SIDE-LIGHTS ON ASTRONOMY

AND KINDRED FIELDS OF POPULAR SCIENCE

ESSAYS AND ADDRESSES

BY

SIMON NEWCOMB

CONTENTS

PREFACE

 I. THE UNSOLVED PROBLEMS OF ASTRONOMY II. THE NEW PROBLEMS OF THE UNIVERSE III. THE STRUCTURE OF THE UNIVERSE IV. THE EXTENT OF THE UNIVERSE V. MAKING AND USING A TELESCOPE VI. WHAT THE ASTRONOMERS ARE DOING VII. LIFE IN THE UNIVERSE VIII. HOW THE PLANETS ARE WEIGHED IX. THE MARINER'S COMPASS X. THE FAIRYLAND OF GEOMETRY XI. THE ORGANIZATION OF SCIENTIFIC RESEARCH XII. CAN WE MAKE IT RAIN? XIII. THE ASTRONOMICAL EPHEMERIS AND NAUTICAL ALMANAC XIV. THE WORLD'S DEBT TO ASTRONOMY XV. AN ASTRONOMICAL FRIENDSHIP XVI. THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR XVII. THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE XVIII. ASPECTS OF AMERICAN ASTRONOMY XIX. THE UNIVERSE AS AN ORGANISM XX. THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS XXI. THE OUTLOOK FOR THE FLYING-MACHINE

ILLUSTRATIONS

SIMON NEWCOMB

PHOTOGRAPH OF THE CORONA OF THE SUN, TAKEN IN TRIPOLI DURING TOTALECLIPSE OF AUGUST 30, 1905. 

A TYPICAL STAR CLUSTER-CENTAURI

THE GLASS DISK

THE OPTICIAN'S TOOL

THE OPTICIAN'S TOOL

GRINDING A LARGE LENS

IMAGE OF CANDLE-FLAME IN OBJECT-GLASS

TESTING ADJUSTMENT OF OBJECT-GLASS

A VERY PRIMITIVE MOUNTING FOR A TELESCOPE

THE HUYGHENIAN EYE-PIECE

SECTION OF THE PRIMITIVE MOUNTING

SPECTRAL IMAGES OF STARS, THE UPPER LINE SHOWING HOW THEY APPEAR WITHTHE EYE-PIECE PUSHED IN, THE LOWER WITH THE EYE-PIECE DRAWN OUT

THE GREAT REFRACTOR OF THE NATIONAL OBSERVATORY AT WASHINGTON

THE "BROKEN-BACKED COMET-SEEKER"

NEBULA IN ORION

DIP OF THE MAGNETIC NEEDLE IN VARIOUS LATITUDES

STAR SPECTRA

PROFESSOR LANGLEY'S AIR-SHIP

PREFACE

In preparing and issuing this collection of essays and addresses, theauthor has yielded to what he could not but regard as the tooflattering judgment of the publishers. Having done this, it becameincumbent to do what he could to justify their good opinion by revisingthe material and bringing it up to date. Interest rather than unity ofthought has determined the selection. 

A prominent theme in the collection is that of the structure, extent, and duration of the universe. Here some repetition of ideas was foundunavoidable, in a case where what is substantially a single theme hasbeen treated in the various forms which it assumed in the light ofconstantly growing knowledge. If the critical reader finds this adefect, the author can plead in extenuation only the difficulty ofavoiding it under the circumstances. Although mainly astronomical, anumber of discussions relating to general scientific subjects have beenincluded. 

Acknowledgment is due to the proprietors of the various periodicalsfrom the pages of which most of the essays have been taken. BesidesHarper's Magazine and the North American Review, these includeMcClure's Magazine, from which were taken the articles "The UnsolvedProblems of Astronomy" and "How the Planets are Weighed. " "TheStructure of the Universe" appeared in the International Monthly, nowthe International Quarterly; "The Outlook for the Flying-Machine" ismainly from The New York Independent, but in part from McClure'sMagazine; "The World's Debt to Astronomy" is from The Chautauquan; and"An Astronomical Friendship" from the Atlantic Monthly. 

SIMON NEWCOMB. WASHINGTON, JUNE, 1906. 

I

THE UNSOLVED PROBLEMS OF ASTRONOMY

The reader already knows what the solar system is: an immense centralbody, the sun, with a number of planets revolving round it at variousdistances. On one of these planets we dwell. Vast, indeed, are thedistances of the planets when measured by our terrestrial standards. Acannon-ball fired from the earth to celebrate the signing of theDeclaration of Independence, and continuing its course ever since witha velocity of eighteen hundred feet per second, would not yet behalf-way to the orbit of Neptune, the outer planet. And yet thethousands of stars which stud the heavens are at distances so muchgreater than that of Neptune that our solar system is like a littlecolony, separated from the rest of the universe by an ocean of voidspace almost immeasurable in extent. The orbit of the earth round thesun is of such size that a railway train running sixty miles an hour, with never a stop, would take about three hundred and fifty years tocross it. Represent this orbit by a lady's finger-ring. Then thenearest fixed star will be about a mile and a half away; the next morethan two miles; a few more from three to twenty miles; the great bodyat scores or hundreds of miles. Imagine the stars thus scattered fromthe Atlantic to the Mississippi, and keep this little finger-ring inmind as the orbit of the earth, and one may have some idea of theextent of the universe. 

One of the most beautiful stars in the heavens, and one that can beseen most of the year, is a Lyrae, or Alpha of the Lyre, known also asVega. In a spring evening it may be seen in the northeast, in the latersummer near the zenith, in the autumn in the northwest. On the scale wehave laid down with the earth's orbit as a finger-ring, its distancewould be some eight or ten miles. The small stars around it in the sameconstellation are probably ten, twenty, or fifty times as far. 

Now, the greatest fact which modern science has brought to light isthat our whole solar system, including the sun, with all its planets, is on a journey towards the constellation Lyra. During our whole lives, in all probability during the whole of human history, we have beenflying unceasingly towards this beautiful constellation with a speed towhich no motion on earth can compare. The speed has recently beendetermined with a fair degree of certainty, though not with entireexactness; it is about ten miles a second, and therefore not far fromthree hundred millions of miles a year. But whatever it may be, it isunceasing and unchanging; for us mortals eternal. We are nearer theconstellation by five or six hundred miles every minute we live; we arenearer to it now than we were ten years ago by thousands of millions ofmiles, and every future generation of our race will be nearer than itspredecessor by thousands of millions of miles. 

When, where, and how, if ever, did this journey begin--when, where, andhow, if ever, will it end? This is the greatest of the unsolvedproblems of astronomy. An astronomer who should watch the heavens forten thousand years might gather some faint suggestion of an answer, orhe might not. All we can do is to seek for some hints by study andcomparison with other stars. 

The stars are suns. To put it in another way, the sun is one of thestars, and rather a small one at that. If the sun is moving in the wayI have described, may not the stars also be in motion, each on ajourney of its own through the wilderness of space? To this questionastronomy gives an affirmative answer. Most of the stars nearest to usare found to be in motion, some faster than the sun, some more slowly, and the same is doubtless true of all; only the century of accurateobservations at our disposal does not show the motion of the distantones. A given motion seems slower the more distant the moving body; wehave to watch a steamship on the horizon some little time to see thatshe moves at all. Thus it is that the unsolved problem of the motion ofour sun is only one branch of a yet more stupendous one: What mean themotions of the stars--how did they begin, and how, if ever, will theyend? So far as we can yet see, each star is going straight ahead on itsown journey, without regard to its neighbors, if other stars can be socalled. Is each describing some vast orbit which, though looking like astraight line during the short period of our observation, will reallybe seen to curve after ten thousand or a hundred thousand years, orwill it go straight on forever? If the laws of motion are true for allspace and all time, as we are forced to believe, then each moving starwill go on in an unbending line forever unless hindered by theattraction of other stars. If they go on thus, they must, aftercountless years, scatter in all directions, so that the inhabitants ofeach shall see only a black, starless sky. 

Mathematical science can throw only a few glimmers of light on thequestions thus suggested. From what little we know of the masses, distances, and numbers of the stars we see a possibility that the moreslow-moving ones may, in long ages, be stopped in their onward coursesor brought into orbits of some sort by the attraction of their millionsof fellows. But it is hard to admit even this possibility in the caseof the swift-moving ones. Attraction, varying as the inverse square ofthe distance, diminishes so rapidly as the distance increases that, atthe distances which separate the stars, it is small indeed. We couldnot, with the most delicate balance that science has yet invented, evenshow the attraction of the greatest known star. So far as we know, thetwo swiftest-moving stars are, first, Arcturus, and, second, one knownin astronomy as 1830 Groombridge, the latter so called because it wasfirst observed by the astronomer Groombridge, and is numbered 1830 inhis catalogue of stars. If our determinations of the distances of thesebodies are to be relied on, the velocity of their motion cannot be muchless than two hundred miles a second. They would make the circuit ofthe earth every two or three minutes. A body massive enough to controlthis motion would throw a large part of the universe into disorder. Thus the problem where these stars came from and where they are goingis for us insoluble, and is all the more so from the fact that theswiftly moving stars are moving in different directions and seem tohave no connection with each other or with any known star. 

It must not be supposed that these enormous velocities seem so to us. Not one of them, even the greatest, would be visible to the naked eyeuntil after years of watching. On our finger-ring scale, 1830Groombridge would be some ten miles and Arcturus thirty or forty milesaway. Either of them would be moving only two or three feet in a year. To the oldest Assyrian priests Lyra looked much as it does to usto-day. Among the bright and well-known stars Arcturus has the mostrapid apparent motion, yet Job himself would not to-day see that itsposition had changed, unless he had noted it with more exactness thanany astronomer of his time. 

Another unsolved problem among the greatest which present themselves tothe astronomer is that of the size of the universe of stars. We knowthat several thousand of these bodies are visible to the naked eye;moderate telescopes show us millions; our giant telescopes of thepresent time, when used as cameras to photograph the heavens, show anumber past count, perhaps one hundred millions. Are all these starsonly those few which happen to be near us in a universe extending outwithout end, or do they form a collection of stars outside of which isempty infinite space? In other words, has the universe a boundary?Taken in its widest scope this question must always remain unansweredby us mortals because, even if we should discover a boundary withinwhich all the stars and clusters we ever can know are contained, andoutside of which is empty space, still we could never prove that thisspace is empty out to an infinite distance. Far outside of what we callthe universe might still exist other universes which we can never see. 

It is a great encouragement to the astronomer that, although he cannotyet set any exact boundary to this universe of ours, he is gatheringfaint indications that it has a boundary, which his successors not manygenerations hence may locate so that the astronomer shall includecreation itself within his mental grasp. It can be shown mathematicallythat an infinitely extended system of stars would fill the heavens witha blaze of light like that of the noonday sun. As no such effect isproduced, it may be concluded that the universe has a boundary. Butthis does not enable us to locate the boundary, nor to say how manystars may lie outside the farthest stretches of telescopic vision. Yetby patient research we are slowly throwing light on these points andreaching inferences which, not many years ago, would have seemedforever beyond our powers. 

Every one now knows that the Milky Way, that girdle of light whichspans the evening sky, is formed of clouds of stars too minute to beseen by the unaided vision. It seems to form the base on which theuniverse is built and to bind all the stars into a system. It comprisesby far the larger number of stars that the telescope has shown toexist. Those we see with the naked eye are almost equally scatteredover the sky. But the number which the telescope shows us become moreand more condensed in the Milky Way as telescope power is increased. The number of new stars brought out with our greatest power is vastlygreater in the Milky Way than in the rest of the sky, so that theformer contains a great majority of the stars. What is yet morecurious, spectroscopic research has shown that a particular kind ofstars, those formed of heated gas, are yet more condensed in thecentral circle of this band; if they were visible to the naked eye, weshould see them encircling the heavens as a narrow girdle formingperhaps the base of our whole system of stars. This arrangement of thegaseous or vaporous stars is one of the most singular facts that modernresearch has brought to light. It seems to show that these particularstars form a system of their own; but how such a thing can be we arestill unable to see. 

The question of the form and extent of the Milky Way thus becomes thecentral one of stellar astronomy. Sir William Herschel began by tryingto sound its depths; at one time he thought he had succeeded; butbefore he died he saw that they were unfathomable with his mostpowerful telescopes. Even today he would be a bold astronomer who wouldprofess to say with certainty whether the smallest stars we canphotograph are at the boundary of the system. Before we decide thispoint we must have some idea of the form and distance of the cloudlikemasses of stars which form our great celestial girdle. A most curiousfact is that our solar system seems to be in the centre of thisgalactic universe, because the Milky Way divides the heavens into twoequal parts, and seems equally broad at all points. Were we looking atsuch a girdle as this from one side or the other, this appearance wouldnot be presented. But let us not be too bold. Perhaps we are thevictims of some fallacy, as Ptolemy was when he proved, by what lookedlike sound reasoning, based on undeniable facts, that this earth ofours stood at rest in the centre of the heavens!

A related problem, and one which may be of supreme importance to thefuture of our race, is, What is the source of the heat radiated by thesun and stars? We know that life on the earth is dependent on the heatwhich the sun sends it. If we were deprived of this heat we should in afew days be enveloped in a frost which would destroy nearly allvegetation, and in a few months neither man nor animal would be alive, unless crouching over fires soon to expire for want of fuel. We alsoknow that, at a time which is geologically recent, the whole of NewEngland was covered with a sheet of ice, hundreds or even thousands offeet thick, above which no mountain but Washington raised its head. Itis quite possible that a small diminution in the supply of heat sent usby the sun would gradually reproduce the great glacier, and once moremake the Eastern States like the pole. But the fact is thatobservations of temperature in various countries for the last two orthree hundred years do not show any change in climate which can beattributed to a variation in the amount of heat received from the sun. 

The acceptance of this theory of the heat of those heavenly bodieswhich shine by their own light--sun, stars, and nebulae--still leavesopen a problem that looks insoluble with our present knowledge. Whatbecomes of the great flood of heat and light which the sun and starsradiate into empty space with a velocity of one hundred and eightythousand miles a second? Only a very small fraction of it can bereceived by the planets or by other stars, because these are merepoints compared with their distance from us. Taking the teaching of ourscience just as it stands, we should say that all this heat continuesto move on through infinite space forever. In a few thousand years itreaches the probable confines of our great universe. But we know of noreason why it should stop here. During the hundreds of millions ofyears since all our stars began to shine, has the first ray of lightand heat kept on through space at the rate of one hundred and eightythousand miles a second, and will it continue to go on for ages tocome? If so, think of its distance now, and think of its still goingon, to be forever wasted! Rather say that the problem, What becomes ofit? is as yet unsolved. 

Thus far I have described the greatest of problems; those which we maysuppose to concern the inhabitants of millions of worlds revolvinground the stars as much as they concern us. Let us now come down fromthe starry heights to this little colony where we live, the solarsystem. Here we have the great advantage of being better able to seewhat is going on, owing to the comparative nearness of the planets. When we learn that these bodies are like our earth in form, size, andmotions, the first question we ask is, Could we fly from planet toplanet and light on the surface of each, what sort of scenery wouldmeet our eyes? Mountain, forest, and field, a dreary waste, or aseething caldron larger than our earth? If solid land there is, wouldwe find on it the homes of intelligent beings, the lairs of wildbeasts, or no living thing at all? Could we breathe the air, would wechoke for breath or be poisoned by the fumes of some noxious gas?

To most of these questions science cannot as yet give a positiveanswer, except in the case of the moon. Our satellite is so near usthat we can see it has no atmosphere and no water, and therefore cannotbe the abode of life like ours. The contrast of its eternal deadnesswith the active life around us is great indeed. Here we have weather ofso many kinds that we never tire of talking about it. But on the moonthere is no weather at all. On our globe so many things are constantlyhappening that our thousands of daily journals cannot begin to recordthem. But on the dreary, rocky wastes of the moon nothing ever happens. So far as we can determine, every stone that lies loose on its surfacehas lain there through untold ages, unchanged and unmoved. 

We cannot speak so confidently of the planets. The most powerfultelescopes yet made, the most powerful we can ever hope to make, wouldscarcely shows us mountains, or lakes, rivers, or fields at a distanceof fifty millions of miles. Much less would they show us any works ofman. Pointed at the two nearest planets, Venus and Mars, they whet ourcuriosity more than they gratify it. Especially is this the case withVenus. Ever since the telescope was invented observers have tried tofind the time of rotation of this planet on its axis. Some have reachedone conclusion, some another, while the wisest have only doubted. Thegreat Herschel claimed that the planet was so enveloped in vapor orclouds that no permanent features could be seen on its surface. Thebest equipped recent observers think they see faint, shadowy patches, which remain the same from day to day, and which show that the planetalways presents the same face to the sun, as the moon does to theearth. Others do not accept this conclusion as proved, believing thatthese patches may be nothing more than variations of light, shade, andcolor caused by the reflection of the sun's light at various anglesfrom different parts of the planet. 

There is also some mystery about the atmosphere of this planet. WhenVenus passes nearly between us and the sun, her dark hemisphere isturned towards us, her bright one being always towards the sun. But sheis not exactly on a line with the sun except on the very rare occasionsof a transit across the sun's disk. Hence, on ordinary occasions, whenshe seems very near on a line with the sun, we see a very small part ofthe illuminated hemisphere, which now presents the form of a very thincrescent like the new moon. And this crescent is supposed to be alittle broader than it would be if only half the planet wereilluminated, and to encircle rather more than half the planet. Now, this is just the effect that would be produced by an atmosphererefracting the sun's light around the edge of the illuminatedhemisphere. 

The difficulty of observations of this kind is such that the conclusionmay be open to doubt. What is seen during transits of Venus over thesun's disk leads to more certain, but yet very puzzling, conclusions. The writer will describe what he saw at the Cape of Good Hope duringthe transit of December 5, 1882. As the dark planet impinged on thebright sun, it of course cut out a round notch from the edge of thesun. At first, when this notch was small, nothing could be seen of theoutline of that part of the planet which was outside the sun. But whenhalf the planet was on the sun, the outline of the part still off thesun was marked by a slender arc of light. A curious fact was that thisarc did not at first span the whole outline of the planet, but onlyshowed at one or two points. In a few moments another part of theoutline appeared, and then another, until, at last, the arc of lightextended around the complete outline. All this seems to show that whilethe planet has an atmosphere, it is not transparent like ours, but isso filled with mist and clouds that the sun is seen through it only asif shining in a fog. 

Not many years ago the planet Mars, which is the next one outside ofus, was supposed to have a surface like that of our earth. Some partswere of a dark greenish gray hue; these were supposed to be seas andoceans. Other parts had a bright, warm tint; these were supposed to bethe continents. During the last twenty years much has been learned asto how this planet looks, and the details of its surface have beenmapped by several observers, using the best telescopes under the mostfavorable conditions of air and climate. And yet it must be confessedthat the result of this labor is not altogether satisfactory. It seemscertain that the so-called seas are really land and not water. When itcomes to comparing Mars with the earth, we cannot be certain of morethan a single point of resemblance. This is that during the Martianwinter a white cap, as of snow, is formed over the pole, whichpartially melts away during the summer. The conclusion that there areoceans whose evaporation forms clouds which give rise to this snowseems plausible. But the telescope shows no clouds, and nothing to makeit certain that there is an atmosphere to sustain them. There is nocertainty that the white deposit is what we call snow; perhaps it isnot formed of water at all. The most careful studies of the surface ofthis planet, under the best conditions, are those made at the LowellObservatory at Flagstaff, Arizona. Especially wonderful is the systemof so-called canals, first seen by Schiaparelli, but mapped in greatdetail at Flagstaff. But the nature and meaning of these mysteriouslines are still to be discovered. The result is that the question ofthe real nature of the surface of Mars and of what we should see aroundus could we land upon it and travel over it are still among theunsolved problems of astronomy. 

If this is the case with the nearest planets that we can study, how isit with more distant ones? Jupiter is the only one of these of thecondition of whose surface we can claim to have definite knowledge. Buteven this knowledge is meagre. The substance of what we know is thatits surface is surrounded by layers of what look like dense clouds, through which nothing can certainly be seen. 

I have already spoken of the heat of the sun and its probable origin. But the question of its heat, though the most important, is not theonly one that the sun offers us. What is the sun? When we say that itis a very hot globe, more than a million times as large as the earth, and hotter than any furnace that man can make, so that literally "theelements melt with fervent heat" even at its surface, while inside theyare all vaporized, we have told the most that we know as to what thesun really is. Of course we know a great deal about the spots, therotation of the sun on its axis, the materials of which it is composed, and how its surroundings look during a total eclipse. But all this doesnot answer our question. There are several mysteries which ingeniousmen have tried to explain, but they cannot prove their explanations tobe correct. One is the cause and nature of the spots. Another is thatthe shining surface of the sun, the "photosphere, " as it is technicallycalled, seems so calm and quiet while forces are acting within it of amagnitude quite beyond our conception. Flames in which our earth andeverything on it would be engulfed like a boy's marble in ablacksmith's forge are continually shooting up to a height of tens ofthousands of miles. One would suppose that internal forces capable ofdoing this would break the surface up into billows of fire a thousandmiles high; but we see nothing of the kind. The surface of the sunseems almost as placid as a lake. 

Yet another mystery is the corona of the sun. This is something weshould never have known to exist if the sun were not sometimes totallyeclipsed by the dark body of the moon. On these rare occasions the sunis seen to be surrounded by a halo of soft, white light, sending outrays in various directions to great distances. This halo is called thecorona, and has been most industriously studied and photographed duringnearly every total eclipse for thirty years. Thus we have learned muchabout how it looks and what its shape is. It has a fibrous, woollystructure, a little like the loose end of a much-worn hempen rope. Acertain resemblance has been seen between the form of these seemingfibres and that of the lines in which iron filings arrange themselveswhen sprinkled on paper over a magnet. It has hence been inferred thatthe sun has magnetic properties, a conclusion which, in a general way, is supported by many other facts. Yet the corona itself remains no lessan unexplained phenomenon. 

[Illustration with caption: PHOTOGRAPH OF THE CORONA OF THE SUN, TAKENIN TRIPOLI DURING TOTAL ECLIPSE OF AUGUST 30, 1905]

A phenomenon almost as mysterious as the solar corona is the "zodiacallight, " which any one can see rising from the western horizon justafter the end of twilight on a clear winter or spring evening. The mostplausible explanation is that it is due to a cloud of small meteoricbodies revolving round the sun. We should hardly doubt this explanationwere it not that this light has a yet more mysterious appendage, commonly called the Gegenschein, or counter-glow. This is a patch oflight in the sky in a direction exactly opposite that of the sun. It isso faint that it can be seen only by a practised eye under the mostfavorable conditions. But it is always there. The latest suggestion isthat it is a tail of the earth, of the same kind as the tail of a comet!

We know that the motions of the heavenly bodies are predicted withextraordinary exactness by the theory of gravitation. When one findsthat the exact path of the moon's shadow on the earth during a totaleclipse of the sun can be mapped out many years in advance, and thatthe planets follow the predictions of the astronomer so closely that, if you could see the predicted planet as a separate object, it wouldlook, even in a good telescope, as if it exactly fitted over the realplanet, one thinks that here at least is a branch of astronomy which issimply perfect. And yet the worlds themselves show slight deviations intheir movements which the astronomer cannot always explain, and whichmay be due to some hidden cause that, when brought to light, shall leadto conclusions of the greatest importance to our race. 

One of these deviations is in the rotation of the earth. Sometimes, forseveral years at a time, it seems to revolve a little faster, and thenagain a little slower. The changes are very slight; they can bedetected only by the most laborious and refined methods; yet they musthave a cause, and we should like to know what that cause is. 

The moon shows a similar irregularity of motion. For half a century, perhaps through a whole century, she will go around the earth a littleahead of her regular rate, and then for another half-century or moreshe will fall behind. The changes are very small; they would never havebeen seen with the unaided eye, yet they exist. What is their cause?Mathematicians have vainly spent years of study in trying to answerthis question. 

The orbit of Mercury is found by observations to have a slight motionwhich mathematicians have vainly tried to explain. For some time it wassupposed to be caused by the attraction of an unknown planet betweenMercury and the sun, and some were so sure of the existence of thisplanet that they gave it a name, calling it Vulcan. But of late yearsit has become reasonably certain that no planet large enough to producethe effect observed can be there. So thoroughly has every possibleexplanation been sifted out and found wanting, that some astronomersare now inquiring whether the law of gravitation itself may not be alittle different from what has always been supposed. A very slightdeviation, indeed, would account for the facts, but cautiousastronomers want other proofs before regarding the deviation ofgravitation as an established fact. 

Intelligent men have sometimes inquired how, after devoting so muchwork to the study of the heavens, anything can remain for astronomersto find out. It is a curious fact that, although they were neverlearning so fast as at the present day, yet there seems to be more tolearn now than there ever was before. Great and numerous as are theunsolved problems of our science, knowledge is now advancing intoregions which, a few years ago, seemed inaccessible. Where it will stopnone can say. 

II

THE NEW PROBLEMS OF THE UNIVERSE

The achievements of the nineteenth century are still a theme ofcongratulation on the part of all who compare the present state of theworld with that of one hundred years ago. And yet, if we should fancythe most sagacious prophet, endowed with a brilliant imagination, tohave set forth in the year 1806 the problems that the century mightsolve and the things which it might do, we should be surprised to seehow few of his predictions had come to pass. He might have fanciedaerial navigation and a number of other triumphs of the same class, buthe would hardly have had either steam navigation or the telegraph inhis picture. In 1856 an article appeared in Harper's Magazine depictingsome anticipated features of life in A. D. 3000. We have since madegreat advances, but they bear little resemblance to what the writerimagined. He did not dream of the telephone, but did describe much thathas not yet come to pass and probably never will. 

The fact is that, much as the nineteenth century has done, its lastwork was to amuse itself by setting forth more problems for thiscentury to solve than it has ever itself succeeded in mastering. Weshould not be far wrong in saying that to-day there are more riddles inthe universe than there were before men knew that it contained anythingmore than the objects they could see. 

So far as mere material progress is concerned, it may be doubtfulwhether anything so epoch-making as the steam-engine or the telegraphis held in store for us by the future. But in the field of purelyscientific discovery we are finding a crowd of things of which ourphilosophy did not dream even ten years ago. 

The greatest riddles which the nineteenth century has bequeathed to usrelate to subjects so widely separated as the structure of the universeand the structure of atoms of matter. We see more and more of thesestructures, and we see more and more of unity everywhere, and yet newfacts difficult of explanation are being added more rapidly than oldfacts are being explained. 

We all know that the nineteenth century was marked by a separation ofthe sciences into a vast number of specialties, to the subdivisions ofwhich one could see no end. But the great work of the twentieth centurywill be to combine many of these specialties. The physical philosopherof the present time is directing his thought to the demonstration ofthe unity of creation. Astronomical and physical researches are nowbeing united in a way which is bringing the infinitely great and theinfinitely small into one field of knowledge. Ten years ago the atomsof matter, of which it takes millions of millions to make a drop ofwater, were the minutest objects with which science could imagineitself to be concerned, Now a body of experimentalists, prominent amongwhom stand Professors J. J. Thompson, Becquerel, and Roentgen, havedemonstrated the existence of objects so minute that they find theirway among and between the atoms of matter as rain-drops do among thebuildings of a city. More wonderful yet, it seems likely, although ithas not been demonstrated, that these little things, called"corpuscles, " play an important part in what is going on among thestars. Whether this be true or not, it is certain that there do existin the universe emanations of some sort, producing visible effects, theinvestigation of which the nineteenth century has had to bequeath tothe twentieth. 

For the purpose of the navigator, the direction of the magnetic needleis invariable in any one place, for months and even years; but whenexact scientific observations on it are made, it is found subject tonumerous slight changes. The most regular of these consists in a dailychange of its direction. It moves one way from morning until noon, andthen, late in the afternoon and during the night, turns back again toits original pointing. The laws of this change have been carefullystudied from observations, which show that it is least at the equatorand larger as we go north into middle latitudes; but no explanation ofit resting on an indisputable basis has ever been offered. 

Besides these regular changes, there are others of a very irregularcharacter. Every now and then the changes in the direction of themagnet are wider and more rapid than those which occur regularly everyday. The needle may move back and forth in a way so fitful as to showthe action of some unusual exciting cause. Such movements of the needleare commonly seen when there is a brilliant aurora. This connectionshows that a magnetic storm and an aurora must be due to the same orsome connected causes. 

Those of us who are acquainted with astronomical matters know that thenumber of spots on the sun goes through a regular cycle of change, having a period of eleven years and one or two months. Now, the curiousfact is, when the number and violence of magnetic storms are recordedand compared, it is found that they correspond to the spots on the sun, and go through the same period of eleven years. The conclusion seemsalmost inevitable: magnetic storms are due to some emanation sent outby the sun, which arises from the same cause that produces the spots. This emanation does not go on incessantly, but only in an occasionalway, as storms follow each other on the earth. What is it? Everyattempt to detect it has been in vain. Professor Hale, at the YerkesObservatory, has had in operation from time to time, for several years, his ingenious spectroheliograph, which photographs the sun by a singleray of the spectrum. This instrument shows that violent actions aregoing on in the sun, which ordinary observation would never lead us tosuspect. But it has failed to show with certainty any peculiaremanation at the time of a magnetic storm or anything connected withsuch a storm. 

A mystery which seems yet more impenetrable is associated with theso-called new stars which blaze forth from time to time. These offer toour sight the most astounding phenomena ever presented to the physicalphilosopher. One hundred years ago such objects offered no mystery. There was no reason to suppose that the Creator of the universe hadceased His functions; and, continuing them, it was perfectly naturalthat He should be making continual additions to the universe of stars. But the idea that these objects are really new creations, made out ofnothing, is contrary to all our modern ideas and not in accord with theobserved facts. Granting the possibility of a really new star--if suchan object were created, it would be destined to take its place amongthe other stars as a permanent member of the universe. Instead of this, such objects invariably fade away after a few months, and are changedinto something very like an ordinary nebula. A question of transcendentinterest is that of the cause of these outbursts. It cannot be saidthat science has, up to the present time, been able to offer anysuggestion not open to question. The most definite one is the collisiontheory, according to which the outburst is due to the clashing togetherof two stars, one or both of which might previously have been dark, like a planet. The stars which may be actually photographed probablyexceed one hundred millions in number, and those which give too littlelight to affect the photographic plate may be vastly more numerous thanthose which do. Dark stars revolve around bright ones in an infinitevariety of ways, and complex systems of bodies, the members of whichpowerfully attract each other, are the rule throughout the universe. Moreover, we can set no limit to the possible number of dark orinvisible stars that may be flying through the celestial spaces. While, therefore, we cannot regard the theory of collision as established, itseems to be the only one yet put forth which can lay any claim to ascientific basis. What gives most color to it is the extreme suddennesswith which the new stars, so far as has yet been observed, invariablyblaze forth. In almost every case it has been only two or three daysfrom the time that the existence of such an object became known untilit had attained nearly its full brightness. In fact, it would seem thatin the case of the star in Perseus, as in most other cases, the greaterpart of the outburst took place within the space of twenty-four hours. This suddenness and rapidity is exactly what would be the result of acollision. 

The most inexplicable feature of all is the rapid formation of a nebulaaround this star. In the first photographs of the latter, theappearance presented is simply that of an ordinary star. But, in thecourse of three or four months, the delicate photographs taken at theLick Observatory showed that a nebulous light surrounded the star, andwas continually growing larger and larger. At first sight, there wouldseem to be nothing extraordinary in this fact. Great masses ofintensely hot vapor, shining by their own light, would naturally bethrown out from the star. Or, if the star had originally beensurrounded by a very rare nebulous fog or vapor, the latter would beseen by the brilliant light emitted by the star. On this was based anexplanation offered by Kapteyn, which at first seemed very plausible. It was that the sudden wave of light thrown out by the star when itburst forth caused the illumination of the surrounding vapor, which, though really at rest, would seem to expand with the velocity of light, as the illumination reached more and more distant regions of thenebula. This result may be made the subject of exact calculation. Thevelocity of light is such as would make a circuit of the earth morethan seven times in a second. It would, therefore, go out from the starat the rate of a million of miles in between five and six seconds. Inthe lapse of one of our days, the light would have filled a spherearound the star having a diameter more than one hundred and fifty timesthe distance of the sun from the earth, and more than five times thedimensions of the whole solar system. Continuing its course andenlarging its sphere day after day, the sight presented to us wouldhave been that of a gradually expanding nebulous mass--a globe of faintlight continually increasing in size with the velocity of light. 

The first sentiment the reader will feel on this subject is doubtlessone of surprise that the distance of the star should be so great asthis explanation would imply. Six months after the explosion, the globeof light, as actually photographed, was of a size which would have beenvisible to the naked eye only as a very minute object in the sky. Is itpossible that this minute object could have been thousands of times thedimensions of our solar system?

To see how the question stands from this point of view, we must havesome idea of the possible distance of the new star. To gain this idea, we must find some way of estimating distances in the universe. For areason which will soon be apparent, we begin with the greateststructure which nature offers to the view of man. We all know that theMilky Way is formed of countless stars, too minute to be individuallyvisible to the naked eye. The more powerful the telescope through whichwe sweep the heavens, the greater the number of the stars that can beseen in it. With the powerful instruments which are now in use forphotographing the sky, the number of stars brought to light must riseinto the hundreds of millions, and the greater part of these belong tothe Milky Way. The smaller the stars we count, the greater theircomparative number in the region of the Milky Way. Of the stars visiblethrough the telescope, more than one-half are found in the Milky Way, which may be regarded as a girdle spanning the entire visible universe. 

Of the diameter of this girdle we can say, almost with certainty, thatit must be more than a thousand times as great as the distance of thenearest fixed star from us, and is probably two or three times greater. According to the best judgment we can form, our solar system is situatenear the central region of the girdle, so that the latter must bedistant from us by half its diameter. It follows that if we can imaginea gigantic pair of compasses, of which the points extend from us toAlpha Centauri, the nearest star, we should have to measure out atleast five hundred spaces with the compass, and perhaps even onethousand or more, to reach the region of the Milky Way. 

With this we have to connect another curious fact. Of eighteen newstars which have been observed to blaze forth during the last fourhundred years, all are in the region of the Milky Way. This seems toshow that, as a rule, they belong to the Milky Way. Accepting this veryplausible conclusion, the new star in Perseus must have been more thanfive hundred times as far as the nearest fixed star. We know that ittakes light four years to reach us from Alpha Centauri. It follows thatthe new star was at a distance through which light would require morethan two thousand years to travel, and quite likely a time two or threetimes this. It requires only the most elementary ideas of geometry tosee that if we suppose a ray of light to shoot from a star at such adistance in a direction perpendicular to the line of sight from us tothe star, we can compute how fast the ray would seem to us to travel. Granting the distance to be only two thousand light years, the apparentsize of the sphere around the star which the light would fill at theend of one year after the explosion would be that of a coin seen at adistance of two thousand times its radius, or one thousand times itsdiameter--say, a five-cent piece at the distance of sixty feet. But, asa matter of fact, the nebulous illumination expanded with a velocityfrom ten to twenty times as great as this. 

The idea that the nebulosity around the new star was formed by theillumination caused by the light of the explosion spreading out on allsides therefore fails to satisfy us, not because the expansion of thenebula seemed to be so slow, but because it was many times as swift asthe speed of light. Another reason for believing that it was not a merewave of light is offered by the fact that it did not take placeregularly in every direction from the star, but seemed to shoot off atvarious angles. 

Up to the present time, the speed of light has been to science, as wellas to the intelligence of our race, almost a symbol of the greatest ofpossible speeds. The more carefully we reflect on the case, the moreclearly we shall see the difficulty in supposing any agency to travelat the rate of the seeming emanations from the new star in Perseus. 

As the emanation is seen spreading day after day, the reader mayinquire whether this is not an appearance due to some other cause thanthe mere motion of light. May not an explosion taking place in thecentre of a star produce an effect which shall travel yet faster thanlight? We can only reply that no such agency is known to science. 

But is there really anything intrinsically improbable in an agencytravelling with a speed many times that of light? In considering thatthere is, we may fall into an error very much like that into which ourpredecessors fell in thinking it entirely out of the range ofreasonable probability that the stars should be placed at suchdistances as we now know them to be. 

Accepting it as a fact that agencies do exist which travel from sun toplanet and from star to star with a speed which beggars all ourprevious ideas, the first question that arises is that of their natureand mode of action. This question is, up to the present time, one whichwe do not see any way of completely answering. The first difficulty isthat we have no evidence of these agents except that afforded by theiraction. We see that the sun goes through a regular course ofpulsations, each requiring eleven years for completion; and we seethat, simultaneously with these, the earth's magnetism goes through asimilar course of pulsations. The connection of the two, therefore, seems absolutely proven. But when we ask by what agency it is possiblefor the sun to affect the magnetism of the earth, and when we trace thepassage of some agent between the two bodies, we find nothing toexplain the action. To all appearance, the space between the earth andthe sun is a perfect void. That electricity cannot of itself passthrough a vacuum seems to be a well-established law of physics. It istrue that electromagnetic waves, which are supposed to be of the samenature with those of light, and which are used in wireless telegraphy, do pass through a vacuum and may pass from the sun to the earth. Butthere is no way of explaining how such waves would either produce oraffect the magnetism of the earth. 

The mysterious emanations from various substances, under certainconditions, may have an intimate relation with yet another of themysteries of the universe. It is a fundamental law of the universe thatwhen a body emits light or heat, or anything capable of beingtransformed into light or heat, it can do so only by the expenditure offorce, limited in supply. The sun and stars are continually sending outa flood of heat. They are exhausting the internal supply of somethingwhich must be limited in extent. Whence comes the supply? How is theheat of the sun kept up? If it were a hot body cooling off, a very fewyears would suffice for it to cool off so far that its surface wouldbecome solid and very soon cold. In recent years, the theoryuniversally accepted has been that the supply of heat is kept up by thecontinual contraction of the sun, by mutual gravitation of its parts asit cools off. This theory has the advantage of enabling us tocalculate, with some approximation to exactness, at what rate the sunmust be contracting in order to keep up the supply of heat which itradiates. On this theory, it must, ten millions of years ago, have hadtwice its present diameter, while less than twenty millions of yearsago it could not have existed except as an immense nebula filling thewhole solar system. We must bear in mind that this theory is the onlyone which accounts for the supply of heat, even through human history. If it be true, then the sun, earth, and solar system must be less thantwenty million years old. 

Here the geologists step in and tell us that this conclusion is whollyinadmissible. The study of the strata of the earth and of many othergeological phenomena, they assure us, makes it certain that the earthmust have existed much in its present condition for hundreds ofmillions of years. During all that time there can have been no greatdiminution in the supply of heat radiated by the sun. 

The astronomer, in considering this argument, has to admit that hefinds a similar difficulty in connection with the stars and nebulas. Itis an impossibility to regard these objects as new; they must be as oldas the universe itself. They radiate heat and light year after year. Inall probability, they must have been doing so for millions of years. Whence comes the supply? The geologist may well claim that until theastronomer explains this mystery in his own domain, he cannot declarethe conclusions of geology as to the age of the earth to be whollyinadmissible. 

Now, the scientific experiments of the last two years have brought thismystery of the celestial spaces right down into our earthlylaboratories. M. And Madame Curie have discovered the singular metalradium, which seems to send out light, heat, and other raysincessantly, without, so far as has yet been determined, drawing therequired energy from any outward source. As we have already pointedout, such an emanation must come from some storehouse of energy. Is thestorehouse, then, in the medium itself, or does the latter draw it fromsurrounding objects? If it does, it must abstract heat from theseobjects. This question has been settled by Professor Dewar, at theRoyal Institution, London, by placing the radium in a medium next tothe coldest that art has yet produced--liquid air. The latter issurrounded by the only yet colder medium, liquid hydrogen, so that noheat can reach it. Under these circumstances, the radium still givesout heat, boiling away the liquid air until the latter has entirelydisappeared. Instead of the radiation diminishing with time, it ratherseems to increase. 

Called on to explain all this, science can only say that a molecularchange must be going on in the radium, to correspond to the heat itgives out. What that change may be is still a complete mystery. It is amystery which we find alike in those minute specimens of the rarest ofsubstances under our microscopes, in the sun, and in the vast nebulousmasses in the midst of which our whole solar system would be but aspeck. The unravelling of this mystery must be the great work ofscience of the twentieth century. What results shall follow for mankindone cannot say, any more than he could have said two hundred years agowhat modern science would bring forth. Perhaps, before futuredevelopments, all the boasted achievements of the nineteenth centurymay take the modest place which we now assign to the science of theeighteenth century--that of the infant which is to grow into a man. 

III

THE STRUCTURE OF THE UNIVERSE

The questions of the extent of the universe in space and of itsduration in time, especially of its possible infinity in either spaceor time, are of the highest interest both in philosophy and science. The traditional philosophy had no means of attacking these questionsexcept considerations suggested by pure reason, analogy, and thatgeneral fitness of things which was supposed to mark the order ofnature. With modern science the questions belong to the realm of fact, and can be decided only by the results of observation and a study ofthe laws to which these results may lead. 

From the philosophic stand-point, a discussion of this subject which isof such weight that in the history of thought it must be assigned aplace above all others, is that of Kant in his "Kritik. " Here we findtwo opposing propositions--the thesis that the universe occupies only afinite space and is of finite duration; the antithesis that it isinfinite both as regards extent in space and duration in time. Both ofthese opposing propositions are shown to admit of demonstration withequal force, not directly, but by the methods of reductio ad absurdum. The difficulty, discussed by Kant, was more tersely expressed byHamilton in pointing out that we could neither conceive of infinitespace nor of space as bounded. The methods and conclusions of modernastronomy are, however, in no way at variance with Kant's reasoning, sofar as it extends. The fact is that the problem with which thephilosopher of Konigsberg vainly grappled is one which our sciencecannot solve any more than could his logic. We may hope to gaincomplete information as to everything which lies within the range ofthe telescope, and to trace to its beginning every process which we cannow see going on in space. But before questions of the absolutebeginning of things, or of the boundary beyond which nothing exists, our means of inquiry are quite powerless. 

Another example of the ancient method is found in the great work ofCopernicus. It is remarkable how completely the first expounder of thesystem of the world was dominated by the philosophy of his time, whichhe had inherited from his predecessors. This is seen not only in thegeneral course of thought through the opening chapters of his work, butamong his introductory propositions. The first of these is that theuniverse--mundus--as well as the earth, is spherical in form. Hisarguments for the sphericity of the earth, as derived from observation, are little more than a repetition of those of Ptolemy, and thereforenot of special interest. His proposition that the universe is sphericalis, however, not based on observation, but on considerations of theperfection of the spherical form, the general tendency of bodies--adrop of water, for example--to assume this form, and the sphericity ofthe sun and moon. The idea retained its place in his mind, although thefundamental conception of his system did away with the idea of theuniverse having any well-defined form. 

The question as attacked by modern astronomy is this: we see scatteredthrough space in every direction many millions of stars of variousorders of brightness and at distances so great as to defy exactmeasurement, except in the case of a few of the nearest. Has thiscollection of stars any well-defined boundary, or is what we see merelythat part of an infinite mass which chances to lie within the range ofour telescopes? If we were transported to the most distant star ofwhich we have knowledge, should we there find ourselves stillsurrounded by stars on all sides, or would the space beyond be void?Granting that, in any or every direction, there is a limit to theuniverse, and that the space beyond is therefore void, what is the formof the whole system and the distance of its boundaries? Preliminary insome sort to these questions are the more approachable ones: Of whatsort of matter is the universe formed? and into what sort of bodies isthis matter collected?

To the ancients the celestial sphere was a reality, instead of a mereeffect of perspective, as we regard it. The stars were set on itssurface, or at least at no great distance within its crystalline mass. Outside of it imagination placed the empyrean. When and how theseconceptions vanished from the mind of man, it would be as hard to sayas when and how Santa Claus gets transformed in the mind of the child. They are not treated as realities by any astronomical writer fromPtolemy down; yet, the impressions and forms of thought to which theygave rise are well marked in Copernicus and faintly evident in Kepler. The latter was perhaps the first to suggest that the sun might be oneof the stars; yet, from defective knowledge of the relative brightnessof the latter, he was led to the conclusion that their distances fromeach other were less than the distance which separated them from thesun. The latter he supposed to stand in the centre of a vast vacantregion within the system of stars. 

For us the great collection of millions of stars which are made knownto us by the telescope, together with all the invisible bodies whichmay be contained within the limits of the system, form the universe. Here the term "universe" is perhaps objectionable because there may beother systems than the one with which we are acquainted. The termstellar system is, therefore, a better one by which to designate thecollection of stars in question. 

It is remarkable that the first known propounder of that theory of theform and arrangement of the system which has been most generallyaccepted seems to have been a writer otherwise unknown inscience--Thomas Wright, of Durham, England. He is said to havepublished a book on the theory of the universe, about 1750. It does notappear that this work was of a very scientific character, and it was, perhaps, too much in the nature of a speculation to excite notice inscientific circles. One of the curious features of the history is thatit was Kant who first cited Wright's theory, pointed out its accordancewith the appearance of the Milky Way, and showed its generalreasonableness. But, at the time in question, the work of thephilosopher of Konigsberg seems to have excited no more notice amonghis scientific contemporaries than that of Wright. 

Kant's fame as a speculative philosopher has so eclipsed his scientificwork that the latter has but recently been appraised at its true value. He was the originator of views which, though defective in detail, embodied a remarkable number of the results of recent research on thestructure and form of the universe, and the changes taking place in it. The most curious illustration of the way in which he arrived at acorrect conclusion by defective reasoning is found in his anticipationof the modern theory of a constant retardation of the velocity withwhich the earth revolves on its axis. He conceived that this effectmust result from the force exerted by the tidal wave, as moving towardsthe west it strikes the eastern coasts of Asia and America. An oppositeconclusion was reached by Laplace, who showed that the effect of thisforce was neutralized by forces producing the wave and acting in theopposite direction. And yet, nearly a century later, it was shown thatwhile Laplace was quite correct as regards the general principlesinvolved, the friction of the moving water must prevent the completeneutralization of the two opposing forces, and leave a small residualforce acting towards the west and retarding the rotation. Kant'sconclusion was established, but by an action different from that whichhe supposed. 

The theory of Wright and Kant, which was still further developed byHerschel, was that our stellar system has somewhat the form of aflattened cylinder, or perhaps that which the earth would assume if, inconsequence of more rapid rotation, the bulging out at its equator andthe flattening at its poles were carried to an extreme limit. This formhas been correctly though satirically compared to that of a grindstone. It rests to a certain extent, but not entirely, on the idea that thestars are scattered through space with equal thickness in everydirection, and that the appearance of the Milky Way is due to the factthat we, situated in the centre of this flattened system, see morestars in the direction of the circumference of the system than in thatof its poles. The argument on which the view in question rests may bemade clear in the following way. 

Let us chose for our observations that hour of the night at which theMilky Way skirts our horizon. This is nearly the case in the eveningsof May and June, though the coincidence with the horizon can never beexact except to observers stationed near the tropics. Using the figureof the grindstone, we at its centre will then have its circumferencearound our horizon, while the axis will be nearly vertical. The pointsin which the latter intersects the celestial sphere are called thegalactic poles. There will be two of these poles, the one at the hourin question near the zenith, the other in our nadir, and thereforeinvisible to us, though seen by our antipodes. Our horizon corresponds, as it were, to the central circle of the Milky Way, which now surroundsus on all sides in a horizontal direction, while the galactic poles are90 degrees distant from every part of it, as every point of the horizonis 90 degrees from the zenith. 

Let us next count the number of stars visible in a powerful telescopein the region of the heavens around the galactic pole, now our zenith, and find the average number per square degree. This will be therichness of the region in stars. Then we take regions nearer thehorizontal Milky Way--say that contained between 10 degrees and 20degrees from the zenith--and, by a similar count, find its richness instars. We do the same for other regions, nearer and nearer to thehorizon, till we reach the galaxy itself. The result of all the countswill be that the richness of the sky in stars is least around thegalactic pole, and increases in every direction towards the Milky Way. 

Without such counts of the stars we might imagine our stellar system tobe a globular collection of stars around which the object in questionpassed as a girdle; and we might take a globe with a chain passingaround it as representative of the possible figure of the stellarsystem. But the actual increase in star-thickness which we have pointedout shows us that this view is incorrect. The nature and validity ofthe conclusions to be drawn can be best appreciated by a statement ofsome features of this tendency of the stars to crowd towards thegalactic circle. 

Most remarkable is the fact that the tendency is seen even among thebrighter stars. Without either telescope or technical knowledge, thecareful observer of the stars will notice that the most brilliantconstellations show this tendency. The glorious Orion, Canis Majorcontaining the brightest star in the heavens, Cassiopeia, Perseus, Cygnus, and Lyra with its bright-blue Vega, not to mention suchconstellations as the Southern Cross, all lie in or near the Milky Way. Schiaparelli has extended the investigation to all the stars visible tothe naked eye. He laid down on planispheres the number of such stars ineach region of the heavens of 5 degrees square. Each region was thenshaded with a tint that was darker as the region was richer in stars. The very existence of the Milky Way was ignored in this work, thoughhis most darkly shaded regions lie along the course of this belt. Bydrawing a band around the sky so as to follow or cover his darkestregions, we shall rediscover the course of the Milky Way without anyreference to the actual object. It is hardly necessary to add that thisresult would be reached with yet greater precision if we included thetelescopic stars to any degree of magnitude--plotting them on a chartand shading the chart in the same way. What we learn from this is thatthe stellar system is not an irregular chaos; and that notwithstandingall its minor irregularities, it may be considered as built up withspecial reference to the Milky Way as a foundation. 

Another feature of the tendency in question is that it is more and moremarked as we include fainter stars in our count. The galactic region isperhaps twice as rich in stars visible to the naked eye as the rest ofthe heavens. In telescopic stars to the ninth magnitude it is three orfour times as rich. In the stars found on the photographs of the skymade at the Harvard and other observatories, and in the stargauges ofthe Herschels, it is from five to ten times as rich. 

Another feature showing the unity of the system is the symmetry of theheavens on the two sides of the galactic belt Let us return to oursupposition of such a position of the celestial sphere, with respect tothe horizon, that the latter coincides with the central line of thisbelt, one galactic pole being near our zenith. The celestial hemispherewhich, being above our horizon, is visible to us, is the one to whichwe have hitherto directed our attention in describing the distributionof the stars. But below our horizon is another hemisphere, that of ourantipodes, which is the counterpart of ours. The stars which itcontains are in a different part of the universe from those which wesee, and, without unity of plan, would not be subject to the same law. But the most accurate counts of stars that have been made fail to showany difference in their general arrangement in the two hemispheres. They are just as thick around the south galactic poles as around thenorth one. They show the same tendency to crowd towards the Milky Wayin the hemisphere invisible to us as in the hemisphere which we see. Slight differences and irregularities, are, indeed, found in theenumeration, but they are no greater than must necessarily arise fromthe difficulty of stopping our count at a perfectly fixed magnitude. The aim of star-counts is not to estimate the total number of stars, for this is beyond our power, but the number visible with a giventelescope. In such work different observers have explored differentparts of the sky, and in a count of the same region by two observers weshall find that, although they attempt to stop at the same magnitude, each will include a great number of stars which the other omits. Thereis, therefore, room for considerable difference in the numbers of starsrecorded, without there being any actual inequality between the twohemispheres. 

A corresponding similarity is found in the physical constitution of thestars as brought out by the spectroscope. The Milky Way is extremelyrich in bluish stars, which make up a considerable majority of thecloudlike masses there seen. But when we recede from the galaxy on oneside, we find the blue stars becoming thinner, while those having ayellow tinge become relatively more numerous. This difference of coloralso is the same on the two sides of the galactic plane. Nor can anysystematic difference be detected between the proper motions of thestars in these two hemispheres. If the largest known proper motion isfound in the one, the second largest is in the other. Counting all theknown stars that have proper motions exceeding a given limit, we findabout as many in one hemisphere as in the other. In this respect, also, the universe appears to be alike through its whole extent. It is theuniformity thus prevailing through the visible universe, as far as wecan see, in two opposite directions, which inspires us with confidencein the possibility of ultimately reaching some well-founded conclusionas to the extent and structure of the system. 

All these facts concur in supporting the view of Wright, Kant, andHerschel as to the form of the universe. The farther out the starsextend in any direction, the more stars we may see in that direction. In the direction of the axis of the cylinder, the distances of theboundary are least, so that we see fewer stars. The farther we directour attention towards the equatorial regions of the system, the greaterthe distance from us to the boundary, and hence the more stars we see. The fact that the increase in the number of stars seen towards theequatorial region of the system is greater, the smaller the stars, isthe natural consequence of the fact that distant stars come within ourview in greater numbers towards the equatorial than towards the polarregions. 

