The Einstein Theory of Relativity A Concise Statement by Prof. H. A. Lorentz of the University of Leyden NOTE Whether it is true or not that not more than twelve persons in all theworld are able to understand Einstein's Theory, it is neverthelessa fact that there is a constant demand for information about thismuch-debated topic of relativity. The books published on the subjectare so technical that only a person trained in pure physics andhigher mathematics is able to fully understand them. In order tomake a popular explanation of this far-reaching theory available, the present book is published. Professor Lorentz is credited by Einstein with sharing the developmentof his theory. He is doubtless better able than any other man--exceptthe author himself--to explain this scientific discovery. The publishers wish to acknowledge their indebtedness to the NewYork Times, The Review of Reviews and The Athenaeum for courteouspermission to reprint articles from their pages. Professor Lorentz'sarticle appeared originally in The Nieuwe Rotterdamsche Courant ofNovember 19, 1919. INTRODUCTION The action of the Royal Society at its meeting in London on November6, in recognizing Dr. Albert Einstein's "theory of relativity"has caused a great stir in scientific circles on both sides of theAtlantic. Dr. Einstein propounded his theory nearly fifteen yearsago. The present revival of interest in it is due to the remarkableconfirmation which it received in the report of the observationsmade during the sun's eclipse of last May to determine whether raysof light passing close to the sun are deflected from their course. The actual deflection of the rays that was discovered by theastronomers was precisely what had been predicted theoretically byEinstein many years since. This striking confirmation has led certainGerman scientists to assert that no scientific discovery of suchimportance has been made since Newton's theory of gravitation waspromulgated. This suggestion, however, was put aside by Dr. Einsteinhimself when he was interviewed by a correspondent of the New YorkTimes at his home in Berlin. To this correspondent he expressed thedifference between his conception and the law of gravitation in thefollowing terms: "Please imagine the earth removed, and in its place suspended a box asbig as a room or a whole house, and inside a man naturally floatingin the center, there being no force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenlyjerked to one side, which is scientifically termed 'difform motion', as opposed to 'uniform motion. ' The person would then naturally reachbottom on the opposite side. The result would consequently be thesame as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difformmotion will in every case produce the same effects as gravitation. "I have applied this new idea to every kind of difform motion andhave thus developed mathematical formulas which I am convinced givemore precise results than those based on Newton's theory. Newton'sformulas, however, are such close approximations that it was difficultto find by observation any obvious disagreement with experience. " Dr. Einstein, it must be remembered, is a physicist and not anastronomer. He developed his theory as a mathematical formula. Theconfirmation of it came from the astronomers. As he himself says, thecrucial test was supplied by the last total solar eclipse. Observationsthen proved that the rays of fixed stars, having to pass close tothe sun to reach the earth, were deflected the exact amount demandedby Einstein's formulas. The deflection was also in the directionpredicted by him. The question must have occurred to many, what has all this to do withrelativity? When this query was propounded by the Times correspondentto Dr. Einstein he replied as follows: "The term relativity refers to time and space. According to Galileo andNewton, time and space were absolute entities, and the moving systemsof the universe were dependent on this absolute time and space. Onthis conception was built the science of mechanics. The resultingformulas sufficed for all motions of a slow nature; it was found, however, that they would not conform to the rapid motions apparentin electrodynamics. "This led the Dutch professor, Lorentz, and myself to developthe theory of special relativity. Briefly, it discards absolutetime and space and makes them in every instance relative to movingsystems. By this theory all phenomena in electrodynamics, as well asmechanics, hitherto irreducible by the old formulae--and there aremultitudes--were satisfactorily explained. "Till now it was believed that time and space existed by themselves, even if there was nothing else--no sun, no earth, no stars--whilenow we know that time and space are not the vessel for the universe, but could not exist at all if there were no contents, namely, no sun, earth and other celestial bodies. "This special relativity, forming the first part of my theory, relates to all systems moving with uniform motion; that is, movingin a straight line with equal velocity. "Gradually I was led to the idea, seeming a very paradox in science, that it might apply equally to all moving systems, even of difformmotion, and thus I developed the conception of general relativitywhich forms the second part of my theory. " As summarized by an American astronomer, Professor Henry NorrisRussell, of Princeton, in the Scientific American for November 29, Einstein's contribution amounts to this: "The central fact which has been proved--and which is of great interestand importance--is that the natural phenomena involving gravitationand inertia (such as the motions of the planets) and the phenomenainvolving electricity and magnetism (including the motion of light)are not independent of one another, but are intimately related, sothat both sets of phenomena should be regarded as parts of one vastsystem, embracing all Nature. The relation of the two is, however, ofsuch a character that it is perceptible only in a very few instances, and then only to refined observations. " Already before the war, Einstein had immense fame among physicists, and among