 1661. [226] Hamilton(_Discussions_, Art. 5, "Dalgarno") does not say a word on this point, beyond quoting Wood; and Hamilton, though he did now and then write abouthis countrymen with a rough-nibbed pen, knew perfectly well how to protecttheir priorities. GREGOIRE DE ST. VINCENT. Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio a Sancto Vincentio Soc. Jesu. , Antwerp, 1647, folio. --Opus Geometricum posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668, folio. [227] The first book has more than 1200 pages, on all kinds of geometry. GregorySt. Vincent is the greatest of circle-squarers, and his investigations ledhim into many truths: he found the property of the area of thehyperbola[228] which led to Napier's logarithms being called _hyperbolic_. Montucla says of him, with sly truth, that no one has ever squared thecircle with so much genius, or, excepting his principal object, with somuch success. [229] His reputation, and the many merits of his work, led toa sharp controversy on his quadrature, which ended in its complete exposureby Huyghens and others. He had a small school of followers, who defendedhim in print. {118} RENE DE SLUSE. Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668, 4to. [230] The Mesolabum is the solution of the problem of finding two meanproportionals, which Euclid's geometry does not attain. Slusius is a truegeometer, and uses the ellipse, etc. : but he is sometimes ranked with thetrisecters, for which reason I place him here, with this explanation. The finding of two mean proportionals is the preliminary to the famous oldproblem of the duplication of the cube, proposed by Apollo (not Apollonius)himself. D'Israeli speaks of the "six follies of science, "--the quadrature, the duplication, the perpetual motion, the philosopher's stone, magic, andastrology. He might as well have added the trisection, to make the mysticnumber seven: but had he done so, he would still have been very lenient;only seven follies in all science, from mathematics to chemistry! Sciencemight have said to such a judge--as convicts used to say who got sevenyears, expecting it for life, "Thank you, my Lord, and may you sit theretill they are over, "--may the Curiosities of Literature outlive the Folliesof Science! JAMES GREGORY. 1668. In this year James Gregory, in his _Vera Circuli et HyperbolæQuadratura_, [231] held himself to have proved that {119} the _geometrical_quadrature of the circle is impossible. Few mathematicians read this veryabstruse speculation, and opinion is somewhat divided. The regularcircle-squarers attempt the _arithmetical_ quadrature, which has long beenproved to be impossible. Very few attempt the geometrical quadrature. Oneof the last is Malacarne, an Italian, who published his _SolutionGéométrique_, at Paris, in 1825. His method would make the circumferenceless than three times the diameter. BEAULIEU'S QUADRATURE. La Géométrie Françoise, ou la Pratique aisée.... La quadracture du cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died in 1674]. [232] If this book had been a fair specimen, I might have pointed to it inconnection with contemporary English works, and made a scornful comparison. But it is not a fair specimen. Beaulieu was attached to the RoyalHousehold, and throughout the century it may be suspected that thehousehold forced a royal road to geometry. Fifty years before, Beaugrand, the king's secretary, made a fool of himself, and [so?] contrived to passfor a geometer. He had interest enough to get Desargues, the most powerfulgeometer of his time, [233] the teacher and friend of Pascal, prohibitedfrom {120} lecturing. See some letters on the History of Perspective, whichI wrote in the _Athenæum_, in October and November, 1861. Montucla, whodoes not seem to know the true secret of Beaugrand's greatness, describeshim as "un certain M. De Beaugrand, mathématicien, fort mal traité parDescartes, et à ce qu'il paroit avec justice. "[234] Beaulieu's quadrature amounts to a geometrical construction[235] whichgives [pi] = [root]10. His depth may be ascertained from the followingextracts. First on Copernicus: "Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctesécrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en laforce de ses Problèmes, si sa trop grande présomption ne l'avoit porté àavancer en cette Science une proposition aussi absurde, qu'elle est contrela Foy et raison, en faisant la circonférence d'un Cercle fixe, immobile, et le centre mobile, sur lequel principe Géométrique, il a avancé en sonTraitté Astrologique le Soleil fixe, et la Terre mobile. "[236] I digress here to point out that though our quadrators, etc. , very often, and our historians sometimes, assert that men of the character ofCopernicus, etc. , were treated with contempt and abuse until their day ofascendancy came, nothing can be more incorrect. From Tycho Brahé[237] toBeaulieu, there is but one expression of admiration for the genius ofCopernicus. There is an exception, which, I {121} believe, has been quitemisunderstood. Maurolycus, [238] in his _De Sphæra_, written many yearsbefore its posthumous publication in 1575, and which it is not certain hewould have published, speaking of the safety with which various authors maybe read after his cautions, says, "Toleratur et Nicolaus Copernicus quiSolem fixum et Terram _in girum circumverti_ posuit: et scutica potius, autflagello, quam reprehensione dignus est. "[239] Maurolycus was a mild andsomewhat contemptuous satirist, when expressing disapproval: as we shouldnow say, he pooh-poohed his opponents; but, unless the above be aninstance, he was never savage nor impetuous. I am fully satisfied that themeaning of the sentence is, that Copernicus, who turned the earth like aboy's top, ought rather to have a whip given him wherewith to keep up hisplaything than a serious refutation. To speak of _tolerating_ a person _asbeing_ more worthy of a flogging than an argument, is almost acontradiction. I will now extract Beaulieu's treatise on algebra, entire. "L'Algebre est la science curieuse des Sçavans et specialement d'un Generald'Armée ou Capitaine, pour promptement ranger une Armée en bataille, etnombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a 5 figuresparticulieres en cette sorte. P signifie _plus_ au commerce, et à l'Armée_Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons. [It is quite true that P and M were used for _plus_ and _minus_ in a greatmany old works. ] R signifie _racine_ en la mesure du Cube, et en l'Armée_rang_. Q signifie _quaré_ en l'un et l'autre usage. C signifie _cube_ enla mesure, et _Cavallerie_ en la composition des bataillons et escadrons. Quant à l'operation de cette science, c'est {122} d'additionner un _plus_d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustraitle moindre du _plus_, et la reste est la somme requise ou nombre trouvé. Jedis seulement cecy en passant pour ceux qui n'en sçavent rien dutout. "[240] This is the algebra of the Royal Household, seventy-three years after thedeath of Vieta. Quære, is it possible that the fame of Vieta, who himselfheld very high stations in the household all his life, could have givenpeople the notion that when such an officer chose to declare himself analgebraist, he must be one indeed? This would explain Beaugrand, Beaulieu, and all the _beaux_. Beaugrand--not only secretary to the king, but"mathematician" to the Duke of Orleans--I wonder what his "fool" could havebeen like, if indeed he kept the offices separate, --would have been in mylist if I had possessed his _Geostatique_, published about 1638. [241] Hemakes bodies diminish in weight as they approach the earth, because theeffect of a weight on a lever is less as it approaches the fulcrum. {123} SIR MATTHEW HALE. Remarks upon two late ingenious discourses.... By Dr. Henry More. [242] London, 1676, 8vo. In 1673 and 1675, Matthew Hale, [243] then Chief Justice, published twotracts, an "Essay touching Gravitation, " and "Difficiles Nugæ" on theTorricellian experiment. Here are the answers by the learned and voluminousHenry More. The whole would be useful to any one engaged in research aboutante-Newtonian notions of gravitation. Observations touching the principles of natural motions; and especially touching rarefaction and condensation.... By the author of _Difficiles Nugæ_. London, 1677, 8vo. This is another tract of Chief Justice Hale, published the year after hisdeath. The reader will remember that _motion_, in old philosophy, meant anychange from state to state: what we now describe as _motion_ was _localmotion_. This is a very philosophical book, about _flux_ and _materiaprima_, _virtus activa_ and _essentialis_, and other fundamentals. I thinkStephen Hales, the author of the "Vegetable Statics, " has the writings ofthe Chief Justice sometimes attributed to him, which is very puny justiceindeed. [244] Matthew Hale died in 1676, and from his devotion to science itprobably arose that his famous _Pleas of the Crown_[245] and other lawworks did not appear until after his death. One of his {124} contemporarieswas the astronomer Thomas Street, whose _Caroline Tables_[246] were severaltimes printed: another contemporary was his brother judge, Sir ThomasStreet. [247] But of the astronomer absolutely nothing is known: it is veryunlikely that he and the judge were the same person, but there is not a bitof positive evidence either for or against, so far as can be ascertained. Halley[248]--no less a person--published two editions of the _CarolineTables_, no doubt after the death of the author: strange indeed thatneither Halley nor any one else should leave evidence that Street was bornor died. Matthew Hale gave rise to an instance of the lengths a lawyer will go whenbefore a jury who cannot detect him. Sir Samuel Shepherd, [249] the AttorneyGeneral, in opening Hone's[250] first trial, calls him "one who was themost learned man that ever adorned the Bench, the most even man that everblessed domestic life, the _most eminent man that ever advanced theprogress of science_, and one of the [very moderate] best and most purelyreligious men that ever lived. " {125} ON THE DISCOVERY OF ANTIMONY. Basil Valentine his triumphant Chariot of Antimony, with annotations of Theodore Kirkringius, M. D. With the true book of the learned Synesius, a Greek abbot, taken out of the Emperour's library, concerning the Philosopher's Stone. London, 1678, 8vo. [251] There are said to be three Hamburg editions of the collected works ofValentine, who discovered the common antimony, and is said to have giventhe name _antimoine_, in a curious way. Finding that the pigs of hisconvent throve upon it, he gave it to his brethren, who died of it. [252]The impulse given to chemistry by R. Boyle[253] seems to have brought out avast number of translations, as in the following tract: ON ALCHEMY. _Collectanea Chymica_: A collection of ten several treatises in chymistry, concerning the liquor Alkehest, the Mercury of Philosophers, and other curiosities worthy the perusal. Written by Eir. Philaletha, [254] Anonymus, J. B. Van-Helmont, [255] Dr. Fr. {126} Antonie, [256] Bernhard Earl of Trevisan, [257] Sir Geo. Ripley, [258] Rog. Bacon, [259] Geo. Starkie, [260] Sir Hugh Platt, [261] and the Tomb of Semiramis. See more in the contents. London, 1684, 8vo. In the advertisements at the ends of these tracts there are upwards of ahundred English tracts, nearly all of the period, and most of themtranslations. Alchemy looks up since the chemists have found perfectlydifferent substances composed of the same elements and proportions. It istrue the chemists cannot yet _transmute_; but they may in time: they pokeabout most assiduously. It seems, then, that the conviction that alchemy_must_ be impossible was a delusion: but we do not mention it. {127} The astrologers and the alchemists caught it in company in the following, of which I have an unreferenced note. "Mendacem et futilem hominem nominare qui volunt, calendariographum dicunt;at qui sceleratum simul ac impostorem, chimicum. [262] "Crede ratem ventis corpus ne crede chimistis; Est quævis chimica tutior aura fide. "[263] Among the smaller paradoxes of the day is that of the _Times_ newspaper, which always spells it _chymistry_: but so, I believe, do Johnson, Walker, and others. The Arabic work is very likely formed from the Greek: but itmay be connected either with [Greek: chêmeia] or with [Greek: chumeia]. Lettre d'un gentil-homme de province à une dame de qualité, sur le sujet de la Comète. Paris, 1681, 4to. An opponent of astrology, whom I strongly suspect to have been one of themembers of the Academy of Sciences under the name of a countrygentleman, [264] writes very good sense on the tremors excited by comets. The Petitioning-Comet: or a brief Chronology of all the famous Comets and their events, that have happened from the birth of Christ to this very day. Together with a modest enquiry into this present comet, London, 1681, 4to. A satirical tract against the cometic prophecy: "This present comet (it's true) is of a menacing aspect, but if the _newparliament_ (for whose convention so many good men pray) continue long tosit, I fear not but the star will lose its virulence and malignancy, or atleast its portent be averted from this our nation; which being the humblerequest to God of all good men, makes me thus entitle it, aPetitioning-Comet. " {128} The following anecdote is new to me: "Queen Elizabeth (1558) being then at Richmond, and being disswaded fromlooking on a comet which did then appear, made answer, _jacta est alea_, the dice are thrown; thereby intimating that the pre-order'd providence ofGod was above the influence of any star or comet. " The argument was worth nothing: for the comet might have been _on the dice_with the event; the astrologers said no more, at least the more rationalones, who were about half of the whole. An astrological and theological discourse upon this present great conjunction (the like whereof hath not (likely) been in some ages) ushered in by a great comet. London, 1682, 4to. By C. N. [265] The author foretells the approaching "sabbatical jubilee, " but will not fixthe date: he recounts the failures of his predecessors. A judgment of the comet which became first generally visible to us in Dublin, December 13, about 15 minutes before 5 in the evening, A. D. 1680. By a person of quality. Dublin, 1682, 4to. The author argues against cometic astrology with great ability. A prophecy on the conjunction of Saturn and Jupiter in this present year 1682. With some prophetical predictions of what is likely to ensue therefrom in the year 1684. By John Case, Student in physic and astrology. [266] London, 1682, 4to. {129} According to this writer, great conjunctions of Jupiter and Saturn occur"in the fiery trigon, " about once in 800 years. Of these there are to beseven: six happened in the several times of Enoch, Noah, Moses, Solomon, Christ, Charlemagne. The seventh, which is to happen at "the lamb'smarriage with the bride, " seems to be that of 1682; but this is onlyvaguely hinted. De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to. Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis. Amsterdam, 1699, 4to. Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam, 1702, 4to. De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to. Who shall contradict Jacob Marcelis?[267] He says the circumferencecontains the diameter exactly times 1008449087377541679894282184894 3 -------------------------------- 6997183637540819440035239271702 But he does not come very near, as the young arithmetician will find. MATHEMATICAL THEOLOGY. Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig. [268] London, 1699, 4to. This is a celebrated speculation, and has been reprinted abroad, andseriously answered. Craig is known in the early history of fluxions, andwas a good mathematician. {130} He professed to calculate, on thehypothesis that the suspicions against historical evidence increase withthe square of the time, how long it will take the evidence of Christianityto die out. He finds, by formulæ, that had it been oral only, it would havegone out A. D. 800; but, by aid of the written evidence, it will last tillA. D. 3150. At this period he places the second coming, which is deferreduntil the extinction of evidence, on the authority of the question "Whenthe Son of Man cometh, shall he find faith on the earth?" It is a pity thatCraig's theory was not adopted: it would have spared a hundred treatises onthe end of the world, founded on no better knowledge than his, and many ofthem falsified by the event. The most recent (October, 1863) is a tract inproof of Louis Napoleon being Antichrist, the Beast, the eighth Head, etc. ;and the present dispensation is to close soon after 1864. In order rightly to judge Craig, who added speculations on the variationsof pleasure and pain treated as functions of time, it is necessary toremember that in Newton's day the idea of force, as a quantity to bemeasured, and as following a law of variation, was very new: so likewisewas that of probability, or belief, as an object of measurement. [269] Thesuccess of the _Principia_ of Newton put it into many heads to speculateabout applying notions of quantity to other things not then brought undermeasurement. Craig imitated Newton's title, and evidently thought he wasmaking a step in advance: but it is not every one who can plough withSamson's heifer. It is likely enough that Craig took a hint, directly or indirectly, fromMohammedan writers, who make a reply to the argument that the Koran has notthe evidence derived {131} from miracles. They say that, as evidence ofChristian miracles is daily becoming weaker, a time must at last arrivewhen it will fail of affording assurance that they were miracles at all:whence would arise the necessity of another prophet and other miracles. Lee, [270] the Cambridge Orientalist, from whom the above words are taken, almost certainly never heard of Craig or his theory. THE ARISTOCRAT AS A SCIENTIST. Copernicans of all sorts convicted ... To which is added a Treatise of the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo. Not all the blood of all the Howards will gain respect for a writer whomaintains that eclipses admit no possible explanation under the Copernicanhypothesis, and who asks how a man can "go 200 yards to any place if themoving superficies of the earth does carry it from him?" Horace Walpole, atthe beginning of his _Royal and Noble Authors_, has mottoed his book withthe Cardinal's address to Ariosto, "Dove diavolo, Messer Ludovico, avetepigliato tante coglionerie?"[271] Walter Scott says you could hardly pickout, on any principle of selection--except badness itself, he means ofcourse--the same number of plebeian authors whose works are so bad. But hisimplied satire on aristocratic writing forgets two points. First, during alarge period of our history, when persons of rank condescended to write, they veiled themselves under "a person of honor, " "a person of quality, "and the like, when not wholly undescribed. Not one of these has Walpolegot; he omits, {132} for instance, Lord Brounker's[272] translation ofDescartes on Music. Secondly, Walpole only takes the heads of houses: thiscuts both ways; he equally eliminates the Hon. Robert Boyle and theprecious Edward Howard. The last writer is hardly out of the time in whicharistocracy suppressed its names; the avowal was then usually meant to makethe author's greatness useful to the book. In our day, literary peers andhonorables are very favorably known, and contain an eminent class. [273]They rough it like others, and if such a specimen as Edw. Howard were nowto appear, he would be greeted with "Hereditary noodle! knowest thou not Who would be wise, himself must make him so?" THE LONGITUDE PROBLEM. A new and easy method to find the longitude at land or sea. London, 1710, 4to. This tract is a little earlier than the great epoch of such publications(1714), and professes to find the longitude by the observed altitudes ofthe moon and two stars. [274] {133} A new method for discovering the longitude both at sea and land, humbly proposed to the consideration of the public. [275] By Wm. Whiston[276] and Humphry Ditton. [277] London, 1714, 8vo. This is the celebrated tract, written by the two Arian heretics. Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it theepigram--if, indeed, that be epigram of which the point is piouswish--which has been so often recited for the purity of its style, a puritywhich transcends modern printing. Perhaps some readers may think that Swiftcared little for Whiston and Ditton, except as a chance hearing of theirplan pointed them out as good marks. But it was not so: the clique hadtheir eye on the guilty pair before the publication of the tract. Thepreface is dated July 7; and ten days afterwards Arbuthnot[278] writes asfollows to Swift: "Whiston has at last published his project of the longitude; the mostridiculous thing that ever was thought on. But a pox on him! he has spoiledone of my papers of Scriblerus, which was a proposition for the longitudenot very unlike his, to this purpose; that since there was no pole for eastand west, that all the princes of Europe should join and build twoprodigious poles, upon high mountains, {134} with a vast lighthouse toserve for a polestar. I was thinking of a calculation of the time, charges, and dimensions. Now you must understand his project is by lighthouses, andexplosion of bombs at a certain hour. " The plan was certainly impracticable; but Whiston and Ditton might haveretorted that they were nearer to the longitude than their satirist to thekingdom of heaven, or even to a bishopric. Arbuthnot, I think, here andelsewhere, reveals himself as the calculator who kept Swift right in hisproportions in the matter of the Lilliputians, Brobdingnagians, etc. Swiftwas very ignorant about things connected with number. He writes to Stellathat he has discovered that leap-year comes every four years, and that allhis life he had thought it came every three years. Did he begin with themistake of Cæsar's priests? Whether or no, when I find the person who didnot understand leap-year inventing satellites of Mars in correct accordancewith Kepler's third law, I feel sure he must have had help. THE AURORA BOREALIS. An essay concerning the late apparition in the heavens on the 6th of March. Proving by mathematical, logical, and moral arguments, that it cou'd not have been produced meerly by the ordinary course of nature, but must of necessity be a prodigy. Humbly offered to the consideration of the Royal Society. London, 1716, 8vo. The prodigy, as described, was what we should call a very decided andunusual aurora borealis. The inference was, that men's sins were bringingon the end of the world. The author thinks that if one of the old"threatening prophets" were then alive, he would give "something like thefollowing. " I quote a few sentences of the notion which the author had ofthe way in which Ezekiel, for instance, would have addressed his Maker inthe reign of George the First: "Begin! Begin! O Sovereign, for once, with an {135} effectual clap ofthunder.... O Deity! either thunder to us no more, or when you thunder, doit home, and strike with vengeance to the mark.... 'Tis not enough to raisea storm, unless you follow it with a blow, and the thunder without thebolt, signifies just nothing at all.... Are then your lightnings of soshort a sight, that they don't know how to hit, unless a mountain standslike a barrier in their way? Or perhaps so many eyes open in the firmamentmake you lose your aim when you shoot the arrow? Is it this? No! but, mydear Lord, it is your custom never to take hold of your arms till you havefirst bound round your majestic countenance with gathered mists andclouds. " The principles of the Philosophy of the Expansive and Contractive Forces ... By Robert Greene, [279] M. A. , Fellow of Clare Hall. Cambridge, 1727, folio. Sanderson[280] writes to Jones, [281] "The gentleman has been reputed madfor these two years last past, but never gave the world such ampletestimony of it before. " This was said of a former work of Greene's, onsolid geometry, published in 1712, in which he gives a quadrature. [282] Hegives the same or another, I do not know which, in the present work, inwhich the circle is 3-1/5 diameters. This volume is of 981 good foliopages, and treats of all things, mental and material. The author is not atall mad, only wrong on {136} many points. It is the weakness of theorthodox follower of any received system to impute insanity to the solitarydissentient: which is voted (in due time) a very wrong opinion aboutCopernicus, Columbus, or Galileo, but quite right about Robert Greene. Ifmisconceptions, acted on by too much self-opinion, be sufficient evidenceof madness, it would be a curious inquiry what is the least per-centage ofthe reigning school which has been insane at any one time. Greene is one ofthe sources for Newton being led to think of gravitation by the fall of anapple: his authority is the gossip of Martin Folkes. [283] Probably Folkeshad it from Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as_his authority_. [284] It is in the draft found among Conduitt's papers ofmemoranda to be sent to Fontenelle. But Fontenelle, though a great retailerof anecdote, does not mention it in his _éloge_ of Newton; whence it may besuspected that it was left out in the copy forwarded to France. D'Israelihas got an improvement on the story: the apple "struck him a smart blow onthe head": no doubt taking him just on the organ of causality. He was"surprised at the force of the stroke" from so small an apple: but then theapple had a mission; Homer would have said {137} it was Minerva in the formof an apple. "This led him to consider the accelerating motion of fallingbodies, " which Galileo had settled long before: "from whence he deduced theprinciple of gravity, " which many had considered before him, but no one had_deduced anything from it_. I cannot imagine whence D'Israeli got the rapon the head, I mean got it for Newton: this is very unlike his usualaccounts of things. The story is pleasant and possible: its only defect isthat various writings, well known to Newton, a very _learned_mathematician, had given more suggestion than a whole sack of apples couldhave done, if they had tumbled on that mighty head all at once. AndPemberton, speaking from Newton himself, says nothing more than that theidea of the moon being retained by the same force which causes the fall ofbodies struck him for the first time while meditating in a garden. Oneparticular tree at Woolsthorpe has been selected as the gallows of theappleshaped goddess: it died in 1820, and Mr. Turnor[285] kept the wood;but Sir D. Brewster[286] brought away a bit of root in 1814, and must havehad it on his conscience for 43 years that he may have killed the tree. Kepler's suggestion of gravitation with the inverse distance, andBouillaud's proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I discoveredtwo anagrams on his name, which are quite conclusive; the notion ofgravitation was _not new_; but Newton _went on_. Some wandering spirit, probably whose business it was to resent any liberty taken with Newton'sname, put into the head of a friend of mine _eighty-one_ anagrams on my ownpair, some of which hit harder than any apple. {138} DE MORGAN ANAGRAMS. This friend, whom I must not name, has since made it up to about 800anagrams on my name, of which I have seen about 650. Two of them I havejoined in the title-page: the reader may find the sense. A few of theothers are personal remarks. "Great gun! do us a sum!" is a sneer at my pursuits: but, "Go! great sum! [Integral]a u^{n} du" is more dignified. "Sunt agro! gaudemus, "[287] is happy as applied to one of whom it may be said: "Ne'er out of town; 'tis such a horrid life; But duly sends his family and wife. " "Adsum, nugator, suge!"[288] is addressed to a student who continues talking after the lecture hascommenced: oh! the rascal! "Graduatus sum! nego"[289] applies to one who declined to subscribe for an M. A. Degree. "Usage mounts guard" symbolizes a person of very fixed habits. "Gus! Gus! a mature don! August man! sure, god! And Gus must argue, O! Snug as mud to argue, Must argue on gauds. A mad rogue stung us. Gag a numerous stud Go! turn us! damage us! Tug us! O drag us! Amen. Grudge us! moan at us! {139} Daunt us! gag us more! Dog-ear us, man! gut us! D---- us! a rogue tugs!" are addressed to me by the circle-squarers; and, "O! Gus! tug a mean surd!" is smart upon my preference of an incommensurable value of [pi] to 3-1/5, or some such simple substitute. While, "Gus! Gus! at 'em a' round!" ought to be the backing of the scientific world to the author of the_Budget of Paradoxes_. The whole collection commenced existence in the head of a powerfulmathematician during some sleepless nights. Seeing how large a number waspracticable, he amused himself by inventing a digested plan of findingmore. Is there any one whose name cannot be twisted into either praise or satire?I have had given to me, "Thomas Babington Macaulay Mouths big: a Cantab anomaly. " NEWTON'S DE MUNDI SYSTEMATE LIBER. A treatise of the system of the world. By Sir Isaac Newton. Translated into English. London, 1728, 8vo. I think I have a right to one little paradox of my own: I greatly doubtthat Newton wrote this book. Castiglione, [290] in his _NewtoniOpuscula_, [291] gives it in the Latin which appeared in 1731, [292] not forthe first time; he says _Angli omnes Newtono tribuunt_. [293] It appearedjust after Newton's death, without the name of any editor, or any allusionto Newton's {140} recent departure, purporting to be that popular treatisewhich Newton, at the beginning of the third book of the _Principia_, sayshe wrote, intending it to be the third book. It is very possible that someobservant turnpenny might construct such a treatise as this from the thirdbook, that it might be ready for publication the moment Newton could notdisown it. It has been treated with singular silence: the name of theeditor has never been given. Rigaud[294] mentions it without a word: Icannot find it in Brewster's _Newton_, nor in the _Biographia Britannica_. There is no copy in the Catalogue of the Royal Society's Library, either inEnglish or Latin, except in Castiglione. I am open to correction; but Ithink nothing from Newton's acknowledged works will prove--as laid down inthe suspected work--that he took Numa's temple of Vesta, with a centralfire, to be intended to symbolize the sun as the center of our system, inthe Copernican sense. [295] Mr. Edleston[296] gives an account of the _lectures_ "de motu corporum, "and gives the corresponding pages of the _Latin_ "De Systemate Mundi" of1731. But no one mentions the _English_ of 1728. This English seems toagree with the Latin; but there is a mystery about it. The preface says, "That this work as here published is genuine will so clearly appear by theintrinsic marks it bears, that it will be but losing words and the reader'stime to take pains in giving him any other satisfaction. " Surely fewerwords would have been lost if the prefator had said at once that the workwas from the manuscript preserved at Cambridge. Perhaps it was a mangledcopy clandestinely taken and interpreted. {141} A BACONIAN CONTROVERSY. Lord Bacon not the author of "The Christian Paradoxes, " being a reprint of "Memorials of Godliness and Christianity, " by Herbert Palmer, B. D. [297] With Introduction, Memoir, and Notes, by the Rev. Alexander B. Grosart, [298] Kenross. (Private circulation, 1864). I insert the above in this place on account of a slight connection with thelast. Bacon's Paradoxes, --so attributed--were first published as his insome asserted "Remains, " 1648. [299] They were admitted into his works in1730, and remain there to this day. The title is "The Character of abelieving Christian, set forth in paradoxes and seeming contradictions. "The following is a specimen: "He believes three to be one and one to be three; a father not to be olderthan his son; a son to be equal with his father; and one proceeding fromboth to be equal with both: he believes three persons in one nature, andtwo natures in one person.... He believes the God of all grace to have beenangry with one that never offended Him; and that God that hates sin to bereconciled to himself though sinning continually, and never making or beingable to make Him any satisfaction. He believes a most just God to havepunished a most just person, and to have justified himself, though a mostungodly sinner. He believes himself freely pardoned, and yet a sufficientsatisfaction was made for him. " Who can doubt that if Bacon had written this it must have been wrong? Manywriters, especially on the {142} Continent, have taken him as sneering at(Athanasian) Christianity right and left. Many Englishmen have taken him tobe quite in earnest, and to have produced a body of edifying doctrine. Morethan a century ago the Paradoxes were published as a penny tract; and, again, at the same price, in the _Penny Sunday Reader_, vol. Vi, No. 148, afew passages were omitted, as _too strong_. But all did not agree: in mycopy of Peter Shaw's [300] edition (vol. Ii, p. 283) the Paradoxes havebeen cut out by the binder, who has left the backs of the leaves. I neverhad the curiosity to see whether other copies of the edition have beenserved in the same way. The Religious Tract Society republished themrecently in _Selections from the Writings of Lord Bacon_, (no date; badplan; about 1863, I suppose). No omissions were made, so far as I find. I never believed that Bacon wrote this paper; it has neither his _sparkle_nor his idiom. I stated my doubts even before I heard that Mr. Spedding, one of Bacon's editors, was of the same mind. (_Athenæum_, July 16, 1864). I was little moved by the wide consent of orthodox men: for I knew howBacon, Milton, Newton, Locke, etc. , were always claimed as orthodox untilalmost the present day. Of this there is a remarkable instance. LOCKE AND SOCINIANISM. Among the books which in my younger day were in some orthodox publicationlists--I think in the list of the Christian Knowledge Society, but I am notsure--was Locke's [301] "Reasonableness of Christianity. " It seems to havecome down from the eighteenth century, when the battle was belief in Christagainst unbelief, _simpliciter_, as the {143} logicians say. Now, if everthere was a Socinian[302] book in the world, it is this work of Locke. "These two, " says Locke, "faith and repentance, i. E. , believing Jesus to bethe Messiah, and a good life, are the indispensable conditions of the newcovenant, to be performed by all those who would obtain eternal life. " Allthe book is amplification of this doctrine. Locke, in this and many otherthings, followed Hobbes, whose doctrine, in the Leviathan, is _fidem, quanta ad salutem necessaria est, contineri in hoc articulo, Jesus estChristus_. [303] For this Hobbes was called an atheist, which {144} manystill believe him to have been: some of his contemporaries called him, rightly, a Socinian. Locke was known for a Socinian as soon as his workappeared: Dr. John Edwards, [304] his assailant, says he is "Socinianizedall over. " Locke, in his reply, says "there is not one word of Socinianismin it:" and he was right: the positive Socinian doctrine has _not one wordof Socinianism in it_; Socinianism consists in omissions. Locke and Hobbesdid not dare _deny_ the Trinity: for such a thing Hobbes might have beenroasted, and Locke might have been strangled. Accordingly, the well-knownway of teaching Unitarian doctrine was the collection of the assertedessentials of Christianity, without naming the Trinity, etc. This is theplan Newton followed, in the papers which have at last been published. [305] So I, for one, thought little about the general tendency of orthodoxwriters to claim Bacon by means of the Paradoxes. I knew that, in his"Confession of Faith"[306] he is a Trinitarian of a heterodox stamp. Hissecond Person takes human nature before he took flesh, not for redemption, but as a condition precedent of creation. "God is so holy, pure, andjealous, that it is impossible for him to be pleased in any creature, though the work of his own hands.... [Gen. I. 10, 12, 18, 21, 25, 31, freely rendered]. But--purposing to become a Creator, and to communicate tohis creatures, he ordained in his eternal counsel that one person of theGodhead should be united to one nature, and to one particular of hiscreatures; that so, in the person of the Mediator, the true ladder might befixed, whereby God might {145} descend to his creatures and his creaturesmight ascend to God.... " This is republished by the Religious Tract Society, and seems to suit theirtheology, for they confess to having omitted some things of which theydisapprove. In 1864, Mr. Grosart published his discovery that the Paradoxes are byHerbert Palmer; that they were first published surreptitiously, andimmediately afterwards by himself, both in 1645; that the "Remains" ofBacon did not appear until 1648; that from 1645 to 1708, thirteen editionsof the "Memorials" were published, all containing the Paradoxes. In spiteof this, the Paradoxes were introduced into Bacon's works in 1730, wherethey have remained. Herbert Palmer was of good descent, and educated as a Puritan. He was anaccomplished man, one of the few of his day who could speak French as wellas English. He went into the Church, and was beneficed by Laud, [307] inspite of his puritanism; he sat in the Assembly of Divines, and was finallyPresident of Queens' College, Cambridge, in which post he died, August 13, 1647, in the 46th year of his age. Mr. Grosart says, speaking of Bacon's "Remains, " "All who have had occasionto examine our early literature are aware that it was a common trick toissue imperfect, false, and unauthorized writings under any recentlydeceased name that might be expected to take. The Puritans, down to JohnBunyan, were perpetually expostulating and protesting against suchprocedure. " I have met with instances of all this; but I did not know thatthere was so much of it: a good collection would be very useful. The workof 1728, attributed to Newton, is likely enough to be one of the class. {146} Demonstration de l'immobilitez de la Terre.... Par M. De la Jonchere, [308] Ingénieur Français. Londres, 1728, 8vo. A synopsis which is of a line of argument belonging to the beginning of thepreceding century. TWO FORGOTTEN CIRCLE SQUARERS. The Circle squared; together with the Ellipsis and several reflections on it. The finding two geometrical mean proportionals, or doubling the cube geometrically. By Richard Locke[309].... London, no date, probably about 1730, 8vo. According to Mr. Locke, the circumference is three diameters, three-fourthsthe difference of the diameter and the side of the inscribed equilateraltriangle, and three-fourths the difference between seven-eighths of thediameter and the side of the same triangle. This gives, he says, 3. 18897. There is an addition to this tract, being an appendix to a book on thelongitude. The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire. London, 1732, 8vo. Here [pi] = 3. 0625. No proof is offered. [310] The longitude discovered by the Eclipses, Occultations, and Conjunctions of Jupiter's planets. By William Whiston. London, 1738. This tract has, in some copies, the celebrated preface containing theaccount of Newton's appearance before the Parliamentary Committee on thelongitude question, in 1714 {147} (Brewster, ii. 257-266). This "historicalpreface, " is an insertion and is dated April 28, 1741, with four additionalpages dated August 10, 1741. The short "preface" is by the publisher, JohnWhiston, [311] the author's son. THE STEAMSHIP SUGGESTED. A description and draught of a new-invented machine for carrying vessels or ships out of, or into any harbour, port, or river, against wind and tide, or in a calm. For which, His Majesty has granted letters patent, for the sole benefit of the author, for the space of fourteen years. By Jonathan Hulls. [312] London: printed for the author, 1737. Price sixpence (folding plate and pp. 48, beginning from title). (I ought to have entered this tract in its place. It is so rare that itsexistence was once doubted. It is the earliest description of steam-powerapplied to navigation. The plate shows a barge, with smoking funnel, andpaddles at the stem, towing a ship of war. The engine, as described, isNewcomen's. [313] In 1855, John Sheepshanks, [314] so well known as a friend of Art and apublic donor, reprinted this tract, in fac-simile, from his own copy;twenty-seven copies of the original 12mo size, and twelve on old paper, small 4to. I have an original copy, wanting the plate, and with "Pricesixpence" carefully erased, to the honor of the book. [315] {148} It is not known whether Hulls actually constructed a boat. [316] In allprobability his tract suggested to Symington, as Symington[317] did toFulton. ) THE NEWTONIANS ATTACKED. Le vrai système de physique générale de M. Isaac Newton exposé et analysé en parallèle avec celui de Descartes. By Louis Castel[318] [Jesuit and F. R. S. ] Paris, 1743, 4to. This is an elaborate correction of Newton's followers, and of Newtonhimself, who it seems did not give his own views with perfect fidelity. Father Castel, for instance, assures us that Newton placed the sun _atrest_ in the center of the system. Newton left the sun to arrange thatmatter with the planets and the rest of the universe. In this volume of 500pages there is right and wrong, both clever. A dissertation on the Æther of Sir Isaac Newton. By Bryan Robinson, [319] M. D. Dublin, 1743, 8vo. [320] {149} A mathematical work professing to prove that the assumed ether causesgravitation. MATHEMATICAL THEOLOGY. Mathematical principles of theology, or the existence of God geometrically demonstrated. By Richard Jack, teacher of Mathematics. London, 1747, 8vo. [321] Propositions arranged after the manner of Euclid, with beings representedby circles and squares. But these circles and squares are logical symbols, not geometrical ones. I brought this book forward to the Royal Commissionon the British Museum as an instance of the absurdity of attempting a_classed_ catalogue from the _titles_ of books. The title of this booksends it either to theology or geometry: when, in fact, it is a logicalvagary. Some of the houses which Jack built were destroyed by the fortuneof war in 1745, at Edinburgh: who will say the rebels did no good whatever?I suspect that Jack copied the ideas of J. B. Morinus, "Quod Deus sit, "Paris, 1636, [322] 4to, containing an attempt of the same kind, but notstultified with diagrams. TWO MODEL INDORSEMENTS. Dissertation, découverte, et démonstrations de la quadrature mathématique du cercle. Par M. De Fauré, géomètre. [_s. L. _, probably Geneva] 1747, 8vo. Analyse de la Quadrature du Cercle. Par M. De Fauré, Gentilhomme Suisse. Hague, 1749, [323] 4to. According to this octavo geometer and quarto gentleman, a diameter of 81gives a circumference of 256. There is an amusing circumstance about thequarto which has been overlooked, if indeed the book has ever been {150}examined. John Bernoulli (the one of the day)[324] and Koenig[325] haveboth given an attestation: my mathematical readers may stare as theyplease, such is the fact. But, on examination, there will be reason tothink the two sly Swiss played their countryman the same trick as themedical man played Miss Pickle, in the novel of that name. The lady onlywanted to get his authority against sousing her little nephew, and said, "Pray, doctor, is it not both dangerous and cruel to be the means ofletting a poor tender infant perish by sousing it in water as cold asice?"--"Downright murder, I affirm, " said the doctor; and certifiedaccordingly. De Fauré had built a tremendous scaffolding of equations, quite out of place, and feeling cock-sure that his solutions, if correct, would square the circle, applied to Bernoulli and Koenig--who after histract of two years before, must have known what he was at--for theirapprobation of the solutions. And he got it, as follows, well guarded: "Suivant les suppositions posées dans ce Mémoire, il est si évident que t doit être = 34, y = 1, et z = 1, que cela n'a besoin ni de preuve ni d'autorité pour être reconnu par tout le monde. [326] "à Basle le 7e Mai 1749. JEAN BERNOULLI. " "Je souscris au jugement de Mr. Bernoulli, en conséquence de ces suppositions. [327] "à la Haye le 21 Juin 1749. S. KOENIG. " On which de Fauré remarks with triumph--as I have no doubt it was intendedhe should do--"il conste clairement par ma présente Analyse etDémonstration, qu'ils y ont déja {151} reconnu et approuvé parfaitement quela quadrature du cercle est mathématiquement démontrée. "[328] It shouldseem that it is easier to square the circle than to get round amathematician. An attempt to demonstrate that all the Phenomena in Nature may be explained by two simple active principles, Attraction and Repulsion, wherein the attraction of Cohesion, Gravity and Magnetism are shown to be one the same. By Gowin Knight. London, 1748, 4to. Dr. Knight[329] was Mr. Panizzi's[330] archetype, the first PrincipalLibrarian of the British Museum. He was celebrated for his magneticalexperiments. This work was long neglected; but is now recognized as ofremarkable resemblance to modern speculations. THOMAS WRIGHT OF DURHAM. An original theory or Hypothesis of the Universe. By Thomas Wright[331] of Durham. London, 4to, 1750. Wright is a speculator whose thoughts are now part of our currentastronomy. He took that view--or most of it--of the milky way whichafterwards suggested itself to William Herschel. I have given an account ofhim and his work in the _Philosophical Magazine_ for April, 1848. Wright was mathematical instrument maker to the King, {152} and kept a shopin Fleet Street. Is the celebrated business of Troughton & Simms, also inFleet Street, a lineal descendant of that of Wright? It is likely enough, more likely that that--as I find him reported to have affirmed--PresterJohn was the descendant of Solomon and the Queen of Sheba. Having settledit thus, it struck me that I might apply to Mr. Simms, and he informs methat it is as I thought, the line of descent being Wright, Cole, JohnTroughton, Edward Troughton, [332] Troughton & Simms. [333] BISHOP HORNE ON NEWTON. The theology and philosophy in Cicero's _Somnium Scipionis_ explained. Or, a brief attempt to demonstrate, that the Newtonian system is perfectly agreeable to the notions of the wisest ancients: and that mathematical principles are the only sure ones. [By Bishop Horne, [334] at the age of nineteen. ] London, 1751, 8vo. This tract, which was not printed in the collected works, and is nowexcessively rare, is mentioned in _Notes and Queries_, 1st S. , v, 490, 573;2d S. , ix, 15. The boyish satire on Newton is amusing. Speaking of oldBenjamin Martin, [335] he goes on as follows: {153} "But the most elegant account of the matter [attraction] is by thathominiform animal, Mr. Benjamin Martin, who having attended Dr. Desaguliers'[336] fine, raree, gallanty shew for some years [Desagulierswas one of the first who gave public experimental lectures, before thesaucy boy was born] in the capacity of a turnspit, has, it seems, taken itinto his head to set up for a philosopher. " Thus is preserved the fact, unknown to his biographers, that Benj. Martinwas an assistant to Desaguliers in his lectures. Hutton[337] says of him, that "he was well skilled in the whole circle of the mathematical andphilosophical sciences, and wrote useful books on every one of them": thisis quite true; and even at this day he is read by twenty where Horne isread by one; see the stalls, _passim_. All that I say of him, indeed myknowledge of the tract, is due to this contemptuous mention of a moredurable man than himself. My assistant secretary at the AstronomicalSociety, the late Mr. Epps, [338] bought the copy at a stall because his eyewas caught by the notice of "Old Ben Martin, " of whom he was a greatreader. Old Ben could not be a Fellow of the Royal Society, because he kepta shop: even though the shop sold nothing but philosophical instruments. Thomas Wright, similarly situated as to shop and goods, never was a Fellow. The Society of our day has greatly degenerated: those of the old time wouldbe pleased, no doubt, that the glories of their day {154} should becommemorated. In the early days of the Society, there was a similardifficulty about Graunt, the author of the celebrated work on mortality. But their royal patron, "who never said a foolish thing, " sent them a sharpmessage, and charged them if they found any more such tradesmen, theyshould "elect them without more ado. " Horne's first pamphlet was published when he was but twenty-one years old. Two years afterwards, being then a Fellow of his college, and having seenmore of the world, he seems to have felt that his manner was a little toopert. He endeavored, it is said, to suppress his first tract: and copiesare certainly of extreme rarity. He published the following as his maturerview: A fair, candid, and impartial state of the case between Sir Isaac Newton and Mr. Hutchinson. [339] In which is shown how far a system of physics is capable of mathematical demonstration; how far Sir Isaac's, as such a system, has that demonstration; and consequently, what regard Mr. Hutchinson's claim may deserve to have paid to it. By George Horne, M. A. Oxford, 1753, 8vo. It must be remembered that the successors of Newton were very apt todeclare that Newton had demonstrated attraction as a _physical_ cause: hehad taken reasonable pains to show that he did not pretend to this. If anyone had said to Newton, I hold that every particle of matter is aresponsible being of vast intellect, ordered by the Creator to move as itwould do if every other particle attracted it, and gifted with power tomake its way in true accordance with that law, as easily as a lady picksher way across the street; what have you to say against it?--Newton musthave replied, Sir! if you really undertake to maintain this as_demonstrable_, your soul had better borrow a little power {155} from theparticles of which your body is made: if you merely ask me to refute it, Itell you that I neither can nor need do it; for whether attraction comes inthis way or in any other, _it comes_, and that is all I have to do with it. The reader should remember that the word attraction, as used by Newton andthe best of his followers, only meant a _drawing towards_, without anyimplication as to the cause. Thus whether they said that matter attractsmatter, or that young lady attracts young gentleman, they were using oneword in one sense. Newton found that the law of the first is the inversesquare of the distance: I am not aware that the law of the second has beendiscovered; if there be any chance, we shall see it at the year 1856 inthis list. In this point young Horne made a hit. He justly censures those who fixedupon Newton a more positive knowledge of what attraction is than hepretended to have. "He has owned over and over he did not know what hemeant by it--it might be this, or it might be that, or it might beanything, or it might be nothing. " With the exception of the _nothing_clause, this is true, though Newton might have answered Horne by "Thou hastsaid it. " (I thought everybody knew the meaning of "Thou hast said it": but I wasmistaken. In three of the evangelists [Greek: Su legeis] is the answer to"Art thou a king?" The force of this answer, as always understood, is "Thatis your way of putting it. " The Puritans, who lived in Bible phrases, sounderstood it: and Walter Scott, who caught all peculiarities of languagewith great effect, makes a marked instance, "Were you armed?--I was not--Iwent in my calling, as a preacher of God's word, to encourage them thatdrew the sword in His cause. In other words, to aid and abet the rebels, said the Duke. _Thou hast spoken it_, replied the prisoner. ") Again, Horne quotes Rowning[340] as follows: {156} "Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon thissame subject of attraction, about every particle of a fluid beingintrenched in three spheres of attraction and repulsion, one withinanother, 'the innermost of which (he says) is a sphere of repulsion, whichkeeps them from approaching into contact; the next, a sphere of attraction, diffused around this of repulsion, by which the particles are disposed torun together into drops; and the outermost of all, a sphere of repulsion, whereby they repel each other, when removed out of the attraction. ' So thatbetween the _urgings_, and _solicitations_, of one and t'other, a poorunhappy particle must ever be at his wit's end, not knowing which way toturn, or whom to obey first. " Rowning has here started the notion which Boscovich[341] afterwardsdeveloped. I may add to what precedes that it cannot be settled that, as Granger[342]says, Desaguliers was the first who gave experimental lectures in London. William Whiston gave some, and Francis Hauksbee[343] made the experiments. The prospectus, as we should now call it, is extant, a quarto tract ofplates and descriptions, without date. Whiston, in his life, {157} gives1714 as the first date of publication, and therefore, no doubt, of thelectures. Desaguliers removed to London soon after 1712, and commenced hislectures soon after that. It will be rather a nice point to settle whichlectured first; probabilities seem to go in favor of Whiston. FALLACIES IN A THEORY OF ANNUITIES. An Essay to ascertain the value of leases, and annuities for years and lives. By W[eyman] L[ee]. London, 1737, 8vo. A valuation of Annuities and Leases certain, for a single life. By Weyman Lee, Esq. Of the Inner Temple. London, 1751, 8vo. Third edition, 1773. Every branch of exact science has its paradoxer. The world at large cannottell with certainty who is right in such questions as squaring the circle, etc. Mr. Weyman Lee[344] was the assailant of what all who had studiedcalled demonstration in the question of annuities. He can be exposed to theworld: for his error arose out of his not being able to see that the wholeis the sum of all its parts. By an annuity, say of £100, now bought, is meant that the buyer is to havefor his money £100 in a year, if he be then alive, £100 at the end of twoyears, if then alive, and so on. It is clear that he would buy a lifeannuity if he should buy the first £100 in one office, the second inanother, and so on. All the difference between buying the whole from oneoffice and buying all the separate contingent payments at differentoffices, is immaterial to calculation. Mr. Lee would have agreed with therest of the world about the payments to be made to the several differentoffices, in consideration of their several contracts: but he differed fromevery one else about the sum to be paid to _one_ office. He contended thatthe way to value an annuity is to find out the term of years which theindividual has an even chance of surviving, and to charge for the lifeannuity the value of an annuity certain for that term. {158} It is very common to say that Lee took the average life, or expectation, asit is wrongly called, for his term: and this I have done myself, taking thecommon story. Having exposed the absurdity of this second supposition, taking it for Lee's, in my _Formal Logic_, [345] I will now do the same withthe first. A mathematical truth is true in its extreme cases. Lee's principle is thatan annuity on a life is the annuity made certain for the term within whichit is an even chance the life drops. If, then, of a thousand persons, 500be sure to die within a year, and the other 500 be immortal, Lee's price ofan annuity to any one of these persons is the present value of one payment:for one year is the term which each one has an even chance of surviving andnot surviving. But the true value is obviously half that of a perpetualannuity: so that at 5 percent Lee's rule would give less than the tenth ofthe true value. It must be said for the poor circle-squarers, that theynever err so much as this. Lee would have said, if alive, that I have put an _extreme case_: but any_universal_ truth is true in its extreme cases. It is not fair to bringforward an extreme case against a person who is speaking as of usualoccurrences: but it is quite fair when, as frequently happens, the proposerinsists upon a perfectly general acceptance of his assertion. And yet manywho go the whole hog protest against being tickled with the tail. Counselin court are good instances: they are paradoxers by trade. June 13, 1849, at Hertford, there was an action about a ship, insured against a _total_loss: some planks were saved, and the underwriters refused to pay. Mr. Z. (for deft. ) "There can be no degrees of totality; and some timbers weresaved. "--L. C. B. "Then if the vessel were burned to the water's edge, andsome rope saved in the boat, there would be no total loss. "--Mr. Z. "Thisis putting a very extreme case. "--L. C. B. "The argument {159} would gothat length. " What would _Judge_ Z. --as he now is--say to the extreme casebeginning somewhere between six planks and a bit of rope? MONTUCLA'S WORK ON THE QUADRATURE. Histoire des recherches sur la quadrature du cercle ... Avec une addition concernant les problèmes de la duplication du cube et de la trisection de l'angle. Paris, 1754, 12mo. [By Montucla. ] This is _the_ history of the subject. [346] It was a little episode to thegreat history of mathematics by Montucla, of which the first editionappeared in 1758. There was much addition at the end of the fourth volumeof the second edition; this is clearly by Montucla, though the bulk of thevolume is put together, with help from Montucla's papers, by Lalande. [347]There is also a second edition of the history of the quadrature, Paris, 1831, 8vo, edited, I think, by Lacroix; of which it is the great fault thatit makes hardly any use of the additional matter just mentioned. Montucla is an admirable historian when he is writing from his own directknowledge: it is a sad pity that he did not tell us when he was dependingon others. We are not to trust a quarter of his book, and we must read manyother books to know which quarter. The fault is common enough, butMontucla's good three-quarters is so good that the fault is greater in himthan in most others: I mean the fault of not acknowledging; for anhistorian cannot read everything. But it must be said that mankind givelittle encouragement to candor on this point. Hallam, in his {160} _Historyof Literature_, states with his own usual instinct of honesty every case inwhich he depends upon others: Montucla does not. And what is theconsequence?--Montucla is trusted, and believed in, and cried up in thebulk; while the smallest talker can lament that Hallam should be so unequaland apt to depend on others, without remembering to mention that Hallamhimself gives the information. As to a universal history of any greatsubject being written entirely upon primary knowledge, it is a thing ofwhich the possibility is not yet proved by an example. Delambre attemptedit with astronomy, and was removed by death before it was finished, [348] tosay nothing of the gaps he left. Montucla was nothing of a bibliographer, and his descriptions of books inthe first edition were insufficient. The Abbé Rive[349] fell foul of him, and as the phrase is, gave it him. Montucla took it with great good humor, tried to mend, and, in his second edition, wished his critic had lived tosee the _vernis de bibliographe_ which he had given himself. I have seen Montucla set down as an _esprit fort_, more than once: wrongly, I think. When he mentions Barrow's[350] address to the Almighty, he adds, "On voit, au reste, par là, que Barrow étoit un pauvre philosophe; car ilcroyait en l'immortalité de l'âme, et en une Divinité autre que la nature{161} universelle. "[351] This is irony, not an expression of opinion. Inthe book of mathematical recreations which Montucla constructed upon thatof Ozanam, [352] and Ozanam upon that of Van Etten, [353] now best known inEngland by Hutton's similar treatment of Montucla, there is an amusingchapter on the quadrators. Montucla refers to his own anonymous book of1754 as a curious book published by Jombert. [354] He seems to have been alittle ashamed of writing about circle-squarers: what a slap on the facefor an unborn Budgeteer! Montucla says, speaking of France, that he finds three notions prevalentamong the cyclometers: (1) that there is a large reward offered forsuccess; (2) that the longitude problem depends on that success; (3) thatthe solution is the great end and object of geometry. The same three {162}notions are equally prevalent among the same class in England. No rewardhas ever been offered by the government of either country. The longitudeproblem in no way depends upon perfect solution; existing approximationsare sufficient to a point of accuracy far beyond what can be wanted. [355]And geometry, content with what exists, has long passed on to othermatters. Sometimes a cyclometer persuades a skipper who has made land inthe wrong place that the astronomers are in fault, for using a wrongmeasure of the circle; and the skipper thinks it a very comfortablesolution! And this is the utmost that the problem ever has to do withlongitude. ANTINEWTONIANISMUS. Antinewtonianismus. [356] By Cælestino Cominale, [357] M. D. Naples, 1754 and 1756, 2 vols. 4to. The first volume upsets the theory of light; the second vacuum, visinertiæ, gravitation, and attraction. I confess I never attempted these bigLatin volumes, numbering 450 closely-printed quarto pages. The man whoslays Newton in a pamphlet is the man for me. But I will lend them toanybody who will give security, himself in £500, and two sureties in £250each, that he will read them through, and give a full abstract; and I willnot exact security for their return. I have never seen any mention of thisbook: it has a printer, but not a publisher, as happens with so manyunrecorded books. {163} OFFICIAL BLOW TO CIRCLE SQUARERS. 1755. The French Academy of Sciences came to the determination not toexamine any more quadratures or kindred problems. This was the consequence, no doubt, of the publication of Montucla's book: the time was well chosen;for that book was a full justification of the resolution. The Royal Societyfollowed the same course, I believe, a few years afterwards. When our Boardof Longitude was in existence, most of its time was consumed in listeningto schemes, many of which included the quadrature of the circle. It iscertain that many quadrators have imagined the longitude problem to beconnected with theirs: and no doubt the notion of a reward offered byGovernment for a true quadrature is a result of the reward offered for thelongitude. Let it also be noted that this longitude reward was not apremium upon excogitation of a mysterious difficulty. The legislature wasmade to know that the rational hopes of the problem were centered in theimprovement of the lunar tables and the improvement of chronometers. Tothese objects alone, and by name, the offer was directed: several personsgained rewards for both; and the offer was finally repealed. AN INTERESTING HOAX. Fundamentalis Figura Geometrica, primas tantum lineas circuli quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo. This was a gift from my oldest friend who was not a relative, Dr. SamuelMaitland of the "Dark Ages. "[358] He found it among his books, and couldnot imagine how he came by it: I could have told him. He once collectedinterpretations of the Apocalypse: and auction lots of such {164} booksoften contain quadratures. The wonder is he never found more than one. The quadrature is not worth notice. Erichsen is the only squarer I have metwith who has distinctly asserted the particulars of that reward which hasbeen so frequently thought to have been offered in England. He says that in1747 the Royal Society on the 2d of June, offered to give a large rewardfor the quadrature of the circle and a true explanation of magnetism, inaddition to £30, 000 previously promised for the same. I need hardly saythat the Royal Society had not £30, 000 at that time, and would not, if ithad had such a sum, have spent it on the circle, nor on magnetic theory;nor would it have coupled the two things. On this book, see _Notes andQueries_, 1st S. , xii, 306. Perhaps Erichsen meant that the £30, 000 hadbeen promised by the Government, and the addition by the Royal Society. October 8, 1866. I receive a letter from a cyclometer who understands thata reward is offered to any one who will square the circle, and that allcompetitors are to send their plans to me. The hoaxers have not yet failedout of the land. TWO JESUIT CONTRIBUTIONS. Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura existentium. Editio _Veneta_ prima. By Roger Joseph Boscovich. Venice, 1763, 4to. The first edition is said to be of Vienna, 1758. [359] This is a celebratedwork on the molecular theory of matter, grounded on the hypothesis ofspheres of alternate attraction and repulsion. Boscovich was a Jesuit ofvaried pursuit. During his measurement of a degree of the meridian, whileon horseback or waiting for his observations, he composed a Latin poem ofabout five thousand verses on eclipses, {165} with notes, which hededicated to the Royal Society: _De Solis et Lunæ defectibus_, [360] London, Millar and Dodsley, 1760, 4to. Traité de paix entre Des Cartes et Newton, _précédé_ des vies littéraires de ces deux chefs de la physique moderne.... By Aimé Henri Paulian. [361] Avignon, 1763, 12mo. I have had these books for many years without feeling the least desire tosee how a lettered Jesuit would atone Descartes and Newton. On looking atmy two volumes, I find that one contains nothing but the literary life ofDescartes; the other nothing but the literary life of Newton. The prefaceindicates more: and Watt mentions _three_ volumes. [362] I dare say thefirst two contain all that is valuable. On looking more attentively at thetwo volumes, I find them both readable and instructive; the account ofNewton is far above that of Voltaire, but not so popular. But he should nothave said that Newton's family came from Newton in Ireland. Sir RowlandHill gives fourteen _Newtons_ in Ireland;[363] twice the number of thecities that contended for the birth of Homer may now contend for the originof Newton, on the word of Father Paulian. Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the Cathedral Church of Worcester. Worcester, 1766, 8vo. The Electrical Philosopher: containing a new system of physics {166} founded upon the principle of an universal Plenum of elementary fire.... By R. Lovett, Worcester, 1774, 8vo. Mr. Lovett[364] was one of those ether philosophers who bring in elasticfluid as an explanation by imposition of words, without deducing any onephenomenon from what we know of it. And yet he says that attraction hasreceived no support from geometry; though geometry, applied to a particularlaw of attraction, had shown how to predict the motions of the bodies ofthe solar system. He, and many of his stamp, have not the least idea of theconfirmation of a theory by accordance of deduced results with observationposterior to the theory. BAILLY'S EXAGGERATED VIEW OF ASTRONOMY. Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie, pour servir de suite aux lettres sur l'origine des Sciences, adressées à M. De Voltaire, par M. Bailly. [365] London and Paris, 1779, 8vo. I might enter here all Bailly's histories of astronomy. [366] The paradoxwhich runs through them all more or less, is the doctrine that astronomy isof immense antiquity, coming from some forgotten source, probably thedrowned island of Plato, peopled by a race whom Bailly makes, as has {167}been said, to teach us everything except their existence and their name. These books, the first scientific histories which belong to readableliterature, made a great impression by power of style: Delambre created astrong reaction, of injurious amount, in favor of history founded oncontemporary documents, which early astronomy cannot furnish. These lettersare addressed to Voltaire, and continue the discussion. There is one letterof Voltaire, being the fourth, dated Feb. 27, 1777, and signed "le vieuxmalade de Ferney, V. Puer centum annorum. "[367] Then begin Bailly'sletters, from January 16 to May 12, 1778. From some ambiguous expressionsin the Preface, it would seem that these are fictitious letters, supposedto be addressed to Voltaire at their dates. Voltaire went to Paris February10, 1778, and died there May 30. Nearly all this interval was his closingscene, and it is very unlikely that Bailly would have troubled him withthese letters. [368] An inquiry into the cause of motion, or a general theory of physics. By S. Miller. London, 1781, 4to Newton all wrong: matter consists of two kinds of particles, one inert, theother elastic and capable of expanding themselves _ad infinitum_. SAINT-MARTIN ON ERRORS AND TRUTH. Des Erreurs et de la Vérité, ou les hommes rappelés au principe universel de la science; ouvrage dans lequel, en faisant remarquer aux observateurs l'incertitude de leurs recherches, et leurs méprises continuelles, on leur indique la route qu'ils auroient dû suivre, pour acquérir l'évidence physique sur l'origine du bien et du mal, sur l'homme, sur la nature matérielle, et la nature sacrée; sur la base des gouvernements {168} politiques, sur l'autorité des souverains, sur la justice civile et criminelle, sur les sciences, les langues, et les arts. Par un Ph.... Inc.... A Edimbourg. 1782. [369] Two vols. 8vo. This is the famous work of Louis Claude de Saint-Martin[370] (1743-1803), for whose other works, vagaries included, the reader must look elsewhere:among other things, he was a translator of Jacob Behmen. [371] The titlepromises much, and the writer has smart thoughts now and then; but thewhole is the wearisome omniscience of the author's day and country, whichno reader of our time can tolerate. Not that we dislike omniscience; but wehave it of our own country, both home-made and imported; and fashions vary. But surely there can be but one omniscience? Must a man have but one wife?Nay, may not a man have a new wife while the old one is living? There was afamous instrumental professor forty years ago, who presented a friend toMadame ----. The friend started, and looked surprised; for, not many weeksbefore, he had been presented to another lady, with the same title, atParis. The musician observed his surprise, and quietly said, "Celle-ci estMadame ---- de Londres. " In like manner we have a London omniscience nowcurrent, which would make any one start who only knew the old Frencharticle. The book was printed at Lyons, but it was a trick of French authors topretend to be afraid of prosecution: it {169} made a book look wicked-liketo have a feigned place of printing, and stimulated readers. A Governmentwhich had undergone Voltaire would never have drawn its sword upon quietSaint-Martin. To make himself look still worse, he was only ph[ilosophe]Inc.... , which is generally read _Inconnu_[372] but sometimes _Incrédule_;[373] most likely the ambiguity was intended. There is an awful paradoxabout the book, which explains, in part, its leaden sameness. It is allabout _l'homme_, _l'homme_, _l'homme_, [374] except as much as treats of_les hommes_, _les hommes_, _les hommes_;[375] but not one single man ismentioned by name in its 500 pages. It reminds one of "Water, water everywhere, And not a drop to drink. " Not one opinion of any other man is referred to, in the way of agreement orof opposition. Not even a town is mentioned: there is nothing which bringsa capital letter into the middle of a sentence, except, by the rarestaccident, such a personification as _Justice_. A likely book to want an_Edimbourg_ godfather! Saint-Martin is great in mathematics. The number _four_ essentially belongsto straight lines, and _nine_ to curves. The object of a straight line isto perpetuate _ad infinitum_ the production of a point from which itemanates. A circle [circle] bounds the production of all its radii, tendsto destroy them, and is in some sort their enemy. How is it possible thatthings so distinct should not be distinguished in their _number_ as well asin their action? If this important observation had been made earlier, immense trouble would have been saved to the mathematicians, who would havebeen prevented from searching for a common measure to lines which havenothing in common. But, though all straight lines have the number _four_, it must not be supposed that they are all equal, for a line is the resultof its law and {170} its number; but though both are the same for all linesof a sort, they act differently, as to force, energy, and duration, indifferent individuals; which explains all differences of length, etc. Icongratulate the reader who understands this; and I do not pity the one whodoes not. Saint-Martin and his works are now as completely forgotten as if they hadnever been born, except so far as this, that some one may take up one ofthe works as of heretical character, and lay it down in disappointment, with the reflection that it is as dull as orthodoxy. For a person who wasonce in some vogue, it would be difficult to pick out a more fossil writer, from Aa to Zypoeus, except, --though it is unusual for (, --) to represent aninterval of more than a year--his unknown opponent. This opponent, in thevery year of the _Des Erreurs_ ... Published a book in two parts with thesame fictitious place of printing; Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et l'Univers. A Edimbourg, 1782, 8vo. [376] There is a motto from the _Des Erreurs_ itself, "Expliquer les choses parl'homme, et non l'homme par les choses. _Des Erreurs et de la Vérité_, parun PH.... INC.... , p. 9. "[377] This work is set down in various cataloguesand biographies as written by the PH.... INC.... Himself. But it is notusual for a writer to publish two works in the same year, one of whichtakes a motto from the other. And the second work is profuse in capitalsand italics, and uses Hebrew learning: its style differs much from thefirst work. The first work sets out from man, and has nothing to do withGod: the second is religious and raps the knuckles of the first as follows:"Si nous voulons nous préserver de toutes {171} les illusions, et surtoutdes amorces de l'orgueil par lesquelles l'homme est si souvent séduit, neprenons jamais les hommes, mais toujours _Dieu_ pour notre terme decomparaison. "[378] The first uses _four_ and _nine_ in various ways, ofwhich I have quoted one: the second says, "Et ici se trouve déjà uneexplication des nombres _quatre_ et _neuf_, qui ont peu embarrassé dansl'ouvrage déjà cité. L'homme s'est égaré en allant de _quatre_ à_neuf_.... "[379] The work cited is the _Erreurs_, etc. , and the citation isin the motto, which is the text of the opposition sermon. A FORERUNNER OF THE METRIC SYSTEM. Method to discover the difference of the earth's diameters; proving its true ratio to be not less variable than as 45 is to 46, and shortest in its pole's axis 174 miles.... Likewise a method for fixing an universal standard for weights and measures. By Thomas Williams. [380] London, 1788, 8vo. Mr. Williams was a paradoxer in his day, and proposed what was, no doubt, laughed at by some. He proposed the sort of plan which theFrench--independently of course--carried into effect a few years after. Hewould have the 52d degree of latitude divided into 100, 000 parts and eachpart a geographical yard. The geographical ton was to be the cube of ageographical yard filled with sea-water taken some leagues from land. Allmultiples and sub-divisions were to be decimal. I was beginning to look up those who had made similar proposals, when alearned article on the proposal of a {172} metrical system came under myeye in the _Times_ of Sept. 15, 1863. The author cites Mouton, [381] whowould have the minute of a degree divided into 10, 000 _virgulæ_; JamesCassini, [382] whose foot was to be six thousandths of a minute; andPaucton, [383] whose foot was the 400, 000th of a degree. I have verified thefirst and third statements; surely the second ought to be the_six-thousandth_. An inquiry into the Copernican system ... Wherein it is proved, in the clearest manner, that the earth has only her diurnal motion ... With an attempt to point out the only true way whereby mankind can receive any real benefit from the study of the heavenly bodies. By John Cunningham. [384] London, 1789, 8vo. The "true way" appears to be the treatment of heaven and earth asemblematical of the Trinity. Cosmology. An inquiry into the cause of what is called gravitation or attraction, in which the motions of the heavenly bodies, and the preservation and operations of all nature, are deduced from an universal principle of efflux and reflux. By T. Vivian, [385] vicar of Cornwood, Devon. Bath, 1792, 12mo. {173} Attraction, an influx of matter to the sun; centrifugal force, the solarrays; cohesion, the pressure of the atmosphere. The confusion aboutcentrifugal _force_, so called, as demanding an external agent, is verycommon. THOMAS PAINE'S RIGHTS OF MAN. The rights of MAN, being an answer to Mr. Burke's attack on the French Revolution. [386] By Thomas Paine. [387] In two parts. 1791-1792. 8vo. (Various editions. )[388] A vindication of the rights of WOMAN, with strictures on political and moral subjects. By Mary Wollstonecraft. [389] 1792. 8vo. A sketch of the rights of BOYS and GIRLS. By Launcelot Light, of Westminster School; and Lætitia Lookabout, of Queen's Square, Bloomsbury. [By the Rev. Samuel Parr, [390] LL. D. ] 1792. 