Objections have been raised to the Herschelian view on the ground thatit assumes an approximately uniform distribution of the stars in space. It has been claimed that the fact of our seeing more stars in onedirection than in another may not arise merely from our looking througha deeper stratum, as Herschel supposed, but may as well be due to thestars being more thinly scattered in the direction of the axis of thesystem than in that of its equatorial region. The great inequalities inthe richness of neighboring regions in the Milky Way show that thehypothesis of uniform distribution does not apply to the equatorialregion. The claim has therefore been made that there is no proof of thesystem extending out any farther in the equatorial than in the polardirection. 

The consideration of this objection requires a closer inquiry as towhat we are to understand by the form of our system. We have alreadypointed out the impossibility of assigning any boundary beyond which wecan say that nothing exists. And even as regards a boundary of ourstellar system, it is impossible for us to assign any exact limitbeyond which no star is visible to us. The analogy of collections ofstars seen in various parts of the heavens leads us to suppose thatthere may be no well-defined form to our system, but that, as we go outfarther and farther, we shall see occasional scattered stars to, possibly, an indefinite distance. The truth probably is that, as inascending a mountain, we find the trees, which may be very dense at itsbase, thin out gradually as we approach the summit, where there may befew or none, so we might find the stars to thin out could we fly to thedistant regions of space. The practical question is whether, in such aflight, we should find this sooner by going in the direction of theaxis of our system than by directing our course towards the Milky Way. If a point is at length reached beyond which there are but fewscattered stars, such a point would, for us, mark the boundary of oursystem. From this point of view the answer does not seem to admit ofdoubt. If, going in every direction, we mark the point, if any, atwhich the great mass of the stars are seen behind us, the totality ofall these points will lie on a surface of the general form thatHerschel supposed. 

There is still another direct indication of the finitude of our stellarsystem upon which we have not touched. If this system extended outwithout limit in any direction whatever, it is shown by a geometricprocess which it is not necessary to explain in the present connection, but which is of the character of mathematical demonstration, that theheavens would, in every direction where this was true, blaze with thelight of the noonday sun. This would be very different from theblue-black sky which we actually see on a clear night, and which, witha reservation that we shall consider hereafter, shows that, how farso-ever our stellar system may extend, it is not infinite. Beyond thisnegative conclusion the fact does not teach us much. Vast, indeed, isthe distance to which the system might extend without the sky appearingmuch brighter than it is, and we must have recourse to otherconsiderations in seeking for indications of a boundary, or even of awell-marked thinning out, of stars. 

If, as was formerly supposed, the stars did not greatly differ in theamount of light emitted by each, and if their diversity of apparentmagnitude were due principally to the greater distance of the fainterstars, then the brightness of a star would enable us to form a more orless approximate idea of its distance. But the accumulated researchesof the past seventy years show that the stars differ so enormously intheir actual luminosity that the apparent brightness of a star affordsus only a very imperfect indication of its distance. While, in thegeneral average, the brighter stars must be nearer to us than thefainter ones, it by no means follows that a very bright star, even ofthe first magnitude, is among the nearer to our system. Two stars areworthy of especial mention in this connection, Canopus and Rigel. Thefirst is, with the single exception of Sirius, the brightest star inthe heavens. The other is a star of the first magnitude in thesouthwest corner of Orion. The most long-continued and completemeasures of parallax yet made are those carried on by Gill, at the Capeof Good Hope, on these two and some other bright stars. The results, published in 1901, show that neither of these bodies has any parallaxthat can be measured by the most refined instrumental means known toastronomy. In other words, the distance of these stars is immeasurablygreat. The actual amount of light emitted by each is certainlythousands and probably tens of thousands of times that of the sun. 

Notwithstanding the difficulties that surround the subject, we can atleast say something of the distance of a considerable number of thestars. Two methods are available for our estimate--measures of parallaxand determination of proper motions. 

The problem of stellar parallax, simple though it is in its conception, is the most delicate and difficult of all which the practicalastronomer has to encounter. An idea of it may be gained by supposing aminute object on a mountain-top, we know not how many miles away, to bevisible through a telescope. The observer is allowed to change theposition of his instrument by two inches, but no more. He is requiredto determine the change in the direction of the object produced by thisminute displacement with accuracy enough to determine the distance ofthe mountain. This is quite analogous to the determination of thechange in the direction in which we see a star as the earth, movingthrough its vast circuit, passes from one extremity of its orbit to theother. Representing this motion on such a scale that the distance ofour planet from the sun shall be one inch, we find that the neareststar, on the same scale, will be more than four miles away, andscarcely one out of a million will be at a less distance than tenmiles. It is only by the most wonderful perfection both in theheliometer, the instrument principally used for these measures, and inmethods of observation, that any displacement at all can be seen evenamong the nearest stars. The parallaxes of perhaps a hundred stars havebeen determined, with greater or less precision, and a few hundred moremay be near enough for measurement. All the others are immeasurablydistant; and it is only by statistical methods based on their propermotions and their probable near approach to equality in distributionthat any idea can be gained of their distances. 

To form a conception of the stellar system, we must have a unit ofmeasure not only exceeding any terrestrial standard, but even anydistance in the solar system. For purely astronomical purposes the mostconvenient unit is the distance corresponding to a parallax of 1", which is a little more than 200, 000 times the sun's distance. But forthe purposes of all but the professional astronomer the most convenientunit will be the light-year--that is, the distance through which lightwould travel in one year. This is equal to the product of 186, 000miles, the distance travelled in one second, by 31, 558, 000, the numberof seconds in a year. The reader who chooses to do so may perform themultiplication for himself. The product will amount to about 63, 000times the distance of the sun. 

[Illustration with caption: A Typical Star Cluster--Centauri]

The nearest star whose distance we know, Alpha Centauri, is distantfrom us more than four light-years. In all likelihood this is reallythe nearest star, and it is not at all probable that any other starlies within six light-years. Moreover, if we were transported to thisstar the probability seems to be that the sun would now be the neareststar to us. Flying to any other of the stars whose parallax has beenmeasured, we should probably find that the average of the six or eightnearest stars around us ranges somewhere between five and sevenlight-years. We may, in a certain sense, call eight light-years astar-distance, meaning by this term the average of the nearestdistances from one star to the surrounding ones. 

To put the result of measures of parallax into another form, let ussuppose, described around our sun as a centre, a system of concentricspheres each of whose surfaces is at the distance of six light-yearsoutside the sphere next within it. The inner is at the distance of sixlight-years around the sun. The surface of the second sphere will betwelve light-years away, that of the third eighteen, etc. The volumesof space within each of these spheres will be as the cubes of thediameters. The most likely conclusion we can draw from measures ofparallax is that the first sphere will contain, beside the sun at itscentre, only Alpha Centauri. The second, twelve light-years away, willprobably contain, besides these two, six other stars, making eight inall. The third may contain twenty-one more, making twenty-seven starswithin the third sphere, which is the cube of three. Within the fourthwould probably be found sixty-four stars, this being the cube of four, and so on. 

Beyond this no measures of parallax yet made will give us muchassistance. We can only infer that probably the same law holds for alarge number of spheres, though it is quite certain that it does nothold indefinitely. For more light on the subject we must have recourseto the proper motions. The latest words of astronomy on this subjectmay be briefly summarized. As a rule, no star is at rest. Each ismoving through space with a speed which differs greatly with differentstars, but is nearly always swift, indeed, when measured by anystandard to which we are accustomed. Slow and halting, indeed, is thatstar which does not make more than a mile a second. With two or threeexceptions, where the attraction of a companion comes in, the motion ofevery star, so far as yet determined, takes place in a straight line. In its outward motion the flying body deviates neither to the right norleft. It is safe to say that, if any deviation is to take place, thousands of years will be required for our terrestrial observers torecognize it. 

Rapid as the course of these objects is, the distances which we havedescribed are such that, in the great majority of cases, all theobservations yet made on the positions of the stars fail to show anywell-established motion. It is only in the case of the nearer of theseobjects that we can expect any motion to be perceptible during theperiod, in no case exceeding one hundred and fifty years, through whichaccurate observations extend. The efforts of all the observatorieswhich engage in such work are, up to the present time, unequal to thetask of grappling with the motions of all the stars that can be seenwith the instruments, and reaching a decision as to the proper motionin each particular case. As the question now stands, the aim of theastronomer is to determine what stars have proper motions large enoughto be well established. To make our statement on this subject clear, itmust be understood that by this term the astronomer does not mean thespeed of a star in space, but its angular motion as he observes it onthe celestial sphere. A star moving forward with a given speed willhave a greater proper motion according as it is nearer to us. To avoidall ambiguity, we shall use the term "speed" to express the velocity inmiles per second with which such a body moves through space, and theterm "proper motion" to express the apparent angular motion which theastronomer measures upon the celestial sphere. 

Up to the present time, two stars have been found whose proper motionsare so large that, if continued, the bodies would make a completecircuit of the heavens in less than 200, 000 years. One of these wouldrequire about 160, 000; the other about 180, 000 years for the circuit. Of other stars having a rapid motion only about one hundred wouldcomplete their course in less than a million of years. 

Quite recently a system of observations upon stars to the ninthmagnitude has been nearly carried through by an internationalcombination of observatories. The most important conclusion from theseobservations relates to the distribution of the stars with reference tothe Milky Way, which we have already described. We have shown thatstars of every magnitude, bright and faint, show a tendency to crowdtowards this belt. It is, therefore, remarkable that no such tendencyis seen in the case of those stars which have proper motions largeenough to be accurately determined. So far as yet appears, such starsare equally scattered over the heavens, without reference to the courseof the Milky Way. The conclusion is obvious. These stars are all insidethe girdle of the Milky Way, and within the sphere which contains themthe distribution in space is approximately uniform. At least there isno well-marked condensation in the direction of the galaxy nor anymarked thinning out towards its poles. What can we say as to the extentof this sphere?

To answer this question, we have to consider whether there is anyaverage or ordinary speed that a star has in space. A great number ofmotions in the line of sight--that is to say, in the direction of theline from us to the star--have been measured with great precision byCampbell at the Lick Observatory, and by other astronomers. Thestatistical investigations of Kaptoyn also throw much light on thesubject. The results of these investigators agree well in showing anaverage speed in space--a straight-ahead motion we may call it--oftwenty-one miles per second. Some stars may move more slowly than thisto any extent; others more rapidly. In two or three cases the speedexceeds one hundred miles per second, but these are quite exceptional. By taking several thousand stars having a given proper motion, we mayform a general idea of their average distance, though a great number ofthem will exceed this average to a considerable extent. The conclusiondrawn in this way would be that the stars having an apparent propermotion of 10" per century or more are mostly contained within, or lienot far outside of a sphere whose surface is at a distance from us of200 light-years. Granting the volume of space which we have shown thatnature seems to allow to each star, this sphere should contain 27, 000stars in all. There are about 10, 000 stars known to have so large aproper motion as 10". But there is no actual discordance between theseresults, because not only are there, in all probability, great numbersof stars of which the proper motion is not yet recognized, but thereare within the sphere a great number of stars whose motion is less thanthe average. On the other hand, it is probable that a considerablenumber of the 10, 000 stars lie at a distance at least one-half greaterthan that of the radius of the sphere. 

On the whole, it seems likely that, out to a distance of 300 or even400 light-years, there is no marked inequality in star distribution. Ifwe should explore the heavens to this distance, we should neither findthe beginning of the Milky Way in one direction nor a very markedthinning out in the other. This conclusion is quite accordant with theprobabilities of the case. If all the stars which form the groundworkof the Milky Way should be blotted out, we should probably find100, 000, 000, perhaps even more, remaining. Assigning to each star thespace already shown to be its quota, we should require a sphere ofabout 3000 light-years radius to contain such a number of stars. Atsome such distance as this, we might find a thinning out of the starsin the direction of the galactic poles, or the commencement of theMilky Way in the direction of this stream. 

Even if this were not found at the distance which we have supposed, itis quite certain that, at some greater distance, we should at leastfind that the region of the Milky Way is richer in stars than theregion near the galactic poles. There is strong reason, based on theappearance of the stars of the Milky Way, their physical constitution, and their magnitudes as seen in the telescope, to believe that, were weplaced on one of these stars, we should find the stars around us to bemore thickly strewn than they are around our system. In other words, the quota of space filled by each star is probably less in the regionof the Milky Way than it is near the centre where we seem to besituated. 

We are, therefore, presented with what seems to be the mostextraordinary spectacle that the universe can offer, a ring of starsspanning it, and including within its limits by far the great majorityof the stars within our system. We have in this spectacle anotherexample of the unity which seems to pervade the system. We mightimagine the latter so arranged as to show diversity to any extent. Wemight have agglomerations of stars like those of the Milky Way situatedin some corner of the system, or at its centre, or scattered through ithere and there in every direction. But such is not the case. There are, indeed, a few star-clusters scattered here and there through thesystem; but they are essentially different from the clusters of theMilky Way, and cannot be regarded as forming an important part of thegeneral plan. In the case of the galaxy we have no such scattering, butfind the stars built, as it were, into this enormous ring, havingsimilar characteristics throughout nearly its whole extent, and havingwithin it a nearly uniform scattering of stars, with here and theresome collected into clusters. Such, to our limited vision, now appearsthe universe as a whole. 

We have already alluded to the conclusion that an absolutely infinitesystem of stars would cause the entire heavens to be filled with ablaze of light as bright as the sun. It is also true that theattractive force within such a universe would be infinitely great insome direction or another. But neither of these considerations enablesus to set a limit to the extent of our system. In two remarkable papersby Lord Kelvin which have recently appeared, the one being an addressbefore the British Association at its Glasgow meeting, in 1901, aregiven the results of some numerical computations pertaining to thissubject. Granting that the stars are scattered promiscuously throughspace with some approach to uniformity in thickness, and are of a knowndegree of brilliancy, it is easy to compute how far out the system mustextend in order that, looking up at the sky, we shall see a certainamount of light coming from the invisible stars. Granting that, in thegeneral average, each star is as bright as the sun, and that theirthickness is such that within a sphere of 3300 light-years there are1, 000, 000, 000 stars, if we inquire how far out such a system must becontinued in order that the sky shall shine with even four per cent ofthe light of the sun, we shall find the distance of its boundary sogreat that millions of millions of years would be required for thelight of the outer stars to reach the centre of the system. In view ofthe fact that this duration in time far exceeds what seems to be thepossible life duration of a star, so far as our knowledge of it canextend, the mere fact that the sky does not glow with any suchbrightness proves little or nothing as to the extent of the system. 

We may, however, replace these purely negative considerations byinquiring how much light we actually get from the invisible stars ofour system. Here we can make a definite statement. Mark out a smallcircle in the sky 1 degree in diameter. The quantity of light which wereceive on a cloudless and moonless night from the sky within thiscircle admits of actual determination. From the measures so faravailable it would seem that, in the general average, this quantity oflight is not very different from that of a star of the fifth magnitude. This is something very different from a blaze of light. A star of thefifth magnitude is scarcely more than plainly visible to ordinaryvision. The area of the whole sky is, in round numbers, about 50, 000times that of the circle we have described. It follows that the totalquantity of light which we receive from all the stars is about equal tothat of 50, 000 stars of the fifth magnitude--somewhat more than 1000 ofthe first magnitude. This whole amount of light would have to bemultiplied by 90, 000, 000 to make a light equal to that of the sun. Itis, therefore, not at all necessary to consider how far the system mustextend in order that the heavens should blaze like the sun. AdoptingLord Kelvin's hypothesis, we shall find that, in order that we mayreceive from the stars the amount of light we have designated, thissystem need not extend beyond some 5000 light-years. But thishypothesis probably overestimates the thickness of the stars in space. It does not seem probable that there are as many as 1, 000, 000, 000 starswithin the sphere of 3300 light-years. Nor is it at all certain thatthe light of the average star is equal to that of the sun. It isimpossible, in the present state of our knowledge, to assign anydefinite value to this average. To do so is a problem similar to thatof assigning an average weight to each component of the animalcreation, from the microscopic insects which destroy our plants up tothe elephant. What we can say with a fair approximation to confidenceis that, if we could fly out in any direction to a distance of 20, 000, perhaps even of 10, 000, light-years, we should find that we had left alarge fraction of our system behind us. We should see its boundary inthe direction in which we had travelled much more certainly than we seeit from our stand-point. 

We should not dismiss this branch of the subject without saying thatconsiderations are frequently adduced by eminent authorities which tendto impair our confidence in almost any conclusion as to the limits ofthe stellar system. The main argument is based on the possibility thatlight is extinguished in its passage through space; that beyond acertain distance we cannot see a star, however bright, because itslight is entirely lost before reaching us. That there could be any lossof light in passing through an absolute vacuum of any extent cannot beadmitted by the physicist of to-day without impairing what he considersthe fundamental principles of the vibration of light. But thepossibility that the celestial spaces are pervaded by matter whichmight obstruct the passage of light is to be considered. We know thatminute meteoric particles are flying through our system in such numbersthat the earth encounters several millions of them every day, whichappear to us in the familiar phenomena of shooting-stars. If suchparticles are scattered through all space, they must ultimatelyobstruct the passage of light. We know little of the size of thesebodies, but, from the amount of energy contained in their light as theyare consumed in the passage through our atmosphere, it does not seem atall likely that they are larger than grains of sand or, perhaps, minutepebbles. They are probably vastly more numerous in the vicinity of thesun than in the interstellar spaces, since they would naturally tend tobe collected by the sun's attraction. In fact there are some reasonsfor believing that most of these bodies are the debris of comets; andthe latter are now known to belong to the solar system, and not to theuniverse at large. 

But whatever view we take of these possibilities, they cannotinvalidate our conclusion as to the general structure of the stellarsystem as we know it. Were meteors so numerous as to cut off a largefraction of the light from the more distant stars, we should see noMilky Way, but the apparent thickness of the stars in every directionwould be nearly the same. The fact that so many more of these objectsare seen around the galactic belt than in the direction of its polesshows that, whatever extinction light may suffer in going through thegreatest distances, we see nearly all that comes from stars not moredistant than the Milky Way itself. 

Intimately connected with the subject we have discussed is the questionof the age of our system, if age it can be said to have. In consideringthis question, the simplest hypothesis to suggest itself is that theuniverse has existed forever in some such form as we now see it; thatit is a self-sustaining system, able to go on forever with only suchcycles of transformation as may repeat themselves indefinitely, andmay, therefore, have repeated themselves indefinitely in the past. Ordinary observation does not make anything known to us which wouldseem to invalidate this hypothesis. In looking upon the operations ofthe universe, we may liken ourselves to a visitor to the earth fromanother sphere who has to draw conclusions about the life of anindividual man from observations extending through a few days. Duringthat time, he would see no reason why the life of the man should haveeither a beginning or an end. He sees a daily round of change, activityand rest, nutrition and waste; but, at the end of the round, theindividual is seemingly restored to his state of the day before. Whymay not this round have been going on forever, and continue in thefuture without end? It would take a profounder course of observationand a longer time to show that, notwithstanding this seemingrestoration, an imperceptible residual of vital energy, necessary tothe continuance of life, has not been restored, and that the loss ofthis residuum day by day must finally result in death. 

The case is much the same with the great bodies of the universe. Although, to superficial observation, it might seem that they couldradiate their light forever, the modern generalizations of physics showthat such cannot be the case. The radiation of light necessarilyinvolves a corresponding loss of heat and with it the expenditure ofsome form of energy. The amount of energy within any body isnecessarily limited. The supply must be exhausted unless the energy ofthe light sent out into infinite space is, in some way, restored to thebody which expended it. The possibility of such a restorationcompletely transcends our science. How can the little vibration whichstrikes our eye from some distant star, and which has been perhapsthousands of years in reaching us, find its way back to its origin? Thelight emitted by the sun 10, 000 years ago is to-day pursuing its way ina sphere whose surface is 10, 000 light-years distant on all sides. Science has nothing even to suggest the possibility of its restoration, and the most delicate observations fail to show any return from theunfathomable abyss. 

Up to the time when radium was discovered, the most carefulinvestigations of all conceivable sources of supply had shown only onewhich could possibly be of long duration. This is the contraction whichis produced in the great incandescent bodies of the universe by theloss of the heat which they radiate. As remarked in the precedingessay, the energy generated by the sun's contraction could not havekept up its present supply of heat for much more than twenty or thirtymillions of years, while the study of earth and ocean shows evidence ofthe action of a series of causes which must have been going on forhundreds of millions of years. 

The antagonism between the two conclusions is even more marked thanwould appear from this statement. The period of the sun's heat set bythe astronomical physicist is that during which our luminary couldpossibly have existed in its present form. The period set by thegeologist is not merely that of the sun's existence, but that duringwhich the causes effecting geological changes have not undergone anycomplete revolution. If, at any time, the sun radiated much less thanits present amount of heat, no water could have existed on the earth'ssurface except in the form of ice; there would have been scarcely anyevaporation, and the geological changes due to erosion could not havetaken place. Moreover, the commencement of the geological operations ofwhich we speak is by no means the commencement of the earth'sexistence. The theories of both parties agree that, for untold aeonsbefore the geological changes now visible commenced, our planet was amolten mass, perhaps even an incandescent globe like the sun. Duringall those aeons the sun must have been in existence as a vast nebulousmass, first reaching as far as the earth's orbit, and slowlycontracting its dimensions. And these aeons are to be included in anyestimate of the age of the sun. 

The doctrine of cosmic evolution--the theory which in former times wasgenerally known as the nebular hypothesis--that the heavenly bodieswere formed by the slow contraction of heated nebulous masses, isindicated by so many facts that it seems scarcely possible to doubt itexcept on the theory that the laws of nature were, at some former time, different from those which we now see in operation. Granting theevolutionary hypothesis, every star has its lifetime. We can even laydown the law by which it passes from infancy to old age. All stars donot have the same length of life; the rule is that the larger the star, or the greater the mass of matter which composes it, the longer will itendure. Up to the present time, science can do nothing more than pointout these indications of a beginning, and their inevitable consequence, that there is to be an end to the light and heat of every heavenlybody. But no cautious thinker can treat such a subject with the ease ofordinary demonstration. The investigator may even be excused if hestands dumb with awe before the creation of his own intellect. Ouraccurate records of the operations of nature extend through only two orthree centuries, and do not reach a satisfactory standard until withina single century. The experience of the individual is limited to a fewyears, and beyond this period he must depend upon the records of hisancestors. All his knowledge of the laws of nature is derived from thisvery limited experience. How can he essay to describe what may havebeen going on hundreds of millions of years in the past? Can he dare tosay that nature was the same then as now?

It is a fundamental principle of the theory of evolution, as developedby its greatest recent expounder, that matter itself is eternal, andthat all the changes which have taken place in the universe, so far asmade up of matter, are in the nature of transformations of this eternalsubstance. But we doubt whether any physical philosopher of the presentday would be satisfied to accept any demonstration of the eternity ofmatter. All he would admit is that, so far as his observation goes, nochange in the quantity of matter can be produced by the action of anyknown cause. It seems to be equally uncreatable and indestructible. Buthe would, at the same time, admit that his experience no more sufficedto settle the question than the observation of an animal for a singleday would settle the question of the duration of its life, or provethat it had neither beginning nor end. He would probably admit thateven matter itself may be a product of evolution. The astronomer findsit difficult to conceive that the great nebulous masses which he seesin the celestial spaces--millions of times larger than the whole solarsystem, yet so tenuous that they offer not the slightest obstruction tothe passage of a ray of light through their whole length--situated inwhat seems to be a region of eternal cold, below anything that we canproduce on the earth's surface, yet radiating light, and with it heat, like an incandescent body--can be made up of the same kind of substancethat we have around us on the earth's surface. Who knows but that theradiant property that Becquerel has found in certain forms of mattermay be a residuum of some original form of energy which is inherent ingreat cosmical masses, and has fed our sun during all the ages requiredby the geologist for the structure of the earth's crusts? It may bethat in this phenomenon we have the key to the great riddle of theuniverse, with which profounder secrets of matter than any we havepenetrated will be opened to the eyes of our successors. 

IV

THE EXTENT OF THE UNIVERSE

We cannot expect that the wisest men of our remotest posterity, who canbase their conclusions upon thousands of years of accurate observation, will reach a decision on this subject without some measure of reserve. Such being the case, it might appear the dictate of wisdom to leave itsconsideration to some future age, when it may be taken up with bettermeans of information than we now possess. But the question is one whichwill refuse to be postponed so long as the propensity to think of thepossibilities of creation is characteristic of our race. The issue isnot whether we shall ignore the question altogether, like Eve in thepresence of Raphael; but whether in studying it we shall confine ourspeculations within the limits set by sound scientific reasoning. Essaying to do this, I invite the reader's attention to what sciencemay suggest, admitting in advance that the sphere of exact knowledge issmall compared with the possibilities of creation, and that outsidethis sphere we can state only more or less probable conclusions. 

The reader who desires to approach this subject in the most receptivespirit should begin his study by betaking himself on a clear, moonlessevening, when he has no earthly concern to disturb the serenity of histhoughts, to some point where he can lie on his back on bench or roof, and scan the whole vault of heaven at one view. He can do this with thegreatest pleasure and profit in late summer or autumn--winter would doequally well were it possible for the mind to rise so far above bodilyconditions that the question of temperature should not enter. Thethinking man who does this under circumstances most favorable for calmthought will form a new conception of the wonder of the universe. Ifsummer or autumn be chosen, the stupendous arch of the Milky Way willpass near the zenith, and the constellation Lyra, led by its beautifulblue Vega of the first magnitude, may be not very far from that point. South of it will be seen the constellation Aquila, marked by the brightAltair, between two smaller but conspicuous stars. The bright Arcturuswill be somewhere in the west, and, if the observation is not made tooearly in the season, Aldebaran will be seen somewhere in the east. Whenattention is concentrated on the scene the thousands of stars on eachside of the Milky Way will fill the mind with the consciousness of astupendous and all-embracing frame, beside which all human affairs sinkinto insignificance. A new idea will be formed of such a well-knownfact of astronomy as the motion of the solar system in space, byreflecting that, during all human history, the sun, carrying the earthwith it, has been flying towards a region in or just south of theconstellation Lyra, with a speed beyond all that art can produce onearth, without producing any change apparent to ordinary vision in theaspect of the constellation. Not only Lyra and Aquila, but every one ofthe thousand stars which form the framework of the sky, were seen byour earliest ancestors just as we see them now. Bodily rest may beobtained at any time by ceasing from our labors, and weary systems mayfind nerve rest at any summer resort; but I know of no way in whichcomplete rest can be obtained for the weary soul--in which the mind canbe so entirely relieved of the burden of all human anxiety--as by thecontemplation of the spectacle presented by the starry heavens underthe conditions just described. As we make a feeble attempt to learnwhat science can tell us about the structure of this starry frame, Ihope the reader will allow me to at least fancy him contemplating it inthis way. 

The first question which may suggest itself to the inquiring reader is:How is it possible by any methods of observation yet known to theastronomer to learn anything about the universe as a whole? We maycommence by answering this question in a somewhat comprehensive way. Itis possible only because the universe, vast though it is, shows certaincharacteristics of a unified and bounded whole. It is not a chaos, itis not even a collection of things, each of which came into existencein its own separate way. If it were, there would be nothing in commonbetween two widely separate regions of the universe. But, as a matterof fact, science shows unity in the whole structure, and diversity onlyin details. The Milky Way itself will be seen by the most ordinaryobserver to form a single structure. This structure is, in some sort, the foundation on which the universe is built. It is a girdle whichseems to span the whole of creation, so far as our telescopes have yetenabled us to determine what creation is; and yet it has elements ofsimilarity in all its parts. What has yet more significance, it is insome respects unlike those parts of the universe which lie without it, and even unlike those which lie in that central region within it whereour system is now situated. The minute stars, individually far beyondthe limit of visibility to the naked eye, which form its cloudlikeagglomerations, are found to be mostly bluer in color, from one extremeto the other, than the general average of the stars which make up therest of the universe. 

In the preceding essay on the structure of the universe, we havepointed out several features of the universe showing the unity of thewhole. We shall now bring together these and other features with a viewof showing their relation to the question of the extent of the universe. 

The Milky Way being in a certain sense the foundation on which thewhole system is constructed, we have first to notice the symmetry ofthe whole. This is seen in the fact that a certain resemblance is foundin any two opposite regions of the sky, no matter where we choose them. If we take them in the Milky Way, the stars are more numerous thanelsewhere; if we take opposite regions in or near the Milky Way, weshall find more stars in both of them than elsewhere; if we take themin the region anywhere around the poles of the Milky Way, we shall findfewer stars, but they will be equally numerous in each of the tworegions. We infer from this that whatever cause determined the numberof the stars in space was of the same nature in every two antipodalregions of the heavens. 

Another unity marked with yet more precision is seen in the chemicalelements of which stars are composed. We know that the sun is composedof the same elements which we find on the earth and into which weresolve compounds in our laboratories. These same elements are found inthe most distant stars. It is true that some of these bodies seem tocontain elements which we do not find on earth. But as these unknownelements are scattered from one extreme of the universe to the other, they only serve still further to enforce the unity which runs throughthe whole. The nebulae are composed, in part at least, of forms ofmatter dissimilar to any with which we are acquainted. But, differentthough they may be, they are alike in their general characterthroughout the whole field we are considering. Even in such a featureas the proper motions of the stars, the same unity is seen. The readerdoubtless knows that each of these objects is flying through space onits own course with a speed comparable with that of the earth aroundthe sun. These speeds range from the smallest limit up to more than onehundred miles a second. Such diversity might seem to detract from theunity of the whole; but when we seek to learn something definite bytaking their average, we find this average to be, so far as can yet bedetermined, much the same in opposite regions of the universe. Quiterecently it has become probable that a certain class of very brightstars known as Orion stars--because there are many of them in the mostbrilliant of our constellations--which are scattered along the wholecourse of the Milky Way, have one and all, in the general average, slower motions than other stars. Here again we have a definablecharacteristic extending through the universe. In drawing attention tothese points of similarity throughout the whole universe, it must notbe supposed that we base our conclusions directly upon them. The pointthey bring out is that the universe is in the nature of an organizedsystem; and it is upon the fact of its being such a system that we areable, by other facts, to reach conclusions as to its structure, extent, and other characteristics. 

One of the great problems connected with the universe is that of itspossible extent. How far away are the stars? One of the unities whichwe have described leads at once to the conclusion that the stars mustbe at very different distances from us; probably the more distant onesare a thousand times as far as the nearest; possibly even farther thanthis. This conclusion may, in the first place, be based on the factthat the stars seem to be scattered equally throughout those regions ofthe universe which are not connected with the Milky Way. To illustratethe principle, suppose a farmer to sow a wheat-field of entirelyunknown extent with ten bushels of wheat. We visit the field and wishto have some idea of its acreage. We may do this if we know how manygrains of wheat there are in the ten bushels. Then we examine a spacetwo or three feet square in any part of the field and count the numberof grains in that space. If the wheat is equally scattered over thewhole field, we find its extent by the simple rule that the size of thefield bears the same proportion to the size of the space in which thecount was made that the whole number of grains in the ten bushels sownbears to the number of grains counted. If we find ten grains in asquare foot, we know that the number of square feet in the whole fieldis one-tenth that of the number of grains sown. So it is with theuniverse of stars. If the latter are sown equally through space, theextent of the space occupied must be proportional to the number ofstars which it contains. 

But this consideration does not tell us anything about the actualdistance of the stars or how thickly they may be scattered. To do thiswe must be able to determine the distance of a certain number of stars, just as we suppose the farmer to count the grains in a certain smallextent of his wheat-field. There is only one way in which we can make adefinite measure of the distance of any one star. As the earth swingsthrough its vast annual circuit round the sun, the direction of thestars must appear to be a little different when seen from one extremityof the circuit than when seen from the other. This difference is calledthe parallax of the stars; and the problem of measuring it is one ofthe most delicate and difficult in the whole field of practicalastronomy. 

The nineteenth century was well on its way before the instruments ofthe astronomer were brought to such perfection as to admit of themeasurement. From the time of Copernicus to that of Bessel manyattempts had been made to measure the parallax of the stars, and morethan once had some eager astronomer thought himself successful. Butsubsequent investigation always showed that he had been mistaken, andthat what he thought was the effect of parallax was due to some othercause, perhaps the imperfections of his instrument, perhaps the effectof heat and cold upon it or upon the atmosphere through which he wasobliged to observe the star, or upon the going of his clock. Thusthings went on until 1837, when Bessel announced that measures with aheliometer--the most refined instrument that has ever been used inmeasurement--showed that a certain star in the constellation Cygnus hada parallax of one-third of a second. It may be interesting to give anidea of this quantity. Suppose one's self in a house on top of amountain looking out of a window one foot square, at a house on anothermountain one hundred miles away. One is allowed to look at that distanthouse through one edge of the pane of glass and then through theopposite edge; and he has to determine the change in the direction ofthe distant house produced by this change of one foot in his ownposition. From this he is to estimate how far off the other mountainis. To do this, one would have to measure just about the amount ofparallax that Bessel found in his star. And yet this star is among thefew nearest to our system. The nearest star of all, Alpha Centauri, visible only in latitudes south of our middle ones, is perhaps half asfar as Bessel's star, while Sirius and one or two others are nearly atthe same distance. About 100 stars, all told, have had their parallaxmeasured with a greater or less degree of probability. The work isgoing on from year to year, each successive astronomer who takes it upbeing able, as a general rule, to avail himself of better instrumentsor to use a better method. But, after all, the distances of even someof the 100 stars carefully measured must still remain quite doubtful. 

Let us now return to the idea of dividing the space in which theuniverse is situated into concentric spheres drawn at various distancesaround our system as a centre. Here we shall take as our standard adistance 400, 000 times that of the sun from the earth. Regarding thisas a unit, we imagine ourselves to measure out in any direction adistance twice as great as this--then another equal distance, makingone three times as great, and so indefinitely. We then have successivespheres of which we take the nearer one as the unit. The total spacefilled by the second sphere will be 8 times the unit; that of the thirdspace 27 times, and so on, as the cube of each distance. Since eachsphere includes all those within it, the volume of space between eachtwo spheres will be proportional to the difference of thesenumbers--that is, to 1, 7, 19, etc. Comparing these volumes with thenumber of stars probably within them, the general result up to thepresent time is that the number of stars in any of these spheres willbe about equal to the units of volume which they comprise, when we takefor this unit the smallest and innermost of the spheres, having aradius 400, 000 times the sun's distance. We are thus enabled to formsome general idea of how thickly the stars are sown through space. Wecannot claim any numerical exactness for this idea, but in the absenceof better methods it does afford us some basis for reasoning. 

Now we can carry on our computation as we supposed the farmer tomeasure the extent of his wheat-field. Let us suppose that there are125, 000, 000 stars in the heavens. This is an exceedingly roughestimate, but let us make the supposition for the time being. Acceptingthe view that they are nearly equally scattered throughout space, itwill follow that they must be contained within a volume equal to125, 000, 000 times the sphere we have taken as our unit. We find thedistance of the surface of this sphere by extracting the cube root ofthis number, which gives us 500. We may, therefore, say, as the resultof a very rough estimate, that the number of stars we have supposedwould be contained within a distance found by multiplying 400, 000 timesthe distance of the sun by 500; that is, that they are contained withina region whose boundary is 200, 000, 000 times the distance of the sun. This is a distance through which light would travel in about 3300 years. 

It is not impossible that the number of stars is much greater than thatwe have supposed. Let us grant that there are eight times as many, or1, 000, 000, 000. Then we should have to extend the boundary of ouruniverse twice as far, carrying it to a distance which light wouldrequire 6600 years to travel. 

There is another method of estimating the thickness with which starsare sown through space, and hence the extent of the universe, theresult of which will be of interest. It is based on the proper motionof the stars. One of the greatest triumphs of astronomy of our time hasbeen the measurement of the actual speed at which many of the stars aremoving to or from us in space. These measures are made with thespectroscope. Unfortunately, they can be best made only on the brighterstars--becoming very difficult in the case of stars not plainly visibleto the naked eye. Still the motions of several hundreds have beenmeasured and the number is constantly increasing. 

A general result of all these measures and of other estimates may besummed up by saying that there is a certain average speed with whichthe individual stars move in space; and that this average is abouttwenty miles per second. We are also able to form an estimate as towhat proportion of the stars move with each rate of speed from thelowest up to a limit which is probably as high as 150 miles per second. Knowing these proportions we have, by observation of the proper motionsof the stars, another method of estimating how thickly they arescattered in space; in other words, what is the volume of space which, on the average, contains a single star. This method gives a thicknessof the stars greater by about twenty-five per cent, than that derivedfrom the measures of parallax. That is to say, a sphere like the secondwe have proposed, having a radius 800, 000 times the distance of thesun, and therefore a diameter 1, 600, 000 times this distance, would, judging by the proper motions, have ten or twelve stars containedwithin it, while the measures of parallax only show eight stars withinthe sphere of this diameter having the sun as its centre. Theprobabilities are in favor of the result giving the greater thicknessof the stars. But, after all, the discrepancy does not change thegeneral conclusion as to the limits of the visible universe. If wecannot estimate its extent with the same certainty that we candetermine the size of the earth, we can still form a general idea of it. 

The estimates we have made are based on the supposition that the starsare equally scattered in space. We have good reason to believe thatthis is true of all the stars except those of the Milky Way. But, afterall, the latter probably includes half the whole number of starsvisible with a telescope, and the question may arise whether ourresults are seriously wrong from this cause. This question can best besolved by yet another method of estimating the average distance ofcertain classes of stars. 

The parallaxes of which we have heretofore spoken consist in the changein the direction of a star produced by the swing of the earth from oneside of its orbit to the other. But we have already remarked that oursolar system, with the earth as one of its bodies, has been journeyingstraightforward through space during all historic times. It follows, therefore, that we are continually changing the position from which weview the stars, and that, if the latter were at rest, we could, bymeasuring the apparent speed with which they are moving in the oppositedirection from that of the earth, determine their distance. But sinceevery star has its own motion, it is impossible, in any one case, todetermine how much of the apparent motion is due to the star itself, and how much to the motion of the solar system through space. Yet, bytaking general averages among groups of stars, most of which areprobably near each other, it is possible to estimate the averagedistance by this method. When an attempt is made to apply it, so as toobtain a definite result, the astronomer finds that the data nowavailable for the purpose are very deficient. The proper motion of astar can be determined only by comparing its observed position in theheavens at two widely separate epochs. Observations of sufficientprecision for this purpose were commenced about 1750 at the GreenwichObservatory, by Bradley, then Astronomer Royal of England. But out of3000 stars which he determined, only a few are available for thepurpose. Even since his time, the determinations made by eachgeneration of astronomers have not been sufficiently complete andsystematic to furnish the material for anything like a precisedetermination of the proper motions of stars. To determine a singleposition of any one star involves a good deal of computation, and if wereflect that, in order to attack the problem in question in asatisfactory way, we should have observations of 1, 000, 000 of thesebodies made at intervals of at least a considerable fraction of acentury, we see what an enormous task the astronomers dealing with thisproblem have before them, and how imperfect must be any determinationof the distance of the stars based on our motion through space. So faras an estimate can be made, it seems to agree fairly well with theresults obtained by the other methods. Speaking roughly, we havereason, from the data so far available, to believe that the stars ofthe Milky Way are situated at a distance between 100, 000, 000 and200, 000, 000 times the distance of the sun. At distances less than thisit seems likely that the stars are distributed through space with someapproach to uniformity. We may state as a general conclusion, indicatedby several methods of making the estimate, that nearly all the starswhich we can see with our telescopes are contained within a sphere notlikely to be much more than 200, 000, 000 times the distance of the sun. 

The inquiring reader may here ask another question. Granting that allthe stars we can see are contained within this limit, may there not beany number of stars outside the limit which are invisible only becausethey are too far away to be seen?

This question may be answered quite definitely if we grant that lightfrom the most distant stars meets with no obstruction in reaching us. The most conclusive answer is afforded by the measure of starlight. Ifthe stars extended out indefinitely, then the number of those of eachorder of magnitude would be nearly four times that of the magnitudenext brighter. For example, we should have nearly four times as manystars of the sixth magnitude as of the fifth; nearly four times as manyof the seventh as of the sixth, and so on indefinitely. Now, it isactually found that while this ratio of increase is true for thebrighter stars, it is not so for the fainter ones, and that theincrease in the number of the latter rapidly falls off when we makecounts of the fainter telescopic stars. In fact, it has long been knownthat, were the universe infinite in extent, and the stars equallyscattered through all space, the whole heavens would blaze with thelight of countless millions of distant stars separately invisible evenwith the telescope. 

The only way in which this conclusion can be invalidated is by thepossibility that the light of the stars is in some way extinguished orobstructed in its passage through space. A theory to this effect waspropounded by Struve nearly a century ago, but it has since been foundthat the facts as he set them forth do not justify the conclusion, which was, in fact, rather hypothetical. The theories of modern scienceconverge towards the view that, in the pure ether of space, no singleray of light can ever be lost, no matter how far it may travel. Butthere is another possible cause for the extinction of light. During thelast few years discoveries of dark and therefore invisible stars havebeen made by means of the spectroscope with a success which would havebeen quite incredible a very few years ago, and which, even to-day, must excite wonder and admiration. The general conclusion is that, besides the shining stars which exist in space, there may be any numberof dark ones, forever invisible in our telescopes. May it not be thatthese bodies are so numerous as to cut off the light which we wouldotherwise receive from the more distant bodies of the universe? It is, of course, impossible to answer this question in a positive way, butthe probable conclusion is a negative one. We may say with certaintythat dark stars are not so numerous as to cut off any important part ofthe light from the stars of the Milky Way, because, if they did, thelatter would not be so clearly seen as it is. Since we have reason tobelieve that the Milky Way comprises the more distant stars of oursystem, we may feel fairly confident that not much light can be cut offby dark bodies from the most distant region to which our telescopes canpenetrate. Up to this distance we see the stars just as they are. Evenwithin the limit of the universe as we understand it, it is likely thatmore than one-half the stars which actually exist are too faint to beseen by human vision, even when armed with the most powerfultelescopes. But their invisibility is due only to their distance andthe faintness of their intrinsic light, and not to any obstructingagency. 

The possibility of dark stars, therefore, does not invalidate thegeneral conclusions at which our survey of the subject points. Theuniverse, so far as we can see it, is a bounded whole. It is surroundedby an immense girdle of stars, which, to our vision, appears as theMilky Way. While we cannot set exact limits to its distance, we may yetconfidently say that it is bounded. It has uniformities running throughits vast extent. Could we fly out to distances equal to that of theMilky Way, we should find comparatively few stars beyond the limits ofthat girdle. It is true that we cannot set any definite limit and saythat beyond this nothing exists. What we can say is that the regioncontaining the visible stars has some approximation to a boundary. Wemay fairly anticipate that each successive generation of astronomers, through coming centuries, will obtain a little more light on thesubject--will be enabled to make more definite the boundaries of oursystem of stars, and to draw more and more probable conclusions as tothe existence or non-existence of any object outside of it. The wiseinvestigator of to-day will leave to them the task of putting theproblem into a more positive shape. 

V

MAKING AND USING A TELESCOPE

The impression is quite common that satisfactory views of the heavenlybodies can be obtained only with very large telescopes, and that theowner of a small one must stand at a great disadvantage alongside ofthe fortunate possessor of a great one. This is not true to the extentcommonly supposed. Sir William Herschel would have been delighted toview the moon through what we should now consider a very modestinstrument; and there are some objects, especially the moon, whichcommonly present a more pleasing aspect through a small telescope thanthrough a large one. The numerous owners of small telescopes throughoutthe country might find their instruments much more interesting thanthey do if they only knew what objects were best suited to examinationwith the means at their command. There are many others, not possessorsof telescopes, who would like to know how one can be acquired, and towhom hints in this direction will be valuable. We shall therefore givesuch information as we are able respecting the construction of atelescope, and the more interesting celestial objects to which it maybe applied. 

Whether the reader does or does not feel competent to undertake themaking of a telescope, it may be of interest to him to know how it isdone. First, as to the general principles involved, it is generallyknown that the really vital parts of the telescope, which by theircombined action perform the office of magnifying the object looked at, are two in number, the OBJECTIVE and the EYE-PIECE. The former bringsthe rays of light which emanate from the object to the focus where theimage of the object is formed. The eye-piece enables the observer tosee this image to the best advantage. 

The functions of the objective as well as those of the eye-piece may, to a certain extent, each be performed by a single lens. Galileo andhis contemporaries made their telescopes in this way, because they knewof no way in which two lenses could be made to do better than one. Butevery one who has studied optics knows that white light passing througha single lens is not all brought to the same focus, but that the bluelight will come to a focus nearer the objective than the red light. There will, in fact, be a succession of images, blue, green, yellow, and red, corresponding to the colors of the spectrum. It is impossibleto see these different images clearly at the same time, because each ofthem will render all the others indistinct. 

The achromatic object-glass, invented by Dollond, about 1750, obviatesthis difficulty, and brings all the rays to nearly the same focus. Nearly every one interested in the subject is aware that thisobject-glass is composed of two lenses--a concave one of flint-glassand a convex one of crown-glass, the latter being on the side towardsthe object. This is the one vital part of the telescope, theconstruction of which involves the greatest difficulty. Once inpossession of a perfect object-glass, the rest of the telescope is amatter of little more than constructive skill which there is nodifficulty in commanding. 

The construction of the object-glass requires two completely distinctprocesses: the making of the rough glass, which is the work of theglass-maker; and the grinding and polishing into shape, which is thework of the optician. The ordinary glass of commerce will not answerthe purpose of the telescope at all, because it is not sufficientlyclear and homogeneous. OPTICAL GLASS, as it is called, must be made ofmaterials selected and purified with the greatest care, and worked in amore elaborate manner than is necessary in any other kind of glass. Inthe time of Dollond it was found scarcely possible to make good disksof flint-glass more than three or four inches in diameter. Early in thepresent century, Guinand, of Switzerland, invented a process by whichdisks of much larger size could be produced. In conjunction with thecelebrated Fraunhofer he made disks of nine or ten inches in diameter, which were employed by his colaborer in constructing the telescopeswhich were so famous in their time. He was long supposed to be inpossession of some secret method of avoiding the difficulties which hispredecessors had met. It is now believed that this secret, if one itwas, consisted principally in the constant stirring of the molten glassduring the process of manufacture. However this may be, it is a curioushistorical fact that the most successful makers of these great disks ofglass have either been of the family of Guinand, or successors, in themanagement of the family firm. It was Feil, a son-in-law or nearrelative, who made the glass from which Clark fabricated the lenses ofthe great telescope of the Lick Observatory. His successor, Mantois, ofParis, carried the art to a point of perfection never beforeapproached. The transparency and uniformity of his disks as well as thegreat size to which he was able to carry them would suggest that he andhis successors have out-distanced all competitors in the process. He itwas who made the great 40-inch lens for the Yerkes Observatory. 

As optical glass is now made, the material is constantly stirred withan iron rod during all the time it is melting in the furnace, and afterit has begun to cool, until it becomes so stiff that the stirring hasto cease. It is then placed, pot and all, in the annealing furnace, where it is kept nearly at a melting heat for three weeks or more, according to the size of the pot. When the furnace has cooled off, theglass is taken out, and the pot is broken from around it, leaving onlythe central mass of glass. Having such a mass, there is no trouble inbreaking it up into pieces of all desirable purity, and sufficientlylarge for moderate-sized telescopes. But when a great telescope of twofeet aperture or upward is to be constructed, very delicate andlaborious operations have to be undertaken. The outside of the glasshas first to be chipped off, because it is filled with impurities fromthe material of the pot itself. But this is not all. Veins of unequaldensity are always found extending through the interior of the mass, noway of avoiding them having yet been discovered. They are supposed toarise from the materials of the pot and stirring rod, which becomemixed in with the glass in consequence of the intense heat to which allare subjected. These veins must, so far as possible, be ground orchipped out with the greatest care. The glass is then melted again, pressed into a flat disk, and once more put into the annealing oven. Infact, the operation of annealing must be repeated every time the glassis melted. When cooled, it is again examined for veins, of which greatnumbers are sure to be found. The problem now is to remove these bycutting and grinding without either breaking the glass in two orcutting a hole through it. If the parts of the glass are onceseparated, they can never be joined without producing a bad scar at thepoint of junction. So long, however, as the surface is unbroken, theinterior parts of the glass can be changed in form to any extent. Having ground out the veins as far as possible, the glass is to beagain melted, and moulded into proper shape. In this mould great caremust be taken to have no folding of the surface. Imagining the latterto be a sort of skin enclosing the melted glass inside, it must beraised up wherever the glass is thinnest, and the latter allowed toslowly run together beneath it. 

[Illustration with caption: THE GLASS DISK. ]

If the disk is of flint, all the veins must be ground out on the firstor second trial, because after two or three mouldings the glass willlose its transparency. A crown disk may, however, be melted a number oftimes without serious injury. In many cases--perhaps the majority--theartisan finds that after all his months of labor he cannot perfectlyclear his glass of the noxious veins, and he has to break it up intosmaller pieces. When he finally succeeds, the disk has the form of athin grindstone two feet or upward in diameter, according to the sizeof the telescope to be made, and from two to three inches in thickness. The glass is then ready for the optician. 

[Illustration with caption: THE OPTICIAN'S TOOL. ]

The first process to be performed by the optician is to grind the glassinto the shape of a lens with perfectly spherical surfaces. The convexsurface must be ground in a saucer-shaped tool of corresponding form. It is impossible to make a tool perfectly spherical in the first place, but success may be secured on the geometrical principle that twosurfaces cannot fit each other in all positions unless both areperfectly spherical. The tool of the optician is a very simple affair, being nothing more than a plate of iron somewhat larger, perhaps afourth, than the lens to be ground to the corresponding curvature. Inorder to insure its changing to fit the glass, it is covered on theinterior with a coating of pitch from an eighth to a quarter of an inchthick. This material is admirably adapted to the purpose because itgives way certainly, though very slowly, to the pressure of the glass. In order that it may have room to change its form, grooves are cutthrough it in both directions, so as to leave it in the form ofsquares, like those on a chess-board. 

[Illustration with caption: THE OPTICIAN'S TOOL. ]

It is then sprinkled over with rouge, moistened with water, and gentlywarmed. The roughly ground lens is then placed upon it, and moved fromside to side. The direction of the motion is slightly changed withevery stroke, so that after a dozen or so of strokes the lines ofmotion will lie in every direction on the tool. This change ofdirection is most readily and easily effected by the operator slowlywalking around as he polishes, at the same time the lens is to beslowly turned around either in the opposite direction or more rapidlyyet in the same direction, so that the strokes of the polisher shallcross the lens in all directions. This double motion insures every partof the lens coming into contact with every part of the polisher, andmoving over it in every direction. 

Then whatever parts either of the lens or of the polisher may be toohigh to form a spherical surface will be gradually worn down, thussecuring the perfect sphericity of both. 

[Illustration with caption: GRINDING A LARGE LENS. ]

When the polishing is done by machinery, which is the custom in Europe, with large lenses, the polisher is slid back and forth over the lens bymeans of a crank attached to a revolving wheel. The polisher is at thesame time slowly revolving around a pivot at its centre, which pivotthe crank works into, and the glass below it is slowly turned in anopposite direction. Thus the same effect is produced as in the othersystem. Those who practice this method claim that by thus usingmachinery the conditions of a uniform polish for every part of thesurface can be more perfectly fulfilled than by a hand motion. Theresults, however, do not support this view. No European optician willclaim to do better than the American firm of Alvan Clark & Sons inproducing uniformly good object-glasses, and this firm always does thework by hand, moving the glass over the polisher, and not the polisherover the glass. 

Having brought both flint and crown glasses into proper figure by thisprocess, they are joined together, and tested by observations eitherupon a star in the heavens, or some illuminated point at a littledistance on the ground. The reflection of the sun from a drop ofquicksilver, a thermometer bulb, or even a piece of broken bottle, makes an excellent artificial star. The very best optician will alwaysfind that on a first trial his glass is not perfect. He will find thathe has not given exactly the proper curves to secure achromatism. Hemust then change the figure of one or both the glasses by polishing itupon a tool of slightly different curvature. He may also find thatthere is some spherical aberration outstanding. He must then alter hiscurve so as to correct this. The correction of these littleimperfections in the figures of the lenses so as to secure perfectvision through them is the most difficult branch of the art of theoptician, and upon his skill in practising it will depend more thanupon anything else his ultimate success and reputation. The shaping ofa pair of lenses in the way we have described is not beyond the powerof any person of ordinary mechanical ingenuity, possessing thenecessary delicacy of touch and appreciation of the problem he isattacking. But to make a perfect objective of considerable size, whichshall satisfy all the wants of the astronomer, is an undertakingrequiring such accuracy of eyesight, and judgment in determining wherethe error lies, and such skill in manipulating so as to remove thedefects, that the successful men in any one generation can be countedon one's fingers. 