all who are interested in the philosophy of science, because of his principle of relativity. Clerk Maxwell had shown that light is electro-magnetic, and had reducedthe whole theory of electro-magnetism to a small number of equations, which are fundamental in all subsequent work. But these equationswere entangled with the hypothesis of the ether, and with the notionof motion relative to the ether. Since the ether was supposed to beat rest, such motion was indistinguishable from absolute motion. Themotion of the earth relatively to the ether should have been differentat different points of its orbit, and measurable phenomena shouldhave resulted from this difference. But none did, and all attempts todetect effects of motions relative to the ether failed. The theory ofrelativity succeeded in accounting for this fact. But it was necessaryincidentally to throw over the one universal time, and substitutelocal times attached to moving bodies and varying according to theirmotion. The equations on which the theory of relativity is based aredue to Lorentz, but Einstein connected them with his general principle, namely, that there must be nothing, in observable phenomena, whichcould be attributed to absolute motion of the observer. In orthodox Newtonian dynamics the principle of relativity had asimpler form, which did not require the substitution of local timefor general time. But it now appeared that Newtonian dynamics is onlyvalid when we confine ourselves to velocities much less than thatof light. The whole Galileo-Newton system thus sank to the levelof a first approximation, becoming progressively less exact as thevelocities concerned approached that of light. Einstein's extension of his principle so as to account for gravitationwas made during the war, and for a considerable period our astronomerswere unable to become acquainted with it, owing to the difficultyof obtaining German printed matter. However, copies of his workultimately reached the outside world and enabled people to learn moreabout it. Gravitation, ever since Newton, had remained isolated fromother forces in nature; various attempts had been made to accountfor it, but without success. The immense unification effected byelectro-magnetism apparently left gravitation out of its scope. Itseemed that nature had presented a challenge to the physicists whichnone of them were able to meet. At this point Einstein intervened with a hypothesis which, apartaltogether from subsequent verification, deserves to rank as oneof the great monuments of human genius. After correcting Newton, it remained to correct Euclid, and it was in terms of non-Euclideangeometry that he stated his new theory. Non-Euclidean geometry isa study of which the primary motive was logical and philosophical;few of its promoters ever dreamed that it would come to be appliedin physics. Some of Euclid's axioms were felt to be not "necessarytruths, " but mere empirical laws; in order to establish this view, self-consistent geometries were constructed upon assumptions otherthan those of Euclid. In these geometries the sum of the angles ofa triangle is not two right angles, and the departure from two rightangles increases as the size of the triangle increases. It is oftensaid that in non-Euclidean geometry space has a curvature, but thisway of stating the matter is misleading, since it seems to imply afourth dimension, which is not implied by these systems. Einstein supposes that space is Euclidean where it is sufficientlyremote from matter, but that the presence of matter causes itto become slightly non-Euclidean--the more matter there is in theneighborhood, the more space will depart from Euclid. By the help ofthis hypothesis, together with his previous theory of relativity, hededuces gravitation--very approximately, but not exactly, accordingto the Newtonian law of the inverse square. The minute differencesbetween the effects deduced from his theory and those deduced fromNewton are measurable in certain cases. There are, so far, threecrucial tests of the relative accuracy of the new theory and the old. (1) The perihelion of Mercury shows a discrepancy which has longpuzzled astronomers. This discrepancy is fully accounted for byEinstein. At the time when he published his theory, this was its onlyexperimental verification. (2) Modern physicists were willing to suppose that light might besubject to gravitation--i. E. , that a ray of light passing near agreat mass like the sun might be deflected to the extent to which aparticle moving with the same velocity would be deflected accordingto the orthodox theory of gravitation. But Einstein's theory requiredthat the light should be deflected just twice as much as this. Thematter could only be tested during an eclipse among a number ofbright stars. Fortunately a peculiarly favourable eclipse occurredlast year. The results of the observations have now been published, and are found to verify Einstein's prediction. The verification is not, of course, quite exact; with such delicate observations that was not tobe expected. In some cases the departure is considerable. But takingthe average of the best series of observations, the deflection atthe sun's limb is found to be 1. 98'', with a probable error of about6 per cent. , whereas the deflection calculated by Einstein's theoryshould be 1. 