8vo. (pp. 64). When did we three meet before? The first work has sunk into oblivion: hadit merited its title, it might have {174} lived. It is what the French calla _pièce de circonstance_; it belongs in time to the French Revolution, andin matter to Burke's opinion of that movement. Those who only know its namethink it was really an attempt to write a philosophical treatise on what wenow call socialism. Silly government prosecutions gave it what it nevercould have got for itself. Mary Wollstonecraft seldom has her name spelled right. I suppose the O! O!character she got made her W_oo_lstonecraft. Watt gives double insinuation, for his cross-reference sends us to G_oo_dwin. [391] No doubt the title ofthe book was an act of discipleship to Paine's _Rights of Man_; but thistitle is very badly chosen. The book was marred by it, especially when theauthoress and her husband assumed the right of dispensing with legalsanction until the approach of offspring brought them to a sense of theirchild's interest. [392] Not a hint of such a claim is found in the book, which is mostly about female education. The right claimed for woman is tohave the education of a rational human being, and not to be considered asnothing but woman throughout youthful training. The maxims of MaryWollstonecraft are now, though not derived from her, largely followed inthe education of girls, especially in home education: just as many of thepolitical principles of Tom Paine, again not derived from him, are theguides of our actual legislation. I remember, forty years ago, an old ladyused to declare that she disliked girls from the age of sixteen tofive-and-twenty. "They are full, " said she, "of _femalities_. " She spoke oftheir behavior to women as well as to men. She {175} would have beenshocked to know that she was a follower of Mary Wollstonecraft, and hadpacked half her book into one sentence. The third work is a satirical attack on Mary Wollstonecraft and Tom Paine. The details of the attack would convince any one that neither has anythingwhich would now excite reprobation. It is utterly unworthy of Dr. Parr, andhas quite disappeared from lists of his works, if it were ever there. Thatit was written by him I take to be evident, as follows. Nichols, [393] whocould not fail to know, says (_Anecd. _, vol. Ix, p. 120): "This is aplayful essay by a first-rate scholar, who is elsewhere noticed in thisvolume, but whose name I shall not bring forward on so trifling anoccasion. " Who the scholar was is made obvious by Master Launcelot beingmade to talk of Bellendenus. [394] Further, the same boy is made to say, "Let Dr. Parr lay his hand upon his heart, if his conscience will let him, and ask himself how many thousands of wagon-loads of this article [birch]he has cruelly misapplied. " How could this apply to Parr, with his handfulof private pupils, [395] and no reputation for severity? Any one excepthimself would have called on the head-master of Westminster or Eton. Idoubt whether the name of Parr could be connected with the rod by anythingin print, except the above and an anecdote of his pupil, Tom Sheridan. [396]The Doctor had dressed for a dinner visit, and {176} was ready a quarter ofan hour too soon to set off. "Tom, " said he, "I think I had better whip younow; you are sure to do something while I am out. "--"I wish you would, sir!" said the boy; "it would be a letter of licence for the wholeevening. " The Doctor saw the force of the retort: my two tutelaries willsee it by this time. They paid in advance; and I have given liberalinterpretation to the order. The following story of Dr. Parr was told me and others, about 1829, by thelate Leonard Horner, [397] who knew him intimately. Parr was staying in ahouse full of company, I think in the north of England. Some gentlemen fromAmerica were among the guests, and after dinner they disputed some ofParr's assertions or arguments. So the Doctor broke out with "Do you knowwhat country you come from? You come from the place to which we used tosend our thieves!" This made the host angry, and he gave Parr such a severerebuke as sent him from the room in ill-humor. The rest walked on the lawn, amusing the Americans with sketches of the Doctor. There was a dark cloudoverhead, and from that cloud presently came a voice which called _Tham_(Parr-lisp for _Sam_). The company were astonished for a moment, butthought the Doctor was calling his servant in the house, and that theapparent direction was an illusion arising out of inattention. Butpresently the sound was repeated, certainly from the cloud, "And nearer, clearer, deadlier than before. " There was now a little alarm: where could the Doctor have got to? They ranto his bedroom, and there they discovered a sufficient rather thansatisfactory explanation. The Doctor had taken his pipe into his bedroom, and had seated himself, in sulky mood, upon the higher bar of a large anddeep old-fashioned grate with a high mantelshelf. Here he had {177} tumbledbackwards, and doubled himself up between the bars and the back of thegrate. He was fixed tight, and when he called for help, he could only throwhis voice up the chimney. The echo from the cloud was the warning whichbrought his friends to the rescue. ATTACKS ON RELIGIOUS CUSTOMS. Days of political paradox were coming, at which we now stare. Cobbett[398]said, about 1830, in earnest, that in the country every man who did nottake off his hat to the clergyman was suspected, and ran a fair chance ofhaving something brought against him. I heard this assertion canvassed, when it was made, in a party of elderly persons. The Radicals backed it, the old Tories rather denied it, but in a way which satisfied me they oughtto have denied it less if they could not deny it more. But it must be saidthat the Governments stopped far short of what their partisans would havehad them do. All who know Robert Robinson's[399] very quiet assault onchurch-made festivals in his _History and Mystery of Good Friday_(1777)[400] will hear or remember with surprise that the _British Critic_pronounced it a direct, unprovoked, and malicious libel on the most {178}sacred institutions of the national Church. It was reprinted again andagain: in 1811 it was in a cheap form at 6s. 6d. A hundred. When theJacobin day came, the State was really in a fright: people thought twicebefore they published what would now be quite disregarded. I examined aquantity of letters addressed to George Dyer[401] (Charles Lamb's G. D. ) andwhat between the autographs of Thelwall, Hardy, Horne Tooke, and all therebels, [402] put together a packet which produced five guineas, orthereabouts, for the widow. Among them were the following verses, sent bythe author--who would not put his name, even in a private letter, for fearof accidents--for consultation whether they could safely be sent to aneditor: and they were _not_ sent. The occasion was the public thanksgivingat St. Paul's for the naval victories, December 19, 1797. "God bless me! what a thing! Have you heard that the King Goes to St. Paul's? {179} Good Lord! and when he's there, He'll roll his eyes in prayer, To make poor Johnny stare At this fine thing. "No doubt the plan is wise To blind poor Johnny's eyes By this grand show; For should he once suppose That he's led by the nose, Down the whole fabric goes, Church, lords, and king. "As he shouts Duncan's[403] praise, Mind how supplies they'll raise In wondrous haste. For while upon the sea We gain one victory, John still a dupe will be And taxes pay. "Till from his little store Three-fourths or even more Goes to the Crown. Ah, John! you little think How fast we downward sink And touch the fatal brink At which we're slaves. " I would have indicted the author for not making his thirds and seventhsrhyme. As to the rhythm, it is not much better than what the French sang inthe Calais theater when the Duke of Clarence[404] took over Louis XVIII in1814. "God save noble Clarence, Who brings our king to France; God save Clarence! He maintains the glory Of the British navy, etc. , etc. " {180} Perhaps had this been published, the Government would have assailedit as a libel on the church service. They got into the way of defendingthemselves by making libels on the Church, of what were libels, if onanything, on the rulers of the State; until the celebrated trials of Honesettled the point for ever, and established that juries will not convictfor one offence, even though it have been committed, when they know theprosecution is directed at another offence and another intent. HONE'S FAMOUS TRIALS. The results of Hone's trials (William Hone, 1779-1842) are among theimportant constitutional victories of our century. He published parodies onthe Creeds, the Lord's Prayer, the Catechism, etc. , with intent to bringthe Ministry into contempt: everybody knew that was his _purpose_. TheGovernment indicted him for impious, profane, blasphemous intent, but notfor seditious intent. They hoped to wear him out by proceeding day by day. December 18, 1817, they hid themselves under the Lord's Prayer, the Creed, and the Commandments; December 19, under the Litany; December 20, under theAthanasian Creed, an odd place for shelter when they could not find it inthe previous places. Hone defended himself for six, seven, and eight hourson the several days: and the jury acquitted him in 15, 105, and 20 minutes. In the second trial the offense was laid both as profanity and as sedition, which seems to have made the jury hesitate. And they probably came to thinkthat the second count was false pretence: but the length of theirdeliberation is a satisfactory addition to the value of the whole. In thefirst trial the Attorney-General (Shepherd) had the impudence to say thatthe libel had nothing of a political tendency about it, but was _avowedly_set off against the religion and worship of the Church of England. Thewhole {181} is political in every sentence; neither more nor less politicalthan the following, which is part of the parody on the Catechism: "What isthy duty towards the Minister? My duty towards the Minister is, to trusthim as much as I can; to honor him with all my words, with all my bows, with all my scrapes, and with all my cringes; to flatter him; to give himthanks; to give up my whole soul to him; to idolize his name, and obey hisword, and serve him blindly all the days of his political life. " And theparody on the Creed begins, "I believe in George, the Regent almighty, maker of new streets and Knights of the Bath. " This is what theAttorney-General said had nothing of a political tendency about it. Butthis was _on the first trial_: Hone was not known. The first day's trialwas under Justice Abbott (afterwards C. J. Tenterden). [405] It wasperfectly understood, when Chief Justice Ellenborough[406] appeared inCourt on the second day, that he was very angry at the first result, andput his junior aside to try his own rougher dealing. But Hone tamed thelion. An eye-witness told me that when he implored of Hone not to detailhis own father Bishop Law's[407] views on the Athanasian Creed, whichhumble petition Hone kindly granted, he held by the desk for support. Andthe same when--which is not reported--the Attorney-General appealed to theCourt for protection against a {182} stinging attack which Hone made on theBar: he _held on_, and said, "Mr. Attorney, what _can_ I do!" I was a boyof twelve years old, but so strong was the feeling of exultation at theverdicts that boys at school were not prohibited from seeing the parodies, which would have been held at any other time quite unfit to meet theireyes. I was not able to comprehend all about the Lord Chief Justice until Iread and heard again in after years. In the meantime, Joe Miller had givenme the story of the leopard which was sent home on board a ship of war, andwas in two days made as docile as a cat by the sailors. [408] "You have gotthat fellow well under, " said an officer. "Lord bless your Honor!" saidJack, "if the Emperor of Marocky would send us a cock rhinoceros, we'dbring him to his bearings in no time!" When I came to the subject again, itpleased me to entertain the question whether, if the Emperor had sent acock rhinoceros to preside on the third day in the King's Bench, Hone wouldhave mastered _him_: I forget how I settled it. There grew up a story thatHone caused Lord Ellenborough's death, but this could not have been true. Lord Ellenborough resigned his seat in a few months, and died just a yearafter the trials; but sixty-eight years may have had more to do with itthan his defeat. A large subscription was raised for Hone, headed by the Duke ofBedford[409] for £105. Many of the leading anti-ministerialists joined: butthere were many of the other side who avowed their disapprobation of thefalse pretense. Many could not venture their names. In the list I find:{183} A member of the House of Lords, an enemy to persecution, andespecially to religious persecution employed for political purposes--Noparodist, but an enemy to persecution--A juryman on the third day'strial--Ellen Borough--My name would ruin me--Oh! minions of Pitt--Oil forthe Hone--The Ghosts of Jeffries[410] and Sir William Roy [Ghosts ofJeffries in abundance]--A conscientious Jury and a conscientious Attorney, £1 6s. 8d. --To Mr. Hone, for defending in his own person the freedom of thepress, attacked for a political object, under the old pretense ofsupporting Religion--A cut at corruption--An Earldom for myself and atranslation for my brother--One who disapproves of parodies, but abhorspersecution--From a schoolboy who wishes Mr. Hone to have a very grandsubscription--"For delicacy's sake forbear, " and "Felix trembled"--"I willgo myself to-morrow"--Judge Jeffries' works rebound in calf by Law--Keep usfrom Law, and from the Shepherd's paw--I must not give you my name, but Godbless you!--As much like Judge Jeffries as the present times willpermit--May Jeffries' fame and Jeffries' fate on every modern Jeffrieswait--No parodist, but an admirer of the man who has proved the fallacy ofthe Lawyer's Law, that when a man is his own advocate he has a fool for hisclient--A Mussulman who thinks it would not be an impious libel to parodythe Koran--May the suspenders of the Habeas Corpus Act be speedilysuspended--Three times twelve for thrice-tried Hone, who cleared the caseshimself alone, and won three heats by twelve to one, £1 16s. --Aconscientious attorney, £1 6s. 8d. --Rev. T. B. Morris, rector ofShelfanger, who disapproves of the parodies, but abhors the making anaffected zeal for religion the pretext for political persecution--A Lawyeropposed in principle to {184} Law--For the Hone that set the razor thatshaved the rats--Rev. Dr. Samuel Parr, who most seriously disapproves ofall parodies upon the hallowed language of Scripture and the contents ofthe Prayer-book, but acquits Mr. Hone of intentional impiety, admires histalents and fortitude, and applauds the good sense and integrity of hisjuries--Religion without hypocrisy, and Law without impartiality--O Law! OLaw! O Law! These are specimens of a great many allusive mottoes. The subscription wasvery large, and would have bought a handsome annuity, but Hone employed itin the bookselling trade, and did not thrive. His _Everyday Book_[411] andhis _Apocryphal New Testament_, [412] are useful books. On an annuity hewould have thriven as an antiquarian writer and collector. It is well thatthe attack upon the right to ridicule Ministers roused a dormant powerwhich was equal to the occasion. Hone declared, on his honor, that he hadnever addressed a meeting in his life, nor spoken a word before more thantwelve persons. Had he--which however could not then be done--employedcounsel and had a _guilty defense_ made for him, he would very likely havebeen convicted, and the work would have been left to be done by another. Noquestion that the parodies disgusted all who reverenced Christianity, andwho could not separate the serious and the ludicrous, and prevent theirexistence in combination. My extracts, etc. , are from the nineteenth, seventeenth, and sixteentheditions of the three trials, which seem to have been contemporaneous (allin 1818) as they are made up into one book, with additional title over all, and the motto "Thrice the brindled cat hath mew'd. " They are published byHone himself, who I should have said was a publisher {185} as well as wasto be. And though the trials only ended Dec. 20, 1817, the preface attachedto this common title is dated Jan. 23, 1818. [413] The spirit which was roused against the false dealing of the Government, i. E. , the pretense of prosecuting for impiety when all the world knew thereal offense was, if anything, sedition--was not got up at the moment:there had been previous exhibitions of it. For example, in the spring of1818 Mr. Russell, a little printer in Birmingham, was indicted forpublishing the Political Litany[414] on which Hone was afterwards tried. Hetook his witnesses to the summer Warwick assizes, and was told that theindictment had been removed by certiorari into the King's Bench. He hadnotice of trial for the spring assizes at Warwick: he took his witnessesthere, and the trial was postponed by the Crown. He then had notice for thesummer assizes at Warwick; and so on. The policy seems to have been to wearout the obnoxious parties, either by delays or by heaping on trials. TheGovernment was odious, and knew it could _not_ get verdicts againstridicule, and _could_ get verdicts against impiety. No difficulty was foundin convicting the sellers of Paine's works, and the like. When Hone washeld to bail it was seen that a crisis was at hand. All parties in politicsfurnished him with parodies in proof of religious persons having madeinstruments of them. The parodies by Addison and Luther were contributed bya Tory lawyer, who was afterwards a judge. Hone had published, in 1817, tracts of purely political ridicule: _OfficialAccount of the Noble Lord's Bite, _[415] _Trial of the Dog for Biting theNoble Lord_, etc. These were not touched. After the trials, it is manifestthat Hone was {186} to be unassailed, do what he might. _The PoliticalHouse that Jack built_, in 1819; _The Man in the Moon_, 1820; _The Queen'sMatrimonial Ladder_, _Non mi ricordo_, _The R--l Fowls_, 1820; _ThePolitical Showman at Home_, with plates by G. Cruickshank, [416] 1821 [hedid all the plates]; _The Spirit of Despotism_, 1821--would have beenlegitimate marks for prosecution in previous years. The biting caricatureof several of these works are remembered to this day. _The Spirit ofDespotism_ was a tract of 1795, of which a few copies had been privatelycirculated with great secrecy. Hone reprinted it, and prefixed thefollowing address to "Robert Stewart, _alias_ Lord Castlereagh"[417]: "Itappears to me that if, unhappily, your counsels are allowed much longer toprevail in the Brunswick Cabinet, they will bring on a crisis, in which theking may be dethroned or the people enslaved. Experience has shown that thepeople will not be enslaved--the alternative is the affair of youremployers. " Hone might say this without notice. In 1819 Mr. Murray[418] published Lord Byron's _Don Juan_, [419] and Honefollowed it with _Don John, or Don Juan Unmasked_, a little account of whatthe publisher to the Admiralty was allowed to issue without prosecution. The parody on the Commandments was a case very much in point: and Honemakes a stinging allusion to the use of the "_unutterable Name_, with aprofane levity unsurpassed by {187} any other two lines in the Englishlanguage. " The lines are "'Tis strange--the Hebrew noun which means 'I am, ' The English always use to govern d----n. " Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord Castlereaghwas suppressed by Mr. Murray from delicacy to Ministers. Q. Why did not Mr. Murray suppress Lord Byron's _parody_ on the Ten Commandments? _A. _ Becauseit contains nothing in ridicule of Ministers, and therefore nothing that_they_ could suppose would lead to the displeasure of Almighty God. " The little matters on which I have dwelt will never appear in history fromtheir political importance, except in a few words of result. As a mode ofthought, silly evasions of all kinds belong to such a work as the present. Ignorance, which seats itself in the chair of knowledge, is a mother ofrevolutions in politics, and of unread pamphlets in circle-squaring. From1815 to 1830 the question of revolution or no revolution lurked in all ourEnglish discussions. The high classes must govern; the high classes shallnot govern; and thereupon issue was to be joined. In 1828-33 the questioncame to issue; and it was, Revolution with or without civil war; choose. The choice was wisely made; and the Reform Bill started a new system sowell dovetailed into the old that the joinings are hardly visible. And now, in 1867, the thing is repeated with a marked subsidence of symptoms; andthe party which has taken the place of the extinct Tories is carryingthrough Parliament a wider extension of the franchise than their opponentswould have ventured. Napoleon used to say that a decided nose was a sign ofpower: on which it has been remarked that he had good reason to say sobefore the play was done. And so had our country; it was saved from areligious war, and from a civil war, by the power of that nose over itscolleagues. {188} THOMAS TAYLOR, THE PLATONIST. The Commentaries of Proclus. [420] Translated by Thomas Taylor. [421] London, 1792, 2 vols. 4to. [422] The reputation of "the Platonist" begins to grow, and will continue togrow. The most authentic account is in the _Penny Cyclopædia_, written byone of the few persons who knew him well, and one of the fewer who possessall his works. At page lvi of the Introduction is Taylor's notion of theway to find the circumference. It is not geometrical, for it proceeds onthe motion of a point: the words "on account of the simplicity of theimpulsive motion, such a line must be either straight or circular" willsuffice to show how Platonic it is. Taylor certainly professed a kind ofheathenism. D'lsraeli said, "Mr. T. Taylor, the Platonic philosopher andthe modern Plethon, [423] consonant to that philosophy, professespolytheism. " Taylor printed this in large type, in a page by itself afterthe dedication, without any disavowal. I have seen the following, Greek andtranslation both, in his handwriting: "[Greek: Pas agathos hêi agathosethnikos; kai pas christianos hêi christianos kakos. ] Every good man, sofar as he is a good man, is a heathen; and every Christian, so far as he isa Christian, is a bad man. " Whether Taylor had in his head the Christian ofthe New Testament, or whether he drew from those members of the "religiousworld" who make manifest the religious flesh and the religious devil, {189}cannot be decided by us, and perhaps was not known to himself. If aheathen, he was a virtuous one. A NEW ERA IN FICTION. (1795. ) This is the date of a very remarkable paradox. The religiousworld--to use a name claimed by a doctrinal sect--had long set its faceagainst amusing literature, and all works of imagination. Bunyan, Milton, and a few others were irresistible; but a long face was pulled at everyattempt to produce something readable for poor people and _poor children_. In 1795, a benevolent association began to circulate the works of a ladywho had been herself a dramatist, and had nourished a pleasant vein ofsatire in the society of Garrick and his friends; all which is carefullysuppressed in some biographies. Hannah More's[424] _Cheap RepositoryTracts_, [425] which were bought by millions of copies, destroyed thevicious publications with which the hawkers deluged the country, by thesimple process of furnishing the hawkers with something more saleable. _Dramatic fiction_, in which the _characters_ are drawn by themselves, was, at the middle of the last century, the monopoly of writers who requiredindecorum, such as Fielding and Smollett. All, or nearly all, which couldbe permitted to the young, was dry narrative, written by people who couldnot make their personages _talk character_; they all spoke {190} alike. Theauthor of the _Rambler_[426] is ridiculed, because his young ladies talkJohnsonese; but the satirists forget that all the presentable novel-writerswere equally incompetent; even the author of _Zeluco_ (1789)[427] is thestrongest possible case in point. Dr. Moore, [428] the father of the hero of Corunna, [429] with good narrativepower, some sly humor, and much observation of character, would have been, in our day, a writer of the _Peacock_[430] family. Nevertheless, to one whois accustomed to our style of things, it is comic to read the dialogue of ajealous husband, a suspected wife, a faithless maid-servant, a tool of anurse, a wrong-headed pomposity of a priest, and a sensible physician, alltalking Dr. Moore through their masks. Certainly an Irish soldier does say"by Jasus, " and a cockney footman "this here" and "that there"; and thisand the like is all the painting of characters which is effected out of themouths of the bearers by a narrator of great power. I suspect that somenovelists repressed their power under a rule that a narrative shouldnarrate, and that the dramatic should be confined to the drama. I make no exception in favor of Miss Burney;[431] though she was theforerunner of a new era. Suppose a country {191} in which dress is alwaysof one color; suppose an importer who brings in cargoes of blue stuff, redstuff, green stuff, etc. , and exhibits dresses of these several colors, that person is the similitude of Miss Burney. It would be a delightfulchange from a universal dull brown, to see one person all red, another allblue, etc. ; but the real inventor of pleasant dress would be the one whocould mix his colors and keep down the bright and gaudy. Miss Burney'sintroduction was so charming, by contrast, that she nailed such men asJohnson, Burke, Garrick, etc. , to her books. But when a person who has readthem with keen pleasure in boyhood, as I did, comes back to them after along period, during which he has made acquaintance with the great novelistsof our century, three-quarters of the pleasure is replaced by wonder thathe had not seen he was at a puppet-show, not at a drama. Take some_labeled_ characters out of our humorists, let them be put together intoone piece, to speak only as labeled: let there be a Dominie with nothingbut "Prodigious!" a Dick Swiveller with nothing but adapted quotations; aDr. Folliott with nothing but sneers at Lord Brougham;[432] and the wholewill pack up into one of Miss Burney's novels. Maria Edgeworth, [433] Sydney Owenson (Lady Morgan), [434] Jane Austen, [435]Walter Scott, [436] etc. , are all of our century; as {192} are, I believe, all the Minerva Press novels, as they were called, which show some of thepower in question. Perhaps dramatic talent found its best encouragement inthe drama itself. But I cannot ascertain that any such power was directedat the multitude, whether educated or uneducated, with natural mixture ofcharacter, under the restraints of decorum, until the use of it by tworeligious writers of the school called "evangelical, " Hannah More andRowland Hill. [437] The _Village Dialogues_, though not equal to the_Repository Tracts_, are in many parts an approach, and perhaps a copy;there is frequently humorous satire, in that most effective form, self-display. They were published in 1800, and, partly at least, by theReligious Tract Society, the lineal successor of the _Repository_association, though knowing nothing about its predecessor. I think it rightto add that Rowland Hill here mentioned is not the regenerator of the PostOffice. [438] Some do not distinguish accurately; I have heard of more thanone who took me to have had a logical controversy with a diplomatist whodied some years before I was born. THE RELIGIOUS TRACT SOCIETY. A few years ago, an attempt was made by myself and others to collect someinformation about the _Cheap Repository_ (see _Notes and Queries_, 3dSeries, vi. 241, 290, 353; _Christian Observer_, Dec. 1864, pp. 944-49). Itappeared that after the Religious Tract Society had existed more than fiftyyears, a friend presented it with a copy of the original prospectus of the_Repository_, a thing the existence of which was not known. In thisprospectus it is announced that from the plan "will be carefully excludedwhatever is enthusiastic, absurd, or superstitious. " The "evangelical"{193} party had, from the foundation of the Religious Tract Society, regretted that the _Repository Tracts_ "did not contain a fuller statementof the great evangelical principles"; while in the prospectus it is alsostated that "no cause of any particular party is intended to be served byit, but general Christianity will be promoted upon practical principles. "This explains what has often been noticed, that the tracts contain a mildform of "evangelical" doctrine, free from that more fervid dogmatism whichappears in the _Village Dialogues_; and such as H. More's friend, BishopPorteus[439]--a great promoter of the scheme--might approve. The ReligiousTract Society (in 1863) republished some of H. More's tracts, withalterations, additions, and omissions _ad libitum_. This is an improper wayof dealing with the works of the dead; especially when the reprints are ofpopular works. A small type addition to the preface contains: "Somealterations and abridgements have been made to adapt them to the presenttimes and the aim of the Religious Tract Society. " I think every publicityought to be given to the existence of such a practice; and I reprint what Isaid on the subject in _Notes and Queries_. Alterations in works which the Society republishes are a necessary part oftheir plan, though such notes as they should judge to be corrective wouldbe the best way of proceeding. But the fact of alteration should be verydistinctly announced on the title of the work itself, not left to a littlebit of small type at the end of the preface, in the place where tradeadvertisements, or directions to the binder, are often found. And theplaces in which alteration has been made should be pointed out, either bymarks of omission, when omission is the alteration, or by putting thealtered sentences in brackets, when change has been made. May any one alterthe works of the dead at his own discretion? {194} We all know that readersin general will take each sentence to be that of the author whose name ison the title; so that a correcting republisher _makes use of his author'sname to teach his own variation_. The tortuous logic of "the trade, " whichis content when "the world" is satisfied, is not easily answered, any morethan an eel is easily caught; but the Religious Tract Society may be_convinced_ [in the old sense] in a sentence. On which course would theyfeel most safe in giving their account to the God of truth? "In your ownconscience, now?" I have tracked out a good many of the variations made by the ReligiousTract Society in the recently published volume of _Repository Tracts_. Mostof them are doctrinal insertions or amplifications, to the matter of whichHannah More would not have objected--all that can be brought against themis the want of notice. But I have found two which the respect I have forthe Religious Tract Society, in spite of much difference on various points, must not prevent my designating as paltry. In the story of Mary Wood, akind-hearted clergyman converses with the poor girl who has ruined herselfby lying. In the original, he "assisted her in the great work ofrepentance;" in the reprint it is to be shown in some detail how he didthis. He is to begin by pointing out that "the heart is deceitful above allthings and desperately wicked. " Now the clergyman's name is _Heartwell_: soto prevent his name from contradicting his doctrine, he is actually cutdown to _Harwell_. Hannah Moore meant this good man for one of thosedescribed in Acts xv. 8, 9, and his name was appropriate. Again, Mr. Flatterwell, in persuasion of Parley the porter to let him intothe castle, declares that the worst he will do is to "play an innocent gameof cards just to keep you awake, or sing a cheerful song with the maids. "Oh fie! Miss Hannah More! and you a single lady too, and a contemporary ofthe virtuous Bowdler![440] Though Flatterwell be an {195} allegory of thedevil, this is really too indecorous, even for him. Out with the three lastwords! and out it is. The Society cuts a poor figure before a literary tribunal. Nothing waswanted except an admission that the remarks made by me were unanswerable, and this was immediately furnished by the Secretary (_N. And Q. _, 3d S. , vi. 290). In a reply of which six parts out of seven are a very amplifiedstatement that the Society did not intend to reprint _all_ Hannah More'stracts, the remaining seventh is as follows: "I am not careful [perhaps this should be _careful not_] to noticeProfessor De Morgan's objections to the changes in 'Mary Wood' or 'Parleythe Porter, ' but would merely reiterate that the tracts were neitherdesigned nor announced to be 'reprints' of the originals [design is onlyknown to the designers; as to announcement, the title is ''Tis all for thebest, The Shepherd of Salisbury Plain, and other narratives by HannahMore']; and much less [this must be _careful not_; further removed fromanswer than _not careful_] can I occupy your space by a treatise on theProfessor's question: 'May any one alter the works of the dead at his owndiscretion?'" To which I say: Thanks for help! I predict that Hannah More's _Cheap Repository Tracts_ will somewhatresemble the _Pilgrim's Progress_ in their fate. Written for the cottage, and long remaining in their original position, they will become classicalworks of their kind. Most assuredly this will happen if my assertion cannotbe upset, namely, that they contain the first specimens of fictionaddressed to the world at large, and widely circulated, in whichdramatic--as distinguished from puppet--power is shown, and withoutindecorum. {196} According to some statements I have seen, but which I have not verified, other publishing bodies, such as the Christian Knowledge Society, havetaken the same liberty with the names of the dead as the Religious TractSociety. If it be so, the impropriety is the work of the smaller spiritswho have not been sufficiently overlooked. There must be an overwhelmingmajority in the higher councils to feel that, whenever _altered_ works arepublished, _the fact of alteration should be made as prominent as the nameof the author_. Everything short of this is suppression of truth, and willultimately destroy the credit of the Society. Equally necessary is it thatthe alterations should be noted. When it comes to be known that the authorbefore him is altered, he knows not where nor how nor by whom, the lowestreader will lose his interest. A TRIBUTE TO WILLIAM FREND. The principles of Algebra. By William Frend. [441] London, 1796, 8vo. Second Part, 1799. This Algebra, says Dr. Peacock, [442] shows "great distrust {197} of theresults of algebraical science which were in existence at the time when itwas written. " Truly it does; for, as Dr. Peacock had shown by fullcitation, it makes war of extermination upon all that distinguishes algebrafrom arithmetic. Robert Simson[443] and Baron Maseres[444] were Mr. Frend'spredecessors in this opinion. The genuine respect which I entertained for my father-in-law did notprevent my canvassing with perfect freedom his anti-algebraical andanti-Newtonian opinions, in a long obituary memoir read at the AstronomicalSociety in February 1842, which was written by me. It was copied into the_Athenæum_ of March 19. It must be said that if the manner in which algebra_was_ presented to the learner had been true algebra, he would have beenright: and if he had confined himself to protesting against the impositionof attraction as a fundamental part of the existence of matter, he wouldhave been in unity with a great many, including Newton himself. I wish hehad preferred amendment to rejection when he was a college tutor: he wroteand spoke English with a clearness which is seldom equaled. His anti-Newtonian discussions are confined to the preliminary chapters ofhis _Evening Amusements_, [445] a series of astronomical lessons in nineteenvolumes, following the moon through a period of the golden numbers. There is a mistake about him which can never be destroyed. It is constantlysaid that, at his celebrated trial in 1792, for sedition and opposition tothe Liturgy, etc. , he was _expelled_ from the University. He was_banished_. People cannot see the difference; but it made all thedifference to {198} Mr. Frend. He held his fellowship and its profits tillhis marriage in 1808, and was a member of the University and of its Senatetill his death in 1841, as any Cambridge Calendar up to 1841 will show. That they would have expelled him if they could, is perfectly true; andthere is a funny story--also perfectly true--about their first proceedingsbeing under a statute which would have given the power, had it not beendiscovered during the proceedings that the statute did not exist. It hadcome so near to existence as to be entered into the Vice-Chancellor's bookfor his signature, which it wanted, as was not seen till Mr. Frend exposedit: in fact, the statute had never actually passed. There is an absurd mistake in Gunning's[446] _Reminiscences of Cambridge_. In quoting a passage of Mr. Frend's pamphlet, which was very obnoxious tothe existing Government, it is printed that the poor market-womencomplained that they were to be _scotched_ a quarter of their wages bytaxation; and attention is called to the word by its being three timesprinted in italics. In the pamphlet it is "sconced"; that very common oldword for fined or mulcted. Lord Lyndhurst, [447] who has [1863] just passed away under a load of yearsand honors, was Mr. Frend's private pupil at Cambridge. At the time of thecelebrated trial, he and two others amused themselves, and vented thefeeling which was very strong among the undergraduates, by chalking thewalls of Cambridge with "Frend for ever!" While thus engaged in what, usingthe term legally, we are probably to call his first publication, he and hisfriends were surprised by the proctors. Flight and chase followed ofcourse: Copley and one of the others, Serjeant Rough, [448] escaped: the{199} third, whose name I forget, but who afterwards, I have been told wasa bishop, [449] being lame, was captured and impositioned. Looking at theCambridge Calendar to verify the fact that Copley was an undergraduate atthe time, I find that there are but two other men in the list of honors ofhis year whose names are now widely remembered. And they were bothcelebrated schoolmasters; Butler[450] of Harrow, and Tate[451] of Richmond. But Mr. Frend had another noted pupil. I once had a conversation with avery remarkable man, who was generally called "Place, [452] the tailor, " butwho was politician, political economist, etc. , etc. He sat in the roomabove his shop--he was then a thriving master tailor at CharingCross--surrounded by books enough for nine, to shame a proverb. The bluebooks alone, cut up into strips, would have measured Great Britain foroh-no-we-never-mention-'ems, the Highlands included. I cannot find abiography of this worthy and able man. I happened to mention William Frend, and he said, "Ah! my old master, as I always call him. Many and many atime, and year after year, did he come in every {200} now and then to giveme instruction, while I was sitting on the board, working for my living, you know. " Place, who really was a sound economist, is joined with Cobbett, becausethey were together at one time, and because he was, in 1800, etc. , a greatRadical. But for Cobbett he had a great contempt. He told me the followingstory. He and others were advising with Cobbett about the defense he was tomake on a trial for seditious libel which was coming on. Said Place, "Youmust put in the letters you have received from Ministers, members of theCommons from the Speaker downwards, etc. , about your Register, and theirwish to have subjects noted. You must then ask the jury whether a person soaddressed must be considered as a common sower of sedition, etc. You willbe acquitted; nay, if your intention should get about, very likely theywill manage to stop proceedings. " Cobbett was too much disturbed to listen;he walked about the room ejaculating "D---- the prison!" and the like. Hehad not the sense to follow the advice, and was convicted. Cobbett, to go on with the chain, was a political acrobat, ready for anykind of posture. A friend of mine gave me several times an account of amission to him. A Tory member--those who know the old Tory world may lookfor his initials in initials of two consecutive words of "Pay his moneywith interest"--who was, of course, a political opponent, thought Cobbetthad been hardly used, and determined to subscribe handsomely towards theexpenses he was incurring as a candidate. My friend was commissioned tohand over the money--a bag of sovereigns, that notes might not be traced. He went into Cobbett's committee-room, told the patriot his errand, and putthe money on the table. "And to whom, sir, am I indebted?" said Cobbett. "The donor, " was the answer, "is Mr. Andrew Theophilus Smith, " or some suchunlikely pair of baptismals. "Ah!" said Cobbett, "I have known Mr. A. T. S. A long time! he was always a true friend of his country!" {201} To return to Place. He is a noted instance of the advantage of our jurysystem, which never asks a man's politics, etc. The late King of Hanover, when Duke of Cumberland, being unpopular, was brought under unjustsuspicions by the suicide of his valet: he must have seduced the wife andmurdered the husband. The charges were as absurd as those brought againstthe Englishman in the Frenchman's attempt at satirical verses upon him: "The Englishman is a very bad man; He drink the beer and he steal the can: He kiss the wife and he beat the man; And the Englishman is a very G---- d----. " The charges were revived in a much later day, and the defense might havegiven some trouble. But Place, who had been the foreman at the inquest, came forward, and settled the question in a few lines. Every one knew thatthe old Radical was quite free of all disposition to suppress truth fromwish to curry favor with royalty. John Speed, [453] the author of the _English History_, [454] (1632) whichBishop Nicolson[455] calls the best chronicle extant, was a man, likePlace, of no education, but what he gave himself. The bishop says he wouldhave done better if he had a better training: but what, he adds, could havebeen expected from a tailor! This Speed was, as well as Place. But he was{202} released from manual labor by Sir Fulk Grevil, [456] who enabled himto study. A STORY ON SIMSON. I have elsewhere noticed that those who oppose the mysteries of algebra donot ridicule them; this I want the cyclometers to do. Of the three whowrote against the great point, the negative quantity, and the uses of 0which are connected with it, only one could fire a squib. That RobertSimson[457] should do such a thing will be judged impossible by all whoadmit tradition. I do not vouch for the following; I give it as a proof ofthe impression which prevailed about him: He used to sit at his open window on the ground floor, as deep in geometryas a Robert Simson ought to be. Here he would be accosted by beggars, towhom he generally gave a trifle, he roused himself to hear a few words ofthe story, made his donation, and instantly dropped down into his depths. Some wags one day stopped a mendicant who was on his way to the window with"Now, my man, do as we tell you, and you will get something from thatgentleman, and a shilling from us besides. You will go and say you are indistress, he will ask you who you are, and you will say you are RobertSimson, son of John Simson of Kirktonhill. " The man did as he was told;Simson quietly gave him a coin, and dropped off. The wags watched a little, and saw him rouse himself again, and exclaim "Robert Simson, son of JohnSimson of Kirktonhill! why, that is myself. That man must be an impostor. "Lord Brougham tells the same story, with some difference of details. {203} BARON MASERES. Baron Maseres[458] was, as a writer, dry; those who knew his writings willfeel that he seldom could have taken in a joke or issued a pun. Maseres wasthe fourth wrangler of 1752, and first Chancellor's medallist (or highestin classics); his second was Porteus[459] (afterward Bishop of London). Waring[460] came five years after him: he could not get Maseres through thesecond page of his first book on algebra; a negative quantity stood like alion in the way. In 1758 he published his _Dissertation on the Use of theNegative Sign_, [461] 4to. There are some who care little about + and -, whowould give it house-room for the sake of the four words "Printed by SamuelRichardson. " Maseres speaks as follows: "A single quantity can never be marked witheither of those signs, or considered as either affirmative or negative; forif any single quantity, as b, is marked either with the sign + or with thesign - without assigning some other quantity, as a, to which it is to beadded, or from which it is to be subtracted, the mark will have no meaningor signification: thus if it be said that the square of -5, or the productof -5 into -5, is equal to +25, such an assertion must either signify nomore than that 5 times 5 is equal to 25 without any regard to the signs, orit must be mere nonsense and unintelligible jargon. I speak according tothe foregoing definition, by which the affirmativeness or negativeness ofany quantity implies a relation to another quantity of the same kind towhich it {204} is added, or from which it is subtracted; for it may perhapsbe very clear and intelligible to those who have formed to themselves someother idea of affirmative and negative quantities different from that abovedefined. " Nothing can be more correct, or more identically logical: +5 and -5, standing alone, are jargon if +5 and -5 are to be understood as withoutreference to another quantity. But those who have "formed to themselvessome other idea" see meaning enough. The great difficulty of the opponentsof algebra lay in want of power or will to see extension of terms. Maseresis right when he implies that extension, accompanied by its refusal, makesjargon. One of my paradoxers was present at a meeting of the Royal Society(in 1864, I think) and asked permission to make some remarks upon a paper. He rambled into other things, and, naming me, said that I had written abook in which two sides of a triangle are pronounced _equal_ to thethird. [462] So they are, in the sense in which the word is used in completealgebra; in which A + B = C makes A, B, C, three sides of a triangle, anddeclares that going over A and B, one after the other, is equivalent, inchange of place, to going over C at once. My critic, who might, if hepleased, have objected to extension, insisted upon reading me in unextendedmeaning. On the other hand, it must be said that those who wrote on the other ideawrote very obscurely about it and justified Des Cartes (_De Methodo_)[463]when he said: "Algebram vero, ut solet doceri, animadverti certis reguliset numerandi formulis ita esse contentam, ut videatur potius ars quædamconfusa, cujus usu ingenium quodam modo turbatur et obscuratur, quamscientia qua excolatur et perspicacius {205} reddatur. "[464] Maseres wrotethis sentence on the title of his own work, now before me; he would havemade it his motto if he had found it earlier. There is, I believe, in Cobbett's _Annual Register_, [465] an account of aninterview between Maseres and Cobbett when in prison. The conversation of Maseres was lively, and full of serious anecdote: butonly one attempt at humorous satire is recorded of him; it is aninstructive one. He was born in 1731 (Dec. 15), and his father was arefugee. French was the language of the house, with the pronunciation ofthe time of Louis XIV. He lived until 1824 (May 19), and saw the race ofrefugees who were driven out by the first Revolution. Their pronunciationdiffered greatly from his own; and he used to amuse himself by mimickingthem. Those who heard him and them had the two schools of pronunciationbefore them at once; a thing which seldom happens. It might even yet beworth while to examine the Canadian pronunciation. Maseres went as Attorney-General to Quebec; and was appointed CursitorBaron of our Exchequer in 1773. There is a curious story about his missionto Canada, which I have heard as good tradition, but have never seen inprint. The reader shall have it as cheap as I; and I confess I ratherbelieve it. Maseres was inveterately honest; he could not, at the bar, bearto see his own client victorious, when he knew his cause was a bad one. Ona certain occasion he was in a cause which he knew would go against him ifa certain case were quoted. Neither the judge nor the opposite counselseemed to remember this case, and Maseres could not help dropping anallusion which brought it out. {206} His business as a barrister fell off, of course. Some time after, Mr. Pitt (Chatham) wanted a lawyer to send toCanada on a private mission, and wanted a _very honest man_. Some onementioned Maseres, and told the above story: Pitt saw that he had got theman he wanted. The mission was satisfactorily performed, and Maseresremained as Attorney-General. The _Doctrine of Life Annuities_[466] (4to, 726 pages, 1783) is a strangeparadox. Its size, the heavy dissertations on the national debt, and thedepth of algebra supposed known, put it out of the question as anelementary work, and it is unfitted for the higher student by its elaborateattempt at elementary character, shown in its rejection of forms derivedfrom chances in favor of _the average_, and its exhibition of the separatevalues of the years of an annuity, as arithmetical illustrations. It is aclimax of unsaleability, unreadability, and inutility. For intrinsicnullity of interest, and dilution of little matter with much ink, I cancompare this book to nothing but that of Claude de St. Martin, elsewherementioned, or the lectures _On the Nature and Properties of Logarithms_, byJames Little, [467] Dublin, 1830, 8vo. (254 heavy pages of many words andfew symbols), a wonderful weight of weariness. The stock of this work on annuities, very little diminished, was given bythe author to William Frend, who paid warehouse room for it until about1835, when he consulted me as to its disposal. As no publisher could befound who would take it as a gift, for any purpose of sale, it wasconsigned, all but a few copies, to a buyer of waste paper. Baron Maseres's republications are well known: the _ScriptoresLogarithmici_[468] is a set of valuable reprints, mixed {207} with muchwhich might better have entered into another collection. It is not so wellknown that there is a volume of optical reprints, _Scriptores Optici_, London, 1823, 4to, edited for the veteran of ninety-two by Mr. Babbage[469]at twenty-nine. This excellent volume contains James Gregory, Des Cartes, Halley, Barrow, and the optical writings of Huyghens, the _Principia_ ofthe undulatory theory. It also contains, by the sort of whim in which suchmen as Maseres, myself, and some others are apt to indulge, a reprint of"The great new Art of weighing Vanity, "[470] by M. Patrick Mathers, Arch-Bedel to the University of St. Andrews, Glasgow, 1672. ProfessorSinclair, [471] of Glasgow, a good man at clearing mines of the water whichthey did not want, and furnishing cities with water which they did want, seems to have written absurdly about hydrostatics, and to have attacked acertain Sanders, [472] M. A. So Sanders, assisted by James Gregory, publisheda heavy bit of jocosity about him. This story of the authorship rested on anote made in his {208} copy by Robert Gray, M. D. ; but it has since beenfully confirmed by a letter of James Gregory to Collins, in theMacclesfield Correspondence. "There is one Master Sinclair, who did writethe _Ars Magna et Nova_, [473] a pitiful ignorant fellow, who hath latelywritten horrid nonsense in the hydrostatics, and hath abused a master inthe University, one Mr. Sanders, in print. This Mr. Sanders ... Is resolvedto cause the Bedel of the University to write against him.... We resolve tomake excellent sport with him. " On this I make two remarks: First, I have learned from experience that oldnotes, made in books by their possessors, are statements of high authority:they are almost always confirmed. I do not receive them without hesitation;but I believe that of all the statements about books which rest on oneauthority, there is a larger percentage of truth in the written word thanin the printed word. Secondly, I mourn to think that when the New Zealanderpicks up his old copy of this book, and reads it by the associations of hisown day, he may, in spite of the many assurances I have received that my_Athenæum Budget_ was amusing, feel me to be as heavy as I feel JamesGregory and Sanders. But he will see that I knew what was coming, whichGregory did not. MR. FREND'S BURLESQUE. It was left for Mr. Frend to prove that an impugner of algebra couldattempt ridicule. He was, in 1803, editor of a periodical _The Gentleman'sMonthly Miscellany_, which lasted a few months. [474] To this, among otherthings, he contributed the following, in burlesque of the use made of 0, towhich he objected. [475] The imitation of Rabelais, a writer {209} in whomhe delighted, is good: to those who have never dipped, it may give such anotion as they would not easily get elsewhere. The point of the satire isnot so good. But in truth it is not easy to make pungent scoffs upon whatis common sense to all mankind. Who can laugh with effect at six timesnothing is nothing, as false or unintelligible? In an article intended forthat undistinguishing know-0 the "general reader, " there would have been noforce of satire, if _division_ by 0 had been separated from multiplicationby the same. I have followed the above by another squib, by the same author, on theEnglish language. The satire is covertly aimed at theological phraseology;and any one who watches this subject will see that it is a very justobservation that the Greek words are not boiled enough. PANTAGRUEL'S DECISION _of the_ QUESTION _about_ NOTHING. "Pantagruel determined to have a snug afternoon with Epistemon and Panurge. Dinner was ordered to be set in a small parlor, and a particular batch ofHermitage with some choice Burgundy to be drawn from a remote corner of thecellar upon the occasion. By way of lunch, about an hour before dinner, Pantagruel was composing his stomach with German sausages, reindeer'stongues, oysters, brawn, and half a dozen different sorts of English beerjust come into fashion, when a most thundering knocking was heard at thegreat gate, and from the noise they expected it to announce the arrival atleast of the First Consul, or king Gargantua. Panurge was sent toreconnoiter, and after a quarter of an hour's absence, returned with thenews that the University of Pontemaca was waiting his highness's leisure inthe great hall, to propound a question which {210} had turned the brains ofthirty-nine students, and had flung twenty-seven more into a high fever. With all my heart, says Pantagruel, and swallowed down three quarts ofBurton ale; but remember, it wants but an hour of dinner time, and thequestion must be asked in as few words as possible; for I cannot deprivemyself of the pleasure I expected to enjoy in the company of my goodfriends for a set of mad-headed masters. I wish brother John was here tosettle these matters with the black gentry. "Having said or rather growled this, he proceeded to the hall of ceremony, and mounted his throne; Epistemon and Panurge standing on each side, buttwo steps below him. Then advanced to the throne the three beadles of theUniversity of Pontemaca with their silver staves on their shoulders, andvelvet caps on their heads, and they were followed by three times threedoctors, and thrice three times three masters of art; for everything wasdone in Pontemaca by the number three, and on this account the address waswritten on parchment, one foot in breadth, and thrice three times thricethree feet in length. The beadles struck the ground with their heads andtheir staves three times in approaching the throne; the doctors struck theground with their heads thrice three times, and the masters did the samethrice each time, beating the ground with their heads thrice three times. This was the accustomed form of approaching the throne, time out of mind, and it was said to be emblematic of the usual prostration of science to thethrone of greatness. "The mathematical professor, after having spit, and hawked, and cleared histhroat, and blown his nose on a handkerchief lent to him, for he hadforgotten to bring his own, began to read the address. In this he wasassisted by three masters of arts, one of whom, with a silver pen, pointedout the stops; the second with a small stick rapped his knuckles when hewas to raise or lower his voice; and a third pulled his hair behind when hewas to look Pantagruel in the face. Pantagruel began to chafe like a lion:{211} he turned first on one side, then on the other: he listened andgroaned, and groaned and listened, and was in the utmost cogitabundity ofcogitation. His countenance began to brighten, when, at the end of an hour, the reader stammered out these words: "'It has therefore been most clearly proved that as all matter may bedivided into parts infinitely smaller than the infinitely smallest part ofthe infinitesimal of nothing, so nothing has all the properties ofsomething, and may become, by just and lawful right, susceptible ofaddition, subtraction, multiplication, division, squaring, and cubing: thatit is to all intents and purposes as good as anything that has been, is, orcan be taught in the nine universities of the land, and to deprive it ofits rights is a most cruel innovation and usurpation, tending to destroyall just subordination in the world, making all universities superfluous, leveling vice-chancellors, doctors, and proctors, masters, bachelors, andscholars, to the mean and contemptible state of butchers andtallow-chandlers, bricklayers and chimney-sweepers, who, if it were not forthese learned mysteries, might think that they knew as much as theirbetters. Every one then, who has the good of science at heart, must prayfor the interference of his highness to put a stop to all the disputesabout nothing, and by his decision to convince all gainsayers that thescience of nothing is taught in the best manner in the universities, to thegreat edification and improvement of all the youth in the land. ' "Here Pantagruel whispered in the ear of Panurge, who nodded to Epistemon, and they two left the assembly, and did not return for an hour, till theorator had finished his task. The three beadles had thrice struck theground with their heads and staves, the doctors had finished theircompliments, and the masters were making their twenty-seven prostrations. Epistemon and Panurge went up to Pantagruel, whom they found fast asleepand snoring; nor could he be roused but by as many tugs as there had been{212} bowings from the corps of learning. At last he opened his eyes, gavea good stretch, made half a dozen yawns, and called for a stoup of wine. Ithank you, my masters, says he; so sound a nap I have not had since I camefrom the island of Priestfolly. Have you dined, my masters? They answeredthe question by as many bows as at entrance; but his highness left them tothe care of Panurge, and retired to the little parlor with Epistemon, wherethey burst into a fit of laughter, declaring that this learned Baragouinabout nothing was just as intelligible as the lawyer's Galimathias. Panurgeconducted the learned body into a large saloon, and each in his way hearinga clattering of plates and glasses, congratulated himself on hisapproaching good cheer. There they were left by Panurge, who took his chairby Pantagruel just as the soup was removed, but he made up for the want ofthat part of his dinner by a pint of champagne. The learning of theuniversity had whetted their appetites; what they each ate it is needlessto recite; good wine, good stories, and hearty laughs went round, and threehours elapsed before one soul of them recollected the hungry students ofPontemaca. "Epistemon reminded them of the business in hand, and orders were given fora fresh dozen of hermitage to be put upon table, and the royal attendantsto get ready. As soon as the dozen bottles were emptied, Pantagruel rosefrom table, the royal trumpets sounded, and he was accompanied by the greatofficers of his court into the large dining hall, where was a table withforty-two covers. Pantagruel sat at the head, Epistemon at the bottom, andPanurge in the middle, opposite an immense silver tureen, which would holdfifty gallons of soup. The wise men of Pontemaca then took their seatsaccording to seniority. Every countenance glistened with delight; the musicstruck up; the dishes were uncovered. Panurge had enough to do to handlethe immense silver ladle: Pantagruel and Epistemon had no time for eating, they were fully employed in carving. The bill {213} of fare announced thenames of a hundred different dishes. From Panurge's ladle came into thesoup plate as much as he took every time out of the tureen; and as it wasthe rule of the court that every one should appear to eat, as long as hesat at table, there was the clattering of nine and thirty spoons againstthe silver soup-plates for a quarter of an hour. They were then removed, and knives and forks were in motion for half an hour. Glasses werecontinually handed round in the mean time, and then everything was removed, except the great tureen of soup. The second course was now served up, indispatching which half an hour was consumed; and at the conclusion the wisemen of Pontemaca had just as much in their stomachs as Pantagruel in hishead from their address: for nothing was cooked up for them in everypossible shape that Panurge could devise. "Wine-glasses, large decanters, fruit dishes, and plates were now set on. Pantagruel and Epistemon alternately gave bumper toasts: the University ofPontemaca, the eye of the world, the mother of taste and good sense anduniversal learning, the patroness of utility, and the second only toPantagruel in wisdom and virtue (for these were her titles), was drankstanding with thrice three times three, and huzzas and clattering ofglasses; but to such wine the wise men of Pontemaca had not beenaccustomed; and though Pantagruel did not suffer one to rise from tabletill the eighty-first glass had been emptied, not even the weakest headedmaster of arts felt his head in the least indisposed. The decanters indeedwere often removed, but they were brought back replenished, filled alwayswith nothing. "Silence was now proclaimed, and in a trice Panurge leaped into the largesilver tureen. Thence he made his bows to Pantagruel and the whole company, and commenced an oration of signs, which lasted an hour and a half, and inwhich he went over all the matter contained in the Pontemaca address; andthough the wise men looked very serious during the whole time, Pantagruelhimself and his whole {214} court could not help indulging in repeatedbursts of laughter. It was universally acknowledged that he excelledhimself, and that the arguments by which he beat the English masters ofarts at Paris were nothing to the exquisite selection of attitudes which hethis day assumed. The greatest shouts of applause were excited when he wasrunning thrice round the tureen on its rim, with his left hand holding hisnose, and the other exercising itself nine and thirty times on his back. Inthis attitude he concluded with his back to the professor of mathematics;and at the instant he gave his last flap, by a sudden jump, and turningheels over head in the air, he presented himself face to face to theprofessor, and standing on his left leg, with his left hand holding hisnose, he presented to him, in a white satin bag, Pantagruel's royal decree. Then advancing his right leg, he fixed it on the professor's head, andafter three turns, in which he clapped his sides with both hands thricethree times, down he leaped, and Pantagruel, Epistemon, and himself tooktheir leaves of the wise men of Pontemaca. "The wise men now retired, and by royal orders were accompanied by a guard, and according to the etiquette of the court, no one having a royal ordercould stop at any public house till it was delivered. The processionarrived at Pontemaca at nine o'clock the next morning, and the sound ofbells from every church and college announced their arrival. Thecongregation was assembled; the royal decree was saluted in the same manneras if his highness had been there in person; and after the properceremonies had been performed, the satin bag was opened exactly at twelveo'clock. A finely emblazoned roll was drawn forth, and the public oratorread to the gaping assembly the following words: "'They who can make something out of nothing shall have nothing to eat atthe court of--PANTAGRUEL. '" {215} ORIGIN _of the_ ENGLISH LANGUAGE, _related by a_ SWEDE. "Some months ago in a party in Holland, consisting of natives of variouscountries, the merit of their respective languages became a topic ofconversation. A Swede, who had been a great traveler, and could converse inmost of the modern languages of Europe, laughed very heartily at anEnglishman, who had ventured to speak in praise of the tongue of his dearcountry. I never had any trouble, says he, in learning English. To my verygreat surprise, the moment I sat foot on shore at Gravesend, I found out, that I could understand, with very little trouble, every word that wassaid. It was a mere jargon, made up of German, French, and Italian, withnow and then a word from the Spanish, Latin or Greek. I had only to bringmy mouth to their mode of speaking, which was done with ease in less than aweek, and I was everywhere taken for a true-born Englishman; a privilege bythe way of no small importance in a country, where each man, God knows why, thinks his foggy island superior to any other part of the world: and thoughhis door is never free from some dun or other coming for a tax, and if hesteps out of it he is sure to be knocked down or to have his pocket picked, yet he has the insolence to think every foreigner a miserable slave, andhis country the seat of everything wretched. They may talk of liberty asthey please, but Spain or Turkey for my money: barring the bowstring andthe inquisition, they are the most comfortable countries under heaven, andyou need not be afraid of either, if you do not talk of religion andpolitics. I do not see much difference too in this respect in England, forwhen I was there, one of their most eminent men for learning was put inprison for a couple of years, and got his death for translating one ofÆsop's fables into English, which every child in Spain and Turkey istaught, as soon as he comes out of his leading strings. Here all thecompany unanimously cried out against the Swede, that it was {216}impossible: for in England, the land of liberty, the only thing its worstenemies could say against it, was, that they paid for their liberty a muchgreater price than it was worth. --Every man there had a fair trialaccording to laws, which everybody could understand; and the judges werecool, patient, discerning men, who never took the part of the crown againstthe prisoner, but gave him every assistance possible for his defense. "The Swede was borne down, but not convinced; and he seemed determined tospit out all his venom. Well, says he, at any rate you will not deny thatthe English have not got a language of their own, and that they came by itin a very odd way. Of this at least I am certain, for the whole history wasrelated to me by a witch in Lapland, whilst I was bargaining for a wind. Here the company were all in unison again for the story. "In ancient times, said the old hag, the English occupied a spot inTartary, where they lived sulkily by themselves, unknowing and unknown. Bya great convulsion that took place in China, the inhabitants of that andthe adjoining parts of Tartary were driven from their seats, and aftervarious wanderings took up their abode in Germany. During this time nobodycould understand the English, for they did not talk, but hissed like somany snakes. The poor people felt uneasy under this circumstance, and inone of their parliaments, or rather hissing meetings, it was determined toseek a remedy: and an embassy was sent to some of our sisterhood thenliving on Mount Hecla. They were put to a nonplus, and summoned the Devilto their relief. To him the English presented their petitions, andexplained their sad case; and he, upon certain conditions, promised tobefriend them, and to give them a language. The poor Devil was little awareof what he had promised; but he is, as all the world knows, a man of toomuch honor to break his word. Up and down the world then he went in questof this new language: visited all the universities, and all {217} theschools, and all the courts of law, and all the play-houses, and all theprisons; never was poor devil so fagged. It would have made your heartbleed to see him. Thrice did he go round the earth in every parallel oflatitude; and at last, wearied and jaded out, back came he to Hecla indespair, and would have thrown himself into the volcano, if he had beenmade of combustible materials. Luckily at that time our sisters wereengaged in settling the balance of Europe; and whilst they were lookingover projects, and counter-projects, and ultimatums, and post ultimatums, the poor Devil, unable to assist them was groaning in a corner andruminating over his sad condition. "On a sudden, a hellish joy overspread his countenance; up he jumped, and, like Archimedes of old, ran like a madman amongst the throng, turning overtables, and papers, and witches, roaring out for a full hour togethernothing else but 'tis found, 'tis found! Away were sent the sisterhood inevery direction, some to traverse all the corners of the earth, and othersto prepare a larger caldron than had ever yet been set upon Hecla. Theaffairs of Europe were at a stand: its balance was thrown aside; primeministers and ambassadors were everywhere in the utmost confusion; and, bythe way, they have never been able to find the balance since that time, andall the fine speeches upon the subject, with which your newspapers areevery now and then filled, are all mere hocus-pocus and rhodomontade. However, the caldron was soon set on, and the air was darkened by witchesriding on broomsticks, bringing a couple of folios under each arm, andacross each shoulder. I remember the time exactly: it was just as thecouncil of Nice had broken up, so that they got books and papers there dogcheap; but it was a bad thing for the poor English, as these were the worstmaterials that entered into the caldron. Besides, as the Devil wanted someamusement, and had not seen an account of the transactions of this famouscouncil, he had all the books brought from it laid before him, and splithis sides almost {218} with laughing, whilst he was reading the speechesand decrees of so many of his old friends and acquaintances. All this whilethe witches were depositing their loads in the great caldron. There werebooks from the Dalai Lama, and from China: there were books from theHindoos, and tallies from the Caffres: there were paintings from Mexico, and rocks of hieroglyphics from Egypt: the last country supplied besidesthe swathings of two thousand mummies, and four-fifths of the famed libraryof Alexandria. Bubble! bubble! toil and trouble! never was a day of morelabor and anxiety; and if our good master had but flung in the Greek booksat the proper time, they would have made a complete job of it. He was alittle too impatient: as the caldron frothed up, he skimmed it off with agreat ladle, and filled some thousands of our wind-bags with the froth, which the English with great joy carried back to their own country. Thesebags were sent to every district: the chiefs first took their fill, andthen the common people; hence they now speak a language which no foreignercan understand, unless he has learned half a dozen other languages; and thepoor people, not one in ten, understand a third part of what is said tothem. The hissing, however, they have not entirely got rid of, and everyseven years, when the Devil, according to agreement, pays them a visit, they entertain him at their common halls and county meetings with theiroriginal language. "The good-natured old hag told me several other circumstances, relative tothis curious transaction, which, as there is an Englishman in company, itwill be prudent to pass over in silence: but I cannot help mentioning onething which she told me as a very great secret. You know, says she to me, that the English have more religions among them than any other nation inEurope, and that there is more teaching and sermonizing with them than inany other country. The fact is this; it matters not who gets up to teachthem, the hard words of the Greek were not sufficiently {219} boiled, andwhenever they get into a sentence, the poor people's brains are turned, andthey know no more what the preacher is talking about, than if he haranguedthem in Arabic. Take my word for it if you please; but if not, when you getto England, desire the bettermost sort of people that you are acquaintedwith to read to you an act of parliament, which of course is written in theclearest and plainest style in which anything can be written, and you willfind that not one in ten will be able to make tolerable sense of it. Thelanguage would have been an excellent language, if it had not been for thecouncil of Nice, and the words had been well boiled. "Here the company burst out into a fit of laughter. The Englishman got upand shook hands with the Swede: _si non è vero_, said he, _è bentrovato_. [476] But, however I may laugh at it here, I would not advise youto tell this story on the other side of the water. So here's a bumper toOld England for ever, and God save the king. " ON YOUTHFUL PRODIGIES. The accounts given of extraordinary children and adolescents frequentlydefy credence. [477] I will give two well-attested instances. The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478]was certainly born in May, 1713. His treatise on curves of double curvature(printed in 1731)[479] received {220} the approbation of the Academy ofSciences, August 23, 1729. Fontenelle, in his certificate of this, callsthe author sixteen years of age, and does not strive to exaggerate thewonder, as he might have done, by reminding his readers that this work, oforiginal and sustained mathematical investigation, must have been comingfrom the pen at the ages of fourteen and fifteen. The truth was, asattested by De Molières, [480] Clairaut had given public proofs of his powerat twelve years old. His age being thus publicly certified, all doubt isremoved: say he had been--though great wonder would still have beenleft--twenty-one instead of sixteen, his appearance, and the remembrancesof his friends, schoolfellows, etc. , would have made it utterly hopeless toknock off five years of that age while he was on view in Paris as a younglion. De Molières, who examined the work officially for the _Garde desSceaux_, is transported beyond the bounds of official gravity, and saysthat it "ne mérite pas seulement d'être imprimé, mais d'être admiré commeun prodige d'imagination, de conception, et de capacité. "[481] That Blaise Pascal was born in June, 1623, is perfectly well establishedand uncontested. [482] That he wrote his conic sections at the age ofsixteen might be difficult to establish, though tolerably well attested, ifit were not for {221} one circumstance, for the book was not published. Thecelebrated theorem, "Pascal's hexagram, "[483] makes all the rest come veryeasy. Now Curabelle, [484] in a work published in 1644, sneers atDesargues, [485] whom he quotes, for having, in 1642, deferred a discussionuntil "cette grande proposition nommée le Pascale verra le jour. "[486] Thatis, by the time Pascal was nineteen, the _hexagram_ was circulating under aname derived from the author. The common story about Pascal, given by hissister, [487] is an absurdity which no doubt has prejudiced many againsttales of early proficiency. He is made, when quite a boy, to inventgeometry _in the order of Euclid's propositions_: as if that order werenatural sequence of investigation. The hexagram at ten years old would be ahundred times less unlikely. The instances named are painfully astonishing: I give one which has fallenout of sight, because it will preserve an imperfect biography. JohnWilson[488] is Wilson of that {222} Ilk, that is, of "Wilson's Theorem. " Itis this: if _p_ be a prime number, the product of all the numbers up to_p_-1, increased by 1, is divisible without remainder by _p_. Allmathematicians know this as Wilson's theorem, but few know who Wilson was. He was born August 6, 1741, at the Howe in Applethwaite, and he was heir toa small estate at Troutbeck in Westmoreland. He was sent to Peterhouse, atCambridge, and while an undergraduate was considered stronger in algebrathan any one in the University, except Professor Waring, one of the mostpowerful algebraists of the century. [489] He was the senior wrangler of1761, and was then for some time a private tutor. When Paley, [490] then inhis third year, determined to make a push for the senior wranglership, which he got, Wilson was recommended to him as a tutor. Both were ardent intheir work, except that sometimes Paley, when he came for his lesson, wouldfind "Gone a fishing" written on his tutor's outer door: which was insultadded to injury, for Paley was very fond of fishing. Wilson soon leftCambridge, and went to the bar. He practised on the northern circuit withgreat success; and, one day, while passing his vacation on his littleproperty at Troutbeck, he received information, to his great surprise, thatLord Thurlow, [491] with whom he had {223} no acquaintance, had recommendedhim to be a Judge of the Court of Common Pleas. He died, Oct. 18, 1793, with a very high reputation as a lawyer and a Judge. These facts are partlyfrom Meadley's _Life of Paley_, [492] no doubt from Paley himself, partlyfrom the _Gentleman's Magazine_, and from an epitaph written by BishopWatson. [493] Wilson did not publish anything: the theorem by which he hascut his name in the theory of numbers was communicated to Waring, by whomit was published. He married, in 1788, a daughter of Serjeant Adair, [494]and left issue. _Had a family_, many will say: but a man and his wife are afamily, even without children. An actuary may be allowed to be accurate inthis matter, of which I was reminded by what an actuary wrote of anotheractuary. William Morgan, [495] in the life of his uncle Dr. RichardPrice, [496] says that the Doctor and his {224} wife were "never blessedwith an addition to their family. " I never met with such accuracyelsewhere. Of William Morgan I add that my surname and pursuits havesometimes, to my credit be it said, made a confusion between him and me. Dates are nothing to the mistaken; the last three years of Morgan's lifewere the first three years of my actuary-life (1830-33). The mistake was tomy advantage as well as to my credit. I owe to it the acquaintance of oneof the noblest of the human race, I mean Elizabeth Fry, [497] who came to mefor advice about a philanthropic design, which involved life questions, under a general impression that some Morgan had attended to suchthings. [498] {225} NEWTON AGAIN OVERTHROWN. A treatise on the sublime science of heliography, satisfactorily demonstrating our great orb of light, the sun, to be absolutely no other than a body of ice! Overturning all the received systems of the universe hitherto extant; proving the celebrated and indefatigable Sir Isaac Newton, in his theory of the solar system, to be as far distant from the truth, as many of the heathen authors of Greece and Rome. By Charles Palmer, [499] Gent. London, 1798, 8vo. Mr. Palmer burned some tobacco with a burning glass, saw that a lens of icewould do as well, and then says: "If we admit that the sun could be removed, and a terrestrial body of iceplaced in its stead, it would produce the same effect. The sun is acrystaline body receiving the radiance of God, and operates on this earthin a similar manner as the light of the sun does when applied to a convexmirror or glass. " Nov. 10, 1801. The Rev. Thomas Cormouls, [500] minister of Tettenhall, addressed a letter to Sir Wm. Herschel, from which I extract the following: "Here it may be asked, then, how came the doctrines of Newton to solve allastronomic Phenomina, and all problems concerning the same, both _a parteante_ and _a parte post_. [501] It is answered that he certainly wrought theprinciples he made use of into strickt analogy with the real Phenomina ofthe heavens, and that the rules and results arizing from them {226} agreewith them and resolve accurately all questions concerning them. Though theyare not fact and true, or nature, but analogous to it, in the manner of theartificial numbers of logarithms, sines, &c. A very important questionarises here, Did Newton mean to impose upon the world? By no means: hereceived and used the doctrines reddy formed; he did a little extend andcontract his principles when wanted, and commit a few oversights ofconsequences. But when he was very much advanced in life, he suspected thefundamental nullity of them: but I have from a certain anecdote strongground to believe that he knew it before his decease and intended to haveretracted his error. But, however, somebody did deceive, if not wilfully, negligently at least. That was a man to whom the world has greatobligations too. It was no less a philosopher than Galileo. " That Newton wanted to retract before his death, is a notion not uncommonamong paradoxers. Nevertheless, there is no retraction in the third editionof the _Principia_, published when Newton was eighty-four years old! Themoral of the above is, that a gentleman who prefers instructing WilliamHerschel to learning how to spell, may find a proper niche in a properplace, for warning to others. It seems that gravitation is not truth, butonly the logarithm of it. BISHOPS AS PARADOXERS. The mathematical and philosophical works of the Right Rev. John Wilkins[502].... In two volumes. London, 1802, 8vo. This work, or at least part of the edition--all for aught I know--isprinted on wood; that is, on paper made from wood-pulp. It has a roughsurface; and when held before a candle is of very unequal transparency. There is in it a reprint of the works on the earth and moon. The discourseon the possibility of going to the moon, in this and the edition of 1640, is incorporated: but from the account in the {227} life prefixed, and amention by D'Israeli, I should suppose that it had originally a separatetitle-page, and some circulation as a separate tract. Wilkins treats thissubject half seriously, half jocosely; he has evidently not quite made uphis mind. He is clear that "arts are not yet come to their solstice, " andthat posterity will bring hidden things to light. As to the difficulty ofcarrying food, he thinks, scoffing Puritan that he is, the Papists may betrained to fast the voyage, or may find the bread of their Eucharist "servewell enough for their _viaticum_. "[503] He also puts the case that thestory of Domingo Gonsales may be realized, namely, that wild geese findtheir way to the moon. It will be remembered--to use the usual substitutefor, It has been forgotten--that the posthumous work of Bishop FrancisGodwin[504] of Llandaff was published in 1638, the very year of Wilkins'sfirst edition, in time for him to mention it at the end. Godwin makesDomingo Gonsales get to the moon in a chariot drawn by wild geese, and, asold books would say, discourses fully on that head. It is not a littleamusing that Wilkins should have been seriously accused of plagiarizingGodwin, Wilkins writing in earnest, or nearly so, and Godwin writingfiction. It may serve to show philosophers how very near pure speculationcomes to fable. From the sublime to the ridiculous is but a step: which isthe sublime, and which the ridiculous, every one must settle for himself. With me, good fiction is the sublime, and bad speculation the ridiculous. The number of bishops in my list is small. I might, had I possessed thebook, have opened the list of quadrators with an Archbishop of Canterbury, or at least with a divine who was not wholly not archbishop. ThomasBradwardine[505] (Bragvardinus, Bragadinus) was elected in {228} 1348; thePope put in another, who died unconsecrated; and Bradwardine was againelected in 1349, and lived five weeks longer, dying, I suppose, unconfirmedand unconsecrated. [506] Leland says he held the see a year, _unus tantumannulus_, [507] which seems to be a confusion: the whole business, from thefirst election, took about a year. He squared the circle, and hisperformance was printed at Paris in 1494. I have never seen it, nor anywork of the author, except a tract on proportion. As Bradwardine's works are very scarce indeed, I give two titles from oneof the Libri catalogues. "ARITHMETIC. BRAUARDINI (Thomæ) Arithmetica speculativa revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black letter, _elegant woodcut title-page_, VERY RARE, _folio. Parisiis, per Thomam Anguelast (pro Olivier Senant), s. A. Circa 1510_. [508] "This book, by Thomas Bradwardine, Archbishop of Canterbury must beexceedingly scarce as it has escaped the notice of Professor De Morgan, who, in his _Arithmetical Books_, speaks of a treatise of the same authoron proportions, [509] printed at Vienna in 1515, but does not mention thepresent work. {229} "Bradwardine (Archbp. T. ). Brauardini (Thomæ) Geometria speculativa, com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo, SCARCE, _folio. Parisiis, J. Petit_, 1511. [510] "In this work we find the _polygones étoilés_, [511] see Chasles (_Aperçu_, pp. 480, 487, 521, 523, &c. ) on the merit of the discoveries of thisEnglish mathematician, who was Archbishop of Canterbury in the XIVthCentury (_tempore_ Edward III. A. D. 1349); and who applied geometry totheology. M. Chasles says that the present work of Bradwardine contains'Une théorie nouvelle qui doit faire honneur au XIVe Siècle. '"[512] The titles do not make it quite sure that Bradwardine is the quadrator; itmay be Peter Sanchez after all. [513] THE QUESTION OF PARALLELS. Nouvelle théorie des parallèles. Par Adolphe Kircher[514] [so signed at the end of the appendix]. Paris, 1803, 8vo. An alleged emendation of Legendre. [515] The author refers {230} to attemptsby Hoffman, [516] 1801, by Hauff, [517] 1799, and to a work of Karsten, [518]or at least a theory of Karsten, contained in "Tentamen novæ parallelarumtheoriæ notione situs fundatæ; auctore G. C. Schwal, [519] Stuttgardæ, 1801, en 8 volumes. " Surely this is a misprint; _eight_ volumes on the theory ofparallels? If there be such a work, I trust I and it may never meet, thoughever so far produced. {231} Soluzione ... Della quadratura del Circolo. By Gaetano Rossi. [520] London, 1804, 8vo. The three remarkable points of this book are, that the household of thePrince of Wales took ten copies, Signora Grassini[521] sixteen, and thatthe circumference is 3-1/5 diameters. That is, the appetite of Grassini forquadrature exceeded that of the whole household (_loggia_) of the Prince ofWales in the ratio in which the semi-circumference exceeds the diameter. And these are the first two in the list of subscribers. Did the author seethis theorem? A PATRIOTIC PARADOX. Britain independent of commerce; or proofs, deduced from an investigation into the true cause of the wealth of nations, that our riches, prosperity, and power are derived from sources inherent in ourselves, and would not be affected, even though our commerce were annihilated. By Wm. Spence. [522] 4th edition, 1808, 8vo. A patriotic paradox, being in alleviation of the Commerce panic which themeasures of Napoleon I. --who _felt_ our Commerce, while Mr. Spence only_saw_ it--had awakened. In this very month (August, 1866), the Pres. Brit. Assoc. Has applied a similar salve to the coal panic; it is fit thatscience, which rubbed the sore, should find a plaster. We ought to have aniron panic and a timber panic; and {232} a solemn embassy to the Americans, to beg them not to whittle, would be desirable. There was a gold panicbeginning, before the new fields were discovered. For myself, I am theunknown and unpitied victim of a chronic gutta-percha panic: I never couldget on without it; to me, gutta percha and Rowland Hill are the greatdiscoveries of our day; and not unconnected either, gutta percha being tothe submarine post what Rowland Hill is to the superterrene. I should besorry to lose cow-choke--I gave up trying to spell it many years ago--butif gutta percha go, I go too. I think, that perhaps when, five hundredyears hence, the people say to the Brit. Assoc. (if it then exist) "Praygentlemen, is it not time for the coal to be exhausted?" they will beanswered out of Molière (who will certainly then exist): "_Cela étaitautrefois ainsi, mais nous avons changé tout cela. _"[523] A great manypeople think that if the coal be used up, it will be announced someunexpected morning by all the yards being shut up and written noticeoutside, "Coal all gone!" just like the "Please, ma'am, there ain't no moresugar, " with which the maid servant damps her mistress just atbreakfast-time. But these persons should be informed that there is everyreason to think that there will be time, as the city gentleman said, to_venienti_ the _occurrite morbo_. [524] SOME SCIENTIFIC PARADOXES. An appeal to the republic of letters in behalf of injured science, from the opinions and proceedings of some modern authors of elements of geometry. By George Douglas. [525] Edinburgh, 1810, 8vo. Mr. Douglas was the author of a very good set of {233} mathematical tables, and of other works. He criticizes Simson, [526] Playfair, [527] andothers, --sometimes, I think, very justly. There is a curious phrase whichoccurs more than once. When he wants to say that something or other wasdone before Simson or another was born, he says "before he existed, atleast as an author. " He seems to reserve the possibility of Simson's_pre-existence_, but at the same time to assume that he never wroteanything in his previous state. Tell me that Simson pre-existed in anyother way than as editor of some pre-existent Euclid? Tell Apella![528] 1810. In this year Jean Wood, Professor of Mathematics in the University ofVirginia (Richmond), [529] addressed a printed circular to "Dr. Herschel, Astronomer, Greenwich Observatory. " No mistake was more common than thenatural one of imagining that the _Private Astronomer_ of the king was the_Astronomer Royal_. The letter was on the {234} difference of velocities ofthe two sides of the earth, arising from the composition of the rotationand the orbital motion. The _paradox_ is a fair one, and deserving ofinvestigation; but, perhaps it would not be easy to deduce from it tides, trade-winds, aerolithes, &c. , as Mr. Wood thought he had done in a workfrom which he gives an extract, and which he describes as published. Thecomposition of rotations, &c. , is not for the world at large: the paradoxof the non-rotation of the moon about her axis is an instance. How manypersons know that when a wheel rolls on the ground, the lowest point ismoving upwards, the highest point forwards, and the intermediate points inall degrees of betwixt and between? This is too short an explanation, withsome good difficulties. The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson, [530] B. D. ] Cambridge, 1815. 