In order that the telescope may finally perform satisfactorily it isnot sufficient that the lenses should both be of proper figure; theymust also both be properly centred in their cells. If either lens istipped aside, or slid out from its proper central line, the definitionwill be injured. As this is liable to happen with almost any telescope, we shall explain how the proper adjustment is to be made. 

The easiest way to test this adjustment is to set the cell with the twoglasses of the objective in it against a wall at night, and going to ashort distance, observe the reflection in the glass of the flame of acandle held in the hand. Three or four reflections will be seen fromthe different surfaces. The observer, holding the candle before hiseye, and having his line of sight as close as possible to the flame, must then move until the different images of the flame coincide witheach other. If he cannot bring them into coincidence, owing todifferent pairs coinciding on different sides of the flame, the glassesare not perfectly centred upon each other. When the centring isperfect, the observer having the light in the line of the axes of thelenses, and (if it were possible to do so) looking through the centreof the flame, would see the three or four images all in coincidence. Ashe cannot see through the flame itself, he must look first on one sideand then on the other, and see if the arrangement of the images seen inthe lenses is symmetrical. If, going to different distances, he findsno deviation from symmetry, in this respect the adjustment is nearenough for all practical purposes. 

A more artistic instrument than a simple candle is a small concavereflector pierced through its centre, such as is used by physicians inexamining the throat. 

[Illustration with caption: IMAGE OF CANDLE-FLAME IN OBJECT-GLASS. ]

[Illustration with caption: TESTING ADJUSTMENT OF OBJECT-GLASS. ]

Place this reflector in the prolongation of the optical axis, set thecandle so that the light from the reflector shall be shown through theglass, and look through the opening. Images of the reflector itselfwill then be seen in the object-glass, and if the adjustment isperfect, the reflector can be moved so that they will all come intocoincidence together. 

When the objective is in the tube of the telescope, it is always wellto examine this adjustment from time to time, holding the candle sothat its light shall shine through the opening perpendicularly upon theobject-glass. The observer looks upon one side of the flame, and thenupon the other, to see if the images are symmetrical in the differentpositions. If in order to see them in this way the candle has to bemoved to one side of the central line of the tube, the whole objectivemust be adjusted. If two images coincide in one position of thecandle-flame, and two in another position, so that they cannot all bebrought together in any position, it shows that the glasses are notproperly adjusted in their cell. It may be remarked that this lastadjustment is the proper work of the optician, since it is so difficultthat the user of the telescope cannot ordinarily effect it. But theperpendicularity of the whole objective to the tube of the telescope isliable to be deranged in use, and every one who uses such an instrumentshould be able to rectify an error of this kind. 

The question may be asked, How much of a telescope can an amateurobserver, under any circumstances, make for himself? As a general rule, his work in this direction must be confined to the tube and themounting. We should not, it is true, dare to assert that any ingeniousyoung man, with a clear appreciation of optical principles, could notsoon learn to grind and polish an object-glass for himself by themethod we have described, and thus obtain a much better instrument thanGalileo ever had at his command. But it would be a wonderful success ifhis home-made telescope was equal to the most indifferent one which canbe bought at an optician's. The objective, complete in itself, can bepurchased at prices depending upon the size. 

[Footnote: The following is a rough rule for getting an idea of theprice of an achromatic objective, made to order, of the finest quality. Take the cube of the diameter in inches, or, which is the same thing, calculate the contents of a cubical box which would hold a sphere ofthe same diameter as the clear aperture of the glass. The price of theglass will then range from $1 to $1. 75 for each cubic inch in this box. For example, the price of a four-inch objective will probably rangefrom $64 to $112. Very small object-glasses of one or two inches may bea little higher than would be given by this rule. Instruments which arenot first-class, but will answer most of the purposes of the amateur, are much cheaper. ]

[Illustration with caption: A VERY PRIMITIVE MOUNTING FOR A TELESCOPE. ]

The tube for the telescope may be made of paper, by pasting a greatnumber of thicknesses around a long wooden cylinder. A yet better tubeis made of a simple wooden box. The best material, however, is metal, because wood and pasteboard are liable both to get out of shape, and toswell under the influence of moisture. Tin, if it be of sufficientthickness, would be a very good material. The brighter it is kept, thebetter. The work of fitting the objective into one end of a tin tube ofdouble thickness, and properly adjusting it, will probably be quitewithin the powers of the ordinary amateur. The fitting of the eye-pieceinto the other end of the tube will require some skill and care both onhis own part and that of his tinsmith. 

Although the construction of the eye-piece is much easier than that ofthe objective, since the same accuracy in adjusting the curves is notnecessary, yet the price is lower in a yet greater degree, so that theamateur will find it better to buy than to make his eye-piece, unlesshe is anxious to test his mechanical powers. For a telescope which hasno micrometer, the Huyghenian or negative eye-piece, as it is commonlycalled, is the best. As made by Huyghens, it consists of twoplano-convex lenses, with their plane sides next the eye, as shown inthe figure. 

[Illustration with caption: THE HUYGHENIAN EYE-PIECE. ]

So far as we have yet described our telescope it is optically complete. If it could be used as a spy-glass by simply holding it in the hand, and pointing at the object we wish to observe, there would be littleneed of any very elaborate support. But if a telescope, even of thesmallest size, is to be used with regularity, a proper "mounting" is asessential as a good instrument. Persons unpractised in the use of suchinstruments are very apt to underrate the importance of thoseaccessories which merely enable us to point the telescope. An idea ofwhat is wanted in the mounting may readily be formed if the reader willtry to look at a star with an ordinary good-sized spy-glass held in thehand, and then imagine the difficulties he meets with multiplied byfifty. 

The smaller and cheaper telescopes, as commonly sold, are mounted on asimple little stand, on which the instrument admits of a horizontal andvertical motion. If one only wants to get a few glimpses of a celestialobject, this mounting will answer his purpose. But to make anythinglike a study of a celestial body, the mounting must be an equatorialone; that is, one of the axes around which the telescope moves must beinclined so as to point towards the pole of the heavens, which is nearthe polar star. This axis will then make an angle with the horizonequal to the latitude of the place. The telescope cannot, however, bemounted directly on this axis, but must be attached to a second one, itself fastened to this one. 

[Illustration with caption: SECTION OF THE PRIMITIVE MOUNTING. P P. Polar axis, bearing a fork at the upper end A. Declination axis passingthrough the fork E. Section of telescope tube C. Weight to balance thetube. ]

When mounted in this way, an object can be followed in its diurnalmotion from east to west by turning on the polar axis alone. But if thegreatest facility in use is required, this motion must be performed byclock-work. A telescope with this appendage will commonly cost onethousand dollars and upward, so that it is not usually applied to verysmall ones. 

We will now suppose that the reader wishes to purchase a telescope oran object-glass for himself, and to be able to judge of itsperformance. He must have the object-glass properly adjusted in itstube, and must use the highest power; that is, the smallest eye-piece, which he intends to use in the instrument. Of course he understandsthat in looking directly at a star or a celestial object it must appearsharp in outline and well defined. But without long practice with goodinstruments, this will not give him a very definite idea. If the personwho selects the telescope is quite unpractised, it is possible that hecan make the best test by ascertaining at what distance he can readordinary print. To do this he should have an eye-piece magnifying aboutfifty times for each inch of aperture of the telescope. For instance, if his telescope is three inches clear aperture, then his eye-pieceshould magnify one hundred and fifty times; if the aperture is fourinches, one magnifying two hundred times may be used. This magnifyingpower is, as a general rule, about the highest that can beadvantageously used with any telescope. Supposing this magnifying powerto be used, this page should be legible at a distance of four feet forevery unit of magnifying power of the telescope. For example, with apower of 100, it should be legible at a distance of 400 feet; with apower of 200, at 800 feet, and so on. To put the condition into anothershape: if the telescope will read the print at a distance of 150 feetfor each inch of aperture with the best magnifying power, itsperformance is at least not very bad. If the magnifying power is lessthan would be given by this rule, the telescope should perform a littlebetter; for instance, a three-inch telescope with a power of 60 shouldmake this page legible at a distance of 300 feet, or four feet for eachunit of power. 

The test applied by the optician is much more exact, and also moreeasy. He points the instrument at a star, or at the reflection of thesun's rays from a small round piece of glass or a globule ofquicksilver several hundred yards away, and ascertains whether the raysare all brought to a focus. This is not done by simply looking at thestar, but by alternately pushing the eye-piece in beyond the point ofdistinct vision and drawing it out past the point. In this way theimage of the star will appear, not as a point, but as a round disk oflight. If the telescope is perfect, this disk will appear round and ofuniform brightness in either position of the eye-piece. But if there isany spherical aberration or differences of density in different partsof the glass, the image will appear distorted in various ways. If thespherical aberration is not correct, the outer rim of the disk will bebrighter than the centre when the eye-piece is pushed in, and thecentre will be the brighter when it is drawn out. If the curves of theglass are not even all around, the image will appear oval in one or theother position. If there are large veins of unequal density, wings ornotches will be seen on the image. If the atmosphere is steady, theimage, when the eye-piece is pushed in, will be formed of a greatnumber of minute rings of light. If the glass is good, these rings willbe round, unbroken, and equally bright. We present several figuresshowing how these spectral images, as they are sometimes called, willappear; first, when the eye-piece is pushed in, and secondly, when itis drawn out, with telescopes of different qualities. 

We have thus far spoken only of the refracting telescope, because it isthe kind with which an observer would naturally seek to supply himself. At the same time there is little doubt that the construction of areflector of moderate size is easier than that of a correspondingrefractor. The essential part of the reflector is a slightly concavemirror of any metal which will bear a high polish. This mirror may beground and polished in the same way as a lens, only the tool must beconvex. 

[Illustration with caption: SPECTRAL IMAGES OF STARS; THE UPPER LINESHOWING HOW THEY APPEAR WITH THE EYE-PIECE PUSHED IN, THE LOWER WITHTHE EYE-PIECE DRAWN OUT. 

A The telescope is all right B Spherical aberration shown by the lightand dark centre C The objective is not spherical but elliptical D Theglass not uniform--a very bad and incurable case E One side of theobjective nearer than the other. Adjust it]

Of late years it has become very common to make the mirror of glass andto cover the reflecting face with an exceedingly thin film of silver, which can be polished by hand in a few minutes. Such a mirror differsfrom our ordinary looking-glass in that the coating of silver is put onthe front surface, so that the light does not pass through the glass. Moreover, the coating of silver is so thin as to be almost transparent:in fact, the sun may be seen through it by direct vision as a faintblue object. Silvered glass reflectors made in this way are extensivelymanufactured in London, and are far cheaper than refracting telescopesof corresponding size. Their great drawback is the want of permanencein the silver film. In the city the film will ordinarily tarnish in afew months from the sulphurous vapors arising from gaslights and othersources, and even in the country it is very difficult to preserve themirror from the contact of everything that will injure it. Inconsequence, the possessor of such a telescope, if he wishes to keep itin order, must always be prepared to resilver and repolish it. To dothis requires such careful manipulation and management of the chemicalsthat it is hardly to be expected that an amateur will take the troubleto keep his telescope in order, unless he has a taste for chemistry aswell as for astronomy. 

The curiosity to see the heavenly bodies through great telescopes is sowide-spread that we are apt to forget how much can be seen and donewith small ones. The fact is that a large proportion of theastronomical observations of past times have been made with what weshould now regard as very small instruments, and a good deal of thesolid astronomical work of the present time is done with meridiancircles the apertures of which ordinarily range from four to eightinches. One of the most conspicuous examples in recent times of how amoderate-sized instrument may be utilized is afforded by thediscoveries of double stars made by Mr. S. W. Burnham, of Chicago. Provided with a little six-inch telescope, procured at his own expensefrom the Messrs. Clark, he has discovered many hundred double stars sodifficult that they had escaped the scrutiny of Maedler and theStruves, and gained for himself one of the highest positions among theastronomers of the day engaged in the observation of these objects. Itwas with this little instrument that on Mount Hamilton, California--afterward the site of the great Lick Observatory--hediscovered forty-eight new double stars, which had remained unnoticedby all previous observers. First among the objects which showbeautifully through moderate instruments stands the moon. People whowant to see the moon at an observatory generally make the mistake oflooking when the moon is full, and asking to see it through the largesttelescope. Nothing can then be made out but a brilliant blaze of light, mottled with dark spots, and crossed by irregular bright lines. Thebest time to view the moon is near or before the first quarter, or whenshe is from three to eight days old. The last quarter is of courseequally favorable, so far as seeing is concerned, only one must be upafter midnight to see her in that position. Seen through a three orfour inch telescope, a day or two before the first quarter, about halfan hour after sunset, and with a magnifying power between fifty and onehundred, the moon is one of the most beautiful objects in the heavens. Twilight softens her radiance so that the eye is not dazzled as it willbe when the sky is entirely dark. The general aspect she then presentsis that of a hemisphere of beautiful chased silver carved out incurious round patterns with a more than human skill. If, however, onewishes to see the minute details of the lunar surface, in which many ofour astronomers are now so deeply interested, he must use a highermagnifying power. The general beautiful effect is then lessened, butmore details are seen. Still, it is hardly necessary to seek for a verylarge telescope for any investigation of the lunar surface. I very muchdoubt whether any one has ever seen anything on the moon which couldnot be made out in a clear, steady atmosphere with a six-inch telescopeof the first class. 

Next to the moon, Saturn is among the most beautiful of celestialobjects. Its aspect, however, varies with its position in its orbit. Twice in the course of a revolution, which occupies nearly thirtyyears, the rings are seen edgewise, and for a few days are invisibleeven in a powerful telescope. For an entire year their form may bedifficult to make out with a small telescope. These unfavorableconditions occur in 1907 and 1921. Between these dates, especially forsome years after 1910, the position of the planet in the sky will bethe most favorable, being in northern declination, near its perihelion, and having its rings widely open. We all know that Saturn is plainlyvisible to the naked eye, shining almost like a star of the firstmagnitude, so that there is no difficulty in finding it if one knowswhen and where to look. In 1906-1908 its oppositions occur in the monthof September. In subsequent years, it will occur a month later everytwo and a half years. The ring can be seen with a common, goodspy-glass fastened to a post so as to be steady. A four or five-inchtelescope will show most of the satellites, the division in the ring, and, when the ring is well opened, the curious dusky ring discovered byBond. This "crape ring, " as it is commonly called, is one of the mostsingular phenomena presented by that planet. 

It might be interesting to the amateur astronomer with a keen eye and atelescope of four inches aperture or upward to frequently scrutinizeSaturn, with a view of detecting any extraordinary eruptions upon hissurface, like that seen by Professor Hall in 1876. On December 7th ofthat year a bright spot was seen upon Saturn's equator. It elongateditself from day to day, and remained visible for several weeks. Such athing had never before been known upon this planet, and had it not beenthat Professor Hall was engaged in observations upon the satellites, itwould not have been seen then. A similar spot on the planet wasrecorded in 1902, and much more extensively noticed. On this occasionthe spot appeared in a higher latitude from the planet's equator thandid Professor Hall's. At this appearance the time of the planet'srevolution on its axis was found to be somewhat greater than in 1876, in accordance with the general law exhibited in the rotations of thesun and of Jupiter. Notwithstanding their transient character, thesetwo spots have afforded the only determination of the time ofrevolution of Saturn which has been made since Herschel the elder. 

[Illustration with caption: THE GREAT REFRACTOR OF THE NATIONALOBSERVATORY AT WASHINGTON]

Of the satellites of Saturn the brightest is Titan, which can be seenwith the smallest telescope, and revolves around the planet in fifteendays. Iapetus, the outer satellite, is remarkable for varying greatlyin brilliancy during its revolution around the planet. Any one havingthe means and ability to make accurate photometrical estimates of thelight of this satellite in all points of its orbit, can thereby rendera valuable service to astronomy. 

The observations of Venus, by which the astronomers of the last centurysupposed themselves to have discovered its time of rotation on itsaxis, were made with telescopes much inferior to ours. Although theirobservations have not been confirmed, some astronomers are stillinclined to think that their results have not been refuted by thefailure of recent observers to detect those changes which the olderones describe on the surface of the planet. With a six-inch telescopeof the best quality, and with time to choose the most favorable moment, one will be as well equipped to settle the question of the rotation ofVenus as the best observer. The few days near each inferior conjunctionare especially to be taken advantage of. 

The questions to be settled are two: first, are there any dark spots orother markings on the disk? second, are there any irregularities in theform of the sharp cusps? The central portions of the disk are muchdarker than the outline, and it is probably this fact which has givenrise to the impression of dark spots. Unless this apparent darknesschanges from time to time, or shows some irregularity in its outline, it cannot indicate any rotation of the planet. The best time toscrutinize the sharp cusps will be when the planet is nearly on theline from the earth to the sun. The best hour of the day is nearsunset, the half-hour following sunset being the best of all. But ifVenus is near the sun, she will after sunset be too low down to be wellseen, and must be looked at late in the afternoon. 

The planet Mars must always be an object of great interest, because ofall the heavenly bodies it is that which appears to bear the greatestresemblance to the earth. It comes into opposition at intervals of alittle more than two years, and can be well seen only for a month ortwo before and after each opposition. It is hopeless to look for thesatellites of Mars with any but the greatest telescopes of the world. But the markings on the surface, from which the time of rotation hasbeen determined, and which indicate a resemblance to the surface of ourown planet, can be well seen with telescopes of six inches aperture andupward. One or both of the bright polar spots, which are supposed to bedue to deposits of snow, can be seen with smaller telescopes when thesituation of the planet is favorable. 

The case is different with the so-called canals discovered bySchiaparelli in 1877, which have ever since excited so much interest, and given rise to so much discussion as to their nature. The astronomerwho has had the best opportunities for studying them is Mr. PercivalLowell, whose observatory at Flaggstaff, Arizona, is finely situatedfor the purpose, while he also has one of the best if not the largestof telescopes. There the canals are seen as fine dark lines; but, eventhen, they must be fifty miles in breadth, so that the word "canal" maybe regarded as a misnomer. 

Although the planet Jupiter does not present such striking features asSaturn, it is of even more interest to the amateur astronomer, becausehe can study it with less optical power, and see more of the changesupon its surface. Every work on astronomy tells in a general way of thebelts of Jupiter, and many speculate upon their causes. The reader ofrecent works knows that Jupiter is supposed to be not a solid mass likethe earth, but a great globe of molten and vaporous matter, intermediate in constitution between the earth and the sun. The outersurface which we see is probably a hot mass of vapor hundreds of milesdeep, thrown up from the heated interior. The belts are probablycloudlike forms in this vaporous mass. Certain it is that they arecontinually changing, so that the planet seldom looks exactly the sameon two successive evenings. The rotation of the planet can be very wellseen by an hour's watching. In two hours an object at the centre of thedisk will move off to near the margin. 

The satellites of this planet, in their ever-varying phases, areobjects of perennial interest. Their eclipses may be observed with avery small telescope, if one knows when to look for them. To do thissuccessfully, and without waste of time, it is necessary to have anastronomical ephemeris for the year. All the observable phenomena arethere predicted for the convenience of observers. Perhaps the mostcurious observation to be made is that of the shadow of the satellitecrossing the disk of Jupiter. The writer has seen this perfectly with asix-inch telescope, and a much smaller one would probably show it well. With a telescope of this size, or a little larger, the satellites canbe seen between us and Jupiter. Sometimes they appear a little brighterthan the planet, and sometimes a little fainter. 

Of the remaining large planets, Mercury, the inner one, and Uranus andNeptune, the two outer ones, are of less interest than the others to anamateur with a small telescope, because they are more difficult to see. Mercury can, indeed, be observed with the smallest instrument, but nophysical configurations or changes have ever been made out upon hissurface. The question whether any such can be observed is still an openone, which can be settled only by long and careful scrutiny. A smalltelescope is almost as good for this purpose as a large one, becausethe atmospheric difficulties in the way of getting a good view of theplanet cannot be lessened by an increase of telescopic power. 

Uranus and Neptune are so distant that telescopes of considerable sizeand high magnifying power are necessary to show their disks. In smalltelescopes they have the appearance of stars, and the observer has noway of distinguishing them from the surrounding stars unless he cancommand the best astronomical appliances, such as star maps, circles onhis instrument, etc. It is, however, to be remarked, as a fact notgenerally known, that Uranus can be well seen with the naked eye if oneknows where to look for it. To recognize it, it is necessary to have anastronomical ephemeris showing its right ascension and declination, andstar maps showing where the parallels of right ascension anddeclination lie among the stars. When once found by the naked eye, there will, of course, be no difficulty in pointing the telescope uponit. 

Of celestial objects which it is well to keep a watch upon, and whichcan be seen to good advantage with inexpensive instruments, the sun maybe considered as holding the first place. Astronomers who make aspecialty of solar physics have, especially in this country, so manyother duties, and their view is so often interrupted by clouds, that acontinuous record of the spots on the sun and the changes they undergois hardly possible. Perhaps one of the most interesting and usefulpieces of astronomical work which an amateur can perform will consistof a record of the origin and changes of form of the solar spots andfaculae. What does a spot look like when it first comes into sight?Does it immediately burst forth with considerable magnitude, or does itbegin as the smallest visible speck, and gradually grow? When severalspots coalesce into one, how do they do it? When a spot breaks up intoseveral pieces, what is the seeming nature of the process? How do thegroups of brilliant points called faculae come, change, and grow? Allthese questions must no doubt be answered in various ways, according tothe behavior of the particular spot, but the record is rather meagre, and the conscientious and industrious amateur will be able to amusehimself by adding to it, and possibly may make valuable contributionsto science in the same way. 

Still another branch of astronomical observation, in which industry andskill count for more than expensive instruments, is the search for newcomets. This requires a very practised eye, in order that the comet maybe caught among the crowd of stars which flit across the field of viewas the telescope is moved. It is also necessary to be well acquaintedwith a number of nebulae which look very much like comets. The searchcan be made with almost any small telescope, if one is careful to use avery low power. With a four-inch telescope a power not exceeding twentyshould be employed. To search with ease, and in the best manner, theobserver should have what among astronomers is familiarly known as a"broken-backed telescope. " This instrument has the eye-piece on the endof the axis, where one would never think of looking for it. By turningthe instrument on this axis, it sweeps from one horizon through thezenith and over to the other horizon without the observer having tomove his head. This is effected by having a reflector in the centralpart of the instrument, which throws the rays of light at right anglesthrough the axis. 

[Illustration: THE "BROKEN-BACKED COMET-SEEKER"]

How well this search can be conducted by observers with limited meansat their disposal is shown by the success of several Americanobservers, among whom Messrs. W. R. Brooks, E. E. Barnard, and LewisSwift are well known. The cometary discoveries of these men afford anexcellent illustration of how much can be done with the smallest meanswhen one sets to work in the right spirit. 

The larger number of wonderful telescopic objects are to be sought forfar beyond the confines of the solar system, in regions from whichlight requires years to reach us. On account of their great distance, these objects generally require the most powerful telescopes to be seenin the best manner; but there are quite a number within the range ofthe amateur. Looking at the Milky Way, especially its southern part, ona clear winter or summer evening, tufts of light will be seen here andthere. On examining these tufts with a telescope, they will be found toconsist of congeries of stars. Many of these groups are of the greatestbeauty, with only a moderate optical power. Of all the groups in theMilky Way the best known is that in the sword-handle of Perseus, whichmay be seen during the greater part of the year, and is distinctlyvisible to the naked eye as a patch of diffused light. With thetelescope there are seen in this patch two closely connected clustersof stars, or perhaps we ought rather to say two centres of condensation. 

Another object of the same class is Proesepe in the constellationCancer. This can be very distinctly seen by the naked eye on a clearmoonless night in winter or spring as a faint nebulous object, surrounded by three small stars. The smallest telescope shows it as agroup of stars. 

Of all stellar objects, the great nebula of Orion is that which hasmost fascinated the astronomers of two centuries. It is distinctlyvisible to the naked eye, and may be found without difficulty on anywinter night. The three bright stars forming the sword-belt of Orionare known to every one who has noticed that constellation. Below thisbelt is seen another triplet of stars, not so bright, and lying in anorth and south direction. The middle star of this triplet is the greatnebula. At first the naked eye sees nothing to distinguish it fromother stars, but if closely scanned it will be seen to have a hazyaspect. A four-inch telescope will show its curious form. Not the leastinteresting of its features are the four stars known as the"Trapezium, " which are located in a dark region near its centre. Infact, the whole nebula is dotted with stars, which add greatly to theeffect produced by its mysterious aspect. 

The great nebula of Andromeda is second only to that of Orion ininterest. Like the former, it is distinctly visible to the naked eye, having the aspect of a faint comet. The most curious feature of thisobject is that although the most powerful telescopes do not resolve itinto stars, it appears in the spectroscope as if it were solid mattershining by its own light. 

The above are merely selections from the countless number of objectswhich the heavens offer to telescopic study. Many such are described inastronomical works, but the amateur can gratify his curiosity to almostany extent by searching them out for himself. 

[Illustration with caption: NEBULA IN ORION]

Ever since 1878 a red spot, unlike any before noticed, has generallybeen visible on Jupiter. At first it was for several years a veryconspicuous object, but gradually faded away, so that since 1890 it hasbeen made out only with difficulty. But it is now regarded as apermanent feature of the planet. There is some reason to believe it wasoccasionally seen long before attention was first attracted to it. Doubtless, when it can be seen at all, practice in observing suchobjects is more important than size of telescope. 

VI

WHAT THE ASTRONOMERS ARE DOING

In no field of science has human knowledge been more extended in ourtime than in that of astronomy. Forty years ago astronomical researchseemed quite barren of results of great interest or value to our race. The observers of the world were working on a traditional system, grinding out results in an endless course, without seeing any prospectof the great generalizations to which they might ultimately lead. Nowthis is all changed. A new instrument, the spectroscope, has beendeveloped, the extent of whose revelations we are just beginning tolearn, although it has been more than thirty years in use. Theapplication of photography has been so extended that, in some importantbranches of astronomical work, the observer simply photographs thephenomenon which he is to study, and then makes his observation on thedeveloped negative. 

The world of astronomy is one of the busiest that can be found to-day, and the writer proposes, with the reader's courteous consent, to takehim on a stroll through it and see what is going on. We may begin ourinspection with a body which is, for us, next to the earth, the mostimportant in the universe. I mean the sun. At the Greenwich Observatorythe sun has for more than twenty years been regularly photographed onevery clear day, with the view of determining the changes going on inits spots. In recent years these observations have been supplemented byothers, made at stations in India and Mauritius, so that by thecombination of all it is quite exceptional to have an entire day passwithout at least one photograph being taken. On these observations mustmainly rest our knowledge of the curious cycle of change in the solarspots, which goes through a period of about eleven years, but of whichno one has as yet been able to establish the cause. 

This Greenwich system has been extended and improved by an American. Professor George E. Hale, formerly Director of the Yerkes Observatory, has devised an instrument for taking photographs of the sun by a singleray of the spectrum. The light emitted by calcium, the base of lime, and one of the substances most abundant in the sun, is often selectedto impress the plate. 

The Carnegie Institution has recently organized an enterprise forcarrying on the study of the sun under a combination of betterconditions than were ever before enjoyed. The first requirement in sucha case is the ablest and most enthusiastic worker in the field, readyto devote all his energies to its cultivation. This requirement isfound in the person of Professor Hale himself. The next requirement isan atmosphere of the greatest transparency, and a situation at a highelevation above sea-level, so that the passage of light from the sun tothe observer shall be obstructed as little as possible by the mists andvapors near the earth's surface. This requirement is reached by placingthe observatory on Mount Wilson, near Pasadena, California, where theclimate is found to be the best of any in the United States, andprobably not exceeded by that of any other attainable point in theworld. The third requirement is the best of instruments, speciallydevised to meet the requirements. In this respect we may be sure thatnothing attainable by human ingenuity will be found wanting. 

Thus provided, Professor Hale has entered upon the task of studying thesun, and recording from day to day all the changes going on in it, using specially devised instruments for each purpose in view. Photography is made use of through almost the entire investigation. Afull description of the work would require an enumeration of technicaldetails, into which we need not enter at present. Let it, therefore, suffice to say in a general way that the study of the sun is beingcarried on on a scale, and with an energy worthy of the most importantsubject that presents itself to the astronomer. Closely associated withthis work is that of Professor Langley and Dr. Abbot, at theAstro-Physical Observatory of the Smithsonian Institution, who haverecently completed one of the most important works ever carried out onthe light of the sun. They have for years been analyzing those of itsrays which, although entirely invisible to our eyes, are of the samenature as those of light, and are felt by us as heat. To do this, Langley invented a sort of artificial eye, which he called a bolometer, in which the optic nerve is made of an extremely thin strip of metal, so slight that one can hardly see it, which is traversed by an electriccurrent. This eye would be so dazzled by the heat radiated from one'sbody that, when in use, it must be protected from all such heat bybeing enclosed in a case kept at a constant temperature by beingimmersed in water. With this eye the two observers have mapped the heatrays of the sun down to an extent and with a precision which werebefore entirely unknown. 

The question of possible changes in the sun's radiation, and of therelation of those changes to human welfare, still eludes our scrutiny. With all the efforts that have been made, the physicist of to-day hasnot yet been able to make anything like an exact determination of thetotal amount of heat received from the sun. The largest measurementsare almost double the smallest. This is partly due to the atmosphereabsorbing an unknown and variable fraction of the sun's rays which passthrough it, and partly to the difficulty of distinguishing the heatradiated by the sun from that radiated by terrestrial objects. 

In one recent instance, a change in the sun's radiation has beennoticed in various parts of the world, and is of especial interestbecause there seems to be little doubt as to its origin. In the latterpart of 1902 an extraordinary diminution was found in the intensity ofthe sun's heat, as measured by the bolometer and other instruments. This continued through the first part of 1903, with wide variations atdifferent places, and it was more than a year after the firstdiminution before the sun's rays again assumed their ordinary intensity. 

This result is now attributed to the eruption of Mount Pelee, duringwhich an enormous mass of volcanic dust and vapor was projected intothe higher regions of the air, and gradually carried over the entireearth by winds and currents. Many of our readers may remember thatsomething yet more striking occurred after the great cataclasm atKrakatoa in 1883, when, for more than a year, red sunsets and redtwilights of a depth of shade never before observed were seen in everypart of the world. 

What we call universology--the knowledge of the structure and extent ofthe universe--must begin with a study of the starry heavens as we seethem. There are perhaps one hundred million stars in the sky within thereach of telescopic vision. This number is too great to allow of allthe stars being studied individually; yet, to form the basis for anyconclusion, we must know the positions and arrangement of as many ofthem as we can determine. 

To do this the first want is a catalogue giving very precise positionsof as many of the brighter stars as possible. The principal nationalobservatories, as well as some others, are engaged in supplying thiswant. Up to the present time about 200, 000 stars visible in ourlatitudes have been catalogued on this precise plan, and the work isstill going on. In that part of the sky which we never see, because itis only visible from the southern hemisphere, the corresponding work isfar from being as extensive. Sir David Gill, astronomer at the Cape ofGood Hope, and also the directors of other southern observatories, areengaged in pushing it forward as rapidly as the limited facilities attheir disposal will allow. 

Next in order comes the work of simply listing as many stars aspossible. Here the most exact positions are not required. It is onlynecessary to lay down the position of each star with sufficientexactness to distinguish it from all its neighbors. About 400, 000 starswere during the last half-century listed in this way at the observatoryof Bonn by Argelander, Schonfeld, and their assistants. This work isnow being carried through the southern hemisphere on a large scale byThome, Director of the Cordoba Observatory, in the Argentine Republic. This was founded thirty years ago by our Dr. B. A. Gould, who turned itover to Dr. Thome in 1886. The latter has, up to the present time, fixed and published the positions of nearly half a million stars. Thiswork of Thome extends to fainter stars than any other yet attempted, sothat, as it goes on, we have more stars listed in a region invisible inmiddle northern latitudes than we have for that part of the sky we cansee. Up to the present time three quarto volumes giving the positionsand magnitudes of the stars have appeared. Two or three volumes more, and, perhaps, ten or fifteen years, will be required to complete thework. 

About twenty years ago it was discovered that, by means of a telescopeespecially adapted to this purpose, it was possible to photograph manymore stars than an instrument of the same size would show to the eye. This discovery was soon applied in various quarters. Sir David Gill, with characteristic energy, photographed the stars of the southern skyto the number of nearly half a million. As it was beyond his power tomeasure off and compute the positions of the stars from his plates, thelatter were sent to Professor J. C. Kapteyn, of Holland, who undertookthe enormous labor of collecting them into a catalogue, the last volumeof which was published in 1899. One curious result of this enterpriseis that the work of listing the stars is more complete for the southernhemisphere than for the northern. 

Another great photographic work now in progress has to do with themillions of stars which it is impossible to handle individually. Fifteen years ago an association of observatories in both hemispheresundertook to make a photographic chart of the sky on the largest scale. Some portions of this work are now approaching completion, but inothers it is still in a backward state, owing to the failure of severalSouth American observatories to carry out their part of the programme. When it is all done we shall have a picture of the sky, the study ofwhich may require the labor of a whole generation of astronomers. 

Quite independently of this work, the Harvard University, under thedirection of Professor Pickering, keeps up the work of photographingthe sky on a surprising scale. On this plan we do not have to leave itto posterity to learn whether there is any change in the heavens, forone result of the enterprise has been the discovery of thirteen of thenew stars which now and then blaze out in the heavens at points wherenone were before known. Professor Pickering's work has been continuallyenlarged and improved until about 150, 000 photographic plates, showingfrom time to time the places of countless millions of stars among theirfellows are now stored at the Harvard Observatory. Not less remarkablethan this wealth of material has been the development of skill inworking it up. Some idea of the work will be obtained by reflectingthat, thirty years ago, careful study of the heavens by astronomersdevoting their lives to the task had resulted in the discovery of sometwo or three hundred stars, varying in their light. Now, at Harvard, through keen eyes studying and comparing successive photographs notonly of isolated stars, but of clusters and agglomerations of stars inthe Milky Way and elsewhere, discoveries of such objects numberinghundreds have been made, and the work is going on with ever-increasingspeed. Indeed, the number of variable stars now known is such thattheir study as individual objects no longer suffices, and they musthereafter be treated statistically with reference to their distributionin space, and their relations to one another, as a census classifiesthe entire population without taking any account of individuals. 

The works just mentioned are concerned with the stars. But the heavenlyspaces contain nebulae as well as stars; and photography can now beeven more successful in picturing them than the stars. A few years agothe late lamented Keeler, at the Lick Observatory, undertook to seewhat could be done by pointing the Crossley reflecting telescope at thesky and putting a sensitive photographic plate in the focus. He wassurprised to find that a great number of nebulae, the existence ofwhich had never before been suspected, were impressed on the plate. Upto the present time the positions of about 8000 of these objects havebeen listed. Keeler found that there were probably 200, 000 nebulae inthe heavens capable of being photographed with the Crossley reflector. But the work of taking these photographs is so great, and the number ofreflecting telescopes which can be applied to it so small, that no onehas ventured to seriously commence it. It is worthy of remark that onlya very small fraction of these objects which can be photographed arevisible to the eye, even with the most powerful telescope. 

This demonstration of what the reflecting telescope can do may beregarded as one of the most important discoveries of our time as to thecapabilities of astronomical instruments. It has long been known thatthe image formed in the focus of the best refracting telescope isaffected by an imperfection arising from the different action of theglasses on rays of light of different colors. Hence, the image of astar can never be seen or photographed with such an instrument, as anactual point, but only as a small, diffused mass. This difficulty isavoided in the reflecting telescope; but a new difficulty is found inthe bending of the mirror under the influence of its own weight. Devices for overcoming this had been so far from successful that, whenMr. Crossley presented his instrument to the Lick Observatory, it wasfeared that little of importance could be done with it. But as oftenhappens in human affairs outside the field of astronomy, when ingeniousand able men devote their attention to the careful study of a problem, it was found that new results could be reached. Thus it was that, before a great while, what was supposed to be an inferior instrumentproved not only to have qualities not before suspected, but to be themeans of making an important addition to the methods of astronomicalinvestigation. 

In order that our knowledge of the position of a star may be complete, we must know its distance. This can be measured only through the star'sparallax--that is to say, the slight change in its direction producedby the swing of our earth around its orbit. But so vast is the distancein question that this change is immeasurably small, except for, perhaps, a few hundred stars, and even for these few its measurementalmost baffles the skill of the most expert astronomer. Progress inthis direction is therefore very slow, and there are probably not yet ahundred stars of which the parallax has been ascertained with anyapproach to certainty. Dr. Chase is now completing an important work ofthis kind at the Yale Observatory. 

To the most refined telescopic observations, as well as to the nakedeye, the stars seem all alike, except that they differ greatly inbrightness, and somewhat in color. But when their light is analyzed bythe spectroscope, it is found that scarcely any two are exactly alike. An important part of the work of the astro-physical observatories, especially that of Harvard, consists in photographing the spectra ofthousands of stars, and studying the peculiarities thus brought out. AtHarvard a large portion of this work is done as part of the work of theHenry Draper Memorial, established by his widow in memory of theeminent investigator of New York, who died twenty years ago. 

By a comparison of the spectra of stars Sir William Huggins hasdeveloped the idea that these bodies, like human beings, have a lifehistory. They are nebulae in infancy, while the progress to old age ismarked by a constant increase in the density of their substance. Theirtemperature also changes in a way analogous to the vigor of the humanbeing. During a certain time the star continually grows hotter andhotter. But an end to this must come, and it cools off in old age. Whatthe age of a star may be is hard even to guess. It is many millions ofyears, perhaps hundreds, possibly even thousands, of millions. 

Some attempt at giving the magnitude is included in every considerablelist of stars. The work of determining the magnitudes with the greatestprecision is so laborious that it must go on rather slowly. It is beingpursued on a large scale at the Harvard Observatory, as well as in thatof Potsdam, Germany. 

We come now to the question of changes in the appearance of brightstars. It seems pretty certain that more than one per cent of thesebodies fluctuate to a greater or less extent in their light. Observations of these fluctuations, in the case of at least thebrighter stars, may be carried on without any instrument more expensivethan a good opera-glass--in fact, in the case of stars visible to thenaked eye, with no instrument at all. 

As a general rule, the light of these stars goes through its changes ina regular period, which is sometimes as short as a few hours, butgenerally several days, frequently a large fraction of a year or eveneighteen months. Observations of these stars are made to determine thelength of the period and the law of variation of the brightness. Anyperson with a good eye and skill in making estimates can make theobservations if he will devote sufficient pains to training himself;but they require a degree of care and assiduity which is not to beexpected of any one but an enthusiast on the subject. One of the mostsuccessful observers of the present time is Mr. W. A. Roberts, aresident of South Africa, whom the Boer war did not prevent fromkeeping up a watch of the southern sky, which has resulted in greatlyincreasing our knowledge of variable stars. There are also quite anumber of astronomers in Europe and America who make this particularstudy their specialty. 

During the past fifteen years the art of measuring the speed with whicha star is approaching us or receding from us has been brought to awonderful degree of perfection. The instrument with which this wasfirst done was the spectroscope; it is now replaced with another of thesame general kind, called the spectrograph. The latter differs from theother only in that the spectrum of the star is photographed, and theobserver makes his measures on the negative. This method was firstextensively applied at the Potsdam Observatory in Germany, and haslately become one of the specialties of the Lick Observatory, whereProfessor Campbell has brought it to its present degree of perfection. The Yerkes Observatory is also beginning work in the same line, whereProfessor Frost is already rivalling the Lick Observatory in theprecision of his measures. 

Let us now go back to our own little colony and see what is being doneto advance our knowledge of the solar system. This consists of planets, on one of which we dwell, moons revolving around them, comets, andmeteoric bodies. The principal national observatories keep up a more orless orderly system of observations of the positions of the planets andtheir satellites in order to determine the laws of their motion. As inthe case of the stars, it is necessary to continue these observationsthrough long periods of time in order that everything possible to learnmay be discovered. 

Our own moon is one of the enigmas of the mathematical astronomer. Observations show that she is deviating from her predicted place, andthat this deviation continues to increase. True, it is not very greatwhen measured by an ordinary standard. The time at which the moon'sshadow passed a given point near Norfolk during the total eclipse ofMay 29, 1900, was only about seven seconds different from the timegiven in the Astronomical Ephemeris. The path of the shadow along theearth was not out of place by more than one or two miles But, smallthough these deviations are, they show that something is wrong, and noone has as yet found out what it is. Worse yet, the deviation isincreasing rapidly. The observers of the total eclipse in August, 1905, were surprised to find that it began twenty seconds before thepredicted time. The mathematical problems involved in correcting thiserror are of such complexity that it is only now and then that amathematician turns up anywhere in the world who is both able and boldenough to attack them. 

There now seems little doubt that Jupiter is a miniature sun, only nothot enough at its surface to shine by its own light The point in whichit most resembles the sun is that its equatorial regions rotate in lesstime than do the regions near the poles. This shows that what we see isnot a solid body. But none of the careful observers have yet succeededin determining the law of this difference of rotation. 

Twelve years ago a suspicion which had long been entertained that theearth's axis of rotation varied a little from time to time was verifiedby Chandler. The result of this is a slight change in the latitude ofall places on the earth's surface, which admits of being determined byprecise observations. The National Geodetic Association has establishedfour observatories on the same parallel of latitude--one atGaithersburg, Maryland, another on the Pacific coast, a third in Japan, and a fourth in Italy--to study these variations by continuousobservations from night to night. This work is now going forward on awell-devised plan. 

A fact which will appeal to our readers on this side of the Atlantic isthe success of American astronomers. Sixty years ago it could not besaid that there was a well-known observatory on the American continent. The cultivation of astronomy was confined to a professor here andthere, who seldom had anything better than a little telescope withwhich he showed the heavenly bodies to his students. But during thepast thirty years all this has been changed. The total quantity ofpublished research is still less among us than on the continent ofEurope, but the number of men who have reached the highest successamong us may be judged by one fact. The Royal Astronomical Society ofEngland awards an annual medal to the English or foreign astronomerdeemed most worthy of it. The number of these medals awarded toAmericans within twenty-five years is about equal to the number awardedto the astronomers of all other nations foreign to the English. Thatthis preponderance is not growing less is shown by the award of medalsto Americans in three consecutive years--1904, 1905, and 1906. Therecipients were Hale, Boss, and Campbell. Of the fifty foreignassociates chosen by this society for their eminence in astronomicalresearch, no less than eighteen--more than one-third--are Americans. 

VII

LIFE IN THE UNIVERSE

So far as we can judge from what we see on our globe, the production oflife is one of the greatest and most incessant purposes of nature. Lifeis absent only in regions of perpetual frost, where it never has anopportunity to begin; in places where the temperature is near theboiling-point, which is found to be destructive to it; and beneath theearth's surface, where none of the changes essential to it can comeabout. Within the limits imposed by these prohibitory conditions--thatis to say, within the range of temperature at which water retains itsliquid state, and in regions where the sun's rays can penetrate andwhere wind can blow and water exist in a liquid form--life is theuniversal rule. How prodigal nature seems to be in its production istoo trite a fact to be dwelt upon. We have all read of the millions ofgerms which are destroyed for every one that comes to maturity. Eventhe higher forms of life are found almost everywhere. Only smallislands have ever been discovered which were uninhabited, and animalsof a higher grade are as widely diffused as man. 

If it would be going too far to claim that all conditions may haveforms of life appropriate to them, it would be going as much too far inthe other direction to claim that life can exist only with the precisesurroundings which nurture it on this planet. It is very remarkable inthis connection that while in one direction we see life coming to anend, in the other direction we see it flourishing more and more up tothe limit. These two directions are those of heat and cold. We cannotsuppose that life would develop in any important degree in a region ofperpetual frost, such as the polar regions of our globe. But we do notfind any end to it as the climate becomes warmer. On the contrary, every one knows that the tropics are the most fertile regions of theglobe in its production. The luxuriance of the vegetation and thenumber of the animals continually increase the more tropical theclimate becomes. Where the limit may be set no one can say. But itwould doubtless be far above the present temperature of the equatorialregions. 

It has often been said that this does not apply to the human race, thatmen lack vigor in the tropics. But human vigor depends on so manyconditions, hereditary and otherwise, that we cannot regard theinferior development of humanity in the tropics as due solely totemperature. Physically considered, no men attain a better developmentthan many tribes who inhabit the warmer regions of the globe. Theinferiority of the inhabitants of these regions in intellectual poweris more likely the result of race heredity than of temperature. 

We all know that this earth on which we dwell is only one of countlessmillions of globes scattered through the wilds of infinite space. Sofar as we know, most of these globes are wholly unlike the earth, beingat a temperature so high that, like our sun, they shine by their ownlight. In such worlds we may regard it as quite certain that noorganized life could exist. But evidence is continually increasing thatdark and opaque worlds like ours exist and revolve around their suns, as the earth on which we dwell revolves around its central luminary. Although the number of such globes yet discovered is not great, thecircumstances under which they are found lead us to believe that theactual number may be as great as that of the visible stars which studthe sky. If so, the probabilities are that millions of them areessentially similar to our own globe. Have we any reason to believethat life exists on these other worlds?

The reader will not expect me to answer this question positively. Itmust be admitted that, scientifically, we have no light upon thequestion, and therefore no positive grounds for reaching a conclusion. We can only reason by analogy and by what we know of the origin andconditions of life around us, and assume that the same agencies whichare at play here would be found at play under similar conditions inother parts of the universe. 

If we ask what the opinion of men has been, we know historically thatour race has, in all periods of its history, peopled other regions withbeings even higher in the scale of development than we are ourselves. The gods and demons of an earlier age all wielded powers greater thanthose granted to man--powers which they could use to determine humandestiny. But, up to the time that Copernicus showed that the planetswere other worlds, the location of these imaginary beings was ratherindefinite. It was therefore quite natural that when the moon andplanets were found to be dark globes of a size comparable with that ofthe earth itself, they were made the habitations of beings like untoourselves. 

The trend of modern discovery has been against carrying this view toits extreme, as will be presently shown. Before considering thedifficulties in the way of accepting it to the widest extent, let usenter upon some preliminary considerations as to the origin andprevalence of life, so far as we have any sound basis to go upon. 

A generation ago the origin of life upon our planet was one of thegreat mysteries of science. All the facts brought out by investigationinto the past history of our earth seemed to show, with hardly thepossibility of a doubt, that there was a time when it was a fiery mass, no more capable of serving as the abode of a living being than theinterior of a Bessemer steel furnace. There must therefore have been, within a certain period, a beginning of life upon its surface. But, sofar as investigation had gone--indeed, so far as it has gone to thepresent time--no life has been found to originate of itself. The livinggerm seems to be necessary to the beginning of any living form. Whence, then, came the first germ? Many of our readers may remember asuggestion by Sir William Thomson, now Lord Kelvin, made twenty orthirty years ago, that life may have been brought to our planet by thefalling of a meteor from space. This does not, however, solve thedifficulty--indeed, it would only make it greater. It still leaves openthe question how life began on the meteor; and granting this, why itwas not destroyed by the heat generated as the meteor passed throughthe air. The popular view that life began through a special act ofcreative power seemed to be almost forced upon man by the failure ofscience to discover any other beginning for it. It cannot be said thateven to-day anything definite has been actually discovered to refutethis view. All we can say about it is that it does not run in with thegeneral views of modern science as to the beginning of things, and thatthose who refuse to accept it must hold that, under certain conditionswhich prevail, life begins by a very gradual process, similar to thatby which forms suggesting growth seem to originate even underconditions so unfavorable as those existing in a bottle of acid. 

But it is not at all necessary for our purpose to decide this question. If life existed through a creative act, it is absurd to suppose thatthat act was confined to one of the countless millions of worldsscattered through space. If it began at a certain stage of evolution bya natural process, the question will arise, what conditions arefavorable to the commencement of this process? Here we are quitejustified in reasoning from what, granting this process, has takenplace upon our globe during its past history. One of the mostelementary principles accepted by the human mind is that like causesproduce like effects. The special conditions under which we find lifeto develop around us may be comprehensively summed up as the existenceof water in the liquid form, and the presence of nitrogen, free perhapsin the first place, but accompanied by substances with which it mayform combinations. Oxygen, hydrogen, and nitrogen are, then, thefundamental requirements. The addition of calcium or other forms ofmatter necessary to the existence of a solid world goes without saying. The question now is whether these necessary conditions exist in otherparts of the universe. 

The spectroscope shows that, so far as the chemical elements go, otherworlds are composed of the same elements as ours. Hydrogen especiallyexists everywhere, and we have reason to believe that the same is trueof oxygen and nitrogen. Calcium, the base of lime, is almost universal. So far as chemical elements go, we may therefore take it for grantedthat the conditions under which life begins are very widely diffused inthe universe. It is, therefore, contrary to all the analogies of natureto suppose that life began only on a single world. 

It is a scientific inference, based on facts so numerous as not toadmit of serious question, that during the history of our globe therehas been a continually improving development of life. As ages upon agespass, new forms are generated, higher in the scale than those whichpreceded them, until at length reason appears and asserts its sway. Ina recent well-known work Alfred Russel Wallace has argued that thisdevelopment of life required the presence of such a rare combination ofconditions that there is no reason to suppose that it prevailedanywhere except on our earth. It is quite impossible in the presentdiscussion to follow his reasoning in detail; but it seems to mealtogether inconclusive. Not only does life, but intelligence, flourishon this globe under a great variety of conditions as regardstemperature and surroundings, and no sound reason can be shown whyunder certain conditions, which are frequent in the universe, intelligent beings should not acquire the highest development. 

Now let us look at the subject from the view of the mathematical theoryof probabilities. A fundamental tenet of this theory is that no matterhow improbable a result may be on a single trial, supposing it at allpossible, it is sure to occur after a sufficient number of trials--andover and over again if the trials are repeated often enough. Forexample, if a million grains of corn, of which a single one was red, were all placed in a pile, and a blindfolded person were required togrope in the pile, select a grain, and then put it back again, thechances would be a million to one against his drawing out the redgrain. If drawing it meant he should die, a sensible person would givehimself no concern at having to draw the grain. The probability of hisdeath would not be so great as the actual probability that he willreally die within the next twenty-four hours. And yet if the wholehuman race were required to run this chance, it is certain that aboutfifteen hundred, or one out of a million, of the whole human familywould draw the red grain and meet his death. 

Now apply this principle to the universe. Let us suppose, to fix theideas, that there are a hundred million worlds, but that the chancesare one thousand to one against any one of these taken at random beingfitted for the highest development of life or for the evolution ofreason. The chances would still be that one hundred thousand of themwould be inhabited by rational beings whom we call human. But where arewe to look for these worlds? This no man can tell. We only infer fromthe statistics of the stars--and this inference is fairly wellgrounded--that the number of worlds which, so far as we know, may beinhabited, are to be counted by thousands, and perhaps by millions. 

In a number of bodies so vast we should expect every variety ofconditions as regards temperature and surroundings. If we suppose thatthe special conditions which prevail on our planet are necessary to thehighest forms of life, we still have reason to believe that these sameconditions prevail on thousands of other worlds. The fact that we mightfind the conditions in millions of other worlds unfavorable to lifewould not disprove the existence of the latter on countless worldsdifferently situated. 

Coming down now from the general question to the specific one, we allknow that the only worlds the conditions of which can be made thesubject of observation are the planets which revolve around the sun, and their satellites. The question whether these bodies are inhabitedis one which, of course, completely transcends not only our powers ofobservation at present, but every appliance of research that we canconceive of men devising. If Mars is inhabited, and if the people ofthat planet have equal powers with ourselves, the problem of merelyproducing an illumination which could be seen in our most powerfultelescope would be beyond all the ordinary efforts of an entire nation. An unbroken square mile of flame would be invisible in our telescopes, but a hundred square miles might be seen. We cannot, therefore, expectto see any signs of the works of inhabitants even on Mars. All that wecan do is to ascertain with greater or less probability whether theconditions necessary to life exist on the other planets of the system. 

The moon being much the nearest to us of all the heavenly bodies, wecan pronounce more definitely in its case than in any other. We knowthat neither air nor water exists on the moon in quantities sufficientto be perceived by the most delicate tests at our command. It iscertain that the moon's atmosphere, if any exists, is less than thethousandth part of the density of that around us. The vacuum is greaterthan any ordinary air-pump is capable of producing. We can hardlysuppose that so small a quantity of air could be of any benefitwhatever in sustaining life; an animal that could get along on solittle could get along on none at all. 