75''. It will be noticed that Einstein's theory gave adeflection twice as large as that predicted by the orthodox theory, and that the observed deflection is slightly larger than Einsteinpredicted. The discrepancy is well within what might be expected inview of the minuteness of the measurements. It is therefore generallyacknowledged by astronomers that the outcome is a triumph for Einstein. (3) In the excitement of this sensational verification, there hasbeen a tendency to overlook the third experimental test to whichEinstein's theory was to be subjected. If his theory is correct as itstands, there ought, in a gravitational field, to be a displacementof the lines of the spectrum towards the red. No such effect hasbeen discovered. Spectroscopists maintain that, so far as can beseen at present, there is no way of accounting for this failure ifEinstein's theory in its present form is assumed. They admit that somecompensating cause may be discovered to explain the discrepancy, butthey think it far more probable that Einstein's theory requires someessential modification. Meanwhile, a certain suspense of judgmentis called for. The new law has been so amazingly successful in twoof the three tests that there must be some thing valid about it, even if it is not exactly right as yet. Einstein's theory has the very highest degree of aesthetic merit:every lover of the beautiful must wish it to be true. It gives avast unified survey of the operations of nature, with a technicalsimplicity in the critical assumptions which makes the wealth ofdeductions astonishing. It is a case of an advance arrived at bypure theory: the whole effect of Einstein's work is to make physicsmore philosophical (in a good sense), and to restore some of thatintellectual unity which belonged to the great scientific systems ofthe seventeenth and eighteenth centuries, but which was lost throughincreasing specialization and the overwhelming mass of detailedknowledge. In some ways our age is not a good one to live in, butfor those who are interested in physics there are great compensations. THE EINSTEIN THEORY OF RELATIVITY A Concise Statement by Prof. H. A. Lorentz, of the University of Leyden The total eclipse of the sun of May 29, resulted in a strikingconfirmation of the new theory of the universal attractive powerof gravitation developed by Albert Einstein, and thus reinforcedthe conviction that the defining of this theory is one of the mostimportant steps ever taken in the domain of natural science. Inresponse to a request by the editor, I will attempt to contributesomething to its general appreciation in the following lines. For centuries Newton's doctrine of the attraction of gravitation hasbeen the most prominent example of a theory of natural science. Throughthe simplicity of its basic idea, an attraction between two bodiesproportionate to their mass and also proportionate to the squareof the distance; through the completeness with which it explainedso many of the peculiarities in the movement of the bodies makingup the solar system; and, finally, through its universal validity, even in the case of the far-distant planetary systems, it compelledthe admiration of all. But, while the skill of the mathematicians was devoted to makingmore exact calculations of the consequences to which it led, noreal progress was made in the science of gravitation. It is truethat the inquiry was transferred to the field of physics, followingCavendish's success in demonstrating the common attraction betweenbodies with which laboratory work can be done, but it always wasevident that natural philosophy had no grip on the universal powerof attraction. While in electric effects an influence exercisedby the matter placed between bodies was speedily observed--thestarting-point of a new and fertile doctrine of electricity--inthe case of gravitation not a trace of an influence exercised byintermediate matter could ever be discovered. It was, and remained, inaccessible and unchangeable, without any connection, apparently, with other phenomena of natural philosophy. Einstein has put an end to this isolation; it is now well establishedthat gravitation affects not only matter, but also light. Thusstrengthened in the faith that his theory already has inspired, we may assume with him that there is not a single physical orchemical phenomenon--which does not feel, although very probably inan unnoticeable degree, the influence of gravitation, and that, on theother side, the attraction exercised by a body is limited in the firstplace by the quantity of matter it contains and also, to some degree, by motion and by the physical and chemical condition in which it moves. It is comprehensible that a person could not have arrived at such afar-reaching change of view by continuing to follow the old beatenpaths, but only by introducing some sort of new idea. Indeed, Einstein arrived at his theory through a train of thought of greatoriginality. Let me try to restate it in concise terms. THE EARTH AS A MOVING CAR Everyone knows that a person may be sitting in any kind of a vehiclewithout noticing its progress, so long as the movement does not varyin direction or speed; in a car of a fast express train objects fallin just the same way as in a coach that is standing still. Only whenwe look at objects outside the train, or when the air can enter thecar, do we notice indications of the motion. We may compare the earthwith such a moving vehicle, which in its course around the sun hasa remarkable speed, of which the direction and velocity during aconsiderable period of time may be regarded as constant. In placeof the air now comes, so it was reasoned formerly, the ether whichfills the spaces of the universe and is the carrier of light and ofelectro-magnetic phenomena; there were good reasons to assume that theearth was entirely permeable for the ether and could travel through itwithout setting it in motion. So here was a case comparable with thatof a railroad coach open on all sides. There certainly should havebeen a powerful "ether wind" blowing through the earth and all ourinstruments, and it was to have been expected that some signs of itwould be noticed in connection with some experiment or other. Everyattempt along that line, however, has remained fruitless; all thephenomena examined were evidently independent of the motion of theearth. That this is the way they do function was brought to the frontby Einstein in his first or "special" theory of relativity. For himthe ether does not function and in the sketch that he draws of naturalphenomena there is no mention of that intermediate matter. If the spaces of the universe are filled with an ether, let us supposewith a substance, in which, aside from eventual vibrations and otherslight movements, there is never any crowding or flowing of one partalongside of another, then we can imagine fixed points existing in it;for example, points in a straight