4to. Of this unpunctuating paradoxer I shall give an account in his own way: hewould not stop for any one; why should I stop for him? It is worth while totry how unpunctuated sentences will read. The reverend J Dobson BD late fellow of saint Johns college Cambridge wasrector of Brandesburton in Yorkshire he was seventh wrangler in 1798 anddied in 1847 he was of that sort of eccentricity which permits account ofhis private life if we may not rather say that in such cases private lifebecomes public there is a tradition that he was called Death Dobson onaccount of his head and aspect of countenance being not very unlike theordinary pictures of a human skull his mode of life is reported to havebeen very singular whenever he visited Cambridge he was never known to gotwice to the same inn he never would sleep at the rectory with anotherperson in the house some ancient charwoman used to attend to the house butnever slept in it he has been known in the time of coach travelling to have{235} deferred his return to Yorkshire on account of his disinclination totravel with a lady in the coach he continued his mathematical studies untilhis death and till his executors sold the type all his tracts to the numberof five were kept in type at the university press none of these tracts hadany stops except full stops at the end of paragraphs only neither had theycapitals except one at the beginning of a paragraph so that a full stop wasgenerally followed by some white as there is not a single proper name inthe whole of the book I have I am not able to say whether he would haveused capitals before proper names I have inserted them as usual for which Ihope his spirit will forgive me if I be wrong he also published theelements of geometry in two volumes quarto Cambridge 1815 this book hadalso no stops except when a comma was wanted between letters as in thestraight lines AB, BC I should also say that though the title isunpunctuated in the author's part it seems the publishers would not standit in their imprint this imprint is punctuated as usual and Deighton andSons to prove the completeness of their allegiance have managed that commasemicolon and period shall all appear in it why could they not havecontrived interrogation and exclamation this is a good precedent toestablish the separate right of the publisher over the imprint it is saidthat only twenty of the tracts were printed and very few indeed of the bookon geometry it is doubtful whether any were sold there is a copy of thegeometry in the university library at Cambridge and I have one myself thematter of the geometry differs entirely from Euclid and is so fearfullyprolix that I am sure no mortal except the author ever read it the man wenton without stops and without stop save for a period at the end of aparagraph this is the unpunctuated account of the unpunctuating geometer_suum cuique tribuito_[531] Mrs Thrale[532] would have been amused {236} ata Dobson who managed to come to a full stop without either of the threewarnings. I do not find any difficulty in reading Dobson's geometry; and I have readmore of it to try reading without stops than I should have done had it beenprinted in the usual way. Those who dip into the middle of my paragraph maybe surprised for a moment to see "on account of his disinclination totravel with a lady in the coach he continued his mathematical studies untilhis death and [further, of course] until his executors sold the type. " Buta person reading straight through would hardly take it so. I should addthat, in order to give a fair trial, I did not compose as I wrote, butcopied the words of the correspondent who gave me the facts, so far as theywent. A RELIGIOUS PARADOX. _Philosophia Sacra, or the principles of natural Philosophy. Extracted from Divine Revelation. _ By the Rev. Samuel Pike. [533] Edited by the Rev. Samuel Kittle. [534] Edinburgh, 1815, 8vo. This is a work of modified Hutchinsonianism, which I have seen cited byseveral. Though rather dark on the subject, it seems not to contradict themotion of the earth, or the doctrine of gravitation. Mr. Kittle gives alist of some Hutchinsonians, --as Bishop Horne;[535] Dr. Stukeley;[536] theRev. {237} W. Jones, [537] author of _Physiological Disquisitions_; Mr. Spearman, [538] author of _Letters on the Septuagint_ and editor ofHutchinson; Mr. Barker, [539] author of _Reflexions on Learning_; Dr. Catcott, [540] author of a work on the creation, &c. ; Dr. Robertson, [541]author of a _Treatise on the Hebrew Language_; _Dr. Holloway_, [542] authorof _Originals, Physical and Theological_; Dr. Walter Hodges, [543] author ofa work on _Elohim_; Lord President Forbes (_ob. _ 1747). [544] The Rev. William Jones, above mentioned (1726-1800), the friend andbiographer of Bishop Horne and his stout {238} defender, is best known asWilliam Jones of Nayland, who (1757)[545] published the _Catholic Doctrineof the Trinity_; he was also strong for the Hutchinsonian physical trinityof fire, light, and spirit. This well-known work was generally recommended, as the defence of the orthodox system, to those who could not go into thelearning of the subject. There is now a work more suited to our time: _TheRock of Ages_, by the Rev. E. H. Bickersteth, [546] now published by theReligious Tract Society, without date, answered by the Rev. Dr. Sadler, [547] in a work (1859) entitled _Gloria Patri_, in which, says Mr. Bickersteth, "the author has not even attempted to grapple with my mainpropositions. " I have read largely on the controversy, and I think I knowwhat this means. Moreover, when I see the note "There are two otherpassages to which Unitarians sometimes refer, but the deduction they drawfrom them is, in each case, refuted by the context"--I think I see why thetwo texts are not named. Nevertheless, the author is a little more disposedto yield to criticism than his foregoers; he does not insist on texts andreadings which the greatest editors have rejected. And he writes withcourtesy, both direct and oblique, towards his antagonists; which, on hisside of this subject, is like letting in fresh air. So that I suspect thetwo books will together make a tolerably good introduction to the subjectfor those who cannot go deep. Mr. Bickersteth's book is well arranged andindexed, which is a point of superiority to Jones of Nayland. There is apoint which I should gravely recommend to writers on the orthodox side. TheUnitarians in {239} England have frequently contended that the method ofproving the divinity of Jesus Christ from the New Testament would equallyprove the divinity of Moses. I have not fallen in the way of any orthodoxanswers specially directed at the repeated tracts written by Unitarians inproof of their assertion. If there be any, they should be more known; ifthere be none, some should be written. Which ever side may be right, thetreatment of this point would be indeed coming to close quarters. Theheterodox assertion was first supported, it is said, by John Bidle orBiddle (1615-1662) of Magdalen College, Oxford, the earliest of the EnglishUnitarian writers, previously known by a translation of part of Virgil andpart of Juvenal. [548] But I cannot find that he wrote on it. [549] It is thesubject of "[Greek: haireseôn anastasis], or a new way of deciding oldcontroversies. By Basanistes. Third edition, enlarged, " London, 1815, 8vo. [550] It is the appendix to the amusing, "Six more letters to GranvilleSharp, Esq. , ... By Gregory Blunt, Esq. " London, 8vo. , 1803. [551] This muchI can confidently say, that the study of these tracts would preventorthodox writers from some curious slips, which are slips obvious to allsides of opinion. The lower defenders of orthodoxy frequently vex thespirits of the higher ones. Since writing the above I have procured Dr. Sadler's answer. I thought Iknew what the challenger meant when he said the respondent had not grappledwith his main {240} propositions. I should say that he is clung on to frombeginning to end. But perhaps Mr. B. Has his own meaning of logical terms, such as "proposition": he certainly has his own meaning of "cumulative. " Hesays his evidence is cumulative; not a catena, the strength of which is inits weakest part, but distinct and independent lines, each of whichcorroborates the other. This is the very opposite of _cumulative_: it is_distributive_. When different arguments are each necessary to aconclusion, the evidence is _cumulative_; when any one will do, even thoughthey strengthen each other, it is _distributive_. The word "cumulative" isa synonym of the law word "constructive"; a whole which will do made out ofparts which separately will not. Lord Strafford [552] opens his defencewith the use of both words: "They have invented a kind of _accumulated_ or_constructive_ evidence; by which many actions, either totally innocent inthemselves, or criminal in a much inferior degree, shall, when united, _amount_ to treason. " The conclusion is, that Mr. B. Is a Cambridge man;the Oxford men do not confuse the elementary terms of logic. O dear oldCambridge! when the New Zealander comes let him find among the relics ofyour later sons some proof of attention to the elementary laws of thought. A little-go of logic, please! Mr. B. , though apparently not a Hutchinsonian, has a nibble at a physicalTrinity. "If, as we gaze on the sun shining in the firmament, we see anyfaint adumbration of the doctrine of the Trinity in the fontal orb, thelight ever generated, and the heat proceeding from the sun and itsbeams--threefold and yet one, the sun, its light, and its {241} heat, --thatluminous globe, and the radiance ever flowing from it, are both evident tothe eye; but the vital warmth is felt, not seen, and is only manifested inthe life it transfuses through creation. The proof of its real existence isself-demonstrating. " We shall see how Revilo[553] illustrates orthodoxy by mathematics. It wasmy duty to have found one of the many illustrations from physics; butperhaps I should have forgotten it if this instance had not come in my way. It is very bad physics. The sun, apart from its light, evident to the eye!Heat more self-demonstrating than light, because _felt_! Heat onlymanifested by the life it diffuses! Light implied not necessary to life!But the theology is worse than Sabellianism[554]. To adumbrate--i. E. , makea picture of--the orthodox doctrine, the sun must be heavenly body, thelight heavenly body, the heat heavenly body; and yet, not three heavenlybodies, but one heavenly body. The truth is, that this illustration andmany others most strikingly illustrate the Trinity of fundamental doctrineheld by the Unitarians, in all its differences from the Trinity of personsheld by the Orthodox. Be right which may, the right or wrong of theUnitarians shines out in the comparison. Dr. Sadler confirms me--by which Imean that I wrote the above before I saw what he says--in the followingwords: "The sun is one object with two _properties_, and these propertieshave a parallel not in the second and third persons of the Trinity, but inthe attributes of Deity. " The letting light alone, as self-evident, and making heatself-demonstrating, because felt--i. E. , perceptible now and then--has thecharacter of the Irishman's astronomy: {242} "Long life to the moon, for a dear noble cratur, Which serves us for lamplight all night in the dark, While the sun only shines in the day, which by natur, Wants no light at all, as ye all may remark. " SIR RICHARD PHILLIPS. _Sir Richard Phillips_[555] (born 1768) was conspicuous in 1793, when hewas sentenced to a year's imprisonment[556] for selling Paine's _Rights ofMan_; and again when, in 1807[557], he was knighted as Sheriff of London. As a bookseller, he was able to enforce his opinions in more ways thanothers. For instance, in James Mitchell's[558] _Dictionary of theMathematical and Physical Sciences_, 1823, 12mo, which, though he was nottechnically a publisher, was printed for him--a book I should recommend tothe collector of works of reference--there is a temperate description ofhis doctrines, which one may almost swear was one of his conditionsprevious to undertaking the work. Phillips himself was not only ananti-Newtonian, but carried to a fearful excess the notion that statesmenand Newtonians were in league to deceive the world. He saw this plot inMrs. Airy's[559] pension, and in Mrs. Somerville's[560]. In 1836, he {243}did me the honor to attempt my conversion. In his first letter he says: "Sir Richard Phillips has an inveterate abhorrence of all the pretendedwisdom of philosophy derived from the monks and doctors of the middle ages, and not less of those of higher name who merely sought to make the monkishphilosophy more plausible, or so to disguise it as to mystify the mob ofsmall thinkers. " So little did his writings show any knowledge of antiquity, that I stronglysuspect, if required to name one of the monkish doctors, he would haveanswered--Aristotle. These schoolmen, and the "philosophical trinity ofgravitating force, projectile force, and void space, " were the bogies ofhis life. I think he began to publish speculations in the _Monthly Magazine_ (ofwhich he was editor) in July 1817: these he republished separately in 1818. In the Preface, perhaps judging the feelings of others by his own, he saysthat he "fully expects to be vilified, reviled, and anathematized, for manyyears to come. " Poor man! he was let alone. He appeals with confidence tothe "impartial decision of posterity"; but posterity does not appoint ahearing for one per cent. Of the appeals which are made; and it is much tobe feared that an article in such a work of reference as this will furnishnearly all her materials fifty years hence. The following, addressed to M. Arago, [561] in 1835, will give posterity as good a notion as she willprobably need: "Even the present year has afforded EVER-MEMORABLE examples, paralleledonly by that of the Romish Conclave which persecuted Galileo. Policy hasadopted that maxim of Machiavel which teaches that it is _more prudent_ to_reward_ {244} partisans than to _persecute_ opponents. Hence, a bigottedparty had influence enough with the late short-lived administration [Ithink he is wrong as to the administration] of Wellington, Peel, &c. , toconfer munificent royal pensions on three writers whose sole distinctionwas their advocacy of the Newtonian philosophy. A Cambridge professor lastyear published an elaborate volume in illustration of _Gravitation_, and onhim has been conferred a pension of 300l. Per annum. A lady has written alight popular view of the Newtonian Dogmas, and she has been complimentedby a pension of 200l. Per annum. And another writer, who has recentlypublished a volume to prove that the only true philosophy is that of Moses, has been endowed with a pension of 200l. Per annum. Neither of them wereneedy persons, and the political and ecclesiastical bearing of the wholewas indicated by another pension of 300l. Bestowed on a political writer, the advocate of all abuses and prejudices. Whether the conduct of theRomish Conclave was more base for visiting with legal penalties thepromulgation of the doctrines that the Earth turns on its axis and revolvesaround the Sun; or that of the British Court, for its craft in conferringpensions on the opponents of the plain corollary, that all the motions ofthe Earth are 'part and parcel' of these great motions, and those again andall like them consecutive displays of still greater motions in equality ofaction and reaction, is A QUESTION which must be reserved for the casuistsof other generations.... I cannot expect that on a sudden you and yourfriends will come to my conclusion, that the present philosophy of theSchools and Universities of Europe, based on faith in witchcraft, magic, &c. , is a system of execrable nonsense, _by which quacks live on the faithof fools_; but I desire a free and fair examination of my Aphorisms, and ifa few are admitted to be true, merely as courteous concessions toarithmetic, my purpose will be effected, for men will thus be led to think;and if they think, then the fabric {245} of false assumptions, anddegrading superstitions will soon tumble in ruins. " This for posterity. For the present time I ground the fame of Sir R. Phillips on his having squared the circle without knowing it, or intendingto do it. In the _Protest_ presently noted he discovered that "the forcetaken as 1 is equal to the sum of all its fractions ... Thus 1 = 1/4 + 1/9+ 1/16 + 1/25, &c. , carried to infinity. " This the mathematician instantlysees is equivalent to the theorem that the circumference of any circle isdouble of the diagonal of the cube on its diameter. [562] I have examined the following works of Sir R. Phillips, and heard of manyothers: Essays on the proximate mechanical causes of the general phenomena of the Universe, 1818, 12mo. [563] Protest against the prevailing principles of natural philosophy, with the development of a common sense system (no date, 8vo, pp. 16). [564] Four dialogues between an Oxford Tutor and a disciple of the common-sense philosophy, relative to the proximate causes of material phenomena. 8vo, 1824. A century of original aphorisms on the proximate causes of the phenomena of nature, 1835, 12mo. Sir Richard Phillips had four valuable qualities; honesty, zeal, ability, and courage. He applied them all to teaching {246} matters about which heknew nothing; and gained himself an uncomfortable life and a ridiculousmemory. Astronomy made plain; or only way the true perpendicular distance of the Sun, Moon, or Stars, from this earth, can be obtained. By Wm. Wood. [565] Chatham, 1819, 12mo. If this theory be true, it will follow, of course, that this earth is theonly one God made, and that it does not whirl round the sun, but _viceversa_, the sun round it. WHATELY'S FAMOUS PARADOX. Historic doubts relative to Napoleon Buonaparte. London, 1819, 8vo. This tract has since been acknowledged by Archbishop Whately[566] andreprinted. It is certainly a paradox: but differs from most of those in mylist as being a joke, and a satire upon the reasoning of those who cannotreceive narrative, no matter what the evidence, which is to them utterlyimprobable _a priori_. But had it been serious earnest, it would not havebeen so absurd as many of those which I have brought forward. The next onthe list is not a joke. The idea of the satire is not new. Dr. King, [567] in the dispute on thegenuineness of Phalaris, proved with humor that Bentley did not write hisown dissertation. An attempt has lately been made, for the honor of Moses, to prove, {247} without humor, that Bishop Colenso did not write his ownbook. This is intolerable: anybody who tries to use such a weapon withoutbanter, plenty and good, and of form suited to the subject, should get thedrubbing which the poor man got in the Oriental tale for striking thedervishes with the wrong hand. The excellent and distinguished author of this tract has ceased to live. Icall him the Paley of our day: with more learning and more purpose than hispredecessor; but perhaps they might have changed places if they had changedcenturies. The clever satire above named is not the only work which hepublished without his name. The following was attributed to him, I believerightly: "Considerations on the Law of Libel, as relating to Publicationson the subject of Religion, by John Search. " London, 1833, 8vo. This tractexcited little attention: for those who should have answered, could not. Moreover, it wanted a prosecution to call attention to it: the fear ofcalling such attention may have prevented prosecutions. Those who have readit will have seen why. The theological review elsewhere mentioned attributes the pamphlet of JohnSearch on blasphemous libel to Lord Brougham. This is quite absurd: thewriter states points of law on credence where the judge must have spokenwith authority. Besides which, a hundred points of style are decisivebetween the two. I think any one who knows Whately's writing will soonarrive at my conclusion. Lord Brougham himself informs me that he has noknowledge whatever of the pamphlet. It is stated in _Notes and Queries_ (3 S. Xi. 511) that Search was answeredby the Bishop of Ferns[568] as S. N. , with {248} a rejoinder by BlancoWhite. [569] These circumstances increase the probability that Whately waswritten against and for. VOLTAIRE A CHRISTIAN. Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820, 12mo. If Voltaire have not succeeded in proving himself a strong theist and astrong anti-revelationist, who is to succeed in proving himself one thingor the other in any matter whatsoever? By occasional confusion betweentheism and Christianity; by taking advantage of the formal phrases ofadhesion to the Roman Church, which very often occur, and are often thehappiest bits of irony in an ironical production; by citations of hismorality, which is decidedly Christian, though often attributed toBrahmins; and so on--the author makes a fair case for his paradox, in theeyes of those who know no more than he tells them. If he had said thatVoltaire was a better Christian than himself knew of, towards all mankindexcept men of letters, I for one should have agreed with him. _Christian!_ the word has degenerated into a synonym of _man_, in what arecalled Christian countries. So we have the parrot who "swore for all theworld like a Christian, " and the two dogs who "hated each other just likeChristians. " When the Irish duellist of the last century, whose name may bespared in consideration of its historic fame {249} and the worthy peoplewho bear it, was (June 12, 1786) about to take the consequence of his lastbrutal murder, the rope broke, and the criminal got up, and exclaimed, "By---- Mr. Sheriff, you ought to be ashamed of yourself! this rope is notstrong enough to hang a dog, far less a Christian!" But such things as thisare far from the worst depravations. As to a word so defiled by usage, itis well to know that there is a way of escape from it, without renouncingthe New Testament. I suppose any one may assume for himself what I havesometimes heard contended for, that no New Testament word is to be used inreligion in any sense except that of the New Testament. This granted, thequestion is settled. The word _Christian_, which occurs three times, isnever recognized as anything but a term of contempt from those without thepale to those within. Thus, Herod Agrippa, who was deep in Jewishliterature, and a correspondent of Josephus, says to Paul (Acts xxvi. 28), "Almost thou persuadest me to be (what I and other followers of the statereligion despise under the name) a Christian. " Again (Acts xi. 26), "Thedisciples (as they called _themselves_) were called (by the surroundingheathens) Christians first in Antioch. " Thirdly (1 Peter iv. 16), "Let noneof you suffer as a _murderer_.... But if as a _Christian_ (as the heathencall it by whom the suffering comes), let him not be ashamed. " That is tosay, no _disciple_ ever called _himself_ a Christian, or applied the name, as from himself, to another disciple, from one end of the New Testament tothe other; and no disciple need apply that name to himself in our day, ifhe dislike the associations with which the conduct of Christians hasclothed it. WRONSKI ON THE LONGITUDE PROBLEM. Address of M. Hoene Wronski to the British Board of Longitude, upon the actual state of the mathematics, their reform, {250} and upon the new celestial mechanics, giving the definitive solution of the problem of longitude. [570] London, 1820, 8vo. M. Wronski[571] was the author of seven quartos on mathematics, showingvery great power of generalization. He was also deep in the transcendentalphilosophy, [572] and had the Absolute at his fingers' ends. All thisknowledge was rendered useless by a persuasion that he had greatly advancedbeyond the whole world, with many hints that the Absolute would not beforthcoming, unless prepaid. He was a man of the widest extremes. At onetime he desired people to see all possible mathematics in F_x_ = A_{0}[Omega]_{0} + A_{1}[Omega]_{1} + A_{2}[Omega]_{2} + A_{3}[Omega]_{3} + &c. which he did not explain, though there is meaning to it in the quartos. Atanother time he was proposing the general solution of the[573] fifth degreeby help of 625 independent equations of one form and 125 of another. Thefirst separate memoir from any Transactions that I ever possessed was givento me when at Cambridge; the refutation (1819) of this asserted solution, presented to the Academy of Lisbon by Evangelista Torriano. I cannot say Iread it. The tract above is an attack on modern mathematicians in general, and on the Board of Longitude, and Dr. Young. [574] {251} DR. MILNER'S PARADOXES. 1820. In this year died Dr. Isaac Milner, [575] President of Queens'College, Cambridge, one of the class of rational paradoxers. Under thisname I include all who, in private life, and in matters which concernthemselves, take their own course, and suit their own notions, no matterwhat other people may think of them. These men will put things to uses theywere never intended for, to the great distress and disgust of theirgregarious friends. I am one of the class, and I could write a little bookof cases in which I have incurred absolute reproach for not "doing as otherpeople do. " I will name two of my atrocities: I took one of thosebutter-dishes which have for a top a dome with holes in it, which is turnedinward, out of reach of accident, when not in use. Turning the domeinwards, I filled the dish with water, and put a sponge in the dome: theholes let it fill with water, and I had a penwiper, always moist, and worthits price five times over. "Why! what do you mean? It was made to holdbutter. You are always at some queer thing or other!" I bought a leadencomb, intended to dye the hair, it being supposed that the application oflead will have this effect. I did not try: but I divided the comb into two, separated the part of closed prongs from the other; and thus I had tworuling machines. The lead marks paper, and by drawing the end of one of themachines along a ruler, I could rule twenty lines at a time, quite fit towrite on. I thought I should have killed a friend to whom I explained it:he could not for the life of him understand how leaden _lines_ on paperwould dye the hair. But Dr. Milner went beyond me. He wanted a seat suited to his shape, and hedefied opinion to a fearful point. {252} He spread a thick block of puttyover a wooden chair and sat in it until it had taken a ceroplast copy ofthe proper seat. This he gave to a carpenter to be imitated in wood. One ofthe few now living who knew him--my friend, General PerronetThompson[576]--answers for the wood, which was shown him by Milner himself;but he does not vouch for the material being putty, which was in the storytold me at Cambridge; William Frend[577] also remembered it. Perhaps theDoctor took off his great seal in green wax, like the Crown; but some softmaterial he certainly adopted; and very comfortable he found the woodencopy. [Illustration] The same gentleman vouches for Milner's lamp: but this had visible_science_ in it; the vulgar see no science in the construction of thechair. A hollow semi-cylinder, but not with a circular curve, revolved onpivots. The curve was calculated on the law that, whatever quantity of oilmight be in the lamp, the position of equilibrium just brought the oil upto the edge of the cylinder, at which a bit of wick was placed. As the wickexhausted the oil, the cylinder slowly revolved about the pivots so as tokeep the oil always touching the wick. Great discoveries are always laughed at; but it is very often not the laughof incredulity; it is a mode of distorting the sense of inferiority into asense of superiority, or a mimicry of superiority interposed between thelaugher and his feeling of inferiority. Two persons in conversation {253}agreed that it was often a nuisance not to be able to lay hands on a bit ofpaper to mark the place in a book, every bit of paper on the table was sureto contain something not to be spared. I very quietly said that I alwayshad a stock of bookmarkers ready cut, with a proper place for them: myreaders owe many of my anecdotes to this absurd practice. My twocolloquials burst into a fit of laughter; about what? Incredulity was outof the question; and there could be nothing foolish in my taking measuresto avoid what they knew was an inconvenience. I was in this matterobviously their superior, and so they laughed at me. Much more candid wasthe Royal Duke of the last century, who was noted for slow ideas. "The raincomes into my mouth, " said he, while riding. "Had not your Royal Highnessbetter shut your mouth?" said the equerry. The Prince did so, and ought, byrule, to have laughed heartily at his adviser; instead of this, he saidquietly, "It doesn't come in now. " HERBART'S MATHEMATICAL PSYCHOLOGY. De Attentionis mensura causisque primariis. By J. F. Herbart. [578] Koenigsberg, 1822, 4to. {254} This celebrated philosopher maintained that mathematics ought to be appliedto psychology, in a separate tract, published also in 1822: the one aboveseems, therefore, to be his challenge on the subject. It is on _attention_, and I think it will hardly support Herbart's thesis. As a specimen of hisformula, let _t_ be the time elapsed since the consideration began, [beta]the whole perceptive intensity of the individual, [phi] the whole of hismental force, and _z_ the force given to a notion by attention during thetime _t_. Then, z = [phi] (1 - [epsilon]^{-[beta]t}) Now for a test. There is a _jactura_, _v_, the meaning of which I do notcomprehend. If there be anything in it, my mathematical readers ought tointerpret it from the formula _v_ = [pi][phi][beta]/(1 - [beta])[epsilon]^{-[beta]t} + C[epsilon]^{-t} and to this task I leave them, wishing them better luck than mine. The timemay come when other manifestations of mind, besides _belief_, shall besubmitted to calculation: at that time, should it arrive, a final decisionmay be passed upon Herbart. ON THE WHIZGIG. The theory of the Whizgig considered; in as much as it mechanically exemplifies the three working properties of nature; which are now set forth under the guise of this toy, for children of all ages. London, 1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden). The toy called the _whizgig_ will be remembered by many. The writer is afollower of Jacob Behmen, [579] William Law, [580] {255} Richard Clarke, [581]and Eugenius Philalethes. [582] Jacob Behmen first announced the threeworking properties of nature, which Newton stole, as described in the_Gentleman's Magazine_, July, 1782, p. 329. These laws are illustrated inthe whizgig. There is the harsh astringent, attractive compression; thebitter compunction, repulsive expansion; and the stinging anguish, duplexmotion. The author hints that he has written other works, to which he givesno clue. I have heard that Behmen was pillaged by Newton, andSwedenborg[583] by Laplace, [584] and Pythagoras by Copernicus, [585] andEpicurus by Dalton, [586] &c. I do not think this mention will reviveBehmen; but it may the whizgig, a very pretty toy, and philosophicalwithal, for few of those who used it could explain it. {256} SOME MYTHOLOGICAL PARADOXES. A Grammar of infinite forms; or the mathematical elements of ancient philosophy and mythology. By Wm. Howison. [587] Edinburgh, 1823, 8vo. A curius combination of geometry and mythology. Perseus, for instance, istreated under the head, "the evolution of diminishing hyperbolic branches. " The Mythological Astronomy of the Ancients; part the second: or the key of Urania, the words of which will unlock all the mysteries of antiquity. Norwich, 1823, 12mo. A Companion to the Mythological Astronomy, &c. , containing remarks on recent publications.... Norwich, 1824, 12mo. A new Theory of the Earth and of planetary motion; in which it is demonstrated that the Sun is vicegerent of his own system. Norwich, 1825, 12mo. The analyzation of the writings of the Jews, so far as they are found to have any connection with the sublime science of astronomy. [This is pp. 97-180 of some other work, being all I have seen. ] These works are all by Sampson Arnold Mackey, [588] for whom see _Notes andQueries_, 1st S. Viii. 468, 565, ix. 89, 179. Had it not been for actualquotations given by one correspondent only (1st S. Viii. 565), that journalwould have handed him down as a man of some real learning. An extraordinaryman he certainly was: it is not one illiterate shoemaker in a thousand whocould work upon such a singular mass of Sanskrit and Greek words, withoutshowing {257} evidence of being able to read a line in any language but hisown, or to spell that correctly. He was an uneducated Godfrey Higgins. [589]A few extracts will put this in a strong light: one for history of science, one for astronomy, and one for philology: "Sir Isaac Newton was of opinion that 'the atmosphere of the earth was thesensory of God; by which he was enabled to see quite round the earth:'which proves that Sir Isaac had no idea that God could see through theearth. "Sir Richard [Phillips] has given the most rational explanation of thecause of the earth's elliptical orbit that I have ever seen in print. It isbecause the earth presents its watery hemisphere to the sun at one time andthat of solid land the other; but why has he made his Oxonian astonished atthe coincidence? It is what I taught in my attic twelve years before. "Again, admitting that the Eloim were powerful and intelligent beings thatmanaged these things, we would accuse _them_ of being the authors of allthe sufferings of Chrisna. And as they and the constellation of Leo werebelow the horizon, and consequently cut off from the end of the zodiac, there were but eleven constellations of the zodiac to be seen; the three atthe end were wanted, but those three would be accused of bringing Chrisnainto the troubles which at last ended in his death. All this would beexpressed in the Eastern language by saying that Chrisna was persecuted bythose Judoth Ishcarioth!!!!! [the five notes of exclamation are theauthor's]. But the astronomy of those distant ages, when the sun was at thesouth pole in winter, would leave five of those Decans cut off from ourview, in the latitude of twenty-eight degrees; hence Chrisna died of {258}wounds from five Decans, but the whole five may be included in JudothIshcarioth! for the phrase means 'the men that are wanted at the extremeparts. ' Ishcarioth is a compound of _ish_, a man, and _carat_ wanted ortaken away, and oth the plural termination, more ancient than _im_.... " I might show at length how Michael is the sun, and the D'-ev-'l in FrenchDi-ob-al, also 'L-evi-ath-an--the evi being the radical part both ofd_evi_l and l_evi_athan--is the Nile, which the sun dried up for Moses topass: a battle celebrated by Jude. Also how _Moses_, the same name as_Muses_, is from _mesha_, drawn out of the water, "and hence we called ourland which is saved from the water by the name of _marsh_. " But it will beof more use to collect the character of S. A. M. From such correspondentsof _Notes and Queries_ as have written after superficial examination. Greatastronomical and philological attainments, much ability and learning; hadevidently read and studied deeply; remarkable for the originality of hisviews upon the very abstruse subject of mythological astronomy, in which heexhibited great sagacity. Certainly his views were _original_; but theirsagacity, if it be allowable to copy his own mode of etymologizing, is ofan _ori-gin-ale_ cast, resembling that of a person who puts to his mouthliquors both distilled and fermented. A KANTESIAN JEWELER. Principles of the Kantesian, or transcendental philosophy. By Thomas Wirgman. [590] London, 1824, 8vo. Mr. Wirgman's mind was somewhat attuned to psychology; but he was crackyand vagarious. He had been a fashionable jeweler in St. James's Street, nodoubt the son or grandson of Wirgman at "the well-known toy-shop in {259}St. James's Street, " where Sam Johnson smartened himself with silverbuckles. (Boswell, _æt. _ 69). He would not have the ridiculous large onesin fashion; and he would give no more than a guinea a pair; such, saysBoswell, in Italics, were the _principles_ of the business: and I thinkthis may be the first place in which the philosophical word was broughtdown from heaven to mix with men. However this may be, _my_ Wirgman soldsnuff-boxes, among other things, and fifty years ago a fashionablesnuff-boxer would be under inducement, if not positively obliged, to have astock with very objectionable pictures. So it happened that Wirgman--byreason of a trifle too much candor--came under the notice of the_Suppression_ Society, and ran considerable risk. Mr. Brougham was hiscounsel; and managed to get him acquitted. Years and years after this, whenMr. Brougham was deep in the formation of the London University (nowUniversity College), Mr. Wirgman called on him. "What now?" said Mr. B. With his most sarcastic look--a very perfect thing of its kind--"you're ina scrape again, I suppose!" "No! indeed!" said W. , "my present object is toask your interest for the chair of Moral Philosophy in the new University!"He had taken up Kant! Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came toconvert me. "I assure you, " said he, "I am nothing but an old brute of ajeweler;" and his eye and manner were of the extreme of jocosity, as goodin their way, as the satire of his former counsel. I mention him as one ofthat class who go away quite satisfied that they have wrought conviction. "Now, " said he, "I'll make it clear to you! Suppose a number of gold-fishesin a glass bowl, --you understand? Well! I come with my cigar and go puff, puff, puff, over the bowl, until there is a little cloud of smoke: now, tell me, what will the gold-fishes say to that?" "I should imagine, " saidI, "That they would not know what to make of it. " "By Jove! you're aKantian;" said he, and with this and the like, he left me, vowing that{260} it was delightful to talk to so intelligent a person. The greatestcompliment Wirgman ever received was from James Mill, who used to say hedid not _understand_ Kant. That such a man as Mill should think this worthsaying is a feather in the cap of the jocose jeweler. Some of my readers will stare at my supposing that Boswell may have beenthe first down-bringer of the word _principles_ into common life; the bestanswer will be a prior instance of the word as true vernacular; it hasnever happened to me to notice one. Many words have very common uses whichare not old. Take the following from Nichols (_Anecd. _ ix. 263): "LordThurlow presents his best respects to Mr. And Mrs. Thicknesse, and assuresthem that he knows of no cause to complain of any part of Mr. Thicknesse'scarriage; least of all the circumstance of sending the head to OrmondStreet. " Surely Mr. T. Had lent Lord T. A satisfactory carriage with amovable head, and the above is a polite answer to inquiries. Not a bit ofit! _carriage_ is here _conduct_, and the _head_ is a _bust_. The vehiclesof the rich, at the time, were coaches, chariots, chaises, etc. , nevercarriages, which were rather _carts_. Gibbon has the word forbaggage-wagons. In Jane Austen's novels the word carriage is established. WALSH'S DELUSIONS. _John Walsh_, [591] of Cork (1786-1847). This discoverer has had the honorof a biography from Professor Boole, who, at my request, collectedinformation about him on the scene of his labors. It is in the_Philosophical Magazine_ for November, 1851, and will, I hope, betransferred to some biographical collection where it may find a largerclass of readers. It is the best biography of a single hero of the kindthat I know. Mr. Walsh introduced himself to me, {261} as he did to manyothers, in the anterowlandian days of the Post-office; his unpaid letterswere double, treble, &c. They contained his pamphlets, and cost theirweight in silver: all have the name of the author, and all are in octavo orin quarto letter-form: most are in four pages, and all dated from Cork. Ihave the following by me: The Geometric Base, 1825. --The theory of plane angles. 1827. --Three Letters to Dr. Francis Sadleir. 1838. --The invention of polar geometry. By Irelandus. 1839. --The theory of partial functions. Letter to Lord Brougham. 1839. --On the invention of polar geometry. 1839. --Letter to the Editor of the Edinburgh Review. 1840. --Irish Manufacture. A new method of tangents. 1841. --The normal diameter in curves. 1843. --Letter to Sir R. Peel. 1845. --[Hints that Government should compel the introduction of Walsh's Geometry into Universities. ]--Solution of Equations of the higher orders. 1845. Besides these, there is a _Metalogia_, and I know not how many others. Mr. Boole, [592] who has taken the moral and social features of Walsh'sdelusions from the commiserating point of view, which makes ridicule out ofplace, has been obliged to treat Walsh as Scott's Alan Fairford treated hisclient Peter Peebles; namely, keep the scarecrow out of court while thecase was argued. My plan requires me to bring him in: and when he comes inat the door, pity and sympathy fly out at the window. Let the readerremember that he was not an ignoramus in mathematics: he might have won hisspurs if he could have first served as an esquire. Though so illiteratethat even in Ireland he never picked up anything more Latin than_Irelandus_, he was a very pretty mathematician spoiled in the making byintense self-opinion. This is part of a private letter to me at the back of a page of print: Ihad never addressed a word to him: {262} "There are no limits in mathematics, and those that assert there are, areinfinite ruffians, ignorant, lying blackguards. There is no differentialcalculus, no Taylor's theorem, no calculus of variations, &c. Inmathematics. There is no quackery whatever in mathematics; no % equal toanything. What sheer ignorant blackguardism that! "In mechanics the parallelogram of forces is quackery, and is dangerous;for nothing is at rest, or in uniform, or in rectilinear motion, in theuniverse. Variable motion is an essential property of matter. Laplace'sdemonstration of the parallelogram of forces is a begging of the question;and the attempts of them all to show that the difference of twenty minutesbetween the sidereal and actual revolution of the earth round the sunarises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfectquackery. The said difference arising from and demonstrating the revolutionof the Sun itself round some distant center. " In the letter to Lord Brougham we read as follows: "I ask the Royal Society of London, I ask the Saxon crew of that crazyhulk, where is the dogma of their philosophic god now?... When the RoyalSociety of London, and the Academy of Sciences of Paris, shall have readthis memorandum, how will they appear? Like two cur dogs in the paws of thenoblest beast of the forest.... Just as this note was going to press, avolume lately published by you was put into my hands, wherein you attemptto defend the fluxions and _Principia_ of Newton. Man! what are you about?You come forward now with your special pleading, and fraught with nationalprejudice, to defend, like the philosopher Grassi, [593] the persecutor ofGalileo, principles {263} and reasoning which, unless you are actuallyinsane, or an ignorant quack in mathematics, you know are mathematicallyfalse. What a moral lesson this for the students of the University ofLondon from its head! Man! demonstrate corollary 3, in this note, by thelying dogma of Newton, or turn your thoughts to something you understand. "WALSH IRELANDUS. " Mr. Walsh--honor to his memory--once had the consideration to save mepostage by addressing a pamphlet under cover to a Member of Parliament, with an explanatory letter. In that letter he gives a candid opinion ofhimself: (1838. ) "Mr. Walsh takes leave to send the enclosed corrected copy to Mr. Hutton as one of the Council of the University of London, and to savepostage for the Professor of Mathematics there. He will find in it geometrymore deep and subtle, and at the same time more simple and elegant, than itwas ever contemplated human genius could invent. " He then proceeds to set forth that a certain "tomfoolery lemma, " with its"tomfoolery" superstructure, "never had existence outside the shallowbrains of its inventor, " Euclid. He then proceeds thus: "The same spirit that animated those philosophers who sent Galileo to theInquisition animates all the philosophers of the present day withoutexception. If anything can free them from the yoke of error, it is the[Walsh] problem of double tangence. But free them it will, how deeplysoever they may be sunk into mental slavery--and God knows that is deeplyenough; and they bear it with an admirable grace; for none bear slaverywith a better grace than tyrants. The lads must adopt my theory.... It willbe a sad reverse for all our great professors to be compelled to becomeschoolboys in their gray years. But the sore scratch is to be compelled, asthey had before been compelled one thousand years ago, to have recourse toIreland for instruction. " {264} The following "Impromptu" is no doubt by Walsh himself: he was more of apoet than of an astronomer: "Through ages unfriended, With sophistry blended, Deep science in Chaos had slept; Its limits were fettered, Its voters unlettered, Its students in movements but crept. Till, despite of great foes, Great WALSH first arose, And with logical might did unravel Those mazes of knowledge, Ne'er known in a college, Though sought for with unceasing travail. With cheers we now hail him, May success never fail him, In Polar Geometrical mining; Till his foes be as tamed As his works are far-famed For true philosophic refining. " Walsh's system is, that all mathematics and physics are wrong: there ishardly one proposition in Euclid which is demonstrated. His example oughtto warn all who rely on their own evidence to their own success. He wasnot, properly speaking, insane; he only spoke his mind more freely thanmany others of his class. The poor fellow died in the Cork union, duringthe famine. He had lived a happy life, contemplating his own perfections, like Brahma on the lotus-leaf. [594] {265} GROWTH OF FREEDOM OF OPINION. The year 1825 brings me to about the middle of my _Athenæum_ list: that is, so far as mere number of names mentioned is concerned. Freedom of opinion, beyond a doubt, is gaining ground, for good or for evil, according to whatthe speaker happens to think: admission of authority is no longer made inthe old way. If we take soul-cure and body-cure, divinity and medicine, itis manifest that a change has come over us. Time was when it was enoughthat dose or dogma should be certified by "Il a été ordonné, Monsieur, il aété ordonné, "[595] as the apothecary said when he wanted to operate uponpoor de Porceaugnac. Very much changed: but whether for good or for evildoes not now matter; the question is, whether contempt of _demonstration_such as our paradoxers show has augmented with the rejection of _dogmaticauthority_. It ought to be just the other way: for the worship of reason isthe system on which, if we trust them, the deniers of guidance ground theirplan of life. The following attempt at an experiment on this point is thebest which I can make; and, so far as I know, the first that ever was made. Say that my list of paradoxers divides in 1825: this of itself provesnothing, because so many of the earlier books are lost, or not likely to become at. It would be a fearful rate of increase which would make the numberof paradoxes since 1825 equal to the whole number before that date. Let usturn now to another collection of mine, arithmetical books, of which I havepublished a list. The two collections are similarly circumstanced as to newand old books; the paradoxes had no care given to the collection of either;the arithmetical books equal care to both. The list of arithmetical books, published in 1847, divides at 1735; the paradoxes, up to 1863, divide at1825. If we take the process which is most against the distinction, andallow every year {266} from 1847 to 1863 to add a year to 1735, we shouldsay that the arithmetical writers divide at 1751. This rough process mayserve, with sufficient certainty, to show that the proportion of paradoxesto books of sober demonstration is on the increase; and probably, quite asmuch as the proportion of heterodoxes to books of orthodox adherence. Sothat divinity and medicine may say to geometry, Don't _you_ sneer: ifrationalism, homoeopathy, and their congeners are on the rise among us, your enemies are increasing quite as fast. But geometry replies--Dearfriends, content yourselves with the rational inference that the rise ofheterodoxy within your pales is not conclusive against you, taken alone;for it rises at the same time within mine. Store within your garners theprecious argument that you are not proved wrong by increase of dissent;because there is increase of dissent against exact science. But do nottherefore _even_ yourselves to me: remember that you, Dame Divinity, haveinflicted every kind of penalty, from the stake to the stocks, in aid ofyour reasoning; remember that you, Mother Medicine, have not many years agoapplied to Parliament for increase of forcible hindrance ofantipharmacopoeal drenches, pills, and powders. Who ever heard of my askingthe legislature to fine blundering circle-squarers? Remember that the D indogma is the D in decay; but the D in demonstration is the D in durability. THE STATUS OF MEDICINE. I have known a medical man--a young one--who was seriously of the opinionthat the country ought to be divided into medical parishes, with apractitioner appointed to each, and a penalty for calling in any but theincumbent curer. How should people know how to choose? The hair-dressersonce petitioned Parliament for an act to compel people to wear wigs. My ownopinion is of the opposite extreme, as in the following letter (_Examiner_, April 5, 1856); which, to my surprise, I saw reprinted in a medicaljournal, as a {267} plan not absolutely to be rejected. I am perfectlysatisfied that it would greatly promote true medical orthodoxy, thepredominance of well educated thinkers, and the development of theirdesirable differences. "SIR. The Medical Bill and the medical question generally is one on whichexperience would teach, if people would be taught. "The great soul question took three hundred years to settle: the littlebody question might be settled in thirty years, if the decisions in theformer question were studied. "Time was when the State believed, as honestly as ever it believedanything, that it _might_, _could_, and _should_ find out the true doctrinefor the poor ignorant community; to which, like a worthy honest state, itadded _would_. Accordingly, by the assistance of the Church, whichundertook the physic, the surgery, and the pharmacy of sound doctrine allby itself, it sent forth its legally qualified teachers into every parish, and woe to the man who called in any other. They burnt that man, theywhipped him, they imprisoned him, they did everything but what wasChristian to him, all for his soul's health and the amendment of hisexcesses. "But men would not submit. To the argument that the State was a father tothe ignorant, they replied that it was at best the ignorant father of anignorant son, and that a blind man could find his way into a ditch withoutanother blind man to help him. And when the State said--But here we havethe Church, which knows all about it, the ignorant community declared thatit had a right to judge that question, and that it would judge it. It alsosaid that the Church was never one thing long, and that it progressed, onthe whole, rather more slowly than the ignorant community. "The end of it was, in this country, that every one who chose taught allwho chose to let him teach, on condition only of an open and trueregistration. The State was {268} allowed to patronize one particularChurch, so that no one need trouble himself to choose a pastor from themere necessity of choosing. But every church is allowed its colleges, itsstudies, its diplomas; and every man is allowed his choice. There is noproof that our souls are worse off than in the sixteenth century; and, judging by fruits, there is much reason to hope they are better off. "Now the little body question is a perfect parallel to the great soulquestion in all its circumstances. The only things in which the parallelfails are the following: Every one who believes in a future state sees thatthe soul question is incomparably more important than the body question, and every one can try the body question by experiment to a larger extentthan the soul question. The proverb, which always has a spark of truth atthe bottom, says that every man of forty is either a fool or a physician;but did even the proverb maker ever dare to say that every man is at anyage either a fool or a fit teacher of religion? "Common sense points out the following settlement of the medical question:and to this it will come sooner or later. "Let every man who chooses--subject to one common law of manslaughter forall the _crass_ cases--doctor the bodies of all who choose to trust him, and recover payment according to agreement in the courts of law. Providedalways that every person practising should be registered at a moderate feein a register to be republished every six months. "Let the register give the name, address, and asserted qualification ofeach candidate--as licentiate, or doctor, or what not, of this or thatcollege, hall, university, &c. , home or foreign. Let it be competent to anyman to describe himself as qualified by study in public schools without adiploma, or by private study, or even by intuition or divine inspiration, if he please. But whatever he holds his qualification to be, that let himdeclare. Let all qualification {269} which of its own nature admits ofproof be proved, as by the diploma or certificate, &c. , leaving thingswhich cannot be proved, as asserted private study, intuition, inspiration, &c. , to work their own way. "Let it be highly penal to assert to the patient any qualification which isnot in the register, and let the register be sold very cheap. Let theregistrar give each registered practitioner a copy of the register in hisown case; let any patient have the power to demand a sight of this copy;and let no money for attendance be recoverable in any case in which therehas been false representation. "Let any party in any suit have a right to produce what medical testimonyhe pleases. Let the medical witness produce his register, and let hisevidence be for the jury, as is that of an engineer or a practitioner ofany art which is not attested by diplomas. "Let any man who practises without venturing to put his name on theregister be liable to fine and imprisonment. "The consequence would be that, as now, anybody who pleases might practise;for the medical world is well aware that there is no power of preventingwhat they call quacks from practising. But very different from what is now, every man who practises would be obliged to tell the whole world what hisclaim is, and would run a great risk if he dared to tell his patient inprivate anything different from what he had told the whole world. "The consequence would be that a real education in anatomy, physiology, chemistry, surgery, and what is known of the thing called medicine, wouldacquire more importance than it now has. "It is curious to see how completely the medical man of the nineteenthcentury squares with the priest of the sixteenth century. The clergy of allsects are now better divines and better men than they ever were. They havelost Bacon's reproach that they took a smaller measure of things than anyother educated men; and the physicians are now {270} in this particular therearguard of the learned world; though it may be true that the rear in ourday is further on in the march than the van of Bacon's day. Nor will theyever recover the lost position until medicine is as free as religion. "To this it must come. To this the public, which will decide for itself, has determined it shall come. To this the public has, in fact, brought it, but on a plan which it is not desirable to make permanent. We will be asfree to take care of our bodies as of our souls and of our goods. This isthe profession of all who sign as I do, and the practice of most of thosewho would not like the name "HETEROPATH. " The motion of the Sun in the Ecliptic, proved to be uniform in a circular orbit ... With preliminary observations on the fallacy of the Solar System. By Bartholomew Prescott, [596] 1825, 8vo. The author had published, in 1803, a _Defence of the Divine System_, whichI never saw; also, _On the inverted scheme of Copernicus_. The above workis clever in its satire. THE CHRISTIAN EVIDENCE SOCIETY. Manifesto of the Christian Evidence Society, established Nov. 12, 1824. Twenty-four plain questions to honest men. These are two broadsides of August and November, 1826, signed by RobertTaylor, [597] A. B. , Orator of the Christian Evidence Society. This gentlemanwas a clergyman, {271} and was convicted of blasphemy in 1827, for which hesuffered imprisonment, and got the name of the _Devil's Chaplain_. Thefollowing are quotations: "For the book of Revelation, there was no original Greek at all, but_Erasmus_ wrote it himself in Switzerland, in the year 1516. BishopMarsh, [598] vol. I. P. 320. "--"Is not God the author of your reason? Can hethen be the author of anything which is contrary to your reason? If reasonbe a sufficient guide, why should God give you any other? if it be not asufficient guide, why has he given you _that_?" I remember a votary of the Society being asked to substitute for _reason_"the right leg, " and for _guide_ "support, " and to answer the two lastquestions: he said there must be a quibble, but he did not see what. It ispleasant to reflect that the _argumentum à carcere_[599] is obsolete. Onegreat defect of it was that it did not go far enough: there should havebeen laws against subscriptions for blasphemers, against dealing at theirshops, and against rich widows marrying them. Had I taken in theology, I must have entered books against Christianity. Imention the above, and Paine's _Age of Reason_, simply because they are theonly English modern works that ever came in my way without my asking forthem. The three parts of the _Age of Reason_ were published in Paris 1793, Paris 1795, and New York 1807. Carlile's[600] edition is of London, 1818, 8vo. It must be republished when the time comes, to show what stuffgovernments and clergy were afraid of at the beginning of this century. Ishould never have seen the book, if it {272} had not been prohibited: abookseller put it under my nose with a fearful look round him; and I coulddo no less, in common curiosity, than buy a work which had been socomplimented by church and state. And when I had read it, I said in my mindto church and state, --Confound you! you have taken me in worse than anyreviewer I ever met with. I forget what I gave for the book, but I ought tohave been able to claim compensation somewhere. THE CABBALA. Cabbala Algebraica. Auctore Gul. Lud. Christmann. [601] Stuttgard, 1827, 4to. Eighty closely printed pages of an attempt to solve equations of everydegree, which has a process called by the author _cabbala_. An anonymouscorrespondent spells _cabbala_ as follows, [Greek: chabball], and makes 666out of its letters. This gentleman has sent me since my Budget commenced, alittle heap of satirical communications, each having a 666 or two; forinstance, alluding to my remarks on the spelling of _chemistry_, he findsthe fated number in [Greek: chimeia]. With these are challenges to explainthem, and hints about the end of the world. All these letters havedifferent fantastic seals; one of them with the legend "keep yourtemper, "--another bearing "bank token five pence. " The only signature is atriangle with a little circle in it, which I interpret to mean that thewriter confesses himself to be the round man stuck in the three-corneredhole, to be explained as in Sydney Smith's joke. {273} There is a kind of Cabbala Alphabetica which the investigators of thenumerals in words would do well to take up: it is the formation ofsentences which contain all the letters of the alphabet, and each onlyonce. No one has done it with _v_ and _j_ treated as consonants; but youand I can do it. Dr. Whewell[602] and I amused ourselves, some years ago, with attempts. He could not make sense, though he joined words: he gave me Phiz, styx, wrong, buck, flame, quid. I gave him the following, which he agreed was "admirable sense": Icertainly think the words would never have come together except in thisway: I, quartz pyx, who fling muck beds. I long thought that no human being could say this under any circumstances. At last I happened to be reading a religious writer--as he thoughthimself--who threw aspersions on his opponents thick and threefold. Heyday!came into my head, this fellow flings muck beds; he must be a quartz pyx. And then I remembered that a pyx is a sacred vessel, and quartz is a hardstone, as hard as the heart of a religious foe-curser. So that the line isthe motto of the ferocious sectarian, who turns his religious vessels intomudholders, for the benefit of those who will not see what he sees. I can find no circumstances for the following, which I received fromanother: Fritz! quick! land! hew gypsum box. From other quarters I have the following: Dumpy quiz! whirl back fogs next. This might be said in time of haze to the queer little figure in the Dutchweather-toy, which comes out or goes in with the change in the atmosphere. Again, {274} Export my fund! Quiz black whigs. This Squire Western might have said, who was always afraid of the whigssending the sinking-fund over to Hanover. But the following is the best: itis good advice to a young man, very well expressed under the circumstances: Get nymph; quiz sad brow; fix luck. Which in more sober English would be, Marry; be cheerful; watch yourbusiness. There is more edification, more religion in this than in all the666-interpretations put together. Such things would make excellent writing copies, for they secure attentionto every letter; _v_ and _j_ might be placed at the end. ON GODFREY HIGGINS. The Celtic Druids. By Godfrey Higgins, [603] Esq. Of Skellow Grange, near Doncaster. London, 1827, 4to. Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis: or an inquiry into the origin of languages, nations, and religions. By Godfrey Higgins, &c... , London, 1836, 2 vols. 4to. The first work had an additional preface and a new index in 1829. Possibly, in future time, will be found bound up with copies of the second work twosheets which Mr. Higgins circulated among his friends in 1831: the first a"Recapitulation, " the second "Book vi. Ch. 1. " The system of these works is that-- "The Buddhists of Upper India (of whom the Phenician Canaanite, Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c. Will be shown to have founded all the ancient mythologies of the world, which, however varied and corrupted in recent times, were originally one, and that one founded on principles sublime, beautiful, and true. " {275} These works contain an immense quantity of learning, very honestly puttogether. I presume the enormous number of facts, and the goodness of theindex, to be the reasons why the _Anacalypsis_ found a permanent place inthe _old_ reading-room of the British Museum, even before the change whichgreatly increased the number of books left free to the reader in that room. Mr. Higgins, whom I knew well in the last six years of his life, andrespected as a good, learned, and (in his own way) _pious_ man, wasthoroughly and completely the man of a system. He had that sort of mentalconnection with his theory that made his statements of his authoritiestrustworthy: for, besides perfect integrity, he had no bias towardsalteration of facts: he saw his system in the way the fact was presented tohim by his authority, be that what it might. He was very sure of a fact which he got from any of his authorities:nothing could shake him. Imagine a conversation between him and an Indianofficer who had paid long attention to Hindoo antiquities and theirremains: a third person was present, _ego qui scribo_. _G. H. _ "You knowthat in the temples of I-forget-who the Ceres is always sculpturedprecisely as in Greece. " _Col. _ ----, "I really do not remember it, and Ihave seen most of these temples. " _G. H. _ "It is so, I assure you, especially at I-forget-where. " _Col. _ ----, "Well, I am sure! I wasencamped for six weeks at the gate of that very temple, and, except alittle shooting, had nothing to do but to examine its details, which I did, day after day, and I found nothing of the kind. " It was of no use at all. Godfrey Higgins began life by exposing and conquering, at the expense oftwo years of his studies, some shocking abuses which existed in the YorkLunatic Asylum. This was a proceeding which called much attention to thetreatment of the insane, and produced much good effect. He was veryresolute and energetic. The magistracy of his {276} time had such scruplesabout using the severity of law to people of such station as well-to-dofarmers, &c. : they would allow a great deal of resistance, and endeavor tomollify the rebels into obedience. A young farmer flatly refused to payunder an order of affiliation made upon him by Godfrey Higgins. He was dulywarned; and persisted: he shortly found himself in gaol. He went there sureto conquer the Justice, and the first thing he did was to demand to see hislawyer. He was told, to his horror, that as soon as he had been cropped andprison-dressed, he might see as many lawyers as he pleased, to be lookedat, laughed at, and advised that there was but one way out of the scrape. Higgins was, in his speculations, a regular counterpart of Bailly; but thecelebrated Mayor of Paris had not his nerve. It was impossible to say, iftheir characters had been changed, whether the unfortunate crisis in whichBailly was not equal to the occasion would have led to very differentresults if Higgins had been in his place: but assuredly constitutionalliberty would have had one chance more. There are two works of his by whichhe was known, apart from his paradoxes. First, _An apology for the life andcharacter of the celebrated prophet of Arabia, called Mohamed, or theIllustrious_. London, 8vo. 1829. The reader will look at this writing ofour English Buddhist with suspicious eye, but he will not be able to avoidconfessing that the Arabian prophet has some reparation to demand at thehands of Christians. Next, _Horæ Sabaticæ; or an attempt to correct certainsuperstitions and vulgar errors respecting the Sabbath_. Second edition, with a large appendix. London, 12mo. 1833. This book was very heterodox atthe time, but it has furnished material for some of the clergy of our day. I never could quite make out whether Godfrey Higgins took that system whichhe traced to the Buddhists to have a Divine origin, or to be the result ofgood men's meditations. Himself a strong theist, and believer in a future{277} state, one would suppose that he would refer a _universal_ religion, spread in different forms over the whole earth from one source, directly tothe universal Parent. And this I suspect he did, whether he knew it or not. The external evidence is balanced. In his preface he says: "I cannot help smiling when I consider that the priests have objected toadmit my former book, _The Celtic Druids_, into libraries, because it wasantichristian; and it has been attacked by Deists, because it wassuperfluously religious. The learned Deist, the Rev. R. Taylor [alreadymentioned], has designated me as the _religious_ Mr. Higgins. " The time will come when some profound historian of literature will makehimself much clearer on the point than I am. ON POPE'S DIPPING NEEDLE. The triumphal Chariot of Friction: or a familiar elucidation of the origin of magnetic attraction, &c. &c. By William Pope. [604] London, 1829, 4to. Part of this work is on a dipping-needle of the author's construction. Itmust have been under the impression that a book of naval magnetism wasproposed, that a great many officers, the Royal Naval Club, etc. Lent theirnames to the subscription list. How must they have been surprised to find, right opposite to the list of subscribers, the plate presenting "the threeemphatic letters, J. A. O. " And how much more when they saw it set forththat if a square be inscribed in a circle, a circle within that, then asquare again, &c. , it is impossible to have more than fourteen circles, letthe first circle be as large as you please. From this the seven attributesof God are unfolded; and further, that all matter was _moral_, untilLucifer _churned_ it into _physical_ "as far as the third circle in Deity":this Lucifer, called Leviathan in Job, being thus the moving cause of {278}chaos. I shall say no more, except that the friction of the air is thecause of magnetism. Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a Key to the Inscriptions. By B. Prescot. [605] London, 1830, 8vo. Mr. Prescot gives the signs of the zodiac a Hebrew origin. THE JACOTOT METHOD. Epitomé de mathématiques. Par F. Jacotot, [606] Avocat. 3ième edition, Paris, 1830, 8vo. (pp. 18). Méthode Jacotot. Choix de propositions mathématiques. Par P. Y. Séprés. [607] 2nde édition. Paris, 1830, 8vo. (pp. 82). Of Jacotot's method, which had some vogue in Paris, the principle was _Toutest dans tout_, [608] and the process _Apprendre quelque chose, et à yrapporter tout le reste_. [609] The first tract has a proposition in conicsections and its preliminaries: the second has twenty exercises, of whichthe first is finding the greatest common measure of two numbers, and thelast is the motion of a point on a surface, acted on by given forces. Thisis topped up with the problem of sound in a tube, and a slice of Laplace'stheory of the tides. All to be studied until known by heart, and all therest will come, or at least join on easily when it comes. There is muchtruth in the assertion that new knowledge {279} hooks on easily to a littleof the old, thoroughly mastered. The day is coming when it will be foundout that crammed erudition, got up for examinations, does not cast out anyhooks for more. Lettre à MM. Les Membres de l'Académie Royale des Sciences, contenant un développement de la réfutation du système de la gravitation universelle, qui leur a été présentée le 30 août, 1830. Par Félix Passot. [610] Paris, 1830, 8vo. Works of this sort are less common in France than in England. In Francethere is only the Academy of Sciences to go to: in England there is areading public out of the Royal Society, &c. A DISCOURSE ON PROBABILITY. About 1830 was published, in the _Library of Useful Knowledge_, the tracton _Probability_, the joint work of the late Sir John Lubbock[611] and Mr. Drinkwater (Bethune). [612] It is one of the best elementary openings of thesubject. A binder put my name on the outside (the work was anonymous) andthe consequence was that nothing could drive out of people's heads that itwas written by me. I do not know how many denials I have made, from apassage in one of my own works to a letter in the _Times_: and I am notsure that I have succeeded in establishing the truth, even now. Iaccordingly note the fact once more. But as a book has no right here unlessit contain a paradox--or thing counter to general opinion or practice--Iwill produce two small ones. Sir John Lubbock, with whom lay the executivearrangement, had a strong objection to the last word in "Theory ofProbabilities, " he maintained that the singular _probability_, should beused; and I hold him quite right. {280} The second case was this: My friend Sir J. L. , with a large cluster ofintellectual qualities, and another of social qualities, had one point ofcharacter which I will not call bad and cannot call good; he never used aslang expression. To such a length did he carry his dislike, that he couldnot bear _head_ and _tail_, even in a work on games of chance: so he used_obverse_ and _reverse_. I stared when I first saw this: but, to mydelight, I found that the force of circumstances beat him at last. He wasobliged to take an example from the race-course, and the name of one of thehorses was _Bessy Bedlam_! And he did not put her down as _ElizabethBethlehem_, but forced himself to follow the jockeys. [Almanach Romain sur la Loterie Royale de France, ou les Etrennes nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M. Menut de St. -Mesmin. Paris, 1830. 12mo. This book contains all the drawings of the French lottery (two or three, each month) from 1758 to 1830. It is intended for those who thought theycould predict the future drawings from the past: and various sets of_sympathetic_ numbers are given to help them. The principle is, thatanything which has not happened for a long time must be soon to come. At_rouge et noir_, for example, when the red has won five times running, sagacious gamblers stake on the black, for they think the turn which mustcome at last is nearer than it was. So it is: but observation would haveshown that if a large number of those cases had been registered which showa run of five for the red, the next game would just as often have made therun into six as have turned in favor of the black. But the gamblingreasoner is incorrigible: if he would but take to squaring the circle, whata load of misery would be saved. A writer of 1823, who appeared to bethoroughly acquainted with the gambling of Paris and London, says that thegamesters by {281} profession are haunted by a secret foreboding of theirfuture destruction, and seem as if they said to the banker at the table, asthe gladiators said to the emperor, _Morituri te salutant_. [613] In the French lottery, five numbers out of ninety were drawn at a time. Anyperson, in any part of the country, might stake any sum upon any event hepleased, as that 27 should be drawn; that 42 and 81 should be drawn; that42 and 81 should be drawn, and 42 first; and so on up to a _quinedéterminé_, if he chose, which is betting on five given numbers in a givenorder. Thus, in July, 1821, one of the drawings was 8 46 16 64 13. A gambler had actually predicted the five numbers (but not their order), and won 131, 350 francs on a trifling stake. M. Menut seems to insinuatethat the hint what numbers to choose was given at his own office. Anotherwon 20, 852 francs on the quaterne, 8, 16, 46, 64, in this very drawing. These gains, of course, were widely advertised: of the multitudes who lostnothing was said. The enormous number of those who played is proved to allwho have studied chances arithmetically by the numbers of simple quaterneswhich were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in1825, nine, &c. The paradoxes of what is called chance, or hazard, might themselves make asmall volume. All the world understands that there is a long run, a generalaverage; but great part of the world is surprised that this general averageshould be computed and predicted. There are many remarkable cases ofverification; and one of them relates to the quadrature of the circle. Igive some account of this and another. Throw a penny time after time until_head_ arrives, which it will do before long: let this be called a _set_. Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. Forabbreviation, let a set in which seven _tails_ {282} occur before _head_turns up be T^{7}H. In an immense number of trials of sets, about half willbe H; about a quarter TH; about an eighth, T^{2}H. Buffon[614] tried 2, 048sets; and several have followed him. It will tend to illustrate theprinciple if I give all the results; namely, that many trials will withmoral certainty show an approach--and the greater the greater the number oftrials--to that average which sober reasoning predicts. In the first columnis the most likely number of the theory: the next column gives Buffon'sresult; the three next are results obtained from trial by correspondents ofmine. In each case the number of trials is 2, 048. H 1, 024 1, 061 1, 048 1, 017 1, 039 TH 512 494 507 547 480 T^{2}H 256 232 248 235 267 T^{3}H 128 137 99 118 126 T^{4}H 64 56 71 72 67 T^{5}H 32 29 38 32 33 T^{6}H 16 25 17 10 19 T^{7}H 8 8 9 9 10 T^{8}H 4 6 5 3 3 T^{9}H 2 3 2 4 T^{10}H 1 1 1 T^{11}H 0 1 T^{12}H 0 0 T^{13}H 1 1 0 T^{14}H 0 0 T^{15}H 1 1 &c. 0 0 ----- ----- ----- ----- ----- 2, 048 2, 048 2, 048 2, 048 2, 048 {283} In very many trials, then, we may depend upon something like the predictedaverage. Conversely, from many trials we may form a guess at what theaverage will be. Thus, in Buffon's experiment the 2, 048 first throws of thesets gave _head_ in 1, 061 cases: we have a right to infer that in the longrun something like 1, 061 out of 2, 048 is the proportion of heads, evenbefore we know the reasons for the equality of chance, which tell us that1, 024 out of 2, 048 is the real truth. I now come to the way in which suchconsiderations have led to a mode in which mere pitch-and-toss has given amore accurate approach to the quadrature of the circle than has beenreached by some of my paradoxers. What would my friend[615] in No. 14 havesaid to this? The method is as follows: Suppose a planked floor of theusual kind, with thin visible seams between the planks. Let there be a thinstraight rod, or wire, not so long as the breadth of the plank. This rod, being tossed up at hazard, will either fall quite clear of the seams, orwill lay across one seam. Now Buffon, and after him Laplace, proved thefollowing: That in the long run the fraction of the whole number of trialsin which a seam is intersected will be the fraction which twice the lengthof the rod is of the circumference of the circle having the breadth of aplank for its diameter. In 1855 Mr. _Ambrose_ Smith, of Aberdeen, made3, 204 trials with a rod three-fifths of the distance between the planks:there were 1, 213 clear intersections, and 11 contacts on which it wasdifficult to decide. Divide these contacts equally, and we have 1, 218½ to3, 204 for the ratio of 6 to 5[pi], presuming that the greatness of thenumber of trials gives something near to the final average, or result inthe long run: this gives [pi] = 3. 1553. If all the 11 contacts had beentreated as intersections, the result would have been {284} [pi] = 3. 1412, exceedingly near. A pupil of mine made 600 trials with a rod of the lengthbetween the seams, and got [pi] = 3. 137. This method will hardly be believed until it has been repeated so oftenthat "there never could have been any doubt about it. " The first experiment strongly illustrates a truth of the theory, wellconfirmed by practice: whatever can happen will happen if we make trialsenough. Who would undertake to throw tail eight times running?Nevertheless, in the 8, 192 sets tail 8 times running occurred 17 times; 9times running, 9 times; 10 times running, twice; 11 times and 13 times, each once; and 15 times twice. ] ON CURIOSITIES OF [pi]. 1830. The celebrated interminable fraction 3. 14159... , which themathematician calls [pi], is the ratio of the circumference to thediameter. But it is thousands of things besides. It is constantly turningup in mathematics: and if arithmetic and algebra had been studied withoutgeometry, [pi] must have come in somehow, though at what stage or underwhat name must have depended upon the casualties of algebraical invention. This will readily be seen when it is stated that [pi] is nothing but fourtimes the series 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... _ad infinitum_. [616] It would be wonderful if so simple a series {285} hadbut one kind of occurrence. As it is, our trigonometry being founded on thecircle, [pi] first appears as the ratio stated. If, for instance, a deepstudy of probable fluctuation from average had preceded, [pi] might haveemerged as a number perfectly indispensable in such problems as: What isthe chance of the number of aces lying between a million + x and a million- x, when six million of throws are made with a die? I have not gone intoany detail of all those cases in which the paradoxer finds out, by hisunassisted acumen, that results of mathematical investigation _cannot be_:in fact, this discovery is only an accompaniment, though a necessary one, of his paradoxical statement of that which _must be_. Logicians arebeginning to see that the notion of _horse_ is inseparably connected withthat of _non-horse_: that the first without the second would be no notionat all. And it is clear that the positive affirmation of that whichcontradicts mathematical demonstration cannot but be accompanied by adeclaration, mostly overtly made, that demonstration is false. If themathematician were interested in punishing this indiscretion, he could makehis denier ridiculous by inventing asserted results which would completelytake him in. More than thirty years ago I had a friend, now long gone, who was amathematician, but not of the higher branches: he was, _inter alia_, thoroughly up in all that relates to mortality, life assurance, &c. Oneday, explaining to him how it should be ascertained what the chance is ofthe survivors of a large number of persons now alive lying between givenlimits of number at the end of a certain time, I came, of course upon theintroduction of [pi], which I could only describe as the ratio of thecircumference of a circle to its diameter. "Oh, my dear friend! that mustbe a delusion; what can the circle have to do with the numbers alive at theend of a given time?"--"I cannot demonstrate it to you; but it isdemonstrated. "--"Oh! stuff! I think you can prove anything with yourdifferential calculus: figment, {286} depend upon it. " I said no more; but, a few days afterwards, I went to him and very gravely told him that I haddiscovered the law of human mortality in the Carlisle Table, of which hethought very highly. I told him that the law was involved in thiscircumstance. Take the table of expectation of life, choose any age, takeits expectation and make the nearest integer a new age, do the same withthat, and so on; begin at what age you like, you are sure to end at theplace where the age past is equal, or most nearly equal, to the expectationto come. "You don't mean that this always happens?"--"Try it. " He did try, again and again; and found it as I said. "This is, indeed, a curious thing;this _is_ a discovery. " I might have sent him about trumpeting the law oflife: but I contented myself with informing him that the same thing wouldhappen with any table whatsoever in which the first column goes up and thesecond goes down; and that if a proficient in the higher mathematics choseto palm a figment upon him, he could do without the circle: _à corsaire, corsaire et demi_, [617] the French proverb says. "Oh!" it was remarked, "Isee, this was Milne!"[618] It was _not_ Milne: I remember well showing theformula to him some time afterwards. He raised no difficulty about [pi]; heknew the forms of Laplace's results, and he was much interested. Besides, Milne never said stuff! and figment! And he would not have been taken in:he would have quietly tried it with the Northampton and all the othertables, and would have got at the truth. {287} EUCLID WITHOUT AXIOMS. The first book of Euclid's Elements. With alterations and familiar notes. Being an attempt to get rid of axioms altogether; and to establish the theory of parallel lines, without the introduction of any principle not common to other parts of the elements. By a member of the University of Cambridge. Third edition. In usum serenissimæ filiolæ. London, 1830. The author was Lieut. Col. (now General) Perronet Thompson, [619] the authorof the "Catechism on the Corn Laws. " I reviewed the fourth edition--whichhad the name of "Geometry without Axioms, " 1833--in the quarterly _Journalof Education_ for January, 1834. Col. Thompson, who then was a contributorto--if not editor of--the _Westminster Review_, replied in an article theauthorship of which could not be mistaken. Some more attempts upon the problem, by the same author, will be found inthe sequel. They are all of acute and legitimate speculation; but they donot conquer the difficulty in the manner demanded by the conditions of theproblem. The paradox of parallels does not contribute much to my pages: itscases are to be found for the most part in geometrical systems, or in notesto them. Most of them consist in the proposal of additional postulates;some are attempts to do without any new postulate. Gen. Perronet Thompson, whose paradoxes are always constructed on much study of previous writers, has collected in the work above named, a budget of attempts, the heads ofwhich are in the _Penny_ and _English Cyclopædias_, at "Parallels. " He hasgiven thirty instances, selected from what he had found. [620] {288} Lagrange, [621] in one of the later years of his life, imagined that he hadovercome the difficulty. He went so far as to write a paper, which he tookwith him to the Institute, and began to read it. But in the first paragraphsomething struck him which he had not observed: he muttered _Il faut quej'y songe encore_, [622] and put the paper in his pocket. THE LUNAR CAUSTIC JOKE. The following paragraph appeared in the _Morning Post_, May 4, 1831: "We understand that although, owing to circumstances with which the publicare not concerned, Mr. Goulburn[623] declined becoming a candidate forUniversity honors, that his scientific attainments are far frominconsiderable. He is well known to be the author of an essay in thePhilosophical Transactions on the accurate rectification of a circular arc, and of an investigation of the equation of a lunar caustic--a problemlikely to become of great use in nautical astronomy. " {289} This hoax--which would probably have succeeded with any journal--was palmedupon the _Morning Post_, which supported Mr. Goulburn, by some Cambridgewags who supported Mr. Lubbock, the other candidate for the University ofCambridge. Putting on the usual concealment, I may say that I alwayssuspected Dr-nkw-t-r B-th-n-[624] of having a share in the matter. Theskill of the hoax lies in avoiding the words "quadrature of the circle, "which all know, and speaking of "the accurate rectification of a circulararc, " which all do not know for its synonyme. The _Morning Post_ next daygave a reproof to hoaxers in general, without referring to any particularcase. It must be added, that although there are _caustics_ in mathematics, there is no _lunar_ caustic. So far as Mr. Goulburn was concerned, the above was poetic justice. He wasthe minister who, in old time, told a deputation from the AstronomicalSociety that the Government "did not care twopence for all the science inthe country. " There may be some still alive who remember this: I heard itfrom more than one of those who were present, and are now gone. Matters aremuch changed. I was thirty years in office at the Astronomical Society;and, to my certain knowledge, every Government of that period, Whig andTory, showed itself ready to help with influence when wanted, and withmoney whenever there was an answer for the House of Commons. The followingcorrection subsequently appeared. Referring to the hoax about Mr. Goulburn, Messrs. C. H. And Thompson Cooper[625] have corrected an error, by statingthat the election which gave rise to the hoax was that in which Messrs. Goulburn {290} and Yates Peel[626] defeated Lord Palmerston[627] and Mr. Cavendish. [628] They add that Mr. Gunning, the well-known Esquire Bedell ofthe University, attributed the hoax to the late Rev. R. Sheepshanks, towhom, they state, are also attributed certain clever fictitiousbiographies--of public men, as I understand it--which were palmed upon theeditor of the _Cambridge Chronicle_, who never suspected their genuinenessto the day of his death. Being in most confidential intercourse with Mr. Sheepshanks, [629] both at the time and all the rest of his life(twenty-five years), and never heard him allude to any such things--whichwere not in his line, though he had satirical power of quite another {291}kind--I feel satisfied he had nothing to do with them. I may add thatothers, his nearest friends, and also members of his family, never heardhim allude to these hoaxes as their author, and disbelieve his authorshipas much as I do myself. I say this not as imputing any blame to the trueauthor, such hoaxes being fair election jokes in all time, but merely toput the saddle off the wrong horse, and to give one more instance of theinsecurity of imputed authorship. Had Mr. Sheepshanks ever told me that hehad perpetrated the hoax, I should have had no hesitation in giving it tohim. I consider all clever election squibs, free from bitterness andpersonal imputation, as giving the multitude good channels for the vent offeelings which but for them would certainly find bad ones. [But I now suspect that Mr. Babbage[630] had some hand in the hoax. Hegives it in his "Passages, &c. " and is evidently writing from memory, forhe gives the wrong year. But he has given the paragraph, though notaccurately, yet with such a recollection of the points as brings suspicionof the authorship upon him, perhaps in conjunction with D. B. [631] Bothwere on Cavendish's committee. Mr. Babbage adds, that "late one evening acab drove up in hot haste to the office of the _Morning Post_, deliveredthe copy as coming from Mr. Goulburn's committee, and at the same timeordered fifty extra copies of the _Post_ to be sent next morning to theircommittee-room. " I think the man--the only one I ever heard of--who knewall about the cab and the extra copies must have known more. ] ON M. DEMONVILLE. _Demonville. _--A Frenchman's Christian name is his own secret, unless therebe two of the surname. M. Demonville is a very good instance of thedifference between a {292} French and English discoverer. In England thereis a public to listen to discoveries in mathematical subjects made withoutmathematics: a public which will hear, and wonder, and think it possiblethat the pretensions of the discoverer have some foundation. The unnoticedman may possibly be right: and the old country-town reputation which I onceheard of, attaching to a man who "had written a book about the signs of thezodiac which all the philosophers in London could not answer, " is fame asfar as it goes. Accordingly, we have plenty of discoverers who, even inastronomy, pronounce the learned in error because of mathematics. InFrance, beyond the sphere of influence of the Academy of Sciences, there isno one to cast a thought upon the matter: all who take the least interestrepose entire faith in the Institute. Hence the French discoverer turns allhis thoughts to the Institute, and looks for his only hearing in thatquarter. He therefore throws no slur upon the means of knowledge, but wouldsay, with M. Demonville: "A l'égard de M. Poisson, [632] j'envie loyalementla millième partie de ses connaissances mathématiques, pour prouver monsystême d'astronomie aux plus incrédules. "[633] This system is that theonly bodies of our system are the earth, the sun, and the moon; all theothers being illusions, caused by reflection of the sun and moon from theice of the polar regions. In mathematics, addition and subtraction are formen; multiplication and division, which are in truth creation anddestruction, are prerogatives of deity. But _nothing_ multiplied by_nothing_ is _one_. M. Demonville obtained an introduction to William theFourth, who desired the opinion of the Royal Society upon his system: the{293} answer was very brief. The King was quite right; so was the Society:the fault lay with those who advised His Majesty on a matter they knewnothing about. The writings of M. Demonville in my possession are asfollows. [634] The dates--which were only on covers torn off inbinding--were about 1831-34: _Petit cours d'astronomie_[635] followed by _Sur l'unitémathématique. _--_Principes de la physique de la création implicitementadmis dans la notice sur le tonnerre par M. Arago. _--_Question de longitudesur mer. _[636]--_Vrai système du monde_[637] (pp. 92). Same title, fourpages, small type. Same title, four pages, addressed to the BritishAssociation. Same title, four pages, addressed to M. Mathieu. Same title, four pages, on M. Bouvard's report. --_Résumé de la physique de la création;troisième partie du vrai système du monde. _[638] PARSEY'S PARADOX. The quadrature of the circle discovered, by Arthur Parsey, [639] author of the 'art of miniature painting. ' Submitted to the consideration of the Royal Society, on whose protection the author humbly throws himself. London, 1832, 8vo. Mr. Parsey was an artist, who also made himself conspicuous by a new viewof perspective. Seeing that the sides of a tower, for instance, wouldappear to meet in a point if the tower were high enough, he thought thatthese sides ought to slope to one another in the picture. On this {294}theory he published a small work, of which I have not the title, with aGrecian temple in the frontispiece, stated, if I remember rightly, to bethe first picture which had ever been drawn in true perspective. Of coursethe building looked very Egyptian, with its sloping sides. The answer tohis notion is easy enough. What is called the picture is not the picturefrom which the mind takes its perception; that picture is on the retina. The _intermediate_ picture, as it may be called--the human artist'swork--is itself seen perspectively. If the tower were so high that thesides, though parallel, appeared to meet in a point, the picture must alsobe so high that the _picture-sides_, though parallel, would appear to meetin a point. I never saw this answer given, though I have seen and heard theremarks of artists on Mr. Parsey's work. I am inclined to think it iscommonly supposed that the artist's picture is the representation whichcomes before the mind: this is not true; we might as well say the same ofthe object itself. In July 1831, reading an article on squaring the circle, and finding that there was a difficulty, he set to work, got a light deniedto all mathematicians in--some would say through--a crack, and advertisedin the _Times_ that he had done the trick. He then prepared this work, inwhich, those who read it will see how, he showed that 3. 14159... Should be3. 0625. He might have found out his error by _stepping_ a draughtsman'scircle with the compasses. Perspective has not had many paradoxes. The only other one I remember isthat of a writer on perspective, whose name I forget, and whose four pagesI do not possess. He circulated remarks on my notes on the subject, published in the _Athenæum_, in which he denies that the stereographicprojection is a case of perspective, the reason being that the wholehemisphere makes too large a picture for the eye conveniently to grasp atonce. That is to say, it is no perspective because there is too muchperspective. {295} ON A COUPLE OF GEOMETRIES. Principles of Geometry familiarly illustrated. By the Rev. W. Ritchie, [640] LL. D. London, 1833, 12mo. A new Exposition of the system of Euclid's Elements, being an attempt to establish his work on a different basis. By Alfred Day, [641] LL. D. London, 1839, 12mo. These works belong to a small class which have the peculiarity of insistingthat in the general propositions of geometry a proposition gives itsconverse: that "Every B is A" follows from "Every A is B. " Dr. Ritchiesays, "If it be proved that the equality of two of the angles of a triangledepends _essentially_ upon the equality of the opposite sides, it followsthat the equality of opposite sides depends _essentially_ on the equalityof the angles. " Dr. Day puts it as follows: "That the converses of Euclid, so called, where no particular limitation isspecified or implied in the leading proposition, more than in the converse, must be necessarily true; for as by the nature of the reasoning the leadingproposition must be universally true, should the converse be not so, itcannot be so universally, but has at least all the exceptions conveyed inthe leading proposition, and the case is therefore unadapted to geometricreasoning; or, what is the same thing, by the very nature of geometricreasoning, the particular exceptions to the extended converse must beidentical with some one or other of the cases under the universalaffirmative proposition with which we set forth, which is absurd. " {296} On this I cannot help transferring to my reader the words of the Pacha whenhe orders the bastinado, --May it do you good! A rational study of logic ismuch wanted to show many mathematicians, of all degrees of proficiency, that there is nothing in the _reasoning_ of mathematics which differs fromother reasoning. Dr. Day repeated his argument in _A Treatise onProportion_, London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. Hepublished, in 1818, a work on arithmetic, with rational explanations. Thiswas too early for such an improvement, and nearly the whole of hisexcellent work was sold as waste paper. His elementary introduction to theDifferential Calculus was drawn up while he was learning the subject latein life. Books of this sort are often very effective on points ofdifficulty. NEWTON AGAIN OBLITERATED. Letter to the Royal Astronomical Society in refutation of Mistaken Notions held in common, by the Society, and by all the Newtonian philosophers. By Capt. Forman, [642] R. N. Shepton-Mallet, 1833, 8vo. Capt. Forman wrote against the whole system of gravitation, and got nonotice. He then wrote to Lord Brougham, Sir J. Herschel, and others Isuppose, desiring them to procure notice of his books in the reviews: thisnot being acceded to, he wrote (in print) to Lord John Russell[643] tocomplain of their "dishonest" conduct. He then sent a manuscript letter tothe Astronomical Society, inviting controversy: he was answered by arecommendation to study {297} dynamics. The above pamphlet was theconsequence, in which, calling the Council of the Society "craven dunghillcocks, " he set them right about their doctrines. From all I can learn, thelife of a worthy man and a creditable officer was completely embittered byhis want of power to see that no person is bound in reason to enter intocontroversy with every one who chooses to invite him to the field. Thismistake is not peculiar to philosophers, whether of orthodoxy or paradoxy;a majority of educated persons imply, by their modes of proceeding, that noone has a right to any opinion which he is not prepared to defend againstall comers. David and Goliath, or an attempt to prove that the Newtonian system of Astronomy is directly opposed to the Scriptures. By Wm. Lauder, [644] Sen. , Mere, Wilts. Mere, 1833, 12mo. Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. Laudertakes five arguments. He expects opposition; for Paul and Jesus both metwith it. Mr. Lauder, in his comparison, seems to put himself in the divinelyinspired class. This would not be a fair inference in every case; but weknow not what to think when we remember that a tolerable number ofcyclometers have attributed their knowledge to direct revelation. The worksof this class are very scarce; I can only mention one or two fromMontucla. [645] Alphonso Cano de Molina, [646] in the last century, upset allEuclid, and squared the circle upon the ruins; he found a follower, Janson, who translated him from Spanish into Latin. He declared that he believed inEuclid, until God, who humbles the proud, taught him better. One Paul Yvon, called from his estate de la Leu, a merchant at Rochelle, supported by hisbook-keeper, M. Pujos, and a {298} Scotchman, John Dunbar, solved theproblem by divine grace, in a manner which was to convert all Jews, Infidels, etc. There seem to have been editions of his work in 1619 and1628, and a controversial "Examen" in 1630, by Robert Sara. There was anoted discussion, in which Mydorge, [647] Hardy, [648] and others took partagainst de la Leu. I cannot find this name either in Lipenius[649] orMurhard, [650] and I should not have known the dates if it had not been forone of the keenest bibliographers of any time, my friend Prince BalthasarBoncompagni, [651] who is trying to find copies of the works, and hasmanaged to find copies of the titles. In 1750, Henry Sullamar, anEnglishman, squared the circle by the number of the Beast: he published apamphlet every two or three years; but I cannot find any mention of him inEnglish works. [652] In France, in 1753, M. De Causans, [653] of the Guards, cut a circular piece of turf, squared it, and {299} deduced original sinand the Trinity. He found out that the circle was equal to the square inwhich it is inscribed; and he offered a reward for detection of any error, and actually deposited 10, 000 francs as earnest of 300, 000. But the courtswould not allow any one to recover. SIR JOHN HERSCHEL. 1834. In this year Sir John Herschel[654] set up his telescope atFeldhausen, Cape of Good Hope. He did much for astronomy, but not much forthe _Budget of Paradoxes_. He gives me, however, the following story. Heshowed a resident a remarkable blood-red star, and some little time afterhe heard of a sermon preached in those parts in which it was asserted thatthe statements of the Bible must be true, for that Sir J. H. Had seen inhis telescope "the very place where wicked people go. " But red is not always the color. Sir J. Herschel has in his possession aletter written to his father, Sir W. H. , [655] dated April 3, 1787, andsigned "Eliza Cumyns, " begging to know if any of the stars be _indigo_ incolor, "because, if there be, I think it may be deemed a strong conjecturalillustration of the expression, so often used by our Saviour in the HolyGospels, that 'the disobedient shall be cast into outer darkness'; for asthe Almighty Being can doubtless confine any of his creatures, whethercorporeal or spiritual, to what part of his creation He pleases, iftherefore any of the stars (which are beyond all doubt so many suns toother systems) be of so dark a color as that above mentioned, they may becalculated to give the most insufferable heat to those dolorous systemsdependent upon them (and to reprobate spirits placed there), without oneray of cheerful light; and may therefore be the scenes of futurepunishments. " This letter is addressed to Dr. Heirschel at Slow. Some haveplaced the infernal regions inside the earth, but {300} others have filledthis internal cavity--for cavity they will have--with refulgent light, andmade it the abode of the blessed. It is difficult to build without knowingthe number to be provided for. A friend of mine heard the following (part)dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thankthere are of the alact on the arth at this moment?--Eh! mabbee adoozen--Hoot! mon! nae so mony as thot!" THE NAUTICAL ALMANAC. 1834. From 1769 to 1834 the _Nautical Almanac_ was published on a planwhich gradually fell behind what was wanted. In 1834 the new series began, under a new superintendent (Lieut. W. S. Stratford). [656] There had been along scientific controversy, which would not be generally intelligible. Toset some of the points before the reader, I reprint a cutting which I haveby me. It is from the Nautical _Magazine_, but I did hear that some had anidea that it was in the Nautical _Almanac_ itself. It certainly was not, and I feel satisfied the Lords of the Admiralty would not have permittedthe insertion; they are never in advance of their age. The Almanac for 1834was published in July 1833. THE NEW NAUTICAL ALMANAC--Extract from the 'Primum Mobile, ' and 'Milky Way Gazette. ' Communicated by AEROLITH. A meeting of the different bodies composing the Solar System was this dayheld at the Dragon's Tail, for the purpose of taking into consideration thealterations and amendments introduced into the New Nautical Almanac. Thehonorable luminaries had been individually summoned {301} by fast-sailingcomets, and there was a remarkably full attendance. Among the visitors we_observed_ several nebulæ, and almost all the stars whose proper motionswould admit of their being present. The SUN was unanimously called to the focus. The small planets took theoaths, and their places, after a short discussion, in which it was decidedthat the places should be those of the Almanac itself, with leave reservedto move for corrections. Petitions were presented from [alpha] and [delta] Ursæ Minoris, complainingof being put on daily duty, and praying for an increase of salary. --Laid onthe plane of the ecliptic. The trustees of the eccentricity[657] and inclination funds reported abalance of . 00001 in the former, and a deficit of 0". 009 in the latter. This announcement caused considerable surprise, and a committee was movedfor, to ascertain which of the bodies had more or less than his share. After some discussion, in which the small planets offered to consent to areduction, if necessary, the motion was carried. The FOCAL BODY then rose to address the meeting. He remarked that thesubject on which they were assembled was one of great importance to theroutes and revolutions of the heavenly bodies. For himself, though aprivate arrangement between two of his honourable neighbours (here helooked hard at the Earth and Venus) had prevented his hitherto paying thatclose attention to the predictions of the Nautical Almanac which hedeclared he always had wished to do; yet he felt consoled by knowing thatthe conductors of that work had every disposition to take his peculiarcircumstances into consideration. He declared that he had never passed thewires of a transit without deeply feeling his inability to adapt himself tothe present state of his theory; a feeling which he was afraid hadsometimes caused a slight tremor in his limb. Before {302} he sat down, heexpressed a hope that honourable luminaries would refrain as much aspossible from eclipsing each other, or causing mutual perturbations. Indeed, he should be very sorry to see any interruption of the harmony ofthe spheres. (Applause. ) The several articles of the New Nautical Almanac were then read overwithout any comment; only we observed that Saturn shook his ring at everynovelty, and Jupiter gave his belt a hitch, and winked at the satellites atpage 21 of each month. The MOON rose to propose a resolution. No one, he said, would be surprisedat his bringing this matter forward in the way he did, when it wasconsidered in how complete and satisfactory a manner his motions were nowrepresented. He must own he had trembled when the Lords of the Admiraltydissolved the Board of Longitude, but his tranquillity was more thanreestablished by the adoption of the new system. He did not know but thatany little assistance he could give in Nautical Astronomy was becoming ofless and less value every day, owing to the improvement of chronometers. But there was one thing, of which nothing could deprive him--he meant theregulation of the tides. And, perhaps, when his attention was not occupiedby more than the latter, he should be able to introduce a little moreregularity into the phenomena. (Here the honourable luminary gave a sort ofmodest libration, which convulsed the meeting with laughter. ) They mightlaugh at his natural infirmity if they pleased, but he could assure them itarose only from the necessity he was under, when young, of watching themotions of his worthy primary. He then moved a resolution highly laudatoryof the alterations which appeared in the New Nautical Almanac. The EARTH rose, to second the motion. His honourable satellite had fullyexpressed his opinions on the subject. He joined his honourable friend inthe focus in wishing to pay every attention to the Nautical Almanac, but, {303} really, when so important an alteration had taken place in hismagnetic pole[658] (hear) and there might, for aught he knew, be asuccessful attempt to reach his pole of rotation, he thought he could notanswer for the preservation of the precession in its present state. (Herethe hon. Luminary, scratching his side, exclaimed, as he sat down, "Moresteamboats--confound 'em!") An honourable satellite (whose name we could not learn) proposed that theresolution should be immediately despatched, corrected for refraction, whenhe was called to order by the Focal Body, who reminded him that it wascontrary to the moving orders of the system to take cognizance of whatpassed inside the atmosphere of any planet. SATURN and PALLAS rose together. (Cries of "New member!" and the formergave way. ) The latter, in a long and eloquent speech, praised theliberality with which he and his colleagues had at length been relievedfrom astronomical disqualifications. He thought that it was contrary to thespirit of the laws of gravitation to exclude any planet from office onaccount of the eccentricity or inclination of his orbit. Honourableluminaries need not talk of the want of convergency of his series. What hadthey to do with any private arrangements between him and the generalequations of the system? (Murmurs from the opposition. ) So long as heobeyed the laws of motion, to which he had that day taken a solemn oath, hewould ask, were old planets, which were now so well known that nobodytrusted them, to.... The FOCAL BODY said he was sorry to break the continuity of theproceedings, but he thought that remarks upon character, with a negativesign, would introduce {304} differences of too high an order. Thehonourable luminary must eliminate the expression which he had brought out, in finite terms, and use smaller inequalities in future. (Hear, hear. ) PALLAS explained, that he was far from meaning to reflect upon the orbitalcharacter of any planet present. He only meant to protest against beingjudged by any laws but those of gravitation, and the differential calculus:he thought it most unjust that astronomers should prevent the small planetsfrom being observed, and then reproach them with the imperfections of thetables, which were the result of their own narrow-minded policy. (Cheers. ) SATURN thought that, as an old planet, he had not been treated with duerespect. (Hear, from his satellites. ) He had long foretold the wreck of thesystem from the friends of innovation. Why, he might ask, were hissatellites to be excluded, when small planets, trumpery comets, which couldnot keep their mean distances (cries of oh! oh!), double stars, withgraphical approximations, and such obscure riff-raff of the heavens (greatuproar) found room enough. So help him Arithmetic, nothing could come ofit, but a stoppage of all revolution. His hon. Friend in the focus mightsmile, for he would be a gainer by such an event; but as for him (Saturn), he had something to lose, and hon. Luminaries well knew that, whatever theymight think _under_ an atmosphere, _above_ it continual revolution was theonly way of preventing perpetual anarchy. As to the hon. Luminary who hadrisen before him, he was not surprised at his remarks, for he hadinvariably observed that he and his colleagues allowed themselves _too muchlatitude_. The stability of the system required that they should be broughtdown, and he, for one, would exert all his powers of attraction toaccomplish that end. If other bodies would cordially unite with him, particularly his noble friend next him, than whom no luminary possessedgreater weight-- JUPITER rose to order. He conceived his noble friend {305} had no right toallude to him in that manner, and was much surprised at his proposal, considering the matters which remained in dispute between them. In thepresent state of affairs, he would take care never to be in conjunctionwith his hon. Neighbour one moment longer than he could help. (Cries of"Order, order, no long inequalities, " during which he sat down. ) SATURN proceeded to say, that he did not know till then that a planet witha ring could affront one who had only a belt, by proposing mutualco-operation. He would now come to the subject under discussion. He shouldthink meanly of his hon. Colleagues if they consented to bestow theirapprobation upon a mere astronomical production. Had they forgotten thatthey once were considered the arbiters of fate, and the prognosticators ofman's destiny? What had lost them that proud position? Was it not theinfernal march of intellect, which, after having turned the earthtopsy-turvy, was now disturbing the very universe? For himself (othersmight do as they pleased), but he stuck to the venerable Partridge, [659]and the Stationers' Company, and trusted that they would outlive infidelsand anarchists, whether of Astronomical or Diffusion of KnowledgeSocieties. (Cries of oh! oh!) MARS said he had been told, for he must confess he had not seen the work, that the places of the planets were given for Sundays. This, he must beallowed to say, was an indecorum he had not expected; and he was convincedthe Lords of the Admiralty had given no orders to that effect. He hopedthis point would be considered in the measure which had been introduced inanother place, and that some {306} one would move that the prohibitionagainst travelling on Sundays extend to the heavenly as well as earthlybodies. Several of the stars here declared, that they had been much annoyed bybeing observed on Sunday evenings, during the hours of divine service. The room was then cleared for a division, but we are unable to state whattook place. Several comets-at-arms were sent for, and we heard rumors of apersonal collision having taken place between two luminaries in opposition. We were afterwards told that the resolution was carried by a majority, andthe luminaries elongated at 2 h. 15 m. 33, 41 s. Sidereal time. * * * It is reported, but we hope without foundation, that Saturn, andseveral other discontented planets, have accepted an invitation from Siriusto join his system, on the most liberal appointments. We believe the reportto have originated in nothing more than the discovery of the annualparallax of Sirius from the orbit of Saturn; but we may safely assure ourreaders that no steps have as yet been taken to open any communication. We are also happy to state, that there is no truth in the rumor of the lawsof gravitation being about to be repealed. We have traced this report, andfind it originated with a gentleman living near Bath (Captain Forman, R. N), [660] whose name we forbear to mention. A great excitement has been observed among the nebulæ, visible to theearth's southern hemisphere, particularly among those which have not yetbeen discovered from thence. We are at a loss to conjecture the cause, butwe shall not fail to report to our readers the news of any movement whichmay take place. (Sir J. Herschel's visit. He could just see this before hewent out. ) {307} WOODLEY'S DIVINE SYSTEM. A Treatise on the Divine System of the Universe, by Captain Woodley, R. N. , [661] and as demonstrated by his Universal Time-piece, and universal method of determining a ship's longitude by the apparent true place of the moon; with an introduction refuting the solar system of Copernicus, the Newtonian philosophy, and mathematics. 1834. [662] 8vo. Description of the Universal Time-piece. (4pp. 12mo. ) I think this divine system was published several years before, and wasrepublished with an introduction in 1834. [663] Capt. Woodley was very surethat the earth does not move: he pointed out to me, in a conversation I hadwith him, something--I forget what--in the motion of the Great Bear, visible to any eye, which could not possibly be if the earth moved. He wasexceedingly ignorant, as the following quotation from his account of theusual opinion will show: "The north pole of the Earth's axis deserts, they say, the north star orpole of the Heavens, at the rate of 1° in 71¾ years.... The fact is, nothing can be more certain than that the Stars have not changed theirlatitudes or declinations _one degree_ in the last 71¾ years. " This is a strong specimen of a class of men by whom all accessible personswho have made any name in science are hunted. It is a pity that they cannotbe admitted into scientific societies, and allowed fairly to state theircases, and stand quiet cross-examination, being kept in their answers veryclose to the questions, and the answers written down. I am perfectlysatisfied that if one meeting in the year were devoted to the hearing ofthose who chose to come forward on such conditions, much good would bedone. But I strongly suspect few would come forward {308} at first, andnone in a little while: and I have had some experience of the method Irecommend, privately tried. Capt. Woodley was proposed, a little after1834, as a Fellow of the Astronomical Society; and, not caring whether hemoved the sun or the earth, or both--I could not have stood _neither_--Isigned the proposal. I always had a sneaking kindness for paradoxers, sucha one, perhaps, as Petit André had for his _lambs_, as he called them. There was so little feeling against his opinions, that he only failed by afraction of a ball. Had I myself voted, he would have been elected; butbeing engaged in conversation, and not having heard the slightest objectionto him, I did not think it worth while to cross the room for the purpose. Iregretted this at the time, but had I known how ignorant he was I shouldnot have supported him. Probably those who voted against him knew more ofhis book than I did. I remember no other instance of exclusion from a scientific society on theground of opinion, even if this be one; of which it may be that ignorancehad more to do with it than paradoxy. Mr. Frend, [664] a stronganti-Newtonian, was a Fellow of the Astronomical Society, and for someyears in the Council. Lieut. Kerigan[665] was elected to the Royal Societyat a time when his proposers must have known that his immediate object wasto put F. R. S. On the title-page of a work against the tides. To give all Iknow, I may add that the editor of some very ignorant bombast about the"forehead of the solar sky, " who did not know the difference between_Bailly_[666] and _Baily_, [667] received hints which induced him towithdraw his proposal for election into the Astronomical Society. But thiswas an act of kindness; {309} for if he had seen Mr. Baily in the chair, with his head on, he might have been political historian enough to faintaway. De la formation des Corps. Par Paul Laurent. [668] Nancy, 1834, 8vo. Atoms, and ether, and ovules or eggs, which are planets, and their eggs, which are satellites. These speculators can create worlds, in which theycannot be refuted; but none of them dare attack the problem of a grain ofwheat, and its passage from a seed to a plant, bearing scores of seeds likewhat it was itself. ON JOHN FLAMSTEED. An account of the Rev. John Flamsteed, [669] the First Astronomer-Royal.... By Francis Baily, [670] Esq. London, 1835, 4to. Supplement, London, 1837, 4to. My friend Francis Baily was a paradoxer: he brought forward things counterto universal opinion. That Newton was impeccable in every point was thenational creed; and failings of temper and conduct would have been utterlydisbelieved, if the paradox had not come supported by very unusualevidence. Anybody who impeached Newton on existing evidence might as wellhave been squaring the circle, for any attention he would have got. Aboutthis book I will tell a story. It was published by the Admiralty fordistribution; and the distribution was entrusted to Mr. Baily. On the eveof its appearance, rumors of its extraordinary revelations got about, andpersons of influence applied to the Admiralty for copies. The Lords were ina difficulty: but on looking at the list they saw names, as they {310}thought, which were so obscure that they had a right to assume Mr. Bailyhad included persons who had no claim to such a compliment as presentationfrom the Admiralty. The Secretary requested Mr. Baily to call upon him. "Mr. Baily, my Lords are inclined to think that some of the persons in thislist are perhaps not of that note which would justify their Lordships inpresenting this work. "--"To whom does your observation apply, Mr. Secretary?"--"Well, now, let us examine the list; let me see;now, --now, --now, --come!--here's Gauss[671]--_who's Gauss_?"--"Gauss, Mr. Secretary, is the oldest mathematician now living, and is generally thoughtto be the greatest. "--"O-o-oh! Well, Mr. Baily, we will see about it, and Iwill write you a letter. " The letter expressed their Lordships' perfectsatisfaction with the list. There was a controversy about the revelations made in this work; but as theeccentric anomalies took no part in it, there is nothing for my purpose. The following valentine from Mrs. Flamsteed, [672] which I found amongBaily's papers, illustrates some of the points: "3 Astronomers' Row, Paradise: February 14, 1836. "Dear Sir, --I suppose you hardly expected to receive a letter from me, dated from this place; but the truth is, a gentleman from our street wasappointed guardian angel to the American Treaty, in which there is someastronomical question about boundaries. He has got leave to go back tofetch some instruments which he left behind, and I take this opportunity ofmaking your acquaintance. That America has become a wonderful place since Iwas down among you; you have no idea how grand the fire at New York {311}looked up here. Poor dear Mr. Flamsteed does not know I am writing a letterto a gentleman on Valentine's day; he is walked out with Sir Isaac Newton(they are pretty good friends now, though they do squabble a littlesometimes) and Sir William Herschel, to see a new nebula. Sir Isaac says hecan't make out at all how it is managed; and I am sure I cannot help him. Inever bothered my head about those things down below, and I don't intend tobegin here. "I have just received the news of your having written a book about my poordear man. It's a chance that I heard it at all; for the truth is, thescientific gentlemen are somehow or other become so wicked, and go solittle to church, that very few of them are considered fit company for thisplace. If it had not been for Dr. Brinkley, [673] who came here of course, Ishould not have heard about it. He seems a nice man, but is not yet used toour ways. As to Mr. Halley, [674] he is of course not here; which is luckyfor him, for Mr. Flamsteed swore the moment he caught him in a place wherethere are no magistrates, he would make a sacrifice of him to heavenlytruth. It was very generous in Mr. F. Not appearing against Sir Isaac whenhe came up, for I am told that if he had, Sir Isaac would not have beenallowed to come in at all. I should have been sorry for that, for he is acompanionable man enough, only holds his head rather higher than he shoulddo. I met him the other day walking with Mr. Whiston, [675] and disputingabout the deluge. 'Well, Mrs. Flamsteed, ' says he, 'does old Poke-the-Starsunderstand gravitation yet?' Now you must know that is rather a sore pointwith poor dear Mr. Flamsteed. He says that Sir Isaac is as crochetty aboutthe moon as ever; and as to {312} what some people say about what has beendone since his time, he says he should like to see somebody who knowssomething about it of himself. For it is very singular that none of thepeople who have carried on Sir Isaac's notions have been allowed to comehere. "I hope you have not forgotten to tell how badly Sir Isaac used Mr. Flamsteed about that book. I have never quite forgiven him; as for Mr. Flamsteed, he says that as long as he does not come for observations, hedoes not care about it, and that he will never trust him with any papersagain as long as he lives. I shall never forget what a rage he came home inwhen Sir Isaac had called him a puppy. He struck the stairs all the way upwith his crutch, and said puppy at every step, and all the evening, as soonas ever a star appeared in the telescope, he called it puppy. I could notthink what was the matter, and when I asked, he only called me puppy. "I shall be very glad to see you if you come our way. Pray keep up someappearances, and go to church a little. St. Peter is always uncommonlycivil to astronomers, and indeed to all scientific persons, and neverbothers them with many questions. If they can make anything out of thecase, he is sure to let them in. Indeed, he says, it is perfectly out ofthe question expecting a mathematician to be as religious as an apostle, but that it is as much as his place is worth to let in the greater numberof those who come. So try if you cannot manage it, for I am very curious toknow whether you found all the letters. I remain, dear sir, your faithfulservant, "MARGARET FLAMSTEED. Francis Baily, Esq. "P. S. Mr. Flamsteed has come in, and says he left Sir Isaac ridingcockhorse upon the nebula, and poring over it as if it were a book. He hasbrought in his old acquaintance Ozanam, [676] who says that it was alwayshis maxim on {313} earth, that 'il appartient aux docteurs de Sorbonne dedisputer, au Pape de prononcer, et au mathématicien d'aller en Paradis enligne perpendiculaire. '"[677] ON STEVIN. The Secretary of the Admiralty was completely extinguished. I can recallbut two instances of demolition as complete, though no doubt there are manyothers. The first is in Simon Stevin[678] and M. Dumortier. Nieuport, 1845, 12mo. M. Dumortier was a member of the Academy of Brussels: there was adiscussion, I believe, about a national Pantheon for Belgium. The name ofStevinus suggested itself as naturally as that of Newton to an Englishman;probably no Belgian is better known to foreigners as illustrious inscience. Stevinus is great in the _Mécanique Analytique_ of Lagrange;[679]Stevinus is great in the _Tristram Shandy_ of Sterne. M. Dumortier, whobelieved that not one Belgian in a thousand knew Stevinus, and whoconfesses with ironical shame that he was not the odd man, protestedagainst placing the statue of an obscure man in the Pantheon, to giveforeigners the notion that Belgium could show nothing greater. The workabove named is a slashing retort: any one who knows the history of scienceever so little may imagine what a dressing was given, by mere extract fromforeign writers. The tract is a letter signed J. Du Fan, but this is apseudonym of Mr. Van de Weyer. [680] The Academician says Stevinus was a manwho was not {314} without merit for the time at which he lived: Sir! is theanswer, he was as much before his own time as you are behind yours. Howcame a man who had never heard of Stevinus to be a member of the BrusselsAcademy? The second story was told me by Mr. Crabb Robinson, [681] who was longconnected with the _Times_, and intimately acquainted with Mr. W***. [682]When W*** was an undergraduate at Cambridge, taking a walk, he came to astile, on which sat a bumpkin who did not make way for him: the gown inthat day looked down on the town. "Why do you not make way for agentleman?"--"Eh?"--"Yes, why do you not move? You deserve a good hiding, and you shall get it if you don't take care!" The bumpkin raised hismuscular figure on its feet, patted his menacer on the head, and said, veryquietly, --"Young man! I'm Cribb. "[683] W*** seized the great pugilist'shand, and shook it warmly, got him to his own rooms in college, collectedsome friends, and had a symposium which lasted until the large end of thesmall hours. FINLEYSON AS A PARADOXER. God's Creation of the Universe as it is, in support of the Scriptures. By Mr. Finleyson. [684] Sixth Edition, 1835, 8vo. {315} This writer, by his own account, succeeded in delivering the famous Lieut. Richard Brothers[685] from the lunatic asylum, and tending him, not as akeeper but as a disciple, till he died. Brothers was, by his own account, the nephew of the Almighty, and Finleyson ought to have been the nephew ofBrothers. For Napoleon came to him in a vision, with a broken sword and anarrow in his side, beseeching help: Finleyson pulled out the arrow, butrefused to give a new sword; whereby poor Napoleon, though he got off withlife, lost the battle of Waterloo. This story was written to the Duke ofWellington, ending with "I pulled out the arrow, but left the broken sword. Your Grace can supply the rest, and what followed is amply recorded inhistory. " The book contains a long account of applications to Government todo three things: to pay 2, 000l. For care taken of Brothers, to pay 10, 000l. For discovery of the longitude, and to prohibit the teaching of theNewtonian system, which makes God a liar. The successive administrationswere threatened that they would have to turn out if they refused, which, itis remarked, came to pass in every case. I have heard of a joke of LordMacaulay, that the House of Commons must be the Beast of the Revelations, since 658 members, with the officers necessary for the action of the House, make 666. Macaulay read most things, and the greater part of the rest: sothat he might be suspected of having appropriated as a joke one ofFinleyson's serious points--"I wrote Earl Grey[686] upon the 13th of July, 1831, informing him that his Reform {316} Bill could not be carried, as itreduced the members below the present amount of 658, which, with the eightprincipal clerks or officers of the House, make the number 666. " But awitness has informed me that Macaulay's joke was made in his hearing agreat many years before the Reform Bill was proposed; in fact, when bothwere students at Cambridge. Earl Grey was, according to Finleyson, adescendant of Uriah the Hittite. For a specimen of Lieut. Brothers, thisbook would be worth picking up. Perhaps a specimen of the Lieutenant'spoetry may be acceptable: Brothers _loquitur_, remember: "Jerusalem ! Jerusalem! shall be built again! More rich, more grand then ever; And through it shall Jordan flow!(!) My people's favourite river. There I'll erect a splendid throne, And build on the wasted place; To fulfil my ancient covenant To King David and his race. * * * * * * "Euphrates' stream shall flow with ships, And also my wedded Nile; And on my coast shall cities rise, Each one distant but a mile. * * * * * * "My friends the Russians on the north With Persees and Arabs round, Do show the limits of my land, Here! Here! then I mark the ground. " ON THEOLOGICAL PARADOXERS. Among the paradoxers are some of the theologians who in their own organs ofthe press venture to criticise science. These may hold their ground whenthey confine themselves to the geology of long past periods and to generalcosmogony: for it is the tug of Greek against Greek; and both sides dealmuch in what is grand when called _hypothesis_, petty when called_supposition_. And very often they are not conspicuous when they ventureupon things within knowledge; {317} wrong, but not quite wrong enough for aBudget of Paradoxes. One case, however, is destined to live, as an instanceof a school which finds writers, editors, and readers. The double starshave been seen from the seventeenth century, and diligently observed bymany from the time of Wm. Herschel, who first devoted continuous attentionto them. The year 1836 was that of a remarkable triumph of astronomicalprediction. The theory of gravitation had been applied to the motion ofbinary stars about each other, in elliptic orbits, and in that year the twostars of [gamma] Virginis, as had been predicted should happen within a fewyears of that time--for years are small quantities in such longrevolutions--the two stars came to their nearest: in fact, they appeared tobe one as much with the telescope as without it. This remarkableturning-point of the history of a long and widely-known branch of astronomywas followed by an article in the _Church of England Quarterly Review_ forApril 1837, written against the Useful Knowledge Society. The notion thatthere are any such things as double stars is (p. 460) implied to beimposture or delusion, as in the following extract. I suspect that I myselfam the _Sidrophel_, and that my companion to the maps of the stars, writtenfor the Society and published in 1836, is the work to which the writerrefers: "We have forgotten the name of that Sidrophel who lately discovered thatthe fixed stars were not single stars, but appear in the heavens like solesat Billingsgate, in pairs; while a second astronomer, under the influenceof that competition in trade which the political economists tell us is soadvantageous to the public, professes to show us, through his superiortelescope, that the apparently single stars are really three. Before suchwondrous mandarins of science, how continually must _homunculi_ likeourselves keep in the background, lest we come between the wind and theirnobility. " If the _homunculus_ who wrote this be still above ground, {318} howdevoutly must he hope he may be able to keep in the background! But thechief blame falls on the editor. The title of the article is: "The new school of superficial pantology; a speech intended to be deliveredbefore a defunct Mechanics' Institute. By Swallow Swift, late M. P. For theBorough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year, month _Ventose_. Long live Charlatan!" As a rule, orthodox theologians should avoid humor, a weapon which allhistory shows to be very difficult to employ in favor of establishment, andwhich, nine times out of ten, leaves its wielder fighting on the side ofheterodoxy. Theological argument, when not enlivened by bigotry, is seldomworse than narcotic: but theological fun, when not covert heresy, is almostalways sialagogue. The article in question is a craze, which no editorshould have admitted, except after severe inspection by qualified persons. The author of this wit committed a mistake which occurs now and then in oldsatire, the confusion between himself and the party aimed at. He ought tobe reviewing this fictitious book, but every now and then the articlebecomes the book itself; not by quotation, but by the writer forgettingthat _he_ is not Mr. Swallow Swift, but his reviewer. In fact he and Mr. S. Swift had each had a dose of the _Devil's Elixir_. A novel so called, published about forty years ago, proceeds upon a legend of this kind. Iftwo parties both drink of the elixir, their identities get curiouslyintermingled; each turns up in the character of the other throughout thethree volumes, without having his ideas clear as to whether he be himselfor the other. There is a similar confusion in the answer made to the famous_Epistolæ Obscurorum Virorum_:[687] it is headed _Lamentationes ObscurorumVirorum_. [688] {319} This is not a retort of the writer, throwing back theimputation: the obscure men who had been satirized are themselves made, byname, to wince under the disapprobation which the Pope had expressed at thesatire upon themselves. Of course the book here reviewed is a transparent forgery. But I do notknow how often it may have happened that the book, in the journals whichalways put a title at the head, may have been written after the review. About the year 1830 a friend showed me the proof of an article of his onthe malt tax, for the next number of the _Edinburgh Review_. Nothing waswanting except the title of the book reviewed; I asked what it was. He satdown, and wrote as follows at the head, "The Maltster's Guide (pp. 124), "and said that would do as well as anything. But I myself, it will be remarked, have employed such humor as I cancommand "in favor of establishment. " What it is worth I am not to judge; asusual in such cases, those who are of my cabal pronounce it good, butcyclometers and other paradoxers either call it very poor, or commend it assheer buffoonery. Be it one or the other, I observe that all the effectiveridicule is, in this subject, on the side of establishment. This is partlydue to the difficulty of quizzing plain and sober demonstration; but somuch, if not more, to the ignorance of the paradoxers. For that whichcannot be _ridiculed_, can be _turned into ridicule_ by those who know how. But by the time a person is deep enough in _negative_ quantities, and_impossible_ quantities, to be able to satirize them, he is caught, andbeing inclined to become a _user_, shrinks from being an _abuser_. Imaginea person with a gift of ridicule, and knowledge enough, trying his hand onthe junction of the assertions which he will find in various books ofalgebra. First, that a negative quantity has no logarithm; secondly, that a{320} negative quantity has no square root; thirdly, that the firstnon-existent is to the second as the circumference of a circle to itsdiameter. One great reason of the allowance of such unsound modes ofexpression is the confidence felt by the writers that [root]-1 and log(-1)will make their way, however inaccurately described. I heartily wish thatthe cyclometers had knowledge enough to attack the weak points ofalgebraical diction: they would soon work a beneficial change. [689] AN EARLY METEOROLOGIST. Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace Marie Forster. [690] Brussels, 1836, 12mo. Mr. Forster, an Englishman settled at Bruges, was an observer in manysubjects, but especially in meteorology. He communicated to theAstronomical Society, in 1848, the information that, in the registers keptby his grandfather, his father, and himself, beginning in 1767, new moon onSaturday was followed, nineteen times out of twenty, by twenty days of rainand wind. This statement being published in the _Athenæum_, a cluster ofcorrespondents averred that the belief is common among seamen, in all partsof the world, and among landsmen too. Some one quoted a distich: "Saturday's moon and Sunday's full Never were fine and never _wull_. " {321} Another brought forward: "If a Saturday's moon Comes once in seven years it comes too soon. " Mr. Forster did not say he was aware of the proverbial character of thephenomenon. He was a very eccentric man. He treated his dogs as friends, and buried them with ceremony. He quarrelled with the _curé_ of his parish, who remarked that he could not take his dogs to heaven with him. I will gonowhere, said he, where I cannot take my dog. He was a sincere Catholic:but there is a point beyond which even churches have no influence. The following is some account of the announcement of 1849. The _Athenæum_(Feb. 17), giving an account of the meeting of the Astronomical Society inDecember, 1858, says: "Dr. Forster of Bruges, who is well known as a meteorologist, made acommunication at which our readers will stare: he declares that by journalsof the weather kept by his grandfather, father, and himself, ever since1767, to the present time, _whenever the new moon has fallen on a Saturday, the following twenty days have been wet and windy_, in nineteen cases outof twenty. In spite of our friend Zadkiel[691] and the others who declarethat we would smother every truth that does not happen to agree with us, weare glad to see that the Society had the sense to publish thiscommunication, coming, as it does, from a veteran observer, and one whoselove of truth is undoubted. It must be that the fact is so set down in thejournals, because Dr. Forster says it: and whether it be only a fact of thejournals, or one of the heavens, can soon be tried. The new moon of Marchnext, falls on _Saturday_ the 24th, at 2 in the afternoon. We shallcertainly look out. " {322} The following appeared in the number of March 31: "The first _Saturday Moon_ since Dr. Forster's announcement came off a weekago. We had previously received a number of letters from differentcorrespondents--all to the effect that the notion of new moon on Saturdaybringing wet weather is one of widely extended currency. One correspondent(who gives his name) states that he has constantly heard it at sea, andamong the farmers and peasantry in Scotland, Ireland, and the North ofEngland. He proceeds thus: 'Since 1826, nineteen years of the time I havespent in a seafaring life. I have constantly observed, though unable toaccount for, the phenomenon. I have also heard the stormy qualities of aSaturday's moon remarked by American, French, and Spanish seamen; and, still more distant, a Chinese pilot, who was once doing duty on board myvessel seemed to be perfectly cognizant of the fact. ' So that it seems wehave, in giving currency to what we only knew as a very curiouscommunication from an earnest meteorologist, been repeating what is commonenough among sailors and farmers. Another correspondent affirms that thething is most devoutly believed in by seamen; who would as soon sail on aFriday as be in the Channel after a Saturday moon. --After a tolerablecourse of dry weather, there was some snow, accompanied by wind on Saturdaylast, here in London; there were also heavy louring clouds. Sunday wascloudy and cold, with a little rain; Monday was louring, Tuesday unsettled;Wednesday quite overclouded, with rain in the morning. The present occasionshows only a general change of weather with a tendency towards rain. If Dr. Forster's theory be true, it is decidedly one of the minor instances, asfar as London weather is concerned. --It will take a good deal of evidenceto make us believe in the omen of a Saturday Moon. But, as we have said ofthe Poughkeepsie Seer, the thing is very curious whether true or false. Whence comes this universal proverb--and a hundred others--while themeteorological observer {323} cannot, when he puts down a long series ofresults, detect any weather cycles at all? One of our correspondents wroteus something of a lecture for encouraging, he said, the notion that _names_could influence the weather. He mistakes the question. If there be anyweather cycles depending on the moon, it is possible that one of them maybe so related to the week cycle of seven days, as to show recurrences whichare of the kind stated, or any other. For example, we know that if the newmoon of March fall on a Saturday in this year, it will most probably fallon a Saturday nineteen years hence. This is not connected with the spellingof Saturday--but with the connection between the motions of the sun andmoon. Nothing but the Moon can settle the question--and we are willing towait on her for further information. If the adage be true, then thephilosopher has missed what lies before his eyes; if false, then the worldcan be led by the nose in spite of the eyes. Both these things happensometimes; and we are willing to take whichever of the two solutions isborne out by future facts. In the mean time, we announce the next SaturdayMoon for the 18th of August. " How many coincidences are required to establish a law of connection? Itdepends on the way in which the mind views the matter in question. Many ofthe paradoxers are quite set up by a very few instances. I will now tell astory about myself, and then ask them a question. So far as instances can prove a law, the following is proved: no failurehas occurred. Let a clergyman be known to me, whether by personalacquaintance or correspondence, or by being frequently brought before me bythose with whom I am connected in private life: that clergyman does not, except in few cases, become a bishop; but _if_ he become a bishop, he issure, first or last, to become an arch-bishop. This has happened in everycase. As follows: 1. My last schoolmaster, a former Fellow of Oriel, was {324} a veryintimate college friend of Richard Whately[692], a younger man. Struck byhis friend's talents, he used to talk of him perpetually, and predict hisfuture eminence. Before I was sixteen, and before Whately had even givenhis Bampton Lectures, I was very familiar with his name, and some of hissayings. I need not say that he became Archbishop of Dublin. 2. When I was a child, a first cousin of John Bird Sumner[693] married asister of my mother. I cannot remember the time when I first heard hisname, but it was made very familiar to me. In time he became Bishop ofChester, and then, Archbishop of Canterbury. My reader may say that Dr. C. R. Sumner, [694] Bishop of Winchester, has just as good a claim: but itis not so: those connected with me had more knowledge of Dr. J. B. Sumner;[695] and said nothing, or next to nothing, of the other. Rumor saysthat the Bishop of Winchester has _declined_ an Archbishopric: if so, myrule is a rule of gradations. 3. Thomas Musgrave, [696] Fellow of Trinity College, Cambridge, was _Dean_of the college when I was an undergraduate: this brought me into connectionwith him, he giving impositions for not going to chapel, I writing them outaccording. We had also friendly intercourse in after life; I forgiving, heprobably forgetting. Honest Tom {325} Musgrave, as he used to be called, became Bishop of Hereford, and Archbishop of York. 4. About the time when I went to Cambridge, I heard a great deal about Mr. C. T. Longley, [697] of Christchurch, from a cousin of my own of the samecollege, long since deceased, who spoke of him much, and mostaffectionately. Dr. Longley passed from Durham to York, and thence toCanterbury. I cannot quite make out the two Archbishoprics; I do notremember any other private channel through which the name came to me:perhaps Dr. Longley, having two strings to his bow, would have been onearchbishop if I had never heard of him. 5. When Dr. Wm. Thomson[698] was appointed to the see of Gloucester in1861, he and I had been correspondents on the subject of logic--on which wehad both written--for about fourteen years. On his elevation I wrote tohim, giving the preceding instances, and informing him that he wouldcertainly be an Archbishop. The case was a strong one, and the law actedrapidly; for Dr. Thomson's elevation to the see of York took place in 1862. Here are five cases; and there is no opposing instance. I have searched thealmanacs since 1828, and can find no instance of a Bishop not finallyArchbishop of whom I had known through private sources, direct or indirect. Now what do my paradoxers say? Is this a pre-established harmony, or achain of coincidences? And how many instances will it require to establisha law?[699] {326} THE HERSCHEL HOAX. Some account of the great astronomical discoveries lately made by Sir John Herschel at the Cape of Good Hope. Second Edition. London, 12mo. 1836. This is a curious hoax, evidently written by a person versed in astronomyand clever at introducing probable circumstances and undesignedcoincidences. [700] It first appeared in a newspaper. It makes Sir J. Herschel discover men, animals, etc. In the moon, of which much detail isgiven. There seems to have been a French edition, the original, and Englisheditions in America, whence the work came into Britain: but whether theFrench was published in America or at Paris I do not know. There is nodoubt that it was produced in the United States, by M. Nicollet, [701] anastronomer, once of Paris, and a fugitive of some kind. About him I haveheard two stories. First that he fled to America with funds not his own, and that this book was a mere device to raise the wind. Secondly, that hewas a protégé of Laplace, and of the Polignac party, and also an outspokenman. That after the revolution he was so obnoxious to the republican partythat he judged it prudent to quit France; which he did in debt, leavingmoney for his creditors, but not enough, with M. Bouvard. In America heconnected himself with an assurance office. {327} The moon-story waswritten, and sent to France, chiefly with the intention of entrapping M. Arago, Nicollet's especial foe, into the belief of it. And those whonarrate this version of the story wind up by saying that M. Arago _was_entrapped, and circulated the wonders through Paris, until a letter fromNicollet to M. Bouvard[702] explained the hoax. I have no personalknowledge of either story: but as the poor man had to endure the first, itis but right that the second should be told with it. SOME MORE METEOROLOGY. The Weather Almanac for the Year 1838. By P. Murphy, [703] Esq. , M. N. S. By M. N. S. Is meant _member of no society. _. This almanac bears on thetitle-page two recommendations. The _Morning Post_ calls it one of the mostimportant-if-true publications of our generation. The _Times_ says: "If thebasis of his theory prove sound, and its principles be sanctioned by a moreextended experience, it is not too much to say that the importance of thediscovery is equal to that of the longitude. " Cautious journalist! Threetimes that of the longitude would have been too little to say. That thelandsman might predict the weather of all the year, at its beginning, Jackwould cheerfully give up astronomical longitude--_the_ problem--altogether, and fall back on chronometers with the older Ls, lead, latitude, andlook-out, applied to dead-reckoning. Mr. Murphy attempted to give theweather day by day: thus the first seven days of March {328} boreChangeable; Rain; Rain; Rain-_wind_; Changeable; Fair; Changeable. To aimat such precision as to put a fair day between two changeable ones byweather theory was going very near the wind and weather too. Murphy openedthe year with cold and frost; and the weather did the same. But Murphy, opposite to Saturday, January 20, put down "Fair, Probable lowest degree ofwinter temperature. " When this Saturday came, it was not merely theprobably coldest of 1838, but certainly the coldest of many consecutiveyears. Without knowing anything of Murphy, I felt it prudent to cover mynose with my glove as I walked the street at eight in the morning. Thefortune of the Almanac was made. Nobody waited to see whether the futurewould dement the prophecy: the shop was beset in a manner which brought thepolice to keep order; and it was said that the Almanac for 1838 was a gainof 5, 000l. To the owners. It very soon appeared that this was only a luckyhit: the weather-prophet had a modified reputation for a few years; and isnow no more heard of. A work of his will presently appear in the list. THE GREAT PYRAMIDS. Letter from Alexandria on the evidence of the practical application of the quadrature of the circle in the great pyramids of Gizeh. By H. C. Agnew, [704] Esq. London, 1838, 4to. {329} Mr. Agnew detects proportions which he thinks were suggested by those ofthe circumference and diameter of a circle. THE MATHEMATICS OF A CREED. The creed of St. Athanasius proved by a mathematical parallel. Before you censure, condemn, or approve; read, examine, and understand. E. B. REVILO. [705] London, 1839, 8vo. This author really believed himself, and was in earnest. He is not the onlyperson who has written nonsense by confounding the mathematical infinite(of quantity) with what speculators now more correctly express by theunlimited, the unconditioned, or the absolute. This tract is worthpreserving, as the extreme case of a particular kind. The following is aspecimen. Infinity being represented by [infinity], as usual, and f, s, g, being finite integers, the three Persons are denoted by [infinity]^{f}, (m[infinity])^{s}, [infinity]^{g}, the finite fraction m representing humannature, as opposed to [infinity]. The clauses of the Creed are then givenwith their mathematical parallels. I extract a couple: "But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one: the glory equal, the Majesty co-eternal. "It has been shown that [infinity]^f, [infinity]^g, and (m [infinity])^s, together, are but [infinity], and that each is [infinity], and any magnitude in existence represented by [infinity] always was and always will be: for it cannot be made, or destroyed, and yet exists. {330} "Equal to the Father, as touching his Godhead: and inferior to the Father, touching his Manhood. " "(m [infinity])^s is equal to [infinity]^f as touching [infinity], but inferior to [infinity]^f as touching m: because m is not infinite. " I might have passed this over, as beneath even my present subject, but forthe way in which I became acquainted with it. A bookseller, _not thepublisher_, handed it to me over his counter: one who had publishedmathematical works. He said, with an air of important communication, Haveyou seen _this_, Sir! In reply, I recommended him to show it to my friendMr. ----, for whom he had published mathematics. Educated men, used to booksand to the converse of learned men, look with mysterious wonder on suchproductions as this: for which reason I have made a quotation which manywill judge had better have been omitted. But it would have been animposition on the public if I were, omitting this and some other uses ofthe Bible and Common Prayer, to pretend that I had given a true picture ofmy school. [Since the publication of the above, it has been stated that the author isMr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on:E. B. Revilo seems to be obviously a reversal. ] LOGIC HAS NO PARADOXERS. Old and new logic contrasted: being an attempt to elucidate, for ordinary comprehension, how Lord Bacon delivered the human mind from its 2, 000 years' enslavement under Aristotle. By Justin Brenan. [706] London, 1839, 12mo. Logic, though the other exact science, has not had the sort of assailantswho have clustered about mathematics. There is a sect which disputes theutility of logic, but there are no special points, like the quadrature ofthe circle, which {331} excite dispute among those who admit other things. The old story about Aristotle having one logic to trammel us, and Baconanother to set us free, --always laughed at by those who really knew eitherAristotle or Bacon, --now begins to be understood by a large section of theeducated world. The author of this tract connects the old logic with theindecencies of the classical writers, and the new with moral purity: heappeals to women, who, "when they see plainly the demoralizing tendency ofsyllogistic logic, they will no doubt exert their powerful influenceagainst it, and support the Baconian method. " This is the only work againstlogic which I can introduce, but it is a rare one, I mean in contents. Iquote the author's idea of a syllogism: "The basis of this system is the syllogism. This is a form of couching thesubstance of your argument or investigation into one short line orsentence--then corroborating or supporting it in another, and drawing yourconclusion or proof in a third. " On this definition he gives an example, as follows: "Every sin deservesdeath, " the substance of the "argument or investigation. " Then comes, "Every unlawful wish is a sin, " which "corroborates or supports" thepreceding: and, lastly, "therefore every unlawful wish deserves death, "which is the "conclusion or proof. " We learn, also, that "sometimes thefirst is called the premises (_sic_), and sometimes the first premiss"; asalso that "the first is sometimes called the proposition, or subject, oraffirmative, and the next the predicate, and sometimes the middle term. " Towhich is added, with a mark of exclamation at the end, "but in analyzingthe syllogism, there is a middle term, and a predicate too, in each of thelines!" It is clear that Aristotle never enslaved this mind. I have said that logic has no paradoxers, but I was speaking of old time. This science has slept until our own day: Hamilton[707] says there has been"no progress made in {332} the _general_ development of the syllogism sincethe time of Aristotle; and in regard to the few _partial_ improvements, theprofessed historians seem altogether ignorant. " But in our time, theparadoxer, the opponent of common opinion, has appeared in this field. I donot refer to Prof. Boole, [708] who is not a _paradoxer_, but a_discoverer_: his system could neither oppose nor support common opinion, for its grounds were not in the conception of any one. I speak especiallyof two others, who fought like cat and dog: one was dogmatical, the othercategorical. The first was Hamilton himself--Sir William Hamilton ofEdinburgh, the metaphysician, not Sir William _Rowan_ Hamilton[709] ofDublin, the mathematician, a combination of peculiar genius withunprecedented learning, erudite in all he could want except mathematics, for which he had no turn, and in which he had not even a schoolboy'sknowledge, thanks to the Oxford of his younger day. The other was theauthor of this work, so fully described in Hamilton's writings that thereis no occasion to describe him here. I shall try to say a few words incommon language about the paradoxers. Hamilton's great paradox was the _quantification of the predicate_; afearful phrase, easily explained. We all know that when we say "Men areanimals, " a form wholly unquantified in phrase, we speak of _all_ men, butnot of all animals: it is _some or all_, some may be all for aught theproposition says. This some-may-be-all-for-aught-we-say, or _not-none, _ isthe logician's _some_. One would suppose {333} that "all men are someanimals, " would have been the logical phrase in all time: but the predicatenever was quantified. The few who alluded to the possibility of such athing found reasons for not adopting it over and above the great reason, that Aristotle did not adopt it. For Aristotle never ruled in physics ormetaphysics _in the old time_ with near so much of absolute sway as he hasruled in logic _down to our own time_. The logicians knew that in theproposition "all men are animals" the "animal" is not _universal_, but_particular_ yet no one dared to say that _all_ men are _some_ animals, andto invent the phrase, "_some_ animals are _all_ men" until Hamilton leapedthe ditch, and not only completed a system of enunciation, but applied itto syllogism. My own case is as peculiar as his: I have proposed to introducemathematical _thought_ into logic to an extent which makes the old stagerscry: "St. Aristotle! what wild notions! Serve a _ne exeat regno_[710] on him!" Hard upon twenty years ago, a friend and opponent who stands high in thesematters, and who is not nearly such a sectary of Aristotle andestablishment as most, wrote to me as follows: "It is said that next to theman who forms the taste of the nation, the greatest genius is the man whocorrupts it. I mean therefore no disrespect, but very much the reverse, when I say that I have hitherto always considered you as a great logicalheresiarch. " Coleridge says he thinks that it was Sir Joshua Reynolds whomade the remark: which, to copy a bull I once heard, I cannot deny, becauseI was not there when he said it. My friend did not call me to repentanceand reconciliation with the church: I think he had a guess that I was areprobate sinner. My offences at that time were but small: I went onspinning syllogism systems, all alien from the common logic, until I hadsix, the initial letters of which, put together, from the {334} names Igave before I saw