But the proof of the absence of life is yet stronger when we considerthe results of actual telescopic observation. An object such as anordinary city block could be detected on the moon. If anything likevegetation were present on its surface, we should see the changes whichit would undergo in the course of a month, during one portion of whichit would be exposed to the rays of the unclouded sun, and duringanother to the intense cold of space. If men built cities, or evenseparate buildings the size of the larger ones on our earth, we mightsee some signs of them. 

In recent times we not only observe the moon with the telescope, butget still more definite information by photography. The whole visiblesurface has been repeatedly photographed under the best conditions. Butno change has been established beyond question, nor does the photographshow the slightest difference of structure or shade which could beattributed to cities or other works of man. To all appearances thewhole surface of our satellite is as completely devoid of life as thelava newly thrown from Vesuvius. We next pass to the planets. Mercury, the nearest to the sun, is in a position very unfavorable forobservation from the earth, because when nearest to us it is between usand the sun, so that its dark hemisphere is presented to us. Nothingsatisfactory has yet been made out as to its condition. We cannot saywith certainty whether it has an atmosphere or not. What seems veryprobable is that the temperature on its surface is higher than any ofour earthly animals could sustain. But this proves nothing. 

We know that Venus has an atmosphere. This was very conclusively shownduring the transits of Venus in 1874 and 1882. But this atmosphere isso filled with clouds or vapor that it does not seem likely that weever get a view of the solid body of the planet through it. Someobservers have thought they could see spots on Venus day after day, while others have disputed this view. On the whole, if intelligentinhabitants live there, it is not likely that they ever see sun orstars. Instead of the sun they see only an effulgence in the vapory skywhich disappears and reappears at regular intervals. 

When we come to Mars, we have more definite knowledge, and there seemsto be greater possibilities for life there than in the case of anyother planet besides the earth. The main reason for denying that lifesuch as ours could exist there is that the atmosphere of Mars is sorare that, in the light of the most recent researches, we cannot befully assured that it exists at all. The very careful comparisons ofthe spectra of Mars and of the moon made by Campbell at the LickObservatory failed to show the slightest difference in the two. If Marshad an atmosphere as dense as ours, the result could be seen in thedarkening of the lines of the spectrum produced by the double passageof the light through it. There were no lines in the spectrum of Marsthat were not seen with equal distinctness in that of the moon. Butthis does not prove the entire absence of an atmosphere. It only showsa limit to its density. It may be one-fifth or one-fourth the densityof that on the earth, but probably no more. 

That there must be something in the nature of vapor at least seems tobe shown by the formation and disappearance of the white polar caps ofthis planet. Every reader of astronomy at the present time knows that, during the Martian winter, white caps form around the pole of theplanet which is turned away from the sun, and grow larger and largeruntil the sun begins to shine upon them, when they gradually growsmaller, and perhaps nearly disappear. It seems, therefore, fairly wellproved that, under the influence of cold, some white substance formsaround the polar regions of Mars which evaporates under the influenceof the sun's rays. It has been supposed that this substance is snow, produced in the same way that snow is produced on the earth, by theevaporation of water. 

But there are difficulties in the way of this explanation. The sunsends less than half as much heat to Mars as to the earth, and it doesnot seem likely that the polar regions can ever receive enough of heatto melt any considerable quantity of snow. Nor does it seem likely thatany clouds from which snow could fall ever obscure the surface of Mars. 

But a very slight change in the explanation will make it tenable. Quitepossibly the white deposits may be due to something like hoar-frostcondensed from slightly moist air, without the actual production ofsnow. This would produce the effect that we see. Even this explanationimplies that Mars has air and water, rare though the former may be. Itis quite possible that air as thin as that of Mars would sustain lifein some form. Life not totally unlike that on the earth may thereforeexist upon this planet for anything that we know to the contrary. Morethan this we cannot say. 

In the case of the outer planets the answer to our question must be inthe negative. It now seems likely that Jupiter is a body very much likeour sun, only that the dark portion is too cool to emit much, if any, light. It is doubtful whether Jupiter has anything in the nature of asolid surface. Its interior is in all likelihood a mass of moltenmatter far above a red heat, which is surrounded by a comparativelycool, yet, to our measure, extremely hot, vapor. The belt-like cloudswhich surround the planet are due to this vapor combined with the rapidrotation. If there is any solid surface below the atmosphere that wecan see, it is swept by winds such that nothing we have on earth couldwithstand them. But, as we have said, the probabilities are very muchagainst there being anything like such a surface. At some great depthin the fiery vapor there is a solid nucleus; that is all we can say. 

The planet Saturn seems to be very much like that of Jupiter in itscomposition. It receives so little heat from the sun that, unless it isa mass of fiery vapor like Jupiter, the surface must be far below thefreezing-point. 

We cannot speak with such certainty of Uranus and Neptune; yet theprobability seems to be that they are in much the same condition asSaturn. They are known to have very dense atmospheres, which are madeknown to us only by their absorbing some of the light of the sun. Butnothing is known of the composition of these atmospheres. 

To sum up our argument: the fact that, so far as we have yet been ableto learn, only a very small proportion of the visible worlds scatteredthrough space are fitted to be the abode of life does not preclude theprobability that among hundreds of millions of such worlds a vastnumber are so fitted. Such being the case, all the analogies of naturelead us to believe that, whatever the process which led to life uponthis earth--whether a special act of creative power or a gradual courseof development--through that same process does life begin in every partof the universe fitted to sustain it. The course of developmentinvolves a gradual improvement in living forms, which by irregularsteps rise higher and higher in the scale of being. We have everyreason to believe that this is the case wherever life exists. It is, therefore, perfectly reasonable to suppose that beings, not onlyanimated, but endowed with reason, inhabit countless worlds in space. It would, indeed, be very inspiring could we learn by actualobservation what forms of society exist throughout space, and see themembers of such societies enjoying themselves by their warm firesides. But this, so far as we can now see, is entirely beyond the possiblereach of our race, so long as it is confined to a single world. 

VIII

HOW THE PLANETS ARE WEIGHED

You ask me how the planets are weighed? I reply, on the same principleby which a butcher weighs a ham in a spring-balance. When he picks theham up, he feels a pull of the ham towards the earth. When he hangs iton the hook, this pull is transferred from his hand to the spring ofthe balance. The stronger the pull, the farther the spring is pulleddown. What he reads on the scale is the strength of the pull. You knowthat this pull is simply the attraction of the earth on the ham. But, by a universal law of force, the ham attracts the earth exactly as muchas the earth does the ham. So what the butcher really does is to findhow much or how strongly the ham attracts the earth, and he calls thatpull the weight of the ham. On the same principle, the astronomer findsthe weight of a body by finding how strong is its attractive pull onsome other body. If the butcher, with his spring-balance and a ham, could fly to all the planets, one after the other, weigh the ham oneach, and come back to report the results to an astronomer, the lattercould immediately compute the weight of each planet of known diameter, as compared with that of the earth. In applying this principle to theheavenly bodies, we at once meet a difficulty that looksinsurmountable. You cannot get up to the heavenly bodies to do yourweighing; how then will you measure their pull? I must begin the answerto this question by explaining a nice point in exact science. Astronomers distinguish between the weight of a body and its mass. Theweight of objects is not the same all over the world; a thing whichweighs thirty pounds in New York would weigh an ounce more than thirtypounds in a spring-balance in Greenland, and nearly an ounce less atthe equator. This is because the earth is not a perfect sphere, but alittle flattened. Thus weight varies with the place. If a ham weighingthirty pounds were taken up to the moon and weighed there, the pullwould only be five pounds, because the moon is so much smaller andlighter than the earth. There would be another weight of the ham forthe planet Mars, and yet another on the sun, where it would weigh someeight hundred pounds. Hence the astronomer does not speak of the weightof a planet, because that would depend on the place where it wasweighed; but he speaks of the mass of the planet, which means how muchplanet there is, no matter where you might weigh it. 

At the same time, we might, without any inexactness, agree that themass of a heavenly body should be fixed by the weight it would have inNew York. As we could not even imagine a planet at New York, because itmay be larger than the earth itself, what we are to imagine is this:Suppose the planet could be divided into a million million millionequal parts, and one of these parts brought to New York and weighed. Wecould easily find its weight in pounds or tons. Then multiply thisweight by a million million million, and we shall have a weight of theplanet. This would be what the astronomers might take as the mass ofthe planet. 

With these explanations, let us see how the weight of the earth isfound. The principle we apply is that round bodies of the same specificgravity attract small objects on their surface with a forceproportional to the diameter of the attracting body. For example, abody two feet in diameter attracts twice as strongly as one of a foot, one of three feet three times as strongly, and so on. Now, our earth isabout 40, 000, 000 feet in diameter; that is 10, 000, 000 times four feet. It follows that if we made a little model of the earth four feet indiameter, having the average specific gravity of the earth, it wouldattract a particle with one ten-millionth part of the attraction of theearth. The attraction of such a model has actually been measured. Sincewe do not know the average specific gravity of the earth--that being infact what we want to find out--we take a globe of lead, four feet indiameter, let us suppose. By means of a balance of the most exquisiteconstruction it is found that such a globe does exert a minuteattraction on small bodies around it, and that this attraction is alittle more than the ten-millionth part of that of the earth. Thisshows that the specific gravity of the lead is a little greater thanthat of the average of the whole earth. All the minute calculationsmade, it is found that the earth, in order to attract with the force itdoes, must be about five and one-half times as heavy as its bulk ofwater, or perhaps a little more. Different experimenters find differentresults; the best between 5. 5 and 5. 6, so that 5. 5 is, perhaps, as nearthe number as we can now get. This is much more than the averagespecific gravity of the materials which compose that part of the earthwhich we can reach by digging mines. The difference arises from thefact that, at the depth of many miles, the matter composing the earthis compressed into a smaller space by the enormous weight of theportions lying above it. Thus, at the depth of 1000 miles, the pressureon every cubic inch is more than 2000 tons, a weight which wouldgreatly condense the hardest metal. 

We come now to the planets. I have said that the mass or weight of aheavenly body is determined by its attraction on some other body. Thereare two ways in which the attraction of a planet may be measured. Oneis by its attraction on the planets next to it. If these bodies did notattract one another at all, but only moved under the influence of thesun, they would move in orbits having the form of ellipses. They arefound to move very nearly in such orbits, only the actual path deviatesfrom an ellipse, now in one direction and then in another, and itslowly changes its position from year to year. These deviations are dueto the pull of the other planets, and by measuring the deviations wecan determine the amount of the pull, and hence the mass of the planet. 

The reader will readily understand that the mathematical processesnecessary to get a result in this way must be very delicate andcomplicated. A much simpler method can be used in the case of thoseplanets which have satellites revolving round them, because theattraction of the planet can be determined by the motions of thesatellite. The first law of motion teaches us that a body in motion, ifacted on by no force, will move in a straight line. Hence, if we see abody moving in a curve, we know that it is acted on by a force in thedirection towards which the motion curves. A familiar example is thatof a stone thrown from the hand. If the stone were not attracted by theearth, it would go on forever in the line of throw, and leave the earthentirely. But under the attraction of the earth, it is drawn down anddown, as it travels onward, until finally it reaches the ground. Thefaster the stone is thrown, of course, the farther it will go, and thegreater will be the sweep of the curve of its path. If it were acannon-ball, the first part of the curve would be nearly a right line. If we could fire a cannon-ball horizontally from the top of a highmountain with a velocity of five miles a second, and if it were notresisted by the air, the curvature of the path would be equal to thatof the surface of our earth, and so the ball would never reach theearth, but would revolve round it like a little satellite in an orbitof its own. Could this be done, the astronomer would be able, knowingthe velocity of the ball, to calculate the attraction of the earth aswell as we determine it by actually observing the motion of fallingbodies around us. 

Thus it is that when a planet, like Mars or Jupiter, has satellitesrevolving round it, astronomers on the earth can observe the attractionof the planet on its satellites and thus determine its mass. The rulefor doing this is very simple. The cube of the distance between theplanet and satellite is divided by the square of the time of revolutionof the satellite. The quotient is a number which is proportional to themass of the planet. The rule applies to the motion of the moon roundthe earth and of the planets round the sun. If we divide the cube ofthe earth's distance from the sun, say 93, 000, 000 miles, by the squareof 365 1/4, the days in a year, we shall get a certain quotient. Let uscall this number the sun-quotient. Then, if we divide the cube of themoon's distance from the earth by the square of its time of revolution, we shall get another quotient, which we may call the earth-quotient. The sun-quotient will come out about 330, 000 times as large as theearth-quotient. Hence it is concluded that the mass of the sun is330, 000 times that of the earth; that it would take this number ofearths to make a body as heavy as the sun. 

I give this calculation to illustrate the principle; it must not besupposed that the astronomer proceeds exactly in this way and has onlythis simple calculation to make. In the case of the moon and earth, themotion and distance of the former vary in consequence of the attractionof the sun, so that their actual distance apart is a changing quantity. So what the astronomer actually does is to find the attraction of theearth by observing the length of a pendulum which beats seconds invarious latitudes. Then, by very delicate mathematical processes, hecan find with great exactness what would be the time of revolution of asmall satellite at any given distance from the earth, and thus can getthe earth-quotient. 

But, as I have already pointed out, we must, in the case of theplanets, find the quotient in question by means of the satellites; andit happens, fortunately, that the motions of these bodies are much lesschanged by the attraction of the sun than is the motion of the moon. Thus, when we make the computation for the outer satellite of Mars, wefind the quotient to be 1/3093500 that of the sun-quotient. Hence weconclude that the mass of Mars is 1/3093500 that of the sun. By thecorresponding quotient, the mass of Jupiter is found to be about 1/1047that of the sun, Saturn 1/3500, Uranus 1/22700, Neptune 1/19500. 

We have set forth only the great principle on which the astronomer hasproceeded for the purpose in question. The law of gravitation is at thebottom of all his work. The effects of this law require mathematicalprocesses which it has taken two hundred years to bring to theirpresent state, and which are still far from perfect. The measurement ofthe distance of a satellite is not a job to be done in an evening; itrequires patient labor extending through months and years, and then isnot as exact as the astronomer would wish. He does the best he can, andmust be satisfied with that. 

IX

THE MARINER'S COMPASS

Among those provisions of Nature which seem to us as especiallydesigned for the use of man, none is more striking than the seemingmagnetism of the earth. What would our civilization have been if themariner's compass had never been known? That Columbus could never havecrossed the Atlantic is certain; in what generation since his time ourcontinent would have been discovered is doubtful. Did the reader everreflect what a problem the captain of the finest ocean liner of our daywould face if he had to cross the ocean without this little instrument?With the aid of a pilot he gets his ship outside of Sandy Hook withoutmuch difficulty. Even later, so long as the sun is visible and the airis clear, he will have some apparatus for sailing by the direction ofthe sun. But after a few hours clouds cover the sky. From that momenthe has not the slightest idea of east, west, north, or south, except sofar as he may infer it from the direction in which he notices the windto blow. For a few hours he may be guided by the wind, provided he issure he is not going ashore on Long Island. Thus, in time, he feels hisway out into the open sea. By day he has some idea of direction withthe aid of the sun; by night, when the sky is clear he can steer by theGreat Bear, or "Cynosure, " the compass of his ancient predecessors onthe Mediterranean. But when it is cloudy, if he persists in steamingahead, he may be running towards the Azores or towards Greenland, or hemay be making his way back to New York without knowing it. So, keepingup steam only when sun or star is visible, he at length finds that heis approaching the coast of Ireland. Then he has to grope along muchlike a blind man with his staff, feeling his way along the edge of aprecipice. He can determine the latitude at noon if the sky is clear, and his longitude in the morning or evening in the same conditions. Inthis way he will get a general idea of his whereabouts. But if heventures to make headway in a fog, he may find himself on the rocks atany moment. He reaches his haven only after many spells of patientwaiting for favoring skies. 

The fact that the earth acts like a magnet, that the needle points tothe north, has been generally known to navigators for nearly a thousandyears, and is said to have been known to the Chinese at a yet earlierperiod. And yet, to-day, if any professor of physical science is askedto explain the magnetic property of the earth, he will acknowledge hisinability to do so to his own satisfaction. Happily this does nothinder us from finding out by what law these forces act, and how theyenable us to navigate the ocean. I therefore hope the reader will beinterested in a short exposition of the very curious and interestinglaws on which the science of magnetism is based, and which are appliedin the use of the compass. 

The force known as magnetic, on which the compass depends, is differentfrom all other natural forces with which we are familiar. It is veryremarkable that iron is the only substance which can become magnetic inany considerable degree. Nickel and one or two other metals have thesame property, but in a very slight degree. It is also remarkable that, however powerfully a bar of steel may be magnetized, not the slightesteffect of the magnetism can be seen by its action on other thanmagnetic substances. It is no heavier than before. Its magnetism doesnot produce the slightest influence upon the human body. No one wouldknow that it was magnetic until something containing iron was broughtinto its immediate neighborhood; then the attraction is set up. Themost important principle of magnetic science is that there are twoopposite kinds of magnetism, which are, in a certain sense, contrary intheir manifestations. The difference is seen in the behavior of themagnet itself. One particular end points north, and the other endsouth. What is it that distinguishes these two ends? The answer is thatone end has what we call north magnetism, while the other has southmagnetism. Every magnetic bar has two poles, one near one end, one nearthe other. The north pole is drawn towards the north pole of the earth, the south pole towards the south pole, and thus it is that thedirection of the magnet is determined. Now, when we bring two magnetsnear each other we find another curious phenomenon. If the two likepoles are brought together, they do not attract but repel each other. But the two opposite poles attract each other. The attraction andrepulsion are exactly equal under the same conditions. There is no moreattraction than repulsion. If we seal one magnet up in a paper or abox, and then suspend another over the box, the north pole of the oneoutside will tend to the south pole of the one in the box, and viceversa. 

Our next discovery is, that whenever a magnet attracts a piece of ironit makes that iron into a magnet, at least for the time being. In thecase of ordinary soft or untempered iron the magnetism disappearsinstantly when the magnet is removed. But if the magnet be made toattract a piece of hardened steel, the latter will retain the magnetismproduced in it and become itself a permanent magnet. 

This fact must have been known from the time that the compass came intouse. To make this instrument it was necessary to magnetize a small baror needle by passing a natural magnet over it. 

In our times the magnetization is effected by an electric current. Thelatter has curious magnetic properties; a magnetic needle broughtalongside of it will be found placing itself at right angles to thewire bearing the current. On this principle is made the galvanometerfor measuring the intensity of a current. Moreover, if a piece of wireis coiled round a bar of steel, and a powerful electric current passthrough the coil, the bar will become a magnet. 

Another curious property of magnetism is that we cannot develop northmagnetism in a bar without developing south magnetism at the same time. If it were otherwise, important consequences would result. A separatenorth pole of a magnet would, if attached to a floating object andthrown into the ocean, start on a journey towards the north all byitself. A possible method of bringing this result about may suggestitself. Let us take an ordinary bar magnet, with a pole at each end, and break it in the middle; then would not the north end be all readyto start on its voyage north, and the south end to make its way south?But, alas! when this experiment is tried it is found that a south poleinstantly develops itself on one side of the break, and a north pole onthe other side, so that the two pieces will simply form two magnets, each with its north and south pole. There is no possibility of making amagnet with only one pole. 

It was formerly supposed that the central portions of the earthconsisted of an immense magnet directed north and south. Although thisview is found, for reasons which need not be set forth in detail, to beuntenable, it gives us a good general idea of the nature of terrestrialmagnetism. One result that follows from the law of poles alreadymentioned is that the magnetism which seems to belong to the north poleof the earth is what we call south on the magnet, and vice versa. 

Careful experiment shows us that the region around every magnet isfilled with magnetic force, strongest near the poles of the magnet, butdiminishing as the inverse square of the distance from the pole. Thisforce, at each point, acts along a certain line, called a line offorce. These lines are very prettily shown by the familiar experimentof placing a sheet of paper over a magnet, and then scattering ironfilings on the surface of the paper. It will be noticed that thefilings arrange themselves along a series of curved lines, diverging inevery direction from each pole, but always passing from one pole to theother. It is a universal law that whenever a magnet is brought into aregion where this force acts, it is attracted into such a position thatit shall have the same direction as the lines of force. Its north polewill take the direction of the curve leading to the south pole of theother magnet, and its south pole the opposite one. 

The fact of terrestrial magnetism may be expressed by saying that thespace within and around the whole earth is filled by lines of magneticforce, which we know nothing about until we suspend a magnet soperfectly balanced that it may point in any direction whatever. Then itturns and points in the direction of the lines of force, which may thusbe mapped out for all points of the earth. 

We commonly say that the pole of the needle points towards the north. The poets tell us how the needle is true to the pole. Every reader, however, is now familiar with the general fact of a variation of thecompass. On our eastern seaboard, and all the way across the Atlantic, the north pointing of the compass varies so far to the west that a shipgoing to Europe and making no allowance for this deviation would findherself making more nearly for the North Cape than for her destination. The "declination, " as it is termed in scientific language, varies fromone region of the earth to another. In some places it is towards thewest, in others towards the east. 

The pointing of the needle in various regions of the world is shown bymeans of magnetic maps. Such maps are published by the United StatesCoast Survey, whose experts make a careful study of the magnetic forceall over the country. It is found that there is a line running nearlynorth and south through the Middle States along which there is novariation of the compass. To the east of it the variation of the northpole of the magnet is west; to the west of it, east. The most rapidchanges in the pointing of the needle are towards the northeast andnorthwest regions. When we travel to the northeastern boundary of Mainethe westerly variation has risen to 20 degrees. Towards the northwestthe easterly variation continually increases, until, in the northernpart of the State of Washington, it amounts to 23 degrees. 

When we cross the Atlantic into Europe we find the west variationdiminishing until we reach a certain line passing through centralRussia and western Asia. This is again a line of no variation. Crossingit, the variation is once more towards the east. This directioncontinues over most of the continent of Asia, but varies in a somewhatirregular manner from one part of the continent to another. 

As a general rule, the lines of the earth's magnetic force are nothorizontal, and therefore one end or the other of a perfectly suspendedmagnet will dip below the horizontal position. This is called the "dipof the needle. " It is observed by means of a brass circle, of which thecircumference is marked off in degrees. A magnet is attached to thiscircle so as to form a diameter, and suspended on a horizontal axispassing through the centre of gravity, so that the magnet shall be freeto point in the direction indicated by the earth's lines of magneticforce. Armed with this apparatus, scientific travellers and navigatorshave visited various points of the earth in order to determine the dip. It is thus found that there is a belt passing around the earth near theequator, but sometimes deviating several degrees from it, in whichthere is no dip; that is to say, the lines of magnetic force arehorizontal. Taking any point on this belt and going north, it will befound that the north pole of the magnet gradually tends downward, thedip constantly increasing as we go farther north. In the southern partof the United States the dip is about 60 degrees, and the direction ofthe needle is nearly perpendicular to the earth's axis. In the northernpart of the country, including the region of the Great Lakes, the dipincreases to 75 degrees. Noticing that a dip of 90 degrees would meanthat the north end of the magnet points straight downward, it followsthat it would be more nearly correct to say that, throughout the UnitedStates, the magnetic needle points up and down than that it pointsnorth and south. 

Going yet farther north, we find the dip still increasing, until at acertain point in the arctic regions the north pole of the needle pointsdownward. In this region the compass is of no use to the traveller orthe navigator. The point is called the Magnetic Pole. Its position hasbeen located several times by scientific observers. The bestdeterminations made during the last eighty years agree fairly well inplacing it near 70 degrees north latitude and 97 degrees longitude westfrom Greenwich. This point is situated on the west shore of theBoothian Peninsula, which is bounded on the south end by McClintockChannel. It is about five hundred miles north of the northwest part ofHudson Bay. There is a corresponding magnetic pole in the AntarcticOcean, or rather on Victoria Land, nearly south of Australia. Itsposition has not been so exactly located as in the north, but it issupposed to be at about 74 degrees of south latitude and 147 degrees ofeast longitude from Greenwich. 

The magnetic poles used to be looked upon as the points towards whichthe respective ends of the needle were attracted. And, as a matter offact, the magnetic force is stronger near the poles than elsewhere. When located in this way by strength of force, it is found that thereis a second north pole in northern Siberia. Its location has not, however, been so well determined as in the case of the American pole, and it is not yet satisfactorily shown that there is any one point inSiberia where the direction of the force is exactly downward. 

[Illustration with caption: DIP OF THE MAGNETIC NEEDLE IN VARIOUSLATITUDES. The arrow points show the direction of the north end of themagnetic needle, which dips downward in north latitudes, while thesouth end dips in south latitudes. ]

The declination and dip, taken together, show the exact direction ofthe magnetic force at any place. But in order to complete the statementof the force, one more element must be given--its amount. The intensityof the magnetic force is determined by suspending a magnet in ahorizontal position, and then allowing it to oscillate back and fortharound the suspension. The stronger the force, the less the time itwill take to oscillate. Thus, by carrying a magnet to various parts ofthe world, the magnetic force can be determined at every point where aproper support for the magnet is obtainable. The intensity thus foundis called the horizontal force. This is not really the total force, because the latter depends upon the dip; the greater the dip, the lesswill be the horizontal force which corresponds to a certain totalforce. But a very simple computation enables the one to be determinedwhen the value of the other is known. In this way it is found that, asa general rule, the magnetic force is least in the earth's equatorialregions and increases as we approach either of the magnetic poles. 

When the most exact observations on the direction of the needle aremade, it is found that it never remains at rest. Beginning with thechanges of shortest duration, we have a change which takes place everyday, and is therefore called diurnal. In our northern latitudes it isfound that during the six hours from nine o'clock at night until threein the morning the direction of the magnet remains nearly the same. Butbetween three and four A. M. It begins to deviate towards the east, going farther and farther east until about 8 A. M. Then, rathersuddenly, it begins to swing towards the west with a much more rapidmovement, which comes to an end between one and two o'clock in theafternoon. Then, more slowly, it returns in an easterly direction untilabout nine at night, when it becomes once more nearly quiescent. Happily, the amount of this change is so small that the navigator neednot trouble himself with it. The entire range of movement rarelyamounts to one-quarter of a degree. 

It is a curious fact that the amount of the change is twice as great inJune as it is in December. This indicates that it is caused by thesun's radiation. But how or why this cause should produce such aneffect no one has yet discovered. 

Another curious feature is that in the southern hemisphere thedirection of the motion is reversed, although its general characterremains the same. The pointing deviates towards the west in themorning, then rapidly moves towards the east until about two o'clock, after which it slowly returns to its original direction. 

The dip of the needle goes through a similar cycle of daily changes. Innorthern latitudes it is found that at about six in the morning the dipbegins to increase, and continues to do so until noon, after which itdiminishes until seven or eight o'clock in the evening, when it becomesnearly constant for the rest of the night. In the southern hemispherethe direction of the movement is reversed. 

When the pointing of the needle is compared with the direction of themoon, it is found that there is a similar change. But, instead offollowing the moon in its course, it goes through two periods in a day, like the tides. When the moon is on the meridian, whether above orbelow us, the effect is in one direction, while when it is rising orsetting it is in the opposite direction. In other words, there is acomplete swinging backward and forward twice in a lunar day. It mightbe supposed that such an effect would be due to the moon, like theearth, being a magnet. But were this the case there would be only oneswing back and forth during the passage of the moon from the meridianuntil it came back to the meridian again. The effect would be oppositeat the rising and setting of the moon, which we have seen is not thecase. To make the explanation yet more difficult, it is found that, asin the case of the sun, the change is opposite in the northern andsouthern hemispheres and very small at the equator, where, by virtue ofany action that we can conceive of, it ought to be greatest. Thepointing is also found to change with the age of the moon and with theseason of the year. But these motions are too small to be set forth inthe present article. 

There is yet another class of changes much wider than these. Theobservations recorded since the time of Columbus show that, in thecourse of centuries, the variation of the compass, at any one point, changes very widely. It is well known that in 1490 the needle pointedeast of north in the Mediterranean, as well as in those portions of theAtlantic which were then navigated. Columbus was therefore muchastonished when, on his first voyage, in mid-ocean, he found that thedeviation was reversed, and was now towards the west. It follows that aline of no variation then passed through the Atlantic Ocean. But thisline has since been moving towards the east. About 1662 it passed themeridian of Paris. During the two hundred and forty years which havesince elapsed, it has passed over Central Europe, and now, as we havealready said, passes through European Russia. 

The existence of natural magnets composed of iron ore, and theirproperty of attracting iron and making it magnetic, have been knownfrom the remotest antiquity. But the question as to who firstdiscovered the fact that a magnetized needle points north and south, and applied this discovery to navigation, has given rise to muchdiscussion. That the property was known to the Chinese about thebeginning of our era seems to be fairly well established, thestatements to that effect being of a kind that could not well have beeninvented. Historical evidence of the use of the magnetic needle innavigation dates from the twelfth century. The earliest compassconsisted simply of a splinter of wood or a piece of straw to which themagnetized needle was attached, and which was floated in water. Acurious obstacle is said to have interfered with the first uses of thisinstrument. Jack is a superstitious fellow, and we may be sure that hewas not less so in former times than he is today. From his point ofview there was something uncanny in so very simple a contrivance as afloating straw persistently showing him the direction in which he mustsail. It made him very uncomfortable to go to sea under the guidance ofan invisible power. But with him, as with the rest of us, familiaritybreeds contempt, and it did not take more than a generation to showthat much good and no harm came to those who used the magic pointer. 

The modern compass, as made in the most approved form for naval andother large ships, is the liquid one. This does not mean that the cardbearing the needle floats on the liquid, but only that a part of theforce is taken off from the pivot on which it turns, so as to make thefriction as small as possible, and to prevent the oscillation back andforth which would continually go on if the card were perfectly free toturn. The compass-card is marked not only with the thirty-two familiarpoints of the compass, but is also divided into degrees. In the mostaccurate navigation it is probable that very little use of the pointsis made, the ship being directed according to the degrees. 

A single needle is not relied upon to secure the direction of the card, the latter being attached to a system of four or even more magnets, allpointing in the same direction. The compass must have no iron in itsconstruction or support, because the attraction of that substance onthe needle would be fatal to its performance. 

From this cause the use of iron as ship-building material introduced adifficulty which it was feared would prove very serious. The thousandsof tons of iron in a ship must exert a strong attraction on themagnetic needle. Another complication is introduced by the fact thatthe iron of the ship will always become more or less magnetic, and whenthe ship is built of steel, as modern ones are, this magnetism will bemore or less permanent. 

We have already said that a magnet has the property of making steel oriron in its neighborhood into another magnet, with its poles pointingin the opposite direction. The consequence is that the magnetism of theearth itself will make iron or steel more or less magnetic. As a shipis built she thus becomes a great repository of magnetism, thedirection of the force of which will depend upon the position in whichshe lay while building. If erected on the bank of an east and weststream, the north end of the ship will become the north pole of amagnet and the south end the south pole. Accordingly, when she islaunched and proceeds to sea, the compass points not exactly accordingto the magnetism of the earth, but partly according to that of the shipalso. 

The methods of obviating this difficulty have exercised the ingenuityof the ablest physicists from the beginning of iron ship building. Onemethod is to place in the neighborhood of the compass, but not too nearit, a steel bar magnetized in the opposite direction from that of theship, so that the action of the latter shall be neutralized. But aperfect neutralization cannot be thus effected. It is all the moredifficult to effect it because the magnetism of a ship is liable tochange. 

The practical method therefore adopted is called "swinging the ship, "an operation which passengers on ocean liners may have frequentlynoticed when approaching land. The ship is swung around so that her bowshall point in various directions. At each pointing the direction ofthe ship is noticed by sighting on the sun, and also the direction ofthe compass itself. In this way the error of the pointing of thecompass as the ship swings around is found for every direction in whichshe may be sailing. A table can then be made showing what the pointing, according to the compass, should be in order that the ship may sail inany given direction. 

This, however, does not wholly avoid the danger. The tables thus madeare good when the ship is on a level keel. If, from any cause whatever, she heels over to one side, the action will be different. Thus there isa "heeling error" which must be allowed for. It is supposed to havebeen from this source of error not having been sufficiently determinedor appreciated that the lamentable wreck of the United States shipHuron off the coast of Hatteras occurred some twenty years ago. 

X

THE FAIRYLAND OF GEOMETRY

If the reader were asked in what branch of science the imagination isconfined within the strictest limits, he would, I fancy, reply that itmust be that of mathematics. The pursuer of this science deals onlywith problems requiring the most exact statements and the most rigorousreasoning. In all other fields of thought more or less room for playmay be allowed to the imagination, but here it is fettered by ironrules, expressed in the most rigid logical form, from which nodeviation can be allowed. We are told by philosophers that absolutecertainty is unattainable in all ordinary human affairs, the only fieldin which it is reached being that of geometric demonstration. 

And yet geometry itself has its fairyland--a land in which theimagination, while adhering to the forms of the strictestdemonstration, roams farther than it ever did in the dreams of Grimm orAndersen. One thing which gives this field its strictly mathematicalcharacter is that it was discovered and explored in the search aftersomething to supply an actual want of mathematical science, and wasincited by this want rather than by any desire to give play to fancy. Geometricians have always sought to found their science on the mostlogical basis possible, and thus have carefully and critically inquiredinto its foundations. The new geometry which has thus arisen is of twoclosely related yet distinct forms. One of these is calledNON-EUCLIDIAN, because Euclid's axiom of parallels, which we shallpresently explain, is ignored. In the other form space is assumed tohave one or more dimensions in addition to the three to which the spacewe actually inhabit is confined. As we go beyond the limits set byEuclid in adding a fourth dimension to space, this last branch as wellas the other is often designated non-Euclidian. But the more commonterm is hypergeometry, which, though belonging more especially to spaceof more than three dimensions, is also sometimes applied to anygeometric system which transcends our ordinary ideas. 

In all geometric reasoning some propositions are necessarily taken forgranted. These are called axioms, and are commonly regarded asself-evident. Yet their vital principle is not so much that of beingself-evident as being, from the nature of the case, incapable ofdemonstration. Our edifice must have some support to rest upon, and wetake these axioms as its foundation. One example of such a geometricaxiom is that only one straight line can be drawn between two fixedpoints; in other words, two straight lines can never intersect in morethan a single point. The axiom with which we are at present concernedis commonly known as the 11th of Euclid, and may be set forth in thefollowing way: We have given a straight line, A B, and a point, P, withanother line, C D, passing through it and capable of being turnedaround on P. Euclid assumes that this line C D will have one positionin which it will be parallel to A B, that is, a position such that ifthe two lines are produced without end, they will never meet. His axiomis that only one such line can be drawn through P. That is to say, ifwe make the slightest possible change in the direction of the line C D, it will intersect the other line, either in one direction or the other. 

The new geometry grew out of the feeling that this proposition ought tobe proved rather than taken as an axiom; in fact, that it could in someway be derived from the other axioms. Many demonstrations of it wereattempted, but it was always found, on critical examination, that theproposition itself, or its equivalent, had slyly worked itself in aspart of the base of the reasoning, so that the very thing to be provedwas really taken for granted. 

[Illustration with caption: FIG. 1]

This suggested another course of inquiry. If this axiom of parallelsdoes not follow from the other axioms, then from these latter we mayconstruct a system of geometry in which the axiom of parallels shallnot be true. This was done by Lobatchewsky and Bolyai, the one aRussian the other a Hungarian geometer, about 1830. 

To show how a result which looks absurd, and is really inconceivable byus, can be treated as possible in geometry, we must have recourse toanalogy. Suppose a world consisting of a boundless flat plane to beinhabited by reasoning beings who can move about at pleasure on theplane, but are not able to turn their heads up or down, or even to seeor think of such terms as above them and below them, and things aroundthem can be pushed or pulled about in any direction, but cannot belifted up. People and things can pass around each other, but cannotstep over anything. These dwellers in "flatland" could construct aplane geometry which would be exactly like ours in being based on theaxioms of Euclid. Two parallel straight lines would never meet, thoughcontinued indefinitely. 

But suppose that the surface on which these beings live, instead ofbeing an infinitely extended plane, is really the surface of an immenseglobe, like the earth on which we live. It needs no knowledge ofgeometry, but only an examination of any globular object--an apple, forexample--to show that if we draw a line as straight as possible on asphere, and parallel to it draw a small piece of a second line, andcontinue this in as straight a line as we can, the two lines will meetwhen we proceed in either direction one-quarter of the way around thesphere. For our "flat-land" people these lines would both be perfectlystraight, because the only curvature would be in the directiondownward, which they could never either perceive or discover. The lineswould also correspond to the definition of straight lines, because anyportion of either contained between two of its points would be theshortest distance between those points. And yet, if these people shouldextend their measures far enough, they would find any two parallellines to meet in two points in opposite directions. For all smallspaces the axioms of their geometry would apparently hold good, butwhen they came to spaces as immense as the semi-diameter of the earth, they would find the seemingly absurd result that two parallel lineswould, in the course of thousands of miles, come together. Anotherresult yet more astonishing would be that, going ahead far enough in astraight line, they would find that although they had been goingforward all the time in what seemed to them the same direction, theywould at the end of 25, 000 miles find themselves once more at theirstarting-point. 

One form of the modern non-Euclidian geometry assumes that a similartheorem is true for the space in which our universe is contained. Although two straight lines, when continued indefinitely, do not appearto converge even at the immense distances which separate us from thefixed stars, it is possible that there may be a point at which theywould eventually meet without either line having deviated from itsprimitive direction as we understand the case. It would follow that, ifwe could start out from the earth and fly through space in a perfectlystraight line with a velocity perhaps millions of times that of light, we might at length find ourselves approaching the earth from adirection the opposite of that in which we started. Our straight-linecircle would be complete. 

Another result of the theory is that, if it be true, space, thoughstill unbounded, is not infinite, just as the surface of a sphere, though without any edge or boundary, has only a limited extent ofsurface. Space would then have only a certain volume--a volume which, though perhaps greater than that of all the atoms in the materialuniverse, would still be capable of being expressed in cubic miles. Ifwe imagine our earth to grow larger and larger in every directionwithout limit, and with a speed similar to that we have described, sothat to-morrow it was large enough to extend to the nearest fixedstars, the day after to yet farther stars, and so on, and we, livingupon it, looked out for the result, we should, in time, see the otherside of the earth above us, coming down upon us? as it were. The spaceintervening would grow smaller, at last being filled up. The earthwould then be so expanded as to fill all existing space. 

This, although to us the most interesting form of the non-Euclidiangeometry, is not the only one. The idea which Lobatchewsky worked outwas that through a point more than one parallel to a given line couldbe drawn; that is to say, if through the point P we have alreadysupposed another line were drawn making ever so small an angle with CD, this line also would never meet the line AB. It might approach thelatter at first, but would eventually diverge. The two lines AB and CD, starting parallel, would eventually, perhaps at distances greater thanthat of the fixed stars, gradually diverge from each other. This systemdoes not admit of being shown by analogy so easily as the other, but anidea of it may be had by supposing that the surface of "flat-land, "instead of being spherical, is saddle-shaped. Apparently straightparallel lines drawn upon it would then diverge, as supposed by Bolyai. We cannot, however, imagine such a surface extended indefinitelywithout losing its properties. The analogy is not so clearly marked asin the other case. 

To explain hypergeometry proper we must first set forth what a fourthdimension of space means, and show how natural the way is by which itmay be approached. We continue our analogy from "flat-land" In thissupposed land let us make a cross--two straight lines intersecting atright angles. The inhabitants of this land understand the crossperfectly, and conceive of it just as we do. But let us ask them todraw a third line, intersecting in the same point, and perpendicular toboth the other lines. They would at once pronounce this absurd andimpossible. It is equally absurd and impossible to us if we require thethird line to be drawn on the paper. But we should reply, "If you allowus to leave the paper or flat surface, then we can solve the problem bysimply drawing the third line through the paper perpendicular to itssurface. "

[Illustration with caption: FIG. 2]

Now, to pursue the analogy, suppose that, after we have drawn threemutually perpendicular lines, some being from another sphere proposesto us the drawing of a fourth line through the same point, perpendicular to all three of the lines already there. We should answerhim in the same way that the inhabitants of "flat-land" answered us:"The problem is impossible. You cannot draw any such line in space aswe understand it. " If our visitor conceived of the fourth dimension, hewould reply to us as we replied to the "flat-land" people: "The problemis absurd and impossible if you confine your line to space as youunderstand it. But for me there is a fourth dimension in space. Drawyour line through that dimension, and the problem will be solved. Thisis perfectly simple to me; it is impossible to you solely because yourconceptions do not admit of more than three dimensions. "

Supposing the inhabitants of "flat-land" to be intellectual beings aswe are, it would be interesting to them to be told what dwellers ofspace in three dimensions could do. Let us pursue the analogy byshowing what dwellers in four dimensions might do. Place a dweller of"flat-land" inside a circle drawn on his plane, and ask him to stepoutside of it without breaking through it. He would go all around, and, finding every inch of it closed, he would say it was impossible fromthe very nature of the conditions. "But, " we would reply, "that isbecause of your limited conceptions. We can step over it. "

"Step over it!" he would exclaim. "I do not know what that means. I canpass around anything if there is a way open, but I cannot imagine whatyou mean by stepping over it. "

But we should simply step over the line and reappear on the other side. So, if we confine a being able to move in a fourth dimension in thewalls of a dungeon of which the sides, the floor, and the ceiling wereall impenetrable, he would step outside of it without touching any partof the building, just as easily as we could step over a circle drawn onthe plane without touching it. He would simply disappear from our viewlike a spirit, and perhaps reappear the next moment outside the prison. To do this he would only have to make a little excursion in the fourthdimension. 

[Illustration with caption: FIG. 3]

Another curious application of the principle is more purelygeometrical. We have here two triangles, of which the sides and anglesof the one are all equal to corresponding sides and angles of theother. Euclid takes it for granted that the one triangle can be laidupon the other so that the two shall fit together. But this cannot bedone unless we lift one up and turn it over. In the geometry of"flat-land" such a thing as lifting up is inconceivable; the twotriangles could never be fitted together. 

[Illustration with caption: FIG 4]

Now let us suppose two pyramids similarly related. All the faces andangles of the one correspond to the faces and angles of the other. Yet, lift them about as we please, we could never fit them together. If wefit the bases together the two will lie on opposite sides, one beingbelow the other. But the dweller in four dimensions of space will fitthem together without any trouble. By the mere turning over of one hewill convert it into the other without any change whatever in therelative position of its parts. What he could do with the pyramids hecould also do with one of us if we allowed him to take hold of us andturn a somersault with us in the fourth dimension. We should then comeback into our natural space, but changed as if we were seen in amirror. Everything on us would be changed from right to left, even theseams in our clothes, and every hair on our head. All this would bedone without, during any of the motion, any change having occurred inthe positions of the parts of the body. 

It is very curious that, in these transcendental speculations, the mostrigorous mathematical methods correspond to the most mystical ideas ofthe Swedenborgian and other forms of religion. Right around us, but ina direction which we cannot conceive any more than the inhabitants of"flat-land" can conceive up and down, there may exist not merelyanother universe, but any number of universes. All that physicalscience can say against the supposition is that, even if a fourthdimension exists, there is some law of all the matter with which we areacquainted which prevents any of it from entering that dimension, sothat, in our natural condition, it must forever remain unknown to us. 

Another possibility in space of four dimensions would be that ofturning a hollow sphere, an india-rubber ball, for example, inside outby simple bending without tearing it. To show the motion in our spaceto which this is analogous, let us take a thin, round sheet ofindia-rubber, and cut out all the central part, leaving only a narrowring round the border. Suppose the outer edge of this ring fasteneddown on a table, while we take hold of the inner edge and stretch itupward and outward over the outer edge until we flatten the whole ringon the table, upside down, with the inner edge now the outer one. Thismotion would be as inconceivable in "flat-land" as turning the ballinside out is to us. 

XI

THE ORGANIZATION OF SCIENTIFIC RESEARCH

The claims of scientific research on the public were never moreforcibly urged than in Professor Ray Lankester's recent Romanes Lecturebefore the University of Oxford. Man is here eloquently pictured asNature's rebel, who, under conditions where his great superior commands"Thou shalt die, " replies "I will live. " In pursuance of thisdetermination, civilized man has proceeded so far in his interferencewith the regular course of Nature that he must either go on and acquirefirmer control of the conditions, or perish miserably by the vengeancecertain to be inflicted on the half-hearted meddler in great affairs. This rebel by every step forward renders himself liable to greater andgreater penalties, and so cannot afford to pause or fail in one singlestep. One of Nature's most powerful agencies in thwarting hisdetermination to live is found in disease-producing parasites. "Wherethere is one man of first-rate intelligence now employed in gainingknowledge of this agency, there should be a thousand. It should be asmuch the purpose of civilized nations to protect their citizens in thisrespect as it is to provide defence against human aggression. "

It was no part of the function of the lecturer to devise a plan forcarrying on the great war he proposes to wage. The object of thepresent article is to contribute some suggestions in this direction;with especial reference to conditions in our own country; and no bettertext can be found for a discourse on the subject than the precedingquotation. In saying that there should be a thousand investigators ofdisease where there is now one, I believe that Professor Lankesterwould be the first to admit that this statement was that of an ideal tobe aimed at, rather than of an end to be practically reached. Everycareful thinker will agree that to gather a body of men, young or old, supply them with laboratories and microscopes, and tell them toinvestigate disease, would be much like sending out an army withouttrained leaders to invade an enemy's country. 

There is at least one condition of success in this line which is betterfulfilled in our own country than in any other; and that is liberalityof support on the part of munificent citizens desirous of so employingtheir wealth as to promote the public good. Combining thisinstrumentality with the general public spirit of our people, it mustbe admitted that, with all the disadvantages under which scientificresearch among us has hitherto labored, there is still no country towhich we can look more hopefully than to our own as the field in whichthe ideal set forth by Professor Lankester is to be pursued. Somethoughts on the question how scientific research may be mosteffectively promoted in our own country through organized effort maytherefore be of interest. Our first step will be to inquire whatgeneral lessons are to be learned from the experience of the past. 

The first and most important of these lessons is that research hasnever reached its highest development except at centres where bodies ofmen engaged in it have been brought together, and stimulated to actionby mutual sympathy and support. We must call to mind that, although thebeginnings of modern science were laid by such men as Copernicus, Galileo, Leonardo da Vinci, and Torricelli, before the middle of theseventeenth century, unbroken activity and progress date from thefoundations of the Academy of Sciences of Paris and the Royal Societyof London at that time. The historic fact that the bringing of mentogether, and their support by an intelligent and interested community, is the first requirement to be kept in view can easily be explained. Effective research involves so intricate a network of problems andconsiderations that no one engaged in it can fail to profit by thesuggestions of kindred spirits, even if less acquainted with thesubject than he is himself. Intelligent discussion suggests new ideasand continually carries the mind to a higher level of thought. We mustnot regard the typical scientific worker, even of the highest class, asone who, having chosen his special field and met with success incultivating it, has only to be supplied with the facilities he may besupposed to need in order to continue his work in the most efficientway. What we have to deal with is not a fixed and permanent body oflearned men, each knowing all about the field of work in which he isengaged, but a changing and growing class, constantly recruited bybeginners at the bottom of the scale, and constantly depleted by theold dropping away at the top. No view of the subject is complete whichdoes not embrace the entire activity of the investigator, from the tyroto the leader. The leader himself, unless engaged in the prosecution ofsome narrow specialty, can rarely be so completely acquainted with hisfield as not to need information from others. Without this, he isconstantly liable to be repeating what has already been better donethan he can do it himself, of following lines which are known to leadto no result, and of adopting methods shown by the experience of othersnot to be the best. Even the books and published researches to which hemust have access may be so voluminous that he cannot find time tocompletely examine them for himself; or they may be inaccessible. Allthis will make it clear that, with an occasional exception, the bestresults of research are not to be expected except at centres wherelarge bodies of men are brought into close personal contact. 

In addition to the power and facility acquired by frequent discussionwith his fellows, the appreciation and support of an intelligentcommunity, to whom the investigator may, from time to time, make knownhis thoughts and the results of his work, add a most effectivestimulus. The greater the number of men of like minds that can bebrought together and the larger the community which interests itself inwhat they are doing, the more rapid will be the advance and the moreeffective the work carried on. It is thus that London, with itsmunificently supported institutions, and Paris and Berlin, with theirbodies of investigators supported either by the government or byvarious foundations, have been for more than three centuries the greatcentres where we find scientific activity most active and mosteffective. Looking at this undoubted fact, which has asserted itselfthrough so long a period, and which asserts itself today more stronglythan ever, the writer conceives that there can be no question as to oneproposition. If we aim at the single object of promoting the advance ofknowledge in the most effective way, and making our own country theleading one in research, our efforts should be directed towardsbringing together as many scientific workers as possible at a singlecentre, where they can profit in the highest degree by mutual help, support, and sympathy. 

In thus strongly setting forth what must seem an indisputableconclusion, the writer does not deny that there are drawbacks to such apolicy, as there are to every policy that can be devised aiming at agood result. Nature offers to society no good that she does notaccompany by a greater or less measure of evil The only question iswhether the good outweighs the evil. In the present case, the seemingevil, whether real or not, is that of centralization. A policy tendingin this direction is held to be contrary to the best interests ofscience in quarters entitled to so much respect that we must inquireinto the soundness of the objection. 

It would be idle to discuss so extreme a question as whether we shalltake all the best scientific investigators of our country from theirseveral seats of learning and attract them to some one point. We knowthat this cannot be done, even were it granted that success would beproductive of great results. The most that can be done is to choosesome existing centre of learning, population, wealth, and influence, and do what we can to foster the growth of science at that centre byattracting thither the greatest possible number of scientificinvestigators, especially of the younger class, and making it possiblefor them to pursue their researches in the most effective way. Thispolicy would not result in the slightest harm to any institution orcommunity situated elsewhere. It would not be even like building up auniversity to outrank all the others of our country; because thefunctions of the new institution, if such should be founded, would inits relations to the country be radically different from those of auniversity. Its primary object would not be the education of youth, butthe increase of knowledge. So far as the interests of any community orof the world at large are concerned, it is quite indifferent whereknowledge may be acquired, because, when once acquired and made public, it is free to the world. The drawbacks suffered by other centres wouldbe no greater than those suffered by our Western cities, because allthe great departments of the government are situated at a singledistant point. Strong arguments could doubtless be made for locatingsome of these departments in the Far West, in the Mississippi Valley, or in various cities of the Atlantic coast; but every one knows thatany local advantages thus gained would be of no importance comparedwith the loss of that administrative efficiency which is essential tothe whole country. 

There is, therefore, no real danger from centralization. The actualdanger is rather in the opposite direction; that the sentiment againstconcentrating research will prove to operate too strongly. There is afeeling that it is rather better to leave every investigator where hechances to be at the moment, a feeling which sometimes finds expressionin the apothegm that we cannot transplant a genius. That such aproposition should find acceptance affords a striking example of thereadiness of men to accept a euphonious phrase without inquiringwhether the facts support the doctrine which it enunciates. The fact isthat many, perhaps the majority, of the great scientific investigatorsof this and of former times have done their best work through beingtransplanted. As soon as the enlightened monarchs of Europe felt theimportance of making their capitals great centres of learning, theybegan to invite eminent men of other countries to their own. Lagrangewas an Italian transplanted to Paris, as a member of the Academy ofSciences, after he had shown his powers in his native country. Hisgreat contemporary, Euler, was a Swiss, transplanted first to St. Petersburg, then invited by Frederick the Great to become a member ofthe Berlin Academy, then again attracted to St. Petersburg. Huyghenswas transplanted from his native country to Paris. Agassiz was anexotic, brought among us from Switzerland, whose activity during thegeneration he passed among us was as great and effective as at any timeof his life. On the Continent, outside of France, the most eminentprofessors in the universities have been and still are brought fromdistant points. So numerous are the cases of which these are examplesthat it would be more in accord with the facts to claim that it is onlyby transplanting a genius that we stimulate him to his best work. 

Having shown that the best results can be expected only by bringinginto contact as many scientific investigators as possible, the nextquestion which arises is that of their relations to one another. It maybe asked whether we shall aim at individualism or collectivism. Shallour ideal be an organized system of directors, professors, associates, assistants, fellows; or shall it be a collection of individual workers, each pursuing his own task in the way he deems best, untrammelled byauthority?

The reply to this question is that there is in this special case noantagonism between the two ideas. The most effective organization willaim both at the promotion of individual effort, and at subordinationand co-operation. It would be a serious error to formulate any generalrule by which all cases should be governed. The experience of the pastshould be our guide, so far as it applies to present and futureconditions; but in availing ourselves of it we must remember thatconditions are constantly changing, and must adapt our policy to theproblems of the future. In doing this, we shall find that differentfields of research require very different policies as regardsco-operation and subordination. It will be profitable to point outthose special differences, because we shall thereby gain a moreluminous insight into the problems which now confront the scientificinvestigator, and better appreciate their variety, and the necessity ofdifferent methods of dealing with them. 

At one extreme, we have the field of normative science, work in whichis of necessity that of the individual mind alone. This embraces puremathematics and the methods of science in their widest range. Thecommon interests of science require that these methods shall be workedout and formulated for the guidance of investigators generally, andthis work is necessarily that of the individual brain. 

At the other extreme, we have the great and growing body of sciences ofobservation. Through the whole nineteenth century, to say nothing ofprevious centuries, organizations, and even individuals, have beenengaged in recording the innumerable phases of the course of nature, hoping to accumulate material that posterity shall be able to utilizefor its benefit. We have observations astronomical, meteorological, magnetic, and social, accumulating in constantly increasing volume, themass of which is so unmanageable with our present organizations thatthe question might well arise whether almost the whole of it will nothave to be consigned to oblivion. Such a conclusion should not beentertained until we have made a vigorous effort to find what puremetal of value can be extracted from the mass of ore. To do thisrequires the co-operation of minds of various orders, quite akin intheir relations to those necessary in a mine or great manufacturingestablishment. Laborers whose duties are in a large measure matters ofroutine must be guided by the skill of a class higher in quality andsmaller in number than their own, and these again by the technicalknowledge of leaders in research. Between these extremes we have agreat variety of systems of co-operation. 

There is another feature of modern research the apprehension of whichis necessary to the completeness of our view. A cursory survey of thefield of science conveys the impression that it embraces only aconstantly increasing number of disconnected specialties, in which eachcultivator knows little or nothing of what is being done by others. Measured by its bulk, the published mass of scientific research isincreasing in a more than geometrical ratio. Not only do thepublications of nearly every scientific society increase in number andvolume, but new and vigorous societies are constantly organized to addto the sum total. The stately quartos issued from the presses of theleading academies of Europe are, in most cases, to be counted byhundreds. The Philosophical Transactions of the Royal Society alreadynumber about two hundred volumes, and the time when the Memoirs of theFrench Academy of Sciences shall reach the thousand mark does notbelong to the very remote future. Besides such large volumes, these andother societies publish smaller ones in a constantly growing number. Inaddition to the publications of learned societies, there are journalsdevoted to each scientific specialty, which seem to propagate theirspecies by subdivision in much the same way as some of the lower ordersof animal life. Every new publication of the kind is suggested by thewants of a body of specialists, who require a new medium for theirresearches and communications. The time has already come when we cannotassume that any specialist is acquainted with all that is being doneeven in his own line. To keep the run of this may well be beyond hisown powers; more he can rarely attempt. 

What is the science of the future to do when this huge mass outgrowsthe space that can be found for it in the libraries, and what are we tosay of the value of it all? Are all these scientific researches to beclassed as really valuable contributions to knowledge, or have we onlya pile in which nuggets of gold are here and there to be sought for?One encouraging answer to such a question is that, taking the interestsof the world as a whole, scientific investigation has paid for itselfin benefits to humanity a thousand times over, and that all that isknown to-day is but an insignificant fraction of what Nature has toshow us. Apart from this, another feature of the science of our timedemands attention. While we cannot hope that the multiplication ofspecialties will cease, we find that upon the process ofdifferentiation and subdivision is now being superposed a form ofevolution, tending towards the general unity of all the sciences, ofwhich some examples may be pointed out. 

Biological science, which a generation ago was supposed to be at theantipodes of exact science, is becoming more and more exact, and iscultivated by methods which are developed and taught by mathematicians. Psychophysics--the study of the operations of the mind by physicalapparatus of the same general nature as that used by the chemist andphysicist--is now an established branch of research. A natural sciencewhich, if any comparisons are possible, may outweigh all others inimportance to the race, is the rising one of "eugenics, "--theimprovement of the human race by controlling the production of itsoffspring. No better example of the drawbacks which our country suffersas a seat of science can be given than the fact that the beginning ofsuch a science has been possible only at the seat of a larger body ofcultivated men than our land has yet been able to bring together. Generations may elapse before the seed sown by Mr. Francis Galton, fromwhich grew the Eugenic Society, shall bear full fruit in the adoptionof those individual efforts and social regulations necessary to thepropagation of sound and healthy offspring on the part of the humanfamily. But when this comes about, then indeed will ProfessorLankester's "rebel against Nature" find his independence acknowledgedby the hitherto merciless despot that has decreed punishment for histreason. 

This new branch of science from which so much may be expected is theoffshoot of another, the rapid growth of which illustrates the rapidinvasion of the most important fields of thought by the methods ofexact science. It is only a few years since it was remarked ofProfessor Karl Pearson's mathematical investigations into the laws ofheredity, and the biological questions associated with these laws, thathe was working almost alone, because the biologists did not understandhis mathematics, while the mathematicians were not interested in hisbiology. Had he not lived at a great centre of active thought, withinthe sphere of influence of the two great universities of England, it isquite likely that this condition of isolation would have been his tothe end. But, one by one, men were found possessing the skill andinterest in the subject necessary to unite in his work, which now hasnot only a journal of its own, but is growing in a way which, thoughslow, has all the marks of healthy progress towards an end theimportance of which has scarcely dawned upon the public mind. 

Admitting that an organized association of investigators is of thefirst necessity to secure the best results in the scientific work ofthe future, we meet the question of the conditions and auspices underwhich they are to be brought together. The first thought to strike usat this point may well be that we have, in our great universities, organizations which include most of the leading men now engaged inscientific research, whose personnel and facilities we should utilize. Admitting, as we all do, that there are already too many universities, and that better work would be done by a consolidation of the smallerones, a natural conclusion is that the end in view will be best reachedthrough existing organizations. But it would be a great mistake to jumpat this conclusion without a careful study of the conditions. The briefargument--there are already too many institutions--instead of havingmore we should strengthen those we have--should not be accepted withoutexamination. Had it been accepted thirty years ago, there are at leasttwo great American universities of to-day which would not have comeinto being, the means devoted to their support having been dividedamong others. These are the Johns Hopkins and the University ofChicago. What would have been gained by applying the argument in thesecases? The advantage would have been that, instead of 146 so-calleduniversities which appear to-day in the Annual Report of the Bureau ofEducation, we should have had only 144. The work of these 144 wouldhave been strengthened by an addition, to their resources, representedby the endowments of Baltimore and Chicago, and sufficient to addperhaps one professor to the staff of each. Would the result have beenbetter than it actually has been? Have we not gained anything byallowing the argument to be forgotten in the cases of these twoinstitutions? I do not believe that any who carefully look at thesubject will hesitate in answering this question in the affirmative. The essential point is that the Johns Hopkins University did not merelyadd one to an already overcrowded list, but that it undertook a missionwhich none of the others was then adequately carrying out. If it didnot plant the university idea in American soil, it at least gave it animpetus which has now made it the dominant one in the higher educationof almost every state. 

The question whether the country at large would have reaped a greaterbenefit, had the professors of the University of Chicago, with theappliances they now command, been distributed among fifty or a hundredinstitutions in every quarter of the land, than it has actually reapedfrom that university, is one which answers itself. Our two youngestuniversities have attained success, not because two have thus beenadded to the number of American institutions of learning, but becausethey had a special mission, required by the advance of the age, forwhich existing institutions were inadequate. 

The conclusion to which these considerations lead is simple. No newinstitution is needed to pursue work on traditional lines, guided bytraditional ideas. But, if a new idea is to be vigorously prosecuted, then a young and vigorous institution, specially organized to put theidea into effect, is necessary. The project of building up in ourmidst, at the most appropriate point, an organization of leadingscientific investigators, for the single purpose of giving a newimpetus to American science and, if possible, elevating the thought ofthe country and of the world to a higher plane, involves a new idea, which can best be realized by an institution organized for the specialpurpose. While this purpose is quite in line with that of the leadinguniversities, it goes too far beyond them to admit of its completeattainment through their instrumentality. The first object of auniversity is the training of the growing individual for the highestduties of life. Additions to the mass of knowledge have not been itsprincipal function, nor even an important function in our own country, until a recent time. The primary object of the proposed institution isthe advance of knowledge and the opening up of new lines of thought, which, it may be hoped, are to prove of great import to humanity. Itdoes not follow that the function of teaching shall be wholly foreignto its activities. It must take up the best young men at the pointwhere universities leave them, and train them in the arts of thinkingand investigating. But this training will be beyond that which anyregular university is carrying out. 

In pursuing our theme the question next arises as to the specialfeatures of the proposed association. The leading requirement is onethat cannot be too highly emphasized. How clearly soever the organizersmay have in their minds' eye the end in view, they must recognize thefact that it cannot be attained in a day. In every branch of work whichis undertaken, there must be a single leader, and he must be the bestthat the country, perhaps even the world, can produce. The required manis not to be found without careful inquiry; in many branches he may beunattainable for years. When such is the case, wait patiently till heappears. Prudence requires that the fewest possible risks would betaken, and that no leader should be chosen except one of triedexperience and world-wide reputation. Yet we should not leave whollyout of sight the success of the Johns Hopkins University in selecting, at its very foundation, young men who were to prove themselves theleaders of the future. This experience may admit of being repeated, ifit be carefully borne in mind that young men of promise are to beavoided and young men of performance only to be considered. Theperformance need not be striking: ex pede Herculem may be possible; butwe must be sure of the soundness of our judgment before accepting ourHercules. This requires a master. Clerk-Maxwell, who never left hisnative island to visit our shores, is entitled to honor as a promoterof American science for seeing the lion's paw in the early efforts ofRowland, for which the latter was unable to find a medium ofpublication in his own country. It must also be admitted that the taskis more serious now than it was then, because, from the constantlyincreasing specialization of science, it has become difficult for aspecialist in one line to ascertain the soundness of work in another. With all the risks that may be involved in the proceeding, it will bequite possible to select an effective body of leaders, young and old, with whom an institution can begin. The wants of these men will be ofthe most varied kind. One needs scarcely more than a study and library;another must have small pieces of apparatus which he can perhaps designand make for himself. Another may need apparatus and appliances soexpensive that only an institution at least as wealthy as an ordinaryuniversity would be able to supply them. The apparatus required byothers will be very largely human--assistants of every grade, fromuniversity graduates of the highest standing down to routine drudgesand day-laborers. Workrooms there must be; but it is hardly probablethat buildings and laboratories of a highly specialized character willbe required at the outset. The best counsel will be necessary at everystep, and in this respect the institution must start from simplebeginnings and grow slowly. Leaders must be added one by one, eachbeing judged by those who have preceded him before becoming in his turna member of the body. As the body grows its members must be kept inpersonal touch, talk together, pull together, and act together. 

The writer submits these views to the great body of his fellow-citizensinterested in the promotion of American science with the feeling that, though his conclusions may need amendment in details, they rest uponfacts of the past and present which have not received the considerationwhich they merit. What he most strongly urges is that the whole subjectof the most efficient method of promoting research upon a higher planeshall be considered with special reference to conditions in our owncountry; and that the lessons taught by the history and progress ofscientific research in all countries shall be fully weighed anddiscussed by those most interested in making this form of effort a moreimportant feature of our national life. When this is done, he will feelthat his purpose in inviting special consideration to his individualviews has been in great measure reached. 

XII

CAN WE MAKE IT RAIN?

To the uncritical observer the possible achievements of invention anddiscovery seem boundless. Half a century ago no idea could haveappeared more visionary than that of holding communication in a fewseconds of time with our fellows in Australia, or having a talk goingon viva voce between a man in Washington and another in Boston. Theactual attainment of these results has naturally given rise to thebelief that the word "impossible" has disappeared from our vocabulary. To every demonstration that a result cannot be reached the answer is, Did not one Lardner, some sixty years ago, demonstrate that a steamshipcould not cross the Atlantic? If we say that for every actual discoverythere are a thousand visionary projects, we are told that, after all, any given project may be the one out of the thousand. 

In a certain way these hopeful anticipations are justified. We cannotset any limit either to the discovery of new laws of nature or to theingenious combination of devices to attain results which now lookimpossible. The science of to-day suggests a boundless field ofpossibilities. It demonstrates that the heat which the sun radiatesupon the earth in a single day would suffice to drive all thesteamships now on the ocean and run all the machinery on the land for athousand years. The only difficulty is how to concentrate and utilizethis wasted energy. From the stand-point of exact science aerialnavigation is a very simple matter. We have only to find the propercombination of such elements as weight, power, and mechanical force. Whenever Mr. Maxim can make an engine strong and light enough, andsails large, strong, and light enough, and devise the machineryrequired to connect the sails and engine, he will fly. Science hasnothing but encouraging words for his project, so far as generalprinciples are concerned. Such being the case, I am not going tomaintain that we can never make it rain. 

But I do maintain two propositions. If we are ever going to make itrain, or produce any other result hitherto unattainable, we must employadequate means. And if any proposed means or agency is already familiarto science, we may be able to decide beforehand whether it is adequate. Let us grant that out of a thousand seemingly visionary projects one isreally sound. Must we try the entire thousand to find the one? By nomeans. The chances are that nine hundred of them will involve no agencythat is not already fully understood, and may, therefore, be set asidewithout even being tried. To this class belongs the project ofproducing rain by sound. As I write, the daily journals are announcingthe brilliant success of experiments in this direction; yet Iunhesitatingly maintain that sound cannot make rain, and propose toadduce all necessary proof of my thesis. The nature of sound is fullyunderstood, and so are the conditions under which the aqueous vapor inthe atmosphere may be condensed. Let us see how the case stands. 

A room of average size, at ordinary temperature and under usualconditions, contains about a quart of water in the form of invisiblevapor. The whole atmosphere is impregnated with vapor in about the sameproportion. We must, however, distinguish between this invisible vaporand the clouds or other visible masses to which the same term is oftenapplied. The distinction may be very clearly seen by watching the steamcoming from the spout of a boiling kettle. Immediately at the spout theescaping steam is transparent and invisible; an inch or two away awhite cloud is formed, which we commonly call steam, and which is seenbelching out to a distance of one or more feet, and perhaps filling aconsiderable space around the kettle; at a still greater distance thiscloud gradually disappears. Properly speaking, the visible cloud is notvapor or steam at all, but minute particles or drops of water in aliquid state. The transparent vapor at the mouth of the kettle is thetrue vapor of water, which is condensed into liquid drops by cooling;but after being diffused through the air these drops evaporate andagain become true vapor. Clouds, then, are not formed of true vapor, but consist of impalpable particles of liquid water floating orsuspended in the air. 

But we all know that clouds do not always fall as rain. In order thatrain may fall the impalpable particles of water which form the cloudmust collect into sensible drops large enough to fall to the earth. Twosteps are therefore necessary to the formation of rain: the transparentaqueous vapor in the air must be condensed into clouds, and thematerial of the clouds must agglomerate into raindrops. 

No physical fact is better established than that, under the conditionswhich prevail in the atmosphere, the aqueous vapor of the air cannot becondensed into clouds except by cooling. It is true that in ourlaboratories it can be condensed by compression. But, for reasons whichI need not explain, condensation by compression cannot take place inthe air. The cooling which results in the formation of clouds and rainmay come in two ways. Rains which last for several hours or days aregenerally produced by the intermixture of currents of air of differenttemperatures. A current of cold air meeting a current of warm, moistair in its course may condense a considerable portion of the moistureinto clouds and rain, and this condensation will go on as long as thecurrents continue to meet. In a hot spring day a mass of air which hasbeen warmed by the sun, and moistened by evaporation near the surfaceof the earth, may rise up and cool by expansion to near thefreezing-point. The resulting condensation of the moisture may thenproduce a shower or thunder-squall. But the formation of clouds in aclear sky without motion of the air or change in the temperature of thevapor is simply impossible. We know by abundant experiments that a massof true aqueous vapor will never condense into clouds or drops so longas its temperature and the pressure of the air upon it remain unchanged. 

Now let us consider sound as an agent for changing the state of thingsin the air. It is one of the commonest and simplest agencies in theworld, which we can experiment upon without difficulty. It is purelymechanical in its action. When a bomb explodes, a certain quantity ofgas, say five or six cubic yards, is suddenly produced. It pushes asideand compresses the surrounding air in all directions, and this motionand compression are transmitted from one portion of the air to another. The amount of motion diminishes as the square of the distance; a simplecalculation shows that at a quarter of a mile from the point ofexplosion it would not be one ten-thousandth of an inch. Thecondensation is only momentary; it may last the hundredth or thethousandth of a second, according to the suddenness and violence of theexplosion; then elasticity restores the air to its original conditionand everything is just as it was before the explosion. A thousanddetonations can produce no more effect upon the air, or upon the wateryvapor in it, than a thousand rebounds of a small boy's rubber ballwould produce upon a stonewall. So far as the compression of the aircould produce even a momentary effect, it would be to prevent ratherthan to cause condensation of its vapor, because it is productive ofheat, which produces evaporation, not condensation. 

The popular notion that sound may produce rain is founded principallyupon the supposed fact that great battles have been followed by heavyrains. This notion, I believe, is not confirmed by statistics; but, whether it is or not, we can say with confidence that it was not thesound of the cannon that produced the rain. That sound as a physicalfactor is quite insignificant would be evident were it not for ourfallacious way of measuring it. The human ear is an instrument ofwonderful delicacy, and when its tympanum is agitated by a sound wecall it a "concussion" when, in fact, all that takes place is a suddenmotion back and forth of a tenth, a hundredth, or a thousandth of aninch, accompanied by a slight momentary condensation. After thesemotions are completed the air is exactly in the same condition as itwas before; it is neither hotter nor colder; no current has beenproduced, no moisture added. 

If the reader is not satisfied with this explanation, he can try a verysimple experiment which ought to be conclusive. If he will explode agrain of dynamite, the concussion within a foot of the point ofexplosion will be greater than that which can be produced by the mostpowerful bomb at a distance of a quarter of a mile. In fact, if thelatter can condense vapor a quarter of a mile away, then anybody cancondense vapor in a room by slapping his hands. Let us, therefore, goto work slapping our hands, and see how long we must continue before acloud begins to form. 

What we have just said applies principally to the condensation ofinvisible vapor. It may be asked whether, if clouds are already formed, something may not be done to accelerate their condensation intoraindrops large enough to fall to the ground. This also may be thesubject of experiment. Let us stand in the steam escaping from a kettleand slap our hands. We shall see whether the steam condenses intodrops. I am sure the experiment will be a failure; and no otherconclusion is possible than that the production of rain by sound orexplosions is out of the question. 

It must, however, be added that the laws under which the impalpableparticles of water in clouds agglomerate into drops of rain are not yetunderstood, and that opinions differ on this subject. Experiments todecide the question are needed, and it is to be hoped that the WeatherBureau will undertake them. For anything we know to the contrary, theagglomeration may be facilitated by smoke in the air. If it be reallytrue that rains have been produced by great battles, we may say withconfidence that they were produced by the smoke from the burning powderrising into the clouds and forming nuclei for the agglomeration intodrops, and not by the mere explosion. If this be the case, if it wasthe smoke and not the sound that brought the rain, then by burninggunpowder and dynamite we are acting much like Charles Lamb's Chinamenwho practised the burning of their houses for several centuries beforefinding out that there was any cheaper way of securing the coveteddelicacy of roast pig. 

But how, it may be asked, shall we deal with the fact that Mr. Dyrenforth's recent explosions of bombs under a clear sky in Texas werefollowed in a few hours, or a day or two, by rains in a region whererain was almost unknown? I know too little about the fact, if such itbe, to do more than ask questions about it suggested by well-knownscientific truths. If there is any scientific result which we canaccept with confidence, it is that ten seconds after the sound of thelast bomb died away, silence resumed her sway. From that momenteverything in the air--humidity, temperature, pressure, and motion--wasexactly the same as if no bomb had been fired. Now, what went on duringthe hours that elapsed between the sound of the last bomb and thefalling of the first drop of rain? Did the aqueous vapor already in thesurrounding air slowly condense into clouds and raindrops in defianceof physical laws? If not, the hours must have been occupied by thepassage of a mass of thousands of cubic miles of warm, moist air comingfrom some other region to which the sound could not have extended. Orwas Jupiter Pluvius awakened by the sound after two thousand years ofslumber, and did the laws of nature become silent at his command? Whenwe transcend what is scientifically possible, all suppositions areadmissible; and we leave the reader to take his choice between theseand any others he may choose to invent. 

One word in justification of the confidence with which I have citedestablished physical laws. It is very generally supposed that mostgreat advances in applied science are made by rejecting or disprovingthe results reached by one's predecessors. Nothing could be fartherfrom the truth. As Huxley has truly said, the army of science has neverretreated from a position once gained. Men like Ohm and Maxwell havereduced electricity to a mathematical science, and it is by accepting, mastering, and applying the laws of electric currents which theydiscovered and expounded that the electric light, electric railway, andall other applications of electricity have been developed. It is byapplying and utilizing the laws of heat, force, and vapor laid down bysuch men as Carnot and Regnault that we now cross the Atlantic in sixdays. These same laws govern the condensation of vapor in theatmosphere; and I say with confidence that if we ever do learn to makeit rain, it will be by accepting and applying them, and not by ignoringor trying to repeal them. 

How much the indisposition of our government to secure expertscientific evidence may cost it is strikingly shown by a recentexample. It expended several million dollars on a tunnel andwater-works for the city of Washington, and then abandoned the wholework. Had the project been submitted to a commission of geologists, thefact that the rock-bed under the District of Columbia would not standthe continued action of water would have been immediately reported, andall the money expended would have been saved. The fact is that there isvery little to excite popular interest in the advance of exact science. Investigators are generally quiet, unimpressive men, rather diffident, and wholly wanting in the art of interesting the public in their work. It is safe to say that neither Lavoisier, Galvani, Ohm, Regnault, norMaxwell could have gotten the smallest appropriation through Congressto help make discoveries which are now the pride of our century. Theyall dealt in facts and conclusions quite devoid of that grandeur whichrenders so captivating the project of attacking the rains in theiraerial stronghold with dynamite bombs. 

XIII

THE ASTRONOMICAL EPHEMERIS AND THE NAUTICAL ALMANAC

[Footnote: Read before the U S Naval Institute, January 10, 1879. ]

Although the Nautical Almanacs of the world, at the present time, areof comparatively recent origin, they have grown from small beginnings, the tracing of which is not unlike that of the origin of species by thenaturalist of the present day. Notwithstanding its familiar name, ithas always been designed rather for astronomical than for nauticalpurposes. Such a publication would have been of no use to the navigatorbefore he had instruments with which to measure the altitudes of theheavenly bodies. The earlier navigators seldom ventured out of sight ofland, and during the night they are said to have steered by the"Cynosure" or constellation of the Great Bear, a practice which hasbrought the name of the constellation into our language of the presentday to designate an object on which all eyes are intently fixed. Thisconstellation was a little nearer the pole in former ages than at thepresent time; still its distance was always so great that its use as amark of the northern point of the horizon does not inspire us withgreat respect for the accuracy with which the ancient navigators soughtto shape their course. 

The Nautical Almanac of the present day had its origin in theAstronomical Ephemerides called forth by the needs of predictions ofcelestial motions both on the part of the astronomer and the citizen. So long as astrology had a firm hold on the minds of men, the positionsof the planets were looked to with great interest. The theories ofPtolemy, although founded on a radically false system, neverthelesssufficed to predict the position of the sun, moon, and planets, withall the accuracy necessary for the purposes of the daily life of theancients or the sentences of their astrologers. Indeed, if his tableswere carried down to the present time, the positions of the heavenlybodies would be so few degrees in error that their recognition would bevery easy. The times of most of the eclipses would be predicted withina few hours, and the conjunctions of the planets within a few days. Thus it was possible for the astronomers of the Middle Ages to preparefor their own use, and that of the people, certain rude predictionsrespecting the courses of the sun and moon and the aspect of theheavens, which served the purpose of daily life and perhaps lessenedthe confusion arising from their complicated calendars. In the signs ofthe zodiac and the different effects which follow from the sun and moonpassing from sign to sign, still found in our farmers' almanacs, wehave the dying traces of these ancient ephemerides. 

The great Kepler was obliged to print an astrological almanac in virtueof his position as astronomer of the court of the King of Austria. But, notwithstanding the popular belief that astronomy had its origin inastrology, the astronomical writings of all ages seem to show that theastronomers proper never had any belief in astrology. To Kepler himselfthe necessity for preparing this almanac was a humiliation to which hesubmitted only through the pressure of poverty. Subsequent ephemerideswere prepared with more practical objects. They gave the longitudes ofthe planets, the position of the sun, the time of rising and setting, the prediction of eclipses, etc. 

They have, of course, gradually increased in accuracy as the tables ofthe celestial motions were improved from time to time. At first theywere not regular, annual publications, issued by governments, as at thepresent time, but the works of individual astronomers who issued theirephemerides for several years in advance, at irregular intervals. Oneman might issue one, two, or half a dozen such volumes, as a privatework, for the benefit of his fellows, and each might cover as manyyears as he thought proper. 

The first publication of this sort, which I have in my possession, isthe Ephemerides of Manfredi, of Bonn, computed for the years 1715 to1725, in two volumes. 

Of the regular annual ephemerides the earliest, so far as I am aware, is the Connaissance des Temps or French Nautical Almanac. The firstissue was in the year 1679, by Picard, and it has been continuedwithout interruption to the present time. Its early numbers were, ofcourse, very small, and meagre in their details. They were issued bythe astronomers of the French Academy of Sciences, under the combinedauspices of the academy and the government. They included not merelypredictions from the tables, but also astronomical observations made atthe Paris Observatory or elsewhere. When the Bureau of Longitudes wascreated in 1795, the preparation of the work was intrusted to it, andhas remained in its charge until the present time. As it is the oldest, so, in respect at least to number of pages, it is the largest ephemerisof the present time. The astronomical portion of the volume for 1879fills more than seven hundred pages, while the table of geographicalpositions, which has always been a feature of the work, contains nearlyone hundred pages more. 

The first issue of the British Nautical Almanac was that for the year1767 and appeared in 1766. It differs from the French Almanac in owingits origin entirely to the needs of navigation. The British nation, asthe leading maritime power of the world, was naturally interested inthe discovery of a method by which the longitude could be found at sea. As most of my hearers are probably aware, there was, for many years, astanding offer by the British government, of ten thousand pounds forthe discovery of a practical and sufficiently accurate method ofattaining this object. If I am rightly informed, the requirement wasthat a ship should be able to determine the Greenwich time within twominutes, after being six months at sea. When the office of AstronomerRoyal was established in 1765, the duty of the incumbent was declaredto be "to apply himself with the most exact care and diligence to therectifying the Tables of the Motions of the Heavens, and the places ofthe Fixed Stars in order to find out the so much desired Longitude atSea for the perfecting the Art of Navigation. "

About the middle of the last century the lunar tables were so farimproved that Dr. Maskelyne considered them available for attainingthis long-wished-for object. The method which I think was then, for thefirst time, proposed was the now familiar one of lunar distances. Several trials of the method were made by accomplished gentlemen whoconsidered that nothing was wanting to make it practical at sea but aNautical Ephemeris. The tables of the moon, necessary for the purpose, were prepared by Tobias Mayer, of Gottingen, and the regular annualissue of the work was commenced in 1766, as already stated. Of thereward which had been offered, three thousand pounds were paid to thewidow of Mayer, and three thousand pounds to the celebratedmathematician Euler for having invented the methods used by Mayer inthe construction of his tables. The issue of the Nautical Ephemeris wasintrusted to Dr. Maskelyne. Like other publications of this sort thisephemeris has gradually increased in volume. During the first sixty orseventy years the data were extremely meagre, including only such aswere considered necessary for the determination of positions. 

In 1830 the subject of improving the Nautical Almanac was referred bythe Lord Commissioners of the Admiralty to a committee of theAstronomical Society of London. A subcommittee, including eleven of themost distinguished astronomers and one scientific navigator, made anexhaustive report, recommending a radical rearrangement and improvementof the work. The recommendations of this committee were first carriedinto effect in the Nautical Almanac for the year 1834. The arrangementof the Navigator's Ephemeris then devised has been continued in theBritish Almanac to the present time. 

A good deal of matter has been added to the British Almanac during theforty years and upwards which have elapsed, but it has been worked inrather by using smaller type and closer printing than by increasing thenumber of pages. The almanac for 1834 contains five hundred andseventeen pages and that for 1880 five hundred and nineteen pages. Thegeneral aspect of the page is now somewhat crowded, yet, consideringthe quantity of figures on each page the arrangement is marvellouslyclear and legible. 

The Spanish "Almanaque Nautico" has been issued since the beginning ofthe century. Like its fellows it has been gradually enlarged andimproved, in recent times, and is now of about the same number of pageswith the British and American almanacs. As a rule there is less matteron a page, so that the data actually given are not so complete as insome other publications. 

In Germany two distinct publications of this class are issued, the onepurely astronomical, the other purely nautical. 

The astronomical publication has been issued for more than a centuryunder the title of "Berliner Astronomisches Jahrbuch. " It is intendedprincipally for the theoretical astronomer, and in respect to matternecessary to the determinations of positions on the earth it is rathermeagre. It is issued by the Berlin Observatory, at the expense of thegovernment. 

The companion of this work, intended for the use of the German marine, is the "Nautisches Jahrbuch, " prepared and issued under the directionof the minister of commerce and public works. It is copied largely fromthe British Nautical Almanac, and in respect to arrangement and data issimilar to our American Nautical Almanac, prepared for the use ofnavigators, giving, however, more matter, but in a less convenientform. The right ascension and declination of the moon are given forevery three hours instead of for every hour; one page of each month isdevoted to eclipses of Jupiter's satellites, phenomena which we neverconsider necessary in the nautical portion of our own almanac. At theend of the work the apparent positions of seventy or eighty of thebrightest stars are given for every ten days, while it is consideredthat our own navigators will be satisfied with the mean places for thebeginning of the year. At the end is a collection of tables which Idoubt whether any other than a German navigator would ever use. Whetherthey use them or not I am not prepared to say. 

The preceding are the principal astronomical and nautical ephemeridesof the world, but there are a number of minor publications, of the sameclass, of which I cannot pretend to give a complete list. Among them isthe Portuguese Astronomical Ephemeris for the meridian of theUniversity of Coimbra, prepared for Portuguese navigators. I do notknow whether the Portuguese navigators really reckon their longitudesfrom this point: if they do the practice must be attended with more orless confusion. All the matter is given by months, as in the solar andlunar ephemeris of our own and the British Almanac. For the sun we haveits longitude, right ascension, and declination, all expressed in arcand not in time. The equation of time and the sidereal time of meannoon complete the ephemeris proper. The positions of the principalplanets are given in no case oftener than for every third day. Thelongitude and latitude of the moon are given for noon and midnight. Onefeature not found in any other almanac is the time at which the moonenters each of the signs of the zodiac. It may be supposed that thisinformation is designed rather for the benefit of the Portugueselandsman than of the navigator. The right ascensions and declinationsof the moon and the lunar distances are also given for intervals oftwelve hours. Only the last page gives the eclipses of the satellitesof Jupiter. The Fixed Stars are wholly omitted. 

An old ephemeris, and one well known in astronomy is that published bythe Observatory of Milan, Italy, which has lately entered upon thesecond century of its existence. Its data are extremely meagre and ofno interest whatever to the navigator. The greater part of the volumeis taken up with observations at the Milan Observatory. 

Since taking charge of the American Ephemeris I have endeavored toascertain what nautical almanacs are actually used by the principalmaritime nations of Europe. I have been able to obtain none exceptthose above mentioned. As a general rule I think the British NauticalAlmanac is used by all the northern nations, as already indicated. TheGerman Nautical Jahrbuch is principally a reprint from the British. TheSwedish navigators, being all well acquainted with the Englishlanguage, use the British Almanac without change. The Russiangovernment, however, prints an explanation of the various terms in thelanguage of their own people and binds it in at the end of the BritishAlmanac. This explanation includes translations of the principal termsused in the heading of pages, such as the names of the months and days, the different planets, constellations, and fixed stars, and thephenomena of angle and time. They have even an index of their own inwhich the titles of the different articles are given in Russian. Thisexplanation occupies, in all, seventy-five pages--more than double thattaken up by the original explanation. 

One of the first considerations which strikes us in comparing thesemultitudinous publications is the confusion which must arise from theuse of so many meridians. If each of these southern nations, theSpanish and Portuguese for instance, actually use a meridian of theirown, the practice must lead to great confusion. If their navigators donot do so but refer their longitudes to the meridian of Greenwich, thentheir almanacs must be as good as useless. They would find it farbetter to buy an ephemeris referred to the meridian of Greenwich thanto attempt to use their own The northern nations, I think, have allbegun to refer to the meridian of Greenwich, and the same thing ishappily true of our own marine. We may, therefore, hope that allcommercial nations will, before long, refer their longitudes to one andthe same meridian, and the resulting confusion be thus avoided. 

The preparation of the American Ephemeris and Nautical Almanac wascommenced in 1849, under the superintendence of the late Rear-Admiral, then Lieutenant, Charles Henry Davis. The first volume to be issued wasthat for the year 1855. Both in the preparation of that work and in theconnected work of mapping the country, the question of the meridian tobe adopted was one of the first importance, and received greatattention from Admiral Davis, who made an able report on the subject. Our situation was in some respects peculiar, owing to the greatdistance which separated us from Europe and the uncertainty of theexact difference of longitude between the two continents. It was hardlypracticable to refer longitudes in our own country to any Europeanmeridian. The attempt to do so would involve continual changes as thetransatlantic longitude was from time to time corrected. On the otherhand, in order to avoid confusion in navigation, it was essential thatour navigators should continue to reckon from the meridian ofGreenwich. The trouble arising from uncertainty of the exact longitudedoes not affect the navigator, because, for his purpose, astronomicalprecision is not necessary. 

The wisest solution was probably that embodied in the act of Congress, approved September 28, 1850, on the recommendation of Lieutenant Davis, if I mistake not. "The meridian of the Observatory at Washington shallbe adopted and used as the American meridian for all astronomicalpurposes, and the meridian of Greenwich shall be adopted for allnautical purposes. " The execution of this law necessarily involves thequestion, "What shall be considered astronomical and what nauticalpurposes?" Whether it was from the difficulty of deciding thisquestion, or from nobody's remembering the law, the latter has beenpractically a dead letter. Surely, if there is any region of the globewhich the law intended should be referred to the meridian ofWashington, it is the interior of our own country. Yet, notwithstandingthe law, all acts of Congress relating to the territories have, so faras I know, referred everything to the meridian of Greenwich and not tothat of Washington. Even the maps issued by our various surveys arereferred to the same transatlantic meridian. The absurdity culminatedin a local map of the city of Washington and the District of Columbia, issued by private parties, in 1861, in which we find even the meridianspassing through the city of Washington referred to a supposed Greenwich. 

This practice has led to a confusion which may not be evident at firstsight, but which is so great and permanent that it may be worthexplaining. If, indeed, we could actually refer all our longitudes toan accurate meridian of Greenwich in the first place; if, for instance, any western region could be at once connected by telegraph with theGreenwich Observatory, and thus exchange longitude signals night afternight, no trouble or confusion would arise from referring to themeridian of Greenwich. But this, practically, cannot be done. All ourinterior longitudes have been and are determined differentially bycomparison with some point in this country. One of the most frequentpoints of reference used this way has been the Cambridge Observatory. Suppose, then, a surveyor at Omaha makes a telegraphic longitudedetermination between that point and the Cambridge Observatory. Sincehe wants his longitude reduced to Greenwich, he finds some supposedlongitude of the Cambridge Observatory from Greenwich and adds that tohis own longitude. Thus, what he gives is a longitude actuallydetermined, plus an assumed longitude of Cambridge, and, unless theassumed longitude of Cambridge is distinctly marked on his maps, we maynot know what it is. 

After a while a second party determines the longitude of Ogden fromCambridge. In the mean time, the longitude of Cambridge from Greenwichhas been corrected, and we have a longitude of Ogden which will bediscordant with that of Omaha, owing to the change in the longitude ofCambridge. A third party determines the longitudes of, let us suppose, St. Louis from Washington, he adds the assumed longitudes of Washingtonfrom Greenwich which may not agree with either of the longitudes ofCambridge and gets his longitude. Thus we have a series of results forour western longitude all nominally referred to the meridian ofGreenwich, but actually referred to a confused collection of meridians, nobody knows what. If the law had only provided that the longitude ofWashington from Greenwich should be invariably fixed at a certainquantity, say 77 degrees 3', this confusion would not have arisen. Itis true that the longitude thus established by law might not have beenperfectly correct, but this would not cause any trouble nor confusion. Our longitude would have been simply referred to a certain assumedGreenwich, the small error of which would have been of no importance tothe navigator or astronomer. It would have differed from the presentsystem only in that the assumed Greenwich would have been invariableinstead of dancing about from time to time as it has done under thepresent system. You understand that when the astronomer, in computingan interior longitude, supposes that of Cambridge from Greenwich to bea certain definite amount, say 4h 44m 30s, what he actually does is tocount from a meridian just that far east of Cambridge. When he changesthe assumed longitude of Cambridge he counts from a meridian farthereast or farther west of his former one: in other words, he alwayscounts from an assumed Greenwich, which changes its position from timeto time, relative to our own country. 

Having two meridians to look after, the form of the American Ephemeris, to be best adapted to the wants both of navigators and astronomers wasnecessarily peculiar. Had our navigators referred their longitudes toany meridian of our own country the arrangement of the work need nothave differed materially from that of foreign ones. But being referredto a meridian far outside our limits and at the same time designed foruse within those limits, it was necessary to make a division of thematter. Accordingly, the American Ephemeris has always been dividedinto two parts: the first for the use of navigators, referred to themeridian of Greenwich, the second for that of astronomers, referred tothe meridian of Washington. The division of the matter without seriousduplication is more easy than might at first be imagined. In explainingit, I will take the ephemeris as it now is, with the small changeswhich have been made from time to time. 

One of the purposes of any ephemeris, and especially of that of thenavigators, is to give the position of the heavenly bodies atequidistant intervals of time, usually one day. Since it is noon atsome point of the earth all the time, it follows that such an ephemeriswill always be referred to noon at some meridian. What meridian thisshall be is purely a practical question, to be determined byconvenience and custom. Greenwich noon, being that necessarily used bythe navigator, is adopted as the standard, but we must not concludethat the ephemeris for Greenwich noon is referred to the meridian ofGreenwich in the sense that we refer a longitude to that meridian. Greenwich noon is 18h 51m 48s, Washington mean time; so the ephemeriswhich gives data for every Greenwich noon may be considered as referredto the meridian of Washington giving the data for 17h 51m 48s, Washington time, every day. The rule adopted, therefore, is to have allthe ephemerides which refer to absolute time, without any reference toa meridian, given for Greenwich noon, unless there may be some specialreason to the contrary. For the needs of the navigator and thetheoretical astronomer these are the most convenient epochs. 

Another part of the ephemeris gives the position of the heavenlybodies, not at equidistant intervals, but at transit over somemeridian. For this purpose the meridian of Washington is chosen forobvious reasons. The astronomical part of our ephemeris, therefore, gives the positions of the principal fixed stars, the sun, moon, andall the larger planets at the moment of transit over our own meridian. 

The third class of data in the ephemeris comprises phenomena to bepredicted and observed. Such are eclipses of the sun and moon, occultations of fixed stars by the moon, and eclipses of Jupiter'ssatellites. These phenomena are all given in Washington mean time asbeing most convenient for observers in our own country. There is apartial exception, however, in the case of eclipses of the sun andmoon. The former are rather for the world in general than for our owncountry, and it was found difficult to arrange them to be referred tothe meridian of Washington without having the maps referred to the samemeridian. Since, however, the meridian of Greenwich is most convenientoutside of our own territory, and since but a small portion of theeclipses are visible within it, it is much the best to have theeclipses referred entirely to the meridian of Greenwich. I am the moreready to adopt this change because when the eclipses are to be computedfor our own country the change of meridians will be very readilyunderstood by those who make the computation. 

It may be interesting to say something of the tables and theories fromwhich the astronomical ephemerides are computed. To understand themcompletely it is necessary to trace them to their origin. The problemof calculating the motions of the heavenly bodies and the changes inthe aspect of the celestial sphere was one of the first with which thestudents of astronomy were occupied. Indeed, in ancient times, the onlyastronomical problems which could be attacked were of this class, forthe simple reason that without the telescope and other instruments ofresearch it was impossible to form any idea of the physicalconstitution of the heavenly bodies. To the ancients the stars andplanets were simply points or surfaces in motion. They might haveguessed that they were globes like that on which we live, but they wereunable to form any theory of the nature of these globes. Thus, in TheAlmagest of Ptolemy, the most complete treatise on the ancientastronomy which we possess, we find the motions of all the heavenlybodies carefully investigated and tables given for the convenientcomputation of their positions. Crude and imperfect though these tablesmay be, they were the beginnings from which those now in use havearisen. 

No radical change was made in the general principles on which thesetheories and tables were constructed until the true system of the worldwas propounded by Copernicus. On this system the apparent motion ofeach planet in the epicycle was represented by a motion of the eartharound the sun, and the problem of correcting the position of theplanet on account of the epicycle was reduced to finding its geocentricfrom its heliocentric position. This was the greatest step ever takenin theoretical astronomy, yet it was but a single step. So far as thematerials were concerned and the mode of representing the planetarymotions, no other radical advance was made by Copernicus. Indeed, it isremarkable that he introduced an epicycle which was not considerednecessary by Ptolemy in order to represent the inequalities in themotions of the planets around the sun. 

The next great advance made in the theory of the planetary motion wasthe discovery by Kepler of the celebrated laws which bear his name. When it was established that each planet moved in an ellipse having thesun in one focus it became possible to form tables of the motions ofthe heavenly bodies much more accurate than had before been known. Suchtables were published by Kepler in 1632, under the name of RudolphineTables, in memory of his patron, the Emperor Rudolph. But the laws ofKepler took no account of the action of the planets on one another. Itis well known that if each planet moved only under the influence of thegravitating force of the sun its motion would accord rigorously withthe laws of Kepler, and the problems of theoretical astronomy would begreatly simplified. When, therefore, the results of Kepler's laws werecompared with ancient and modern observations it was found that theywere not exactly represented by the theory. It was evident that theelliptic orbits of the planets were subject to change, but it wasentirely beyond the power of investigation, at that time, to assign anycause for such changes. Notwithstanding the simplicity of the causeswhich we now know to produce them, they are in form extremely complex. Without the knowledge of the theory of gravitation it would be entirelyout of the question to form any tables of the planetary motions whichwould at all satisfy our modern astronomers. 

When the theory of universal gravitation was propounded by Newton heshowed that a planet subjected only to the gravitation of a centralbody, like the sun, would move in exact accordance with Kepler's laws. But by his theory the planets must attract one another and theseattractions must cause the motions of each to deviate slightly from thelaws in question. Since such deviations were actually observed it wasvery natural to conclude that they were due to this cause, but howshall we prove it? To do this with all the rigor required in amathematical investigation it is necessary to calculate the effect ofthe mutual action of the planets in changing their orbits. Thiscalculation must be made with such precision that there shall be nodoubt respecting the results of the theory. Then its results must becompared with the best observations. If the slightest outstandingdifference is established there is something wrong and the requirementsof astronomical science are not satisfied. The complete solution ofthis problem was entirely beyond the power of Newton. When his methodsof research were used he was indeed able to show that the mutual actionof the planets would produce deviations in their motions of the samegeneral nature with those observed, but he was not able to calculatethese deviations with numerical exactness. His most successful attemptin this direction was perhaps made in the case of the moon. He showedthat the sun's disturbing force on this body would produce severalinequalities the existence of which had been established byobservation, and he was also able to give a rough estimate of theiramount, but this was as far as his method could go. A great improvementhad to be made, and this was effected not by English, but bycontinental mathematicians. 

The latter saw, clearly, that it was impossible to effect the requiredsolution by the geometrical mode of reasoning employed by Newton. Theproblem, as it presented itself to their minds, was to find algebraicexpressions for the positions of the planets at any time. The latitude, longitude, and radius-vector of each planet are constantly varying, butthey each have a determined value at each moment of time. They maytherefore be regarded as functions of the time, and the problem was toexpress these functions by algebraic formulae. These algebraicexpressions would contain, besides the time, the elements of theplanetary orbits to be derived from observation. The time which we maysuppose to be represented algebraically by the symbol t, would remainas an unknown quantity to the end. What the mathematician sought to dowas to present the astronomer with a series of algebraic expressionscontaining t as an indeterminate quantity, and so, by simplysubstituting for t any year and fraction of a year whatever--1600, 1700, 1800, for example, the result would give the latitude, longitude, or radius-vector of a planet. 

The problem as thus presented was one of the most difficult we canperceive of, but the difficulty was only an incentive to attacking itwith all the greater energy. So long as the motion was supposed purelyelliptical, so long as the action of the planets was neglected, theproblem was a simple one, requiring for its solution only the analyticgeometry of the ellipse. The real difficulties commenced when themutual action of the planets was taken into account. It is, of course, out of the question to give any technical description or analysis ofthe processes which have been invented for solving the problem; but abrief historical sketch may not be out of place. A complete andrigorous solution of the problem is out of the question--that is, it isimpossible by any known method to form an algebraic expression for theco-ordinates of a planet which shall be absolutely exact in amathematical sense. In whatever way we go to work the expression comesout in the form of an infinite series of terms, each term being, on thewhole, a little smaller as we increase the number. So, by increasingthe number of these various terms, we can approach nearer and nearer toa mathematical exactness, but can never reach it. The mathematician andastronomer have to be satisfied when they have carried the solution sofar that the neglected quantities are entirely beyond the powers ofobservation. 

Mathematicians have worked upon the problem in its various phases fornearly two centuries, and many improvements in detail have, from timeto time, been made, but no general method, applicable to all cases, hasbeen devised. One plan is to be used in treating the motion of themoon, another for the interior planets, another for Jupiter and Saturn, another for the minor planets, and so on. Under these circumstances itwill not surprise you to learn that our tables of the celestial motionsdo not, in general, correspond in accuracy to the present state ofpractical astronomy. There is no authority and no office in the worldwhose duty it is to look after the preparations of the formulae I havedescribed. The work of computing them has been almost entirely left toindividual mathematicians whose taste lay in that direction, and whohave sometimes devoted the greater part of their lives to calculationson a single part of the work. As a striking instance of this, the lastgreat work on the Motion of the Moon, that of Delaunay, of Paris, involved some fifteen years of continuous hard labor. 

Hansen, of Germany, who died five years ago, devoted almost his wholelife to investigations of this class and to the development of newmethods of computation. His tables of the moon are those now used forpredicting the places of the moon in all the ephemerides of the world. 

The only successful attempt to prepare systematic tables for all thelarge planets is that completed by Le Verrier just before his death;but he used only a small fraction of the material at his disposal, anddid not employ the modern methods, confining himself wholly to thoseinvented by his countrymen about the beginning of the present century. For him Jacobi and Hansen had lived in vain. 

The great difficulty which besets the subject arises from the fact thatmathematical processes alone will not give us the position of a planet, there being seven unknown quantities for each planet which must bedetermined by observations. A planet, for instance, may move in anyellipse whatever, having the sun in one focus, and it is impossible totell what ellipse it is, except from observation. The mean motion of aplanet, or its period of revolution, can only be determined by a longseries of observations, greater accuracy being obtained the longer theobservations are continued. Before the time of Bradley, who commencedwork at the Greenwich Observatory about 1750, the observations were sofar from accurate that they are now of no use whatever, unless inexceptional cases. Even Bradley's observations are in many cases farless accurate than those made now. In consequence, we have notheretofore had a sufficiently extended series of observations to forman entirely satisfactory theory of the celestial motions. 

As a consequence of the several difficulties and drawbacks, when thecomputation of our ephemeris was started, in the year 1849, there wereno tables which could be regarded as really satisfactory in use. In theBritish Nautical Almanac the places of the moon were derived from thetables of Burckhardt published in the year 1812. You will understand, in a case like this, no observations subsequent to the issue of thetables are made use of; the place of the moon of any day, hour, andminute of Greenwich time, mean time, was precisely what Burckhardtwould have computed nearly a half a century before. Of the tables ofthe larger planets the latest were those of Bouvard, published in 1812, while the places of Venus were from tables published by Lindenau in1810. Of course such tables did not possess astronomical accuracy. Atthat time, in the case of the moon, completely new tables wereconstructed from the results reached by Professor Airy in his reductionof the Greenwich observations of the moon from 1750 to 1830. These wereconstructed under the direction of Professor Pierce and represented theplaces of the moon with far greater accuracy than the older tables ofBurckhardt. For the larger planets corrections were applied to theolder tables to make them more nearly represent observations before newones were constructed. These corrections, however, have not provedsatisfactory, not being founded on sufficiently thoroughinvestigations. Indeed, the operation of correcting tables byobservation, as we would correct the dead-reckoning of a ship, is amakeshift, the result of which must always be somewhat uncertain, andit tends to destroy that unity which is an essential element of theastronomical ephemeris designed for permanent future use. The result ofintroducing them, while no doubt an improvement on the old tables, hasnot been all that should be desired. The general lack of unity in thetables hitherto employed is such that I can only state what has beendone by mentioning each planet in detail. 

For Mercury, new tables were constructed by Professor Winlock, fromformulae published by Le Verrier in 1846. These tables have, however, been deviating from the true motion of the planet, owing to the motionof the perihelion of Mercury, subsequently discovered by Le Verrierhimself. They are now much less accurate than the newer tablespublished by Le Verrier ten years later. 

Of Venus new tables were constructed by Mr. Hill in 1872. They are moreaccurate than any others, being founded on later data than those of LeVerrier, and are therefore satisfactory so far as accuracy ofprediction is concerned. 

The place of Mars, Jupiter, and Saturn are still computed from the oldtables, with certain necessary corrections to make them betterrepresent observations. 

The places of Uranus and Neptune are derived from new tables which willprobably be sufficiently accurate for some time to come. 

For the moon, Pierce's tables have been employed up to the year 1882inclusive. Commencing with the ephemeris for the year 1883, Hansen'stables are introduced with corrections to the mean longitude founded ontwo centuries of observation. 

With so great a lack of uniformity, and in the absence of any existingtables which have any other element of unity than that of being thework of the same authors, it is extremely desirable that we should beable to compute astronomical ephemerides from a single uniform andconsistent set of astronomical data. I hope, in the course of years, torender this possible. 

When our ephemeris was first commenced, the corrections applied toexisting tables rendered it more accurate than any other. Since thattime, the introduction into foreign ephemerides of the improved tablesof Le Verrier have rendered them, on the whole, rather more accuratethan our own. In one direction, however, our ephemeris will hereafterbe far ahead of all others. I mean in its positions of the fixed stars. This portion of it is of particular importance to us, owing to theextent to which our government is engaged in the determination ofpositions on this continent, and especially in our western territories. Although the places of the stars are determined far more easily thanthose of the planets, the discussion of star positions has been inalmost as backward a state as planetary positions. The errors of oldobservers have crept in and been continued through two generations ofastronomers. A systematic attempt has been made to correct the placesof the stars for all systematic errors of this kind, and the work ofpreparing a catalogue of stars which shall be completely adapted to thedetermination of time and longitude, both in the fixed observatory andin the field, is now approaching completion. The catalogue cannot besufficiently complete to give places of the stars for determining thelatitude by the zenith telescope, because for such a purpose a muchgreater number of stars is necessary than can be incorporated in theephemeris. 

From what I have said, it will be seen that the astronomical tables, ingeneral, do not satisfy the scientific condition of completelyrepresenting observations to the last degree of accuracy. Few, I think, have an idea how unsystematically work of this kind has hitherto beenperformed. Until very lately the tables we have possessed have been thework of one man here, another there, and another one somewhere else, each using different methods and different data. The result of this isthat there is nothing uniform and systematic among them, and that theyhave every range of precision. This is no doubt due in part to the factthat the construction of such tables, founded on the mass ofobservation hitherto made, is entirely beyond the power of any one man. What is wanted is a number of men of different degrees of capacity, allco-operating on a uniform system, so as to obtain a uniform result, like the astronomers in a large observatory. The Greenwich Observatorypresents an example of co-operative work of this class extending overmore than a century. But it has never extended its operations faroutside the field of observation, reduction, and comparison withexisting tables. It shows clearly, from time to time, the errors of thetables used in the British Nautical Almanac, but does nothing further, occasional investigations excepted, in the way of supplying new tables. An exception to this is a great work on the theory of the moon'smotion, in which Professor Airy is now engaged. 