what they would make, bar all repentance by the words RUE NOT! leaving to the followers of the old school the comfortable option ofplacing the letters thus: TRUE? NO! It should however be stated that the question is not about absolute truthor falsehood. No one denies that anything I call an inference is aninference: they say that my alterations are _extra-logical_; that they are_material_, not _formal_; and that logic is a _formal_ science. The distinction between material and formal is easily made, where the usualperversions are not required. A _form_ is an empty machine, such as "EveryX is Y"; it may be supplied with _matter_, as in "Every _man_ is _animal_. "The logicians will not see that their _formal_ proposition, "Every X is Y, "is material in three points, the degree of assertion, the quantity of theproposition, and the copula. The purely formal proposition is "There is theprobability [alpha] that X stands in the relation L to Y. " The time willcome when it will be regretted that logic went without paradoxers for twothousand years: and when much that has been said on the distinction of formand matter will breed jokes. I give one instance of one mood of each of the systems, in the order of theletters first written above. _Relative. _--In this system the formal relation is taken, that is, thecopula may be any whatever. As a material instance, in which the_relations_ are those of consanguinity (of men understood), take thefollowing: X is the brother of Y; X is not the uncle of Z; therefore, Z isnot the child of Y. The discussion of relation, and of the objections tothe extension, is in the _Cambridge Transactions_, Vol. X, Part 2; acrabbed conglomerate. _Undecided. _--In this system one premise, and want of power over another, infer want of power over a conclusion. {335} As "Some men are not capableof tracing consequences; we cannot be sure that there are beingsresponsible for consequences who are incapable of tracing consequences;therefore, we cannot be sure that all men are responsible for theconsequences of their actions. " _Exemplar. _--This, long after it suggested itself to me as a means ofcorrecting a defect in Hamilton's system, I saw to be the very system ofAristotle himself, though his followers have drifted into another. It makesits subject and predicate examples, thus: Any one man is an animal; any oneanimal is a mortal; therefore, any one man is a mortal. _Numerical. _--Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs beYs, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could notgeneralize on symbols, saw that the word _most_ would come under thissystem, and admitted, as valid, such a syllogism as "most Ys are Xs; mostYs are Zs; therefore, some Xs are Zs. " _Onymatic. _--This is the ordinary system much enlarged in propositionalforms. It is fully discussed in my _Syllabus of Logic_. _Transposed. _--In this syllogism the quantity in one premise is transposedinto the other. As, some Xs are not Ys; for every X there is a Y which isZ; therefore, some Zs are not Xs. Sir William Hamilton of Edinburgh was one of the best friends and allies Iever had. When I first began to publish speculation on this subject, heintroduced me to the logical world as having plagiarized from him. Thisdrew their attention: a mathematician might have written about logic underforms which had something of mathematical look long enough before theAristotelians would have troubled themselves with him: as was done by JohnBernoulli, [711] {336} James Bernoulli, [712] Lambert, [713] andGergonne;[714] who, when our discussion began, were not known even toomnilegent Hamilton. He retracted his accusation of _wilful_ theft in amanly way when he found it untenable; but on this point he wavered alittle, and was convinced to the last that I had taken his principleunconsciously. He thought I had done the same with Ploucquet[715] andLambert. It was his pet notion that I did not understand the commonestprinciples of logic, that I did not always know the difference between themiddle term of a syllogism and its conclusion. It went against his grain toimagine that a mathematician could be a logician. So long as he took me tobe riding my own hobby, he laughed consumedly: but when he thought he couldmake out that I was mounted behind Ploucquet or Lambert, the current ranthus: "It would indeed have been little short of a miracle had he, ignoranteven of the common principles of logic, been able of himself to rise togeneralization so lofty and so accurate as are supposed in the peculiardoctrines of both the rival logicians, Lambert and Ploucquet--how uselesssoever these may in practice prove to be. " All this has been sufficientlydiscussed elsewhere: "but, masters, remember that I am an ass. " I know that I never saw Lambert's work until after all Hamilton supposed meto have taken was written: he himself, who read almost everything, knewnothing about it until after I did. I cannot prove what I say about myknowledge of Lambert: but the means of doing it may turn up. For, by thecasual turning up of an old letter, I _have_ {337} found the means ofclearing myself as to Ploucquet. Hamilton assumed that (unconsciously) Itook from Ploucquet the notion of a logical notation in which the symbol ofthe conclusion is seen in the joint symbols of the premises. For example, in my own fashion I write down ( . ) ( . ), two symbols of premises. Bythese symbols I see that there is a valid conclusion, and that it may bewritten in symbol by striking out the two middle parentheses, which gives (. . ) and reading the two negative dots as an affirmative. And so I see in( . ) ( . ) that ( ) is the conclusion. This, in full, is the perceptionthat "all are either Xs or Ys" and "all are either Ys or Zs" necessitates"some Xs are Zs. " Now in Ploucquet's book of 1763, is found, "Deleatur inpræmissis medius; id quod restat indicat conclusionem. "[716] In the paperin which I explain my symbols--which are altogether different fromPloucquet's--there is found "Erase the symbols of the middle term; theremaining symbols show the inference. " There is very great likeness: and Iwould have excused Hamilton for his notion if he had fairly given referenceto the part of the book in which his quotation was found. For I had shownin my _Formal Logic_ what part of Ploucquet's book I had used: and a fairdisputant would either have strengthened his point by showing that I hadbeen at his part of the book, or allowed me the advantage of it beingapparent that I had not given evidence of having seen that part of thebook. My good friend, though an honest man, was sometimes unwilling toallow due advantage to controversial opponents. But to my point. The only work of Ploucquet I ever saw was lent me by myfriend Dr. Logan, [717] with whom I have often corresponded on logic, etc. Ichanced (in 1865) {338} to turn up the letter which he sent me (Sept. 12, 1847) _with the book_. Part of it runs thus: "I congratulate you on yoursuccess in your logical researches [that is, in asking for the book, I haddescribed some results]. Since the reading of your first paper I have beensatisfied as to the possibility of inventing a logical notation in whichthe rationale of the inference is contained in the symbol, though I neverattempted to verify it [what I communicated, then, satisfied the writerthat I had done and communicated what he, from my previous paper, suspectedto be practicable]. I send you Ploucquet's dissertation.... ' It now being manifest that I cannot be souring grapes which have been takenfrom me, I will say what I never said in print before. There is not theslightest merit in making the symbols of the premises yield that of theconclusion by erasure: _the thing must do itself in every system whichsymbolises quantities_. For in every syllogism (except the inverted_Bramantip_ of the Aristotelians) the conclusion is manifest in this waywithout symbols. This _Bramantip_ destroys system in the Aristotelian lot:and circumstances which I have pointed out destroy it in Hamilton's owncollection. But in that enlargement of the reputed Aristotelian systemwhich I have called _onymatic_, and in that correction of Hamilton's systemwhich I have called _exemplar_, the rule of erasure is universal, and maybe seen without symbols. Our first controversy was in 1846. In 1847, in my _Formal Logic_, I gavehim back a little satire for satire, just to show, as I stated, that Icould employ ridicule if I pleased. He was so offended with the appendix inwhich this was contained, that he would not accept the copy of the book Isent him, but returned it. Copies of controversial works, sent fromopponent to opponent, are not _presents_, in the usual sense: it was amarked success to make him angry enough to forget this. It had some effecthowever: during the rest of his life I wished to avoid provocation; for I{339} could not feel sure that excitement might not produce consequences. Iallowed his slashing account of me in the _Discussions_ to pass unanswered:and before that, when he proposed to open a controversy in the _Athenæum_upon my second Cambridge paper, I merely deferred the dispute until thenext edition of my _Formal Logic_. I cannot expect the account in the_Discussions_ to amuse an unconcerned reader as much as it amused myself:but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongsassault, I can particularly recommend it. I never knew, until I read it, how much I should enjoy a thundering onslought on myself, done with racyinsolence by a master hand, to whom my good genius had whispered _Ita feriut se sentiat emori_. [718] Since that time I have, as the Irishman said, become "dry moulded for want of a bating. " Some of my paradoxers have donetheir best: but theirs is mere twopenny--"small swipes, " as Peter Peeblessaid. Brandy for heroes! I hope a reviewer or two will have mercy on me, and will give me as good discipline as Strafford would have given Hampdenand his set: "much beholden, " said he, "should they be to any one thatshould thoroughly take pains with them in that kind"--meaning _objective_flagellation. And I shall be the same to any one who will serve me so--butin a literary and periodical sense: my corporeal cuticle is as thin as myneighbors'. Sir W. H. Was suffering under local paralysis before our controversycommenced: and though his mind was quite unaffected, a retort of asdownright a character as the attack might have produced serious effect upona person who had shown himself sensible of ridicule. Had a second attack ofhis disorder followed an answer from me, I should have been held to havecaused it: though, looking at Hamilton's genial love of combat, I stronglysuspected that a retort in kind {340} "Would cheer his heart, and warm his blood, And make him fight, and do him good. " But I could not venture to risk it. So all I did, in reply to the articlein the _Discussions_, was to write to him the following note: which, asillustrating an etiquette of controversy, I insert. "I beg to acknowledge and thank you for.... It is necessary that I shouldsay a word on my retention of this work, with reference to your return ofthe copy of my _Formal Logic_, which I presented to you on its publication:a return made on the ground of your disapproval of the account of ourcontroversy which that work contained. According to my view of the subject, any one whose dealing with the author of a book is specially attacked init, has a right to expect from the author that part of the book in whichthe attack is made, together with so much of the remaining part as isfairly context. And I hold that the acceptance by the party assailed ofsuch work or part of a work does not imply any amount of approval of thecontents, or of want of disapproval. On this principle (though I am notprepared to add the word _alone_) I forwarded to you the whole of my workon _Formal Logic_ and my second Cambridge Memoir. And on this principle Ishould have held you wanting in due regard to my literary rights if you hadnot forwarded to me your asterisked pages, with all else that was necessaryto a full understanding of their scope and meaning, so far as the contentsof the book would furnish it. For the remaining portion, which it would bea hundred pities to separate from the pages in which I am directlyconcerned, I am your debtor on another principle; and shall be glad toremain so if you will allow me to make a feint of balancing the account bythe offer of two small works on subjects as little connected with ourdiscussion as the _Epistolæ Obscurorum Virorum_, or the Lutheran dispute. Itrust that by accepting my _Opuscula_ you will enable me to avoid the {341}use of the knife, and leave me to cut you up with the pen as occasion shallserve, I remain, etc. (April 21, 1852). " I received polite thanks, but not a word about the body of the letter: myargument, I suppose, was admitted. SOME DOGGEREL AND COUNTER DOGGEREL. I find among my miscellaneous papers the following _jeu d'esprit_, or _jeude bêtise_, [719] whichever the reader pleases--I care not--intended, beforeI saw ground for abstaining, to have, as the phrase is, come in somehow. Ithink I could manage to bring anything into anything: certainly into aBudget of Paradoxes. Sir W. H. Rather piqued himself upon some caniculars, or doggerel verses, which he had put together _in memoriam_ [_technicam_]of the way in which A E I O are used in logic: he added U, Y, for theaddition of _meet_, etc. , to the system. I took the liberty of concoctingsome counter-doggerel, just to show that a mathematician may havearchitectonic power as well as a metaphysician. DOGGEREL. BY SIR W. HAMILTON. A it affirms of _this_, _these_, _all_, Whilst E denies of _any_; I it affirms (whilst O denies) Of some (or few, or many). Thus A affirms, as E denies, And definitely either; Thus I affirms, as O denies, And definitely neither. A half, left semidefinite, Is worthy of its score; U, then, affirms, as Y denies, This, neither less nor more. Indefinito-definites, I, UI, YO, last we come; {342} And this affirms, as that denies Of _more_, _most_ (_half_, _plus_, _some_). COUNTER DOGGEREL. BY PROF. DE MORGAN. (1847. ) Great A affirms of all; Sir William does so too: When the subject is "my suspicion, " And the predicate "must be true. " Great E denies of all; Sir William of all but one: When he speaks about this present time, And of those who in logic have done. Great I takes up but _some_; Sir William! my dear soul! Why then in all your writings, Does "Great I" fill[720] the whole! Great O says some are not; Sir William's readers catch, That some (modern) Athens is not without An Aristotle to match. "A half, left semi-definite, Is worthy of its score:" This looked very much like balderdash, And neither less nor more. It puzzled me like anything; In fact, it puzzled me worse: Isn't schoolman's logic hard enough, Without being in Sibyl's verse? {343} At last, thinks I, 'tis German; And I'll try it with some beer! The landlord asked what bothered me so, And at once he made it clear. It's _half-and-half_, the gentleman means; Don't you see he talks of _score_? That's the bit of memorandum That we chalk behind the door. _Semi-definite_'s outlandish; But I see, in half a squint, That he speaks of the lubbers who call for a quart, When they can't manage more than a pint. Now I'll read it into English, And then you'll answer me this: If it isn't good logic all the world round, I should like to know what is? When you call for a pot of half-and-half, If you're lost to sense of shame, You may leave it _semi-definite_, But you pay for it all just the same. * * * * * * I am unspeakably comforted when I look over the above in remembering thatthe question is not whether it be Pindaric or Horatian, but whether thecopy be as good as the original. And I say it is: and will take no denial. Long live--long will live--the glad memory of William Hamilton, Good, Learned, Acute, and Disputatious! He fought upon principle: the motto ofhis book is: "Truth, like a torch, the more it's shook it shines. " There is something in this; but metaphors, like puddings, quarrels, rivers, and arguments, always have two sides to them. For instance, "Truth, like a torch, the more it's shook it shines; But those who want to use it, hold it steady. They shake the flame who like a glare to gaze at, They keep it still who want a light to see by. " {344} ANOTHER THEORY OF PARALLELS. Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the Equiangular Spiral. By Lieut-Col. G. Perronet Thompson. [721] The same, second edition, revised and corrected. The same, third edition, shortened, and freed from dependence on the theory of limits. The same, fourth edition, ditto, ditto. All London, 1840, 8vo. To explain these editions it should be noted that General Thompson rapidlymodified his notions, and republished his tracts accordingly. SOME PRIMITIVE DARWINISM. Vestiges of the Natural History of Creation. [722] London, 1840, 12mo. This is the first edition of this celebrated work. Its form is a case ofthe theory: the book is an undeniable duodecimo, but the size of its papergives it the look of not the smallest of octavos. Does not this illustratethe law of development, the gradation of families, the transference ofspecies, and so on? If so, I claim the discovery of this esoteric testimonyof the book to its own contents; I defy any one to point out the reviewerwho has mentioned it. The work itself is described by its author as "thefirst attempt to connect the natural sciences into a history of creation. "The attempt was commenced, and has been carried on, both with markedtalent, and will be continued. Great advantage will result: at the worst weare but in the alchemy of some new chemistry, or the astrology of some newastronomy. Perhaps it would be as well not to be too sure on the matter, until we have an antidote to possible consequences as exhibited underanother theory, on which {345} it is as reasonable to speculate as on thatof the _Vestiges_. I met long ago with a splendid player on the guitar, whoassured me, and was confirmed by his friends, that he _never practised_, except in thought, and did not possess an instrument: he kept his fingersacting in his mind, until they got their habits; and thus he learnt themost difficult novelties of execution. Now what if this should be a minorsegment of a higher law? What if, by constantly thinking of ourselves asdescended from primeval monkeys, we should--if it be true--actually _getour tails again_? What if the first man who was detected with such anappendage should be obliged to confess himself the author of the_Vestiges_--a person yet unknown--who would naturally get the start of hisspecies by having had the earliest habit of thinking on the matter? Iconfess I never hear a man of note talk fluently about it without a curiousglance at his proportions, to see whether there may be ground to conjecturethat he may have more of "mortal coil" than others, in anaxyridicalconcealment. I do not feel sure that even a paternal love for his theorywould induce him, in the case I am supposing, to exhibit himself at theBritish Association, With a hole behind which his tail peeped through. The first sentence of this book (1840) is a cast of the log, which showsour rate of progress. "It is familiar knowledge that the earth which weinhabit is a globe of somewhat less than 8, 000 miles in diameter, being oneof a series of eleven which revolve at different distances around the sun. "The _eleven_! Not to mention the Iscariot which Le Verrier and Adamscalculated into existence, there is more than a septuagint of _new_planetoids. ON RELIGIOUS INSURANCE. The Constitution and Rules of the Ancient and Universal 'Benefit Society' established by Jesus Christ, exhibited, and its advantages and claims maintained, against all Modern and {346} merely Human Institutions of the kind: A Letter very respectfully addressed to the Rev. James Everett, [723] and occasioned by certain remarks made by him, in a speech to the Members of the 'Wesleyan Centenary Institute' Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith. [724] 12mo, (pp. 8. ) The Wesleyan minister addressed had advocated provision against old age, etc. : the writer declares all _private_ provision un-Christian. Afterdecent maintenance and relief of family claims of indigence, he holds thatall the rest is to go to the "Benefit Society, " of which he draws up therules, in technical form, with chapters of "Officers, " "Contributors" etc. , from the Acts of the Apostles, etc. , and some of the early Fathers. Heholds that a Christian may not "make a _private_ provision against thecontingencies of the future": and that the great "Benefit Society" is thedivinely-ordained recipient of all the surplus of his income; capital, beyond what is necessary for business, he is to have none. A real goodspeculator shuts his eyes by instinct, when opening them would not servethe purpose: he has the vizor of the Irish fairy tale, which fell of itselfover the eyes of the wearer the moment he turned them upon the enchantedlight which would have destroyed him if he had caught sight of it. "Whilesit remained, was it not thine own? and after it was sold, was it (thepurchase-money) not in thine own power?" would have been awkward to quote, and accordingly nothing is stated except the well-known result, which isrule 3, cap. 5, "Prevention of Abuses. " By putting his principles together, the author can be made, logically, to mean that the successors of theapostles should put to death all contributors who are detected in notpaying their full premiums. {347} I have known one or two cases in which policy-holders have surrenderedtheir policies through having arrived at a conviction that direct provisionis unlawful. So far as I could make it out, these parties did not think itunlawful to lay by out of income, except when this was done in a mannerwhich involved calculation of death-chances. It is singular they did notsee that the entrance of chance of death was the entrance of the veryprinciple of the benefit society described in the Acts of the Apostles. Thefamily of the one who died young received more in proportion to _premiums_paid than the family of one who died old. Every one who understands lifeassurance sees that--_bonus_ apart--the difference between an assuranceoffice and a savings bank consists in the adoption, _pro tanto_, of theprinciple of community of goods. In the original constitution of the oldestassurance office, the _Amicable Society_, the plan with which they startedwas nothing but this: persons of all ages under forty-five paid one commonpremium, and the proceeds were divided among the representatives of thosewho died within the year. THE TWO OLD PARADOXES AGAIN. [I omitted from its proper place a manuscript quadrature (3. 1416 exactly)addressed to an eminent mathematician, dated in 1842 from the debtor's wardof a country gaol. The unfortunate speculator says, "I have labored manyyears to find the precise ratio. " I have heard of several cases in whichsquaring the circle has produced an inability to square accounts. I remindthose who feel a kind of inspiration to employ native genius upondifficulties, without gradual progression from elements, that the call isone which becomes stronger and stronger, and may lead, as it has led, toabandonment of the duties of life, and all the consequences. ] {348} 1842. Provisional Prospectus of the Double Acting Rotary Engine Company. Also Mechanic's Magazine, March 26, 1842. Perpetual motion by a drum with one vertical half in mercury, the other ina vacuum: the drum, I suppose, working round forever to find an easyposition. Steam to be superseded: steam and electricity convulsions ofnature never intended by Providence for the use of man. The price of thepresent engines, as old iron, will buy new engines that will work withoutfuel and at no expense. Guaranteed by the Count de Predaval, [725] thediscoverer. I was to have been a Director, but my name got no further thanink, and not so far as official notification of the honor, partly owing tomy having communicated to the _Mechanic's Magazine_ information privatelygiven to me, which gave premature publicity, and knocked up the plan. An Exposition of the Nature, Force, Action, and other properties of Gravitation on the Planets. London, 1842, 12mo. An Investigation of the principles of the Rules for determining the Measures of the Areas and Circumferences of Circular Plane Surfaces ... London, 1844, 8vo. These are anonymous; but the author (whom I believe to be Mr. Denison, [726]presently noted) is described as author of a new system of mathematics, andalso of mechanics. He had need have both, for he shows that the line whichhas a square equal to a given circle, has a cube equal to the sphere on thesame diameter: that is, in old mathematics, the diameter is to thecircumference as 9 to 16! Again, admitting that the velocities of planetsin circular orbits are inversely as the square roots of their distances, that is, admitting Kepler's law, he manages to prove that gravitation isinversely as the square _root_ of the distance: and suspects magnetism ofdoing the difference between this and Newton's law. {349} Magnetism andelectricity are, in physics, the member of parliament and the cabman--atevery man's bidding, as Henry Warburton[727] said. The above is an outrageous quadrature. In the preceding year, 1841, waspublished what I suppose at first to be a Maori quadrature, by Maccook. ButI get it from a cutting out of some French periodical, and I incline tothink that it must be by a Mr. M^cCook. He makes [pi] to be 2 +2[root](8[root]2 - 11). THE DUPLICATION PROBLEM. Refutation of a Pamphlet written by the Rev. John Mackey, R. C. P. , [728] entitled "A method of making a cube double of a cube, founded on the principles of elementary geometry, " wherein his principles are proved erroneous, and the required solution not yet obtained. By Robert Murphy. [729] Mallow, 1824, 12mo. This refutation was the production of an Irish boy of eighteen years old, self-educated in mathematics, the son of a shoemaker at Mallow. He died in1843, leaving a name which is well known among mathematicians. His works onthe theory of equations and on electricity, and his papers in the_Cambridge Transactions_, are all of high genius. The only account of himwhich I know of is that which I wrote for the _Supplement_ of the _PennyCyclopædia_. He was thrown by his talents into a good income at Cambridge, with no social training except penury, and very little intellectualtraining except mathematics. He fell into dissipation, and his scientificcareer was almost arrested: but he had great good in him, to my knowledge. A sentence in {350} a letter from the late Dean Peacock[730] to me--givingsome advice about the means of serving Murphy--sets out the old case:"Murphy is a man whose _special_ education is in advance of his _general_;and such men are almost always difficult subjects to manage. " This articlehaving been omitted in its proper place, I put it at 1843, the date ofMurphy's death. A NEW VALUE OF [pi]. The Invisible Universe disclosed; or, the real Plan and Government of the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo. The book opens abruptly with: "First demonstration. Concerning the centre: showing that, because thecentre is an innermost point at an equal distance between two extremepoints of a right line, and from every two relative and oppositeintermediate points, it is composed of the two extreme internal points ofeach half of the line; each extreme internal point attracting towardsitself all parts of that half to which it belongs.... " Of course the circle is squared: and the circumference is 3-1/21 diameters. SOME MODERN ASTROLOGY. Combination of the Zodiacal and Cometical Systems. Printed for the London Society, Exeter Hall. Price Sixpence. (n. D. 1843. ) What this London Society was, or the "combination, " did not appear. Therewas a remarkable comet in 1843, the tail of which was at first confoundedwith what is called the _zodiacal light_. This nicely-printed little tract, evidently got up with less care for expense than is usual in such works, brings together all the announcements of the astronomers, and adds a shorthead and tail piece, which I shall quote entire. As the announcements arevery ordinary {351} astronomy, the reader will be able to detect, ifdetection be possible, what is the meaning and force of the "Combination ofthe Zodiacal and Cometical Systems": "_Premonition. _ It has pleased the AUTHOR _of_ CREATION to cause (to His_human and reasoning_ Creatures of this generation, by a '_combined_'appearance in His _Zodiacal_ and _Cometical_ system) a '_warning Crisis_'of universal concernment to this our GLOBE. It is this '_Crisis_' that hasso generally 'ROUSED' at this moment the '_nations throughout the Earth_'that no equal interest has ever before been excited by MAN; unless it be inthat caused by the 'PAGAN-TEMPLE IN ROME, ' which is recorded by the elderPliny, '_Nat. Hist. _' i. 23. Iii. 3. HARDOUIN. " After the accounts given by the unperceiving astronomers, comes whatfollows: "Such has been (_hitherto_) the only object discerned by the '_Wise of thisWorld_, ' in this _twofold union_ of the '_Zodiacal_' and '_Cometical_'systems: yet it is nevertheless a most '_Thrilling Warning_, ' to _all_ theinhabitants of this precarious and transitory EARTH. We have no authorizedintimation or reasonable prospective contemplation, of '_current time_'beyond a year 1860, of the present century; or rather, except '_theinterval which may now remain from the present year 1843, to a year 1860_'([Greek: hêmeras HEXÊKONTA]--'_threescore or sixty days_'--'_I haveappointed each_ "DAY" _for a_ "YEAR, "' _Ezek. _ iv. 6): and we know, fromour '_common experience_, ' how speedily such a measure of time will passaway. "No words can be '_more explicit_' than these of OUR BLESSED LORD: viz. 'THIS GOSPEL _of the Kingdom shall be preached in_ ALL the EARTH, _for aWitness to_ ALL NATIONS; AND THEN, _shall the_ END COME. ' The '_next 18years_' must therefore supply the interval of the '_special Episcopalforerunners_. ' (Matt. Xxiv. 14. ) "See the 'JEWISH INTELLIGENCER' of the present month (_April_), p. 153, forthe '_Debates in Parliament_, ' respecting {352} the BISHOP OF JERUSALEM, _viz. _ Dr. Bowring, [731] Mr. Hume, [732] Sir R. Inglis, [733] Sir R. Peel, [734] Viscount Palmerston. [735]" I have quoted this at length, to show the awful threats which werepublished at a time of some little excitement about the phenomenon, underthe name of the _London Society_. The assumption of a corporate appearanceis a very unfair trick: and there are junctures at which harm might be doneby it. THE NUMBER OF THE BEAST. _Wealth_ the name and number of the Beast, 666, in the Book of Revelation. [by John Taylor. [736]] London, 1844, 8vo. Whether Junius or the Beast be the more difficult to identify, must bereferred to Mr. Taylor, the only person who has attempted both. His cogentargument on the political secret is not unworthily matched in his treatmentof the theological riddle. He sees the solution in [Greek: euporia], whichoccurs in the Acts of the Apostles as the word for wealth in one of itsmost disgusting forms, and makes 666 in the most straightforward way. Thisexplanation has as good a chance as any other. The work contains a general{353} attempt at explanation of the Apocalypse, and some history of opinionon the subject. It has not the prolixity which is so common a fault ofapocalyptic commentators. A practical Treatise on Eclipses ... With remarks on the anomalies of the present Theory of the Tides. By T. Kerigan, [737] F. R. S. 1844, 8vo. Containing also a refutation of the theory of the tides, and afterwardsincreased by a supplement, "Additional facts and arguments against thetheory of the tides, " in answer to a short notice in the _Athenæum_journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission tothe Royal Society just before the publication of his book. A new theory of Gravitation. By Joseph Denison, [738] Esq. London, 1844, 12mo. Commentaries on the Principia. By the author of 'A new theory of Gravitation. ' London, 1846, 8vo. Honor to the speculator who can be put in his proper place by one sentence, be that place where it may. "But we have shown that the velocities are inversely as the square roots ofthe mean distances from the sun; wherefore, by equality of ratios, theforces of the sun's gravitation upon them are also inversely as the squareroots of their distances from the sun. " EASTER DAY PARADOXERS. In the years 1818 and 1845 the full moon fell on Easter Day, having beenparticularly directed to fall before it in the act for the change of styleand in the English missals and prayer-books of all time: perhaps it wouldbe more correct to say that Easter Day was directed to fall after the fullmoon; "but the principle is the same. " No explanation was given in 1818, but Easter was kept by the tables, {354} in defiance of the rule, and ofseveral protests. A chronological panic was beginning in December 1844, which was stopped by the _Times_ newspaper printing extracts from anarticle of mine in the _Companion to the Almanac_ for 1845, which had thenjust appeared. No one had guessed the true reason, which is that the thingcalled the moon in the Gregorian Calendar is not the moon of the heavens, but a fictitious imitation put wrong on purpose, as will presently appear, partly to keep Easter out of the way of the Jews' Passover, partly forconvenience of calculation. The apparent error happens but rarely; and allthe work will perhaps have to be gone over next time. I now give two bitsof paradox. Some theologians were angry at this explanation. A review called the_Christian Observer_ (of which Christianity I do not know) got up acrushing article against me. I did not look at it, feeling sure that anarticle on such a subject which appeared on January 1, 1845, against apublication made in December 1844, must be a second-hand job. But someyears afterwards (Sept. 10, 1850), the reviews, etc. Having been justplaced at the disposal of readers in the _old_ reading-room of the Museum, I made a tour of inspection, came upon my critic on his perch, and took alook at him. I was very glad to remember this, for, though expecting onlysecond-hand, yet even of this there is good and bad; and I expected to findsome hints in the good second-hand of a respectable clerical publication. Iread on, therefore, attentively, but not long: I soon came to theinformation that some additions to Delambre's[739] statement of the rulefor finding Easter, belonging to distant years, had been made by Sir HarrisNicolas![740] Now as I myself furnished my friend Sir H. N. With Delambre'sdigest of {355} Clavius's[741] rule, which I translated out of algebra intocommon language for the purpose, I was pretty sure this was the ignorantreading of a person to whom Sir H. N. Was the highest _arithmetical_authority on the subject. A person pretending to chronology, without beingable to distinguish the historical points--so clearly as they stand out--inwhich Sir H. N. Speaks with authority, from the arithmetical points of purereckoning on which he does not pretend to do more than directly repeatothers, must be as fit to talk about the construction of Easter Tables asthe Spanish are to talk French. I need hardly say that the additions fordistant years are as much from Clavius as the rest: my reviewer was notdeep enough in his subject to know that Clavius made and published, fromhis rules, the full table up to A. D. 5000, for all the movable feasts ofevery year! I gave only a glance at the rest: I found I was either knave orfool, with a leaning to the second opinion; and I came away satisfied thatmy critic was either ignoramus or novice, with a leaning to the first. Iafterwards found an ambiguity of expression in Sir H. N. 's account--whetherhis or mine I could not tell--which might mislead a novice or content anignoramus, but would have been properly read or further inquired into by acompetent person. The second case is this. Shortly after the publication of my article, agentleman called at my house, and, finding I was not at home, sent up hiscard--with a stylish west-end club on it--to my wife, begging for a fewwords on pressing business. With many well-expressed apologies, he statedthat he had been alarmed by hearing that Prof. De M. Had an intention ofaltering Easter next year. Mrs. De M. Kept her countenance, and assured himthat I had no such intention, and further, that she greatly doubted myhaving the power to do it. Was she quite sure? his authority was very good:fresh assurances given. He was greatly relieved, for he had some horsestraining for after Easter, which {356} would not be ready to run if it werealtered the wrong way. A doubt comes over him: would Mrs. De M. , in theevent of her being mistaken, give him the very earliest information?Promise given; profusion of thanks; more apologies; and departure. Now, candid reader!--or uncandid either!--which most deserves to be laughedat? A public instructor, who undertakes to settle for the world whether areader of Clavius, the constructor of the Gregorian Calendar, is fool orknave, upon information derived from a compiler--in this matter--of his ownday; or a gentleman of horse and dog associations, who, misapprehendingsomething which he heard about a current topic, infers that the reader ofClavius had the ear of the Government on a proposed alteration. I supposethe querist had heard some one say, perhaps, that the day ought to be setright, and some one else remark that I might be consulted, as the onlyperson who had discussed the matter from the original source of theCalendar. To give a better chance of the explanation being at once produced, nexttime the real full moon and Easter Day shall fall together, I insert here asummary which was printed in the Irish Prayer-book of the EcclesiasticalSociety. If the amusement given by paradoxers should prevent a uselessdiscussion some years hence, I and the paradoxers shall have done a littlegood between us--at any rate, I have done my best to keep the heavy weightafloat by tying bladders to it. I think the next occurrence will be in1875. EASTER DAY. In the years 1818 and 1845, Easter Day, as given by the _rules in_ 24 Geo. II cap. 23. (known as the act for the _change of style_) contradicted the_precept_ given in the preliminary explanations. The precept is as follows: "_Easter Day_, on which the rest" of the moveable feasts "depend, is alwaysthe First Sunday after the Full Moon, which happens upon or next after theTwenty-first Day of {357} _March_; and if the Full Moon happens upon aSunday, _Easter Day_ is the Sunday after. " But in 1818 and 1845, the full moon fell on a Sunday, and yet the rulesgave _that same Sunday_ for Easter Day. Much discussion was produced bythis circumstance in 1818: but a repetition of it in 1845 was nearlyaltogether prevented by a timely[742] reference to the intention of thosewho conducted the Gregorian reformation of the Calendar. Nevertheless, seeing that the apparent error of the Calendar is due to the precept in theAct of Parliament, which is both erroneous and insufficient, and that thedifficulty will recur so often as Easter Day falls on the day of full moon, it may be advisable to select from the two articles cited in the note suchof their conclusions and rules, without proof or controversy, as willenable the reader to understand the main points of the Easter question, and, should he desire it, to calculate for himself the Easter of the old ornew style, for any given year. 1. In the very earliest age of Christianity, a controversy arose as to themode of keeping Easter, some desiring to perpetuate the _Passover_, othersto keep the _festival of the Resurrection_. The first afterwards obtainedthe name of _Quartadecimans_, from their Easter being always kept on the_fourteenth day_ of the moon (Exod. Xii. 18, Levit. Xxiii. 5. ). But thoughit is unquestionable that a Judaizing party existed, it is also likely thatmany dissented on chronological grounds. It is clear that no _perfect_anniversary can take place, except when the fourteenth of the moon, andwith it the passover, falls on a Friday. Suppose, for instance, it falls ona Tuesday: one of three things must be {358} done. Either (which seemsnever to have been proposed) the crucifixion and resurrection must becelebrated on Tuesday and Sunday, with a wrong interval; or the former onTuesday, the latter on Thursday, abandoning the first day of the week; orthe former on Friday, and the latter on Sunday, abandoning the paschalcommemoration of the crucifixion. The last mode has been, as every one knows, finally adopted. The disputesof the first three centuries did not turn on any _calendar_ questions. TheEaster question was merely the symbol of the struggle between what we maycall the Jewish and Gentile sects of Christians: and it nearly divided theChristian world, the Easterns, for the most part, being _Quartadecimans_. It is very important to note that there is no recorded dispute about amethod of predicting the new moon, that is, no general dispute leading toformation of sects: there may have been difficulties, and discussions aboutthem. The Metonic cycle, presently mentioned, must have been used by many, perhaps most, churches. 2. The question came before the Nicene Council (A. D. 325) not as anastronomical, but as a doctrinal, question: it was, in fact, this, Shallthe _passover_[743] be treated as a part of Christianity? The Councilresolved this question in the negative, and the only information on itspremises and conclusion, or either, which comes from itself, is containedin the following sentence of the synodical epistle, which epistle ispreserved by Socrates[744] and Theodoret. [745] "We also send {359} you thegood news concerning the unanimous consent of all in reference to thecelebration of the most solemn feast of Easter, for this difference alsohas been made up by the assistance of your prayers: so that all thebrethren in the East, who formerly celebrated this festival _at the sametime as the Jews_, will in future conform _to the Romans and to us_, and toall who have of old observed _our manner_ of celebrating Easter. " This isall that can be found on the subject: none of the stories about the Councilordaining the astronomical mode of finding Easter, and introducing theMetonic cycle into ecclesiastical reckoning, have any contemporaryevidence: the canons which purport to be those of the Nicene Council do notcontain a word about Easter; and this is evidence, whether we suppose thosecanons to be genuine or spurious. 3. The astronomical dispute about a lunar cycle for the prediction ofEaster either commenced, or became prominent, by the extinction of greaterones, soon after the time of the Nicene Council. Pope Innocent I[746] metwith difficulty in 414. S. Leo, [747] in 454, ordained that Easter of 455should be April 24; which is right. It is useless to record details ofthese disputes in a summary: the result was, that in the year 463, PopeHilarius[748] employed Victorinus[749] of Aquitaine to correct theCalendar, and Victorinus formed a rule which lasted until the sixteenthcentury. He combined the Metonic cycle and the solar cycle presentlydescribed. But {360} this cycle bears the name of Dionysius Exiguus, [750] aScythian settled at Rome, about A. D. 530, who adapted it to his new yearlyreckoning, when he abandoned the era of Diocletian as a commencement, andconstructed that which is now in common use. 4. With Dionysius, if not before, terminated all difference as to the modeof keeping Easter which is of historical note: the increasing defects ofthe Easter Cycle produced in time the remonstrance of persons versed inastronomy, among whom may be mentioned Roger Bacon, [751] Sacrobosco, [752]Cardinal Cusa, [753] Regiomontanus, [754] etc. From the middle of the sixthto that of the sixteenth century, one rule was observed. 5. The mode of applying astronomy to chronology has always involved thesetwo principles. First, the actual position of the heavenly body is not theobject of consideration, but what astronomers call its _mean place_, whichmay be described thus. Let a fictitious sun or moon move in the heavens, insuch manner as to revolve among the fixed stars at an average rate, avoiding the alternate accelerations and retardations which take place inevery planetary motion. Thus the fictitious (say _mean_) sun and moon arealways very near to the real sun and moon. The ordinary clocks show time bythe mean, not the real, sun: and it was always laid down that Easterdepends on the opposition (or full moon) of the mean sun and moon, not ofthe real ones. Thus we see that, were the Calendar ever so correct {361} asto the _mean_ moon, it would be occasionally false as to the _true_ one:if, for instance, the opposition of the mean sun and moon took place at onesecond before midnight, and that of the real bodies only two secondsafterwards, the calendar day of full moon would be one day before that ofthe common almanacs. Here is a way in which the discussions of 1818 and1845 might have arisen: the British legislature has defined _the moon_ asthe regulator of the paschal calendar. But this was only a part of themistake. 6. Secondly, in the absence of perfectly accurate knowledge of the solarand lunar motion (and for convenience, even if such knowledge existed), cycles are, and always have been taken, which serve to represent thosemotions nearly. The famous Metonic cycle, which is introduced intoecclesiastical chronology under the name of the cycle of the goldennumbers, is a period of 19 Julian[755] years. This period, in the oldCalendar, was taken to contain exactly 235 _lunations_, or intervalsbetween new moons, of the mean moon. Now the state of the case is: 19 average Julian years make 6939 days 18 hours. 235 average lunations make 6939 days 16 hours 31 minutes. So that successive cycles of golden numbers, supposing the first to startright, amount to making the new moons fall too late, gradually, so that themean moon _of this cycle_ gains 1 hour 29 minutes in 19 years upon the meanmoon of the heavens, or about a day in 300 years. When the Calendar wasreformed, the calendar new moons were four days in advance of the mean moonof the heavens: so that, for instance, calendar full moon on the 18thusually meant real full moon on the 14th. 7. If the difference above had not existed, the moon of the heavens (themean moon at least), would have returned {362} permanently to the same daysof the month in 19 years; with an occasional slip arising from the unequaldistribution of the leap years, of which a period contains sometimes fiveand sometimes four. As a general rule, the days of new and full moon in anyone year would have been also the days of new and full moon of a yearhaving 19 more units in its date. Again, if there had been no leap years, the days of the month would have returned to the same days of the weekevery seven years. The introduction of occasional 29ths of Februarydisturbs this, and makes the permanent return of month days to week daysoccur only after 28 years. If all had been true, the lapse of 28 times 19, or 532 years, would have restored the year in every point: that is, A. D. 1, for instance, and A. D. 533, would have had the same almanac in every matterrelating to week days, month days, sun, and moon (mean sun and moon atleast). And on the supposition of its truth, the old system of Dionysiuswas framed. Its errors, are, first, that the moments of mean new moonadvance too much by 1 h. 29 m. In 19 average Julian years; secondly, thatthe average Julian year of 365¼ days is too long by 11 m. 10 s. 8. The Council of Trent, moved by the representations made on the state ofthe Calendar, referred the consideration of it to the Pope. In 1577, Gregory XIII[756] submitted to the Roman Catholic Princes and Universitiesa plan presented to him by the representatives of Aloysius Lilius, [757]then deceased. This plan being approved of, the Pope nominated a commissionto consider its details, the working member of which was the JesuitClavius. A short work was prepared by Clavius, descriptive of the newCalendar: this {363} was published[758] in 1582, with the Pope's bull(dated February 24, 1581) prefixed. A larger work was prepared by Clavius, containing fuller explanation, and entitled _Romani Calendarii a GregorioXIII. Pontifice Maximo restituti Explicatio_. This was published at Rome in1603, and again in the collection of the works of Clavius in 1612. 9. The following extracts from Clavius settle the question of the meaningof the term _moon_, as used in the Calendar: "Who, except a few who think they are very sharp-sighted in this matter, isso blind as not to see that the 14th of the moon and the full moon are notthe same things in the Church of God?... Although the Church, in findingthe new moon, and from it the 14th day, _uses neither the true nor the meanmotion of the moon_, but measures only according to the order of a cycle, it is nevertheless undeniable that the mean full moons found fromastronomical tables are of the greatest use in determining the cycle whichis to be preferred ... The new moons of which cycle, in order to the duecelebration of Easter, should be so arranged that the 14th days of thosemoons, reckoning from the day of new moon _inclusive_, should not fall twoor more days before the mean full moon, but only one day, or else on thevery day itself, or not long after. And even thus far the Church need nottake very great pains ... For it is sufficient that all should reckon bythe 14th day of the moon in the cycle, even though sometimes it _should bemore than one day before or after_ the mean full moon.... We have takenpains that in our cycle the new moons should _follow_ the real new moons, so that the 14th of the moon should fall either the day before the meanfull moon, or on that day, or not long after; and this was done on purpose, for if the new moon of the cycle fell on the same day as the mean new moonof the {364} astronomers, it might chance that we should celebrate Easteron the same day as the Jews or the Quartadeciman heretics, which would beabsurd, or else before them, which would be still more absurd. " From this it appears that Clavius continued the Calendar of hispredecessors in the choice of the _fourteenth_ day of the moon. Ourlegislature lays down the day of the _full moon_: and this mistake appearsto be rather English than Protestant; for it occurs in missals published inthe reign of Queen Mary. The calendar lunation being 29½ days, the middleday is the _fifteenth_ day, and this is and was reckoned as the day of thefull moon. There is every right to presume that the original passover was afeast of the _real full moon_: but it is most probable that the moons werethen reckoned, not from the astronomical conjunction with the sun, whichnobody sees except at an eclipse, but from the day of _first visibility_ ofthe new moon. In fine climates this would be the day or two days afterconjunction; and the fourteenth day from that of first visibilityinclusive, would very often be the day of full moon. The following is thenthe proper correction of the precept in the Act of Parliament: Easter Day, on which the rest depend, is always the First Sunday after the_fourteenth day_ of the _calendar_ moon which happens upon or next afterthe Twenty-first day of March, _according to the rules laid down for theconstruction of the Calendar_; and if the _fourteenth day_ happens upon aSunday, Easter Day is the Sunday after. 10. Further, it appears that Clavius valued the celebration of the festivalafter the Jews, etc. , more than astronomical correctness. He givescomparison tables which would startle a believer in the astronomicalintention of his Calendar: they are to show that a calendar in which themoon is always made a day older than by him, _represents the heavens betterthan he has done, or meant to do_. But it must be observed that thisdiminution of the real moon's age has {365} a tendency to make the Englishexplanation often practically accordant with the Calendar. For thefourteenth day of Clavius _is_ generally the fifteenth day of the mean moonof the heavens, and therefore most often that of the real moon. But forthis, 1818 and 1845 would not have been the only instances of our day inwhich the English precept would have contradicted the Calendar. 11. In the construction of the Calendar, Clavius adopted the ancient cycleof 532 years, but, we may say, without ever allowing it to run out. Atcertain periods, a shift is made from one part of the cycle into another. This is done whenever what should be Julian leap year is made a commonyear, as in 1700, 1800, 1900, 2100, etc. It is also done at certain timesto correct the error of 1 h. 19 m. , before referred to, in each cycle ofgolden numbers: Clavius, to meet his view of the amount of that error, putforward the moon's age a day 8 times in 2, 500 years. As we cannot enter atfull length into the explanation, we must content ourselves with giving aset of rules, independent of tables, by which the reader may find Easterfor himself in any year, either by the old Calendar or the new. Any one whohas much occasion to find Easters and movable feasts should procureFrancoeur's[759] tables. 12. _Rule for determining Easter Day of the Gregorian Calendar in any yearof the new style. _ To the several parts {366} of the rule are annexed, byway of example, the results for the year 1849. I. Add 1 to the given year. (1850). II. Take the quotient of the given year divided by 4, neglecting theremainder. (462). III. Take 16 from the centurial figures of the given year, if it can bedone, and take the remainder. (2). IV. Take the quotient of III. Divided by 4, neglecting the remainder. (0). V. From the sum of I, II, and IV. , subtract III. (2310). VI. Find the remainder of V. Divided by 7. (0). VII. Subtract VI. From 7; this is the number of the dominical letter 1 2 3 4 5 6 7 (7; dominical letter G). A B C D E F G VIII. Divide I. By 19, the remainder (or 19, if no remainder) is the_golden number_. (7). IX. From the centurial figures of the year subtract 17, divide by 25, andkeep the quotient. (0). X. Subtract IX. And 15 from the centurial figures, divide by 3, and keepthe quotient. (1). XI. To VIII. Add ten times the next less number, divide by 30, and keep theremainder. (7). XII. To XI. Add X. And IV. , and take away III. , throwing out thirties, ifany. If this give 24, change it into 25. If 25, change it into 26, wheneverthe golden number is greater than 11. If 0, change it into 30. Thus we havethe epact, or age of the _Calendar_ moon at the beginning of the year. (6). _When the Epact is 23, or less. _ XIII. Subtract XII. , the epact, from 45. (39). XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder. (7) _When the Epact is greater than 23. _ XIII. Subtract XII. , the epact, from 75. XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder. XV. To XIII. Add VII. , the dominical number, (and 7 besides, if XIV. Begreater than VII. , ) and subtract XIV. , the result is the day of March, orif more than 31, subtract 31, and {367} the result is the day of April, onwhich Easter Sunday falls. (39; Easter Day is April 8). In the following examples, the several results leading to the finalconclusion are tabulated. ======================================================== GIVEN YEAR | 1592 | 1637 | 1723 | 1853 | 2018 | 4686 -------------------------------------------------------- I. | 1593 | 1638 | 1724 | 1854 | 2019 | 4687 II. | 398 | 409 | 430 | 463 | 504 | 1171 III. | --- | 0 | 1 | 2 | 4 | 30 IV. | --- | 0 | 0 | 0 | 1 | 7 V. | 1991 | 2047 | 2153 | 2315 | 2520 | 5835 VI. | 3 | 3 | 4 | 5 | 0 | 4 VII. | 4 | 4 | 3 | 2 | 7 | 3 VIII. | 16 | 4 | 14 | 11 | 5 | 13 IX. | --- | --- | 0 | 0 | 0 | 1 X. | 0 | 0 | 0 | 1 | 1 | 10 XI. | 16 | 4 | 24 | 21 | 15 | 13 XII. | 16 | 4 | 23 | 20 | 13 |0 say 30 XIII. | 29 | 41 | 22 | 25 | 32 | 45 XIV. | 4 | 2 | 4 | 7 | 7 | 6 XV. | 29 | 43 | 28 | 27 | 32 | 49 Easter Day |Mar. 29|Apr. 12|Mar. 28|Mar. 27|Apr. 1 | Apr. 18 -------------------------------------------------------- 13. _Rule for determining Easter Day of the Antegregorian Calendar in anyyear of the old style. _ To the several parts of the rule are annexed, byway of example, the results for the year 1287. The steps are numbered tocorrespond with the steps of the Gregorian rule, so that it can be seenwhat augmentations the latter requires. I. Set down the given year. (1287). II. Take the quotient of the given year divided by 4, neglecting theremainder (321). V. Take 4 more than the sum of I. And II. (1612). VI. Find the remainder of V. Divided by 7. (2). VII. Subtract VI. From 7; this is the number of the dominical letter 1 2 3 4 5 6 7 (5; dominical letter E). A B C D E F G VIII. Divide one more than the given year by 19, the remainder (or 19 if noremainder) is the golden number. (15). XII. Divide 3 less than 11 times VIII. By 30; the remainder (or 30 if therebe no remainder) is the epact. (12). {368} _When the Epact is 23, or less. _ XIII. Subtract XII. , the epact, from 45. (33). XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder, (1). _When the Epact is greater than 23. _ XIII. Subtract XII. , the epact, from 75. XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder. XV. To XIII. Add VII. , the dominical number, (and 7 besides if XIV. Begreater than VII. , ) and subtract XIV. , the result is the day of March, orif more than 31, subtract 31, and the result is the day of April, on whichEaster Sunday (old style) falls. (37; Easter Day is April 6). These rules completely represent the old and new Calendars, so far asEaster is concerned. For further explanation we must refer to the articlescited at the commencement. The annexed is the table of new and full moons of the Gregorian Calendar, cleared of the errors made for the purpose of preventing Easter fromcoinciding with the Jewish Passover. The second table (page 370) contains _epacts_, or ages of the moon at thebeginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. Thistable goes from 1850 to 1999: should the New Zealander not have arrived bythat time, and should the churches of England and Rome then survive, theepact table may be continued from their liturgy-books. The way of using thetable is as follows: Take the epact of the required year, and find it inthe first or last column of the first table, in line with it are seen thecalendar days of new and full moon. Thus, when the epact is 17, the new andfull moons of March fall on the 13th and 28th. The result is, for the mostpart, correct: but in a minority of cases there is an error of a day. Whenthis happens, the error is almost always a fraction of a day much less thantwelve hours. Thus, when the table gives full moon on the 27th, and thereal truth is the 28th, we may be sure it is early on the 28th. {369} ------------------------------------------------------------------------- |Jan. |Feb. |Mar. |Apr. |May |June|July|Aug. |Sep. |Oct. |Nov. |Dec. | ------------------------------------------------------------------------- 1 | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | 1 | 14 | 13 | 14 | 13 | 12 | 11 | 10 | 9 | 7 | 7 | 5 | 5 | ------------------------------------------------------------------------- 2 | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | 2 | 13 | 12 | 13 | 12 | 11 | 10 | 9 | 8 | 6 | 6 | 4 | 4 | ------------------------------------------------------------------------- 3 | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | 3 | 12 | 11 | 12 | 11 | 10 | 9 | 8 | 7 | 5 | 5 | 3 | 3 | ------------------------------------------------------------------------- 4 | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | 4 | 11 | 10 | 11 | 10 | 9 | 8 | 7 | 6 | 4 | 4 | 2 |2, 31| ------------------------------------------------------------------------- 5 | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | 5 | 10 | 9 | 10 | 9 | 8 | 7 | 6 | 5 | 3 | 3 | 1 |1, 30| ------------------------------------------------------------------------- 6 | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | 6 | 9 | 8 | 9 | 8 | 7 | 6 | 5 | 4 | 2 |2, 31| 30 | 29 | ------------------------------------------------------------------------- 7 | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | 7 | 8 | 7 | 8 | 7 | 6 | 5 | 4 | 3 | 1 |1, 30| 29 | 28 | ------------------------------------------------------------------------- 8 | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | 8 | 7 | 6 | 7 | 6 | 5 | 4 | 3 |2, 31| 30 | 29 | 28 | 27 | ------------------------------------------------------------------------- 9 | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | 9 | 6 | 5 | 6 | 5 | 4 | 3 | 2 |1, 30| 29 | 28 | 27 | 26 | ------------------------------------------------------------------------- 10 | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 | 10 | 5 | 4 | 5 | 4 | 3 | 2 |1, 31| 29 | 28 | 27 | 26 | 25 | ------------------------------------------------------------------------- 11 | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 | 9 | 11 | 4 | 3 | 4 | 3 | 2 |1, 30| 30 | 28 | 27 | 26 | 25 | 24 | ------------------------------------------------------------------------- 12 | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 | 9 | 8 | 12 | 3 | 2 | 3 | 2 |1, 31| 29 | 29 | 27 | 26 | 25 | 24 | 23 | ------------------------------------------------------------------------- 13 | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 | 9 | 8 | 7 | 13 | 2 | 1 | 2 |1, 30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | ------------------------------------------------------------------------- 14 | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 | 9 | 8 | 7 | 6 | 14 |1, 31| -- |1, 31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | ------------------------------------------------------------------------- 15 | 15 | 13 | 15 | 13 | 13 | 11 | 11 | 9 | 8 | 7 | 6 | 5 | 15 | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | ------------------------------------------------------------------------- 16 | 14 | 12 | 14 | 12 | 12 | 10 | 10 | 8 | 7 | 6 | 5 | 4 | 16 | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | ------------------------------------------------------------------------- 17 | 13 | 11 | 13 | 11 | 11 | 9 | 9 | 7 | 6 | 5 | 4 | 3 | 17 | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | ------------------------------------------------------------------------- 18 | 12 | 10 | 12 | 10 | 10 | 8 | 8 | 6 | 5 | 4 | 3 | 2 | 18 | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | ------------------------------------------------------------------------- 19 | 11 | 9 | 11 | 9 | 9 | 7 | 7 | 5 | 4 | 3 | 2 |1, 31| 19 | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | ------------------------------------------------------------------------- 20 | 10 | 8 | 10 | 8 | 8 | 6 | 6 | 4 | 3 | 2 |1, 31| 30 | 20 | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | ------------------------------------------------------------------------- 21 | 9 | 7 | 9 | 7 | 7 | 5 | 5 | 3 | 2 |1, 31| 29 | 29 | 21 | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | ------------------------------------------------------------------------- 22 | 8 | 6 | 8 | 6 | 6 | 4 | 4 | 2 |1, 30| 30 | 28 | 28 | 22 | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | ------------------------------------------------------------------------- 23 | 7 | 5 | 7 | 5 | 5 | 3 | 3 |1, 31| 29 | 29 | 27 | 27 | 23 | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | ------------------------------------------------------------------------- 24 | 6 | 5 | 6 | 5 | 4 | 3 | 2 |1, 30| 29 | 28 | 27 | 26 | 24 | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | ------------------------------------------------------------------------- 25 | 5 | 4 | 5 | 4 | 3 | 2 |1, 31| 29 | 28 | 27 | 26 | 25 | 25 | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 | ------------------------------------------------------------------------- 26 | 4 | 3 | 4 | 3 | 2 |1, 30| 30 | 28 | 27 | 26 | 25 | 24 | 26 | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 | ------------------------------------------------------------------------- 27 | 3 | 2 | 3 | 2 |1, 31| 29 | 29 | 27 | 26 | 25 | 24 | 23 | 27 | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 | 9 | 9 | ------------------------------------------------------------------------- 28 | 2 | 1 | 2 |1, 30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | 28 | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 | 8 | 8 | ------------------------------------------------------------------------- 29 |1, 31| -- |1, 31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | 29 | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 | 9 | 9 | 7 | 7 | ------------------------------------------------------------------------- 30 | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | 30 | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 | 8 | 8 | 6 | 6 | ------------------------------------------------------------------------- |Jan. |Feb. |Mar. |Apr. |May |June|July|Aug. |Sep. |Oct. |Nov. |Dec. | ------------------------------------------------------------------------- {370} ======================================================= | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ------------------------------------------------------- 185 | 17 | 28 | 9 | 20 | 2 | 12 | 23 | 4 | 15 | 26 ------------------------------------------------------- 186 | 7 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 ------------------------------------------------------- 187 | 28 | 9 | 20 | 1 | 12 | 23 | 4 | 15 | 26 | 7 ------------------------------------------------------- 188 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 | 28 ------------------------------------------------------- 189 | 9 | 21 | 1 | 12 | 23 | 4 | 15 | 26 | 7 | 18 ------------------------------------------------------- 190 | 29 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 ------------------------------------------------------- 191 | 19 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 ------------------------------------------------------- 192 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 ------------------------------------------------------- 193 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 ------------------------------------------------------- 194 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 ------------------------------------------------------- 195 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 ------------------------------------------------------- 196 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 ------------------------------------------------------- 197 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 ------------------------------------------------------- 198 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 | 22 ------------------------------------------------------- 199 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 | 13 ======================================================= For example, the year 1867. The epact is 25, and we find in the table: J. F. M. AP. M. JU. JL. AU. S. O. N. D. New 5+ 4 5+ 4 3+ 2 1, 31 29 28- 27 26 25 Full 20 19- 20 19- 18 17 16 15 13- 13 11+ 11 When the truth is the day after + is written after the date; when the daybefore, -. Thus, the new moon of March is on the 6th; the full moon ofApril is on the 18th. {371} I now introduce a small paradox of my own; and as I am not able to proveit, I am compelled to declare that any one who shall dissent must be eithervery foolish or very dishonest, and will make me quite uncomfortable aboutthe state of his soul. This being settled once for all, I proceed to saythat the necessity of arriving at the truth about the assertions that theNicene Council laid down astronomical tests led me to look at Fathers, Church histories, etc. To an extent which I never dreamed of before. Oneconclusion which I arrived at was, that the Nicene Fathers had a knack ofsticking to the question which many later councils could not acquire. Inour own day, it is not permitted to Convocation seriously to discuss anyone of the points which are bearing so hard upon their resources ofdefence--the cursing clauses of the Athanasian Creed, for example. And itmay be collected that the prohibition arises partly from fear that there isno saying where a beginning, if allowed, would end. There seems to be asuspicion that debate, once let loose, would play up old Trent with theliturgy, and bring the whole book to book. But if any one will examine thereal Nicene Creed, without the augmentation, he will admire the way inwhich the framers stuck to the point, and settled what they had to decide, according to their view of it. With such a presumption of good sense intheir favor, it becomes easier to believe in any claim which may be made ontheir behalf to tact or sagacity in settling any other matter. And Istrongly suspect such a claim may be made for them on the Easter question. I collect from many little indications, both before and after the Council, that the division of the Christian world into Judaical and Gentile, thoughnot giving rise to a sectarian distinction expressed by names, was of fargreater force and meaning than historians prominently admit. I took _note_of many indications of this, but not _notes_, as it was not to my purpose. If it were so, we must admire the discretion of the Council. The Easterquestion was the {372} fighting ground of the struggle: the Eastern orJudaical Christians, with some varieties of usage and meaning, would havethe Passover itself to be the great feast, but taken in a Christian sense;the Western or Gentile Christians, would have the commemoration of theResurrection, connected with the Passover only by chronology. To shift thePassover in time, under its name, _Pascha_, without allusion to any of theforce of the change, was gently cutting away the ground from under the feetof the Conservatives. And it was done in a very quiet way: no allusion tothe precise character of the change; no hint that the question was abouttwo different festivals: "all the brethren in the East, who formerlycelebrated this festival at the same time as the Jews, will in futureconform to the Romans and to us. " The Judaizers meant to be keeping thePassover _as_ a Christian feast: they are gently assumed to be keeping, _not_ the Passover, _but_ a Christian feast; and a doctrinal decision isquietly, but efficiently, announced under the form of a chronologicalordinance. Had the Council issued theses of doctrine, and excommunicatedall dissentients, the rupture of the East and West would have taken placeearlier by centuries than it did. The only place in which I ever saw anypart of my paradox advanced, was in an article in the _Examiner_ newspaper, towards the end of 1866, after the above was written. A story about Christopher Clavius, the workman of the new Calendar. Ichanced to pick up "Albertus Pighius Campensis de æquinoctiorumsolsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis, De que Restitutione ecclesiastici Kalendarii, " Paris, 1520, folio. [760] Onthe title-page were decayed words followed by ".. _hristophor.. C.. Ii_, 1556(or 8), " the last blank not entirely erased by time, but showing the lowerhalves of an _l_ and of an _a_, and {373} rather too much room for a _v_. It looked very like _E Libris Christophori Clavii_ 1556. By the courtesy ofsome members of the Jesuit body in London, I procured a tracing of thesignature of Clavius from Rome, and the shapes of the letters, and themodes of junction and disjunction, put the matter beyond question. Even theextra space was explained; he wrote himself Cla_u_ius. Now in 1556, Claviuswas nineteen years old: it thus appears probable that the framer of theGregorian Calendar was selected, not merely as a learned astronomer, but asone who had attended to the calendar, and to works on its reformation, fromearly youth. When on the subject I found reason to think that Clavius hadreally read this work, and taken from it a phrase or two and a notion ortwo. Observe the advantage of writing the baptismal name at full length. A COUPLE OF MINOR PARADOXES. The discovery of a general resolution of all superior finite equations, of every numerical both algebraick and transcendent form. By A. P. Vogel, [761] mathematician at Leipzick. Leipzick and London, 1845, 8vo. This work is written in the English of a German who has not mastered theidiom: but it is always intelligible. It professes to solve equations ofevery degree "in a more extent sense, and till to every degree ofexactness. " The general solution of equations of _all_ degrees is a vexedquestion, which cannot have the mysterious interest of the circle problem, and is of a comparatively modern date. [762] Mr. Vogel {374} announces aforthcoming treatise in which are resolved the "last impossibilities ofpure mathematics. " Elective Polarity the Universal Agent. By Frances Barbara Burton, authoress of 'Astronomy familiarized, ' 'Physical Astronomy, ' &c. London, 1845, 8vo. [763] The title gives a notion of the theory. The first sentence states, that12, 500 years ago [alpha] Lyræ was the pole-star, and attributes the immensemagnitude of the now fossil animals to a star of such "polaric intensity asVega pouring its magnetic streams through our planet. " Miss Burton was alady of property, and of very respectable acquirements, especially inHebrew; she was eccentric in all things. 1867. --Miss Burton is revived by the writer of a book on meteorology whichmakes use of the planets: she is one of his leading minds. [764] SPECULATIVE THOUGHT IN ENGLAND. In the year 1845 the old _Mathematical Society_ was merged in theAstronomical Society. The circle-squarers, etc. , thrive more in Englandthan in any other country: there are most weeds where there is the largestcrop. Speculation, though not encouraged by our Government so much as bythose of the Continent, has had, not indeed such forcing, but much widerdiffusion: few tanks, but many rivulets. On this point I quote from thepreface to the reprint of the work of Ramchundra, [765] which Isuperintended for the late Court of Directors of the East India Company. {375} "That sound judgment which gives men well to know what is best for them, aswell as that faculty of invention which leads to development of resourcesand to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced without, a great taste for purespeculation among the general mass of the people, down to the lowest ofthose who can read and write. England is a marked example. Many personswill be surprised at this assertion. They imagine that our country is thegreat instance of the refusal of all _unpractical_ knowledge in favor ofwhat is _useful_. I affirm, on the contrary, that there is no country inEurope in which there has been so wide a diffusion of speculation, theory, or what other unpractical word the reader pleases. In our country, thescientific _society_ is always formed and maintained by the people; inevery other, the scientific _academy_--most aptly named--has been thecreation of the government, of which it has never ceased to be thenursling. In all the parts of England in which manufacturing pursuits havegiven the artisan some command of time, the cultivation of mathematics andother speculative studies has been, as is well known, a very frequentoccupation. In no other country has the weaver at his loom bent over the_Principia_ of Newton; in no other country has the man of weekly wagesmaintained his own scientific periodical. With us, since the beginning ofthe last century, scores upon scores--perhaps hundreds, for I am far fromknowing all--of annuals have run, some their ten years, some theirhalf-century, some their century and a half, containing questions to beanswered, from which many of our examiners in the universities have culledmaterials for the academical contests. And these questions have always beenanswered, and in cases without number by the lower order of purchasers, themechanics, the weavers, and the printers' workmen. I cannot here digress topoint out the manner in which the concentration of manufactures, and thegeneral diffusion of education, have affected the {376} state of things; Ispeak of the time during which the present system took its rise, and of thecircumstances under which many of its most effective promoters weretrained. In all this there is nothing which stands out, like thestate-nourished academy, with its few great names and brilliant singleachievements. This country has differed from all others in the widediffusion of the disposition to speculate, which disposition has found itsplace among the ordinary habits of life, moderate in its action, healthy inits amount. " THE OLD MATHEMATICAL SOCIETY. Among the most remarkable proofs of the diffusion of speculation was theMathematical Society, which flourished from 1717 to 1845. Its habitat wasSpitalfields, and I think most of its existence was passed in CrispinStreet. It was originally a plain society, belonging to the studiousartisan. The members met for discussion once a week; and I believe I amcorrect in saying that each man had his pipe, his pot, and his problem. Oneof their old rules was that, "If any member shall so far forget himself andthe respect due to the Society as in the warmth of debate to threaten oroffer personal violence to any other member, he shall be liable toimmediate expulsion, or to pay such fine as the majority of the memberspresent shall decide. " But their great rule, printed large on the back ofthe title page of their last book of regulations, was "By the constitutionof the Society, it is the duty of every member, if he be asked anymathematical or philosophical question by another member, to instruct himin the plainest and easiest manner he is able. " We shall presently seethat, in old time, the rule had a more homely form. I have been told that De Moivre[766] was a member of this {377} Society. This I cannot verify: circumstances render it unlikely; even though theFrench refugees clustered in Spitalfields; many of them were of theSociety, which there is some reason to think was founded by them. ButDolland, [767] Thomas Simpson, [768] Saunderson, [769] Crossley, [770] andothers of known name, were certainly members. The Society graduallydeclined, and in 1845 was reduced to nineteen members. An arrangement wasmade by which sixteen of these members, who where not already in theAstronomical Society became Fellows without contribution, all the books andother property of the old Society being transferred to the new one. I wasone of the committee which made the preliminary inquiries, and the reasonof the decline was soon manifest. The only question which could arise waswhether the members of the society of working men--for this repute stillcontinued--were of that class of educated men who could associate with theFellows of the Astronomical Society on terms agreeable to all parties. Wefound that the artisan element had been extinct for many years; there wasnot a man but might, as to education, manners, and position, have become aFellow in the usual way. The fact was that life in Spitalfields had becomeharder: and the weaver could {378} only live from hand to mouth, and not upto the brain. The material of the old Society no longer existed. In 1798, experimental lectures were given, a small charge for admissionbeing taken at the door: by this hangs a tale--and a song. Many years ago, I found among papers of a deceased friend, who certainly never had anythingto do with the Society, and who passed all his life far from London, asong, headed "Song sung by the Mathematical Society in London, at a dinnergiven Mr. Fletcher, [771] a solicitor, who had defended the Society gratis. "Mr. Williams, [772] the Assistant Secretary of the Astronomical Society, formerly Secretary of the Mathematical Society, remembered that the Societyhad had a solicitor named Fletcher among the members. Some years elapsedbefore it struck me that my old friend Benjamin Gompertz, [773] who had longbeen a member, might have some recollection of the matter. The following isan extract of a letter from him (July 9, 1861): "As to the Mathematical Society, of which I was a member when only 18 yearsof age, [Mr. G. Was born in 1779], having been, contrary to the rules, elected under the age of 21. How I came to be a member of that Society--andcontinued so until it joined the Astronomical Society, and was then thePresident--was: I happened to pass a bookseller's small shop, ofsecond-hand books, kept by a poor taylor, but a good mathematician, JohnGriffiths. I was very pleased to meet a mathematician, and I asked him ifhe would give me some lessons; and his reply was that I was more capable toteach him, but he belonged to a society of mathematicians, and he wouldintroduce me. I accepted the offer, and I was elected, and had manyscholars then to teach, as {379} one of the rules was, if a member askedfor information, and applied to any one who could give it, he was obligedto give it, or fine one penny. Though I might say much with respect to theSociety which would be interesting, I will for the present reply only toyour question. I well knew Mr. Fletcher, who was a very clever and veryscientific person. He did, as solicitor, defend an action brought by aninformer against the Society--I think for 5, 000l. --for giving lectures tothe public in philosophical subjects [i. E. , for unlicensed publicexhibition with money taken at the doors]. I think the price for admissionwas one shilling, and we used to have, if I rightly recollect, from two tothree hundred visitors. Mr. Fletcher was successful in his defence, and wegot out of our trouble. There was a collection made to reward his services, but he did not accept of any reward: and I think we gave him a dinner, asyou state, and enjoyed ourselves; no doubt with astronomical songs andother songs; but my recollection does not enable me to say if theastronomical song was a drinking song. I think the anxiety caused by thataction was the cause of some of the members' death. [They had, no doubt, broken the law in ignorance; and by the sum named, the informer must havebeen present, and sued for a penalty on every shilling he could prove tohave been taken]. " I by no means guarantee that the whole song I proceed to give is what wassung at the dinner: I suspect, by the completeness of the chain, thataugmentations have been made. My deceased friend was just the man to addsome verses, or the addition may have been made before it came into hishands, or since his decease, for the scraps containing the verses passedthrough several hands before they came into mine. We may, however, bepretty sure that the original is substantially contained in what is given, and that the character is therefore preserved. I have had myself to repairdamages every now and then, in the way of conjectural restoration ofdefects caused by ill-usage. {380} THE ASTRONOMER'S DRINKING SONG. "Whoe'er would search the starry sky, Its secrets to divine, sir, Should take his glass--I mean, should try A glass or two of wine, sir! True virtue lies in golden mean, And man must wet his clay, sir; Join these two maxims, and 'tis seen He should drink his bottle a day, sir! "Old Archimedes, reverend sage! By trump of fame renowned, sir, Deep problems solved in every page, And the sphere's curved surface found, [774] sir: Himself he would have far outshone, And borne a wider sway, sir, Had he our modern secret known, And drank a bottle a day, sir! "When Ptolemy, [775] now long ago, Believed the earth stood still, sir, He never would have blundered so, Had he but drunk his fill, sir: He'd then have felt[776] it circulate, And would have learnt to say, sir, The true way to investigate Is to drink your bottle a day, sir! "Copernicus, [777] that learned wight, The glory of his nation, With draughts of wine refreshed his sight, And saw the earth's rotation; {381} Each planet then its orb described, The moon got under way, sir; These truths from nature he imbibed For he drank his bottle a day, sir! "The noble[778] Tycho placed the stars, Each in its due location; He lost his nose[779] by spite of Mars, But that was no privation: Had he but lost his mouth, I grant He would have felt dismay, sir, Bless you! _he_ knew what he should want To drink his bottle a day, sir! "Cold water makes no lucky hits; On mysteries the head runs: Small drink let Kepler[780] time his wits On the regular polyhedrons: He took to wine, and it changed the chime, His genius swept away, sir, Through area varying[781] as the time At the rate of a bottle a day, sir! "Poor Galileo, [782] forced to rat Before the Inquisition, _E pur si muove_[783] was the pat He gave them in addition: {382} He meant, whate'er you think you prove, The earth must go its way, sirs; Spite of your teeth I'll make it move, For I'll drink my bottle a day, sirs! "Great Newton, who was never beat Whatever fools may think, sir; Though sometimes he forgot to eat, He never forgot to drink, sir: Descartes[784] took nought but lemonade, To conquer him was play, sir; The first advance that Newton made Was to drink his bottle a day, sir! "D'Alembert, [785] Euler, [786] and Clairaut, [787] Though they increased our store, sir, Much further had been seen to go Had they tippled a little more, sir! Lagrange[788] gets mellow with Laplace, [789] And both are wont to say, sir, The _philosophe_ who's not an ass Will drink his bottle a day, sir! "Astronomers! what can avail Those who calumniate us; Experiment can never fail With such an apparatus: Let him who'd have his merits known Remember what I say, sir; Fair science shines on him alone Who drinks his bottle a day, sir! {383} "How light we reck of those who mock By this we'll make to appear, sir, We'll dine by the sidereal[790] clock For one more bottle a year, sir: But choose which pendulum you will, You'll never make your way, sir, Unless you drink--and drink your fill, -- At least a bottle a day, sir!" Old times are changed, old manners gone! There is a new Mathematical Society, [791] and I am, at this present writing(1866), its first President. We are very high in the newest developments, and bid fair to take a place among the scientific establishments. BenjaminGompertz, who was President of the old Society when it expired, was thelink between the old and new body: he was a member of _ours_ at his death. But not a drop of liquor is seen at our meetings, except a decanter ofwater: all our heavy is a fermentation of symbols; and we do not draw itmild. There is no penny fine for reticence or occult science; and as to asong! not the ghost of a chance. 