It will be understood that several distinct conditions not yetfulfilled are desirable in astronomical tables; one is that each set oftables shall be founded on absolutely consistent data, for instance, that the masses of the planets shall be the same throughout. Anotherrequirement is that this data shall be as near the truth asastronomical data will suffice to determine them. The third is that theresults shall be correct in theory. That is, whether they agree ordisagree with observations, they shall be such as result mathematicallyfrom the adopted data. 

Tables completely fulfilling these conditions are still a work of thefuture. It is yet to be seen whether such co-operation as is necessaryto their production can be secured under any arrangement whatever. 

XIV

THE WORLD'S DEBT TO ASTRONOMY

Astronomy is more intimately connected than any other science with thehistory of mankind. While chemistry, physics, and we might say allsciences which pertain to things on the earth, are comparativelymodern, we find that contemplative men engaged in the study of thecelestial motions even before the commencement of authentic history. The earliest navigators of whom we know must have been aware that theearth was round. This fact was certainly understood by the ancientGreeks and Egyptians, as well as it is at the present day. True, theydid not know that the earth revolved on its axis, but thought that theheavens and all that in them is performed a daily revolution around ourglobe, which was, therefore, the centre of the universe. It was thecynosure, or constellation of the Little Bear, by which the sailorsused to guide their ships before the discovery of the mariner'scompass. Thus we see both a practical and contemplative side toastronomy through all history. The world owes two debts to thatscience: one for its practical uses, and the other for the ideas it hasafforded us of the immensity of creation. 

The practical uses of astronomy are of two kinds: One relates togeography; the other to times, seasons, and chronology. Every navigatorwho sails long out of sight of land must be something of an astronomer. His compass tells him where are east, west, north, and south, but itgives him no information as to where on the wide ocean he may be, orwhither the currents may be carrying him. Even with the swiftest modernsteamers it is not safe to trust to the compass in crossing theAtlantic. A number of years ago the steamer City of Washington set outon her usual voyage from Liverpool to New York. By rare bad luck theweather was stormy or cloudy during her whole passage, so that thecaptain could not get a sight on the sun, and therefore had to trust tohis compass and his log-line, the former telling him in what directionhe had steamed, and the latter how fast he was going each hour. Theresult was that the ship ran ashore on the coast of Nova Scotia, whenthe captain thought he was approaching Nantucket. 

Not only the navigator but the surveyor in the western wilds mustdepend on astronomical observations to learn his exact position on theearth's surface, or the latitude and longitude of the camp which heoccupies. He is able to do this because the earth is round, and thedirection of the plumb-line not exactly the same at any two places. Letus suppose that the earth stood still, so as not to revolve on its axisat all. Then we should always see the stars at rest and the star whichwas in the zenith of any place, say a farm-house in New York, at anytime, would be there every night and every hour of the year. Now thezenith is simply the point from which the plumb-line seems to drop. Lieon the ground; hang a plummet above your head, sight on the line withone eye, and the direction of the sight will be the zenith of yourplace. Suppose the earth was still, and a certain star was at yourzenith. Then if you went to another place a mile away, the direction ofthe plumb-line would be slightly different. The change would, indeed, be very small, so small that you could not detect it by sighting withthe plumb-line. But astronomers and surveyors have vastly more accurateinstruments than the plumb-line and the eye, instruments by which adeviation that the unaided eye could not detect can be seen andmeasured. Instead of the plumb-line they use a spirit-level or a basinof quicksilver. The surface of quicksilver is exactly level and so atright angles to the true direction of the plumb-line or the force ofgravity. Its direction is therefore a little different at two differentplaces on the surface, and the change can be measured by its effect onthe apparent direction of a star seen by reflection from the surface. 

It is true that a considerable distance on the earth's surface willseem very small in its effect on the position of a star. Suppose therewere two stars in the heavens, the one in the zenith of the place whereyou now stand, and the other in the zenith of a place a mile away. Tothe best eye unaided by a telescope those two stars would look like asingle one. But let the two places be five miles apart, and the eyecould see that there were two of them. A good telescope coulddistinguish between two stars corresponding to places not more than ahundred feet apart. The most exact measurements can determine distancesranging from thirty to sixty feet. If a skilful astronomical observershould mount a telescope on your premises, and determine his latitudeby observations on two or three evenings, and then you should try totrick him by taking up the instrument and putting it at another pointone hundred feet north or south, he would find out that something waswrong by a single night's work. 

Within the past three years a wobbling of the earth's axis has beendiscovered, which takes place within a circle thirty feet in radius andsixty feet in diameter. Its effect was noticed in astronomicalobservations many years ago, but the change it produced was so smallthat men could not find out what the matter was. The exact nature andamount of the wobbling is a work of the exact astronomy of the presenttime. 

We cannot measure across oceans from island to island. Until a recenttime we have not even measured across the continent, from New York toSan Francisco, in the most precise way. Without astronomy we shouldknow nothing of the distance between New York and Liverpool, except bythe time which it took steamers to run it, a measure which would bevery uncertain indeed. But by the aid of astronomical observations andthe Atlantic cables the distance is found within a few hundred yards. Without astronomy we could scarcely make an accurate map of the UnitedStates, except at enormous labor and expense, and even then we couldnot be sure of its correctness. But the practical astronomer being ableto determine his latitude and longitude within fifty yards, thepositions of the principal points in all great cities of the countryare known, and can be laid down on maps. 

The world has always had to depend on astronomy for all its knowledgeconcerning times and seasons. The changes of the moon gave us the firstmonth, and the year completes its round as the earth travels in itsorbit. The results of astronomical observation are for us condensedinto almanacs, which are now in such universal use that we never thinkof their astronomical origin. But in ancient times people had noalmanacs, and they learned the time of year, or the number of days inthe year, by observing the time when Sirius or some other bright starrose or set with the sun, or disappeared from view in the sun's rays. At Alexandria, in Egypt, the length of the year was determined yet moreexactly by observing when the sun rose exactly in the east and setexactly in the west, a date which fixed the equinox for them as for us. More than seventeen hundred years ago, Ptolemy, the great author of TheAlmagest, had fixed the length of the year to within a very fewminutes. He knew it was a little less than 365 1/2 days. The dates ofevents in ancient history depend very largely on the chronologicalcycles of astronomy. Eclipses of the sun and moon sometimes fixed thedate of great events, and we learn the relation of ancient calendars toour own through the motions of the earth and moon, and can thus measureout the years for the events in ancient history on the same scale thatwe measure out our own. 

At the present day, the work of the practical astronomer is made use ofin our daily life throughout the whole country in yet another way. Ourfore-fathers had to regulate their clocks by a sundial, or perhaps by amark at the corner of the house, which showed where the shadow of thehouse fell at noon. Very rude indeed was this method; and it wasuncertain for another reason. It is not always exactly twenty-fourhours between two noons by the sun, Sometimes for two or three monthsthe sun will make it noon earlier and earlier every day; and duringseveral other months later and later every day. The result is that, ifa clock is perfectly regulated, the sun will be sometimes a quarter ofan hour behind it, and sometimes nearly the same amount before it. Anyeffort to keep the clock in accord with this changing sun was in vain, and so the time of day was always uncertain. 

Now, however, at some of the principal observatories of the countryastronomical observations are made on every clear night for the expresspurpose of regulating an astronomical clock with the greatestexactness. Every day at noon a signal is sent to various parts of thecountry by telegraph, so that all operators and railway men who hearthat signal can set their clock at noon within two or three seconds. People who live near railway stations can thus get their time from it, and so exact time is diffused into every household of the land which isat all near a railway station, without the trouble of watching the sun. Thus increased exactness is given to the time on all our railroads, increased safety is obtained, and great loss of time saved to everyone. If we estimated the money value of this saving alone we should nodoubt find it to be greater than all that our study of astronomy costs. 

It must therefore be conceded that, on the whole, astronomy is ascience of more practical use than one would at first suppose. To thethoughtless man, the stars seem to have very little relation to hisdaily life; they might be forever hid from view without his being theworse for it. He wonders what object men can have in devotingthemselves to the study of the motions or phenomena of the heavens. Butthe more he looks into the subject, and the wider the range which hisstudies include, the more he will be impressed with the great practicalusefulness of the science of the heavens. And yet I think it would be aserious error to say that the world's greatest debt to astronomy wasowing to its usefulness in surveying, navigation, and chronology. Themore enlightened a man is, the more he will feel that what makes hismind what it is, and gives him the ideas of himself and creation whichhe possesses, is more important than that which gains him wealth. Itherefore hold that the world's greatest debt to astronomy is that ithas taught us what a great thing creation is, and what an insignificantpart of the Creator's work is this earth on which we dwell, andeverything that is upon it. That space is infinite, that wherever we gothere is a farther still beyond it, must have been accepted as a factby all men who have thought of the subject since men began to think atall. But it is very curious how hard even the astronomers found it tobelieve that creation is as large as we now know it to be. The Greekshad their gods on or not very far above Olympus, which was a sort offootstool to the heavens. Sometimes they tried to guess how far itprobably was from the vault of heaven to the earth, and they had a mythas to the time it took Vulcan to fall. Ptolemy knew that the moon wasabout thirty diameters of the earth distant from us, and he knew thatthe sun was many times farther than the moon; he thought it abouttwenty times as far, but could not be sure. We know that it is nearlyfour hundred times as far. 

When Copernicus propounded the theory that the earth moved around thesun, and not the sun around the earth, he was able to fix the relativedistances of the several planets, and thus make a map of the solarsystem. But he knew nothing about the scale of this map. He knew, forexample, that Venus was a little more than two-thirds the distance ofthe earth from the sun, and that Mars was about half as far again asthe earth, Jupiter about five times, and Saturn about ten times; but heknew nothing about the distance of any one of them from the sun. He hadhis map all right, but he could not give any scale of miles or anyother measurements upon it. The astronomers who first succeeded himfound that the distance was very much greater than had formerly beensupposed; that it was, in fact, for them immeasurably great, and thatwas all they could say about it. 

The proofs which Copernicus gave that the earth revolved around the sunwere so strong that none could well doubt them. And yet there was adifficulty in accepting the theory which seemed insuperable. If theearth really moved in so immense an orbit as it must, then the starswould seem to move in the opposite direction, just as, if you were in atrain that is shunting off cars one after another, as the train movesback and forth you see its motion in the opposite motion of everyobject around you. If then the earth at one side of its orbit wasexactly between two stars, when it moved to the other side of its orbitit would not be in a line between them, but each star would have seemedto move in the opposite direction. 

For centuries astronomers made the most exact observations that theywere able without having succeeded in detecting any such apparentmotion among the stars. Here was a mystery which they could not solve. Either the Copernican system was not true, after all, and the earth didnot move in an orbit, or the stars were at such immense distances thatthe whole immeasurable orbit of the earth is a mere point incomparison. Philosophers could not believe that the Creator would wasteroom by allowing the inconceivable spaces which appeared to lie betweenour system and the fixed stars to remain unused, and so thought theremust be something wrong in the theory of the earth's motion. 

Not until the nineteenth century was well in progress did the mostskilful observers of their time, Bessel and Struve, having at commandthe most refined instruments which science was then able to devise, discover the reality of the parallax of the stars, and show that thenearest of these bodies which they could find was more than 400, 000times as far as the 93, 000, 000 of miles which separate the earth fromthe sun. During the half-century and more which has elapsed since thisdiscovery, astronomers have been busily engaged in fathoming theheavenly depths. The nearest star they have been able to find is about280, 000 times the sun's distance. A dozen or a score more are within1, 000, 000 times that distance. Beyond this all is unfathomable by anysounding-line yet known to man. 

The results of these astronomical measures are stupendous beyondconception. No mere statement in numbers conveys any idea of it. Nearlyall the brighter stars are known to be flying through space at speedswhich generally range between ten and forty or fifty miles per second, some slower and some swifter, even up to one or two hundred miles asecond. Such a speed would carry us across the Atlantic while we werereading two or three of these sentences. These motions take place somein one direction and some in another. Some of the stars are comingalmost straight towards us. Should they reach us, and pass through oursolar system, the result would be destructive to our earth, and perhapsto our sun. 

Are we in any danger? No, because, however madly they may come, whetherten, twenty, or one hundred miles per second, so many millions of yearsmust elapse before they reach us that we need give ourselves no concernin the matter. Probably none of them are coming straight to us; theircourse deviates just a hair's-breadth from our system, but thathair's-breadth is so large a quantity that when the millions of yearselapse their course will lie on one side or the other of our system andthey will do no harm to our planet; just as a bullet fired at an insecta mile away would be nearly sure to miss it in one direction or theother. 

Our instrument makers have constructed telescopes more and morepowerful, and with these the whole number of stars visible is carriedup into the millions, say perhaps to fifty or one hundred millions. Foraught we know every one of those stars may have planets like our owncircling round it, and these planets may be inhabited by beings equalto ourselves. To suppose that our globe is the only one thus inhabitedis something so unlikely that no one could expect it. It would be verynice to know something about the people who may inhabit these bodies, but we must await our translation to another sphere before we can knowanything on the subject. Meanwhile, we have gained what is of morevalue than gold or silver; we have learned that creation transcends allour conceptions, and our ideas of its Author are enlarged accordingly. 

XV

AN ASTRONOMICAL FRIENDSHIP

There are few men with whom I would like so well to have a quiet talkas with Father Hell. I have known more important and more interestingmen, but none whose acquaintance has afforded me a serenersatisfaction, or imbued me with an ampler measure of a feeling that Iam candid enough to call self-complacency. The ties that bind us arepeculiar. When I call him my friend, I do not mean that we everhobnobbed together. But if we are in sympathy, what matters it that hewas dead long before I was born, that he lived in one century and I inanother? Such differences of generation count for little in thebrotherhood of astronomy, the work of whose members so extends throughall time that one might well forget that he belongs to one century orto another. 

Father Hell was an astronomer. Ask not whether he was a very great one, for in our science we have no infallible gauge by which we try men andmeasure their stature. He was a lover of science and an indefatigableworker, and he did what in him lay to advance our knowledge of thestars. Let that suffice. I love to fancy that in some other sphere, either within this universe of ours or outside of it, all who havesuccessfully done this may some time gather and exchange greetings. Should this come about there will be a few--Hipparchus and Ptolemy, Copernicus and Newton, Galileo and Herschel--to be surrounded byadmiring crowds. But these men will have as warm a grasp and as kind aword for the humblest of their followers, who has merely discovered acomet or catalogued a nebula, as for the more brilliant of theirbrethren. 

My friend wrote the letters S. J. After his name. This would indicatethat he had views and tastes which, in some points, were very differentfrom my own. But such differences mark no dividing line in thebrotherhood of astronomy. My testimony would count for nothing were Icalled as witness for the prosecution in a case against the order towhich my friend belonged. The record would be very short: Deponentsaith that he has at various times known sundry members of the saidorder; and that they were lovers of sound learning, devoted to thediscovery and propagation of knowledge; and further deponent saith not. 

If it be true that an undevout astronomer is mad, then was Father Hellthe sanest of men. In his diary we find entries like these:"Benedicente Deo, I observed the Sun on the meridian to-day. .. . Deoquoque benedicente, I to-day got corresponding altitudes of the Sun'supper limb. " How he maintained the simplicity of his faith in the truespirit of the modern investigator is shown by his proceedings during amomentous voyage along the coast of Norway, of which I shall presentlyspeak. He and his party were passengers on a Norwegian vessel. Fortwelve consecutive days they had been driven about by adverse storms, threatened with shipwreck on stony cliffs, and finally compelled totake refuge in a little bay, with another ship bound in the samedirection, there to wait for better weather. 

Father Hell was philosopher enough to know that unusual events do nothappen without cause. Perhaps he would have undergone a week of stormwithout its occurring to him to investigate the cause of such a badspell of weather. But when he found the second week approaching its endand yet no sign of the sun appearing or the wind abating, he wassatisfied that something must be wrong. So he went to work in thespirit of the modern physician who, when there is a sudden outbreak oftyphoid fever, looks at the wells and examines their water with themicroscope to find the microbes that must be lurking somewhere. Helooked about, and made careful inquiries to find what wickednesscaptain and crew had been guilty of to bring such a punishment. Successsoon rewarded his efforts. The King of Denmark had issued a regulationthat no fish or oil should be sold along the coast except by theregular dealers in those articles. And the vessel had on boardcontraband fish and blubber, to be disposed of in violation of this law. 

The astronomer took immediate and energetic measures to insure thepublic safety. He called the crew together, admonished them of theirsin, the suffering they were bringing on themselves, and the necessityof getting back to their families. He exhorted them to throw the fishoverboard, as the only measure to secure their safety. In the goodnessof his heart, he even offered to pay the value of the jettison as soonas the vessel reached Drontheim. 

But the descendants of the Vikings were stupid and unenlightenedmen--"educatione sua et professione homines crassissimi"--and would notswallow the medicine so generously offered. They claimed that, as theyhad bought the fish from the Russians, their proceedings were quitelawful. As for being paid to throw the fish overboard, they must havespot cash in advance or they would not do it. 

After further fruitless conferences, Father Hell determined to escapethe danger by transferring his party to the other vessel. They had notmore than got away from the wicked crew than Heaven began to smile ontheir act--"factum comprobare Deus ipse videtur"--the clouds clearedaway, the storm ceased to rage, and they made their voyage toCopenhagen under sunny skies. I regret to say that the narrative issilent as to the measure of storm subsequently awarded to the hominescrassissimi of the forsaken vessel. 

For more than a century Father Hell had been a well-known figure inastronomical history. His celebrity was not, however, of such a kind asthe Royal Astronomer of Austria that he was ought to enjoy. A notunimportant element in his fame was a suspicion of his being a blacksheep in the astronomical flock. He got under this cloud throughengaging in a trying and worthy enterprise. On June 3, 1769, an eventoccurred which had for generations been anticipated with the greatestinterest by the whole astronomical world. This was a transit of Venusover the disk of the sun. Our readers doubtless know that at that timesuch a transit afforded the most accurate method known of determiningthe distance of the earth from the sun. To attain this object, partieswere sent to the most widely separated parts of the globe, not onlyover wide stretches of longitude, but as near as possible to the twopoles of the earth. One of the most favorable and important regions ofobservation was Lapland, and the King of Denmark, to whom that countrythen belonged, interested himself in getting a party sent thither. After a careful survey of the field he selected Father Hell, Chief ofthe Observatory at Vienna, and well known as editor and publisher of anannual ephemeris, in which the movements and aspects of the heavenlybodies were predicted. The astronomer accepted the mission andundertook what was at that time a rather hazardous voyage. His stationwas at Vardo in the region of the North Cape. What made it mostadvantageous for the purpose was its being situated several degreeswithin the Arctic Circle, so that on the date of the transit the sundid not set. The transit began when the sun was still two or threehours from his midnight goal, and it ended nearly an equal timeafterwards. The party consisted of Hell himself, his friend andassociate, Father Sajnovics, one Dominus Borgrewing, of whom history, so far as I know, says nothing more, and an humble individual who inthe record receives no other designation than "Familias. " This implies, we may suppose, that he pitched the tent and made the coffee. If he didnothing but this we might pass him over in silence. But we learn thaton the day of the transit he stood at the clock and counted theall-important seconds while the observations were going on. 

The party was favored by cloudless weather, and made the requiredobservations with entire success. They returned to Copenhagen, andthere Father Hell remained to edit and publish his work. Astronomerswere naturally anxious to get the results, and showed some impatiencewhen it became known that Hell refused to announce them until they wereall reduced and printed in proper form under the auspices of his royalpatron. While waiting, the story got abroad that he was delaying thework until he got the results of observations made elsewhere, in orderto "doctor" his own and make them fit in with the others. One went sofar as to express a suspicion that Hell had not seen the transit atall, owing to clouds, and that what he pretended to publish were purefabrications. But his book came out in a few months in such good formthat this suspicion was evidently groundless. Still, the fears that theobservations were not genuine were not wholly allayed, and the resultsderived from them were, in consequence, subject to some doubt. Hellhimself considered the reflections upon his integrity too contemptibleto merit a serious reply. It is said that he wrote to some one offeringto exhibit his journal free from interlineations or erasures, but itdoes not appear that there is any sound authority for this statement. What is of some interest is that he published a determination of theparallax of the sun based on the comparison of his own observationswith those made at other stations. The result was 8". 70. It was then, and long after, supposed that the actual value of the parallax wasabout 8". 50, and the deviation of Hell's result from this wasconsidered to strengthen the doubt as to the correctness of his work. It is of interest to learn that, by the most recent researches, thenumber in question must be between 8". 75 and 8". 80, so that in realityHell's computations came nearer the truth than those generally currentduring the century following his work. 

Thus the matter stood for sixty years after the transit, and for ageneration after Father Hell had gone to his rest. About 1830 it wasfound that the original journal of his voyage, containing the record ofhis work as first written down at the station, was still preserved atthe Vienna Observatory. Littrow, then an astronomer at Vienna, made acritical examination of this record in order to determine whether ithad been tampered with. His conclusions were published in a little bookgiving a transcript of the journal, a facsimile of the most importantentries, and a very critical description of the supposed alterationsmade in them. He reported in substance that the original record hadbeen so tampered with that it was impossible to decide whether theobservations as published were genuine or not. The vital figures, thosewhich told the times when Venus entered upon the sun, had been erased, and rewritten with blacker ink. This might well have been done afterthe party returned to Copenhagen. The case against the observer seemedso well made out that professors of astronomy gave their hearers alesson in the value of truthfulness, by telling them how Father Hellhad destroyed what might have been very good observations by trying tomake them appear better than they really were. 

In 1883 I paid a visit to Vienna for the purpose of examining the greattelescope which had just been mounted in the observatory there byGrubb, of Dublin. The weather was so unfavorable that it was necessaryto remain two weeks, waiting for an opportunity to see the stars. Oneevening I visited the theatre to see Edwin Booth, in his celebratedtour over the Continent, play King Lear to the applauding Viennese. Butevening amusements cannot be utilized to kill time during the day. Among the works I had projected was that of rediscussing all theobservations made on the transits of Venus which had occurred in 1761and 1769, by the light of modern discovery. As I have already remarked, Hell's observations were among the most important made, if they wereonly genuine. So, during my almost daily visits to the observatory, Iasked permission of the director to study Hell's manuscript, which wasdeposited in the library of the institution. Permission was freelygiven, and for some days I pored over the manuscript. It is a verycommon experience in scientific research that a subject which seemsvery unpromising when first examined may be found more and moreinteresting as one looks further into it. Such was the case here. Forsome time there did not seem any possibility of deciding the questionwhether the record was genuine. But every time I looked at it some newpoint came to light. I compared the pages with Littrow's publisheddescription and was struck by a seeming want of precision, especiallywhen he spoke of the ink with which the record had been made. Eraserswere doubtless unknown in those days--at least our astronomer had noneon his expedition--so when he found he had written the wrong word hesimply wiped the place off with, perhaps, his finger and wrote what hewanted to say. In such a case Littrow described the matter as erasedand new matter written. When the ink flowed freely from the quill penit was a little dark. Then Littrow said a different kind of ink hadbeen used, probably after he had got back from his journey. On theother hand, there was a very singular case in which there had been asubsequent interlineation in ink of quite a different tint, whichLittrow said nothing about. This seemed so curious that I wrote in mynotes as follows:

"That Littrow, in arraying his proofs of Hell's forgery, should havefailed to dwell upon the obvious difference between this ink and thatwith which the alterations were made leads me to suspect a defect inhis sense of color. "

The more I studied the description and the manuscript the stronger thisimpression became. Then it occurred to me to inquire whether perhapssuch could have been the case. So I asked Director Weiss whetheranything was known as to the normal character of Littrow's power ofdistinguishing colors. His answer was prompt and decisive. "Oh yes, Littrow was color-blind to red. He could not distinguish between thecolor of Aldebaran and the whitest star. " No further research wasnecessary. For half a century the astronomical world had based animpression on the innocent but mistaken evidence of a color-blindman--respecting the tints of ink in a manuscript. 

It has doubtless happened more than once that when an intimate friendhas suddenly and unexpectedly passed away, the reader has ardentlywished that it were possible to whisper just one word of appreciationacross the dark abyss. And so it is that I have ever since felt that Iwould like greatly to tell Father Hell the story of my work at Viennain 1883. 

XVI

THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR

[Footnote: Presidential address at the opening of the InternationalCongress of Arts and Science, St. Louis Exposition, September 21: 1904. ]

As we look at the assemblage gathered in this hall, comprising so manynames of widest renown in every branch of learning--we might almost sayin every field of human endeavor--the first inquiry suggested must beafter the object of our meeting. The answer is that our purposecorresponds to the eminence of the assemblage. We aim at nothing lessthan a survey of the realm of knowledge, as comprehensive as ispermitted by the limitations of time and space. The organizers of ourcongress have honored me with the charge of presenting such preliminaryview of its field as may make clear the spirit of our undertaking. 

Certain tendencies characteristic of the science of our day clearlysuggest the direction of our thoughts most appropriate to the occasion. Among the strongest of these is one towards laying greater stress onquestions of the beginnings of things, and regarding a knowledge of thelaws of development of any object of study as necessary to theunderstanding of its present form. It may be conceded that theprinciple here involved is as applicable in the broad field before usas in a special research into the properties of the minutest organism. It therefore seems meet that we should begin by inquiring what agencyhas brought about the remarkable development of science to which theworld of to-day bears witness. This view is recognized in the plan ofour proceedings by providing for each great department of knowledge areview of its progress during the century that has elapsed since thegreat event commemorated by the scenes outside this hall. But suchreviews do not make up that general survey of science at large which isnecessary to the development of our theme, and which must include theaction of causes that had their origin long before our time. Themovement which culminated in making the nineteenth century evermemorable in history is the outcome of a long series of causes, actingthrough many centuries, which are worthy of especial attention on suchan occasion as this. In setting them forth we should avoid layingstress on those visible manifestations which, striking the eye of everybeholder, are in no danger of being overlooked, and search rather forthose agencies whose activities underlie the whole visible scene, butwhich are liable to be blotted out of sight by the very brilliancy ofthe results to which they have given rise. It is easy to draw attentionto the wonderful qualities of the oak; but, from that very fact, it maybe needful to point out that the real wonder lies concealed in theacorn from which it grew. 

Our inquiry into the logical order of the causes which have made ourcivilization what it is to-day will be facilitated by bringing to mindcertain elementary considerations--ideas so familiar that setting themforth may seem like citing a body of truisms--and yet so frequentlyoverlooked, not only individually, but in their relation to each other, that the conclusion to which they lead may be lost to sight. One ofthese propositions is that psychical rather than material causes arethose which we should regard as fundamental in directing thedevelopment of the social organism. The human intellect is the reallyactive agent in every branch of endeavor--the primum mobile ofcivilization--and all those material manifestations to which ourattention is so often directed are to be regarded as secondary to thisfirst agency. If it be true that "in the world is nothing great butman; in man is nothing great but mind, " then should the key-note of ourdiscourse be the recognition of this first and greatest of powers. 

Another well-known fact is that those applications of the forces ofnature to the promotion of human welfare which have made our age whatit is are of such comparatively recent origin that we need go back onlya single century to antedate their most important features, andscarcely more than four centuries to find their beginning. It followsthat the subject of our inquiry should be the commencement, not manycenturies ago, of a certain new form of intellectual activity. 

Having gained this point of view, our next inquiry will be into thenature of that activity and its relation to the stages of progresswhich preceded and followed its beginning. The superficial observer, who sees the oak but forgets the acorn, might tell us that the specialqualities which have brought out such great results are expertscientific knowledge and rare ingenuity, directed to the application ofthe powers of steam and electricity. From this point of view the greatinventors and the great captains of industry were the first agents inbringing about the modern era. But the more careful inquirer will seethat the work of these men was possible only through a knowledge of thelaws of nature, which had been gained by men whose work took precedenceof theirs in logical order, and that success in invention has beenmeasured by completeness in such knowledge. While giving all due honorto the great inventors, let us remember that the first place is that ofthe great investigators, whose forceful intellects opened the way tosecrets previously hidden from men. Let it be an honor and not areproach to these men that they were not actuated by the love of gain, and did not keep utilitarian ends in view in the pursuit of theirresearches. If it seems that in neglecting such ends they were leavingundone the most important part of their work, let us remember thatNature turns a forbidding face to those who pay her court with the hopeof gain, and is responsive only to those suitors whose love for her ispure and undefiled. Not only is the special genius required in theinvestigator not that generally best adapted to applying thediscoveries which he makes, but the result of his having sordid ends inview would be to narrow the field of his efforts, and exercise adepressing effect upon his activities. The true man of science has nosuch expression in his vocabulary as "useful knowledge. " His domain isas wide as nature itself, and he best fulfils his mission when heleaves to others the task of applying the knowledge he gives to theworld. 

We have here the explanation of the well-known fact that the functionsof the investigator of the laws of nature, and of the inventor whoapplies these laws to utilitarian purposes, are rarely united in thesame person. If the one conspicuous exception which the past centurypresents to this rule is not unique, we should probably have to go backto Watt to find another. 

From this view-point it is clear that the primary agent in the movementwhich has elevated man to the masterful position he now occupies is thescientific investigator. He it is whose work has deprived plague andpestilence of their terrors, alleviated human suffering, girdled theearth with the electric wire, bound the continent with the iron way, and made neighbors of the most distant nations. As the first agentwhich has made possible this meeting of his representatives, let hisevolution be this day our worthy theme. As we follow the evolution ofan organism by studying the stages of its growth, so we have to showhow the work of the scientific investigator is related to theineffectual efforts of his predecessors. 

In our time we think of the process of development in nature as onegoing continuously forward through the combination of the oppositeprocesses of evolution and dissolution. The tendency of our thought hasbeen in the direction of banishing cataclysms to the theological limbo, and viewing Nature as a sleepless plodder, endowed with infinitepatience, waiting through long ages for results. I do not contest thetruth of the principle of continuity on which this view is based. Butit fails to make known to us the whole truth. The building of a shipfrom the time that her keel is laid until she is making her way acrossthe ocean is a slow and gradual process; yet there is a cataclysmicepoch opening up a new era in her history. It is the moment when, afterlying for months or years a dead, inert, immovable mass, she issuddenly endowed with the power of motion, and, as if imbued with life, glides into the stream, eager to begin the career for which she wasdesigned. 

I think it is thus in the development of humanity. Long ages may passduring which a race, to all external observation, appears to be makingno real progress. Additions may be made to learning, and the records ofhistory may constantly grow, but there is nothing in its sphere ofthought, or in the features of its life, that can be called essentiallynew. Yet, Nature may have been all along slowly working in a way whichevades our scrutiny, until the result of her operations suddenlyappears in a new and revolutionary movement, carrying the race to ahigher plane of civilization. 

It is not difficult to point out such epochs in human progress. Thegreatest of all, because it was the first, is one of which we find norecord either in written or geological history. It was the epoch whenour progenitors first took conscious thought of the morrow, first usedthe crude weapons which Nature had placed within their reach to killtheir prey, first built a fire to warm their bodies and cook theirfood. I love to fancy that there was some one first man, the Adam ofevolution, who did all this, and who used the power thus acquired toshow his fellows how they might profit by his example. When the membersof the tribe or community which he gathered around him began toconceive of life as a whole--to include yesterday, to-day, andto-morrow in the same mental grasp--to think how they might apply thegifts of Nature to their own uses--a movement was begun which shouldultimately lead to civilization. 

Long indeed must have been the ages required for the development ofthis rudest primitive community into the civilization revealed to us bythe most ancient tablets of Egypt and Assyria. After spoken languagewas developed, and after the rude representation of ideas by visiblemarks drawn to resemble them had long been practised, some Cadmus musthave invented an alphabet. When the use of written language was thusintroduced, the word of command ceased to be confined to the range ofthe human voice, and it became possible for master minds to extendtheir influence as far as a written message could be carried. Then werecommunities gathered into provinces; provinces into kingdoms, kingdomsinto great empires of antiquity. Then arose a stage of civilizationwhich we find pictured in the most ancient records--a stage in whichmen were governed by laws that were perhaps as wisely adapted to theirconditions as our laws are to ours--in which the phenomena of naturewere rudely observed, and striking occurrences in the earth or in theheavens recorded in the annals of the nation. 

Vast was the progress of knowledge during the interval between theseempires and the century in which modern science began. Yet, if I amright in making a distinction between the slow and regular steps ofprogress, each growing naturally out of that which preceded it, and theentrance of the mind at some fairly definite epoch into an entirely newsphere of activity, it would appear that there was only one such epochduring the entire interval. This was when abstract geometricalreasoning commenced, and astronomical observations aiming at precisionwere recorded, compared, and discussed. Closely associated with it musthave been the construction of the forms of logic. The radicaldifference between the demonstration of a theorem of geometry and thereasoning of every-day life which the masses of men must have practisedfrom the beginning, and which few even to-day ever get beyond, is soevident at a glance that I need not dwell upon it. The principalfeature of this advance is that, by one of those antinomies of humanintellect of which examples are not wanting even in our own time, thedevelopment of abstract ideas preceded the concrete knowledge ofnatural phenomena. When we reflect that in the geometry of Euclid thescience of space was brought to such logical perfection that evento-day its teachers are not agreed as to the practicability of anygreat improvement upon it, we cannot avoid the feeling that a veryslight change in the direction of the intellectual activity of theGreeks would have led to the beginning of natural science. But it wouldseem that the very purity and perfection which was aimed at in theirsystem of geometry stood in the way of any extension or application ofits methods and spirit to the field of nature. One example of this isworthy of attention. In modern teaching the idea of magnitude asgenerated by motion is freely introduced. A line is described by amoving point; a plane by a moving line; a solid by a moving plane. Itmay, at first sight, seem singular that this conception finds no placein the Euclidian system. But we may regard the omission as a mark oflogical purity and rigor. Had the real or supposed advantages ofintroducing motion into geometrical conceptions been suggested toEuclid, we may suppose him to have replied that the theorems of spaceare independent of time; that the idea of motion necessarily impliestime, and that, in consequence, to avail ourselves of it would be tointroduce an extraneous element into geometry. 

It is quite possible that the contempt of the ancient philosophers forthe practical application of their science, which has continued in someform to our own time, and which is not altogether unwholesome, was apowerful factor in the same direction. The result was that, in keepinggeometry pure from ideas which did not belong to it, it failed to formwhat might otherwise have been the basis of physical science. Itsfounders missed the discovery that methods similar to those ofgeometric demonstration could be extended into other and wider fieldsthan that of space. Thus not only the development of applied geometrybut the reduction of other conceptions to a rigorous mathematical formwas indefinitely postponed. 

There is, however, one science which admitted of the immediateapplication of the theorems of geometry, and which did not require theapplication of the experimental method. Astronomy is necessarily ascience of observation pure and simple, in which experiment can have noplace except as an auxiliary. The vague accounts of striking celestialphenomena handed down by the priests and astrologers of antiquity werefollowed in the time of the Greeks by observations having, in form atleast, a rude approach to precision, though nothing like the degree ofprecision that the astronomer of to-day would reach with the naked eye, aided by such instruments as he could fashion from the tools at thecommand of the ancients. 

The rude observations commenced by the Babylonians were continued withgradually improving instruments--first by the Greeks and afterwards bythe Arabs--but the results failed to afford any insight into the truerelation of the earth to the heavens. What was most remarkable in thisfailure is that, to take a first step forward which would have led onto success, no more was necessary than a course of abstract thinkingvastly easier than that required for working out the problems ofgeometry. That space is infinite is an unexpressed axiom, tacitlyassumed by Euclid and his successors. Combining this with the mostelementary consideration of the properties of the triangle, it would beseen that a body of any given size could be placed at such a distancein space as to appear to us like a point. Hence a body as large as ourearth, which was known to be a globe from the time that the ancientPhoenicians navigated the Mediterranean, if placed in the heavens at asufficient distance, would look like a star. The obvious conclusionthat the stars might be bodies like our globe, shining either by theirown light or by that of the sun, would have been a first step to theunderstanding of the true system of the world. 

There is historic evidence that this deduction did not wholly escapethe Greek thinkers. It is true that the critical student will assignlittle weight to the current belief that the vague theory ofPythagoras--that fire was at the centre of all things--implies aconception of the heliocentric theory of the solar system. But thetestimony of Archimedes, confused though it is in form, leaves noserious doubt that Aristarchus of Samos not only propounded the viewthat the earth revolves both on its own axis and around the sun, butthat he correctly removed the great stumbling-block in the way of thistheory by adding that the distance of the fixed stars was infinitelygreater than the dimensions of the earth's orbit. Even the world ofphilosophy was not yet ready for this conception, and, so far fromseeing the reasonableness of the explanation, we find Ptolemy arguingagainst the rotation of the earth on grounds which careful observationsof the phenomena around him would have shown to be ill-founded. 

Physical science, if we can apply that term to an uncoordinated body offacts, was successfully cultivated from the earliest times. Somethingmust have been known of the properties of metals, and the art ofextracting them from their ores must have been practised, from the timethat coins and medals were first stamped. The properties of the mostcommon compounds were discovered by alchemists in their vain search forthe philosopher's stone, but no actual progress worthy of the namerewarded the practitioners of the black art. 

Perhaps the first approach to a correct method was that of Archimedes, who by much thinking worked out the law of the lever, reached theconception of the centre of gravity, and demonstrated the firstprinciples of hydrostatics. It is remarkable that he did not extend hisresearches into the phenomena of motion, whether spontaneous orproduced by force. The stationary condition of the human intellect ismost strikingly illustrated by the fact that not until the time ofLeonardo was any substantial advance made on his discovery. To sum upin one sentence the most characteristic feature of ancient and medievalscience, we see a notable contrast between the precision of thoughtimplied in the construction and demonstration of geometrical theoremsand the vague indefinite character of the ideas of natural phenomenagenerally, a contrast which did not disappear until the foundations ofmodern science began to be laid. 

We should miss the most essential point of the difference betweenmedieval and modern learning if we looked upon it as mainly adifference either in the precision or the amount of knowledge. Thedevelopment of both of these qualities would, under any circumstances, have been slow and gradual, but sure. We can hardly suppose that anyone generation, or even any one century, would have seen the completesubstitution of exact for inexact ideas. Slowness of growth is asinevitable in the case of knowledge as in that of a growing organism. The most essential point of difference is one of those seemingly slightones, the importance of which we are too apt to overlook. It was likethe drop of blood in the wrong place, which some one has told us makesall the difference between a philosopher and a maniac. It was all thedifference between a living tree and a dead one, between an inert massand a growing organism. The transition of knowledge from the dead tothe living form must, in any complete review of the subject, be lookedupon as the really great event of modern times. Before this event theintellect was bound down by a scholasticism which regarded knowledge asa rounded whole, the parts of which were written in books and carriedin the minds of learned men. The student was taught from the beginningof his work to look upon authority as the foundation of his beliefs. The older the authority the greater the weight it carried. So effectivewas this teaching that it seems never to have occurred to individualmen that they had all the opportunities ever enjoyed by Aristotle ofdiscovering truth, with the added advantage of all his knowledge tobegin with. Advanced as was the development of formal logic, thatpractical logic was wanting which could see that the last of a seriesof authorities, every one of which rested on those which preceded it, could never form a surer foundation for any doctrine than that suppliedby its original propounder. 

The result of this view of knowledge was that, although during thefifteen centuries following the death of the geometer of Syracuse greatuniversities were founded at which generations of professors expoundedall the learning of their time, neither professor nor student eversuspected what latent possibilities of good were concealed in the mostfamiliar operations of Nature. Every one felt the wind blow, saw waterboil, and heard the thunder crash, but never thought of investigatingthe forces here at play. Up to the middle of the fifteenth century themost acute observer could scarcely have seen the dawn of a new era. 

In view of this state of things it must be regarded as one of the mostremarkable facts in evolutionary history that four or five men, whosemental constitution was either typical of the new order of things, orwho were powerful agents in bringing it about, were all born during thefifteenth century, four of them at least, at so nearly the same time asto be contemporaries. 

Leonardo da Vinci, whose artistic genius has charmed succeedinggenerations, was also the first practical engineer of his time, and thefirst man after Archimedes to make a substantial advance in developingthe laws of motion. That the world was not prepared to make use of hisscientific discoveries does not detract from the significance whichmust attach to the period of his birth. 

Shortly after him was born the great navigator whose bold spirit was tomake known a new world, thus giving to commercial enterprise thatimpetus which was so powerful an agent in bringing about a revolutionin the thoughts of men. 

The birth of Columbus was soon followed by that of Copernicus, thefirst after Aristarchus to demonstrate the true system of the world. Inhim more than in any of his contemporaries do we see the strugglebetween the old forms of thought and the new. It seems almost patheticand is certainly most suggestive of the general view of knowledge takenat that time that, instead of claiming credit for bringing to lightgreat truths before unknown, he made a labored attempt to show that, after all, there was nothing really new in his system, which he claimedto date from Pythagoras and Philolaus. In this connection it is curiousthat he makes no mention of Aristarchus, who I think will be regardedby conservative historians as his only demonstrated predecessor. To thehold of the older ideas upon his mind we must attribute the fact thatin constructing his system he took great pains to make as little changeas possible in ancient conceptions. 

Luther, the greatest thought-stirrer of them all, practically of thesame generation with Copernicus, Leonardo and Columbus, does not comein as a scientific investigator, but as the great loosener of chainswhich had so fettered the intellect of men that they dared not thinkotherwise than as the authorities thought. 

Almost coeval with the advent of these intellects was the invention ofprinting with movable type. Gutenberg was born during the first decadeof the century, and his associates and others credited with theinvention not many years afterwards. If we accept the principle onwhich I am basing my argument, that in bringing out the springs of ourprogress we should assign the first place to the birth of those psychicagencies which started men on new lines of thought, then surely was thefifteenth the wonderful century. 

Let us not forget that, in assigning the actors then born to theirplaces, we are not narrating history, but studying a special phase ofevolution. It matters not for us that no university invited Leonardo toits halls, and that his science was valued by his contemporaries onlyas an adjunct to the art of engineering. The great fact still is thathe was the first of mankind to propound laws of motion. It is not foranything in Luther's doctrines that he finds a place in our scheme. Nomatter for us whether they were sound or not. What he did towards theevolution of the scientific investigator was to show by his examplethat a man might question the best-established and most venerableauthority and still live--still preserve his intellectualintegrity--still command a hearing from nations and their rulers. Itmatters not for us whether Columbus ever knew that he had discovered anew continent. His work was to teach that neither hydra, chimera norabyss--neither divine injunction nor infernal machination--was in theway of men visiting every part of the globe, and that the problem ofconquering the world reduced itself to one of sails and rigging, hulland compass. The better part of Copernicus was to direct man to aview-point whence he should see that the heavens were of like matterwith the earth. All this done, the acorn was planted from which the oakof our civilization should spring. The mad quest for gold whichfollowed the discovery of Columbus, the questionings which absorbed theattention of the learned, the indignation excited by the seemingvagaries of a Paracelsus, the fear and trembling lest the strangedoctrine of Copernicus should undermine the faith of centuries, wereall helps to the germination of the seed--stimuli to thought whichurged it on to explore the new fields opened up to its occupation. Thisgiven, all that has since followed came out in regular order ofdevelopment, and need be here considered only in those phases having aspecial relation to the purpose of our present meeting. 

So slow was the growth at first that the sixteenth century may scarcelyhave recognized the inauguration of a new era. Torricelli and Benedettiwere of the third generation after Leonardo, and Galileo, the first tomake a substantial advance upon his theory, was born more than acentury after him. Only two or three men appeared in a generation who, working alone, could make real progress in discovery, and even thesecould do little in leavening the minds of their fellowmen with the newideas. 

Up to the middle of the seventeenth century an agent which allexperience since that time shows to be necessary to the most productiveintellectual activity was wanting. This was the attrition of likeminds, making suggestions to one another, criticising, comparing, andreasoning. This element was introduced by the organization of the RoyalSociety of London and the Academy of Sciences of Paris. 

The members of these two bodies seem like ingenious youth suddenlythrown into a new world of interesting objects, the purposes andrelations of which they had to discover. The novelty of the situationis strikingly shown in the questions which occupied the minds of theincipient investigators. One natural result of British maritimeenterprise was that the aspirations of the Fellows of the Royal Societywere not confined to any continent or hemisphere. Inquiries were sentall the way to Batavia to know "whether there be a hill in Sumatrawhich burneth continually, and a fountain which runneth pure balsam. "The astronomical precision with which it seemed possible thatphysiological operations might go on was evinced by the inquiry whetherthe Indians can so prepare that stupefying herb Datura that "they makeit lie several days, months, years, according as they will, in a man'sbody without doing him any harm, and at the end kill him withoutmissing an hour's time. " Of this continent one of the inquiries waswhether there be a tree in Mexico that yields water, wine, vinegar, milk, honey, wax, thread and needles. 

Among the problems before the Paris Academy of Sciences those ofphysiology and biology took a prominent place. The distillation ofcompounds had long been practised, and the fact that the morespirituous elements of certain substances were thus separated naturallyled to the question whether the essential essences of life might not bediscoverable in the same way. In order that all might participate inthe experiments, they were conducted in open session of the academy, thus guarding against the danger of any one member obtaining for hisexclusive personal use a possible elixir of life. A wide range of theanimal and vegetable kingdom, including cats, dogs and birds of variousspecies, were thus analyzed. The practice of dissection was introducedon a large scale. That of the cadaver of an elephant occupied severalsessions, and was of such interest that the monarch himself was aspectator. 

To the same epoch with the formation and first work of these two bodiesbelongs the invention of a mathematical method which in its importanceto the advance of exact science may be classed with the invention ofthe alphabet in its relation to the progress of society at large. Theuse of algebraic symbols to represent quantities had its origin beforethe commencement of the new era, and gradually grew into a highlydeveloped form during the first two centuries of that era. But thismethod could represent quantities only as fixed. It is true that theelasticity inherent in the use of such symbols permitted of their beingapplied to any and every quantity; yet, in any one application, thequantity was considered as fixed and definite. But most of themagnitudes of nature are in a state of continual variation; indeed, since all motion is variation, the latter is a universal characteristicof all phenomena. No serious advance could be made in the applicationof algebraic language to the expression of physical phenomena until itcould be so extended as to express variation in quantities, as well asthe quantities themselves. This extension, worked out independently byNewton and Leibnitz, may be classed as the most fruitful of conceptionsin exact science. With it the way was opened for the unimpeded andcontinually accelerated progress of the last two centuries. 

The feature of this period which has the closest relation to thepurpose of our coming together is the seemingly unending subdivision ofknowledge into specialties, many of which are becoming so minute and soisolated that they seem to have no interest for any but their fewpursuers. Happily science itself has afforded a corrective for its owntendency in this direction. The careful thinker will see that in theseseemingly diverging branches common elements and common principles arecoming more and more to light. There is an increasing recognition ofmethods of research, and of deduction, which are common to largebranches, or to the whole of science. We are more and more recognizingthe principle that progress in knowledge implies its reduction to moreexact forms, and the expression of its ideas in language more or lessmathematical. The problem before the organizers of this Congress was, therefore, to bring the sciences together, and seek for the unity whichwe believe underlies their infinite diversity. 

The assembling of such a body as now fills this hall was scarcelypossible in any preceding generation, and is made possible now onlythrough the agency of science itself. It differs from all precedinginternational meetings by the universality of its scope, which aims toinclude the whole of knowledge. It is also unique in that none butleaders have been sought out as members. It is unique in that so manylands have delegated their choicest intellects to carry on its work. They come from the country to which our republic is indebted for athird of its territory, including the ground on which we stand; fromthe land which has taught us that the most scholarly devotion to thelanguages and learning of the cloistered past is compatible withleadership in the practical application of modern science to the artsof life; from the island whose language and literature have found a newfield and a vigorous growth in this region; from the last seat of theholy Roman Empire; from the country which, remembering a monarch whomade an astronomical observation at the Greenwich Observatory, hasenthroned science in one of the highest places in its government; fromthe peninsula so learned that we have invited one of its scholars tocome and tells us of our own language; from the land which gave birthto Leonardo, Galileo, Torricelli, Columbus, Volta--what an array ofimmortal names!--from the little republic of glorious history which, breeding men rugged as its eternal snow-peaks, has yet been the seat ofscientific investigation since the day of the Bernoullis; from the landwhose heroic dwellers did not hesitate to use the ocean itself toprotect it against invaders, and which now makes us marvel at theamount of erudition compressed within its little area; from the nationacross the Pacific, which, by half a century of unequalled progress inthe arts of life, has made an important contribution to evolutionaryscience through demonstrating the falsity of the theory that the mostancient races are doomed to be left in the rear of the advancingage--in a word, from every great centre of intellectual activity on theglobe I see before me eminent representatives of that world--advance inknowledge which we have met to celebrate. May we not confidently hopethat the discussions of such an assemblage will prove pregnant of afuture for science which shall outshine even its brilliant past. 

Gentlemen and scholars all! You do not visit our shores to find greatcollections in which centuries of humanity have given expression oncanvas and in marble to their hopes, fears, and aspirations. Nor do youexpect institutions and buildings hoary with age. But as you feel thevigor latent in the fresh air of these expansive prairies, which hascollected the products of human genius by which we are here surrounded, and, I may add, brought us together; as you study the institutionswhich we have founded for the benefit, not only of our own people, butof humanity at large; as you meet the men who, in the short space ofone century, have transformed this valley from a savage wilderness intowhat it is today--then may you find compensation for the want of a pastlike yours by seeing with prophetic eye a future world-power of whichthis region shall be the seat. If such is to be the outcome of theinstitutions Which we are now building up, then may your present visitbe a blessing both to your posterity and ours by making that power onefor good to all man-kind. Your deliberations will help to demonstrateto us and to the world at large that the reign of law must supplantthat of brute force in the relations of the nations, just as it hassupplanted it in the relations of individuals. You will help to showthat the war which science is now waging against the sources ofdiseases, pain, and misery offers an even nobler field for the exerciseof heroic qualities than can that of battle. We hope that when, afteryour all too-fleeting sojourn in our midst, you return to your ownshores, you will long feel the influence of the new air you havebreathed in an infusion of increased vigor in pursuing your variedlabors. And if a new impetus is thus given to the great intellectualmovement of the past century, resulting not only in promoting theunification of knowledge, but in widening its field through newcombinations of effort on the part of its votaries, the projectors, organizers and supporters of this Congress of Arts and Science will bejustified of their labors. 

XVII

THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE

[Footnote: Address at the dedication of the Flower Observatory, University of Pennsylvania, May 12, 1897--Science, May 21, 1897]

Assembled, as we are, to dedicate a new institution to the promotion ofour knowledge of the heavens, it appeared to me that an appropriate andinteresting subject might be the present and future problems ofastronomy. Yet it seemed, on further reflection, that, apart from thedifficulty of making an adequate statement of these problems on such anoccasion as the present, such a wording of the theme would not fullyexpress the idea which I wish to convey. The so-called problems ofastronomy are not separate and independent, but are rather the parts ofone great problem, that of increasing our knowledge of the universe inits widest extent. Nor is it easy to contemplate the edifice ofastronomical science as it now stands, without thinking of the past aswell as of the present and future. The fact is that our knowledge ofthe universe has been in the nature of a slow and gradual evolution, commencing at a very early period in human history, and destined to goforward without stop, as we hope, so long as civilization shall endure. The astronomer of every age has built on the foundations laid by hispredecessors, and his work has always formed, and must ever form, thebase on which his successors shall build. The astronomer of to-day maylook back upon Hipparchus and Ptolemy as the earliest ancestors of whomhe has positive knowledge. He can trace his scientific descent fromgeneration to generation, through the periods of Arabian and medievalscience, through Copernicus, Kepler, Newton, Laplace, and Herschel, down to the present time. The evolution of astronomical knowledge, generally slow and gradual, offering little to excite the attention ofthe public, has yet been marked by two cataclysms. One of these is seenin the grand conception of Copernicus that this earth on which we dwellis not a globe fixed in the centre of the universe, but is simply oneof a number of bodies, turning on their own axes and at the same timemoving around the sun as a centre. It has always seemed to me that thereal significance of the heliocentric system lies in the greatness ofthis conception rather than in the fact of the discovery itself. Thereis no figure in astronomical history which may more appropriately claimthe admiration of mankind through all time than that of Copernicus. Scarcely any great work was ever so exclusively the work of one man aswas the heliocentric system the work of the retiring sage ofFrauenburg. No more striking contrast between the views of scientificresearch entertained in his time and in ours can be found than thatafforded by the fact that, instead of claiming credit for his greatwork, he deemed it rather necessary to apologize for it and, so far aspossible, to attribute his ideas to the ancients. 

A century and a half after Copernicus followed the second great step, that taken by Newton. This was nothing less than showing that theseemingly complicated and inexplicable motions of the heavenly bodieswere only special cases of the same kind of motion, governed by thesame forces, that we see around us whenever a stone is thrown by thehand or an apple falls to the ground. The actual motions of the heavensand the laws which govern them being known, man had the key with whichhe might commence to unlock the mysteries of the universe. 