1826. The time may have come when the original documents connected with thediscovery of Neptune may be worth revising. The following are extracts fromthe _Athenæum_ of October 3 and October 17: LE VERRIER'S[792] PLANET. We have received, at the last moment before making up for press, thefollowing letter from Sir John Herschel, [793] {384} in reference to thematter referred to in the communication from Mr. Hind[794] given below: "Collingwood, Oct. 1. "In my address to the British Association assembled at Southampton, on theoccasion of my resigning the chair to Sir R. Murchison, [795] I stated, among the remarkable astronomical events of the last twelvemonth, that ithad added a new planet to our list, --adding, 'it has done more, --it hasgiven us the probable prospect of the discovery of another. We see it asColumbus saw America from the shores of Spain. Its movements have beenfelt, trembling along the far-reaching line of our analysis, with acertainty hardly inferior to that of ocular demonstration. '--Theseexpressions are not reported in any of the papers which profess to give anaccount of the proceedings, but I appeal to all present whether they werenot used. "Give me leave to state my reasons for this confidence; and, in so doing, to call attention to some facts which deserve to be put on record in thehistory of this noble discovery. On July 12, 1842, the late illustriousastronomer, Bessel, [796] honored me with a visit at my present residence. On the evening of that day, conversing on the great work of the planetaryreductions undertaken by the Astronomer Royal[797]--then in progress, andsince published, [798]--M. Bessel remarked that the motions of Uranus, as hehad satisfied {385} himself by careful examination of the recordedobservations, could not be accounted for by the perturbations of the knownplanets; and that the deviations far exceeded any possible limits of errorof observation. In reply to the question, Whether the deviations inquestion might not be due to the action of an unknown planet?--he statedthat he considered it highly probable that such was the case, --beingsystematic, and such as might be produced by an exterior planet. I theninquired whether he had attempted, from the indications afforded by theseperturbations, to discover the position of the unknown body, --in order that'a hue and cry' might be raised for it. From his reply, the words of whichI do not call to mind, I collected that he had not then gone into thatinquiry; but proposed to do so, having now completed certain works whichhad occupied too much of his time. And, accordingly, in a letter which Ireceived from him after his return to Königsberg, dated November 14, 1842, he says, --'In reference to our conversation at Collingwood, I _announce_ toyou (_melde_ ich Ihnen) that Uranus is not forgotten. ' Doubtless, therefore, among his papers will be found some researches on the subject. "The remarkable calculations of M. Le Verrier--which have pointed out, asnow appears, nearly the true situation of the new planet, by resolving theinverse problem of the perturbations--if uncorroborated by repetition ofthe numerical calculations by another hand, or by independent investigationfrom another quarter, would hardly justify so strong an assurance as thatconveyed by my expressions above alluded to. But it was known to me, atthat time, (I will take the liberty to cite the Astronomer Royal as myauthority) that a similar investigation had been independently enteredinto, and a conclusion as to the situation of the new planet very nearlycoincident with M. Le Verrier's arrived at (in entire ignorance of hisconclusions), by a young Cambridge mathematician, Mr. Adams;[799]--whowill, I hope, {386} pardon this mention of his name (the matter being oneof great historical moment), --and who will, doubtless, in his own good timeand manner, place his calculations before the public. "J. F. W. HERSCHEL. " _Discovery of Le Verrier's Planet. _ Mr. Hind announces to the _Times_ that he has received a letter from Dr. Brünnow, of the Royal Observatory at Berlin, giving the very importantinformation that Le Verrier's planet was found by M. Galle, on the night ofSeptember 23. "In announcing this grand discovery, " he says, "I think itbetter to copy Dr. Brünnow's[800] letter. " "Berlin, Sept. 25. "My dear Sir--M. Le Verrier's planet was discovered here the 23d ofSeptember, by M. Galle. [801] It is a star of the 8th magnitude, but with adiameter of two or three seconds. Here are its places: h. M. S. R. A. Declination. Sept. 23, 12 0 14. 6 M. T. 328° 19' 16. 0" -13° 24' 8. 2" Sept. 24, 8 54 40. 9 M. T. 328° 18' 14. 3" -13° 24' 29. 7" The planet is now retrograde, its motion amounting daily to four seconds oftime. "Yours most respectfully, BRÜNNOW. " "This discovery, " Mr. Hind says, "may be justly considered one of thegreatest triumphs of theoretical astronomy;" and he adds, in a postscript, that the planet was observed at Mr. Bishop's[802] Observatory, in theRegent's Park, {387} on Wednesday night, notwithstanding the moonlight andhazy sky. "It appears bright, " he says, "and with a power of 320 I can seethe disc. The following position is the result of instrumental comparisonswith 33 Aquarii: Sept. 30, at 8h. 16m. 21s. Greenwich mean time-- Right ascension of planet 21h. 52m. 47. 15s. South declination 13° 27' 20". " THE NEW PLANET. "Cambridge Observatory, Oct. 15. "The allusion made by Sir John Herschel, in his letter contained in the_Athenæum_ of October 3, to the theoretical researches of Mr. Adams, respecting the newly-discovered planet, has induced me to request that youwould make the following communication public. It is right that I shouldfirst say that I have Mr. Adams's permission to make the statements thatfollow, so far as they relate to his labors. I do not propose to enter intoa detail of the steps by which Mr. Adams was led, by his spontaneous andindependent researches, to a conclusion that a planet must exist moredistant than Uranus. The matter is of too great historical moment not toreceive a more formal record than it would be proper to give here. Myimmediate object is to show, while the attention of the scientific publicis more particularly directed to the subject, that, with respect to thisremarkable discovery, English astronomers may lay claim to some merit. "Mr. Adams formed the resolution of trying, by calculation, to account forthe anomalies in the motion of Uranus on the hypothesis of a more distantplanet, when he was an undergraduate in this university, and when hisexertions for the academical distinction, which he obtained in January1843, left him no time for pursuing the research. In the course of thatyear, he arrived at an approximation to the position of the supposedplanet; which, however, he did not consider to be worthy of confidence, onaccount of his not {388} having employed a sufficient number ofobservations of Uranus. Accordingly, he requested my intervention to obtainfor him the early Greenwich observations, then in course ofreduction;--which the Astronomer Royal immediately supplied, in the kindestpossible manner. This was in February, 1844. In September, 1845, Mr. Adamscommunicated to me values which he had obtained for the heliocentriclongitude, excentricity of orbit, longitude of perihelion, and mass, of anassumed exterior planet, --deduced entirely from unaccounted-forperturbations of Uranus. The same results, somewhat corrected, hecommunicated, in October, to the Astronomer Royal. M. Le Verrier, in aninvestigation which was published in June of 1846, assigned very nearly thesame heliocentric longitude for the probable position of the planet as Mr. Adams had arrived at, but gave no results respecting its mass and the formof its orbit. The coincidence as to position from two entirely independentinvestigations naturally inspired confidence; and the Astronomer Royalshortly after suggested the employing of the Northumberland telescope ofthis observatory in a systematic search after the hypothetical planet;recommending, at the same time, a definite plan of operations. I undertookto make the search, --and commenced observing on July 29. The observationswere directed, in the first instance, to the part of the heavens whichtheory had pointed out as the most probable place of the planet; inselecting which I was guided by a paper drawn up for me by Mr. Adams. Nothaving hour xxi. Of the Berlin star-maps--of the publication of which I wasnot aware--I had to proceed on the principle of comparison of observationsmade at intervals. On July 30, I went over a zone 9' broad, in such amanner as to include all stars to the eleventh magnitude. On August 4, Itook a broader zone and recorded a place of the planet. My nextobservations were on August 12; when I met with a star of the eighthmagnitude in the zone which I had gone over on July 30, --and which did notthen {389} contain this star. Of course, this was the planet;--the place ofwhich was, thus, recorded a second time in four days of observing. Acomparison of the observations of July 30 and August 12 would, according tothe principle of search which I employed, have shown me the planet. I didnot make the comparison till after the detection of it at Berlin--partlybecause I had an impression that a much more extensive search was requiredto give any probability of discovery--and partly from the press of otheroccupation. The planet, however, was _secured_, and two positions of itrecorded six weeks earlier here than in any other observatory, --and in asystematic search expressly undertaken for that purpose. I give now thepositions of the planet on August 4 and August 12. Greenwich mean time. Aug. 4, 13h. 36m. 25s. {R. A. 21h. 58m. 14. 70s. {N. P. D. 102° 57' 32. 2" Aug. 12, 13h. 3m. 26s. {R. A. 21h. 57m. 26. 13s. {N. P. D. 103° 2' 0. 2" "From these places compared with recent observations Mr. Adams has obtainedthe following results: Distance of the planet from the sun 30. 05 Inclination of the orbit 1° 45' Longitude of the descending node 309° 43' Heliocentric longitude, Aug. 4 326° 39' "The present distance from the sun is, therefore, thirty times the earth'smean distance;--which is somewhat less than the theory had indicated. Theother elements of the orbit cannot be approximated to till the observationsshall have been continued for a longer period. "The part taken by Mr. Adams in the theoretical search after this planetwill, perhaps, be considered to justify the suggesting of a name. With hisconsent, I mention _Oceanus_ as one which may possibly receive the votes ofastronomers. --I {390} have authority to state that Mr. Adams'sinvestigations will in a short time, be published in detail. "J. CHALLIS. "[803] ASTRONOMICAL POLICE REPORT. "An ill-looking kind of a body, who declined to give any name, was broughtbefore the Academy of Sciences, charged with having assaulted a gentlemanof the name of Uranus in the public highway. The prosecutor was a youngishlooking person, wrapped up in two or three great coats; and looked chillierthan anything imaginable, except the prisoner, --whose teeth absolutelyshook, all the time. Policeman Le Verrier[804] stated that he saw the prosecutor walking alongthe pavement, --and sometimes turning sideways, and sometimes running up tothe railings and jerking about in a strange way. Calculated that somebodymust be pulling his coat, or otherwise assaulting him. It was so dark thathe could not see; but thought, if he watched the direction in which thenext odd move was made, he might find out something. When the time came, heset Brünnow, a constable in another division of the same force, to watchwhere he told him; and Brünnow caught the prisoner lurking about in thevery spot, --trying to look as if he was minding his own business. Hadsuspected for a long time that somebody was lurking about in theneighborhood. Brünnow was then called, and deposed to his catching theprisoner as described. _M. Arago. _--Was the prosecutor sober? _Le Verrier. _--Lord, yes, your worship; no man who had a drop in him everlooks so cold as he did. _M. Arago. _--Did you see the assault? _Le Verrier. _--I can't say I did; but I told Brünnow exactly how he'd becrouched down;--just as he was. {391} _M. Arago (to Brünnow). _--Did _you_ see the assault? _Brünnow. _--No, your worship; but I caught the prisoner. _M. Arago. _--How did you know there was any assault at all? _Le Verrier. _--I reckoned it couldn't be otherwise, when I saw theprosecutor making those odd turns on the pavement. _M. Arago. _--You reckon and you calculate! Why, you'll tell me, next, thatyou policemen may sit at home and find out all that's going on in thestreets by arithmetic. Did you ever bring a case of this kind before metill now? _Le Verrier. _--Why, you see, your worship, the police are growing clevererand cleverer every day. We can't help it:--it grows upon us. _M. Arago. _--You're getting too clever for me. What does the prosecutorknow about the matter? The prosecutor said, all he knew was that he was pulled behind by somebodyseveral times. On being further examined, he said that he had seen theprisoner often, but did not know his name, nor how he got his living; buthad understood he was called Neptune. He himself had paid rates and taxes agood many years now. Had a family of six, --two of whom got their ownliving. The prisoner being called on for his defence, said that it was a quarrel. He had pushed the prosecutor--and the prosecutor had pushed him. They hadknown each other a long time, and were always quarreling;--he did not knowwhy. It was their nature, he supposed. He further said, that the prosecutorhad given a false account of himself;--that he went about under differentnames. Sometimes he was called Uranus, sometimes Herschel, and sometimesGeorgium Sidus; and he had no character for regularity in the neighborhood. Indeed, he was sometimes not to be seen for a long time at once. The prosecutor, on being asked, admitted, after a little hesitation, thathe had pushed and pulled the prisoner too. {392} In the altercation whichfollowed, it was found very difficult to make out which began:--and theworthy magistrate seemed to think they must have begun together. _M. Arago. _--Prisoner, have you any family? The prisoner declined answering that question at present. He said hethought the police might as well reckon it out whether he had or not. _M. Arago_ said he didn't much differ from that opinion. --He then addressedboth prosecutor and prisoner; and told them that if they couldn't settletheir differences without quarreling in the streets, he should certainlycommit them both next time. In the meantime, he called upon both to enterinto their own recognizances; and directed the police to have an eye uponboth, --observing that the prisoner would be likely to want it a long time, and the prosecutor would be not a hair the worse for it. " This quib was written by a person who was among the astronomers: and itillustrates the fact that Le Verrier had sole possession of the field untilMr. Challis's letter appeared. Sir John Herschel's previous communicationshould have paved the way: but the wonder of the discovery drove it out ofmany heads. There is an excellent account of the whole matter in ProfessorGrant's[805] _History of Physical Astronomy_. The squib scandalized somegrave people, who wrote severe admonitions to the editor. There areformalists who spend much time in writing propriety to journals, to whichthey serve as foolometers. In a letter to the _Athenæum_, speaking of theway in which people hawk fine terms for common things, I said that thesepeople ought to have a new translation of the Bible, which should containthe verse "gentleman and lady, created He them. " The editor was handsomelyfired and brimstoned! {393} A NEW THEORY OF TIDES. A new theory of the tides: in which the errors of the usual theory are demonstrated; and proof shewn that the full moon is not the cause of a concomitant spring tide, but actually the cause of the neaps.... By Comm^r. Debenham, [806] R. N. London, 1846, 8vo. The author replied to a criticism in the _Athenæum_, and I remember how, ina very few words, he showed that he had read nothing on the subject. Thereviewer spoke of the forces of the planets (i. E. , the Sun and Moon) on theocean, on which the author remarks, "But N. B. The Sun is no planet, Mr. Critic. " Had he read any of the actual investigations on the usual theory, he would have known that to this day the sun and moon continue to be called_planets_--though the phrase is disappearing--in speaking of the tides; thesense, of course, being the old one, wandering bodies. A large class of the paradoxers, when they meet with something which takenin their sense is absurd, do not take the trouble to find out the intendedmeaning, but walk off with the words laden with their own firstconstruction. Such men are hardly fit to walk the streets without aninterpreter. I was startled for a moment, at the time when a recenthappy--and more recently happier--marriage occupied the public thoughts, byseeing in a haberdasher's window, in staring large letters, an unpunctuatedsentence which read itself to me as "Princess Alexandra! collar and cuff!"It immediately occurred to me that had I been any one of some scores of myparadoxers, I should, no doubt, have proceeded to raise the mob against theunscrupulous person who dared to hint to a young bride such maleficent--orat least immellificent--conduct towards her new lord. But, as it was, certain material contexts in the shop window suggested a less {394} savageexplanation. A paradoxer should not stop at reading the advertisements ofNewton or Laplace; he should learn to look at the stock of goods. I think I must have an eye for double readings, when presented: though Inever guess riddles. On the day on which I first walked into the _Panizzi_reading room[807]--as it ought to be called--at the Museum, I began mycircuit of the wall-shelves at the ladies' end: and perfectly coincided inthe propriety of the Bibles and theological works being placed there. Butthe very first book I looked on the back of had, in flaming gold letters, the following inscription--"Blast the Antinomians!"[808] If a line had beendrawn below the first word, Dr. Blast's history of the Antinomians wouldnot have been so fearfully misinterpreted. It seems that neither the bindernor the arranger of the room had caught my reading. The book was removedbefore the catalogue of books of reference was printed. AN ASTRONOMICAL PARADOXER. Two systems of astronomy: first, the Newtonian system, showing the rise and progress thereof, with a short historical account; the general theory with a variety of remarks thereon: second, the system in accordance with the Holy Scriptures, showing the rise and progress from Enoch, the seventh from Adam, the prophets, Moses, and others, in the first Testament; our Lord Jesus Christ, and his apostles, in the new or second Testament; Reeve and Muggleton, in the third and last Testament; with a variety of remarks thereon. By Isaac Frost. [809] London, 1846, 4to. {395} A very handsomely printed volume, with beautiful plates. Many readers whohave heard of Muggletonians have never had any distinct idea of LodowickMuggleton, [810] the inspired tailor, (1608-1698) who about 1650 receivedhis commission from heaven, wrote a Testament, founded a sect, anddescended to posterity. Of Reeve[811] less is usually said; according toMr. Frost, he and Muggleton are the two "witnesses. " I shall content myselfwith one specimen of Mr. Frost's science: "I was once invited to hear read over 'Guthrie[812] on Astronomy, ' and whenthe reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs insupport of his theory of the earth revolving round the sun: all the rest isassertion without any proofs. '--'What are they?' inquired theDoctor. --'Well, ' I said, 'they are, first, the power of {396} attraction tokeep the earth to the sun; the second is the power of repulsion, by virtueof the centrifugal motion of the earth: all the rest appears to meassertion without proof. ' The Doctor considered a short time and then said, 'It certainly did appear so. ' I said, 'Sir Isaac has certainly obtained thecredit of completing the system, but really he has only half done hiswork. '--'How is that, ' inquired my friend the Doctor. My reply was this:'You will observe his system shows the earth traverses round the sun on aninclined plane; the consequence is, there are four powers required to makehis system complete: 1st. The power of _attraction_. 2ndly. The power of _repulsion_. 3rdly. The power of _ascending_ the inclined plane. 4thly. The power of _descending_ the inclined plane. You will thus easily see the _four_ powers required, and Newton has onlyaccounted for _two_; the work is therefore only half done. ' Upon duereflection the Doctor said, 'It certainly was necessary to have these_four_ points cleared up before the system could be said to be complete. '" I have no doubt that Mr. Frost, and many others on my list, have reallyencountered doctors who could be puzzled by such stuff as this, or nearlyas bad, among the votaries of existing systems, and have been encouragedthereby to print their objections. But justice requires me to say that fromthe words "power of repulsion by virtue of the centrifugal motion of theearth, " Mr. Frost may be suspected of having something more like a notionof the much-mistaken term "centrifugal force" than many paradoxers ofgreater fame. The Muggletonian sect is not altogether friendless: over andabove this handsome volume, the works of Reeve and Muggleton were printed, in 1832, in three quarto volumes. See _Notes and Queries, 1st Series_, v, 80; 3d Series, iii, 303. {397} [The system laid down by Mr. Frost, though intended to be substantiallythat of Lodowick Muggleton, is not so vagarious. It is worthy of note howvery different have been the fates of two contemporary paradoxers, Muggleton and George Fox. [813] They were friends and associates, [814] andcommenced their careers about the same time, 1647-1650. The followers ofFox have made their sect an institution, and deserve to be called thepioneers of philanthropy. But though there must still be Muggletonians, since expensive books are published by men who take the name, no sect ofthat name is known to the world. Nevertheless, Fox and Muggleton are men ofone type, developed by the same circumstances: it is for those whoinvestigate such men to point out why their teachings have had fates sodifferent. Macaulay says it was because Fox found followers of more sensethan himself. True enough: but why did Fox find such followers and notMuggleton? The two were equally crazy, to all appearance: and thedifference required must be sought in the doctrines themselves. Fox was not a _rational_ man: but the success of his sect and doctrinesentitles him to a letter of alteration of the phrase which I am surprisedhas not become current. When Conduitt, [815] the husband of Newton'shalf-niece, wrote a circular to Newton's friends, just after his death, inviting them to bear their parts in a proper biography, he said, "As SirI. Newton was a _national_ man, I think every one ought to contribute to awork intended to do him justice. " Here is the very phrase which is oftenwanted to signify that {398} celebrity which puts its mark, good or bad, onthe national history, in a manner which cannot be asserted of manynotorious or famous historical characters. Thus George Fox and Newton areboth _national_ men. Dr. Roget's[816] _Thesaurus_ gives more than fiftysynonyms--_colleagues_ would be the better word--of "_celebrated_, " any oneof which might be applied, either in prose or poetry, to Newton or to hisworks, no one of which comes near to the meaning which Conduitt's adjectiveimmediately suggests. The truth is, that we are too _monarchical_ to be _national_. We have theQueen's army, the Queen's navy, the Queen's highway, the Queen's English, etc. ; nothing is national except the _debt_. That this remark is not new isan addition to its force; it has hardly been repeated since it was firstmade. It is some excuse that _nation_ is not vernacular English: the_country_ is our word, and _country man_ is appropriated. ] Astronomical Aphorisms, or Theory of Nature; founded on the immutable basis of Meteoric Action. By P. Murphy, [817] Esq. London, 1847, 12mo. This is by the framer of the Weather Almanac, who appeals to that work ascorroborative of his theory of planetary temperature, years after all theworld knew by experience that this meteorological theory was just as goodas the others. {399} The conspiracy of the Bullionists as it affects the present system of the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16). This pamphlet is one of a class of which I know very little, in which theeffects of the laws relating to this or that political bone of contentionare imputed to deliberate conspiracy of one class to rob another of whatthe one knew ought to belong to the other. The success of such writers inbelieving what they have a bias to believe, would, if they knew themselves, make them think it equally likely that the inculpated classes might reallybelieve what it is _their_ interest to believe. The idea of a _guilty_understanding existing among fundholders, or landholders, or any holders, all the country over, and never detected except by bouncing pamphleteers, is a theory which should have been left for Cobbett[818] to propose, andfor Apella to believe. [819] [_August_, 1866. A pamphlet shows how to pay the National Debt. Advancepaper to railways, etc. , receivable in payment of taxes. The railways payinterest and principal in money, with which you pay your national debt, andredeem your notes. Twenty-five years of interest redeems the notes, andthen the principal pays the debt. Notes to be kept up to value bypenalties. ] THEISM INDEPENDENT OF REVELATION. The Reasoner. No. 45. Edited by G. J. Holyoake. [820] Price _2d. _ Is there sufficient proof of the existence of God? 8vo. 1847. This acorn of the holy oak was forwarded to me with a manuscript note, signed by the editor, on the part of the {400} "London Society ofTheological Utilitarians, " who say, "they trust you may be induced to givethis momentous subject your consideration. " The supposition that amiddle-aged person, known as a student of thought on more subjects thanone, had that particular subject yet to begin, is a specimen of what I willcall the _assumption-trick_ of controversy, a habit which pervades allsides of all subjects. The tract is a proof of the good policy of lettingopinions find their level, without any assistance from the Court of Queen'sBench. Twenty years earlier the thesis would have been positive, "There issufficient proof of the non-existence of God, " and bitter in its tone. Asit stands, we have a moderate and respectful treatment--wrong only inmaking the opponent argue absurdly, as usually happens when one sideinvents the other--of a question in which a great many Christians haveagreed with the atheist: that question being--Can the existence of God beproved independently of revelation? Many very religious persons answer thisquestion in the negative, as well as Mr. Holyoake. And, this point beingsettled, all who agree in the negative separate into those who can endurescepticism, and those who cannot: the second class find their way toChristianity. This very number of _The Reasoner_ announces the secession ofone of its correspondents, and his adoption of the Christian faith. Thiswould not have happened twenty years before: nor, had it happened, would ithave been respectfully announced. There are people who are very unfortunate in the expression of theirmeaning. Mr. Holyoake, in the name of the "London Society" etc. , forwardeda pamphlet on the existence of God, and said that the Society trusted I"may be induced to give" the subject my "consideration. " How could I knowthe Society was one person, who supposed I had arrived at a conclusion andwanted a "_guiding word_"? But so it seems it was: Mr. Holyoake, in the_English {401} Leader_ of October 15, 1864, and in a private letter to me, writes as follows: "The gentleman who was the author of the argument, and who asked me to sendit to Mr. De Morgan, never assumed that that gentleman had 'that particularsubject to begin'--on the contrary, he supposed that one whom we all knewto be eminent as a thinker _had_ come to a conclusion upon it, and wouldperhaps vouchsafe a guiding word to one who was, as yet, seeking thesolution of the Great Problem of Theology. I told my friend that 'Mr. DeMorgan was doubtless preoccupied, and that he must be content to wait. Onsome day of courtesy and leisure he might have the kindness to write. ' Norwas I wrong--the answer appears in your pages at the lapse of seventeenyears. " I suppose Mr. Holyoake's way of putting his request was the _stylus curiæ_of the Society. A worthy Quaker who was sued for debt in the King's Benchwas horrified to find himself charged in the declaration with detaining hiscreditor's money by force and arms, contrary to the peace of our Lord theKing, etc. It's only the _stylus curiæ_, said a friend: I don't know_curiæ_, said the Quaker, but he shouldn't style us peace-breakers. The notion that the _non_-existence of God can be _proved_, has died outunder the light of discussion: had the only lights shone from the pulpitand the prison, so great a step would never have been made. The questionnow is as above. The dictum that Christianity is "part and parcel of thelaw of the land" is also abrogated: at the same time, and the coincidenceis not an accident, it is becoming somewhat nearer the truth that the lawof the land is part and parcel of Christianity. It must also be noticedthat _Christianity_ was part and parcel of the articles of _war_; and sowas _duelling_. Any officer speaking against religion was to be cashiered;and any officer receiving an affront without, in the last resort, attempting to kill his opponent, was also to be cashiered. Though somewhatof a book-hunter, I {402} have never been able to ascertain the date of thecollected remonstrances of the prelates in the House of Lords against thisovert inculcation of murder, under the soft name of _satisfaction_: it isneither in Watt, [821] nor in Lowndes, [822] nor in any edition ofBrunet;[823] and there is no copy in the British Museum. Was the collectededition really published? [The publication of the above in the _Athenæum_ has not produced referenceto a single copy. The collected edition seems to be doubted. I have evenmet one or two persons who doubt the fact of the Bishops havingremonstrated at all: but their doubt was founded on an absurd supposition, namely, that it was _no business of theirs_; that it was not the businessof the prelates of the church in union with the state to remonstrateagainst the Crown commanding murder! Some say that the edition waspublished, but under an irrelevant title, which prevented people fromknowing what it was about. Such things have happened: for example, arrangedextracts from Wellington's general orders, which would have attractedattention, fell dead under the title of "Principles of War. " It is surmisedthat the book I am looking for also contains the protests of the Reverendbench against other things besides the Thou-shalt-do-murder of the Articles(of war), and is called "First Elements of Religion" or some similar title. Time clears up all things. ] * * * * * Notes [1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p61. [2] In the first edition this reference was to page 11. [3] In the first edition this read "at page 438, " the work then appearingin a single volume. [4] "Just as it would surely have been better not to have considered it(i. E. , the trinity) as a mystery, and with Cl. Kleckermann to haveinvestigated by the aid of philosophy according to the teaching of truelogic what it might be, before they determined what it was; just so wouldit have been better to withdraw zealously and industriously into thedeepest caverns and darkest recesses of metaphysical speculations andsuppositions in order to establish their opinion beyond danger from theweapons of their adversaries.... Indeed that great man so explains anddemonstrates this dogma (although to theologians the word has not muchcharm) from the immovable foundations of philosophy, that with but fewchanges and additions a mind sincerely devoted to truth can desire nothingmore. " [5] Mrs. Wititterly, in _Nicholas Nickleby_. --A. De M. [6] The brackets mean that the paragraph is substantially from some one ofthe _Athenæum Supplements_. --S. E. De M. [7] "It is annoying that this ingenious naturalist who has already given usmore useful works and has still others in preparation, uses for this odioustask, a pen dipped in gall and wormwood. It is true that many of hisremarks have some foundation, and that to each error that he points out heat the same time adds its correction. But he is not always just and neverfails to insult. After all, what does his book prove except that aforty-fifth part of a very useful review is not free from mistakes? Must weconfuse him with those superficial writers whose liberty of body does notpermit them to restrain their fruitfulness, that crowd of savants of thehighest rank whose writings have adorned and still adorn the_Transactions_? Has he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres, Hans Sloanes, etc. Have been seen frequently? and thatstill are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an author whom Mr. Hill prefers to all others, I mean Mr. Hillhimself?" [8] "Let no free man be seized or imprisoned or in any way harmed except bytrial of his peers. " [9] "The master can rob, wreck and punish his slave according to hispleasure save only that he may not maim him. " [10] An Irish antiquary informs me that Virgil is mentioned in annals atA. D. 784, as "Verghil, i. E. , the geometer, Abbot of Achadhbo [and Bishop ofSaltzburg] died in Germany in the thirteenth year of his bishoprick. " Noallusion is made to his opinions; but it seems he was, by tradition, amathematician. The Abbot of Aghabo (Queen's County) was canonized byGregory IX, in 1233. The story of the second, or scapegoat, Virgil would bemuch damaged by the character given to the real bishop, if there wereanything in it to dilapidate. --A. De M. [11] "He performed many acts befitting the Papal dignity, and likewise manyexcellent (to be sure!) works. " [12] "After having been on the throne during ten years of pestilence. " [13] The work is the _Questiones Joannis Buridani super X librosAristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio. It also appeared at Paris in editions of 1499, 1513, and 1518, and atOxford in 1637. [14] Jean Buridan was born at Béthune about 1298, and died at Paris about1358. He was professor of philosophy at the University of Paris and severaltimes held the office of Rector. As a philosopher he was classed among thenominalists. [15] So in the original. [16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, thepantheistic philosopher, excommunicated from the Jewish faith for heresy, was born at Amsterdam in 1632 and died there in 1677. [17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire, Scotland, and died about 1291. He was one of the best known savants of thecourt of Emperor Frederick II, and wrote upon astrology, alchemy, and theoccult sciences. He was looked upon as a great magician and is mentionedamong the wizards in Dante's _Inferno_. "That other, round the loins So slender of his shape, was Michael Scot, Practised in every slight of magic wile. " _Inferno_, XX. Boccaccio also speaks of him: "It is not long since there was in this city(Florence) a great master in necromancy, who was called Michele Scotto, because he was a Scot. " _Decameron_, Dec. Giorno. Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_, is well known: "In these fair climes, it was my lot To meet the wondrous Michael Scott; A wizard of such dreaded fame, That when, in Salamanca's cave, Him listed his magic wand to wave, The bells would ring in Notre Dame!" Sir Walter's notes upon him are of interest. [18] These were some of the forgeries which Michel Chasles (1793-1880) wasduped into buying. They purported to be a correspondence between Pascal andNewton and to show that the former had anticipated some of the discoveriesof the great English physicist and mathematician. That they were forgerieswas shown by Sir David Brewster in 1855. [19] "Let the serpent also break from its appointed path. " [20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born atFlorence in 1803; died at Fiesole in 1869. His _Histoire des SciencesMathématiques_ appeared at Paris in 1838, the entire first edition ofvolume I, save some half dozen that he had carried home, being burned onthe day that the printing was completed. He was a great collector of earlyprinted works on mathematics, and was accused of having stolen largenumbers of them from other libraries. This accusation took him to London, where he bitterly attacked his accusers. There were two auction sales ofhis library, and a number of his books found their way into De Morgan'scollection. [21] Philo of Gadara lived in the second century B. C. He was a pupil ofSporus, who worked on the problem of the two mean proportionals. [22] In his _Histoire des Mathématiques_, the first edition of whichappeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and diedat Versailles in 1799. He was therefore only thirty-three years old whenhis great work appeared. The second edition, with additions by D'Alembert, appeared in 1799-1802. He also wrote a work on the quadrature of thecircle, _Histoire des recherches sur la Quadrature du Cercle_, whichappeared in 1754. [23] Eutocius of Ascalon was born in 480 A. D. He wrote commentaries on thefirst four books of the conics of Apollonius of Perga (247-222 B. C. ). Healso wrote on the Sphere and Cylinder and the Quadrature of the Circle, andon the two books on Equilibrium of Archimedes (287-212 B. C. ) [24] Edward Cocker was born in 1631 and died between 1671 and 1677. Hisfamous arithmetic appeared in 1677 and went through many editions. It waswritten in a style that appealed to teachers, and was so popular that theexpression "According to Cocker" became a household phrase. Early in thenineteenth century there was a similar saying in America, "According toDaboll, " whose arithmetic had some points of analogy to that of Cocker. Each had a well-known prototype in the ancient saying, "He reckons likeNicomachus of Gerasa. " [25] So in the original, for Barrême. François Barrême was to France whatCocker was to England. He was born at Lyons in 1640, and died at Paris in1703. He published several arithmetics, dedicating them to his patron, Colbert. One of the best known of his works is _L'arithmétique, ou le livrefacile pour apprendre l'arithmétique soi-mème_, 1677. The French word_barême_ or _barrême_, a ready-reckoner, is derived from his name. [26] Born at Rome, about 480 A. D. ; died at Pavia, 524. Gibbon speaks of himas "the last of the Romans whom Cato or Tully could have acknowledged fortheir countryman. " His works on arithmetic, music, and geometry wereclassics in the medieval schools. [27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV(1261-1264). He was one of the early medieval translators of Euclid fromthe Arabic into Latin, and the first printed edition of the _Elements_(Venice, 1482) was from his translation. In this work he probably dependednot a little upon at least two or three earlier scholars. He also wrote _Decomputo ecclesiastico Calendarium_, and _De quadratura circuli_. [28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of thecircumference to the diameter of a circle. [29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arrangedand inaccurate, but it is still a helpful bibliography. De Morgan speakssomewhere of his indebtedness to it. [30] Abraham Gotthelf Kästner was born at Leipsic in 1719, and died atGöttingen in 1800. He was professor of mathematics and physics atGöttingen. His _Geschichte der Mathematik_ (1796-1800) was a work ofconsiderable merit. In the text of the _Budget of Paradoxes_ the nameappears throughout as Kastner instead of Kästner. [31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in1476; died at Rome in 1558. He was an astrologer and mathematician, and wasprofessor of mathematics at Ferrara in 1531. In 1545 he became bishop ofCività Ducale. [32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in1892. He and Leverrier predicted the discovery of Neptune from theperturbations in Uranus. [33] Urbain-Jean-Joseph Leverrier was born at Saint-Lô, Manche, in 1811, and died at Paris in 1877. It was his data respecting the perturbations ofUranus that were used by Adams and himself in locating Neptune. [34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which DeMorgan refers, appeared at Leyden in 1594. [35] The title is: _In hoc libra contenta.... Introductio igeometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere. Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boüelles, Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died atNoyon about 1533. He was canon and professor of theology at Noyon. His_Introductio_ contains considerable work on star polygons, a favorite studyin the Middle Ages and early Renaissance. His work _Que hoc voluminecontin[=e]tur. Liber de intellectu. Liber de sensu_, etc. , appeared atParis in 1509-10. [36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on theMosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positionsof honor in the church, including the bishopric of Brescia. He was made acardinal in 1448. He wrote several works on mathematics, his _Opusculavaria_ appearing about 1490, probably at Strasburg, but published withoutdate or place. His _Opera_ appeared at Paris in 1511 and again in 1514, andat Basel in 1565. [37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) wasone of the most successful printers of his day. He was known as_Typographus Parisiensis_, and to his press we owe some of the best worksof the period. [38] Jacobus Faber Stapulensis (Jacques le Fèvre d'Estaples) was born atEstaples, near Amiens, in 1455, and died at Nérac in 1536. He was a priest, vicar of the bishop of Meaux, lecturer on philosophy at the Collège Lemoinein Paris, and tutor to Charles, son of Francois I. He wrote on philosophy, theology, and mathematics. [39] Claude-François Milliet de Challes was born at Chambéry in 1621, anddied at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660, and published a _Cursus seu mundus mathematicus_, which included a shorthistory of mathematics, in 1674. He also wrote on mathematical geography. [40] This date should be 1503, if he refers to the first edition. It iswell known that this is the first encyclopedia worthy the name to appear inprint. It was written by Gregorius Reisch (born at Balingen, and died atFreiburg in 1487), prior of the cloister at Freiburg and confessor toMaximilian I. The first edition appeared at Freiburg in 1503, and it passedthrough many editions in the sixteenth and seventeenth centuries. The titleof the 1504 edition reads: _Aepitoma omnis phylosophiae. Alias Margaritaphylosophica tractans de omni genere scibili: Cum additionibus: Quae inalijs non habentur_. [41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitomererum geometricarum ex geometrica introductio C. Bovilli. De quadraturacirculi demonstratio ex Campano_, that appeared without date about 1507. [42] Born at Liverpool in 1805, and died there about 1872. He was amerchant, and in 1865 he published, at Liverpool, a work entitled _TheQuadrature of the Circle, or the True Ratio between the Diameter andCircumference geometrically and mathematically demonstrated_. In this hegives the ratio as exactly 3-1/8. [43] "That it would be impossible to tell him exactly, since no one had yetbeen able to find precisely the ratio of the circumference to thediameter. " [44] This is the Paris edition: "Parisiis: ex officina Ascensiana annoChristi ... MDXIIII, " as appears by the colophon of the second volume towhich De Morgan refers. [45] Regiomontanus, or Johann Müller of Königsberg (Regiomontanus), wasborn at Königsberg in Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at Vienna under the great astronomer Peuerbach, and washis most famous pupil. He wrote numerous works, chiefly on astronomy. He isalso known by the names Ioannes de Monte Regio, de Regiomonte, IoannesGermanus de Regiomonte, etc. [46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either atLyons in 1534 or at Grenoble in 1535. He was professor of theology atCologne and also at Turin. After the publication of his _De OccultaPhilosophia_ he was imprisoned for sorcery. Both works appeared at Antwerpin 1530, and each passed through a large number of editions. A Frenchtranslation appeared in Paris in 1582, and an English one in London in1651. [47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in1600. He was a jurist and historian, and held the office of procuratorgeneral to the Duke of Lorraine. [48] This was at the storming of the city by the British on May 4, 1799. From his having been born in India, all this appealed strongly to theinterests of De Morgan. [49] Orontius Finaeus, or Oronce Finé, was born at Briançon in 1494 anddied at Paris, October 6, 1555. He was imprisoned by François I forrefusing to recognize the concordat (1517). He was made professor ofmathematics in the Collège Royal (later called the Collège de France) in1532. He wrote extensively on astronomy and geometry, but was by no means agreat scholar. He was a pretentious man, and his works went through severaleditions. His _Protomathesis_ appeared at Paris in 1530-32. The workreferred to by De Morgan is the _Quadratura circuli tandem inventa &clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_, published at Paris, the subtitle is: _Quibus inter cætera, Circuliquadratura Centum modis, & suprà, per eundem Orontium recenter excogitatis, demonstratus_, so that he kept up his efforts until his death. [50] Johannes Buteo (Boteo, Butéon, Bateon) was born in Dauphiné c. 1485-1489, and died in a cloister in 1560 or 1564. Some writers giveCharpey as the place and 1492 as the date of his birth, and state that hedied at Canar in 1572. He belonged to the order of St. Anthony, and wrotechiefly on geometry, exposing the pretenses of Finaeus. His _Operageometrica_ appeared at Lyons in 1554, and his _Logistica_ and _Dequadratura circuli libri duo_ at Lyons in 1559. [51] This is the great French algebraist, François Viète (Vieta), who wasborn at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603. His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His_Opera mathematica_ was edited by Van Schooten in 1646. [52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_, that appeared in Paris in 1556. For the title page see Smith, D. E. , _RaraArithmetica_, Boston, 1908, p. 280. [53] The title is correct except for a colon after _Astronomicum_. NicolausRaimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and diedat Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _Deastronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oderAlgebra_ (1601). [54] Born at Dôle, Franche-Comté, about 1550, died in Holland about 1600. The work to which reference is made is the _Quadrature du cercle, oumanière de trouver un quarré égal au cercle donné_, which appeared at Delftin 1584. Duchesne had the courage of his convictions, not only oncircle-squaring but on religion as well, for he was obliged to leave Francebecause of his conversion to Calvinism. De Morgan's statement that his realname is Van der Eycke is curious, since he was French born. The Dutch mayhave translated his name when he became professor at Delft, but we mightequally well say, that his real name was Quercetanus or à Quercu. [55] This was the father of Adriaan Metius (1571-1635). He was amathematician and military engineer, and suggested the ratio 355/113 for[pi], a ratio afterwards published by his son. The ratio, then new toEurope, had long been known and used in China, having been found by TsuCh'ung-chih (428-499 A. D. ). [56] This was Jost Bürgi, or Justus Byrgius, the Swiss mathematician ofwhom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis anteeditionem Neperianam viam præiverunt ad hos ipsissimos logarithmos. " Heconstructed a table of antilogarithms (_Arithmetische und geometrischeProgress-Tabulen_), but it was not published until after Napier's workappeared. [57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610. It was he who first carried the computation of [pi] to 35 decimal places. [58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847. [59] I do not know this edition. There was one "Antverpiae apud PetrumBellerum sub scuto Burgundiae, " 4to, in 1591. [60] Archytas of Tarentum (430-365 B. C. ) who wrote on proportions, irrationals, and the duplication of the cube. [61] _The Circle Speaks. _ "At first a circle I was called, And was a curve around about Like lofty orbit of the sun Or rainbow arch among the clouds. A noble figure then was I-- And lacking nothing but a start, And lacking nothing but an end. But now unlovely do I seem Polluted by some angles new. This thing Archytas hath not done Nor noble sire of Icarus Nor son of thine, Iapetus. What accident or god can then Have quadrated mine area?" _The Author Replies. _ "By deepest mouth of Turia And lake of limpid clearness, lies A happy state not far removed From old Saguntus; farther yet A little way from Sucro town. In this place doth a poet dwell, Who oft the stars will closely scan, And always for himself doth claim What is denied to wiser men;-- An old man musing here and there And oft forgetful of himself, Not knowing how to rightly place The compasses, nor draw a line, As he doth of himself relate. This craftsman fine, in sooth it is Hath quadrated thine area. " [62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in1601. His work on the Mystery of Numbers is one of the most exhaustive anderudite ones of the mystic writers. The first edition appeared at Bergamoin 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan callsthe second, in 1591. Other editions, before the Paris edition to which herefers, appeared in 1599 and 1614; and the colophon of the Paris edition isdated 1617. See the editor's _Rara Arithmetica_, pp. 380-383. [63] William Warburton (1698-1779), Bishop of Gloucester, whose works gothim into numerous literary quarrels, being the subject of frequent satire. [64] Thomas Galloway (1796-1851), who was professor of mathematics atSandhurst for a time, and was later the actuary of the Amicable LifeAssurance Company of London. In the latter capacity he naturally came to beassociated with De Morgan. [65] Giordano Bruno was born near Naples about 1550. He left the Dominicanorder to take up Calvinism, and among his publications was _L'expulsion dela bête triomphante_. He taught philosophy at Paris and Wittenberg, andsome of his works were published in England in 1583-86. Whether or not hewas roasted alive "for the maintenance and defence of the holy Church, " asDe Morgan states, depends upon one's religious point of view. At any rate, he was roasted as a heretic. [66] Referring to part of his _Discours de la méthode_, Leyden, 1637. [67] Bartholomew Legate, who was born in Essex about 1575. He denied thedivinity of Christ and was the last heretic burned at Smithfield. [68] Edward Wightman, born probably in Staffordshire. He wasanti-Trinitarian, and claimed to be the Messiah. He was the last man burnedfor heresy in England. [69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649;grammarian, philologist, and satirist. [70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in1613. He was a jurist of some power. [71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. Hewrote on the history of philosophy (1731-36, and 1742-44). [72] Daniel Georg Morhof, born at Wismar in 1639, died at Lübeck in 1691. He was rector of the University of Kiel, and professor of eloquence, poetry, and history. [73] In the _Histoire des Sciences Mathématiques_, vol. IV, note X, pp. 416-435 of the 1841 edition. [74] Colenso (1814-1883), missionary bishop of Natal, was one of theleaders of his day in the field of higher biblical criticism. De Morganmust have admired his mathematical works, which were not without merit. [75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in1866. He was an excellent linguist and a critical student of the Bible. Hebecame librarian at Lambeth in 1838. [76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of theopponents of the Roman Catholic Relief bill, the Reform bill, and theJewish Civil Disabilities Relief bill. [77] We have, in America at least, almost forgotten the great stir made byEdward B. Pusey (1800-1882) in the great Oxford movement in the middle ofthe nineteenth century. He was professor of Hebrew at Oxford, and canon ofChrist Church. [78] That is, his _Magia universalis naturae et artis sive reconditanaturalium et artificialium rerum scientia_, Würzburg, 1657, 4to, witheditions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott(Königshofen 1608, Würzburg 1666) was a physicist and mathematician, devoting most of his attention to the curiosities of his sciences. His typeof mind must have appealed to De Morgan. [79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tumnaturalis, tum geometrica_, etc. , 1608. --_Consideratio nova in opusculumArchimedis de circuli dimensione_, etc. , 1609. [80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection ofbiographies which was published at Heidelberg and Frankfort from 1615 to1620. [81] Born at Baden in 1524; died at Basel in 1583. The Erastians wererelated to the Zwinglians, and opposed all power of excommunication and theinfliction of penalties by a church. [82] See Acts xii. 20. [83] Theodore de Bèse, a French theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in 1605. [84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's timethrough his attempt to introduce music and written prayers into the serviceof the Scotch Presbyterian church. [85] Born at Veringen, Hohenzollern, in 1512; died at Röteln in 1564. [86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His_Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was aninfluential work. [87] The title was carelessly copied by De Morgan, not an unusual thing inhis case. The original reads: A Plaine Discovery, of the whole Revelationof S. Iohn: set downe in two treatises ... Set foorth by John Napier L. OfMarchiston ... Whereunto are annexed, certaine Oracles of Sibylla ... London ... 1611. [88] I have not seen the first edition, but it seems to have appeared inEdinburgh, in 1593, with a second edition there in 1594. The 1611 editionwas the third. [89] It seems rather certain that Napier felt his theological work ofgreater importance than that in logarithms. He was born at Merchiston, near(now a part of) Edinburgh, in 1550, and died there in 1617, three yearsafter the appearance of his _Mirifici logarithmorum canonis descriptio_. [90] Followed, in the third edition, from which he quotes, by a comma. [91] There was an edition published at Stettin in 1633. An Englishtranslation by P. F. Mottelay appeared at London in 1893. Gilbert(1540-1603) was physician to Queen Elizabeth and President of the Collegeof Physicians at London. His _De Magnete_ was the first noteworthy treatiseon physics printed in England. He treated of the earth as a sphericalmagnet and suggested the variation and declination of the needle as a meansof finding latitude at sea. [92] The title says "ab authoris fratre collectum, " although it was editedby J. Gruterus. [93] Porta was born at Naples in 1550 and died there in 1615. He studiedthe subject of lenses and the theory of sight, did some work in hydraulicsand agriculture, and was well known as an astrologer. His _Magiae naturalislibri XX_ was published at Naples in 1589. The above title should read_curvilineorum_. [94] Cataldi was born in 1548 and died at Bologna in 1626. He was professorof mathematics at Perugia, Florence, and Bologna, and is known inmathematics chiefly for his work in continued fractions. He was one of thescholarly men of his day. [95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died atCaschau, Hungary, in 1576. He was one of the most prominent pupils ofCopernicus, his _Narratio de libris revolutionum Copernici_ (Dantzig, 1540)having done much to make the theory of his master known. [96] Henry Briggs, who did so much to make logarithms known, and who usedthe base 10, was born at Warley Wood, in Yorkshire, in 1560, and died atOxford in 1630. He was Savilian professor of mathematics at Oxford, and hisgrave may still be seen there. [97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His_Regola e modo facilissimo di quadrare il cerchio_ was published at Reggioin 1609. [98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Romein 1612. He was a Jesuit priest and taught mathematics in the JesuitCollege at Rome. He wrote a number of works on mathematics, includingexcellent text-books on arithmetic and algebra. [99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and amathematician, and he wrote a little upon the subject of projections. His_Prospectiva nova coelestis_ appeared at Rome in 1612. [100] The name should, of course, be Lansbergii in the genitive, and is soin the original title. Philippus Lansbergius was born at Ghent in 1560, anddied at Middelburg in 1632. He was a Protestant theologian, and was also aphysician and astronomer. He was a well-known supporter of Galileo andCopernicus. His _Commentationes in motum terrae diurnum et annuum_ appearedat Middelburg in 1630 and did much to help the new theory. [101] I have never seen the work. It is rare. [102] The African explorer, born in Somersetshire in 1827, died at Bath in1864. He was the first European to cross Central Africa from north tosouth. He investigated the sources of the Nile. [103] Prester (Presbyter, priest) John, the legendary Christian king whoserealm, in the Middle Ages, was placed both in Asia and in Africa, is firstmentioned in the chronicles of Otto of Freisingen in the 12th century. Inthe 14th century his kingdom was supposed to be Abyssinia. [104] "It is a profane and barbarous nation, dirty and slovenly, who eattheir meat half raw and drink mare's milk, and who use table-cloths andnapkins only to wipe their hands and mouths. " [105] "The great Prester John, who is the fourth in rank, is emperor ofEthiopia and of the Abyssinians, and boasts of his descent from the race ofDavid, as having descended from the Queen of Sheba, Queen of Ethiopia. She, having gone to Jerusalem to see the wisdom of Solomon, about the year ofthe world 2952, returned pregnant with a son whom they called Moylech, fromwhom they claim descent in a direct line. And so he glories in being themost ancient monarch in the world, saying that his empire has endured formore than three thousand years, which no other empire is able to assert. Healso puts into his titles the following: 'We, the sovereign in my realms, uniquely beloved of God, pillar of the faith, sprung from the race ofJudah, etc. ' The boundaries of this empire touch the Red Sea and themountains of Azuma on the east, and on the western side it is bordered bythe River Nile which separates it from Nubia. To the north lies Egypt, andto the south the kingdoms of Congo and Mozambique. It extends forty degreesin length, or one thousand twenty-five leagues, from Congo or Mozambique onthe south to Egypt on the north; and in width it reaches from the Nile onthe west to the mountains of Azuma on the east, seven hundred twenty-fiveleagues, or twenty-nine degrees. This empire contains thirty largeprovinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon (_sic_), Guegiera, Bally, Dobora, and Macheda. Allof these provinces are situated directly under the equinoctial line betweenthe tropics of Capricorn and Cancer; but they are two hundred fifty leaguesnearer our tropic than the other. The name of Prester John signifies GreatLord, and is not Priest [Presbyter] as many think. He has always been aChristian, but often schismatic. At the present time he is a Catholic andrecognizes the Pope as sovereign pontiff. I met one of his bishops inJerusalem, and often conversed with him through the medium of our guide. Hewas of grave and serious bearing, pleasant of speech, but wonderfullysubtle in everything he said. He took great delight in what I had to relateconcerning our beautiful ceremonies and the dignity of our prelates intheir pontifical vestments. As to other matters I will only say that theEthiopian is joyous and merry, not at all like the Tartar in the matter offilth, nor like the wretched Arab. They are refined and subtle, trusting noone, wonderfully suspicious, and very devout. They are not at all black asis commonly supposed, by which I refer to those who do not live under theequator or too near to it, for these are Moors as we shall see. " With respect to this translation it should be said that the original formsof the proper names have been preserved, although they are not those foundin modern works. It should also be stated that the meaning of Prester isnot the one that was generally accepted by scholars at the time the workwas written, nor is it the one accepted to-day. There seems to be no doubtthat the word is derived from Presbyter as stated in note 103 on page 71, since the above-mentioned chronicles of Otto, bishop of Freisingen aboutthe middle of the twelfth century, states this fact clearly. Otto receivedhis information from the bishop of Gabala (the Syrian Jibal) who told himthe story of John, _rex et sacerdos_, or Presbyter John as he liked to becalled. He goes on to say "Should it be asked why, with all this power andsplendor, he calls himself merely 'presbyter, ' this is because of hishumility, and because it was not fitting for one whose server was a primateand king, whose butler an archbishop and king, whose chamberlain a bishopand king, whose master of the horse an archimandrite and king, whose chiefcook an abbot and king, to be called by such titles as these. " [106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631. He was professor of medicine at Louvain. Besides the editions mentionedbelow, his _De cometis anni 1618_ appeared at Leipsic in 1656. He alsowrote a _Disputatio an coelum moveatur et terra quiescat_, which appearedat Antwerp in 1619, and again at Leipsic in 1656. [107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of theCollege Church at Harcourt, and professor at Louvain. The name also appearsas Froidmont and Froimont. [108] _L. Fromondi ... Meteorologicorum libri sex.... Cui accessit T. Fieniet L. Fromondi dissertationes de cometa anni 1618.... _ This is from the1670 edition. The 1619 edition was published at Antwerp. The_Meteorologicorum libri VI_, appeared at Antwerp in 1627. He also wrote_Anti-Aristarchus sive orbis terrae immobilis liber unicus_ (Antwerp, 1631); _Labyrrinthus sive de compositione continui liber unus, Philosophis, Mathematicis, Theologis utilis et jucundus_ (Antwerp, 1631) and _Vesta siveAnti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) etcopernicanos_ (Antwerp, 1634). [109] Snell was born at Leyden in 1591, and died there in 1626. He studiedunder Tycho Brahe and Kepler, and is known for Snell's law of therefraction of light. He was the first to determine the size of the earth bymeasuring the arc of a meridian with any fair degree of accuracy. The titleshould read: _Willebrordi Snellii R. F. Cyclometricus, de circulidimensione secundum Logistarum abacos, et ad Mechanicem accuratissima.... _ [110] Bacon was born at York House, London, in 1561, and died nearHighgate, London, in 1626. His _Novum Organum Scientiarum or New Method ofemploying the reasoning faculties in the pursuits of Truth_ appeared atLondon in 1620. He had previously published a work entitled _Of theProficience and Advancement of Learning, divine and humane_ (London, 1605), which again appeared in 1621. His _De augmentis scientiarum Libri IX_appeared at Paris in 1624, and his _Historia naturalis et experimentalis deventis_ at Leyden in 1638. He was successively solicitor general, attorneygeneral, lord chancellor (1619), Baron Verulam and Viscount St. Albans. Hewas deprived of office and was imprisoned in the Tower of London in 1621, but was later pardoned. [111] The Greek form, _Organon_, is sometimes used. [112] James Spedding (1808-1881), fellow of Cambridge, who devoted his lifeto his edition of Bacon. [113] R. Leslie Ellis (1817-1859), editor of the _Cambridge MathematicalJournal_. He also wrote on Roman aqueducts, on Boole's Laws of Thought, andon the formation of a Chinese dictionary. [114] Douglas Derion Heath (1811-1897), a classical and mathematicalscholar. [115] There have been numerous editions of Bacon's complete works, including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765, 1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition towhich De Morgan refers is that of 1857-74, 14 vols. , of which five wereapparently out at the time he wrote. There were also French editions in1800 and 1835. [116] So in the original for Tycho Brahe. [117] In general these men acted before Baron wrote, or at any rate, beforehe wrote the _Novum Organum_, but the statement must not be taken tooliterally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe, 1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642;Harvey, 1578-1657. For example, Harvey's _Exercitatio Anatomica de MotuCordis et Sanguinis_ did not appear until 1628, and his _Exercitationes deGeneratione_ until 1651. [118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was"Curator of Experiments" to the Royal Society and its secretary, and wasprofessor of geometry at Gresham College, London. It is true that he was"very little of a mathematician" although he wrote on the motion of theearth (1674), on helioscopes and other instruments (1675), on the rotationof Jupiter (1666), and on barometers and sails. [119] The son of the Sir William mentioned below. He was born in 1792 anddied in 1871. He wrote a treatise on light (1831) and one on astronomy(1836), and established an observatory at the Cape of Good Hope where hemade observations during 1834-1838, publishing them in 1847. On his returnto England he was knighted, and in 1848 was made president of the RoyalSociety. The title of the work to which reference is made is: _Apreliminary discourse on the Study of Natural Philosophy_. It appeared atLondon in 1831. [120] Sir William was horn at Hanover in 1738 and died at Slough, nearWindsor in 1822. He discovered the planet Uranus and six satellites, besides two satellites of Saturn. He was knighted by George III. [121] This was the work of 1836. He also published a work entitled_Outlines of Astronomy_ in 1849. [122] While Newton does not tell the story, he refers in the _Principia_(1714 edition, p. 293) to the accident caused by his cat. [123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared atRome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. And_Apollonius redivivus_ at Venice in 1607. He was a nobleman and wasambassador from Venice to Rome. [124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He wasan engineer and a soldier, and his _La Disme_ (1585) was the first separatetreatise on the decimal fraction. The contribution referred to above isprobably that on the center of gravity of three bodies (1586). [125] Habakuk Guldin (1577-1643), who took the name Paul on his conversionto Catholicism. He became a Jesuit, and was professor of mathematics atVienna and later at Gratz. In his _Centrobaryca seu de centro gravitatistrium specierum quantitatis continuae_ (1635), of the edition of 1641, appears the Pappus rule for the volume of a solid formed by the revolutionof a plane figure about an axis, often spoken of as Guldin's Theorem. [126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and diedat London in 1615. He was a fellow of Caius College, Cambridge, and in hiswork entitled _The correction of certain errors in Navigation_ (1599) hegives the principle of Mercator's projection. He translated the _Portuuminvestigandorum ratio_ of Stevin in 1599. [127] De Morgan never wrote a more suggestive sentence. Its message is notfor his generation alone. [128] The eminent French physicist, Jean Baptiste Biot (1779-1862), professor in the Collège de France. His work _Sur les observatoiresmétéorologiques_ appeared in 1855. [129] George Biddell Airy (1801-1892), professor of astronomy and physicsat Cambridge, and afterwards director of the Observatory at Greenwich. [130] De Morgan would have rejoiced in the rôle played by Intuition in themathematics of to-day, notably among the followers of Professor Klein. [131] Colburn was the best known of the calculating boys produced inAmerica. He was born at Cabot, Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown remarkable skill in numbers as early as1810, he was taken to London in 1812, whence he toured through GreatBritain and to Paris. The Earl of Bristol placed him in Westminster School(1816-1819). On his return to America he became a preacher, and later ateacher of languages. [132] The history of calculating boys is interesting. Mathieu le Coc (about1664), a boy of Lorraine, could extract cube roots at sight at the age ofeight. Tom Fuller, a Virginian slave of the eighteenth century, althoughilliterate, gave the number of seconds in 7 years 17 days 12 hours afteronly a minute and a half of thought. Jedediah Buxton, an Englishman of theeighteenth century, was studied by the Royal Society because of hisremarkable powers. Ampère, the physicist, made long calculations withpebbles at the age of four. Gauss, one of the few infant prodigies tobecome an adult prodigy, corrected his father's payroll at the age ofthree. One of the most remarkable of the French calculating boys was HenriMondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, forthe Académie des Sciences, and a report was written by Cauchy. Hisspecialty was the solution of algebraic problems mentally. He seems to havecalculated squares and cubes by a binomial formula of his own invention. Hedied in obscurity, but was the subject of a _Biographie_ by Jacoby (1846). George P. Bidder, the Scotch engineer (1806-1878), was exhibited as anarithmetical prodigy at the age of ten, and did not attend school until hewas twelve. Of the recent cases two deserve special mention, Inaudi andDiamandi. Jacques Inaudi (born in 1867) was investigated for the Académiein 1892 by a commission including Poincaré, Charcot, and Binet. (See the_Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of theSorbonne). He has frequently exhibited his remarkable powers in America. Périclès Diamandi was investigated by the same commission in 1893. SeeAlfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_, Paris, 1894. [133] John Flamsteed's (1646-1719) "old white house" was the firstGreenwich observatory. He was the Astronomer Royal and first head of thisobservatory. [134] It seems a pity that De Morgan should not have lived to lash those ofour time who are demanding only the immediately practical in mathematics. His satire would have been worth the reading against those who seek tostifle the science they pretend to foster. [135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in1694. He was well known as an astronomer, mathematician, and jurist. Helived with De Thou at Paris, and accompanied him to Holland. He traveledextensively, and was versed in the astronomical work of the Persians andArabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) thathe attacked Kepler's laws. His tables were shown to be erroneous by thefact that the solar eclipse did not take place as predicted by him in 1645. [136] As it did, until 1892, when Airy had reached the ripe age ofninety-one. [137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584. [138] "The false Pythagorean doctrine, absolutely opposed to the HolyScriptures, concerning the mobility of the earth and the immobility of thesun. " [139] Paolo Antonio Foscarini (1580-1616), who taught theology andphilosophy at Naples and Messina, was one of the first to champion thetheories of Copernicus. This was in his _Lettera sopra l'opinione de'Pittagorici e del Copernico, della mobilità della Terra e stabilità delSole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. Thecondemnation of the Congregation was published in the following spring, andin the year of Foscarini's death at the early age of thirty-six. [140] "To be wholly prohibited and condemned, " because "it seeks to showthat the aforesaid doctrine is consonant with truth and is not opposed tothe Holy Scriptures. " [141] "As repugnant to the Holy Scriptures and to its true and Catholicinterpretation (which in a Christian man cannot be tolerated in the least), he does not hesitate to treat (of his subject) '_by hypothesis_', but heeven adds '_as most true_'!" [142] "To the places in which he discusses not by hypothesis but by makingassertions concerning the position and motion of the earth. " [143] "_Copernicus. _ If by chance there shall be vain talkers who, althoughignorant of all mathematics, yet taking it upon themselves to sit injudgment upon the subject on account of a certain passage of Scripturebadly distorted for their purposes, shall have dared to criticize andcensure this teaching of mine, I pay no attention to them, even to theextent of despising their judgment as rash. For it is not unknown thatLactantius, a writer of prominence in other lines although but littleversed in mathematics, spoke very childishly about the form of the earthwhen he ridiculed those who declared that it was spherical. Hence it shouldnot seem strange to the learned if some shall look upon us in the same way. Mathematics is written for mathematicians, to whom these labors of ourswill seem, if I mistake not, to add something even to the republic of theChurch.... _Emend. _ Here strike out everything from 'if by chance' to thewords 'these labors of ours, ' and adapt it thus: 'But these labors ofours. '" [144] "_Copernicus. _ However if we consider the matter more carefully itwill be seen that the investigation is not yet completed, and thereforeought by no means to be condemned. _Emend. _ However, if we consider thematter more carefully it is of no consequence whether we regard the earthas existing in the center of the universe or outside of the center, so faras the solution of the phenomena of celestial movements is concerned. " [145] "The whole of this chapter may be cut out, since it avowedly treatsof the earth's motion, while it refutes the reasons of the ancients provingits immobility. Nevertheless, since it seems to speak problematically, inorder that it may satisfy the learned and keep intact the sequence andunity of the book let it be emended as below. " [146] "_Copernicus. _ Therefore why do we still hesitate to concede to itmotion which is by nature consistent with its form, the more so because thewhole universe is moving, whose end is not and cannot be known, and notconfess that there is in the sky an appearance of daily revolution, whileon the earth there is the truth of it? And in like manner these things areas if Virgil's Æneas should say, 'We are borne from the harbor' ... _Emend. _ Hence I cannot concede motion to this form, the more so becausethe universe would fall, whose end is not and cannot be known, and whatappears in the heavens is just as if ... " [147] "_Copernicus_. I also add that it would seem very absurd that motionshould be ascribed to that which contains and locates, and not rather tothat which is contained and located, that is the earth. _Emend. _ I also addthat it is not more difficult to ascribe motion to the contained andlocated, which is the earth, than to that which contains it. " [148] "_Copernicus. _ You see, therefore, that from all these things themotion of the earth is more probable than its immobility, especially in thedaily revolution which is as it were a particular property of it. _Emend. _Omit from 'You see' to the end of the chapter. " [149] "_Copernicus. _ Therefore, since there is nothing to hinder the motionof the earth, it seems to me that we should consider whether it has severalmotions, to the end that it may be looked upon as one of the moving stars. _Emend. _ Therefore, since I have assumed that the earth moves, it seems tome that we should consider whether it has several motions. " [150] "_Copernicus. _ We are not ashamed to acknowledge ... That this ispreferably verified in the motion of the earth. _Emend. _ We are not ashamedto assume ... That this is consequently verified in the motion. " [151] "_Copernicus. _ So divine is surely this work of the Best andGreatest. _Emend. _ Strike out these last words. " [152] This should be Cap. 11, lib. I, p. 10. [153] "_Copernicus. _ Demonstration of the threefold motion of the earth. _Emend. _ On the hypothesis of the threefold motion of the earth and itsdemonstration. " [154] This should be Cap. 20, lib. Iv, p. 122. [155] "_Copernicus. _ Concerning the size of these three stars, the sun, themoon and the earth. _Emend. _ Strike out the words 'these three stars, 'because the earth is not a star as Copernicus would make it. " [156] He seems to speak problematically in order to satisfy the learned. [157] One of the Church Fathers, born about 250 A. D. , and died about 330, probably at Trèves. He wrote _Divinarum Institutionum Libri VII. _ and othercontroversial and didactic works against the learning and philosophy of theGreeks. [158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theologyat Parma and Bologna, and was later professor of astronomy. His _Almagestumnovum_ appeared in 1651, and his _Argomento fisico-matematico contro ilmoto diurno della terra_ in 1668. [159] He was a native of Arlington, Sussex, and a pensioner of Christ'sCollege, Cambridge. In 1603 he became a master of arts at Oxford. [160] Straying, i. E. , from the right way. [161] "Private subjects may, in the presence of danger, defend themselvesor their families against a monarch as against any malefactor, if themonarch assaults them like a bandit or a ravisher, and provided they areunable to summon the usual protection and cannot in any way escape thedanger. " [162] Daniel Neal (1678-1743), an independent minister, wrote a _History ofthe Puritans_ that appeared in 1732. The account may be found in the NewYork edition of 1843-44, vol. I, p. 271. [163] Anthony Wood (1632-1695), whose _Historia et AntiquitatesUniversitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are amongthe classics on Oxford. [164] Part of the title, not here quoted, shows the nature of the work moreclearly: "liber unicus, in quo decretum S. Congregationis S. R. E. Cardinal. An. 1616, adversus Pythagorico-Copernicanos editum defenditur. " [165] This was John Elliot Drinkwater Bethune (1801-1851), the statesmanwho did so much for legislative and educational reform in India. Hisfather, John Drinkwater Bethune, wrote a history of the siege of Gibraltar. [166] The article referred to is about thirty years old; since it appearedanother has been given (_Dubl. Rev. _, Sept. 1865) which is of much greaterdepth. In it will also be found the Roman view of Bishop Virgil (_ante_, p. 32). --A. De M. [167] Jean Baptiste Morin (1583-1656), in his younger days physician to theBishop of Boulogne and the Duke of Luxemburg, became in 1630 professor ofmathematics at the Collège Royale. His chief contribution to the problem ofthe determination of longitude is his _Longitudinum terrestrium etcoelestium nova et hactenus optata scientia_ (1634). He also wrote againstCopernicus in his _Famosi problematis de telluris motu vel quiete hactenusoptata solutio_ (1631), and against Lansberg in his _Responsio pro tellurisquiete_ (1634). [168] The work appeared at Leyden in 1626, at Amsterdam in 1634, atCopenhagen in 1640 and again at Leyden in 1650. The title of the 1640edition is _Arithmeticae Libri II et Geometriae Libri VI_. The work onwhich it is based is the _Arithmeticae et Geometriae Practica_, whichappeared in 1611. [169] The father's name was Adriaan, and Lalande says that it was Montuclawho first made the mistake of calling him Peter, thinking that the initialsP. M. Stood for Petrus Metius, when in reality they stood for _piaememoriae_! The ratio 355/113 was known in China hundreds of years beforehis time. See note 55, page 52. [170] Adrian Metius (1571-1635) was professor of medicine at the Universityof Franeker. His work was, however, in the domain of astronomy, and in thisdomain he published several treatises. [171] The first edition was entitled: _The Discovery of a World in theMoone. Or, a Discourse Tending to prove that 'tis probable there may beanother habitable World in that Planet_. 