When Huyghens, in 1656, published his Systema Saturnium, where he firstset forth the mystery of the rings of Saturn, which, for nearly half acentury, had perplexed telescopic observers, he prefaced it with aremark that many, even among the learned, might condemn his course indevoting so much time and attention to matters far outside the earth, when he might better be studying subjects of more concern to humanity. Notwithstanding that the inventor of the pendulum clock was, perhaps, the last astronomer against whom a neglect of things terrestrial couldbe charged, he thought it necessary to enter into an elaborate defenceof his course in studying the heavens. Now, however, the more distantobjects are in space--I might almost add the more distant events are intime--the more they excite the attention of the astronomer, if only hecan hope to acquire positive knowledge about them. Not, however, because he is more interested in things distant than in things near, but because thus he may more completely embrace in the scope of hiswork the beginning and the end, the boundaries of all things, and thus, indirectly, more fully comprehend all that they include. From hisstand-point, "All are but parts of one stupendous whole, Whose body Nature is and God the soul. "

Others study Nature and her plans as we see them developed on thesurface of this little planet which we inhabit, the astronomer wouldfain learn the plan on which the whole universe is constructed. Themagnificent conception of Copernicus is, for him, only an introductionto the yet more magnificent conception of infinite space containing acollection of bodies which we call the visible universe. How far doesthis universe extend? What are the distances and arrangements of thestars? Does the universe constitute a system? If so, can we comprehendthe plan on which this system is formed, of its beginning and of itsend? Has it bounds outside of which nothing exists but the black andstarless depths of infinity itself? Or are the stars we see simply suchmembers of an infinite collection as happen to be the nearest oursystem? A few such questions as these we are perhaps beginning toanswer; but hundreds, thousands, perhaps even millions, of years mayelapse without our reaching a complete solution. Yet the astronomerdoes not view them as Kantian antinomies, in the nature of thingsinsoluble, but as questions to which he may hopefully look for at leasta partial answer. 

The problem of the distances of the stars is of peculiar interest inconnection with the Copernican system. The greatest objection to thissystem, which must have been more clearly seen by astronomersthemselves than by any others, was found in the absence of any apparentparallax of the stars. If the earth performed such an immeasurablecircle around the sun as Copernicus maintained, then, as it passed fromside to side of its orbit, the stars outside the solar system mustappear to have a corresponding motion in the other direction, and thusto swing back and forth as the earth moved in one and the otherdirection. The fact that not the slightest swing of that sort could beseen was, from the time of Ptolemy, the basis on which the doctrine ofthe earth's immobility rested. The difficulty was not grappled with byCopernicus or his immediate successors. The idea that Nature would notsquander space by allowing immeasurable stretches of it to go unusedseems to have been one from which medieval thinkers could not entirelybreak away. The consideration that there could be no need of any sucheconomy, because the supply was infinite, might have been theoreticallyacknowledged, but was not practically felt. The fact is thatmagnificent as was the conception of Copernicus, it was dwarfed by theconception of stretches from star to star so vast that the whole orbitof the earth was only a point in comparison. 

An indication of the extent to which the difficulty thus arising wasfelt is seen in the title of a book published by Horrebow, the Danishastronomer, some two centuries ago. This industrious observer, one ofthe first who used an instrument resembling our meridian transit of thepresent day, determined to see if he could find the parallax of thestars by observing the intervals at which a pair of stars in oppositequarters of the heavens crossed his meridian at opposite seasons of theyear. When, as he thought, he had won success, he published hisobservations and conclusions under the title of Copernicus Triumphans. But alas! the keen criticism of his successors showed that what hesupposed to be a swing of the stars from season to season arose from aminute variation in the rate of his clock, due to the differenttemperatures to which it was exposed during the day and the night. Themeasurement of the distance even of the nearest stars evadedastronomical research until Bessel and Struve arose in the early partof the present century. 

On some aspects of the problem of the extent of the universe light isbeing thrown even now. Evidence is gradually accumulating which pointsto the probability that the successive orders of smaller and smallerstars, which our continually increasing telescopic power brings intoview, are not situated at greater and greater distances, but that weactually see the boundary of our universe. This indication lends apeculiar interest to various questions growing out of the motions ofthe stars. Quite possibly the problem of these motions will be thegreat one of the future astronomer. Even now it suggests thoughts andquestions of the most far-reaching character. 

I have seldom felt a more delicious sense of repose than when crossingthe ocean during the summer months I sought a place where I could liealone on the deck, look up at the constellations, with Lyra near thezenith, and, while listening to the clank of the engine, try tocalculate the hundreds of millions of years which would be required byour ship to reach the star a Lyrae, if she could continue her course inthat direction without ever stopping. It is a striking example of howeasily we may fail to realize our knowledge when I say that I havethought many a time how deliciously one might pass those hundredmillions of years in a journey to the star a Lyrae, without itsoccurring to me that we are actually making that very journey at aspeed compared with which the motion of a steamship is slow indeed. Through every year, every hour, every minute, of human history from thefirst appearance of man on the earth, from the era of the builders ofthe Pyramids, through the times of Caesar and Hannibal, through theperiod of every event that history records, not merely our earth, butthe sun and the whole solar system with it, have been speeding theirway towards the star of which I speak on a journey of which we knowneither the beginning nor the end. We are at this moment thousands ofmiles nearer to a Lyrae than we were a few minutes ago when I beganthis discourse, and through every future moment, for untold thousandsof years to come, the earth and all there is on it will be nearer to aLyrae, or nearer to the place where that star now is, by hundreds ofmiles for every minute of time come and gone. When shall we get there?Probably in less than a million years, perhaps in half a million. Wecannot tell exactly, but get there we must if the laws of nature andthe laws of motion continue as they are. To attain to the stars was theseemingly vain wish of an ancient philosopher, but the whole human raceis, in a certain sense, realizing this wish as rapidly as a speed often miles a second can bring it about. 

I have called attention to this motion because it may, in the notdistant future, afford the means of approximating to a solution of theproblem already mentioned--that of the extent of the universe. Notwithstanding the success of astronomers during the present centuryin measuring the parallax of a number of stars, the most recentinvestigations show that there are very few, perhaps hardly more than ascore, of stars of which the parallax, and therefore the distance, hasbeen determined with any approach to certainty. Many parallaxesdetermined about the middle of the nineteenth century have had todisappear before the powerful tests applied by measures with theheliometer; others have been greatly reduced and the distances of thestars increased in proportion. So far as measurement goes, we can onlysay of the distances of all the stars, except the few whose parallaxeshave been determined, that they are immeasurable. The radius of theearth's orbit, a line more than ninety millions of miles in length, notonly vanishes from sight before we reach the distance of the great massof stars, but becomes such a mere point that when magnified by thepowerful instruments of modern times the most delicate appliances failto make it measurable. Here the solar motion comes to our help. Thismotion, by which, as I have said, we are carried unceasingly throughspace, is made evident by a motion of most of the stars in the oppositedirection, just as passing through a country on a railway we see thehouses on the right and on the left being left behind us. It is clearenough that the apparent motion will be more rapid the nearer theobject. We may therefore form some idea of the distance of the starswhen we know the amount of the motion. It is found that in the greatmass of stars of the sixth magnitude, the smallest visible to the nakedeye, the motion is about three seconds per century. As a measure thusstated does not convey an accurate conception of magnitude to one notpractised in the subject, I would say that in the heavens, to theordinary eye, a pair of stars will appear single unless they areseparated by a distance of 150 or 200 seconds. Let us, then, imagineourselves looking at a star of the sixth magnitude, which is at restwhile we are carried past it with the motion of six to eight miles persecond which I have described. Mark its position in the heavens as wesee it to-day; then let its position again be marked five thousandyears hence. A good eye will just be able to perceive that there aretwo stars marked instead of one. The two would be so close togetherthat no distinct space between them could be perceived by unaidedvision. It is due to the magnifying power of the telescope, enlargingsuch small apparent distances, that the motion has been determined inso small a period as the one hundred and fifty years during whichaccurate observations of the stars have been made. 

The motion just described has been fairly well determined for what, astronomically speaking, are the brighter stars; that is to say, thosevisible to the naked eye. But how is it with the millions of fainttelescopic stars, especially those which form the cloud masses of theMilky Way? The distance of these stars is undoubtedly greater, and theapparent motion is therefore smaller. Accurate observations upon suchstars have been commenced only recently, so that we have not yet hadtime to determine the amount of the motion. But the indication seems tobe that it will prove quite a measurable quantity and that before thetwentieth century has elapsed, it will be determined for very muchsmaller stars than those which have heretofore been studied. Aphotographic chart of the whole heavens is now being constructed by anassociation of observatories in some of the leading countries of theworld. I cannot say all the leading countries, because then we shouldhave to exclude our own, which, unhappily, has taken no part in thiswork. At the end of the twentieth century we may expect that the workwill be repeated. Then, by comparing the charts, we shall see theeffect of the solar motion and perhaps get new light upon the problemin question. 

Closely connected with the problem of the extent of the universe isanother which appears, for us, to be insoluble because it brings usface to face with infinity itself. We are familiar enough witheternity, or, let us say, the millions or hundreds of millions of yearswhich geologists tell us must have passed while the crust of the earthwas assuming its present form, our mountains being built, our rocksconsolidated, and successive orders of animals coming and going. Hundreds of millions of years is indeed a long time, and yet, when wecontemplate the changes supposed to have taken place during that time, we do not look out on eternity itself, which is veiled from our sight, as it were, by the unending succession of changes that mark theprogress of time. But in the motions of the stars we are brought faceto face with eternity and infinity, covered by no veil whatever. Itwould be bold to speak dogmatically on a subject where the springs ofbeing are so far hidden from mortal eyes as in the depths of theuniverse. But, without declaring its positive certainty, it must besaid that the conclusion seems unavoidable that a number of stars aremoving with a speed such that the attraction of all the bodies of theuniverse could never stop them. One such case is that of Arcturus, thebright reddish star familiar to mankind since the days of Job, andvisible near the zenith on the clear evenings of May and June. Yetanother case is that of a star known in astronomical nomenclature as1830 Groombridge, which exceeds all others in its angular proper motionas seen from the earth. We should naturally suppose that it seems tomove so fast because it is near us. But the best measurements of itsparallax seem to show that it can scarcely be less than two milliontimes the distance of the earth from the sun, while it may be muchgreater. Accepting this result, its velocity cannot be much less thantwo hundred miles per second, and may be much more. With this speed itwould make the circuit of our globe in two minutes, and had it goneround and round in our latitudes we should have seen it fly past us anumber of times since I commenced this discourse. It would make thejourney from the earth to the sun in five days. If it is now near thecentre of our universe it would probably reach its confines in amillion of years. So far as our knowledge goes, there is no force innature which would ever have set it in motion and no force which canever stop it. What, then, was the history of this star, and, if thereare planets circulating around, what the experience of beings who mayhave lived on those planets during the ages which geologists andnaturalists assure us our earth has existed? Was there a period whenthey saw at night only a black and starless heaven? Was there a timewhen in that heaven a small faint patch of light began gradually toappear? Did that patch of light grow larger and larger as million aftermillion of years elapsed? Did it at last fill the heavens and break upinto constellations as we now see them? As millions more of yearselapse will the constellations gather together in the opposite quarterand gradually diminish to a patch of light as the star pursues itsirresistible course of two hundred miles per second through thewilderness of space, leaving our universe farther and farther behindit, until it is lost in the distance? If the conceptions of modernscience are to be considered as good for all time--a point on which Iconfess to a large measure of scepticism--then these questions must beanswered in the affirmative. 

The problems of which I have so far spoken are those of what may becalled the older astronomy. If I apply this title it is because thatbranch of the science to which the spectroscope has given birth isoften called the new astronomy. It is commonly to be expected that anew and vigorous form of scientific research will supersede that whichis hoary with antiquity. But I am not willing to admit that such is thecase with the old astronomy, if old we may call it. It is more pregnantwith future discoveries today than it ever has been, and it is moredisposed to welcome the spectroscope as a useful handmaid, which mayhelp it on to new fields, than it is to give way to it. How useful itmay thus become has been recently shown by a Dutch astronomer, whofinds that the stars having one type of spectrum belong mostly to theMilky Way, and are farther from us than the others. 

In the field of the newer astronomy perhaps the most interesting workis that associated with comets. It must be confessed, however, that thespectroscope has rather increased than diminished the mystery which, insome respects, surrounds the constitution of these bodies. The olderastronomy has satisfactorily accounted for their appearance, and wemight also say for their origin and their end, so far as questions oforigin can come into the domain of science. It is now known that cometsare not wanderers through the celestial spaces from star to star, butmust always have belonged to our system. But their orbits are so veryelongated that thousands, or even hundreds of thousands, of years arerequired for a revolution. Sometimes, however, a comet passing near toJupiter is so fascinated by that planet that, in its vain attempts tofollow it, it loses so much of its primitive velocity as to circulatearound the sun in a period of a few years, and thus to become, apparently, a new member of our system. If the orbit of such a comet, or in fact of any comet, chances to intersect that of the earth, thelatter in passing the point of intersection encounters minute particleswhich cause a meteoric shower. 

But all this does not tell us much about the nature and make-up of acomet. Does it consist of nothing but isolated particles, or is there asolid nucleus, the attraction of which tends to keep the mass together?No one yet knows. The spectroscope, if we interpret its indications inthe usual way, tells us that a comet is simply a mass of hydrocarbonvapor, shining by its own light. But there must be something wrong inthis interpretation. That the light is reflected sunlight seems tofollow necessarily from the increased brilliancy of the comet as itapproaches the sun and its disappearance as it passes away. 

Great attention has recently been bestowed upon the physicalconstitution of the planets and the changes which the surfaces of thosebodies may undergo. In this department of research we must feelgratified by the energy of our countrymen who have entered upon it. Should I seek to even mention all the results thus made known I mightbe stepping on dangerous ground, as many questions are still unsettled. While every astronomer has entertained the highest admiration for theenergy and enthusiasm shown by Mr. Percival Lowell in founding anobservatory in regions where the planets can be studied under the mostfavorable conditions, they cannot lose sight of the fact that theablest and most experienced observers are liable to error when theyattempt to delineate the features of a body 50, 000, 000 or 100, 000, 000miles away through such a disturbing medium as our atmosphere. Even onsuch a subject as the canals of Mars doubts may still be felt. Thatcertain markings to which Schiaparelli gave the name of canals exist, few will question. But it may be questioned whether these markings arethe fine, sharp, uniform lines found on Schiaparelli's map anddelineated in Lowell's beautiful book. It is certainly curious thatBarnard at Mount Hamilton, with the most powerful instrument and underthe most favorable circumstances, does not see these markings as canals. 

I can only mention among the problems of the spectroscope the elegantand remarkable solution of the mystery surrounding the rings of Saturn, which has been effected by Keeler at Allegheny. That these rings couldnot be solid has long been a conclusion of the laws of mechanics, butKeeler was the first to show that they really consist of separateparticles, because the inner portions revolve more rapidly than theouter. 

The question of the atmosphere of Mars has also received an importantadvance by the work of Campbell at Mount Hamilton. Although it is notproved that Mars has no atmosphere, for the existence of someatmosphere can scarcely be doubted, yet the Mount Hamilton astronomerseems to have shown, with great conclusiveness, that it is so rare asnot to produce any sensible absorption of the solar rays. 

I have left an important subject for the close. It belongs entirely tothe older astronomy, and it is one with which I am glad to say thisobservatory is expected to especially concern itself. I refer to thequestion of the variation of latitudes, that singular phenomenonscarcely suspected ten years ago, but brought out by observations inGermany during the past eight years, and reduced to law with suchbrilliant success by our own Chandler. The north pole is not a fixedpoint on the earth's surface, but moves around in rather an irregularway. True, the motion is small; a circle of sixty feet in diameter willinclude the pole in its widest range. This is a very small matter sofar as the interests of daily life are concerned; but it is veryimportant to the astronomer. It is not simply a motion of the pole ofthe earth, but a wobbling of the solid earth itself. No one knows whatconclusions of importance to our race may yet follow from a study ofthe stupendous forces necessary to produce even this slight motion. 

The director of this new observatory has already distinguished himselfin the delicate and difficult work of investigating this motion, and Iam glad to know that he is continuing the work here with one of thefinest instruments ever used for the purpose, a splendid product ofAmerican mechanical genius. I can assure you that astronomers the worldover will look with the greatest interest for Professor Doolittle'ssuccess in the arduous task he has undertaken. 

There is one question connected with these studies of the universe onwhich I have not touched, and which is, nevertheless, of transcendentinterest. What sort of life, spiritual and intellectual, exists indistant worlds? We cannot for a moment suppose that our little planetis the only one throughout the whole universe on which may be found thefruits of civilization, family affection, friendship, the desire topenetrate the mysteries of creation. And yet this question is notto-day a problem of astronomy, nor can we see any prospect that it everwill be, for the simple reason that science affords us no hope of ananswer to any question that we may send through the fathomless abyss. When the spectroscope was in its infancy it was suggested that possiblysome difference might be found in the rays reflected from livingmatter, especially from vegetation, that might enable us to distinguishthem from rays reflected by matter not endowed with life. But this hopehas not been realized, nor does it seem possible to realize it. Theastronomer cannot afford to waste his energies on hopeless speculationabout matters of which he cannot learn anything, and he thereforeleaves this question of the plurality of worlds to others who are ascompetent to discuss it as he is. All he can tell the world is:

 He who through vast immensity can pierce, See worlds on worlds compose one universe; Observe how system into system runs, What other planets circle other suns, What varied being peoples every star, May tell why Heaven has made us as we are. 

XVIII

ASPECTS OF AMERICAN ASTRONOMY

[Footnote: Address delivered at the University of Chicago, October 22, 1897, in connection with the dedication of the Yerkes Observatory. Printed in the Astro physical Journal. November, 1897. ]

The University of Chicago yesterday accepted one of the most munificentgifts ever made for the promotion of any single science, and withappropriate ceremonies dedicated it to the increase of our knowledge ofthe heavenly bodies. 

The president of your university has done me the honor of inviting meto supplement what was said on that occasion by some remarks of a moregeneral nature suggested by the celebration. One is naturally disposedto say first what is uppermost in his mind. At the present moment thiswill naturally be the general impression made by what has been seen andheard. The ceremonies were attended, not only by a remarkabledelegation of citizens, but by a number of visiting astronomers whichseems large when we consider that the profession itself is not at allnumerous in any country. As one of these, your guests, I am sure that Igive expression only to their unanimous sentiment in saying that wehave been extremely gratified in many ways by all that we have seen andheard. The mere fact of so munificent a gift to science cannot butexcite universal admiration. We knew well enough that it was nothingmore than might have been expected from the public spirit of this greatWest; but the first view of a towering snowpeak is none the lessimpressive because you have learned in your geography how many feethigh it is, and great acts are none the less admirable because theycorrespond to what you have heard and read, and might therefore be ledto expect. 

The next gratifying feature is the great public interest excited by theoccasion. That the opening of a purely scientific institution shouldhave led so large an assemblage of citizens to devote an entire day, including a long journey by rail, to the celebration of yesterday issomething most suggestive from its unfamiliarity. A great manyscientific establishments have been inaugurated during the lasthalf-century, but if on any such occasion so large a body of citizenshas gone so great a distance to take part in the inauguration, the facthas at the moment escaped my mind. 

That the interest thus shown is not confined to the hundreds ofattendants, but must be shared by your great public, is shown by theunfailing barometer of journalism. Here we have a field in which thenon-survival of the unfit is the rule in its most ruthless form. Thejournals that we see and read are merely the fortunate few of acountless number, dead and forgotten, that did not know what the publicwanted to read about. The eagerness shown by the representatives ofyour press in recording everything your guests would say wasaccomplished by an enterprise in making known everything that occurred, and, in case of an emergency requiring a heroic measure, what did NOToccur, showing that smart journalists of the East must have learnedtheir trade, or at least breathed their inspiration, in these regions. I think it was some twenty years since I told a European friend thatthe eighth wonder of the world was a Chicago daily newspaper. Sincethat time the course of journalistic enterprise has been in the reversedirection to that of the course of empire, eastward instead of westward. 

It has been sometimes said--wrongfully, I think--that scientific menform a mutual admiration society. One feature of the occasion made mefeel that we, your guests, ought then and there to have organized sucha society and forthwith proceeded to business. This feature consistedin the conferences on almost every branch of astronomy by which thecelebration of yesterday was preceded. The fact that beyond theacceptance of a graceful compliment I contributed nothing to theseconferences relieves me from the charge of bias or self-assertion insaying that they gave me a new and most inspiring view of the energynow being expended in research by the younger generation ofastronomers. All the experience of the past leads us to believe thatthis energy will reap the reward which nature always bestows upon thosewho seek her acquaintance from unselfish motives. In one way it mightappear that little was to be learned from a meeting like that of thepresent week. Each astronomer may know by publications pertaining tothe science what all the others are doing. But knowledge obtained inthis way has a sort of abstractness about it a little like ourknowledge of the progress of civilization in Japan, or of the greatextent of the Australian continent. It was, therefore, a most happythought on the part of your authorities to bring together the largestpossible number of visiting astronomers from Europe, as well asAmerica, in order that each might see, through the attrition ofpersonal contact, what progress the others were making in theirresearches. To the visitors at least I am sure that the result of thismeeting has been extremely gratifying. They earnestly hope, one andall, that the callers of the conference will not themselves be moredisappointed in its results; that, however little they may haveactually to learn of methods and results, they will feel stimulated towell-directed efforts and find themselves inspired by thoughts which, however familiar, will now be more easily worked out. 

We may pass from the aspects of the case as seen by the strictlyprofessional class to those general aspects fitted to excite theattention of the great public. From the point of view of the latter itmay well appear that the most striking feature of the celebration isthe great amount of effort which is shown to be devoted to thecultivation of a field quite outside the ordinary range of humaninterests. The workers whom we see around us are only a detachment froman army of investigators who, in many parts of the world, are seekingto explore the mysteries of creation. Why so great an expenditure ofenergy? Certainly not to gain wealth, for astronomy is perhaps the onefield of scientific work which, in our expressive modern phrase, "hasno money in it. " It is true that the great practical use ofastronomical science to the country and the world in affording us themeans of determining positions on land and at sea is frequently pointedout. It is said that an Astronomer Royal of England once calculatedthat every meridian observation of the moon made at Greenwich was wortha pound sterling, on account of the help it would afford to thenavigation of the ocean. An accurate map of the United States cannot beconstructed without astronomical observations at numerous pointsscattered over the whole country, aided by data which greatobservatories have been accumulating for more than a century, and mustcontinue to accumulate in the future. 

But neither the measurement of the earth, the making of maps, nor theaid of the navigator is the main object which the astronomers of to-dayhave in view. If they do not quite share the sentiment of that eminentmathematician, who is said to have thanked God that his science was onewhich could not be prostituted to any useful purpose, they still knowwell that to keep utilitarian objects in view would only prove &handicap on their efforts. Consequently they never ask in what waytheir science is going to benefit mankind. As the great captain ofindustry is moved by the love of wealth, and the political leader bythe love of power over men, so the astronomer is moved by the love ofknowledge for its own sake, and not for the sake of its usefulapplications. Yet he is proud to know that his science has been worthmore to mankind than it has cost. He does not value its results merelyas a means of crossing the ocean or mapping the country, for he feelsthat man does not live by bread alone. If it is not more than bread toknow the place we occupy in the universe, it is certainly somethingwhich we should place not far behind the means of subsistence. That wenow look upon a comet as something very interesting, of which the sightaffords us a pleasure unmixed with fear of war, pestilence, or othercalamity, and of which we therefore wish the return, is a gain wecannot measure by money. In all ages astronomy has been an index to thecivilization of the people who cultivated it. It has been crude orexact, enlightened or mingled with superstition, according to thecurrent mode of thought. When once men understand the relation of theplanet on which they dwell to the universe at large, superstition isdoomed to speedy extinction. This alone is an object worth more thanmoney. 

Astronomy may fairly claim to be that science which transcends allothers in its demands upon the practical application of our reasoningpowers. Look at the stars that stud the heavens on a clear evening. What more hopeless problem to one confined to earth than that ofdetermining their varying distances, their motions, and their physicalconstitution? Everything on earth we can handle and investigate. Buthow investigate that which is ever beyond our reach, on which we cannever make an experiment? On certain occasions we see the moon pass infront of the sun and hide it from our eyes. To an observer a few milesaway the sun was not entirely hidden, for the shadow of the moon in atotal eclipse is rarely one hundred miles wide. On another continent noeclipse at all may have been visible. Who shall take a map of the worldand mark upon it the line on which the moon's shadow will travel duringsome eclipse a hundred years hence? Who shall map out the orbits of theheavenly bodies as they are going to appear in a hundred thousandyears? How shall we ever know of what chemical elements the sun and thestars are made? All this has been done, but not by the intellect of anyone man. The road to the stars has been opened only by the efforts ofmany generations of mathematicians and observers, each of whom beganwhere his predecessor had left off. 

We have reached a stage where we know much of the heavenly bodies. Wehave mapped out our solar system with great precision. But how withthat great universe of millions of stars in which our solar system isonly a speck of star-dust, a speck which a traveller through the wildsof space might pass a hundred times without notice? We have learnedmuch about this universe, though our knowledge of it is still dim. Wesee it as a traveller on a mountain-top sees a distant city in a cloudof mist, by a few specks of glimmering light from steeples or roofs. Wewant to know more about it, its origin and its destiny; its limits intime and space, if it has any; what function it serves in the universaleconomy. The journey is long, yet we want, in knowledge at least, tomake it. Hence we build observatories and train observers andinvestigators. Slow, indeed, is progress in the solution of thegreatest of problems, when measured by what we want to know. Somequestions may require centuries, others thousands of years for theiranswer. And yet never was progress more rapid than during our time. Insome directions our astronomers of to-day are out of sight of those offifty years ago; we are even gaining heights which twenty years agolooked hopeless. Never before had the astronomer so much work--good, hard, yet hopeful work--before him as to-day. He who is leaving thestage feels that he has only begun and must leave his successors withmore to do than his predecessors left him. 

To us an interesting feature of this progress is the part taken in itby our own country. The science of our day, it is true, is of nocountry. Yet we very appropriately speak of American science from thefact that our traditional reputation has not been that of a peopledeeply interested in the higher branches of intellectual work. Men yetliving can remember when in the eyes of the universal church oflearning, all cisatlantic countries, our own included, were partesinfidelium. 

Yet American astronomy is not entirely of our generation. In the middleof the last century Professor Winthrop, of Harvard, was an industriousobserver of eclipses and kindred phenomena, whose work was recorded inthe transactions of learned societies. But the greatest astronomicalactivity during our colonial period was that called out by the transitof Venus in 1769, which was visible in this country. A committee of theAmerican Philosophical Society, at Philadelphia, organized an excellentsystem of observations, which we now know to have been fully assuccessful, perhaps more so, than the majority of those made on othercontinents, owing mainly to the advantages of air and climate. Amongthe observers was the celebrated Rittenhouse, to whom is due thedistinction of having been the first American astronomer whose work hasan important place in the history of the science. In addition to theobservations which he has left us, he was the first inventor orproposer of the collimating telescope, an instrument which has becomealmost a necessity wherever accurate observations are made. The factthat the subsequent invention by Bessel may have been independent doesnot detract from the merits of either. 

Shortly after the transit of Venus, which I have mentioned, the war ofthe Revolution commenced. The generation which carried on that war andthe following one, which framed our Constitution and laid the bases ofour political institutions, were naturally too much occupied with thesegreat problems to pay much attention to pure science. While the greatmathematical astronomers of Europe were laying the foundation ofcelestial mechanics their writings were a sealed book to every one onthis side of the Atlantic, and so remained until Bowditch appeared, early in the present century. His translation of the Mecanique Celestemade an epoch in American science by bringing the great work of Laplacedown to the reach of the best American students of his time. 

American astronomers must always honor the names of Rittenhouse andBowditch. And yet in one respect their work was disappointing ofresults. Neither of them was the founder of a school. Rittenhouse leftno successor to carry on his work. The help which Bowditch afforded hisgeneration was invaluable to isolated students who, here and there, dived alone and unaided into the mysteries of the celestial motions. His work was not mainly in the field of observational astronomy, andtherefore did not materially influence that branch of science. In 1832Professor Airy, afterwards Astronomer Royal of England, made a reportto the British Association on the condition of practical astronomy invarious countries. In this report he remarked that he was unable to sayanything about American astronomy because, so far as he knew, no publicobservatory existed in the United States. 

William C. Bond, afterwards famous as the first director of the HarvardObservatory, was at that time making observations with a smalltelescope, first near Boston and afterwards at Cambridge. But with someagre an outfit his establishment could scarcely lay claim to being anastronomical observatory, and it was not surprising if Airy did notknow anything of his modest efforts. 

If at this time Professor Airy had extended his investigations into yetanother field, with a view of determining the prospects for a greatcity at the site of Fort Dearborn, on the southern shore of LakeMichigan, he would have seen as little prospect of civic growth in thatregion as of a great development of astronomy in the United States atlarge. A plat of the proposed town of Chicago had been prepared twoyears before, when the place contained perhaps half a dozen families. In the same month in which Professor Airy made his report, August, 1832, the people of the place, then numbering twenty-eight voters, decided to become incorporated, and selected five trustees to carry ontheir government. 

In 1837 a city charter was obtained from the legislature of Illinois. The growth of this infant city, then small even for an infant, into thegreat commercial metropolis of the West has been the just pride of itspeople and the wonder of the world. I mention it now because of aremarkable coincidence. With this civic growth has quietly gone onanother, little noted by the great world, and yet in its way equallywonderful and equally gratifying to the pride of those who measuregreatness by intellectual progress. Taking knowledge of the universe asa measure of progress, I wish to invite attention to the fact thatAmerican astronomy began with your city, and has slowly but surely keptpace with it, until to-day our country stands second only to Germany inthe number of researches being prosecuted, and second to none in thenumber of men who have gained the highest recognition by their labors. 

In 1836 Professor Albert Hopkins, of Williams College, and ProfessorElias Loomis, of Western Reserve College, Ohio, both commenced littleobservatories. Professor Loomis went to Europe for all his instruments, but Hopkins was able even then to get some of his in this country. Shortly afterwards a little wooden structure was erected by CaptainGilliss on Capitol Hill, at Washington, and supplied with a transitinstrument for observing moon culminations, in conjunction with CaptainWilkes, who was then setting out on his exploring expedition to thesouthern hemisphere. The date of these observatories was practicallythe same as that on which a charter for the city of Chicago wasobtained from the legislature. With their establishment the populationof your city had increased to 703. 

The next decade, 1840 to 1850, was that in which our practicalastronomy seriously commenced. The little observatory of CaptainGilliss was replaced by the Naval, then called the NationalObservatory, erected at Washington during the years 1843-44, and fittedout with what were then the most approved instruments. About the sametime the appearance of the great comet of 1843 led the citizens ofBoston to erect the observatory of Harvard College. Thus it is littlemore than a half-century since the two principal observatories in theUnited States were established. But we must not for a moment supposethat the mere erection of an observatory can mark an epoch inscientific history. What must make the decade of which I speak evermemorable in American astronomy was not merely the erection ofbuildings, but the character of the work done by astronomers away fromthem as well as in them. 

The National Observatory soon became famous by two remarkable stepswhich raised our country to an important position among those applyingmodern science to practical uses. One of these consisted of theresearches of Sears Cook Walker on the motion of the newly discoveredplanet Neptune. He was the first astronomer to determine fairly goodelements of the orbit of that planet, and, what is yet more remarkable, he was able to trace back the movement of the planet in the heavens forhalf a century and to show that it had been observed as a fixed star byLalande in 1795, without the observer having any suspicion of the truecharacter of the object. 

The other work to which I refer was the application to astronomy and tothe determination of longitudes of the chronographic method ofregistering transits of stars or other phenomena requiring an exactrecord of the instant of their occurrence. It is to be regretted thatthe history of this application has not been fully written. In somepoints there seems to be as much obscurity as with the discovery ofether as an anaesthetic, which took place about the same time. Happily, no such contest has been fought over the astronomical as over thesurgical discovery, the fact being that all who were engaged in theapplication of the new method were more anxious to perfect it than theywere to get credit for themselves. We know that Saxton, of the CoastSurvey; Mitchell and Locke, of Cincinnati; Bond, at Cambridge, as wellas Walker, and other astronomers at the Naval Observatory, all workedat the apparatus; that Maury seconded their efforts with untiring zeal;that it was used to determine the longitude of Baltimore as early as1844 by Captain Wilkes, and that it was put into practical use inrecording observations at the Naval Observatory as early as 1846. 

At the Cambridge Observatory the two Bonds, father and son, speedilybegan to show the stuff of which the astronomer is made. A well-devisedsystem of observations was put in operation. The discovery of the darkring of Saturn and of a new satellite to that planet gave additionalfame to the establishment. 

Nor was activity confined to the observational side of the science. Thesame decade of which I speak was marked by the beginning of ProfessorPierce's mathematical work, especially his determination of theperturbations of Uranus and Neptune. At this time commenced the work ofDr. B. A. Gould, who soon became the leading figure in Americanastronomy. Immediately on graduating at Harvard in 1845, he determinedto devote all the energies of his life to the prosecution of hisfavorite science. He studied in Europe for three years, took thedoctor's degree at Gottingen, came home, founded the AstronomicalJournal, and took an active part in that branch of the work of theCoast Survey which included the determination of longitudes byastronomical methods. 

An episode which may not belong to the history of astronomy must beacknowledged to have had a powerful influence in exciting publicinterest in that science. Professor O. M. Mitchell, the founder andfirst director of the Cincinnati Observatory, made the masses of ourintelligent people acquainted with the leading facts of astronomy bycourses of lectures which, in lucidity and eloquence, have never beenexcelled. The immediate object of the lectures was to raise funds forestablishing his observatory and fitting it out with a fine telescope. The popular interest thus excited in the science had an importanteffect in leading the public to support astronomical research. Ifpublic support, based on public interest, is what has made the presentfabric of American astronomy possible, then should we honor the name ofa man whose enthusiasm leavened the masses of his countrymen withinterest in our science. 

The Civil War naturally exerted a depressing influence upon ourscientific activity. The cultivator of knowledge is no less patrioticthan his fellow-citizens, and vies with them in devotion to the publicwelfare. The active interest which such cultivators took, first in theprosecution of the war and then in the restoration of the Union, naturally distracted their attention from their favorite pursuits. Butno sooner was political stability reached than a wave of intellectualactivity set in, which has gone on increasing up to the present time. If it be true that never before in our history has so much attentionbeen given to education as now; that never before did so many mendevote themselves to the diffusion of knowledge, it is no less truethat never was astronomical work so energetically pursued among us asat the present time. 

One deplorable result of the Civil War was that Gould's AstronomicalJournal had to be suspended. Shortly after the restoration of peace, instead of re-establishing the journal, its founder conceived theproject of exploring the southern heavens. The northern hemispherebeing the seat of civilization, that portion of the sky which could notbe seen from our latitudes was comparatively neglected. What had beendone in the southern hemisphere was mostly the occasional work ofindividuals and of one or two permanent observatories. The latter wereso few in number and so meagre in their outfit that a splendid fieldwas open to the inquirer. Gould found the patron which he desired inthe government of the Argentine Republic, on whose territory he erectedwhat must rank in the future as one of the memorable astronomicalestablishments of the world. His work affords a most striking exampleof the principle that the astronomer is more important than hisinstruments. Not only were the means at the command of the ArgentineObservatory slender in the extreme when compared with those of thefavored institutions of the North, but, from the very nature of thecase, the Argentine Republic could not supply trained astronomers. Thedifficulties thus growing out of the administration cannot beoverestimated. And yet the sixteen great volumes in which the work ofthe institution has been published will rank in the future among theclassics of astronomy. 

Another wonderful focus of activity, in which one hardly knows whetherhe ought most to admire the exhaustless energy or the admirableingenuity which he finds displayed, is the Harvard Observatory. Itswork has been aided by gifts which have no parallel in the liberalitythat prompted them. Yet without energy and skill such gifts would havebeen useless. The activity of the establishment includes bothhemispheres. Time would fail to tell how it has not only mapped outimportant regions of the heavens from the north to the south pole, butanalyzed the rays of light which come from hundreds of thousands ofstars by recording their spectra in permanence on photographic plates. 

The work of the establishment is so organized that a new star cannotappear in any part of the heavens nor a known star undergo anynoteworthy change without immediate detection by the photographic eyeof one or more little telescopes, all-seeing and never-sleepingpolicemen that scan the heavens unceasingly while the astronomer maysleep, and report in the morning every case of irregularity in theproceedings of the heavenly bodies. 

Yet another example, showing what great results may be obtained withlimited means, is afforded by the Lick Observatory, on Mount Hamilton, California. During the ten years of its activity its astronomers havemade it known the world over by works and discoveries too varied andnumerous to be even mentioned at the present time. 

The astronomical work of which I have thus far spoken has been almostentirely that done at observatories. I fear that I may in this way havestrengthened an erroneous impression that the seat of importantastronomical work is necessarily connected with an observatory. It mustbe admitted that an institution which has a local habitation and amagnificent building commands public attention so strongly thatvaluable work done elsewhere may be overlooked. A very important partof astronomical work is done away from telescopes and meridian circlesand requires nothing but a good library for its prosecution. One who isdevoted to this side of the subject may often feel that the public doesnot appreciate his work at its true relative value from the very factthat he has no great buildings or fine instruments to show. I maytherefore be allowed to claim as an important factor in the Americanastronomy of the last half-century an institution of which few haveheard and which has been overlooked because there was nothing about itto excite attention. 

In 1849 the American Nautical Almanac office was established by aCongressional appropriation. The title of this publication is somewhatmisleading in suggesting a simple enlargement of the family almanacwhich the sailor is to hang up in his cabin for daily use. The fact isthat what started more than a century ago as a nautical almanac hassince grown into an astronomical ephemeris for the publication ofeverything pertaining to times, seasons, eclipses, and the motions ofthe heavenly bodies. It is the work in which astronomical observationsmade in all the great observatories of the world are ultimatelyutilized for scientific and public purposes. Each of the leadingnations of western Europe issues such a publication. When thepreparation and publication of the American ephemeris was decided uponthe office was first established in Cambridge, the seat of HarvardUniversity, because there could most readily be secured the technicalknowledge of mathematics and theoretical astronomy necessary for thework. 

A field of activity was thus opened, of which a number of able youngmen who have since earned distinction in various walks of life availedthemselves. The head of the office, Commander Davis, adopted a policywell fitted to promote their development. He translated the classicwork of Gauss, Theoria Motus Corporum Celestium, and made the office asort of informal school, not, indeed, of the modern type, but rathermore like the classic grove of Hellas, where philosophers conductedtheir discussions and profited by mutual attrition. When, after a fewyears of experience, methods were well established and a routineadopted, the office was removed to Washington, where it has sinceremained. The work of preparing the ephemeris has, with experience, been reduced to a matter of routine which may be continuedindefinitely, with occasional changes in methods and data, andimprovements to meet the increasing wants of investigators. 

The mere preparation of the ephemeris includes but a small part of thework of mathematical calculation and investigation required inastronomy. One of the great wants of the science to-day is thereduction of the observations made during the first half of the presentcentury, and even during the last half of the preceding one. The laborwhich could profitably be devoted to this work would be more than thatrequired in any one astronomical observatory. It is unfortunate forthis work that a great building is not required for its prosecutionbecause its needfulness is thus very generally overlooked by thatportion of the public interested in the progress of science. Anorganization especially devoted to it is one of the scientific needs ofour time. 

In such an epoch-making age as the present it is dangerous to cite anyone step as making a new epoch. Yet it may be that when the historianof the future reviews the science of our day he will find the mostremarkable feature of the astronomy of the last twenty years of ourcentury to be the discovery that this steadfast earth of which thepoets have told us is not, after all, quite steadfast; that the northand south poles move about a very little, describing curves socomplicated that they have not yet been fully marked out. The periodicvariations of latitude thus brought about were first suspected about1880, and announced with some modest assurance by Kustner, of Berlin, afew years later. The progress of the views of astronomical opinion fromincredulity to confidence was extremely slow until, about 1890, Chandler, of the United States, by an exhaustive discussion ofinnumerable results of observations, showed that the latitude of everypoint on the earth was subject to a double oscillation, one having aperiod of a year, the other of four hundred and twenty-seven days. 

Notwithstanding the remarkable parallel between the growth of Americanastronomy and that of your city, one cannot but fear that if a foreignobserver had been asked only half a dozen years ago at what point inthe United States a great school of theoretical and practicalastronomy, aided by an establishment for the exploration of theheavens, was likely to be established by the munificence of privatecitizens, he would have been wiser than most foreigners had he guessedChicago. Had this place been suggested to him, I fear he would havereplied that were it possible to utilize celestial knowledge inacquiring earthly wealth, here would be the most promising seat forsuch a school. But he would need to have been a little wiser than hisgeneration to reflect that wealth is at the base of all progress inknowledge and the liberal arts; that it is only when men are relievedfrom the necessity of devoting all their energies to the immediatewants of life that they can lead the intellectual life, and that weshould therefore look to the most enterprising commercial centre as thelikeliest seat for a great scientific institution. 

Now we have the school, and we have the observatory, which we hope willin the near future do work that will cast lustre on the name of itsfounder as well as on the astronomers who may be associated with it. You will, I am sure, pardon me if I make some suggestions on thesubject of the future needs of the establishment. We want this newlyfounded institution to be a great success, to do work which shall showthat the intellectual productiveness of your community will not beallowed to lag behind its material growth The public is very apt tofeel that when some munificent patron of science has mounted a greattelescope under a suitable dome, and supplied all the apparatus whichthe astronomer wants to use, success is assured. But such is not thecase. The most important requisite, one more difficult to command thantelescopes or observatories, may still be wanting. A great telescope isof no use without a man at the end of it, and what the telescope may dodepends more upon this appendage than upon the instrument itself. Theplace which telescopes and observatories have taken in astronomicalhistory are by no means proportional to their dimensions. Many a greatinstrument has been a mere toy in the hands of its owner. Many a smallone has become famous. 

Twenty years ago there was here in your own city a modest littleinstrument which, judged by its size, could not hold up its head withthe great ones even of that day. It was the private property of a youngman holding no scientific position and scarcely known to the public. And yet that little telescope is to-day among the famous ones of theworld, having made memorable advances in the astronomy of double stars, and shown its owner to be a worthy successor of the Herschels andStruves in that line of work. 

A hundred observers might have used the appliances of the LickObservatory for a whole generation without finding the fifth satelliteof Jupiter; without successfully photographing the cloud forms of theMilky Way; without discovering the extraordinary patches of nebulouslight, nearly or quite invisible to the human eye, which fill someregions of the heavens. 

When I was in Zurich last year I paid a visit to the little, but notunknown, observatory of its famous polytechnic school. The professor ofastronomy was especially interested in the observations of the sun withthe aid of the spectroscope, and among the ingenious devices which hedescribed, not the least interesting was the method of photographingthe sun by special rays of the spectrum, which had been worked out atthe Kenwood Observatory in Chicago. The Kenwood Observatory is not, Ibelieve, in the eye of the public, one of the noteworthy institutionsof your city which every visitor is taken to see, and yet thisinvention has given it an important place in the science of our day. 

Should you ask me what are the most hopeful features in the greatestablishment which you are now dedicating, I would say that they arenot alone to be found in the size of your unequalled telescope, nor inthe cost of the outfit, but in the fact that your authorities haveshown their appreciation of the requirements of success by adding tothe material outfit of the establishment the three men whose works Ihave described. 

Gentlemen of the trustees, allow me to commend to your fostering carethe men at the end of the telescope. The constitution of the astronomershows curious and interesting features. If he is destined to advancethe science by works of real genius, he must, like the poet, be born, not made. The born astronomer, when placed in command of a telescope, goes about using it as naturally and effectively as the babe availsitself of its mother's breast. He sees intuitively what less gifted menhave to learn by long study and tedious experiment. He is moved tocelestial knowledge by a passion which dominates his nature. He can nomore avoid doing astronomical work, whether in the line of observationsor research, than a poet can chain his Pegasus to earth. I do not meanby this that education and training will be of no use to him. They willcertainly accelerate his early progress. If he is to become great onthe mathematical side, not only must his genius have a bend in thatdirection, but he must have the means of pursuing his studies. And yetI have seen so many failures of men who had the best instruction, andso many successes of men who scarcely learned anything of theirteachers, that I sometimes ask whether the great American celestialmechanician of the twentieth century will be a graduate of a universityor of the backwoods. 

Is the man thus moved to the exploration of nature by an unconquerablepassion more to be envied or pitied? In no other pursuit does successcome with such certainty to him who deserves it. No life is soenjoyable as that whose energies are devoted to following out theinborn impulses of one's nature. The investigator of truth is littlesubject to the disappointments which await the ambitious man in otherfields of activity. It is pleasant to be one of a brotherhood extendingover the world, in which no rivalry exists except that which comes outof trying to do better work than any one else, while mutual admirationstifles jealousy. And yet, with all these advantages, the experience ofthe astronomer may have its dark side. As he sees his field wideningfaster than he can advance he is impressed with the littleness of allthat can be done in one short life. He feels the same want ofsuccessors to pursue his work that the founder of a dynasty may feelfor heirs to occupy his throne. He has no desire to figure in historyas a Napoleon of science whose conquests must terminate with his life. Even during his active career his work may be such a kind as to requirethe co-operation of others and the active support of the public. If heis disappointed in commanding these requirements, if he finds neitherco-operation nor support, if some great scheme to which he may havedevoted much of his life thus proves to be only a castle in the air, hemay feel that nature has dealt hardly with him in not endowing him withpassions like to those of other men. 

In treating a theme of perennial interest one naturally tries to fancywhat the future may have in store If the traveller, contemplating theruins of some ancient city which in the long ago teemed with the lifeand activities of generations of men, sees every stone instinct withemotion and the dust alive with memories of the past, may he not besimilarly impressed when he feels that he is looking around upon a seatof future empire--a region where generations yet unborn may take aleading part in moulding the history of the world? What may we notexpect of that energy which in sixty years has transformed a stragglingvillage into one of the world's great centres of commerce? May it notexercise a powerful influence on the destiny not only of the countrybut of the world? If so, shall the power thus to be exercised prove anagent of beneficence, diffusing light and life among nations, or shallit be the opposite?

The time must come ere long when wealth shall outgrow the field inwhich it can be profitably employed. In what direction shall itspossessors then look? Shall they train a posterity which will so useits power as to make the world better that it has lived in it? Will thefuture heir to great wealth prefer the intellectual life to the life ofpleasure?

We can have no more hopeful answer to these questions than theestablishment of this great university in the very focus of thecommercial activity of the West. Its connection with the institution wehave been dedicating suggests some thoughts on science as a factor inthat scheme of education best adapted to make the power of a wealthycommunity a benefit to the race at large. When we see what a factorscience has been in our present civilization, how it has transformedthe world and increased the means of human enjoyment by enabling men toapply the powers of nature to their own uses, it is not wonderful thatit should claim the place in education hitherto held by classicalstudies. In the contest which has thus arisen I take no part but thatof a peace-maker, holding that it is as important to us to keep intouch with the traditions of our race, and to cherish the thoughtswhich have come down to us through the centuries, as it is to enjoy andutilize what the present has to offer us. Speaking from this point ofview, I would point out the error of making the utilitarianapplications of knowledge the main object in its pursuit. It is anhistoric fact that abstract science--science pursued without anyutilitarian end--has been at the base of our progress in theutilization of knowledge. If in the last century such men as Galvaniand Volta had been moved by any other motive than love of penetratingthe secrets of nature they would never have pursued the seeminglyuseless experiments they did, and the foundation of electrical sciencewould not have been laid. Our present applications of electricity didnot become possible until Ohm's mathematical laws of the electriccurrent, which when first made known seemed little more thanmathematical curiosities, had become the common property of inventors. Professional pride on the part of our own Henry led him, after makingthe discoveries which rendered the telegraph possible, to go no furtherin their application, and to live and die without receiving a dollar ofthe millions which the country has won through his agency. 

In the spirit of scientific progress thus shown we have patriotism inits highest form--a sentiment which does not seek to benefit thecountry at the expense of the world, but to benefit the world by meansof one's country. Science has its competition, as keen as that which isthe life of commerce. But its rivalries are over the question who shallcontribute the most and the best to the sum total of knowledge; whoshall give the most, not who shall take the most. Its animating spiritis love of truth. Its pride is to do the greatest good to the greatestnumber. It embraces not only the whole human race but all nature in itsscope. The public spirit of which this city is the focus has made thedesert blossom as the rose, and benefited humanity by the diffusion ofthe material products of the earth. Should you ask me how it is in thefuture to use its influence for the benefit of humanity at large, Iwould say, look at the work now going on in these precincts, and studyits spirit. Here are the agencies which will make "the voice of law theharmony of the world. " Here is the love of country blended with love ofthe race. Here the love of knowledge is as unconfined as yourcommercial enterprise. Let not your youth come hither merely to learnthe forms of vertebrates and the properties of oxides, but rather toimbibe that catholic spirit which, animating their growing energies, shall make the power they are to wield an agent of beneficence to allmankind. 

XIX

THE UNIVERSE AS AN ORGANISM

[Footnote: Address before the Astronomical and Astrophysical Society ofAmerica, December 29, 1902]

If I were called upon to convey, within the compass of a singlesentence, an idea of the trend of recent astronomical and physicalscience, I should say that it was in the direction of showing theuniverse to be a connected whole. The farther we advance in knowledge, the clearer it becomes that the bodies which are scattered through thecelestial spaces are not completely independent existences, but have, with all their infinite diversity, many attributes in common. 

In this we are going in the direction of certain ideas of the ancientswhich modern discovery long seemed to have contradicted. In the infancyof the race, the idea that the heavens were simply an enlarged anddiversified earth, peopled by beings who could roam at pleasure fromone extreme to the other, was a quite natural one. The crystallinesphere or spheres which contained all formed a combination of machineryrevolving on a single plan. But all bonds of unity between the starsbegan to be weakened when Copernicus showed that there were no spheres, that the planets were isolated bodies, and that the stars were vastlymore distant than the planets. As discovery went on and our conceptionsof the universe were enlarged, it was found that the system of thefixed stars was made up of bodies so vastly distant and so completelyisolated that it was difficult to conceive of them as standing in anydefinable relation to one another. It is true that they all emittedlight, else we could not see them, and the theory of gravitation, ifextended to such distances, a fact not then proved, showed that theyacted on one another by their mutual gravitation. But this was all. Leaving out light and gravitation, the universe was still, in the timeof Herschel, composed of bodies which, for the most part, could notstand in any known relation one to the other. 

When, forty years ago, the spectroscope was applied to analyze thelight coming from the stars, a field was opened not less fruitful thanthat which the telescope made known to Galileo. The first conclusionreached was that the sun was composed almost entirely of the sameelements that existed upon the earth. Yet, as the bodies of our solarsystem were evidently closely related, this was not remarkable. Butvery soon the same conclusion was, to a limited extent, extended to thefixed stars in general. Such elements as iron, hydrogen, and calciumwere found not to belong merely to our earth, but to form importantconstituents of the whole universe. We can conceive of no reason why, out of the infinite number of combinations which might make up aspectrum, there should not be a separate kind of matter for eachcombination. So far as we know, the elements might merge into oneanother by insensible gradations. It is, therefore, a remarkable andsuggestive fact when we find that the elements which make up bodies sowidely separate that we can hardly imagine them having anything incommon, should be so much the same. 

In recent times what we may regard as a new branch of astronomicalscience is being developed, showing a tendency towards unity ofstructure throughout the whole domain of the stars. This is what we nowcall the science of stellar statistics. The very conception of such ascience might almost appall us by its immensity. The widest statisticalfield in other branches of research is that occupied by sociology. Every country has its census, in which the individual inhabitants areclassified on the largest scale and the combination of these statisticsfor different countries may be said to include all the interest of thehuman race within its scope. Yet this field is necessarily confined tothe surface of our planet. In the field of stellar statistics millionsof stars are classified as if each taken individually were of no moreweight in the scale than a single inhabitant of China in the scale ofthe sociologist. And yet the most insignificant of these suns may, foraught we know, have planets revolving around it, the interests of whoseinhabitants cover as wide a range as ours do upon our own globe. 

The statistics of the stars may be said to have commenced withHerschel's gauges of the heavens, which were continued from time totime by various observers, never, however, on the largest scale. Thesubject was first opened out into an illimitable field of researchthrough a paper presented by Kapteyn to the Amsterdam Academy ofSciences in 1893. The capital results of this paper were that differentregions of space contain different kinds of stars and, more especially, that the stars of the Milky Way belong, in part at least, to adifferent class from those existing elsewhere. Stars not belonging tothe Milky Way are, in large part, of a distinctly different class. 