1638, 8vo. The fourth editionappeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College, Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He wasinfluential in founding the Royal Society. [172] The first edition was entitled: _C. Hugenii_ [Greek: Kosmotheôros], _sive de Terris coelestibus, earumque ornatu, conjecturae_, The Hague, 1698, 4to. There were several editions. It was also translated into French(1718), and there was another English edition (1722). Huyghens (1629-1695)was one of the best mathematical physicists of his time. [173] It is hardly necessary to say that science has made enormous advancein the chemistry of the universe since these words were written. [174] William Whewell (1794-1866) is best known through his _History of theInductive Sciences_ (1837) and _Philosophy of the Inductive Sciences_(1840). [175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. Thesediscourses were delivered while he was minister in a large parish in thepoorest part of Glasgow, and in them he attempted to bring science intoharmony with the Bible. He was afterwards professor of moral philosophy atSt. Andrew's (1823-28), and professor of theology at Edinburgh (1828). Hebecame the leader of a schism from the Scotch Presbyterian Church, --theFree Church. [176] That is, in Robert Watt's (1774-1819) _Bibliotheca Britannica_(posthumous, 1824). Nor is it given in the _Dictionary of NationalBiography_. [177] The late Greek satirist and poet, c. 120-c. 200 A. D. [178] François Rabelais (c. 1490-1553) the humorist who created Pantagruel(1533) and Gargantua (1532). His work as a physician and as editor of theworks of Galen and Hippocrates is less popularly known. [179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besidessome valuable historical works he wrote _The Man in the Moone, or aDiscourse of a voyage thither by Domingo Gonsales, the Speed Messenger ofLondon_, 1638. [180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic, mathematician, Secretary of the Académie des Sciences, and member of theAcadémie Française. His _Entretien sur la pluralité des mondes_ appeared atParis in 1686. [181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics andphilosophy, and later of Hebrew and Syriac, at Wurzburg; still laterprofessor of mathematics and Hebrew at Rome. He wrote several works onphysics. His collection of mathematical instruments and other antiquitiesbecame the basis of the Kircherian Museum at Rome. [182] "Both belief and non-belief are dangerous. Hippolitus died becausehis stepmother was believed. Troy fell because Cassandra was not believed. Therefore the truth should be investigated long before foolish opinion canproperly judge. " (Prove = probe?). [183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 anddied at Paris in 1672. He was professor of theology and philosophy in theJesuit colleges at Rennes, Tours, Rouen, and other places. He wrote severalworks on astronomy. [184] "And I, if I be lifted up from the earth, will draw all men unto me. "John xii. 32. [185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, andcomputed ephemerides from 1621 to 1700. [186] So in the original edition of the _Budget_. It is Johannem Pellum inthe original title. John Pell (1610 or 1611-1685) studied at Cambridge andOxford, and was professor of mathematics at Amsterdam (1643-46) and Breda(1646-52). He left many manuscripts but published little. His name attachesby accident to an interesting equation recently studied with care by Dr. E. E. Whitford (New York, 1912). [187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was anassistant of Tycho Brahe and accepted the diurnal while denying the orbitalmotion of the earth. His _Cyclometria e lunulis reciproce demonstrata_appeared in 1612 under the name of Christen Severin, the latter being hisfamily name. He wrote several other works on the quadrature problem, andsome treatises on astronomy. [188] The names are really pretty well known. Giles Persone de Roberval wasborn at Roberval near Beauvais in 1602, and died at Paris in 1675. He wasprofessor of philosophy at the Collège Gervais at Paris, and later at theCollège Royal. He claimed to have discovered the theory of indivisiblesbefore Cavalieri, and his work is set forth in his _Traité desindivisibles_ which appeared posthumously in 1693. Hobbes (1588-1679), the political and social philosopher, lived a good partof his time (1610-41) in France where he was tutor to several youngnoblemen, including the Cavendishes. His _Leviathan_ (1651) is said to haveinfluenced Spinoza, Leibnitz, and Rousseau. His _Quadratura circuli, cubatio sphaerae, duplicatio cubi ... _ (London, 1669), _Rosetum geometricum... _ (London, 1671), and _Lux Mathematica, censura doctrinae Wallisianaecontra Rosetum Hobbesii_ (London, 1674) are entirely forgotten to-day. (Seea further note, _infra_. ) Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was amember of parliament, royal librarian, and member of the Académie desSciences. His attempt to prove the impossibility of the quadrature appearedin 1645. He was a frequent correspondent of Descartes. Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morganhimself, a bibliophile in the domain of mathematics. His life was one ofstruggle, his term as member of parliament under Charles I being followedby gallant service in the royal army. After the war he sought refuge on thecontinent where he met most of the mathematicians of his day. He left anumber of manuscripts on mathematics, which his widow promptly disposed offor waste paper. If De Morgan's manuscripts had been so treated we shouldnot have had his revision of his _Budget of Paradoxes_. Marin Mersenne (1588-1648), a minorite, living in the cloisters at Neversand Paris, was one of the greatest Franciscan scholars. He edited Euclid, Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translatedthe Mechanics of Galileo into French (1634), wrote _Harmonicorum Libri XII_(1636), and _Cogitata physico-mathematica_ (1644), and taught theology andphilosophy at Nevers. Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654. He was professor of mathematics in the Gymnasium at Hamburg, and wrotenumerous works on astronomy, chronology, statics, and elementarymathematics. Johann Ludwig, Baron von Wolzogen, seems to have been one of the earlyunitarians, called _Fratres Polonorum_ because they took refuge in Poland. Some of his works appear in the _Bibliotheca Fratrum Polonorum_ (Amsterdam, 1656). I find no one by the name who was contributing to mathematics atthis time. Descartes is too well known to need mention in this connection. Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, andprofessor of mathematics at Bologna. His greatest work, _Geometriaindivisibilibus continuorum nova quadam ratione promota_, in which he makesa noteworthy step towards the calculus, appeared in 1635. Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in1667. His travels in Morocco and Asia Minor (1622-1629) gave him suchknowledge of Arabic that he became professor of that language at Leyden. After Snell's death he became professor of mathematics there. He translatedArabic works on mathematics and astronomy into Latin. [189] It would be interesting to follow up these rumors, beginning perhapswith the tomb of Archimedes. The Ludolph van Ceulen story is very likely amyth. The one about Fagnano may be such. The Bernoulli tomb does have thespiral, however (such as it is), as any one may see in the cloisters atBasel to-day. [190] Collins (1625-1683) was secretary of the Royal Society, and was "akind of register of all new improvements in mathematics. " His officebrought him into correspondence with all of the English scientists, and hewas influential in the publication of various important works, includingBranker's translation of the algebra by Rhonius, with notes by Pell, whichwas the first work to contain the present English-American symbol ofdivision. He also helped in the publication of editions of Archimedes andApollonius, of Kersey's Algebra, and of the works of Wallis. His professionwas that of accountant and civil engineer, and he wrote three unimportantworks on mathematics (one published posthumously, and the others in 1652and 1658). Heinrich Christian Schumacher (1780-1850) was professor of astronomy atCopenhagen and director of the observatory at Altona. His translation ofCarnot's _Géométrie de position_ (1807) brought him into personal relationswith Gauss, and the friendship was helpful to Schumacher. He was a memberof many learned societies and had a large circle of acquaintances. Hepublished numerous monographs and works on astronomy. Gassendi (1592-1655) might well have been included by De Morgan in thegroup, since he knew and was a friend of most of the importantmathematicians of his day. Like Mersenne, he was a minorite, but he was afriend of Galileo and Kepler, and wrote a work under the title _Institutioastronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei_(1645). He taught philosophy at Aix, and was later professor of mathematicsat the College Royal at Paris. Burnet is the Bishop Gilbert Burnet (1643-1715) who was so stronglyanti-Romanistic that he left England during the reign of James II andjoined the ranks of the Prince of Orange. William made him bishop ofSalisbury. [191] There is some substantial basis for De Morgan's doubts as to theconnection of that _mirandula_ of his age, Sir Kenelm Digby (1603-1665), with the famous _poudre de sympathie_. It is true that he was just the oneto prepare such a powder. A dilletante in everything, --learning, war, diplomacy, religion, letters, and science--he was the one to exploit afraud of this nature. He was an astrologer, an alchemist, and a fabricatorof tales, and well did Henry Stubbes characterize him as "the very Pliny ofour age for lying. " He first speaks of the powder in a lecture given atMontpellier in 1658, and in the same year he published the address at Parisunder the title: _Discours fait en une célèbre assemblée par le chevalierDigby .... Touchant la guérison de playes par la poudre de sympathie_. TheLondon edition referred to by De Morgan also came out in 1658, and severaleditions followed it in England, France and Germany. But Nathaniel Highmorein his _History of Generation_ (1651) referred to the concoction as"Talbot's Powder" some years before Digby took it up. The basis seems tohave been vitriol, and it was claimed that it would heal a wound by simplybeing applied to a bandage taken from it. [192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch wasa voluminous writer on English history. He was a friend of Dr. Johnson andof Walpole, and he wrote a life of Robert Boyle. [193] We know so much about John Evelyn (1620-1706) through the diary whichhe began at the age of eleven, that we forget his works on navigation andarchitecture. [194] I suppose this was the seventh Earl of Shrewsbury (1553-1616). [195] This is interesting in view of the modern aseptic practice of surgeryand the antiseptic treatment of wounds inaugurated by the late Lord Lister. [196] Perhaps De Morgan had not heard the _bon mot_ of Dr. Holmes: "Ifirmly believe that if the whole _materia medica_ could be sunk to thebottom of the sea, it would be all the better for mankind and all the worsefor the fishes. " [197] The full title is worth giving, because it shows the mathematicalinterests of Hobbes, and the nature of the six dialogues: _Examinatio etemendatio mathematicae hodiernae qualis explicatur in libris JohannisWallisii geometriae professoris Saviliani in Academia Oxoniensi: distributain sex dialogos (1. De mathematicae origine ... ; 2. De principiis traditisab Euclide; 3. De demonstratione operationum arithmeticarum ... ; 4. Derationibus; 5. De angula contactus, de sectionibus coni, et arithmeticainfinitorum; 6. Dimensio circuli tribus methodis demonstrata ... Itemcycloidis verae descriptio et proprietates aliquot. )_ Londini, 1660 (not1666). For a full discussion of the controversy over the circle, see GeorgeCroom Robertson's biography of Hobbes in the eleventh edition of the_Encyclopaedia Britannica_. [198] This is his _Animadversions upon Mr. Hobbes' late book De principiiset ratiocinatione geometrarum_, 1666, or his _Hobbianae quadraturaecirculi, cubationis sphaerae et duplicationis cubi confutatio_, also of1669. [199] This is the work of 1669 referred to above. [200] Gregoire de St. Vincent (1584-1667) published his _Opus geometricumquadraturae circuli et sectionum coni_ at Antwerp in 1647. [201] This appears in _J. Scaligeri cyclometrica elementa duo_, LugduniBatav. , 1594. [202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteendecimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his_In Archimedis circuli dimensionem expositio & analysis_ in 1597. [203] Kästner. See note 30 on page 43. [204] Bentley (1662-1742) might have done it, for as the head of TrinityCollege, Cambridge, and a follower of Newton, he knew some mathematics. Erasmus (1466-1536) lived a little too early to attempt it, although hisbrilliant satire might have been used to good advantage against those whodid try. [205] "In grammar, to give the winds to the ships and to give the ships tothe winds mean the same thing. But in geometry it is one thing to assumethe circle BCD not greater than thirty-six segments BCDF, and another (toassume) the thirty-six segments BCDF not greater than the circle. The oneassumption is true, the other false. " [206] The Greek scholar (1559-1614) who edited a Greek and Latin edition ofAristotle in 1590. [207] Jacques Auguste de Thou (1553-1617), the historian and statesman. [208] "To value Scaliger higher even when wrong, than the multitude whenright. " [209] "I would rather err with Scaliger than be right with Clavius. " [210] "The perimeter of the dodecagon to be inscribed in a circle isgreater than the perimeter of the circle. And the more sides a polygon tobe inscribed in a circle successively has, so much the greater will theperimeter of the polygon be than the perimeter of the circle. " [211] De Morgan took, perhaps, the more delight in speaking thus of SirWilliam Hamilton (1788-1856) because of a spirited controversy that theyhad in 1847 over the theory of logic. Possibly, too, Sir William's lowopinion of mathematics had its influence. [212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in whichhe gave a scathing burlesque on Warburton's Shakespeare. It went throughsix editions. [213] Antoine Teissier (born in 1632) published his _Eloges des hommessavants, tirés de l'histoire de M. De Thou_ in 1683. [214] "He boasted without reason of having found the quadrature of thecircle. The glory of this admirable discovery was reserved for JosephScaliger, as Scévole de St. Marthe has written. " [215] _Natural and political observations mentioned in the following Index, and made upon the Bills of Mortality.... With reference to the government, religion, trade, growth, ayre, and diseases of the said city. _ London, 1662, 4to. The book went through several editions. [216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last, " as wenow say. [217] The author (1632-1695) of the _Historia et Antiquitates UniversitatisOxoniensis_ (1674). See note 163, page 98. [218] The mathematical guild owes Samuel Pepys (1633-1703) for somethingbesides his famous diary (1659-1669). Not only was he president of theRoyal Society (1684), but he was interested in establishing Sir WilliamBoreman's mathematical school at Greenwich. [219] John Graunt (1620-1674) was a draper by trade, and was a member ofthe Common Council of London until he lost office by turning Romanist. Although a shopkeeper, he was elected to the Royal Society on the specialrecommendation of Charles II. Petty edited the fifth edition of his work, adding much to its size and value, and this may be the basis of Burnet'saccount of the authorship. [220] Petty (1623-1687) was a mathematician and economist, and a friend ofPell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell, was one of the first to be made on a large scale in a scientific manner. Hewas one of the founders of the Royal Society. [221] The story probably arose from Graunt's recent conversion to the RomanCatholic faith. [222] He was born in 1627 and died in 1704. He published a series ofephemerides, beginning in 1659. He was imprisoned in 1679, at the time ofthe "Popish Plot, " and again for treason in 1690. His importantastrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654)and _The Nativity of the late King Charls_ (1659). [223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_(1791), speaking of Lilly, says: "I shall observe of this egregiousastronomer, that there is in this work, so much artless narrative, and atthe same time so much palpable imposture, that it is difficult to know whenhe is speaking what he really believes to be the truth. " He goes on to saythat Lilly relates that "those adepts whose characters he has drawn werethe lowest miscreants of the town. Most of them had taken the air in thepillory, and others had conjured themselves up to the gallows. This seems atrue statement of facts. " [224] It is difficult to estimate William Lilly (1602-1681) fairly. His_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought hima great deal of money. Sir George Wharton (1617-1681) also published analmanac annually from 1641 to 1666. He tried to expose John Booker(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, anAnti-caveat to all such, as have (heretofore) had the misfortune to beCheated and Deluded by that Grand and Traiterous Impostor of thisRebellious Age, John Booker_, 1644. Booker was "licenser of mathematical[astrological] publications, " and as such he had quarrels with Lilly, Wharton, and others. [225] See note 171 on page 100. [226] This is the _Ars Signorum, vulgo character universalis et linguaphilosophica_, that appeared at London in 1661, 8vo. George Dalgarnoanticipated modern methods in the teaching of the deaf and dumb. [227] See note 200 on page 110. [228] If the hyperbola is referred to the asymptotes as axes, the areabetween two ordinates (x = a, x = b) is the difference of the logarithms ofa and b to the base e. E. G. , in the case of the hyperbola xy = 1, the areabetween x = a and x = 1 is log a. [229] "On ne peut lui refuser la justice de remarquer que personne avantlui ne s'est porté dans cette recherche avec autant de génie, & même, sinous en exceptons son objet principal, avec autant de succès. " _Quadraturedu Cercle_, p. 66. [230] The title proceeds: _Seu duae mediae proportionales inter extremasdatas per circulum et per infinitas hyperbolas, vel ellipses et perquamlibet exhibitae_.... René Francois, Baron de Sluse (1622-1685) wascanon and chancellor of Liège, and a member of the Royal Society. He alsopublished a work on tangents (1672). The word _mesolabium_ is from theGreek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented byEratosthenes for finding two mean proportionals. [231] The full title has some interest: _Vera circuli et hyperbolaequadratura cui accedit geometriae pars universalis inserviens quantitatumcurvarum transmutationi et mensurae. Authore Jacobo Gregorio AbredonensiScoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen(he was really born near but not in the city), a good Scot, was publishinghis work down in Padua. The reason was that he had been studying in Italy, and that this was a product of his youth. He had already (1663) publishedhis _Optica promota_, and it is not remarkable that his brilliancy broughthim a wide circle of friends on the continent and the offer of a pensionfrom Louis XIV. He became professor of mathematics at St Andrews and laterat Edinburgh, and invented the first successful reflecting telescope. Thedistinctive feature of his _Vera quadratura_ is his use of an infiniteconverging series, a plan that Archimedes used with the parabola. [232] Jean de Beaulieu wrote several works on mathematics, including _Lalumière de l'arithmétique_ (n. D. ), _La lumière des mathématiques_ (1673), _Nouvelle invention d'arithmétique_ (1677), and some mathematical tables. [233] A just estimate. There were several works published by GérardDesargues (1593-1661), of which the greatest was the _Brouillon Proiect_(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_by M. Poudra, Paris, 1864. [234] "A certain M. De Beaugrand, a mathematician, very badly treated byDescartes, and, as it appears, rightly so. " [235] This is a very old approximation for [pi]. One of the latestpretended geometric proofs resulting in this value appeared in New York in1910, entitled _Quadrimetry_ (privately printed). [236] "Copernicus, a German, made himself no less illustrious by hislearned writings; and we might say of him that he stood alone and unique inthe strength of his problems, if his excessive presumption had not led himto set forth in this science a proposition so absurd that it is contrary tofaith and reason, namely that the circumference of a circle is fixed andimmovable while the center is movable: on which geometrical principle hehas declared in his astrological treatise that the sun is fixed and theearth is in motion. " [237] So in the original. [238] Franciscus Maurolycus (1494-1575) was really the best mathematicianproduced by Sicily for a long period. He made Latin translations ofTheodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote oncosmography and other mathematical subjects. [239] "Nicolaus Copernicus is also tolerated who asserted that the sun isfixed and that the earth whirls about it; and he rather deserves a whip ora lash than a reproof. " [240] "Algebra is the curious science of scholars, and particularly for ageneral of an army, or a captain, in order quickly to draw up an army inbattle array and to number the musketeers and pikemen who compose it, without the figures of arithmetic. This science has five special figures ofthis kind: P means _plus_ in commerce and _pikemen_ in the army; M means_minus_, and _musketeer_ in the art of war;... R signifies _root_ in themeasurement of a cube, and _rank_ in _the army_; Q means _square_ (French_quarè_, as then spelled) in both cases; C means _cube_ in mensuration, and_cavalry_ in arranging batallions and squadrons. As for the operations ofthis science, they are as follows: to add a _plus_ and a _plus_, the sumwill be _plus_; to add _minus_ with _plus_, take the less from the greaterand the remainder will be the sum required or the number to be found. I saythis only in passing, for the benefit of those who are wholly ignorant ofit. " [241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de variopondere gravium secundum varia a terrae (centro) intervalla dissertatiomathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all ofRoberval's theorems on the cycloid and Fermat's on maxima and minima toGalileo in 1638, pretending that they were his own. [242] More (1614-1687) was a theologian, a fellow of Christ College, Cambridge, and a Christian Platonist. [243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tractson scientific, moral, and religious subjects. These were collected andpublished in 1805. [244] They might have been attributed to many a worse man than Dr. Hales(1677-1761), who was a member of the Royal Society and of the ParisAcademy, and whose scheme for the ventilation of prisons reduced themortality at the Savoy prison from one hundred to only four a year. Thebook to which reference is made is _Vegetable Staticks or an Account ofsome statical experiments on the sap in Vegetables_, 1727. [245] _Pleas of the Crown; or a Methodical Summary of the Principal Mattersrelating to the subject_, 1678. [246] _Thomae Streete Astronomia Carolina, a new theory of the celestialmotions_, 1661. It also appeared at Nuremberg in 1705, and at London in1710 and 1716 (Halley's editions). He wrote other works on astronomy. [247] This was the Sir Thomas Street (1626-1696) who passed sentence ofdeath on a Roman Catholic priest for saying mass. The priest was reprievedby the king, but in the light of the present day one would think thejustice more in need of pardon. He took part in the trial of the Rye HouseConspirators in 1683. [248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilianprofessor of mathematics at Oxford, and Flamsteed (1720) as head of theGreenwich observatory. It is of interest to note that he was instrumentalin getting Newton's _Principia_ printed. [249] Shepherd (born in 1760) was one of the most famous lawyers of hisday. He was knighted in 1814 and became Attorney General in 1817. [250] This was William Hone (1780-1842), a book publisher, who wrotesatires against the government, and who was tried three times because ofhis parodies on the catechism, creed, and litany (illustrated byCruikshank). He was acquitted on all of the charges. [251] Valentinus was a Benedictine monk and was still living at Erfurt in1413. His _Currus triumphalis antimonii_ appeared in 1624. Synesius wasBishop of Ptolemaide, who died about 430. His works were printed at Parisin 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's. Besides the commentary on Valentine he left several works on anatomy. Hiscommentary appeared at Amsterdam in 1671. There were several editions ofthe _Chariot_. [252] The chief difficulty with this curious "monk-bane" etymology is itsabsurdity. The real origin of the word has given etymologists a good dealof trouble. [253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhapshis best-known discovery is the law concerning the volume of gases. [254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. Itmay have been Childe. He claimed to have discovered the philosopher's stonein 1645. His tract in this work is _The Secret of the Immortal LiquorAlkahest or Ignis-Aqua_. See note 260, _infra_. [255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries appeared in his _Ortus medicinae_(1648), which went through many editions. [256] De Morgan should have written up Francis Anthony (1550-1623), whose_Panacea aurea sive tractatus duo de auro potabili_ (Hamburg, 1619)described a panacea that he gave for every ill. He was repeatedlyimprisoned for practicing medicine without a license from the Royal Collegeof Physicians. [257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary, Egypt, Palestine, and Persia in search of the philosopher's stone. He wroteseveral works on alchemy, --_De Chemica_ (1567), _De Chemico Miraculo_(1583), _Traité de la nature de l'oeuf des philosophes_ (1659), etc. , allpublished long after his death. [258] George Ripley (1415-1490) was an Augustinian monk, later achamberlain of Innocent VIII, and still later a Carmelite monk. His _Liberde mercuris philosophico_ and other tracts first appeared in _Opusculaquaedam chymica_ (Frankfort, 1614). [259] Besides the _Opus majus_, and other of the better known works of thiscelebrated Franciscan (1214-1294), there are numerous tracts on alchemythat appeared in the _Thesaurus chymicus_ (Frankfort, 1603). [260] George Starkey (1606-1665 or 1666) has special interest for Americanreaders. He seems to have been born in the Bermudas and to have obtainedthe bachelor's degree in England. He then went to America and in 1646obtained the master's degree at Harvard, apparently under the name ofStirk. He met Eirenaeus Philalethes (see note 254 above) in America andlearned alchemy from him. Returning to England, he sold quack medicinesthere, and died in 1666 from the plague after dissecting a patient who haddied of the disease. Among his works was the _Liquor Alcahest, or aDiscourse of that Immortal Dissolvent of Paracelsus and Helmont_, whichappeared (1675) some nine years after his death. [261] Platt (1552-1611) was the son of a London brewer. Although he left amanuscript on alchemy, and wrote a book entitled _Delights for Ladies toadorne their Persons_ (1607), he was knighted for some serious work on thechemistry of agriculture, fertilizing, brewing, and the preserving offoods, published in _The Jewell House of Art and Nature_ (1594). [262] "Those who wish to call a man a liar and deceiver speak of him awriter of almanacs; but those who (would call him) a scoundrel and animposter (speak of him as) a chemist. " [263] "Trust your barque to the winds but not your body to a chemist; anybreeze is safer than the faith of a chemist. " [264] Probably the Jesuit, Père Claude François Menestrier (1631-1705), awell known historian. [265] The author was Christopher Nesse (1621-1705), a belligerentCalvinist, who wrote many controversial works and succeeded in gettingexcommunicated four times. One of his most virulent works was _A ProtestantAntidote against the Poison of Popery_. [266] John Case (c. 1660-1700) was a famous astrologer and physician. Hesucceeded to Lilly's practice in London. In a darkened room, wherein hekept an array of mystical apparatus, he pretended to show the credulous theghosts of their departed relatives. Besides his astrological works he wroteone serious treatise, the _Compendium Anatomicum nova methodo institutum_(1695), in which he defends Harvey's theories of embryology. [267] Marcelis (1636-after 1714) was a soap maker of Amsterdam. It is to behoped that he made better soap than values of [pi]. [268] John Craig (died in 1731) was a Scotchman, but most of his life wasspent at Cambridge reading and writing on mathematics. He endeavored tointroduce the Leibnitz differential calculus into England. His mathematicalworks include the _Methodus Figurarum ... Quadraturas determinandi_ (1685), _Tractatus ... De Figurarum Curvilinearum Quadraturis et locis Geometricis_(1693), and _De Calculo Fluentium libri duo_ (1718). [269] As is well known, this subject owes much to the Bernoullis. Craig'sworks on the calculus brought him into controversy with them. He also wroteon other subjects in which they were interested, as in his memoir _On theCurve of the quickest descent_ (1700), _On the Solid of least resistance_(1700), and the _Solution of Bernoulli's problem on Curves_ (1704). [270] This is Samuel Lee (1783-1852), the young prodigy in languages. Hewas apprenticed to a carpenter at twelve and learned Greek while working atthe trade. Before he was twenty-five he knew Hebrew, Chaldee, Syriac, Samaritan, Persian, and Hindustani. He later became Regius professor ofHebrew at Cambridge. [271] "Where the devil, Master Ludovico, did you pick up such acollection?" [272] Lord William Brounker (c. 1620-1684), the first president of theRoyal Society, is best known in mathematics for his contributions tocontinued fractions. [273] Horace Walpole (1717-1797) published his _Catalogue of the Royal andNoble Authors of England_ in 1758. Since his time a number of worthy namesin the domain of science in general and of mathematics in particular mightbe added from the peerage of England. [274] It was written by Charles Hayes (1678-1760), a mathematician andscholar of no mean attainments. He travelled extensively, and was deputygovernor of the Royal African Company. His _Treatise on Fluxions_ (London, 1704) was the first work in English to explain Newton's calculus. He wrotea work entitled _The Moon_ (1723) to prove that our satellite shines by itsown as well as by reflected light. His _Chronographia Asiatica & Aegyptica_(1758) gives the results of his travels. [275] _Publick_ in the original. [276] Whiston (1667-1752) succeeded Newton as Lucasian professor ofmathematics at Cambridge. In 1710 he turned Arian and was expelled from theuniversity. His work on _Primitive Christianity_ appeared the followingyear. He wrote many works on astronomy and religion. [277] Ditton (1675-1715) was, on Newton's recommendation, made Head of themathematical school at Christ's Hospital, London. He wrote a work onfluxions (1706). His idea for finding longitude at sea was to placestations in the Atlantic to fire off bombs at regular intervals, the timebetween the sound and the flash giving the distance. He also correspondedwith Huyghens concerning the use of chronometers for the purpose. [278] This was John Arbuthnot (c. 1658-1735), the mathematician, physicianand wit. He was intimate with Pope and Swift, and was Royal physician toQueen Anne. Besides various satires he published a translation ofHuyghens's work on probabilities (1692) and a well-known treatise onancient coins, weights, and measures (1727). [279] Greene (1678-1730) was a very eccentric individual and was generallyridiculed by his contemporaries. In his will he directed that his body bedissected and his skeleton hung in the library of King's College, Cambridge. Unfortunately for his fame, this wish was never carried out. [280] This was the historian, Robert Sanderson (1660-1741), who spent mostof his life at Cambridge. [281] I presume this was William Jones (1675-1749) the friend of Newton andHalley, vice-president of the Royal Society, in whose _Synopsis PalmariorumMatheseos_ (1706) the symbol [pi] is first used for the circle ratio. [282] This was the _Geometrica solidorum, sive materiae, seu de variacompositione, progressione, rationeque velocitatum_, Cambridge, 1712. Thework was parodied in _A Taste of Philosophical Fanaticism ... By agentleman of the University of Gratz_. [283] The antiquary and scientist (1690-1754), president of the RoyalSociety, member of the Académie, friend of Newton, and authority onnumismatics. [284] She was Catherine Barton, Newton's step-niece. She married JohnConduitt, master of the mint, who collected materials for a life of Newton. _A propos_ of Mrs. Conduitt's life of her illustrious uncle, Sir GeorgeGreenhill tells a very good story on Poincaré, the well-known Frenchmathematician. At an address given by the latter at the InternationalCongress of Mathematicians held in Rome in 1908 he spoke of the story ofNewton and the apple as a mere fable. After the address Sir George askedhim why he had done so, saying that the story was first published byVoltaire, who had heard it from Newton's niece, Mrs. Conduitt. Poincarélooked blank and said, "Newton, et la nièce de Newton, et Voltaire, --non!je ne vous comprends pas!" He had thought Sir George meant ProfessorVolterra of Rome, whose name in French is Voltaire, and who could notpossibly have known a niece of Newton without bridging a century or so. [285] This was the Edmund Turnor (1755-1829) who wrote the _Collections forthe Town and Soke of Grantham, containing authentic Memoirs of Sir IsaacNewton, from Lord Portsmouth's Manuscripts_, London, 1806. [286] It may be recalled to mind that Sir David (1781-1868) wrote a life ofNewton (1855). [287] "They are in the country. We rejoice. " [288] "I am here, chatterbox, suck!" [289] "I have been graduated! I decline!" [290] Giovanni Castiglioni (Castillon, Castiglione), was born atCastiglione, in Tuscany, in 1708, and died at Berlin in 1791. He wasprofessor of mathematics at Utrecht and at Berlin. He wrote on De Moivre'sequations (1762), Cardan's rule (1783), and Euclid's treatment of parallels(1788-89). [291] This was the _Isaaci Newtoni, equitis aurati, opuscula mathematica, philosophica et philologica_, Lausannae & Genevae, 1744. [292] At London, 4to. [293] "All the English attribute it to Newton. " [294] Stephen Peter Rigaud (1774-1839), Savilian professor of geometry atOxford (1810-27) and later professor of astronomy and head of the RadcliffeObservatory. He wrote _An historical Essay on first publication of SirIsaac Newton's Principia_, Oxford, 1838, and a two-volume work entitled_Correspondence of Scientific Men of the 17th Century_, 1841. [295] It is no longer considered by scholars as the work of Newton. [296] J. Edleston, the author of the _Correspondence of Sir Isaac Newtonand Professor Cotes_, London, 1850. [297] Palmer (1601-1647) was Master of Queen's College, Cambridge, aPuritan but not a separatist. His work, _The Characters of a believingChristian, in Paradoxes and seeming contradictions_, appeared in 1645. [298] Grosart (1827-1899) was a Presbyterian clergyman. He was a greatbibliophile, and issued numerous reprints of rare books. [299] This was the year after Palmer's death. The title was, _The Remainesof ... Francis Lord Verulam.... ; being Essays and severall Letters toseverall great personages, and other pieces of various and high concernmentnot heretofore published_, London, 1648, 4to. [300] Shaw (1694-1763) was physician extraordinary to George II. He wroteon chemistry and medicine, and his edition of the _Philosophical Works ofFrancis Bacon_ appeared at London in 1733. [301] John Locke (1632-1704), the philosopher. This particular workappeared in 1695. There was an edition in 1834 (vol. 25 of the _SacredClassics_) and one in 1836 (vol. 2 of the _Christian Library_). [302] I use the word _Socinian_ because it was so much used in Locke'stime: it is used in our own day by the small fry, the unlearned clergy andtheir immediate followers, as a term of reproach for _all_ Unitarians. Isuspect they have a kind of liking for the _word_; it sounds like _sosinful_. The learned clergy and the higher laity know better: they knowthat the bulk of the modern Unitarians go farther than Socinus, and are notcorrectly named as his followers. The Unitarians themselves neither desirenor deserve a name which puts them one point nearer to orthodoxy than theyput themselves. That point is the doctrine that direct prayer to JesusChrist is lawful and desirable: this Socinus held, and the modernUnitarians do not hold. Socinus, in treating the subject in his own_Institutio_, an imperfect catechism which he left, lays much more stresson John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to thinkthat _Patrem_ should be in the first citation, where some put it; but hesays that to ask the Father in the name of the Son is nothing but prayingto the Son in prayer to the Father. He labors the point with obvious wishto secure a conclusive sanction. In the Racovian Catechism, of whichFaustus Socinus probably drew the first sketch, a clearer light is arrivedat. The translation says: "But wherein consists the divine honor due toChrist? In adoration likewise and invocation. For we ought at all times toadore Christ, and may in our necessities address our prayers to him asoften as we please; and there are many reasons to induce us to do thisfreely. " There are some who like accuracy, even in aspersion--A. De M. Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian whobelieved in prayer and homage to Christ. Leaving Italy after his viewsbecame known, he repaired to Basel, but his opinions were too extreme evenfor the Calvinists. He then tried Transylvania, attempting to convert tohis views the antitrinitarian Bishop Dávid. The only result of his effortswas the imprisonment of Dávid and his own flight to Poland, in whichcountry he spent the rest of his life (1579-1604). His complete worksappeared first at Amsterdam in 1668, in the _Bibliotheca FratresPolonorum_. The _Racovian Catechism_ (1605) appeared after his death, butit seems to have been planned by him. [303] "As much of faith as is necessary to salvation is contained in thisarticle, Jesus is the Christ. " [304] Edwards (1637-1716) was a Cambridge fellow, strongly Calvinistic. Hepublished many theological works, attacking the Arminians and Socinians. Locke and Whiston were special objects of attack. [305] _Sir I. Newton's views on points of Trinitarian Doctrine; hisArticles of Faith, and the General Coincidence of his Opinions with thoseof J. Locke; a Selection of Authorities, with Observations_, London, 1856. [306] _A Confession of the Faith_, Bristol, 1752, 8vo. [307] This was really very strange, because Laud (1573-1644), while he wasArchbishop of Canterbury, forced a good deal of High Church ritual on thePuritan clergy, and even wished to compel the use of a prayer book inScotland. It was this intolerance that led to his impeachment andexecution. [308] The name is Jonchère. He was a man of some merit, proposing (1718) animportant canal in Burgundy, and publishing a work on the _Découverte deslongitudes estimées généralement impossible à trouver_, 1734 (or 1735). [309] Locke invented a kind of an instrument for finding longitude, and itis described in the appendix, but I can find nothing about the man. Therewas published some years later (London, 1751) another work of his, _A newProblem to discover the longitude at sea_. [310] Baxter, concerning whom I know merely that he was a schoolmaster, starts with the assumption of this value, and deduces from it some fourteenproperties relating to the circle. [311] John, who died in 1780, was a well-known character in his way. He wasa bookseller on Fleet Street, and his shop was a general rendezvous for theliterary men of his time. He wrote the _Memoirs of the Life and Writings ofMr. William Whiston_ (1749, with another edition in 1753). He was one ofthe first to issue regular catalogues of books with prices affixed. [312] The name appears both as Hulls and as Hull. He was born inGloucestershire in 1699. In 1754 he published _The Art of Measuring madeEasy by the help of a new Sliding Scale_. [313] Thomas Newcomen (1663-1729) invented the first practical steam engineabout 1710. It was of about five and a half horse power, and was used forpumping water from coal mines. Savery had described such an engine in 1702, but Newcomen improved upon it and made it practical. [314] The well-known benefactor of art (1787-1863). [315] The tract was again reprinted in 1860. [316] Hulls made his experiment on the Avon, at Evesham, in 1737, havingpatented his machine in 1736. He had a Newcomen engine connected with sixpaddles. This was placed in the front of a small tow boat. The experimentwas a failure. [317] William Symington (1763-1831). In 1786 he constructed a working modelof a steam road carriage. The machinery was applied to a small boat in1788, and with such success as to be tried on a larger boat in 1789. Themachinery was clumsy, however, and in 1801 he took out a new patent for thestyle of engine still used on paddle wheel steamers. This engine wassuccessfully used in 1802, on the Charlotte Dundas. Fulton (1765-1815) wason board, and so impressed Robert Livingston with the idea that the latterfurnished the money to build the Clermont (1807), the beginning ofsuccessful river navigation. [318] Louis Bertrand Castel (1688-1757), most of whose life was spent intrying to perfect his _Clavecin oculaire_, an instrument on the order ofthe harpsichord, intended to produce melodies and harmonies of color. Healso wrote _L'Optique des couleurs_ (1740) and _Sur le fond de la Musique_(1754). [319] Dr. Robinson (1680-1754) was professor of physic at Trinity College, Dublin, and three times president of King and Queen's College ofPhysicians. In his _Treatise on the Animal Economy_ (1732-3, with a thirdedition in 1738) he anticipated the discoveries of Lavoisier and Priestleyon the nature of oxygen. [320] There was another edition, published at London in 1747, 8vo. [321] The author seems to have shot his only bolt in this work. I can findnothing about him. [322] _Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, ejusqueprovidentia gubernetur. Selecta aliquot theoremata adversos atheos_, etc. , Paris, 1635, 4to. [323] The British Museum Catalogue mentions a copy of 1740, but this ispossibly a misprint. [324] This was Johann II (1710-1790), son of Johann I, who succeeded hisfather as professor of mathematics at Basel. [325] Samuel Koenig (1712-1757), who studied under Johann Bernoulli I. Hebecame professor of mathematics at Franeker (1747) and professor ofphilosophy at the Hague (1749). [326] "In accordance with the hypotheses laid down in this memoir it is soevident that t must = 34, y = 1, and z = 1, that there is no need of proofor authority for it to be recognized by every one. " [327] "I subscribe to the judgment of Mr. Bernoulli as a result of thesehypotheses. " [328] "It clearly appears from my present analysis and demonstration thatthey have already recognized and perfectly agreed to the fact that thequadrature of the circle is mathematically demonstrated. " [329] Dr. Knight (died in 1772) made some worthy contributions to theliterature of the mariner's compass. As De Morgan states, he was librarianof the British Museum. [330] Sir Anthony Panizzi (1797-1879) fled from Italy under sentence ofdeath (1822). He became assistant (1831) and chief (1856) librarian of theBritish Museum, and was knighted in 1869. He began the catalogue of printedbooks of the Museum. [331] Wright (1711-1786) was a physicist. He was offered the professorshipof mathematics at the Imperial Academy of St. Petersburg but declined toaccept it. This work is devoted chiefly to the theory of the Milky Way, the_via lactea_ as he calls it after the manner of the older writers. [332] Troughton (1753-1835) was one of the world's greatest instrumentmakers. He was apprenticed to his brother John, and the two succeeded(1770) Wright and Cole in Fleet Street. Airy called his method ofgraduating circles the greatest improvement ever made in instrument making. He constructed (1800) the first modern transit circle, and his instrumentswere used in many of the chief observatories of the world. [333] William Simms (1793-1860) was taken into partnership by Troughton(1826) after the death of the latter's brother. The firm manufactured somewell-known instruments. [334] This was George Horne (1730-1792), fellow of Magdalen College, Oxford, vice-Chancellor of the University (1776), Dean of Canterbury(1781), and Bishop of Norwich (1790). He was a great satirist, but most ofhis pamphlets against men like Adam Smith, Swedenborg, and Hume, wereanonymous, as in the case of this one against Newton. He was so liberal inhis attitude towards the Methodists that he would not have John Wesleyforbidden to preach in his diocese. He was twenty-one when this tractappeared. [335] Martin (1704-1782) was by no means "old Benjamin Martin" when Hornewrote this pamphlet in 1749. In fact he was then only forty-five. He was aphysicist and a well-known writer on scientific instruments. He also wrote_Philosophia Britannica or a new and comprehensive system of the NewtonianPhilosophy_ (1759). [336] Jean Théophile Desaguliers, or Des Aguliers (1683-1744) was the sonof a Protestant who left France after the revocation of the Edict ofNantes. He became professor of physics at Oxford, and afterwards gavelectures in London. Later he became chaplain to the Prince of Wales. Hepublished several works on physics. [337] Charles Hutton (1737-1823), professor of mathematics at Woolwich(1772-1807). His _Mathematical Tables_ (1785) and _Mathematical andPhilosophical Dictionary_ (1795-1796) are well known. [338] James Epps (1773-1839) contributed a number of memoirs on the use andcorrections of instruments. He was assistant secretary of the AstronomicalSociety. [339] John Hutchinson (1674-1737) was one of the first to try to reconcilethe new science of geology with Genesis. He denied the Newtonian hypothesisas dangerous to religion, and because it necessitated a vacuum. He was amystic in his interpretation of the Scriptures, and created a sect thatwent under the name of Hutchinsonians. [340] John Rowning, a Lincolnshire rector, died in 1771. He wrote onphysics, and published a memoir on _A machine for finding the roots ofequations universally_ (1770). [341] It is always difficult to sanction this spelling of the name of thisJesuit father who is so often mentioned in the analytic treatment ofconics. He was born in Ragusa in 1711, and the original spelling wasRu[=d]er Josip Bo[vs]kovi['c]. When he went to live in Italy, as professorof mathematics at Rome (1740) and at Pavia, the name was spelled RuggieroGiuseppe Boscovich, although Boscovicci would seem to a foreigner morenatural. His astronomical work was notable, and in his _De maculissolaribus_ (1736) there is the first determination of the equator of aplanet by observing the motion of spots on its surface. Boscovich came nearhaving some contact with America, for he was delegated to observe inCalifornia the transit of Venus in 1755, being prevented by the dissolutionof his order just at that time. He died in 1787, at Milan. [342] James Granger (1723-1776) who wrote the _Biographical History ofEngland_, London, 1769. His collection of prints was remarkable, numberingsome fourteen thousand. [343] He was curator of experiments for the Royal Society. He wrote a largenumber of books and monographs on physics. He died about 1713. [344] Lee seems to have made no impression on biographers. [345] This work appeared at London in 1852. [346] Of course this is no longer true. The most scholarly work to-day isthat of Rudio, _Archimedes, Huygens, Lambert, Legendre, vier Abhandlungenüber die Kreismessung ... Mit einer Uebersicht über die Geschichte desProblems von der Quadratur des Zirkels, von den ältesten Zeiten bis aufunsere Tage_, Leipsic, 1892. [347] Joseph Jérome le François de Lalande (1732-1807), professor ofastronomy in the Collège de France (1753) and director of the ParisObservatory (1761). His writings on astronomy and his _Bibliographieastronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802_(Paris, 1803) are well known. [348] De Morgan refers to his _Histoire de l'Astronomie au 18e siècle_, which appeared in 1827, five years after Delambre's death. Jean BaptisteJoseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande, following his master as professor of astronomy in the Collège de France. His work on the measurements for the metric system is well known, and hisfour histories of astronomy, _ancienne_ (1817), _au moyen âge_ (1819), _moderne_ (1821), and _au 18e siècle_ (posthumous, 1827) are highlyesteemed. [349] Jean-Joseph Rive (1730-1792), a priest who left his cure under gravecharges, and a quarrelsome character. His attack on Montucla was a case ofthe pot calling the kettle black; for while he was a brilliant writer hewas a careless bibliographer. [350] Isaac Barrow (1630-1677) was quite as well known as a theologian ashe was from his Lucasian professorship of mathematics at Cambridge. [351] "Besides we can see by this that Barrow was a poor philosopher; forhe believed in the immortality of the soul and in a Divinity other thanuniversal nature. " [352] The _Récréations mathématiques et physiques_ (Paris, 1694) of JacquesOzanam (1640-1717) is a work that is still highly esteemed. Among variousother works he wrote a _Dictionnaire mathématique ou Idée générale desmathématiques_ (1690) that was not without merit. The _Récréations_ wentthrough numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, andthe Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of1803 and the Riddle edition of 1840; Dublin, 1790). [353] Hendryk van Etten, the _nom de plume_ of Jean Leurechon (1591-1670), rector of the Jesuit college at Bar, and professor of philosophy andmathematics. He wrote on astronomy (1619) and horology (1616), and is knownfor his _Selecta Propositiones in tota sparsim mathematica pulcherrimepropositae in solemni festo SS. Ignatii et Francesci Xaverii_, 1622. Thebook to which De Morgan refers is his _Récréation mathématicque, composéede plusieurs problèmes plaisants et facetieux_, Lyons, 1627, with anedition at Pont-à-Mousson, 1629. There were English editions published atLondon in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672. I do not understand how De Morgan happened to miss owning the work byClaude Gaspar Bachet de Meziriac (1581-1638), _Problèmes plaisans etdélectables_, which appeared at Lyons in 1612, 8vo, with a second editionin 1624. There was a fifth edition published at Paris in 1884. [354] His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCCLIV. " This was Charles-Antoine Jombert (1712-1784), a printer and bookseller withsome taste for painting and architecture. He wrote several works and editeda number of early treatises. [355] The late Professor Newcomb made the matter plain even to thenon-mathematical mind, when he said that "ten decimal places are sufficientto give the circumference of the earth to the fraction of an inch, andthirty decimal places would give the circumference of the whole visibleuniverse to a quantity imperceptible with the most powerful microscope. " [356] _Antinewtonianismi pars prima, in qua Newtoni de coloribus systema expropriis principiis geometrice evertitur, et nova de coloribus theorialuculentissimis experimentis demonstrantur_.... Naples, 1754; _parssecunda_, Naples, 1756. [357] Celestino Cominale (1722-1785) was professor of medicine at theUniversity of Naples. [358] The work appeared in the years from 1844 to 1849. [359] There was a Vienna edition in 1758, 4to, and another in 1759, 4to. This edition is described on the title page as _Editio Veneta prima ipsoauctore praesente, et corrigente_. [360] The first edition was entitled _De solis ac lunae defectibus libriV. P. Rogerii Josephi Boscovich ... Cum ejusdem auctoris adnotationibus_, London, 1760. It also appeared in Venice in 1761, and in French translationby the Abbé de Baruel in 1779, and was a work of considerable influence. [361] Paulian (1722-1802) was professor of physics at the Jesuit college atAvignon. He wrote several works, the most popular of which, the_Dictionnaire de physique_ (Avignon, 1761), went through nine editions by1789. [362] This is correct. [363] Probably referring to the fact that Hill (1795-1879), who had done somuch for postal reform, was secretary to the postmaster general (1846), andhis name was a synonym for the post office directory. [364] Richard Lovett (1692-1780) was a good deal of a charlatan. He claimedto have studied electrical phenomena, and in 1758 advertised that he couldeffect marvelous cures, especially of sore throat, by means of electricity. Before publishing the works mentioned by De Morgan he had issued others ofsimilar character, including _The Subtile Medium proved_ (London, 1756) and_The Reviewers Reviewed_ (London, 1760). [365] Jean Sylvain Bailly (1736-1793), member of the _Académie française_and of the _Académie des sciences_, first deputy elected to represent Parisin the _Etats-généraux_ (1789), president of the first National Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in keeping thepeace, and for his manly defence of the Queen, he was guillotined. He wasan astronomer of ability, but is best known for his histories of thescience. [366] These were the _Histoire de l'Astronomie ancienne_ (1775), _Histoirede l'Astronomie moderne_ (1778-1783), _Histoire de l'Astronomie indienne etorientale_ (1787), and _Lettres sur l'origine des peuples de l'Asie_(1775). [367] "The sick old man of Ferney, V. , a boy of a hundred years. " Voltairewas born in 1694, and hence was eighty-three at this time. [368] In Palmézeaux's _Vie de Bailly_, in Bailly's _Ouvrage Posthume_(1810), M. De Sales is quoted as saying that the _Lettres sur l'Atlantide_were sent to Voltaire and that the latter did not approve of the theory setforth. [369] The British Museum catalogue gives two editions, 1781 and 1782. [370] A mystic and a spiritualist. His chief work was the one mentionedhere. [371] Jacob Behmen, or Böhme (1575-1624), known as "the Germantheosophist, " was founder of the sect of Boehmists, a cult allied to theSwedenborgians. He was given to the study of alchemy, and brought thevocabulary of the science into his mystic writings. His sect was revived inEngland in the eighteenth century through the efforts of William Law. Saint-Martin translated into French two of his Latin works under the titles_L'Aurore naissante, ou la Racine de la philosophie_ (1800), and _Les troisprincipes de l'essence divine_ (1802). The originals had appeared nearlytwo hundred years earlier, --_Aurora_ in 1612, and _De tribus principiis_ in1619. [372] "Unknown. " [373] "Skeptical. " [374] "Man, man, man. " [375] "Men, men, men. " [376] It is interesting to read De Morgan's argument against Saint-Martin'sauthorship of this work. It is attributed to Saint-Martin both by the_Biographie Universelle_ and by the _British Museum Catalogue_, and DeMorgan says by "various catalogues and biographies. " [377] "To explain things by man and not man by things. _On Errors andTruth_, by a Ph.... Inc.... " [378] "If we would preserve ourselves from all illusions, and above allfrom the allurements of pride, by which man is so often seduced, we shouldnever take man, but always God, for our term of comparison. " [379] "And here is found already an explanation of the numbers four andnine which caused some perplexity in the work cited above. Man is lost inpassing from four to nine. " [380] Williams also took part in the preparation of some tables for thegovernment to assist in the determination of longitude. He had published awork two years before the one here cited, on the same subject, --_An entirenew work and method to discover the variation of the Earth's Diameters_, London, 1786. [381] This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggestedas a basis for a natural system of measures the _mille_, a minute of adegree of the meridian. This appeared in his _Observationes diametrorumsolis et lunae apparentium, meridianarumque aliquot altitudinum cum tabuladeclinationum solis_.... Lyons, 1670. [382] Jacques Cassini (1677-1756), one of the celebrated Cassini family ofastronomers. After the death of his father he became director of theobservatory at Paris. The basis for a metric unit was set forth by him inhis _Traité de la grandeur et de la figure de la terre_, Paris, 1720. Hewas a prolific writer on astronomy. [383] Alexis Jean Pierre Paucton (1732-1798). He was, for a time, professorof mathematics at Strassburg, but later (1796) held office in Paris. Hisleading contribution to metrology was his _Métrologie ou Traité desmesures_, Paris, 1780. [384] He was an obscure writer, born at Deptford. [385] He was also a writer of no scientific merit, his chief contributionsbeing religious tracts. One of his productions, however, went through manyeditions, even being translated into French; _Three dialogues between aMinister and one of his Parishioners; on the true principles of Religionand salvation for sinners by Jesus Christ_. The twentieth edition appearedat Cambridge in 1786. [386] This was the _Reflections on the Revolution in France, and on theproceedings in certain societies in London relative to that event_ (London, 1790) by Edmund Burke (1729-1797). Eleven editions of the work appeared thefirst year. [387] Paine (1736-1809) was born in Norfolkshire, of Quaker parents. Hewent to America at the beginning of the Revolution and published, inJanuary 1776, a violent pamphlet entitled _Common Sense_. He was a privatesoldier under Washington, and on his return to England after the war hepublished _The Rights of Man_. He was indicted for treason and was outlawedto France. He was elected to represent Calais at the French convention, buthis plea for moderation led him perilously near the guillotine. His _Age ofReason_ (1794) was dedicated to Washington. He returned to America in 1802and remained there until his death. [388] Part I appeared in 1791 and was so popular that eight editionsappeared in that year. It was followed in 1792 by Part II, of which nineeditions appeared in that year. Both parts were immediately republished inParis, and there have been several subsequent editions. [389] Mary Wollstonecraft (1759-1797) was only thirty-three when this workcame out. She had already published _An historical and moral View of theOrigin and Progress of the French Revolution_ (1790), and _Original Storiesfrom Real Life_ (1791). She went to Paris in 1792 and remained during theReign of Terror. [390] Samuel Parr (1747-1827) was for a time head assistant at Harrow(1767-1771), afterwards headmaster in other schools. At the time this bookwas written he was vicar of Hatton, where he took private pupils(1785-1798) to the strictly limited number of seven. He was a violent Whigand a caustic writer. [391] On Mary Wollstonecraft's return from France she married (1797)William Godwin (1756-1836). He had started as a strong CalvinisticNonconformist minister, but had become what would now be called ananarchist, at least by conservatives. He had written an _Inquiry concerningPolitical Justice_ (1793) and a novel entitled _Caleb Williams, or Thingsas they are_ (1794), both of which were of a nature to attract his futurewife. [392] This child was a daughter. She became Shelley's wife, and Godwin'sinfluence on Shelley was very marked. [393] This was John Nichols (1745-1826), the publisher and antiquary. Heedited the _Gentleman's Magazine_ (1792-1826) and his works include the_Literary Anecdotes of the Eighteenth Century_ (1812-1815), to which DeMorgan here refers. [394] William Bellenden, a Scotch professor at the University of Paris, whodied about 1633. His textbooks are now forgotten, but Parr edited anedition of his works in 1787. The Latin preface, _Praefatio ad Bellendum deStatu_, was addressed to Burke, North, and Fox, and was a satire on theirpolitical opponents. [395] As we have seen, he had been head-master before he began taking "hishandful of private pupils. " [396] The story has evidently got mixed up in the telling, for Tom Sheridan(1721-1788), the great actor, was old enough to have been Dr. Parr'sfather. It was his son, Richard Brinsley Sheridan (1751-1816), thedramatist and politician, who was the pupil of Parr. He wrote _The Rivals_(1775) and _The School for Scandal_ (1777) soon after Parr left Harrow. [397] Horner (1785-1864) was a geologist and social reformer. He was veryinfluential in improving the conditions of child labor. [398] William Cobbett (1762-1835), the journalist, was a character notwithout interest to Americans. Born in Surrey, he went to America at theage of thirty and remained there eight years. Most of this time he wasoccupied as a bookseller in Philadelphia, and while thus engaged he wasfined for libel against the celebrated Dr. Rush. On his return to Englandhe edited the _Weekly Political Register_ (1802-1835), a popular journalamong the working classes. He was fined and imprisoned for two yearsbecause of his attack (1810) on military flogging, and was also (1831)prosecuted for sedition. He further showed his paradox nature by his_History of the Protestant Reformation_ (1824-1827), an attack on theprevailing Protestant opinion. He also wrote a _Life of Andrew Jackson_(1834). After repeated attempts he succeeded in entering parliament, aresult of the Reform Bill. [399] Robinson (1735-1790) was a Baptist minister who wrote severaltheological works and a number of hymns. His work at Cambridge so offendedthe students that they at one time broke up the services. [400] This work had passed through twelve editions by 1823. [401] Dyer (1755-1841), the poet and reformer, edited Robinson's_Ecclesiastical Researches_ (1790). He was a life-long friend of CharlesLamb, and in their boyhood they were schoolmates at Christ's Hospital. His_Complaints of the Poor People of England_ (1793) made him a worthycompanion of the paradoxers above mentioned. [402] These were John Thelwall (1764-1834) whose _Politics for the Peopleor Hogswash_ (1794) took its title from the fact that Burke called thepeople the "swinish multitude. " The book resulted in sending the author tothe Tower for sedition. In 1798 he gave up politics and started a school ofelocution which became very famous. Thomas Hardy (1752-1832), who kept abootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, beingarrested for high treason. He was founder (1792) of The LondonCorresponding Society, a kind of clearing house for radical associationsthroughout the country. Horne Tooke was really John Horne (1736-1812), hehaving taken the name of his friend William Tooke in 1782. He was a radicalof the radicals, and organized a number of reform societies. Among thesewas the Constitutional Society that voted money (1775) to assist theAmerican revolutionists, appointing him to give the contribution toFranklin. For this he was imprisoned for a year. With his fellow rebels inthe Tower in 1794, however, he was acquitted. As a philologist he is knownfor his early advocacy of the study of Anglo-Saxon and Gothic, and his_Diversions of Purley_ (1786) is still known to readers. [403] This was the admiral, Adam Viscount Duncan (1731-1804), who defeatedthe Dutch off Camperdown in 1797. [404] He was created Duke of Clarence and St. Andrews in 1789 and wasAdmiral of the Fleet escorting Louis XVIII on his return to France in 1814. He became Lord High Admiral in 1827, and reigned as William IV from 1830 to1837. [405] This was Charles Abbott (1762-1832) first Lord Tenterden. Hesucceeded Lord Ellenborough as Chief Justice (1818) and was raised to thepeerage in 1827. He was a strong Tory and opposed the Catholic Relief Bill, the Reform Bill, and the abolition of the death penalty for forgery. [406] Edward Law (1750-1818), first Baron Ellenborough. He was chiefcounsel for Warren Hastings, and his famous speech in defense of his clientis well known. He became Chief Justice and was raised to the peerage in1802. He opposed all efforts to modernize the criminal code, insisting uponthe reactionary principle of new death penalties. [407] Edmund Law (1703-1787), Bishop of Carlisle (1768), was a good dealmore liberal than his son. His _Considerations on the Propriety ofrequiring subscription to the Articles of Faith_ (1774) was publishedanonymously. In it he asserts that not even the clergy should be requiredto subscribe to the thirty-nine articles. [408] Joe Miller (1684-1738), the famous Drury Lane comedian, was soilliterate that he could not have written the _Joe Miller's Jests, or theWit's Vade-Mecum_ that appeared the year after his death. It was oftenreprinted and probably contained more or less of Miller's own jokes. [409] The sixth duke (1766-1839) was much interested in parliamentaryreform. He was a member of the Society of Friends of the People. He was forfourteen years a member of parliament (1788-1802) and was later LordLieutenant of Ireland (1806-1807). He afterwards gave up politics andbecame interested in agricultural matters. [410] George Jeffreys (c. 1648-1689), the favorite of James II, who wasactive in prosecuting the Rye House conspirators. He was raised to thepeerage in 1684 and held the famous "bloody assize" in the following year, being made Lord Chancellor as a result. He was imprisoned in the Tower byWilliam III and died there. [411] _The Every Day Book, forming a Complete History of the Year, Months, and Seasons, and a perpetual Key to the Almanack_, 1826-1827. [412] The first and second editions appeared in 1820. Two others followedin 1821. [413] _The three trials of W. H. , for publishing three parodies; viz thelate John Wilkes' Catechism, the Political Litany, and the SinecuristsCreed; on three ex-officio informations, at Guildhall, London, ... Dec. 18, 19, & 20, 1817_, ... London, 1818. [414] The _Political Litany_ appeared in 1817. [415] That is, Castlereagh's. [416] The well-known caricaturist (1792-1878), then only twenty-nine yearsold. [417] Robert Stewart (1769-1822) was second Marquis of Londonderry andViscount Castlereagh. As Chief Secretary for Ireland he was largelyinstrumental in bringing about the union of Ireland and Great Britain. Hewas at the head of the war department during most of the Napoleonic wars, and was to a great extent responsible for the European coalition againstthe Emperor. He suicided in 1822. [418] John Murray (1778-1843), the well-known London publisher. He refusedto finish the publication of Don Juan, after the first five cantos, becauseof his Tory principles. [419] Only the first two cantos appeared in 1819. [420] Proclus (412-485), one of the greatest of the neo-Platonists, studiedat Alexandria and taught philosophy at Athens. He left commentaries onPlato and on part of Euclid's _Elements_. [421] Thomas Taylor (1758-1835), called "the Platonist, " had a liking formathematics, and was probably led by his interest in number mysticism to astudy of neo-Platonism. He translated a number of works from the Latin andGreek, and wrote two works on theoretical arithmetic (1816, 1823). [422] There was an earlier edition, 1788-89. [423] Georgius Gemistus, or Georgius Pletho (Plethon), lived in thefourteenth and fifteenth centuries. He was a native of Constantinople, butspent most of his time in Greece. He devoted much time to the propagationof the Platonic philosophy, but also wrote on divinity, geography, andhistory. [424] Hannah More (1745-1833), was, in her younger days, a friend of Burke, Reynolds, Dr. Johnson, and Garrick. At this time she wrote a number ofpoems and aspired to become a dramatist. Her _Percy_ (1777), with aprologue and epilogue by Garrick, had a long run at Covent Garden. Somewhatlater she came to believe that the playhouse was a grave public evil, andrefused to attend the revival of her own play with Mrs. Siddons in theleading part. After 1789 she and her sisters devoted themselves to startingschools for poor children, teaching them religion and housework, butleaving them illiterate. [425] These were issued at the rate of three each month, --a story, aballad, and a Sunday tract. They were collected and published in one volumein 1795. It is said that two million copies were sold the first year. Therewere also editions in 1798, 1819, 1827, and 1836-37. [426] That is, Dr. Johnson (1709-1784). The _Rambler_ was published in1750-1752, and was an imitation of Addison's _Spectator_. [427] Dr. Moore, referred to below. [428] Dr. John Moore (1729-1802), physician and novelist, is now best knownfor his _Journal during a Residence in France from the beginning of Augustto the middle of December, 1792_, a work quoted frequently by Carlyle inhis _French Revolution_. [429] Sir John Moore (1761-1809), Lieutenant General in the Napoleonicwars. He was killed in the battle of Corunna. The poem by Charles Wolfe(1791-1823), _The Burial of Sir John Moore_ (1817), is well known. [430] Referring to the novels of Thomas Love Peacock (1785-1866), whosucceeded James Mill as chief examiner of the East India Company, and wasin turn succeeded by John Stuart Mill. [431] Frances Burney, Madame d'Arblay (1752-1840), married Generald'Arblay, a French officer and companion of Lafayette, in 1793. She wasonly twenty-five when she acquired fame by her _Evelina, or a Young Lady'sEntrance into the World_. Her _Letters and Diaries_ appeared posthumously(1842-45). [432] Henry Peter, Baron Brougham and Vaux (1778-1868), well known inpolitics, science, and letters. He was one of the founders of the_Edinburgh Review_, became Lord Chancellor in 1830, and took part with menlike William Frend, De Morgan's father-in-law, in the establishing ofLondon University. He was also one of the founders of the Society for theDiffusion of Useful Knowledge. He was always friendly to De Morgan, whoentered the faculty of London University, whose work on geometry waspublished by the Society mentioned, and who was offered the degree ofdoctor of laws by the University of Edinburgh while Lord Brougham was LordRector. The Edinburgh honor was refused by De Morgan who said he "did notfeel like an LL. D. " [433] Maria Edgeworth (1767-1849). [434] Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, a well-knownsurgeon, in 1812. Her Irish stories were very popular with the patriots butwere attacked by the _Quarterly Review_. _The Wild Irish Girl_ (1806) wentthrough seven editions in two years. [435] 1775-1817. [436] 1771-1832. [437] The famous preacher (1732-1808). He was the first chairman of theReligious Tract Society. He is also known as one of the earliest advocatesof vaccination, in his _Cow-pock Inoculation vindicated and recommendedfrom matters of fact_, 1806. [438] Sir Rowland Hill (1795-1879), the father of penny postage. [439] Beilby Porteus (1731-1808), Bishop of Chester (1776) and Bishop ofLondon (1787). He encouraged the Sunday-school movement and thedissemination of Hannah More's tracts. He was an active opponent ofslavery, but also of Catholic emancipation. [440] Henrietta Maria Bowdler (1754-1830), generally known as Mrs. HarrietBowdler. She was the author of many religious tracts and poems. Her _Poemsand Essays_ (1786) were often reprinted. The story goes that on theappearance of her _Sermons on the Doctrines and duties of Christianity_(published anonymously), Bishop Porteus offered the author a living underthe impression that it was written by a man. [441] William Frend (1757-1841), whose daughter Sophia Elizabeth became DeMorgan's wife (1837), was at one time a clergyman of the EstablishedChurch, but was converted to Unitarianism (1787). He came under De Morgan'sdefinition of a true paradoxer, carrying on a zealous warfare for what hethought right. As a result of his _Address to the Inhabitants of Cambridge_(1787), and his efforts to have abrogated the requirement that candidatesfor the M. A. Must subscribe to the thirty-nine articles, he was deprived ofhis tutorship in 1788. A little later he was banished (see De Morgan'sstatement in the text) from Cambridge because of his denunciation of theabuses of the Church and his condemnation of the liturgy. His eccentricityis seen in his declining to use negative quantities in the operations ofalgebra. He finally became an actuary at London and was prominent inradical associations. He was a mathematician of ability, having been secondwrangler and having nearly attained the first place, and he was also anexcellent scholar in Latin, Greek, and Hebrew. [442] George Peacock (1791-1858), Fellow of Trinity College, Cambridge, Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tombmay be seen at Ely where he spent the latter part of his life. He was oneof the group that introduced the modern continental notation of thecalculus into England, replacing the cumbersome notation of Newton, passingfrom "the _dot_age of fluxions to the _de_ism of the calculus. " [443] Robert Simson (1687-1768); professor of mathematics at Glasgow. Hisrestoration of Apollonius (1749) and his translation and restoration ofEuclid (1756, and 1776--posthumous) are well known. [444] Francis Maseres (1731-1824), a prominent lawyer. His mathematicalworks had some merit. [445] These appeared annually from 1804 to 1822. [446] Henry Gunning (1768-1854) was senior esquire bedell of Cambridge. The_Reminiscences_ appeared in two volumes in 1854. [447] John Singleton Copley, Baron Lyndhurst (1772-1863), the son of JohnSingleton Copley the portrait painter, was born in Boston. He was educatedat Trinity College, Cambridge, and became a lawyer. He was made LordChancellor in 1827. [448] Sir William Rough (c. 1772-1838), a lawyer and poet, became ChiefJustice of Ceylon in 1836. He was knighted in 1837. [449] Herbert Marsh, afterwards Bishop of Peterborough, a relation of myfather. --S. E. De M. He was born in 1757 and died in 1839. On the trial of Frend he publiclyprotested against testifying against a personal confidant, and was excused. He was one of the first of the English clergy to study modern highercriticism of the Bible, and amid much opposition he wrote numerous works onthe subject. He was professor of theology at Cambridge (1707), Bishop ofLlandaff (1816), and Bishop of Peterborough. [450] George Butler (1774-1853), Headmaster of Harrow (1805-1829), Chancellor of Peterborough (1836), and Dean of Peterborough (1842). [451] James Tate (1771-1843), Headmaster of Richmond School (1796-1833) andCanon of St. Paul's Cathedral (1833). He left several works on theclassics. [452] Francis Place (1771-1854), at first a journeyman breeches maker, andlater a master tailor. He was a hundred years ahead of his time as a strikeleader, but was not so successful as an agitator as he was as a tailor, since his shop in Charing Cross made him wealthy. He was a well-knownradical, and it was largely due to his efforts that the law against thecombinations of workmen was repealed in 1824. His chief work was _ThePrinciples of Population_ (1822). [453] Speed (1552-1629) was a tailor until Grevil (Greville) made himindependent of his trade. He was not only an historian of some merit, but askilful cartographer. His maps of the counties were collected in the_Theatre of the Empire of Great Britaine_, 1611. About this same time healso published _Genealogies recorded in Sacred Scripture_, a work that hadpassed through thirty-two editions by 1640. [454] _The history of Great Britaine under the conquests of ye Romans, Saxons, Danes, and Normans.... _ London, 1611, folio. The second editionappeared in 1623; the third, to which De Morgan here refers, posthumouslyin 1632; and the fourth in 1650. [455] William Nicolson (1655-1727) became Bishop of Carlisle in 1702, andBishop of Derry in 1718. His chief work was the _Historical Library_(1696-1724), in the form of a collection of documents and chronicles. Itwas reprinted in 1736 and in 1776. [456] Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite ofQueen Elizabeth, Chancellor of the Exchequer under James I, a patron ofliterature, and a friend of Sir Philip Sidney. [457] See note 443 on page 197. [458] See note 444 on page 197. [459] See note 439 on page 193. [460] Edward Waring (1736-1796) was Lucasian professor of mathematics atCambridge. He published several works on analysis and curves. The workreferred to was the _Miscellanea Analytica de aequationibus algebraicis etcurvarum proprietatibus_, Cambridge, 1762. [461] _A Dissertation on the use of the Negative Sign in Algebra... ; towhich is added, Machin's Quadrature of the Circle_, London, 1758. [462] The paper was probably one on complex numbers, or possibly one onquaternions, in which direction as well as absolute value is involved. [463] De Morgan quotes from one of the Latin editions. Descartes wrote inFrench, the title of his first edition being: _Discours de la méthode pourbien conduire sa raison et chercher la vérité dans les sciences, plus ladioptrique, les météores et la géométrie qui sont des essais de cetteméthode_, Leyden, 1637, 4to. [464] "I have observed that algebra indeed, as it is usually taught, is sorestricted by definite rules and formulas of calculation, that it seemsrather a confused kind of an art, by the practice of which the mind is in acertain manner disturbed and obscured, than a science by which it iscultivated and made acute. " [465] It appeared in 93 volumes, from 1758 to 1851. [466] _The principles of the doctrine of life-annuities; explained in afamiliar manner ... With a variety of new tables_ ... , London, 1783. [467] I suppose the one who wrote _Conjectures on the physical causes ofEarthquakes and Volcanoes_, Dublin, 1820. [468] _Scriptores Logarithmici; or, a Collection of several curious__tracts on the nature and construction of Logarithms ... Together with sametracts on the Binomial Theorem_ ... , 6 vols. , London, 1791-1807. [469] Charles Babbage (1792-1871), whose work on the calculating machine iswell known. Maseres was, it is true, ninety-two at this time, but Babbagewas thirty-one instead of twenty-nine. He had already translated Lacroix's_Treatise on the differential and integral calculus_ (1816), incollaboration with Herschel and Peacock. He was Lucasian professor ofmathematics at Cambridge from 1828 to 1839. [470] _The great and new Art of weighing Vanity, or a discovery of theignorance of the great and new artist in his pseudo-philosophicalwritings. _ The "great and new artist" was Sinclair. [471] George Sinclair, probably a native of East Lothian, who died in 1696. He was professor of philosophy and mathematics at Glasgow, and was one ofthe first to use the barometer in measuring altitudes. The work to which DeMorgan refers is his _Hydrostaticks_ (1672). He was a firm believer in evilspirits, his work on the subject going through four editions: _Satan'sInvisible World Discovered; or, a choice collection of modern relations, proving evidently against the Saducees and Athiests of this present age, that there are Devils, Spirits, Witches, and Apparitions_, Edinburgh, 1685. [472] This was probably William Sanders, Regent of St. Leonard's College, whose _Theses philosophicae_ appeared in 1674, and whose _Elementageometriae_ came out a dozen years later. [473] _Ars nova et magna gravitatis et levitatis; sive dialogorumphilosophicorum libri sex de aeris vera ac reali gravitate_, Rotterdam, 1669, 4to. [474] Volume I, Nos. 1 and 2, appeared in 1803. [475] His daughter, Mrs. De Morgan, says in her _Memoir_ of her husband:"My father had been second wrangler in a year in which the two highest wereclose together, and was, as his son-in-law afterwards described him, anexceedingly clear thinker. It is possible, as Mr. De Morgan said, that thismental clearness and directness may have caused his mathematical heresy, the rejection of the use of negative quantities in algebraical operations;and it is probable that he thus deprived himself of an instrument of work, the use of which might have led him to greater eminence in the higherbranches. " _Memoir of Augustus De Morgan_, London, 1882, p. 19. [476] "If it is not true it is a good invention. " A well-known Italianproverb. [477] See page 86, note 132. [478] He was born at Paris in 1713, and died there in 1765. [479] _Recherches sur les courbes à double courbure_, Paris, 1731. Clairautwas then only eighteen, and was in the same year made a member of theAcadémie des sciences. His _Elémens de géométrie_ appeared in 1741. Meantime he had taken part in the measurement of a degree in Lapland(1736-1737). His _Traité de la figure de la terre_ was published in 1741. The Academy of St. Petersburg awarded him a prize for his _Théorie de lalune_ (1750). His various works on comets are well known, particularly his_Théorie du mouvement des comètes_ (1760) in which he applied the "problemof three bodies" to Halley's comet as retarded by Jupiter and Saturn. [480] Joseph Privat, Abbé de Molières (1677-1742), was a priest of theCongregation of the Oratorium. In 1723 he became a professor in the Collègede France. He was well known as an astronomer and a mathematician, andwrote in defense of Descartes's theory of vortices (1728, 1729). He alsocontributed to the methods of finding prime numbers (1705). [481] "Deserves not only to be printed, but to be admired as a marvel ofimagination, of understanding, and of ability. " [482] Blaise Pascal (1623-1662), the well-known French philosopher andmathematician. He lived for some time with the Port Royalists, and defendedthem against the Jesuits in his _Provincial Letters_. Among his works arethe following: _Essai pour les coniques_ (1640); _Recit de la grandeexpérience de l'équilibre des liqueurs_ (1648), describing his experimentin finding altitudes by barometric readings; _Histoire de la roulette_(1658); _Traité du triangle arithmétique_ (1665); _Aleae geometria_ (1654). [483] This proposition shows that if a hexagon is inscribed in a conic (inparticular a circle) and the opposite sides are produced to meet, the threepoints determined by their intersections will be in the same straight line. [484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris, 1644. He also published without date a work entitled: _Foiblesse pitoyabledu Sr. G. Desargues employée contre l'examen fait de ses oeuvres_. [485] See page 119, note 233. [486] Until "this great proposition called Pascal's should see the light. " [487] The story is that his father, Etienne Pascal, did not wish him tostudy geometry until he was thoroughly grounded in Latin and Greek. Havingheard the nature of the subject, however, he began at the age of twelve toconstruct figures by himself, drawing them on the floor with a piece ofcharcoal. When his father discovered what he was doing he was attempting todemonstrate that the sum of the angles of a triangle equals two rightangles. The story is given by his sister, Mme. Perier. [488] Sir John Wilson (1741-1793) was knighted in 1786 and becameCommissioner of the Great Seal in 1792. He was a lawyer and jurist ofrecognized merit. He stated his theorem without proof, the firstdemonstration having been given by Lagrange in the Memoirs of the BerlinAcademy for 1771, --_Demonstration d'un théorème nouveau concernant lesnombres premiers_. Euler also gave a proof in his _Miscellanea Analytica_(1773). Fermat's works should be consulted in connection with the earlyhistory of this theorem. [489] He wrote, in 1760, a tract in defense of Waring, a point of whosealgebra had been assailed by a Dr. Powell. Waring wrote another tract ofthe same date. --A. De M. William Samuel Powell (1717-1775) was at this time a fellow of St. John'sCollege, Cambridge. In 1765 he became Vice Chancellor of the University. Waring was a Magdalene man, and while candidate for the Lucasianprofessorship he circulated privately his _Miscellanea Analytica_. Powellattacked this in his _Observations on the First Chapter of a Book calledMiscellanea_ (1760). This attack was probably in the interest of anothercandidate, a man of his own college (St. John's), William Ludlam. [490] William Paley (1743-1805) was afterwards a tutor at Christ's College, Cambridge. He never contributed anything to mathematics, but his _Evidencesof Christianity_ (1794) was long considered somewhat of a classic. He alsowrote _Principles of Morality and Politics_ (1785), and _Natural Theology_(1802). [491] Edward, first Baron Thurlow (1731-1806) is known to Americans becauseof his strong support of the Royal prerogative during the Revolution. Hewas a favorite of George III, and became Lord Chancellor in 1778. [492] George Wilson Meadley (1774-1818) published his _Memoirs of ... Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. Hewas a merchant and banker, and had traveled extensively in Europe and theEast. He was a convert to unitarianism, to which sect Paley had a strongleaning. [493] Watson (1737-1816) was a strange kind of man for a bishopric. He wasprofessor of chemistry at Cambridge (1764) at the age of twenty-seven. Itwas his experiments that led to the invention of the black-bulbthermometer. He is said to have saved the government £100, 000 a year by hisadvice on the manufacture of gunpowder. Even after he became professor ofdivinity at Cambridge (1771) he published four volumes of _Chemical Essays_(vol. I, 1781). He became Bishop of Llandaff in 1782. [494] James Adair (died in 1798) was counsel for the defense in the trialof the publishers of the _Letters of Junius_ (1771). As King's Serjeant heassisted in prosecuting Hardy and Horne Tooke. [495] Morgan (1750-1833) was actuary of the Equitable Assurance Society ofLondon (1774-1830), and it was to his great abilities that the success ofthat company was due at a time when other corporations of similar kind weremeeting with disaster. The Royal Society awarded him a medal (1783) for apaper on _Probability of Survivorship_. He wrote several important works oninsurance and finance. [496] Dr. Price (1723-1791) was a non-conformist minister and a writer onethics, economics, politics, and insurance. He was a defender of theAmerican Revolution and a personal friend of Franklin. In 1778 Congressinvited him to America to assist in the financial administration of the newrepublic, but he declined. His famous sermon on the French Revolution issaid to have inspired Burke's _Reflections on the Revolution in France_. [497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry(1800), a London merchant. She was the prime mover in the Association forthe Improvement of the Female Prisoners in Newgate, founded in 1817. Herinfluence in prison reform extended throughout Europe, and she visited theprisons of many countries in her efforts to improve the conditions of penalservitude. The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme for a female benefit society proved worthless from the actuarialstandpoint, and would have been disastrous to all concerned if it had beencarried out, and it was therefore fortunate that De Morgan was consulted intime. Mrs. De Morgan speaks of the consultation in these words: "Myhusband, who was very sensitive on such points, was charmed with Mrs. Fry'svoice and manner as much as by the simple self-forgetfulness with which sheentered into this business; her own very uncomfortable share of it notbeing felt as an element in the question, as long as she could be useful inpromoting good or preventing mischief. I can see her now as she came intoour room, took off her little round Quaker cap, and laying it down, went atonce into the matter. 'I have followed thy advice, and I think nothingfurther can be done in this case; but all harm is prevented. ' In thefollowing year I had an opportunity of seeing the effect of her mostmusical tones. I visited her at Stratford, taking my little baby and nursewith me, to consult her on some articles on prison discipline, which I hadwritten for a periodical. The baby--three months old--was restless, and thenurse could not quiet her, neither could I entirely, until Mrs. Fry beganto read something connected with the subject of my visit, when the infant, fixing her large eyes on the reader, lay listening till she fell asleep. "_Memoirs_, p. 91. [498] Mrs. Fry certainly believed that the writer was the old actuary ofthe Equitable, when she first consulted him upon the benevolent Assuranceproject; but we were introduced to her by our old and dear friend Lady NoelByron, by whom she had been long known and venerated, and who referred herto Mr. De Morgan for advice. An unusual degree of confidence in, andappreciation of each other, arose on their first meeting between the two, who had so much that was externally different, and so much that wasessentially alike, in their natures. --S. E. De M. Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when bothtook the additional name of Noel, her mother's name. They were separated in1816. [499] An obscure writer not mentioned in the ordinary biographies. [500] Not mentioned in the ordinary biographies, and for obvious reasons. [501] "Before" and "after. " [502] On Bishop Wilkins see note 171 on page 100. [503] Provision for a journey. [504] See note 179 on page 103. [505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctorand professor of theology at Oxford, and afterwards Chancellor of St. Paul's and confessor to Edward III. The English ascribed their success atCrécy to his prayers. [506] He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year. [507] "One paltry little year. " [508] The title is carelessly copied, as is so frequently the case incatalogues, even of the Libri class. It should read: _Arithmetica thomebrauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant invico diui Jacobi sub signo beate Barbare sedente_. The colophon reads:_Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa etcorrecta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]teParisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of1495, 1496, 1498, s. A. (c. 1500), 1502, 1504, 1505, s. A. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare, " although ofcourse no works of that period are common. See the editor's _RaraArithmetica_, page 61. [509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505;Vienna, 1515, with other editions. [510] The colophon of the 1495 edition reads: _Et sic explicit GeometriaThome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petrosanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresseparisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. Die. 20, maij. _ This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. Hestudied mathematics and philosophy at Paris, and took the doctor's degreethere. He taught at the University of Alcalà and became canon of theCathedral at Salamanca. Besides his editions of Bradwardine he wroteseveral works, among them the _Liber arithmeticae practicae qui dicituralgorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artiumliberalium_ (Alcalà, 1516). [511] Star polygons, a subject of considerable study in the later MiddleAges. See note 35 on page 44. [512] "A new theory that adds lustre to the fourteenth century. " [513] There is nothing in the edition of 1495 that leads to thisconclusion. [514] The full title is: _Nouvelle théorie des parallèles, avec unappendice contenant la manière de perfectionner la théorie des parallèlesde A. M. Legendre_. The author had no standing as a scientist. [515] Adrien Marie Legendre (1752-1833) was one of the great mathematiciansof the opening of the nineteenth century. His _Eléments de géométrie_(1794) had great influence on the geometry of the United States. His _Essaisur la théorie des nombres_ (1798) is one of the classics upon the subject. The work to which Kircher refers is the _Nouvelle théorie des parallèles_(1803), in which the attempt is made to avoid using Euclid's postulate ofparallels, the result being merely the substitution of another assumptionthat was even more unsatisfactory. The best presentations of the generaltheory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910, and Engel and Stäckel's _Die Theorie der Parallellinien von Euclid bis aufGauss_, Leipsic, 1895. Legendre published a second work on the theory theyear of his death, _Réflexions sur ... La théorie des parallèles_ (1833). His other works include the _Nouvelles méthodes pour la détermination desorbites des comètes_ (1805), in which he uses the method of least squares;the _Traité des fonctions elliptiques et des intégrales_ (1827-1832), andthe _Exercises de calcul intégral_ (1811, 1816, 1817). [516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor ofmathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807, and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859. He wrote other works on mathematics, but none of his contributions was ofany importance. [517] Johann Karl Friedrich Hauff (1766-1846) was successively professor ofmathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics andphysics at Ghent. The work to which Kircher refers is his memoirs on theEuclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III(1799), an article of no merit in the general theory. [518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logicat Rostock (1758) and Butzow (1760), and later became professor ofmathematics and physics at Halle. His work on parallels is the _Versucheiner völlig berichtigten Theorie der Parallellinien_ (1779). He also wrotea work entitled _Anfangsgründe der mathematischen Wissenschaften_ (1780), but neither of these works was more than mediocre. [519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wishwas met, for the catalogues give "c. Fig. 8, " so that it evidently hadeight illustrations instead of eight volumes. He wrote several other workson the principles of geometry, none of any importance. [520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morganshould have given a little more of the title: _Solusione esatta e regolare... Del ... Problema della quadratura del circolo_. There was a secondedition, London, 1805. [521] This identifies Rossi, for Joséphine Grassini (1773-1850) was awell-known contralto, _prima donna_ at Napoleon's court opera. [522] William Spence (1783-1860) was an entomologist and economist of somestanding, a fellow of the Royal Society, and one of the founders of theEntomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in asingle year. He also wrote _Agriculture the Source of Britain's Wealth_(1808) and _Objections against the Corn Bill refuted_ (1815), besides awork in four volumes on entomology (1815-1826) in collaboration withWilliam Kirby. [523] "That used to be so, but we have changed all that. " [524] "Meet the coming disease. " [525] George Douglas (or Douglass) was a Scotch writer. He got out anedition of the _Elements of Euclid_ in 1776, with an appendix ontrigonometry and a set of tables. His work on _Mathematical Tables_appeared in 1809, and his _Art of Drawing in Perspective, from mathematicalprinciples_, in 1810. [526] See note 443, on page 197. [527] John Playfair (1748-1848) was professor of mathematics (1785) andnatural philosophy (1805) at the University of Edinburgh. His _Elements ofGeometry_ went through many editions. [528] "Tell Apella" was an expression current in classical Rome to indicateincredulity and to show the contempt in which the Jew was held. Horacesays: _Credat Judæus Apella_, "Let Apella the Jew believe it. " Our "Tell itto the marines, " is a similar phrase. [529] As De Morgan says two lines later, "No mistake is more common thanthe natural one of imagining that the"--University of Virginia is atRichmond. The fact is that it is not there, and that it did not exist in1810. It was not chartered until 1819, and was not opened until 1825, andthen at Charlottesville. The act establishing the Central College, fromwhich the University of Virginia developed, was passed in 1816. The JeanWood to whom De Morgan refers was one John Wood who was born about 1775 inScotland and who emigrated to the United States in 1800. He published a_History of the Administration of J. Adams_ (New York, 1802) that wassuppressed by Aaron Burr. This act called forth two works, a _Narrative ofthe Suppression, by Col. Burr, of the 'History of the Administration ofJohn Adams'_ (1802), in which Wood was sustained; and the _Antidote to JohnWood's Poison_ (1802), in which he was attacked. The work referred to inthe "printed circular" may have been the _New theory of the diurnalrotation of the earth_ (Richmond, Va. , 1809). Wood spent the last years ofhis life in Richmond, Va. , making county maps. He died there in 1822. Acareful search through works relating to the University of Virginia failsto show that Wood had any connection with it. [530] There seems to be nothing to add to Dobson's biography beyond what DeMorgan has so deliciously set forth. [531] "Give to each man his due. " [532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then marriedGabriel Piozzi (1784), an Italian musician. Her _Anecdotes of the lateSamuel Johnson_ (1786) and _Letters to and from Samuel Johnson_ (1788) arewell known. She also wrote numerous essays and poems. [533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapelin London and a theological school in his house. He later became a discipleof Robert Sandeman and left the Independents for the Sandemanian church(1765). The _Philosophia Sacra_ was first published at London in 1753. DeMorgan here cites the second edition. [534] Pike had been dead over forty years when Kittle published this secondedition. Kittle had already published a couple of works: _King Solomon'sportraiture of Old Age_ (Edinburgh, 1813), and _Critical and PracticalLectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor_(London, 1814). [535] See note 334, on page 152. [536] William Stukely (1687-1765) was a fellow of the Royal Society and ofthe College of Physicians and Surgeons. He afterwards (1729) entered theChurch. He was prominent as an antiquary, especially in the study of theRoman and Druidic remains of Great Britain. He was the author of numerousworks, chiefly on paleography. [537] William Jones (1726-1800), who should not be confused with hisnamesake who is mentioned in note 281 on page 135. He was a lifelong friendof Bishop Horne, and his vicarage at Nayland was a meeting place of aninfluential group of High Churchmen. Besides the _PhysiologicalDisquisitions_ (1781) he wrote _The Catholic Doctrine of the Trinity_(1756) and _The Grand Analogy_ (1793). [538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and notonly edited his works but wrote his life. He wrote a work against theNewtonian physics, entitled _An Enquiry after Philosophy and Theology_(Edinburgh, 1755), besides the _Letters to a Friend concerning theSeptuagint Translation_ (Edinburgh, 1759) to which De Morgan refers. [539] A writer of no importance, at least in the minds of Britishbiographers. [540] Alexander Catcott (1725-1779), a theologian and geologist, wrote notonly a work on the creation (1756) but a _Treatise on the Deluge_ (1761, with a second edition in 1768). Sir Charles Lyell considered the latterwork a valuable contribution to geology. [541] James Robertson (1714-1795), professor of Hebrew at the University ofEdinburgh. Probably De Morgan refers to his _Grammatica Linguae Hebrææ_(Edinburgh, 1758; with a second edition in 1783). He also wrote _ClavisPentateuchi_ (1770). [542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. Hetranslated Woodward's _Naturalis Historia Telluris_, and was introduced byWoodward to Hutchinson. The work referred to by De Morgan appeared atOxford in two volumes in 1754. [543] His work was _The Christian plan exhibited in the interpretation ofElohim: with observations upon a few other matters relative to the samesubject_, Oxford, 1752, with a second edition in 1755. [544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law atLeyden. He was Lord President of the Court of Sessions (1737). He wrote anumber of theological works. [545] Should be 1756. [546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900);published _The Rock of Ages; or scripture testimony to the one EternalGodhead of the Father, and of the Son, and of the Holy Ghost_ at Hampsteadin 1859. A second edition appeared at London in 1860. [547] Thomas Sadler (1822-1891) took his Ph. D. At Erlangen in 1844, andbecame a Unitarian minister at Hampstead, where Bickersteth's work waspublished. Besides writing the _Gloria Patri_ (1859), he edited CrabbRobinson's Diaries. [548] This was his _Virgil's Bucolics and the two first Satyrs of Juvenal_, 1634. [549] Possibly in his _Twelve Questions or Arguments drawn out ofScripture, wherein the commonly received Opinion touching the Deity of theHoly Spirit is clearly and fully refuted_, 1647. This was his firstheretical work, and it was followed by a number of others that were writtenduring the intervals in which the Puritan parliament allowed him out ofprison. It was burned by the hangman as blasphemous. Biddle finally died inprison, unrepentant to the last. [550] The first edition of the anonymous [Greek: Haireseôn anastasis] (byVicars?) appeared in 1805. [551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter'sCollege, Cambridge, and a Unitarian minister. [552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, andwas executed there in 1641. He was privy councilor to Charles I, and wasLord Deputy of Ireland. On account of his repressive measures to uphold theabsolute power of the king he was impeached by the Long Parliament and wasexecuted for treason. The essence of his defence is in the sentence quotedby De Morgan, to which Pym replied that taken as a whole, the acts tendedto show an intention to change the government, and this was in itselftreason. [553] The name assumed by a writer who professed to give a mathematicalexplanation of the Trinity, see farther on. --S. E. De M. [554] Sabellius (fl. 230 A. D. ) was an early Christian of Libyan origin. Hetaught that Father, Son, and Holy Spirit were different names for the sameperson. [555] Sir Richard Phillips was born in London in 1767 (not 1768 as statedabove), and died there in 1840. He was a bookseller and printer inLeicester, where he also edited a radical newspaper. He went to London tolive in 1795 and started the _Monthly Magazine_ there in 1796. Besides theworks mentioned by De Morgan he wrote on law and economics. [556] It was really eighteen months. [557] While he was made sheriff in 1807 he was not knighted until thefollowing year. [558] James Mitchell (c. 1786-1844) was a London actuary, or rather aScotch actuary living a good part of his life in London. Besides the workmentioned he compiled a _Dictionary of Chemistry, Mineralogy, and Geology_(1823), and wrote _On the Plurality of Worlds_ (1813) and _The Elements ofAstronomy_ (1820). [559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page85) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 ayear to Airy, who requested that it be settled on his wife. [560] Mary Fairfax (1780-1872) married as her second husband Dr. WilliamSomerville. In 1826 she presented to the Royal Society a paper on _TheMagnetic Properties of the Violet Rays of the Solar Spectrum_, whichattracted much attention. It was for her _Mechanism of the Heavens_ (1831), a popular translation of Laplace's _Mécanique Céleste_, that she waspensioned. [561] Dominique François Jean Arago (1786-1853) the celebrated Frenchastronomer and physicist. [562] For there is a well-known series 1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6. If, therefore, the given series equals 1, we have 2 = 1/6 [pi]^2 or [pi]^2 = 12, whence [pi] = 2 [root]3. But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d[root]3. [563] There was a second edition in 1821. [564] London, 1830. [565] He was a resident of Chatham, and seems to have published no otherworks. [566] Richard Whately (1787-1863) was, as a child, a calculating prodigy(see note 132, page 86), but lost the power as is usually the case withwell-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825became principal of St. Alban Hall. He was a friend of Newman, Keble, andothers who were interested in the religious questions of the day. He becamearchbishop of Dublin in 1831. He was for a long time known to studentsthrough his _Logic_ (1826) and _Rhetoric_ (1828). [567] William King, D. C. L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) isa satirical attack on Bentley. [568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He becameprovost of the college in 1811, bishop of Limerick in 1820, and bishop ofLeighlin and Ferns in 1822. His edition of Euclid was reprinted a dozentimes. The _Reply to John Search's Considerations on the Law of Libel_appeared at Dublin in 1834. [569] Joseph Blanco White (1775-1841) was the son of an Irishman living inSpain. He was born at Seville and studied for orders there, being ordainedpriest in 1800. He lost his faith in the Roman Catholic Church, and gave upthe ministry, escaping to England at the time of the French invasion. AtLondon he edited _Español_, a patriotic journal extensively circulated inSpain, and for this service he was pensioned after the expulsion of theFrench. He then studied at Oriel College, Oxford, and became intimate withmen like Whately, Newman, and Keble. In 1835 he became a Unitarian. Amonghis theological writings is his _Evidences against Catholicism_ (1825). The"rejoinder" to which De Morgan refers consisted of two letters: _The law ofanti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to someFriendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_(Dublin, 1834). [570] The work was translated from the French. [571] J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as anartillery officer in Kosciusko's army (1791-1794). He was imprisoned afterthe battle of Maciejowice. He afterwards lived in Germany, and (after 1810)in Paris. For the bibliography of his works see S. Dickstein's article inthe _Bibliotheca Mathematica_, vol. VI (2), page 48. [572] Perhaps referring to his _Introduction à la philosophie desmathématiques_ (1811). [573] Read "equation of the. " [574] Thomas Young (1773-1829), physician and physicist, sometimes calledthe founder of physiological optics. He seems to have initiated the theoryof color blindness that was later developed by Helmholtz. The attackreferred to was because of his connection with the Board of Longitude, hehaving been made (1818) superintendent of the Nautical Almanac andsecretary of the Board. He opposed introducing into the Nautical Almanacanything not immediately useful to navigation, and this antagonized manyscientists. [575] Isaac Milner (1750-1820) was professor of natural philosophy atCambridge (1783) and later became, as De Morgan states, president ofQueens' College (1788). In 1791 he became dean of Carlisle, and in 1798Lucasian professor of mathematics. His chief interest was in chemistry andphysics, but he contributed nothing of importance to these sciences or tomathematics. [576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works oneconomics and politics he wrote a _Geometry without Axioms_ (1830) that DeMorgan includes later on in his _Budget_. In it Thompson endeavored toprove the parallel postulate. [577] De Morgan's father-in-law. See note 441, page 196. [578] Johann Friedrich Herbart (1776-1841), successor of Kant as professorof philosophy at Königsberg (1809-1833), where he established a school ofpedagogy. From 1833 until his death he was professor of philosophy atGöttingen. The title of the pamphlet is: _De Attentionis mensura causisqueprimariis. Psychologiae principia statica et mechanica exemploillustraturus.... Regiomonti, ... 1822_. The formulas in question are givenon pages 15 and 17, and De Morgan has omitted the preliminary steps, whichare, for the first one: [beta] ([phi] - z) [delta]t = [delta]z unde [beta]t= Const / ([phi] - z). Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z). z = [phi] (1 - [epsilon]^{-[beta]t}); et [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t} These are, however, quite elementary as compared with other portions of thetheory. [579] See note 371, page 168. [580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was sofree in his charities that the village in which he lived became so infestedby beggars that he was urged by the citizens to leave. He wrote _A seriouscall to a devout and holy life_ (1728). [581] He was a curate at Cheshunt, and wrote the _Spiritual voice to theChristian Church and to the Jews_ (London, 1760), _A second warning to theworld by the Spirit of Prophecy_ (London, 1760), and _Signs of the Times;or a Voice to Babylon_ (London, 1773). [582] His real name was Thomas Vaughan (1622-1666). He was a fellow ofJesus College, Oxford, taking orders, but was deprived of his living onaccount of drunkenness. He became a mystic philosopher and gave attentionto alchemy. His works had a large circulation, particularly on thecontinent. He wrote _Magia Adamica_ (London, 1650), _Euphrates; or theWaters of the East_ (London, 1655), and _The Chymist's key to shut, and toopen; or the True Doctrine of Corruption and Generation_ (London, 1657). [583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is notcommonly known to mathematicians that he was one of their guild, but hewrote on both mathematics and chemistry. Among his works are the_Regelkonst eller algebra_ (Upsala, 1718) and the _Methodus nova inveniendilongitudines locorum, terra marique, ope lunae_ (Amsterdam, 1721, 1727, and1766). After 1747 he devoted his attention to mystic philosophy. [584] Pierre Simon Laplace (1749-1827), whose _Exposition du système dumonde_ (1796) and _Traité de mécanique celeste_ (1799) are well known. [585] See note 117, page 76. [586] John Dalton (1766-1844), who taught mathematics and physics at NewCollege, Manchester (1793-1799) and was the first to state the law of theexpansion of gases known by his name and that of Gay-Lussac. His _Newsystem of Chemical Philosophy_ (Vol. I, pt. I, 1808; pt. Ii, 1810; vol. II, 1827) sets forth his atomic theory. [587] Howison was a poet and philosopher. He lived in Edinburgh and was afriend of Sir Walter Scott. This work appeared in 1822. [588] He was a shoemaker, born about 1765 at Haddiscoe, and his"astro-historical" lectures at Norwich attracted a good deal of attentionat one time. He traced all geologic changes to differences in theinclination of the earth's axis to the plane of its orbit. Of the worksmentioned by De Morgan the first appeared at Norwich in 1822-1823, andthere was a second edition in 1824. The second appeared in 1824-1825. Thefourth was _Urania's Key to the Revelation; or the analyzation of thewritings of the Jews... _, and was first published at Norwich in 1823, therebeing a second edition at London in 1833. His books were evidently not afinancial success, for Mackey died in an almshouse at Norwich. [589] Godfrey Higgins (1773-1833), the archeologist, was interested in thehistory of religious beliefs and in practical sociology. He wrote _HoraeSabbaticae_ (1826), _The Celtic Druids_ (1827 and 1829), and _Anacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry intothe Origin of Languages, Nations, and Religions_ (posthumously published, 1836), and other works. See also page 274, _infra_. [590] The work also appeared in French. Wirgman wrote, or at least began, two other works: _Divarication of the New Testament into Doctrine andHistory; part I, The Four Gospels_ (London, 1830), and _Mental Philosophy;part I, Grammar of the five senses; being the first step to infanteducation_ (London, 1838). [591] He was born at Shandrum, County Limerick, and supported himself byteaching writing and arithmetic. He died in an almshouse at Cork. [592] George Boole (1815-1864), professor of mathematics at Queens'College, Cork. His _Laws of Thought_ (1854) was the first work on thealgebra of logic. [593] Oratio Grassi (1582-1654), the Jesuit who became famous for hiscontroversy with Galileo over the theory of comets. Galileo ridiculed himin _Il Saggiatore_, although according to the modern view Grassi was themore nearly right. It is said that the latter's resentment led to thepersecution of Galileo. [594] De Morgan might have found much else for his satire in the letters ofWalsh. He sought, in his _Theory of Partial Functions_, to substitute"partial equations" for the differential calculus. In his diary there is anentry: "Discovered the general solution of numerical equations of the fifthdegree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nineo'clock in the forenoon of July 7th, 1844; exactly twenty-two years afterthe invention of the Geometry of Partial Equations, and the expulsion ofthe differential calculus from Mathematical Science. " [595] "It has been ordered, sir, it has been ordered. " [596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives thiscorrect spelling on page 278. He died after 1849. His _Inverted Scheme ofCopernicus_ appeared in Liverpool in 1822. [597] Robert Taylor (1784-1844) had many more ups and downs than De Morganmentions. He was a priest of the Church of England, but resigned his parishin 1818 after preaching against Christianity. He soon recanted and tookanother parish, but was dismissed by the Bishop almost immediately on theground of heresy. As stated in the text, he was convicted of blasphemy in1827 and was sentenced to a year's imprisonment, and again for two years onthe same charge in 1831. He then married a woman who was rich in money andin years, and was thereupon sued for breach of promise by another woman. Toescape paying the judgment that was rendered against him he fled to Tourswhere he took up surgery. [598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199. [599] "Argument from the prison. " [600] Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note 250, page 124) after they had beensuppressed, and an edition of Thomas Paine (1818). He was repeatedlyimprisoned, serving nine years in all. His continued conflict with theauthorities proved a good advertisement for his bookshop. [601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman andteacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, hebecame a confirmed misanthrope and is said never to have left his houseduring the last ten years of his life. He wrote several works: _Ein Wortüber Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814);_Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _UeberTradition und Schrift, Logos und Kabbala_ (1829), besides the one mentionedabove. The word _coss_ in the above titles was a German name for algebra, from the Italian _cosa_ (thing), the name for the unknown quantity. Itappears in English in the early name for algebra, "the cossic art. " [602] See note 174, page 101. [603] See note 589, page 257. [604] He seems to have written nothing else. [605] See note 596 on page 270. The name is here spelled correctly. [606] Joseph Jacotot (1770-1840), the father of this Fortuné Jacotot, wasan infant prodigy. At nineteen he was made professor of the humanities atDijon. He served in the army, and then became professor of mathematics atDijon. He continued in his chair until the restoration of the Bourbons, andthen fled to Louvain. It was here that he developed the method with whichhis name is usually connected. He wrote a _Mathématiques_ in 1827, whichwent through four editions. The _Epitomé_ is by his son, Fortuné. [607] He wrote on educational topics and a _Sacred History_ that wentthrough several editions. [608] "All is in all. " [609] "Know one thing and refer everything else to it, " as it is oftentranslated. [610] A writer of no reputation. [611] Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time. [612] See note 165, page 99. [613] "Those about to die salute you. " [614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in his_Invention des miroirs ardens pour brûler à une grande distance_ (1747). The reference here may be to his _Resolution des problèmes qui regardent lejeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_(36 volumes, 1749-1788) has overshadowed the credit due to him for histranslation of Newton's work on Fluxions. [615] See page 285. This article was a supplement to No. 14 in the_Athenæum_ Budget. --A. De M. [616] There are many similar series and products. Among the moreinteresting are the following: [pi] 2·2·4·4·6·6·8... ---- = ----------------, 2 1·3·3·5·5·7·7... [pi]-3 = 1 1 1 ------ = ----- - ----- + ----- - ... , 4 2·3·4 4·5·6 6·7·8 [pi] 1 1 1 1 1 ---- = sqrt - · (1 - --- + ----- - ----- + ----- - ... ), 6 3 3·3 3^2·5 3^3·7 3^4·9 [pi] 1 1 1 1 ---- = 4 ( - - ----- + ----- - ----- + ... ) 4 5 3·5^3 5·5^5 7·5^7 1 1 1 - ( --- - ------- + ------- - ... ). 239 3·239^3 5·239^5 [617] "To a privateer, a privateer and a half. " [618] Joshua Milne (1776-1851) was actuary of the Sun Life AssuranceSociety. He wrote _A Treatise on the Valuation of Annuities and Assuranceson Lives and Survivorships; on the Construction of tables of mortality; andon the Probabilities and Expectations of Life_, London, 1815. Upon thebasis of the Carlisle bills of mortality of Dr. Heysham he reconstructedthe mortality tables then in use and which were based upon the Northamptontable of Dr. Price. His work revolutionized the actuarial science of thetime. In later years he devoted his attention to natural history. [619] See note 576, page 252. He also wrote the _Theory of Parallels. Theproof of Euclid's axiom looked for in the properties of the equiangularspiral_ (London, 1840), which went through four editions, and the _Theoryof Parallels. The proof that the three angles of a triangle are equal totwo right angles looked for in the inflation of the sphere_ (London, 1853), of which there were three editions. [620] For the latest summary, see W. B. Frankland, _Theories ofParallelism, an historical critique_, Cambridge, 1910. [621] Joseph Louis Lagrange (1736-1813), author of the _Mécaniqueanalytique_ (1788), _Théorie des functions analytiques_ (1797), _Traité dela résolution des équations numériques de tous degrés_ (1798), _Leçons surle calcul des fonctions_ (1806), and many memoirs. Although born in Turinand spending twenty of his best years in Germany, he is commonly lookedupon as the great leader of French mathematicians. The last twenty-sevenyears of his life were spent in Paris, and his remarkable productivitycontinued to the time of his death. His genius in the theory of numbers wasprobably never excelled except by Fermat. He received very high honors atthe hands of Napoleon and was on the first staff of the Ecole polytechnique(1797). [622] "I shall have to think it over again. " [623] Henry Goulburn (1784-1856) held various government posts. He wasunder-secretary for war and the colonies (1813), commissioner to negotiatepeace with America (1814), chief secretary to the Lord Lieutenant ofIreland (1821), and several times Chancellor of the Exchequer. On theoccasion mentioned by De Morgan he was standing for parliament, and wassuccessful. [624] On Drinkwater Bethune see note 165, page 99. [625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. Hewas town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_(1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in the _AthenaeCantabrigiensis_ (1858). [626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, hewhose name degenerated into the familiar title of the London "Bobby" or"Peeler. " Yates Peel was a member of parliament almost continuously from1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835. [627] Henry John Temple, third Viscount of Palmerston (1784-1865), wasmember for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and1830. He failed of reelection in 1831 because of his advocacy of reform. This must have been the time when Goulburn defeated him. He was ForeignSecretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and1846-1851). It is said of him that he "created Belgium, saved Portugal andSpain from absolutism, rescued Turkey from Russia and the highway to Indiafrom France. " He was Prime Minister almost continuously from 1855 to 1865, a period covering the Indian Mutiny and the American Civil War. [628] William Cavendish, seventh Duke of Devonshire (1808-1891). He wasmember for Cambridge from 1829 to 1831, but was defeated in 1831 because hehad favored parliamentary reform. He became Earl of Burlington in 1834, andDuke of Devonshire in 1858. He was much interested in the promotion ofrailroads and in the iron and steel industries. [629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks thebenefactor of art. (See note 314, p. 147. ) He was a fellow of TrinityCollege, Cambridge, a fellow of the Royal Society and secretary of theAstronomical Society. Babbage (See note 469, p. 207) suspected him ofadvising against the government support of his calculating machine andattacked him severely in his _Exposition of 1851_, in the chapter on _TheIntrigues of Science_. Babbage also showed that Sheepshanks got anastronomical instrument of French make through the custom house by havingTroughton's (See note 332, page 152) name engraved on it. Sheepshanksadmitted this second charge, but wrote a _Letter in Reply to the Calumniesof Mr. Babbage_, which was published in 1854. He had a highly controversialnature. [630] See note 469, page 207. The work referred to is _Passages from theLife of a Philosopher_, London, 1864. [631] Drinkwater Bethune. See note 165, page 99. [632] Siméon-Denis Poisson (1781-1840) was professor of calculus andmechanics at the Ecole polytechnique. He was made a baron by Napoleon, andwas raised to the peerage in 1837. His chief works are the _Traité demécanìque_ (1811) and the _Traité mathématique de la chaleur_ (1835). [633] "As to M. Poisson, I really wish I had a thousandth part of hismathematical knowledge that I might prove my system to the incredulous. " [634] This list includes most of the works of Antoine-Louis-GuénardDemonville. There was also the _Nouveau système du monde ... Et hypothèsesconformes aux expériences sur les vents, sur la lumière et sur le fluideélectro-magnétique_, Paris, 1830. [635] Paris, 1835. [636] Paris, 1833. [637] The second part appeared in 1837. There were also editions in 1850and 1852, and one edition appeared without date. [638] Paris, 1842. [639] Parsey also wrote _The Art of Miniature Painting on Ivory_ (1831), _Perspective Rectified_ (1836), and _The Science of Vision_ (1840), thethird being a revision of the second. [640] William Ritchie (1790-1837) was a physicist who had studied at Parisunder Biot and Gay-Lussac. He contributed several papers on electricity, heat, and elasticity, and was looked upon as a good experimenter. Besidesthe geometry he wrote the _Principles of the Differential and IntegralCalculus_ (1836). [641] Alfred Day (1810-1849) was a man who was about fifty years ahead ofhis time in his attempt to get at the logical foundations of geometry. Itis true that he laid himself open to criticism, but his work was by nomeans bad. He also wrote _A Treatise on Harmony_ (1849, second edition1885), _The Rotation of the Pendulum_ (1851), and several works on Greekand Latin Grammar. [642] Walter Forman wrote a number of controversial tracts. His first seemsto have been _A plan for improving the Revenue without adding to theburdens of the people_, a letter to Canning in 1813. He also wrote _A NewTheory of the Tides_ (1822). His _Letter to Lord John Russell, on LordBrougham's most extraordinary conduct; and another to Sir J. Herschel, onthe application of Kepler's third law_ appeared in 1832. [643] Lord John Russell (1792-1878) first Earl Russell, was one of thestrongest supporters of the reform measures of the early Victorian period. He became prime minister in 1847, and again in 1865. [644] Lauder seems never to have written anything else. [645] See note 22, page 40. [646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have nostanding in the history of the subject beyond what would be inferred fromDe Morgan's remark. [647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was adilletante in mathematics who read much but accomplished little. His_Récréations mathématiques_ is his chief work. Boncompagni published the"Problèmes de Mydorge" in his _Bulletino_. [648] Claude Hardy was born towards the end of the 16th century and died atParis in 1678. In 1625 he edited the _Data Euclidis_, publishing the Greektext with a Latin translation. He was a friend of Mydorge and Descartes, but an opponent of Fermat. [649] That is, in the _Bibliotheca Realis_ of Martin Lipen, or Lipenius(1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685. [650] See note 29, page 43. [651] Baldassare Boncompagni (1821-1894) was the greatest general collectorof mathematical works that ever lived, possibly excepting Libri. Hismagnificent library was dispersed at his death. His _Bulletino_ (1868-1887)is one of the greatest source books on the history of mathematics that wehave. He also edited the works of Leonardo of Pisa. [652] He seems to have attracted no attention since De Morgan's search, forhe is not mentioned in recent bibliographies. [653] Joseph-Louis Vincens de Mouléon de Causans was born about thebeginning of the l8th century. He was a Knight of Malta, colonel in theinfantry, prince of Conti, and governor of the principality of Orange. Hisworks on geometry are the _Prospectus apologétique pour la quadrature ducercle_ (1753), and _La vraie géométrie transcendante_ (1754). [654] See note 119, page 80. [655] See note 120, page 81. [656] Lieut. William Samuel Stratford (1791-1853), was in active serviceduring the Napoleonic wars but retired from the army in 1815. He was firstsecretary of the Astronomical Society (1820) and became superintendent ofthe Nautical Almanac in 1831. With Francis Baily he compiled a starcatalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets. [657] See Sir J. Herschel's _Astronomy_, p. 369. --A. De M. [658] Captain Ross had just stuck a bit of brass there. --A. De M. Sir James Clark Ross (1800-1862) was a rear admiral in the British navy andan arctic and antarctic explorer of prominence. De Morgan's reference is toRoss's discovery of the magnetic pole on June 1, 1831. In 1838 he wasemployed by the Admiralty on a magnetic survey of the United Kingdom. Hewas awarded the gold medal of the geographical societies of London andParis in 1842. [659] John Partridge (1644-1715), the well-known astrologer and almanacmaker. Although bound to a shoemaker in his early boyhood, he had acquiredenough Latin at the age of eighteen to read the works of the astrologers. He then mastered Greek and Hebrew and studied medicine. In 1680 he beganthe publication of his almanac, the _Merlinus Liberatus_, a book thatacquired literary celebrity largely through the witty comments upon it bysuch writers as Swift and Steele. [660] See note 642 on page 296. [661] William Woodley also published several almanacs (1838, 1839, 1840)after his rejection by the Astronomical Society in 1834. [662] It appeared at London. [663] The first edition appeared in 1830, also at London. [664] See note 441, page 196. [665] Thomas Kerigan wrote _The Young Navigator's Guide to the siderial andplanetary parts of Nautical Astronomy_ (London, 1821, second edition 1828), a work on eclipses (London, 1844), and the work on tides (London, 1847) towhich De Morgan refers. [666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166. [667] See note 670, page 309. [668] Laurent seems to have had faint glimpses of the modern theory ofmatter. He is, however, unknown. [669] See note 133, page 87. [670] Francis Baily (1774-1844) was a London stockbroker. His interest inscience in general and in astronomy in particular led to his membership inthe Royal Society and to his presidency of the Astronomical Society. Hewrote on interest and annuities (1808), but his chief works were onastronomy. [671] If the story is correctly told Baily must have enjoyed his statementthat Gauss was "the oldest mathematician now living. " As a matter of facthe was then only 58, three years the junior of Baily himself. Gauss wasborn in 1777 and died in 1855, and Baily was quite right in saying that hewas "generally thought to be the greatest" mathematician then living. [672] Margaret Cooke, who married Flamsteed in 1692. [673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man(1788), Andrews professor of astronomy at Dublin, first Astronomer Royalfor Ireland (1792), F. R. S. (1803), Copley medallist, president of the RoyalSociety and Bishop of Cloyne. His _Elements of Astronomy_ appeared in 1808. [674] See note 248, page 124. [675] See note 276, page 133. [676] See note 352, page 161. [677] "It becomes the doctors of the Sorbonne to dispute, the Pope todecree, and the mathematician to go to Paradise on a perpendicular line. " [678] See note 124, page 83. [679] See note 621, page 288. [680] Sylvain van de Weyer, who was born at Louvain in 1802. He was ajurist and statesman, holding the portfolio for foreign affairs(1831-1833), and being at one time ambassador to England. [681] Henry Crabb Robinson (1775-1867), correspondent of the _Times_ atAltona and in the Peninsula, and later foreign editor. He was one of thefounders of the Athenæum Club and of University College, London. He seemsto have known pretty much every one of his day, and his posthumous _Diary_attracted attention when it appeared. [682] Was this Whewell, who was at Trinity from 1812 to 1816 and became afellow in 1817? [683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coalporter and hence received his nickname, the Black Diamond. [684] John Finleyson, or Finlayson, was born in Scotland in 1770 and diedin London in 1854. He published a number of pamphlets that made a pretenseto being scientific. Among his striking phrases and sentences are thestatements that the stars were made "to amuse us in observing them"; thatthe earth is "not shaped like a garden turnip as the Newtonians make it, "and that the stars are "oval-shaped immense masses of frozen water. " Thefirst edition of the work here mentioned appeared at London in 1830. [685] Richard Brothers (1757-1824) was a native of Newfoundland. He went toLondon when he was about 30, and a little later set forth his claim tobeing a descendant of David, prince of the Hebrews, and ruler of the world. He was confined as a criminal lunatic in 1795 but was released in 1806. [686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was thenPrime Minister. The Reform Bill was introduced and defeated in 1831. Thefollowing year, with the Royal guarantees to allow him to create peers, hefinally carried the bill in spite of "the number of the beast. " [687] The letters of obscure men, the _Epistolæ obscurorum virorum advenerabilem virum Magistrum Ortuinum Gratium Dauentriensem_, by JoannesCrotus, Ulrich von Hutten, and others appeared at Venice about 1516. [688] The lamentations of obscure men, the _Lamentationes obscurorumvirorum, non prohibete per sedem Apostolicam. Epistola D. ErasmiRoterodami: quid de obscuris sentiat_, by G. Ortwinus, appeared at Colognein 1518. [689] The criticism was timely when De Morgan wrote it. At present it wouldhave but little force with respect to the better class of algebras. [690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than onewould infer from this satire upon his theory. He was a naturalist, astronomer, and physiologist. In 1812 he published his _Researches aboutAtmospheric Phenomena_, and seven years later (July 3, 1819) he discovereda comet. With Sir Richard Phillips he founded a Meteorological Society, butit was short lived. He declined a fellowship in the Royal Society becausehe disapproved of certain of its rules, so that he had a recognizedstanding in his day. The work mentioned by De Morgan is the second edition, the first having appeared at Frankfort on the Main in 1835 under the title, _Recueil des ouvrages et des pensées d'un physicien et metaphysicien_. [691] Zadkiel, whose real name was Richard James Morrison (1795-1874), wasin his early years an officer in the navy. In 1831 he began the publicationof the _Herald of Astrology_, which was continued as _Zadkiel's Almanac_. His name became familiar throughout Great Britain as a result. [692] See note 566, page 246. [693] Sumner (1780-1862) was an Eton boy. He went to King's College, Cambridge, and was elected fellow in 1801. He took many honors, and in 1807became M. A. He was successively Canon of Durham (1820), Bishop of Chester(1828), and Archbishop of Canterbury (1848). Although he voted for theCatholic Relief Bill (1829) and the Reform Bill (1832), he opposed theremoval of Jewish disabilities. [694] Charles Richard Sumner (1790-1874) was not only Bishop of Winchester(1827), but also Bishop of Llandaff and Dean of St. Paul's, London (1826). He lost the king's favor by voting for the Catholic Relief Bill. [695] John Bird Sumner, brother of Charles Richard. [696] Thomas Musgrave (1788-1860) became Fellow of Trinity in 1812, andsenior proctor in 1831. He was also Dean of Bristol. [697] Charles Thomas Longley (1794-1868) was educated at Westminster Schooland at Christ Church, Oxford. He became M. A. In 1818 and D. D. In 1829. Besides the bishoprics mentioned he was Bishop of Ripon (1836-1856), andbefore that was headmaster of Harrow (1829-1836). [698] Thomson (1819-1890) was scholar and fellow of Queen's College, Oxford. He became chaplain to the Queen in 1859. [699] This is worthy of the statistical psychologists of the present day. [700] The famous Moon Hoax was written by Richard Adams Locke, who was bornin New York in 1800 and died in Staten Island in 1871. He was at one timeeditor of the _Sun_, and the Hoax appeared in that journal in 1835. It wasreprinted in London (1836) and Germany, and was accepted seriously by mostreaders. It was published in book form in New York in 1852 under the title_The Moon Hoax_. Locke also wrote another hoax, the _Lost Manuscript ofMungo Park_, but it attracted relatively little attention. [701] It is true that Jean-Nicolas Nicollet (1756-1843) was at that time inthe United States, but there does not seem to be any very tangible evidenceto connect him with the story. He was secretary and librarian of the Parisobservatory (1817), member of the Bureau of Longitudes (1822), and teacherof mathematics in the Lycée Louis-le-Grand. Having lost his money throughspeculations he left France for the United States in 1831 and becameconnected with the government survey of the Mississippi Valley. [702] This was Alexis Bouvard (1767-1843), who made most of thecomputations for Laplace's _Mécanique céleste_ (1793). He discovered eightnew comets and calculated their orbits. In his tables of Uranus (1821) heattributed certain perturbations to the presence of an undiscovered planet, but unlike Leverrier and Adams he did not follow up this clue and thusdiscover Neptune. [703] Patrick Murphy (1782-1847) awoke to find himself famous because ofhis natural guess that there would be very cold weather on January 20, although that is generally the season of lowest temperature. It turned outthat his forecasts were partly right on 168 days and very wrong on 197days. [704] He seems to have written nothing else. If one wishes to enter intothe subject of the mathematics of the Great Pyramid there is an extensiveliterature awaiting him. Richard William Howard Vyse (1784-1853) publishedin 1840 his _Operations carried on at the Pyramids of Gizeh in 1837_, andin this he made a beginning of a scientific metrical study of the subject. Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland (1845-1888)was much carried away with the number mysticism of the Great Pyramid, somuch so that he published in 1864 a work entitled _Our Inheritance in theGreat Pyramid_, in which his vagaries were set forth. Although he was thena Fellow of the Royal Society (1857), his work was so ill received thatwhen he offered a paper on the subject it was rejected (1874) and heresigned in consequence of this action. The latest and perhaps the mostscholarly of all investigators of the subject is William Matthew FlindersPetrie (born in 1853), Edwards professor of Egyptology at UniversityCollege, London, whose _Pyramids and Temples of Gizeh_ (1883) andsubsequent works are justly esteemed as authorities. [705] As De Morgan subsequently found, this name reversed becomes OliverB... E, for Oliver Byrne, one of the odd characters among the minormathematical writers of the middle of the last century. One of his mostcurious works is _The first six Books of the Elements of Euclid; in whichcoloured diagrams and symbols are used instead of letters_ (1847). There issome merit in speaking of the red triangle instead of the triangle ABC, butnot enough to give the method any standing. His _Dual Arithmetic_(1863-1867) was also a curious work. [706] Brenan also wrote on English composition (1829), a work that wentthrough fourteen editions by 1865; a work entitled _The Foreigner's EnglishConjugator_ (1831), and a work on the national debt. [707] See note 211, page 112. [708] See note 592, page 261. [709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions(1852), was an infant prodigy, competing with Zerah Colburn as a child. Hewas a linguist of remarkable powers, being able, at thirteen years of age, to boast that he knew as many languages as he had lived years. When onlysixteen he found an error in Laplace's _Mécanique céleste_. When onlytwenty-two he was appointed Andrews professor of astronomy, and he soonafter became Astronomer Royal of Ireland. He was knighted in 1835. Hisearlier work was on optics, his _Theory of Systems of Rays_ appearing in1823. In 1827 he published a paper on the principle of _Varying Action_. Healso wrote on dynamics. [710] "Let him not leave the kingdom, "--a legal phrase. [711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807), who edited Lambert's _Logische und philosophische Abhandlungen_, Berlin, 1782. He was astronomer of the Academy of Sciences at Berlin. [712] Jacob Bernoulli (1654-1705) was one of the two brothers who foundedthe famous Bernoulli family of mathematicians, the other being Johann I. His _Ars conjectandi_ (1713), published posthumously, was the firstdistinct treatise on probabilities. [713] Johann Heinrich Lambert (1728-1777) was one of the most learned menof his time. Although interested chiefly in mathematics, he wrote also onscience, logic, and philosophy. [714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, andfounder of the _Annales de mathématiques_ (1810). [715] Gottfried Ploucquet (1716-1790) was at first a clergyman, butafterwards became professor of logic at Tübingen. [716] "In the premises let the middle term be omitted; what remainsindicates the conclusion. " [717] Probably Sir William Edmond Logan (1789-1875), who became sointerested in geology as to be placed at the head of the geological surveyof Canada (1842). The University of Montreal conferred the title LL. D. Uponhim, and Napoleon III gave him the cross of the Legion of Honor. [718] "So strike that he may think himself to die. " [719] "Witticism or piece of stupidity. " [720] A very truculently unjust assertion: for Sir W. Was as great a setterup of some as he was a puller down of others. His writings are a congeriesof praises and blames, both _cruel smart_, as they say in the States. Butthe combined instigation of prose, rhyme, and retort would send Aristideshimself to Tartarus, if it were not pretty certain that Minos would grant a_stet processus_ under the circumstances. The first two verses areexaggerations standing on a basis of truth. The fourth verse is quite true:Sir W. H. Was an Edinburgh Aristotle, with the difference of ancient andmodern Athens well marked, especially the _perfervidum ingeniumScotorum_. --A. De M. [721] See note 576, p. 252. There was also a _Theory of Parallels_ thatdiffered from these, London, 1853, second edition 1856, third edition 1856. [722] The work was written by Robert Chambers (1802-1871), the Edinburghpublisher, a friend of Scott and of many of his contemporaries in theliterary field. He published the _Vestiges of the Natural History ofCreation_ in 1844, not 1840. [723] Everett (1784-1872) was at that time a good Wesleyan, but wasexpelled from the ministry in 1849 for having written _Wesleyan Takings_and as under suspicion for having started the _Fly Sheets_ in 1845. In 1857he established the United Methodist Free Church. [724] Smith was a Primitive Methodist preacher. He also wrote an _EarnestAddress to the Methodists_ (1841) and _The Wealth Question_ (1840?). [725] He wrote the _Nouveau traité de Balistique_, Paris, 1837. [726] Joseph Denison, known to fame only through De Morgan. See also page353. [727] The radical (1784?-1858), advocate of the founding of Londonuniversity (1826), of medical reform (1827-1834), and of the repeal of theduties on newspapers and corn, and an ardent champion of penny postage. [728] I. E. , Roman Catholic Priest. [729] Murphy (1806-1843) showed extraordinary powers in mathematics evenbefore the age of thirteen. He became a fellow of Caius College, Cambridge, in 1829, dean in 1831, and examiner in mathematics in London University in1838. [730] See note 442, page 196. [731] Sir John Bowring (1792-1872), the linguist, writer, and traveler, member of many learned societies and a writer of high reputation in histime. His works were not, however, of genuine merit. [732] Joseph Hume (1777-1855) served as a surgeon with the British army inIndia early in the nineteenth century. He returned to England in 1808 andentered parliament as a radical in 1812. He was much interested in allreform movements. [733] Sir Robert Harry Inglis (1786-1855), a strong Tory, known for hisnumerous addresses in the House of Commons rather than for any realability. [734] Sir Robert Peel (1788-1850) began his parliamentary career in 1809and was twice prime minister. He was prominent in most of the great reformsof his time. [735] See note 627, page 290. [736] John Taylor (1781-1864) was a publisher, and published severalpamphlets opposed to Peel's currency measures. De Morgan refers to his workon the Junius question. This was done early in his career, and resulted in_A Discovery of the author of the Letters of Junius_ (1813), and _TheIdentity of Junius with a distinguished living character established_(1816), this being Sir Philip Francis. [737] See note 665, page 308. [738] See page 348. [739] See note 348, page 160. [740] Sir Nicholas Harris Nicolas (1799-1848) was a reformer in variouslines, --the Record Commission, the Society of Antiquaries, and the BritishMuseum, --and his work was not without good results. [741] See note 98, page 69. [742] In the _Companion to the Almanac_ for 1845 is a paper by Prof. DeMorgan, "On the Ecclesiastical Calendar, " the statements of which, so faras concerns the Gregorian Calendar, are taken direct from the work ofClavius, the principal agent in the arrangement of the reformed reckoning. This was followed, in the _Companion to the Almanac_ for 1846, by a secondpaper, by the same author, headed "On the Earliest Printed Almanacs, " muchof which is written in direct supplement to the former article. --S. E. DeMorgan. [743] It may be necessary to remind some English readers that in Latin andits derived European languages, what we call Easter is called the passover(_pascha_). The Quartadecimans had the _name_ on their side: a possessionwhich often is, in this world, nine points of the law. --A. De M. [744] Socrates Scholasticus was born at Constantinople c. 379, and diedafter 439. His _Historia Ecclesiastica_ (in Greek) covers the period fromConstantine the Great to about 439, and includes the Council of Nicæa. Thework was printed in Paris 1544. [745] Theodoretus or Theodoritus was born at Antioch and died about 457. Hewas one of the greatest divines of the fifth century, a man of learning, piety, and judicial mind, and a champion of freedom of opinion in allreligious matters. [746] He died in 417. He was a man of great energy and of high attainments. [747] He died in 461, having reigned as pope for twenty-one years. It washe who induced Attila to spare Rome in 452. [748] He succeeded Leo as pope in 461, and reigned for seven years. [749] Victorinus or Victorius Marianus seems to have been born at Limoges. He was a mathematician and astronomer, and the cycle mentioned by De Morganis one of 532 years, a combination of the Metonic cycle of 19 years withthe solar cycle of 28 years. His canon was published at Antwerp in 1633 or1634, _De doctrina temporum sive commentarius in Victorii Aquitani etaliorum canones paschales_. [750] He went to Rome about 497, and died there in 540. He wrote his _Liberde paschate_ in 525, and it was in this work that the Christian era wasfirst used for calendar purposes. [751] See note 259, page 126. [752] Johannes de Sacrobosco (Holy wood), or John of Holywood. The name wasoften written, without regard to its etymology, Sacrobusto. He was educatedat Oxford and taught in Paris until his death (1256). He did much to makethe Hindu-Arabic numerals known to European scholars. [753] See note 36, page 44. [754] See note 45, page 48. [755] The Julian year is a year of the Julian Calendar, in which there isleap year every fourth year. Its average length is therefore 365 days and aquarter. --A. De M. [756] Ugo Buoncompagno (1502-1585) was elected pope in 1572. [757] He was a Calabrian, and as early as 1552 was professor of medicine atPerugia. In 1576 his manuscript on the reform of the calendar was presentedto the Roman Curia by his brother, Antonius. The manuscript was not printedand it has not been preserved. [758] The title of this work, which is the authority on all points of thenew Calendar, is _Kalendarium Gregorianum Perpetuum. Cum Privilegio SummiPontificis Et Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII. Cum Licentia Superiorum_ (quarto, pp. 60). --A. De M. [759] _Manuels-Roret. Théorie du Calendrier et collection de tous lesCalendriers des Années passées et futures_.... Par L. B. Francoeur, ... Paris, à la librairie encyclopédique de Roret, rue Hautefeuille, 10 bis. 1842. (12mo. ) In this valuable manual, the 35 possible almanacs are givenat length, with such preliminary tables as will enable any one to find, bymere inspection, which almanac he is to choose for any year, whether of oldor new style. [1866. I may now refer to my own _Book of Almanacs_, for thesame purpose]. --A. De M. Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecolepolytechnique (1804) and the Lycée Charlemagne (1805), became professor ofhigher algebra in the University of Paris (1809). His _Cours complet desmathématiques pures_ was well received, and he also wrote on mechanics, astronomy, and geodesy. [760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 anddied at Utrecht in 1542. He was a mathematician and a firm defender of thefaith, asserting the supremacy of the Pope and attacking both Luther andCalvin. He spent some time in Rome. His greatest work was his _Hierarchiæecclesiasticæ assertio_ (1538). [761] This was A. F. Vogel. The work was his translation from the Germanedition which appeared at Leipsic the same year, _Entdeckung einernumerischen General-Auflösung aller höheren endlichen Gleichungen von jederbeliebigen algebraischen und transcendenten Form_. [762] The latest edition of Burnside and Panton's _Theory of Equations_ hasthis brief summary of the present status of the problem: "Demonstrationshave been given by Abel and Wantzel (see Serret's _Cours d'AlgèbreSupérieure_, Art. 516) of the impossibility of resolving algebraicallyequations unrestricted in form, of a degree higher than the fourth. Atranscendental solution, however, of the quintic has been given by M. Hermite, in a form involving elliptic integrals. " [763] There was a second edition of this work in 1846. The author's_Astronomy Simplified_ was published in 1838, and the _Thoughts on PhysicalAstronomy_ in 1840, with a second edition in 1842. [764] This was _The Science of the Weather, by several authors... Edited byB. _, Glasgow, 1867. [765] This was Y. Ramachandra, son of Sundara L[=a]la. He was a teacher ofscience in Delhi College, and the work to which De Morgan refers is _ATreatise on problems of Maxima and Minima solved by Algebra_, whichappeared at Calcutta in 1850. De Morgan's edition was published at Londonnine years later. [766] Abraham de Moivre (1667-1754), French refugee in London, poor, studying under difficulties, was a man with tastes in some respects likethose of De Morgan. For one thing, he was a lover of books, and he had agood deal of interest in the theory of probabilities to which De Morganalso gave much thought. His introduction of imaginary quantities intotrigonometry was an event of importance in the history of mathematics, andthe theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]+ i sin n[phi], is one of the most important ones in all analysis. [767] John Dolland (1706-1761), the silk weaver who became the greatestmaker of optical instruments in his time. [768] Thomas Simpson (1710-1761), also a weaver, taking his leisure fromhis loom at Spitalfields to teach mathematics. His _New Treatise onFluxions_ (1737) was written only two years after he began working inLondon, and six years later he was appointed professor of mathematics atWoolwich. He wrote many works on mathematics and Simpson's Formulas forcomputing trigonometric tables are still given in the text-books. [769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost hiseyesight through smallpox when only a year old. At the age of 25 he beganlecturing at Cambridge on the principles of the Newtonian philosophy. His_Algebra_, in two large volumes, was long the standard treatise on thesubject. [770] He was not in the class with the others mentioned. [771] Not known in the literature of mathematics. [772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in1842, with a third edition in 1855. [773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a universityeducation. He studied mathematics privately and became president of theMathematical Society. De Morgan knew him professionally through the factthat he was prominent in actuarial work. [774] Referring to the contributions of Archimedes (287-212 B. C. ) to themensuration of the sphere. [775] The famous Alexandrian astronomer (c. 87-c. 165 A. D. ), author of the_Almagest_, a treatise founded on the works of Hipparchus. [776] Dr. Whewell, when I communicated this song to him, started theopinion, which I had before him, that this was a very good idea, of whichtoo little was made. --A. De M. [777] See note 117, page 76. [778] The common epithet of rank: _nobilis Tycho_, as he was a nobleman. The writer had been at history. --A. De M. See note 117, page 76. [779] He lost it in a duel, with Manderupius Pasbergius. A contemporary, T. B. Laurus, insinuates that they fought to settle which was the bestmathematician! This seems odd, but it must be remembered they fought in thedark, "_in tenebris densis_"; and it is a nice problem to shave off a nosein the dark, without any other harm. --A. De M. Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro(1581-1621), the poet and writer? [780] See note 117, page 76. [781] Referring to Kepler's celebrated law of planetary motion. He hadpreviously wasted his time on analogies between the planetary orbits andthe polyhedrons. --A. De M. [782] See note 117, page 76. [783] "It does move though. " [784] As great a lie as ever was told: but in 1800 a compliment to Newtonwithout a fling at Descartes would have been held a lopsided structure. --A. De M. [785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left onthe steps of Jean-le-Rond in Paris, and who became one of the greatestmathematical physicists and astronomers of his century. [786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest ofSwiss mathematicians, prominent in the theory of numbers, and known fordiscoveries in all lines of mathematics as then studied. [787] See notes 478, 479, page 219. [788] See note 621, page 288. [789] See note 584, page 255. [790] The _siderial_ day is about four minutes short of the solar; thereare 366 sidereal days in the year. --A. De M. [791] The founding of the London Mathematical Society is discussed by Mrs. De Morgan in her _Memoir_ (p. 281). The idea came from a conversationbetween her brilliant son, George Campbell De Morgan, and his friend ArthurCowper Ranyard in 1864. The meeting of organization was held on Nov. 7, 1864, with Professor De Morgan in the chair, and the first regular meetingon January 16, 1865. [792] See note 33, page 43. [793] See note 119, page 80. [794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 hediscovered ten planetoids. [795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He wasknighted in 1846 and devoted the latter part of his life to the work of theRoyal Geographical Society and to the geology of Scotland. [796] Friedrich Wilhelm Bessel (1784-1846), the astronomer and physicist. He was professor of astronomy at Königsberg. [797] This was the _Reduction of the Observations of Planets made ... From1750 to 1830: computed ... Under the superintendence of George BiddellAiry_ (1848). See note 129, page 85. [798] The expense of this magnificent work was defrayed by Governmentgrants, obtained, at the instance of the British Association, in 1833--A. De M. [799] See note 32, page 43. [800] Franz Friedrich Ernst Brünnow (1821-1891) was at that time or shortlybefore director of the observatory at Dusseldorf. He then went to Berlinand thence (1854) to Ann Arbor, Michigan. He then went to Dublin andfinally became Royal Astronomer of Ireland. [801] Johann Gottfried Galle (1812-1910), at that time connected with theBerlin observatory, and later professor of astronomy at Breslau. [802] George Bishop (1785-1861), in whose observatory in Regent's Parkimportant observations were made by Dawes, Hind, and Marth. [803] James Challis (1803-1882), director of the Cambridge observatory, andsuccessor of Airy as Plumian professor of astronomy. [804] On Leverrier and Arago see note 33, page 43, and note 561, page 243. [805] Robert Grant's (1814-1892) _History of Physical Astronomy from theEarliest Ages to the Middle of the Nineteenth Century_ appeared in 1852. Hewas professor of astronomy and director of the observatory at Glasgow. [806] John Debenham was more interested in religion than in astronomy. Hewrote _The Strait Gate; or, the true scripture doctrine of salvationclearly explained_, London, 1843, and _Tractatus de magis et Bethlehemæstella et Christi in deserto tentatione_, privately printed at London in1845. [807] More properly the Sydney Smirke reading room, since it was built fromhis designs. [808] The Antinomians were followers of Johannes Agricola (1494-1566). Theybelieved that Christians as such were released from all obligations to theOld Testament. Some went so far as to assert that, since all Christianswere sanctified, they could not lose this sanctity even though theydisobeyed God. The sect was prominent in England in the seventeenthcentury, and was transferred to New England. Here it suffered a check inthe condemnation of Mrs. Ann Hutchinson (1636) by the Newton Synod. [809] Aside from this work and his publications on Reeve and Muggleton hewrote nothing. With Joseph Frost he published _A list_ _of Books andgeneral index to J. Reeve and L. Muggleton's works_ (1846), _Divine Songsof the Muggletonians_ (1829), and the work mentioned on page 396. _Theworks of J. Reeve and L. Muggleton_ (1832). [810] About 1650 he and his cousin John Reeve (1608-1658) began to havevisions. As part of their creed they taught that astronomy was opposed bythe Bible. They asserted that the sun moves about the earth, and Reevefigured out that heaven was exactly six miles away. Both Muggleton andReeve were imprisoned for their unitarian views. Muggleton wrote a_Transcendant Spirituall Treatise_ (1652). I have before me _A trueInterpretation of All the Chief Texts ... Of the whole Book of theRevelation of St. John.... By Lodowick Muggleton, one of the two lastCommissioned Witnesses & Prophets of the onely high, immortal, gloriousGod, Christ Jesus_ (1665), in which the interpretation of the "number ofthe beast" occupies four pages without arriving anywhere. [811] In 1652 he was, in a vision, named as the Lord's "last messenger, "with Muggleton as his "mouth, " and died six years later, probably ofnervous tension resulting from his divine "illumination. " He was the morespiritual of the two. [812] William Guthrie (1708-1770) was a historian and political writer. His_History of England_ (1744-1751) was the first attempt to base history onparliamentary records. He also wrote a _General History of Scotland_ in 10volumes (1767). The work to which Frost refers is the _Geographical, Historical, and Commercial Grammar_ (1770) which contained an astronomicalpart by J. Ferguson. By 1827 it had passed through 24 editions. [813] George Fox (1624-1691), founder of the Society of Friends; a mysticand a disciple of Boehme. He was eight times imprisoned for heresy. [814] If they were friends they were literary antagonists, for Muggletonwrote against Fox _The Neck of the Quakers Broken_ (1663), and Fox repliedin 1667. Muggleton also wrote _A Looking Glass for George Fox_. [815] John Conduitt (1688-1737), who married (1717) Newton's half niece, Mrs. Katherine Barton. See note 284, page 136. [816] Probably Peter Mark Roget's (1779-1869) _Thesaurus of English Words_(1852) is not much used at present, but it went through 28 editions in hislifetime. Few who use the valuable work are aware that Roget was aprofessor of physiology at the Royal Institution (London), that he achievedhis title of F. R. S. Because of his work in perfecting the slide rule, andthat he followed Sir John Herschel as secretary of the Royal Society. [817] See note 703, page 327. This work went into a second edition in theyear of its first publication. [818] See note 398, page 177. [819] See note 528, page 233. [820] George Jacob Holyoake (1817-1906) entered into a controversial lifeat an early age. In 1841 he was imprisoned for six months for blasphemy. Hefounded and edited _The Reasoner_ (Vols. 1-26, 1846-1861). In his laterlife he did much to promote cooperation among the working class. [821] See note 176, page 102. [822] William Thomas Lowndes (1798-1843), whose _Bibliographer's Manual ofEnglish Literature_, 4 vols. , London, 1834 (also 1857-1864, and 1869) is aclassic in its line. [823] Jacques Charles Brunet (1780-1867), the author of the great Frenchbibliography, the _Manuel du Libraire_ (1810). * * * * * Corrections made to printed original. Page 5, "direct acquaintance with the whole of his mental ancestry":'acquantance' in original. Page 100, "The error is at the rate": 'it' (for 'is') in original. Page 192, "the lineal successor of the Repository association":'successsor' in original. Page 211, "the doctors had finished their compliments": 'docters' inoriginal. Page 302, "causing mutual perturbations": 'peturbations' in original. Page 344, "The work itself is described": 'decribed' in original. Page 370, The entry for 1852 is printed as 19, it appears that the correctvalue should be 9. Page 392, "Sir John Herschel's previous communication": 'pervious' inoriginal. Note 317, "he constructed a working model of a steam road carriage":'contructed' in original. Note 380, "the variation of the Earth's Diameters": 'Diaameters' inoriginal. Note 550, "The first edition of the anonymous [Greek]": 'anonynous' inoriginal.