The outcome of Kapteyn's conclusions is that we are able to describethe universe as a single object, with some characters of an organizedwhole. A large part of the stars which compose it may be considered asdivisible into two groups. One of these comprises the stars composingthe great girdle of the Milky Way. These are distinguished from theothers by being bluer in color, generally greater in absolutebrilliancy, and affected, there is some reason to believe, with ratherslower proper motions The other classes are stars with a greater orless shade of yellow in their color, scattered through a sphericalspace of unknown dimensions, but concentric with the Milky Way. Thus asphere with a girdle passing around it forms the nearest approach to aconception of the universe which we can reach to-day. The number ofstars in the girdle is much greater than that in the sphere. 

The feature of the universe which should therefore command ourattention is the arrangement of a large part of the stars which composeit in a ring, seemingly alike in all its parts, so far as generalfeatures are concerned. So far as research has yet gone, we are notable to say decisively that one region of this ring differs essentiallyfrom another. It may, therefore, be regarded as forming a structurebuilt on a uniform plan throughout. 

All scientific conclusions drawn from statistical data require acritical investigation of the basis on which they rest. If we aregoing, from merely counting the stars, observing their magnitudes anddetermining their proper motions, to draw conclusions as to thestructure of the universe in space, the question may arise how we canform any estimate whatever of the possible distance of the stars, aconclusion as to which must be the very first step we take. We canhardly say that the parallaxes of more than one hundred stars have beenmeasured with any approach to certainty. The individuals of this onehundred are situated at very different distances from us. We hope, bylong and repeated observations, to make a fairly approximatedetermination of the parallaxes of all the stars whose distance is lessthan twenty times that of a Centauri. But how can we know anythingabout the distance of stars outside this sphere? What can we sayagainst the view of Kepler that the space around our sun is very muchthinner in stars than it is at a greater distance; in fact, that, thegreat mass of the stars may be situated between the surfaces of twoconcentrated spheres not very different in radius. May not thisuniverse of stars be somewhat in the nature of a hollow sphere?

This objection requires very careful consideration on the part of allwho draw conclusions as to the distribution of stars in space and as tothe extent of the visible universe. The steps to a conclusion on thesubject are briefly these: First, we have a general conclusion, thebasis of which I have already set forth, that, to use a looseexpression, there are likenesses throughout the whole diameter of theuniverse. There is, therefore, no reason to suppose that the region inwhich our system is situated differs in any essential degree from anyother region near the central portion. Again, spectroscopicexaminations seem to show that all the stars are in motion, and that wecannot say that those in one part of the universe move more rapidlythan those in another. This result is of the greatest value for ourpurpose, because, when we consider only the apparent motions, asordinarily observed, these are necessarily dependent upon the distanceof the star. We cannot, therefore, infer the actual speed of a starfrom ordinary observations until we know its distance. But the resultsof spectroscopic measurements of radial velocity are independent of thedistance of the star. 

But let us not claim too much. We cannot yet say with certainty thatthe stars which form the agglomerations of the Milky Way have, beyonddoubt, the same average motion as the stars in other regions of theuniverse. The difficulty is that these stars appear to us so faintindividually, that the investigation of their spectra is still beyondthe powers of our instruments. But the extraordinary feat performed atthe Lick Observatory of measuring the radial motion of 1830Groombridge, a star quite invisible to the naked eye, and showing thatit is approaching our system with a speed of between fifty and sixtymiles a second, may lead us to hope for a speedy solution of thisquestion. But we need not await this result in order to reach veryprobable conclusions. The general outcome of researches on propermotions tends to strengthen the conclusions that the Keplerian sphere, if I may use this expression, has no very well marked existence. Thelaws of stellar velocity and the statistics of proper motions, whilegiving some color to the view that the space in which we are situatedis thinner in stars than elsewhere, yet show that, as a general rule, there are no great agglomerations of stars elsewhere than in the regionof the Milky Way. 

With unity there is always diversity; in fact, the unity of theuniverse on which I have been insisting consists in part of diversity. It is very curious that, among the many thousands of stars which havebeen spectroscopically examined, no two are known to have absolutelythe same physical constitution. It is true that there are a great manyresemblances. Alpha Centauri, our nearest neighbor, if we can use sucha word as "near" in speaking of its distance, has a spectrum very likethat of our sun, and so has Capella. But even in these cases carefulexamination shows differences. These differences arise from variety inthe combinations and temperature of the substances of which the star ismade up. Quite likely also, elements not known on the earth may existon the stars, but this is a point on which we cannot yet speak withcertainty. 

Perhaps the attribute in which the stars show the greatest variety isthat of absolute luminosity. One hundred years ago it was naturallysupposed that the brighter stars were the nearest to us, and this isdoubtless true when we take the general average. But it was soon foundthat we cannot conclude that because a star is bright, therefore it isnear. The most striking example of this is afforded by the absence ofmeasurable parallaxes in the two bright stars, Canopus and Rigel, showing that these stars, though of the first magnitude, areimmeasurably distant. A remarkable fact is that these conclusionscoincide with that which we draw from the minuteness of the propermotions. Rigel has no motion that has certainly been shown by more thana century of observation, and it is not certain that Canopus haseither. From this alone we may conclude, with a high degree ofprobability, that the distance of each is immeasurably great. We maysay with certainty that the brightness of each is thousands of timesthat of the sun, and with a high degree of probability that it ishundreds of thousands of times. On the other hand, there are starscomparatively near us of which the light is not the hundredth part ofthe sun. 

[Illustration with caption: Star Spectra]

The universe may be a unit in two ways. One is that unity of structureto which our attention has just been directed. This might subsistforever without one body influencing another. The other form of unityleads us to view the universe as an organism. It is such by mutualaction going on between its bodies. A few years ago we could hardlysuppose or imagine that any other agents than gravitation and lightcould possibly pass through spaces so immense as those which separatethe stars. 

The most remarkable and hopeful characteristic of the unity of theuniverse is the evidence which is being gathered that there are otheragencies whose exact nature is yet unknown to us, but which do passfrom one heavenly body to another. The best established example of thisyet obtained is afforded in the case of the sun and the earth. 

The fact that the frequency of magnetic storms goes through a period ofabout eleven years, and is proportional to the frequency of sun-spots, has been well established. The recent work of Professor Bigelow showsthe coincidence to be of remarkable exactness, the curves of the twophenomena being practically coincident so far as their general featuresare concerned. The conclusion is that spots on the sun and magneticstorms are due to the same cause. This cause cannot be any change inthe ordinary radiation of the sun, because the best records oftemperature show that, to whatever variations the sun's radiation maybe subjected, they do not change in the period of the sun-spots. Toappreciate the relation, we must recall that the researches of Halewith the spectro-heliograph show that spots are not the primaryphenomenon of solar activity, but are simply the outcome of processesgoing on constantly in the sun which result in spots only in specialregions and on special occasions. It does not, therefore, necessarilyfollow that a spot does cause a magnetic storm. What we should concludeis that the solar activity which produces a spot also produces themagnetic storm. 

When we inquire into the possible nature of these relations betweensolar activity and terrestrial magnetism, we find ourselves socompletely in the dark that the question of what is really proved bythe coincidence may arise. Perhaps the most obvious explanation offluctuations in the earth's magnetic field to be inquired into would bebased on the hypothesis that the space through which the earth ismoving is in itself a varying magnetic field of vast extent. Thisexplanation is tested by inquiring whether the fluctuations in questioncan be explained by supposing a disturbing force which actssubstantially in the same direction all over the globe. But a veryobvious test shows that this explanation is untenable. Were it thecorrect one, the intensity of the force in some regions of the earthwould be diminished and in regions where the needle pointed in theopposite direction would be increased in exactly the same degree. Butthere is no relation traceable either in any of the regularfluctuations of the magnetic force, or in those irregular ones whichoccur during a magnetic storm. If the horizontal force is increased inone part of the earth, it is very apt to show a simultaneous increasethe world over, regardless of the direction in which the needle maypoint in various localities. It is hardly necessary to add that none ofthe fluctuations in terrestrial magnetism can be explained on thehypothesis that either the moon or the sun acts as a magnet. In such acase the action would be substantially in the same direction at thesame moment the world over. 

Such being the case, the question may arise whether the actionproducing a magnetic storm comes from the sun at all, and whether thefluctuations in the sun's activity, and in the earth's magnetic fieldmay not be due to some cause external to both. All we can say in replyto this is that every effort to find such a cause has failed and thatit is hardly possible to imagine any cause producing such an effect. Itis true that the solar spots were, not many years ago, supposed to bedue in some way to the action of the planets. But, for reasons which itwould be tedious to go into at present, we may fairly regard thishypothesis as being completely disproved. There can, I conclude, belittle doubt that the eleven-year cycle of change in the solar spots isdue to a cycle going on in the sun itself. Such being the case, thecorresponding change in the earth's magnetism must be due to the samecause. 

We may, therefore, regard it as a fact sufficiently established tomerit further investigation that there does emanate from the sun, in anirregular way, some agency adequate to produce a measurable effect onthe magnetic needle. We must regard it as a singular fact that noobservations yet made give us the slightest indication as to what thisemanation is. The possibility of defining it is suggested by thediscovery within the past few years, that under certain conditions, heated matter sends forth entities known as Rontgen rays, Becquerelcorpuscles and electrons. I cannot speak authoritatively on thissubject, but, so far as I am aware, no direct evidence has yet beengathered showing that any of these entities reach us from the sun. Wemust regard the search for the unknown agency so fully proved as amongthe most important tasks of the astronomical physicist of the presenttime. From what we know of the history of scientific discovery, itseems highly probable that, in the course of his search, he will, before he finds the object he is aiming at, discover many other thingsof equal or greater importance of which he had, at the outset, noconception. 

The main point I desire to bring out in this review is the tendencywhich it shows towards unification in physical research. Heretoforedifferentiation--the subdivision of workers into a continuallyincreasing number of groups of specialists--has been the rule. Now wesee a coming together of what, at first sight, seem the most widelyseparated spheres of activity. What two branches could be more widelyseparated than that of stellar statistics, embracing the whole universewithin its scope, and the study of these newly discovered emanations, the product of our laboratories, which seem to show the existence ofcorpuscles smaller than the atoms of matter? And yet, the phenomenawhich we have reviewed, especially the relation of terrestrialmagnetism to the solar activity, and the formation of nebulous massesaround the new stars, can be accounted for only by emanations or formsof force, having probably some similarity with the corpuscles, electrons, and rays which we are now producing in our laboratories. Thenineteenth century, in passing away, points with pride to what it hasdone. It has become a word to symbolize what is most important in humanprogress Yet, perhaps its greatest glory may prove to be that the lastthing it did was to lay a foundation for the physical science of thetwentieth century. What shall be discovered in the new fields is, atpresent, as far without our ken as were the modern developments ofelectricity without the ken of the investigators of one hundred yearsago. We cannot guarantee any special discovery. What lies before us isan illimitable field, the existence of which was scarcely suspected tenyears ago, the exploration of which may well absorb the activities ofour physical laboratories, and of the great mass of our astronomicalobservers and investigators for as many generations as were required tobring electrical science to its present state. We of the oldergeneration cannot hope to see more than the beginning of thisdevelopment, and can only tender our best wishes and most heartycongratulations to the younger school whose function it will be toexplore the limitless field now before it. 

XX

THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS [Footnote: Anaddress before the Washington Philosophical Society]

Among those subjects which are not always correctly apprehended, evenby educated men, we may place that of the true significance ofscientific method and the relations of such method to practicalaffairs. This is especially apt to be the case in a country like ourown, where the points of contact between the scientific world on theone hand, and the industrial and political world on the other, arefewer than in other civilized countries. The form which thismisapprehension usually takes is that of a failure to appreciate thecharacter of scientific method, and especially its analogy to themethods of practical life. In the judgment of the ordinary intelligentman there is a wide distinction between theoretical and practicalscience. The latter he considers as that science directly applicable tothe building of railroads, the construction of engines, the inventionof new machinery, the construction of maps, and other useful objects. The former he considers analogous to those philosophic speculations inwhich men have indulged in all ages without leading to any result whichhe considers practical. That our knowledge of nature is increased byits prosecution is a fact of which he is quite conscious, but heconsiders it as terminating with a mere increase of knowledge, and notas having in its method anything which a person devoted to materialinterests can be expected to appreciate. 

This view is strengthened by the spirit with which he sees scientificinvestigation prosecuted. It is well understood on all sides that whensuch investigations are pursued in a spirit really recognized asscientific, no merely utilitarian object is had in view. Indeed, it iseasy to see how the very fact of pursuing such an object would detractfrom that thoroughness of examination which is the first condition of areal advance. True science demands in its every research a completenessfar beyond what is apparently necessary for its practical applications. The precision with which the astronomer seeks to measure the heavensand the chemist to determine the relations of the ultimate molecules ofmatter has no limit, except that set by the imperfections of theinstruments of research. There is no such division recognized as thatof useful and useless knowledge. The ultimate aim is nothing less thanthat of bringing all the phenomena of nature under laws as exact asthose which govern the planetary motions. 

Now the pursuit of any high object in this spirit commands from men ofwide views that respect which is felt towards all exertion having inview more elevated objects than the pursuit of gain. Accordingly, it isvery natural to classify scientists and philosophers with the men whoin all ages have sought after learning instead of utility. But there isanother aspect of the question which will show the relations ofscientific advance to the practical affairs of life in a differentlight. I make bold to say that the greatest want of the day, from apurely practical point of view, is the more general introduction of thescientific method and the scientific spirit into the discussion ofthose political and social problems which we encounter on our road to ahigher plane of public well being. Far from using methods too refinedfor practical purposes, what most distinguishes scientific from otherthought is the introduction of the methods of practical life into thediscussion of abstract general problems. A single instance willillustrate the lesson I wish to enforce. 

The question of the tariff is, from a practical point of view, one ofthe most important with which our legislators will have to deal duringthe next few years. The widest diversity of opinion exists as to thebest policy to be pursued in collecting a revenue from imports. Opposing interests contend against one another without any common basisof fact or principle on which a conclusion can be reached. The opinionsof intelligent men differ almost as widely as those of the men who areimmediately interested. But all will admit that public action in thisdirection should be dictated by one guiding principle--that thegreatest good of the community is to be sought after. That policy isthe best which will most promote this good. Nor is there any seriousdifference of opinion as to the nature of the good to be had in view;it is in a word the increase of the national wealth and prosperity. Thequestion on which opinions fundamentally differ is that of the effectsof a higher or lower rate of duty upon the interests of the public. Ifit were possible to foresee, with an approach to certainty, what effecta given tariff would have upon the producers and consumers of anarticle taxed, and, indirectly, upon each member of the community inany way interested in the article, we should then have an exact datumwhich we do not now possess for reaching a conclusion. If somesuperhuman authority, speaking with the voice of infallibility, couldgive us this information, it is evident that a great national wantwould be supplied. No question in practical life is more important thanthis: How can this desirable knowledge of the economic effects of atariff be obtained?

The answer to this question is clear and simple. The subject must bestudied in the same spirit, and, to a certain extent, by the samemethods which have been so successful in advancing our knowledge ofnature. Every one knows that, within the last two centuries, a methodof studying the course of nature has been introduced which has been sosuccessful in enabling us to trace the sequence of cause and effect asalmost to revolutionize society. The very fact that scientific methodhas been so successful here leads to the belief that it might beequally successful in other departments of inquiry. 

The same remarks will apply to the questions connected with banking andcurrency; the standard of value; and, indeed, all subjects which have afinancial bearing. On every such question we see wide differences ofopinion without any common basis to rest upon. 

It may be said, in reply, that in these cases there are really nogrounds for forming an opinion, and that the contests which arise overthem are merely those between conflicting interests. But this claim isnot at all consonant with the form which we see the discussion assume. Nearly every one has a decided opinion on these several subjects;whereas, if there were no data for forming an opinion, it would beunreasonable to maintain any whatever. Indeed, it is evident that theremust be truth somewhere, and the only question that can be open is thatof the mode of discovering it. No man imbued with a scientific spiritcan claim that such truth is beyond the power of the human intellect. He may doubt his own ability to grasp it, but cannot doubt that bypursuing the proper method and adopting the best means the problem canbe solved. It is, in fact, difficult to show why some exact resultscould not be as certainly reached in economic questions as in those ofphysical science. It is true that if we pursue the inquiry far enoughwe shall find more complex conditions to encounter, because the futurecourse of demand and supply enters as an uncertain element. But aremarkable fact to be considered is that the difference of opinion towhich we allude does not depend upon different estimates of the future, but upon different views of the most elementary and general principlesof the subject. It is as if men were not agreed whether air wereelastic or whether the earth turns on its axis. Why is it that while inall subjects of physical science we find a general agreement through awide range of subjects, and doubt commences only where certainty is notattained, yet when we turn to economic subjects we do not find thebeginning of an agreement?

No two answers can be given. It is because the two classes of subjectsare investigated by different instruments and in a different spirit. The physicist has an exact nomenclature; uses methods of research welladapted to the objects he has in view; pursues his investigationswithout being attacked by those who wish for different results; and, above all, pursues them only for the purpose of discovering the truth. In economic questions the case is entirely different. Only in rarecases are they studied without at least the suspicion that the studenthas a preconceived theory to support. If results are attained whichoppose any powerful interest, this interest can hire a competinginvestigator to bring out a different result. So far as the public cansee, one man's result is as good as another's, and thus the object isas far off as ever. We may be sure that until there is an intelligentand rational public, able to distinguish between the speculations ofthe charlatan and the researches of the investigator, the present stateof things will continue. What we want is so wide a diffusion ofscientific ideas that there shall be a class of men engaged in studyingeconomic problems for their own sake, and an intelligent public able tojudge what they are doing. There must be an improvement in the objectsat which they aim in education, and it is now worth while to inquirewhat that improvement is. 

It is not mere instruction in any branch of technical science that iswanted. No knowledge of chemistry, physics, or biology, howeverextensive, can give the learner much aid in forming a correct opinionof such a question as that of the currency. If we should claim thatpolitical economy ought to be more extensively studied, we would be metby the question, which of several conflicting systems shall we teach?What is wanted is not to teach this system or that, but to give such atraining that the student shall be able to decide for himself whichsystem is right. 

It seems to me that the true educational want is ignored both by thosewho advocate a classical and those who advocate a scientific education. What is really wanted is to train the intellectual powers, and thequestion ought to be, what is the best method of doing this? Perhaps itmight be found that both of the conflicting methods could be improvedupon. The really distinctive features, which we should desire to seeintroduced, are two in number: the one the scientific spirit; the otherthe scientific discipline. Although many details may be classifiedunder each of these heads, yet there is one of pre-eminent importanceon which we should insist. 

The one feature of the scientific spirit which outweighs all others inimportance is the love of knowledge for its own sake. If by our systemof education we can inculcate this sentiment we shall do what is, froma public point of view, worth more than any amount of technicalknowledge, because we shall lay the foundation of all knowledge. Solong as men study only what they think is going to be useful theirknowledge will be partial and insufficient. I think it is to theconstant inculcation of this fact by experience, rather than to anyreasoning, that is due the continued appreciation of a liberaleducation. Every business-man knows that a business-college training isof very little account in enabling one to fight the battle of life, andthat college-bred men have a great advantage even in fields where mereeducation is a secondary matter. We are accustomed to seeing ridiculethrown upon the questions sometimes asked of candidates for the civilservice because the questions refer to subjects of which a knowledge isnot essential. The reply to all criticisms of this kind is that thereis no one quality which more certainly assures a man's usefulness tosociety than the propensity to acquire useless knowledge. Most of ourcitizens take a wide interest in public affairs, else our form ofgovernment would be a failure. But it is desirable that their study ofpublic measures should be more critical and take a wider range. It isespecially desirable that the conclusions to which they are led shouldbe unaffected by partisan sympathies. The more strongly the love ofmere truth is inculcated in their nature the better this end will beattained. 

The scientific discipline to which I ask mainly to call your attentionconsists in training the scholar to the scientific use of language. Although whole volumes may be written on the logic of science there isone general feature of its method which is of fundamental significance. It is that every term which it uses and every proposition which itenunciates has a precise meaning which can be made evident by properdefinitions. This general principle of scientific language is much moreeasily inculcated by example than subject to exact description; but Ishall ask leave to add one to several attempts I have made to defineit. If I should say that when a statement is made in the language ofscience the speaker knows what he means, and the hearer either knows itor can be made to know it by proper definitions, and that thiscommunity of understanding is frequently not reached in otherdepartments of thought, I might be understood as casting a slur onwhole departments of inquiry. Without intending any such slur, I maystill say that language and statements are worthy of the namescientific as they approach this standard; and, moreover, that a greatdeal is said and written which does not fulfil the requirement. Thefact that words lose their meaning when removed from the connections inwhich that meaning has been acquired and put to higher uses, is onewhich, I think, is rarely recognized. There is nothing in the historyof philosophical inquiry more curious than the frequency ofinterminable disputes on subjects where no agreement can be reachedbecause the opposing parties do not use words in the same sense. Thatthe history of science is not free from this reproach is shown by thefact of the long dispute whether the force of a moving body wasproportional to the simple velocity or to its square. Neither of theparties to the dispute thought it worth while to define what they meantby the word "force, " and it was at length found that if a definitionwas agreed upon the seeming difference of opinion would vanish. Perhapsthe most striking feature of the case, and one peculiar to a scientificdispute, was that the opposing parties did not differ in their solutionof a single mechanical problem. I say this is curious, because the veryfact of their agreeing upon every concrete question which could havebeen presented ought to have made it clear that some fallacy waslacking in the discussion as to the measure of force. The good effectof a scientific spirit is shown by the fact that this discussion isalmost unique in the history of science during the past two centuries, and that scientific men themselves were able to see the fallacyinvolved, and thus to bring the matter to a conclusion. 

If we now turn to the discussion of philosophers, we shall find atleast one yet more striking example of the same kind. The question ofthe freedom of the human will has, I believe, raged for centuries. Itcannot yet be said that any conclusion has been reached. Indeed, I haveheard it admitted by men of high intellectual attainments that thequestion was insoluble. Now a curious feature of this dispute is thatnone of the combatants, at least on the affirmative side, have made anyserious attempt to define what should be meant by the phrase freedom ofthe will, except by using such terms as require definition equally withthe word freedom itself. It can, I conceive, be made quite clear thatthe assertion, "The will is free, " is one without meaning, until weanalyze more fully the different meanings to be attached to the wordfree. Now this word has a perfectly well-defined signification inevery-day life. We say that anything is free when it is not subject toexternal constraint. We also know exactly what we mean when we say thata man is free to do a certain act. We mean that if he chooses to do itthere is no external constraint acting to prevent him. In all cases arelation of two things is implied in the word, some active agent orpower, and the presence or absence of another constraining agent. Now, when we inquire whether the will itself is free, irrespective ofexternal constraints, the word free no longer has a meaning, becauseone of the elements implied in it is ignored. 

To inquire whether the will itself is free is like inquiring whetherfire itself is consumed by the burning, or whether clothing is itselfclad. It is not, therefore, at all surprising that both parties havebeen able to dispute without end, but it is a most astonishingphenomenon of the human intellect that the dispute should go ongeneration after generation without the parties finding out whetherthere was really any difference of opinion between them on the subject. I venture to say that if there is any such difference, neither partyhas ever analyzed the meaning of the words used sufficiently far toshow it. The daily experience of every man, from his cradle to hisgrave, shows that human acts are as much the subject of external causalinfluences as are the phenomena of nature. To dispute this would belittle short of the ludicrous. All that the opponents of freedom, as aclass, have ever claimed is the assertion of a causal connectionbetween the acts of the will and influences independent of the will. True, propositions of this sort can be expressed in a variety of waysconnoting an endless number of more or less objectionable ideas, butthis is the substance of the matter. 

To suppose that the advocates on the other side meant to take issue onthis proposition would be to assume that they did not know what theywere saying. The conclusion forced upon us is that though men spendtheir whole lives in the study of the most elevated department of humanthought it does not guard them against the danger of using wordswithout meaning. It would be a mark of ignorance, rather than ofpenetration, to hastily denounce propositions on subjects we are notwell acquainted with because we do not understand their meaning. I donot mean to intimate that philosophy itself is subject to thisreproach. When we see a philosophical proposition couched in terms wedo not understand, the most modest and charitable view is to assumethat this arises from our lack of knowledge. Nothing is easier than forthe ignorant to ridicule the propositions of the learned. And yet, withevery reserve, I cannot but feel that the disputes to which I havealluded prove the necessity of bringing scientific precision oflanguage into the whole domain of thought. If the discussion had beenconfined to a few, and other philosophers had analyzed the subject, andshowed the fictitious character of the discussion, or had pointed outwhere opinions really might differ, there would be nothing derogatoryto philosophers. But the most suggestive circumstance is that althougha large proportion of the philosophic writers in recent times havedevoted more or less attention to the subject, few, or none, have madeeven this modest contribution. I speak with some little confidence onthis subject, because several years ago I wrote to one of the mostacute thinkers of the country, asking if he could find in philosophicliterature any terms or definitions expressive of the three differentsenses in which not only the word freedom, but nearly all wordsimplying freedom were used. His search was in vain. 

Nothing of this sort occurs in the practical affairs of life. All termsused in business, however general or abstract, have that well-definedmeaning which is the first requisite of the scientific language. Nowone important lesson which I wish to inculcate is that the language ofscience in this respect corresponds to that of business; in that eachand every term that is employed has a meaning as well defined as thesubject of discussion can admit of. It will be an instructive exerciseto inquire what this peculiarity of scientific and business languageis. It can be shown that a certain requirement should be fulfilled byall language intended for the discovery of truth, which is fulfilledonly by the two classes of language which I have described. It is oneof the most common errors of discourse to assume that any commonexpression which we may use always conveys an idea, no matter what thesubject of discourse. The true state of the case can, perhaps, best beseen by beginning at the foundation of things and examining under whatconditions language can really convey ideas. 

Suppose thrown among us a person of well-developed intellect, butunacquainted with a single language or word that we use. It isabsolutely useless to talk to him, because nothing that we say conveysany meaning to his mind. We can supply him no dictionary, because byhypothesis he knows no language to which we have access. How shall weproceed to communicate our ideas to him? Clearly there is but onepossible way--namely, through his senses. Outside of this means ofbringing him in contact with us we can have no communication with him. We, therefore, begin by showing him sensible objects, and letting himunderstand that certain words which we use correspond to those objects. After he has thus acquired a small vocabulary, we make him understandthat other terms refer to relations between objects which he canperceive by his senses. Next he learns, by induction, that there areterms which apply not to special objects, but to whole classes ofobjects. Continuing the same process, he learns that there are certainattributes of objects made known by the manner in which they affect hissenses, to which abstract terms are applied. Having learned all this, we can teach him new words by combining words without exhibitingobjects already known. Using these words we can proceed yet further, building up, as it were, a complete language. But there is one limit atevery step. Every term which we make known to him must dependultimately upon terms the meaning of which he has learned from theirconnection with special objects of sense. 

To communicate to him a knowledge of words expressive of mental statesit is necessary to assume that his own mind is subject to these statesas well as our own, and that we can in some way indicate them by ouracts. That the former hypothesis is sufficiently well established canbe made evident so long as a consistency of different words and ideasis maintained. If no such consistency of meaning on his part wereevident, it might indicate that the operations of his mind were sodifferent from ours that no such communication of ideas was possible. Uncertainty in this respect must arise as soon as we go beyond thosemental states which communicate themselves to the senses of others. 

We now see that in order to communicate to our foreigner a knowledge oflanguage, we must follow rules similar to those necessary for thestability of a building. The foundation of the building must be welllaid upon objects knowable by his five senses. Of course the mind, aswell as the external object, may be a factor in determining the ideaswhich the words are intended to express; but this does not in anymanner invalidate the conditions which we impose. Whatever theory wemay adopt of the relative part played by the knowing subject, and theexternal object in the acquirement of knowledge, it remains none theless true that no knowledge of the meaning of a word can be acquiredexcept through the senses, and that the meaning is, therefore, limitedby the senses. If we transgress the rule of founding each meaning uponmeanings below it, and having the whole ultimately resting upon asensuous foundation, we at once branch off into sound without sense. Wemay teach him the use of an extended vocabulary, to the terms of whichhe may apply ideas of his own, more or less vague, but there will be noway of deciding that he attaches the same meaning to these terms thatwe do. 

What we have shown true of an intelligent foreigner is necessarily trueof the growing child. We come into the world without a knowledge of themeaning of words, and can acquire such knowledge only by a processwhich we have found applicable to the intelligent foreigner. But toconfine ourselves within these limits in the use of language requires acourse of severe mental discipline. The transgression of the rule willnaturally seem to the undisciplined mind a mark of intellectual vigorrather than the reverse. In our system of education every temptation isheld out to the learner to transgress the rule by the fluent use oflanguage to which it is doubtful if he himself attaches clear notions, and which he can never be certain suggests to his hearer the ideaswhich he desires to convey. Indeed, we not infrequently see, even amongpractical educators, expressions of positive antipathy to scientificprecision of language so obviously opposed to good sense that they canbe attributed only to a failure to comprehend the meaning of thelanguage which they criticise. 

Perhaps the most injurious effect in this direction arises from thenatural tendency of the mind, when not subject to a scientificdiscipline, to think of words expressing sensible objects and theirrelations as connoting certain supersensuous attributes. This isfrequently seen in the repugnance of the metaphysical mind to receive ascientific statement about a matter of fact simply as a matter of fact. This repugnance does not generally arise in respect to the every-daymatters of life. When we say that the earth is round we state a truthwhich every one is willing to receive as final. If without denying thatthe earth was round, one should criticise the statement on the groundthat it was not necessarily round but might be of some other form, weshould simply smile at this use of language. But when we take a moregeneral statement and assert that the laws of nature are inexorable, and that all phenomena, so far as we can show, occur in obedience totheir requirements, we are met with a sort of criticism with which allof us are familiar, but which I am unable adequately to describe. Noone denies that as a matter of fact, and as far as his experienceextends, these laws do appear to be inexorable. I have never heard ofany one professing, during the present generation, to describe anatural phenomenon, with the avowed belief that it was not a product ofnatural law; yet we constantly hear the scientific view criticised onthe ground that events MAY occur without being subject to natural law. The word "may, " in this connection, is one to which we can attach nomeaning expressive of a sensuous relation. 

The analogous conflict between the scientific use of language and theuse made by some philosophers is found in connection with the idea ofcausation. Fundamentally the word cause is used in scientific languagein the same sense as in the language of common life. When we discusswith our neighbors the cause of a fit of illness, of a fire, or of coldweather, not the slightest ambiguity attaches to the use of the word, because whatever meaning may be given to it is founded only on anaccurate analysis of the ideas involved in it from daily use. Nophilosopher objects to the common meaning of the word, yet wefrequently find men of eminence in the intellectual world who will nottolerate the scientific man in using the word in this way. In everyexplanation which he can give to its use they detect ambiguity. Theyinsist that in any proper use of the term the idea of power must beconnoted. But what meaning is here attached to the word power, and howshall we first reduce it to a sensible form, and then apply its meaningto the operations of nature? Whether this can be done, I do notinquire. All I maintain is that if we wish to do it, we must passwithout the domain of scientific statement. 

Perhaps the greatest advantage in the use of symbolic and othermathematical language in scientific investigation is that it cannotpossibly be made to connote anything except what the speaker means. Itadheres to the subject matter of discourse with a tenacity which nocriticism can overcome. In consequence, whenever a science is reducedto a mathematical form its conclusions are no longer the subject ofphilosophical attack. To secure the same desirable quality in all otherscientific language it is necessary to give it, so far as possible, thesame simplicity of signification which attaches to mathematicalsymbols. This is not easy, because we are obliged to use words ofordinary language, and it is impossible to divest them of whatever theymay connote to ordinary hearers. 

I have thus sought to make it clear that the language of sciencecorresponds to that of ordinary life, and especially of business life, in confining its meaning to phenomena. An analogous statement may bemade of the method and objects of scientific investigation. I thinkProfessor Clifford was very happy in defining science as organizedcommon-sense. The foundation of its widest general creations is laid, not in any artificial theories, but in the natural beliefs andtendencies of the human mind. Its position against those who deny thesegeneralizations is quite analogous to that taken by the Scottish schoolof philosophy against the scepticism of Hume. 

It may be asked, if the methods and language of science correspond tothose of practical life, why is not the every-day discipline of thatlife as good as the discipline of science? The answer is, that thepower of transferring the modes of thought of common life to subjectsof a higher order of generality is a rare faculty which can be acquiredonly by scientific discipline. What we want is that in public affairsmen shall reason about questions of finance, trade, national wealth, legislation, and administration, with the same consciousness of thepractical side that they reason about their own interests. When thishabit is once acquired and appreciated, the scientific method willnaturally be applied to the study of questions of social policy. When ascientific interest is taken in such questions, their boundaries willbe extended beyond the utilities immediately involved, and oneimportant condition of unceasing progress will be complied with. 

XXI

THE OUTLOOK FOR THE FLYING-MACHINE

Mr. Secretary Langley's trial of his flying-machine, which seems tohave come to an abortive issue for the time, strikes a sympatheticchord in the constitution of our race. Are we not the lords ofcreation? Have we not girdled the earth with wires through which wespeak to our antipodes? Do we not journey from continent to continentover oceans that no animal can cross, and with a speed of which ourancestors would never have dreamed? Is not all the rest of the animalcreation so far inferior to us in every point that the best thing itcan do is to become completely subservient to our needs, dying, if needbe, that its flesh may become a toothsome dish on our tables? And yethere is an insignificant little bird, from whose mind, if mind it has, all conceptions of natural law are excluded, applying the rules ofaerodynamics in an application of mechanical force to an end we havenever been able to reach, and this with entire ease and absence ofconsciousness that it is doing an extraordinary thing. Surely ourknowledge of natural laws, and that inventive genius which has enabledus to subordinate all nature to our needs, ought also to enable us todo anything that the bird can do. Therefore we must fly. If we cannotyet do it, it is only because we have not got to the bottom of thesubject. Our successors of the not distant future will surely succeed. 

This is at first sight a very natural and plausible view of the case. And yet there are a number of circumstances of which we should takeaccount before attempting a confident forecast. Our hope for the futureis based on what we have done in the past. But when we draw conclusionsfrom past successes we should not lose sight of the conditions on whichsuccess has depended. There is no advantage which has not its attendantdrawbacks; no strength which has not its concomitant weakness. Wealthhas its trials and health its dangers. We must expect our greatsuperiority to the bird to be associated with conditions which wouldgive it an advantage at some point. A little study will make theseconditions clear. 

We may look on the bird as a sort of flying-machine complete in itself, of which a brain and nervous system are fundamentally necessary parts. No such machine can navigate the air unless guided by something havinglife. Apart from this, it could be of little use to us unless itcarried human beings on its wings. We thus meet with a difficulty atthe first step--we cannot give a brain and nervous system to ourmachine. These necessary adjuncts must be supplied by a man, who is nopart of the machine, but something carried by it. The bird is acomplete machine in itself. Our aerial ship must be machine plus man. Now, a man is, I believe, heavier than any bird that flies. The limitwhich the rarity of the air places upon its power of supporting wings, taken in connection with the combined weight of a man and a machine, make a drawback which we should not too hastily assume our ability toovercome. The example of the bird does not prove that man can fly. Thehundred and fifty pounds of dead weight which the manager of themachine must add to it over and above that necessary in the bird maywell prove an insurmountable obstacle to success. 

I need hardly remark that the advantage possessed by the bird has itsattendant drawbacks when we consider other movements than flying. Itswings are simply one pair of its legs, and the human race could notafford to abandon its arms for the most effective wings that nature orart could supply. 

Another point to be considered is that the bird operates by theapplication of a kind of force which is peculiar to the animalcreation, and no approach to which has ever been made in any mechanism. This force is that which gives rise to muscular action, of which thenecessary condition is the direct action of a nervous system. We cannothave muscles or nerves for our flying-machine. We have to replace themby such crude and clumsy adjuncts as steam-engines and electricbatteries. It may certainly seem singular if man is never to discoverany combination of substances which, under the influence of some suchagency as an electric current, shall expand and contract like a muscle. But, if he is ever to do so, the time is still in the future. We do notsee the dawn of the age in which such a result will be brought forth. 

Another consideration of a general character may be introduced. As arule it is the unexpected that happens in invention as well asdiscovery. There are many problems which have fascinated mankind eversince civilization began which we have made little or no advance insolving. The only satisfaction we can feel in our treatment of thegreat geometrical problems of antiquity is that we have shown theirsolution to be impossible. The mathematician of to-day admits that hecan neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admitthat aerial flight is one of that great class of problems with whichman can never cope, and give up all attempts to grapple with it?

[Illustration with caption: PROFESSOR LANGLEY'S AIR-SHIP]

The fact is that invention and discovery have, notwithstanding theirseemingly wide extent, gone on in rather narrower lines than iscommonly supposed. If, a hundred years ago, the most sagacious ofmortals had been told that before the nineteenth century closed theface of the earth would be changed, time and space almost annihilated, and communication between continents made more rapid and easy than itwas between cities in his time; and if he had been asked to exercisehis wildest imagination in depicting what might come--the airship andthe flying-machine would probably have had a prominent place in hisscheme, but neither the steamship, the railway, the telegraph, nor thetelephone would have been there. Probably not a single new agency whichhe could have imagined would have been one that has come to pass. 

It is quite clear to me that success must await progress of a differentkind from that which the inventors of flying-machines are aiming at. Wewant a great discovery, not a great invention. It is an unfortunatefact that we do not always appreciate the distinction between progressin scientific discovery and ingenious application of discovery to thewants of civilization. The name of Marconi is familiar to every ear;the names of Maxwell and Herz, who made the discoveries which renderedwireless telegraphy possible, are rarely recalled. Modern progress isthe result of two factors: Discoveries of the laws of nature and ofactions or possibilities in nature, and the application of suchdiscoveries to practical purposes. The first is the work of thescientific investigator, the second that of the inventor. 

In view of the scientific discoveries of the past ten years, which, after bringing about results that would have seemed chimerical ifpredicted, leading on to the extraction of a substance which seems toset the laws and limits of nature at defiance by radiating a flood ofheat, even when cooled to the lowest point that science can reach--asubstance, a few specks of which contain power enough to start arailway train, and embody perpetual motion itself, almost--he would bea bold prophet who would set any limit to possible discoveries in therealm of nature. We are binding the universe together by agencies whichpass from sun to planet and from star to star. We are determined tofind out all we can about the mysterious ethereal medium supposed tofill all space, and which conveys light and heat from one heavenly bodyto another, but which yet evades all direct investigation. We arepeering into the law of gravitation itself with the full hope ofdiscovering something in its origin which may enable us to evade itsaction. From time to time philosophers fancy the road open to success, yet nothing that can be practically called success has yet been reachedor even approached. When it is reached, when we are able to stateexactly why matter gravitates, then will arise the question how thishitherto unchangeable force may be controlled and regulated. With thisquestion answered the problem of the interaction between ether andmatter may be solved. That interaction goes on between ethers andmolecules is shown by the radiation of heat by all bodies. When themolecules are combined into a mass, this interaction ceases, so thatthe lightest objects fly through the ether without resistance. Why isthis? Why does ether act on the molecule and not the mass? When we canproduce the latter, and when the mutual action can be controlled, thenmay gravitation be overcome and then may men build, not merelyairships, but ships which shall fly above the air, and transport theirpassengers from continent to continent with the speed of the celestialmotions. 

The first question suggested to the reader by these considerations iswhether any such result is possible; whether it is within the power ofman to discover the nature of luminiferous ether and the cause ofgravitation. To this the profoundest philosopher can only answer, "I donot know. " Quite possibly the gates at which he is beating are, in thevery nature of things, incapable of being opened. It may be that themind of man is incapable of grasping the secrets within them. Thequestion has even occurred to me whether, if a being of suchsupernatural power as to understand the operations going on in amolecule of matter or in a current of electricity as we understand theoperations of a steam-engine should essay to explain them to us, hewould meet with any more success than we should in explaining to a fishthe engines of a ship which so rudely invades its domain. As wasremarked by William K. Clifford, perhaps the clearest spirit that hasever studied such problems, it is possible that the laws of geometryfor spaces infinitely small may be so different from those of largerspaces that we must necessarily be unable to conceive them. 

Still, considering mere possibilities, it is not impossible that thetwentieth century may be destined to make known natural forces whichwill enable us to fly from continent to continent with a speed farexceeding that of the bird. 

But when we inquire whether aerial flight is possible in the presentstate of our knowledge, whether, with such materials as we possess, acombination of steel, cloth, and wire can be made which, moved by thepower of electricity or steam, shall form a successful flying-machine, the outlook may be altogether different. To judge it sanely, let usbear in mind the difficulties which are encountered in anyflying-machine. The basic principle on which any such machine must beconstructed is that of the aeroplane. This, by itself, would be thesimplest of all flyers, and therefore the best if it could be put intooperation. The principle involved may be readily comprehended by theaccompanying figure. A M is the section of a flat plane surface, say athin sheet of metal or a cloth supported by wires. It moves through theair, the latter being represented by the horizontal rows of dots. Thedirection of the motion is that of the horizontal line A P. Theaeroplane has a slight inclination measured by the proportion betweenthe perpendicular M P and the length A P. We may raise the edge M up orlower it at pleasure. Now the interesting point, and that on which thehopes of inventors are based, is that if we give the plane any giveninclination, even one so small that the perpendicular M P is only twoor three per cent of the length A M, we can also calculate a certainspeed of motion through the air which, if given to the plane, willenable it to bear any required weight. A plane ten feet square, forexample, would not need any great inclination, nor would it require aspeed higher than a few hundred feet a second to bear a man. What is ofyet more importance, the higher the speed the less the inclinationrequired, and, if we leave out of consideration the friction of the airand the resistance arising from any object which the machine may carry, the less the horse-power expended in driving the plane. 

[Illustration]

Maxim exemplified this by experiment several years ago. He found that, with a small inclination, he could readily give his aeroplane, when itslid forward upon ways, such a speed that it would rise from the waysof itself. The whole problem of the successful flying-machine is, therefore, that of arranging an aeroplane that shall move through theair with the requisite speed. 

The practical difficulties in the way of realizing the movement of suchan object are obvious. The aeroplane must have its propellers. Thesemust be driven by an engine with a source of power. Weight is anessential quality of every engine. The propellers must be made ofmetal, which has its weakness, and which is liable to give way when itsspeed attains a certain limit. And, granting complete success, imaginethe proud possessor of the aeroplane darting through the air at a speedof several hundred feet per second! It is the speed alone that sustainshim. How is he ever going to stop? Once he slackens his speed, down hebegins to fall. He may, indeed, increase the inclination of hisaeroplane. Then he increases the resistance to the sustaining force. Once he stops he falls a dead mass. How shall he reach the groundwithout destroying his delicate machinery? I do not think the mostimaginative inventor has yet even put upon paper a demonstrativelysuccessful way of meeting this difficulty. The only ray of hope isafforded by the bird. The latter does succeed in stopping and reachingthe ground safely after its flight. But we have already mentioned thegreat advantages which the bird possesses in the power of applyingforce to its wings, which, in its case, form the aeroplanes. But wehave already seen that there is no mechanical combination, and no wayof applying force, which will give to the aeroplanes the flexibilityand rapidity of movement belonging to the wings of a bird. With all theimprovements that the genius of man has made in the steamship, thegreatest and best ever constructed is liable now and then to meet withaccident. When this happens she simply floats on the water until thedamage is repaired, or help reaches her. Unless we are to suppose forthe flying-machine, in addition to everything else, an immunity fromaccident which no human experience leads us to believe possible, itwould be liable to derangements of machinery, any one of which would benecessarily fatal. If an engine were necessary not only to propel aship, but also to make her float--if, on the occasion of any accidentshe immediately went to the bottom with all on board--there would not, at the present day, be any such thing as steam navigation. That thisdifficulty is insurmountable would seem to be a very fair deduction, not only from the failure of all attempts to surmount it, but from thefact that Maxim has never, so far as we are aware, followed up hisseemingly successful experiment. 

There is, indeed, a way of attacking it which may, at first sight, seemplausible. In order that the aeroplane may have its full sustainingpower, there is no need that its motion be continuously forward. Anearly horizontal surface, swinging around in a circle, on a verticalaxis, like the wings of a windmill moving horizontally, will fulfil allthe conditions. In fact, we have a machine on this simple principle inthe familiar toy which, set rapidly whirling, rises in the air. Whymore attempts have not been made to apply this system, with two sets ofsails whirling in opposite directions, I do not know. Were there anypossibility of making a flying-machine, it would seem that we shouldlook in this direction. 

The difficulties which I have pointed out are only preliminary ones, patent on the surface. A more fundamental one still, which the writerfeels may prove insurmountable, is based on a law of nature which weare bound to accept. It is that when we increase the size of anyflying-machine without changing its model we increase the weight inproportion to the cube of the linear dimensions, while the effectivesupporting power of the air increases only as the square of thosedimensions. To illustrate the principle let us make two flying-machinesexactly alike, only make one on double the scale of the other in allits dimensions. We all know that the volume and therefore the weight oftwo similar bodies are proportional to the cubes of their dimensions. The cube of two is eight. Hence the large machine will have eight timesthe weight of the other. But surfaces are as the squares of thedimensions. The square of two is four. The heavier machine willtherefore expose only four times the wing surface to the air, and sowill have a distinct disadvantage in the ratio of efficiency to weight. 

Mechanical principles show that the steam pressures which the engineswould bear would be the same, and that the larger engine, though itwould have more than four times the horse-power of the other, wouldhave less than eight times. The larger of the two machines wouldtherefore be at a disadvantage, which could be overcome only byreducing the thickness of its parts, especially of its wings, to thatof the other machine. Then we should lose in strength. It follows thatthe smaller the machine the greater its advantage, and the smallestpossible flying-machine will be the first one to be successful. 

We see the principle of the cube exemplified in the animal kingdom. Theagile flea, the nimble ant, the swift-footed greyhound, and theunwieldy elephant form a series of which the next term would be ananimal tottering under its own weight, if able to stand or move at all. The kingdom of flying animals shows a similar gradation. The mostnumerous fliers are little insects, and the rising series stops withthe condor, which, though having much less weight than a man, is saidto fly with difficulty when gorged with food. 

Now, suppose that an inventor succeeds, as well he may, in making amachine which would go into a watch-case, yet complete in all itsparts, able to fly around the room. It may carry a button, but nothingheavier. Elated by his success, he makes one on the same model twice aslarge in every dimension. The parts of the first, which are one inch inlength, he increases to two inches. Every part is twice as long, twiceas broad, and twice as thick. The result is that his machine is eighttimes as heavy as before. But the sustaining surface is only four timesas great. As compared with the smaller machine, its ratio ofeffectiveness is reduced to one-half. It may carry two or threebuttons, but will not carry over four, because the total weight, machine plus buttons, can only be quadrupled, and if he more thanquadruples the weight of the machine, he must less than quadruple thatof the load. How many such enlargements must he make before his machinewill cease to sustain itself, before it will fall as an inert mass whenwe seek to make it fly through the air? Is there any size at which itwill be able to support a human being? We may well hesitate before weanswer this question in the affirmative. 

Dr. Graham Bell, with a cheery optimism very pleasant to contemplate, has pointed out that the law I have just cited may be evaded by notmaking a larger machine on the same model, but changing the latter in away tantamount to increasing the number of small machines. This isquite true, and I wish it understood that, in laying down the law Ihave cited, I limit it to two machines of different sizes on the samemodel throughout. Quite likely the most effective flying-machine wouldbe one carried by a vast number of little birds. The veraciouschronicler who escaped from a cloud of mosquitoes by crawling into animmense metal pot and then amused himself by clinching the antennae ofthe insects which bored through the pot until, to his horror, theybecame so numerous as to fly off with the covering, was more scientificthan he supposed. Yes, a sufficient number of humming-birds, if wecould combine their forces, would carry an aerial excursion party ofhuman beings through the air. If the watch-maker can make a machinewhich will fly through the room with a button, then, by combining tenthousand such machines he may be able to carry a man. But how shall thecombined forces be applied?

The difficulties I have pointed out apply only to the flying-machineproperly so-called, and not to the dirigible balloon or airship. It isof interest to notice that the law is reversed in the case of a bodywhich is not supported by the resistance of a fluid in which it isimmersed, but floats in it, the ship or balloon, for example. When wedouble the linear dimensions of a steamship in all its parts, weincrease not only her weight but her floating power, her carryingcapacity, and her engine capacity eightfold. But the resistance whichshe meets with when passing through the water at a given speed is onlymultiplied four times. Hence, the larger we build the steamship themore economical the application of the power necessary to drive it at agiven speed. It is this law which has brought the great increase in thesize of ocean steamers in recent times. The proportionately diminishingresistance which, in the flying-machine, represents the floating poweris, in the ship, something to be overcome. Thus there is a completereversal of the law in its practical application to the two cases. 

The balloon is in the same class with the ship. Practical difficultiesaside, the larger it is built the more effective it will be, and themore advantageous will be the ratio of the power which is necessary todrive it to the resistance to be overcome. 

If, therefore, we are ever to have aerial navigation with our presentknowledge of natural capabilities, it is to the airship floating in theair, rather than the flying-machine resting on the air, to which we areto look. In the light of the law which I have laid down, the subject, while not at all promising, seems worthy of more attention than it hasreceived. It is not at all unlikely that if a skilful and experiencednaval constructor, aided by an able corps of assistants, should designan airship of a diameter of not less than two hundred feet, and alength at least four or five times as great, constructed, possibly, ofa textile substance impervious to gas and borne by a light framework, but, more likely, of exceedingly thin plates of steel carried by aframe fitted to secure the greatest combination of strength andlightness, he might find the result to be, ideally at least, a shipwhich would be driven through the air by a steam-engine with a velocityfar exceeding that of the fleetest Atlantic liner. Then would come thepractical problem of realizing the ship by overcoming the mechanicaldifficulties involved in the construction of such a huge and lightframework. I would not be at all surprised if the result of the exactcalculation necessary to determine the question should lead to anaffirmative conclusion, but I am quite unable to judge whether steelcould be rolled into parts of the size and form required in themechanism. 

In judging of the possibility of commercial success the cheapness ofmodern transportation is an element in the case that should not beoverlooked. I believe the principal part of the resistance which alimited express train meets is the resistance of the air. This would beas great for an airship as for a train. An important fraction of thecost of transporting goods from Chicago to London is that of gettingthem into vehicles, whether cars or ships, and getting them out again. The cost of sending a pair of shoes from a shop in New York to theresidence of the wearer is, if I mistake not, much greater than themere cost of transporting them across the Atlantic. Even if a dirigibleballoon should cross the Atlantic, it does not follow that it couldcompete with the steamship in carrying passengers and freight. 

I may, in conclusion, caution the reader on one point. I should be verysorry if my suggestion of the advantage of the huge airship leads tothe subject being taken up by any other than skilful engineers orconstructors, able to grapple with all problems relating to thestrength and resistance of materials. As a single example of what is tobe avoided I may mention the project, which sometimes has been mooted, of making a balloon by pumping the air from a very thin, hollowreceptacle. Such a project is as futile as can well be imagined; noknown substance would begin to resist the necessary pressure. Ouraerial ship must be filled with some substance lighter than air. Whether heated air would answer the purpose, or whether we should haveto use a gas, is a question for the designer. 

To return to our main theme, all should admit that if any hope for theflying-machine can be entertained, it must be based more on generalfaith in what mankind is going to do than upon either reasoning orexperience. We have solved the problem of talking between two widelyseparated cities, and of telegraphing from continent to continent andisland to island under all the oceans--therefore we shall solve theproblem of flying. But, as I have already intimated, there is anothergreat fact of progress which should limit this hope. As an almostuniversal rule we have never solved a problem at which our predecessorshave worked in vain, unless through the discovery of some agency ofwhich they have had no conception. The demonstration that no possiblecombination of known substances, known forms of machinery, and knownforms of force can be united in a practicable machine by which menshall fly long distances through the air, seems to the writer ascomplete as it is possible for the demonstration of any physical factto be. But let us discover a substance a hundred times as strong assteel, and with that some form of force hitherto unsuspected which willenable us to utilize this strength, or let us discover some way ofreversing the law of gravitation so that matter may be repelled by theearth instead of attracted--then we may have a flying-machine. But wehave every reason to believe that mere ingenious contrivances with ourpresent means and forms of force will be as vain in the future as theyhave been in the past.