line, located one meter apart, pointsin a level plain, like the angles or squares on a chess board extendingout into infinity, and finally, points in space as they are obtainedby repeatedly shifting that level spot a distance of a meter in thedirection perpendicular to it. If, consequently, one of the pointsis chosen as an "original point" we can, proceeding from that point, reach any other point through three steps in the common perpendiculardirections in which the points are arranged. The figures showing howmany meters are comprized in each of the steps may serve to indicatethe place reached and to distinguish it from any other; these are, asis said, the "co-ordinates" of these places, comparable, for example, with the numbers on a map giving the longitude and latitude. Letus imagine that each point has noted upon it the three numbers thatgive its position, then we have something comparable with a measurewith numbered subdivisions; only we now have to do, one might say, with a good many imaginary measures in three common perpendiculardirections. In this "system of co-ordinates" the numbers that fixthe position of one or the other of the bodies may now be read offat any moment. This is the means which the astronomers and their mathematicalassistants have always used in dealing with the movement of theheavenly bodies. At a determined moment the position of each bodyis fixed by its three co-ordinates. If these are given, then oneknows also the common distances, as well as the angles formed by theconnecting lines, and the movement of a planet is to be known as soonas one knows how its co-ordinates are changing from one moment tothe other. Thus the picture that one forms of the phenomena standsthere as if it were sketched on the canvas of the motionless ether. EINSTEIN'S DEPARTURE Since Einstein has cut loose from the ether, he lacks this canvas, andtherewith, at the first glance, also loses the possibility of fixingthe positions of the heavenly bodies and mathematically describingtheir movement--i. E. , by giving comparisons that define the positionsat every moment. How Einstein has overcome this difficulty may besomewhat elucidated through a simple illustration. On the surface of the earth the attraction of gravitation causesall bodies to fall along vertical lines, and, indeed, when one omitsthe resistance of the air, with an equally accelerated movement; thevelocity increases in equal degrees in equal consecutive divisions oftime at a rate that in this country gives the velocity attained atthe end of a second as 981 centimeters (32. 2 feet) per second. Thenumber 981 defines the "acceleration in the field of gravitation, "and this field is fully characterized by that single number; with itshelp we can also calculate the movement of an object hurled out in anarbitrary direction. In order to measure the acceleration we let thebody drop alongside of a vertical measure set solidly on the ground;on this scale we read at every moment the figure that indicates theheight, the only co-ordinate that is of importance in this rectilinearmovement. Now we ask what would we be able to see if the measure werenot bound solidly to the earth, if it, let us suppose, moved down orup with the place where it is located and where we are ourselves. Ifin this case the speed were constant, then, and this is in accord withthe special theory of relativity, there would be no motion observed atall; we should again find an acceleration of 981 for a falling body. Itwould be different if the measure moved with changeable velocity. If it went down with a constant acceleration of 981 itself, then anobject could remain permanently at the same point on the measure, or could move up or down itself alongside of it, with constantspeed. The relative movement of the body with regard to the measureshould be without acceleration, and if we had to judge only by whatwe observed in the spot where we were and which was falling itself, then we should get the impression that there was no gravitation atall. If the measure goes down with an acceleration equal to a halfor a third of what it just was, then the relative motion of the bodywill, of course, be accelerated, but we should find the increasein velocity per second one-half or two-thirds of 981. If, finally, we let the measure rise with a uniformly accelerated movement, thenwe shall find a greater acceleration than 981 for the body itself. Thus we see that we, also when the measure is not attached to theearth, disregarding its displacement, may describe the motion of thebody in respect to the measure always in the same way--i. E. , as oneuniformly accelerated, as we ascribe now and again a fixed value tothe acceleration of the sphere of gravitation, in a particular casethe value of zero. Of course, in the case here under consideration the use of a measurefixed immovably upon the earth should merit all recommendation. Butin the spaces of the solar system we have, now that we have abandonedthe ether, no such support. We can no longer establish a system ofco-ordinates, like the one just mentioned, in a universal intermediatematter, and if we were to arrive in one way or another at a definitesystem of lines crossing each other in three directions, then we shouldbe able to use just as well another similar system that in respect tothe first moves this or that way. We should also be able to remodel thesystem of co-ordinates in all kinds of ways, for example by extensionor compression. That in all these cases for fixed bodies that do notparticipate in the movement or the remodelling of the system otherco-ordinates will be read off again and again is clear. NEW SYSTEM OR CO-ORDINATES What way Einstein had to follow is now apparent. He must--thishardly needs to be said--in calculating definite, particular casesmake use of a chosen system of co-ordinates, but as he had no meansof limiting his choice beforehand and in general, he had to reservefull liberty of action in this respect. Therefore he made it his aimso to arrange the theory that, no matter how the choice was made, thephenomena of gravitation, so far as its effects and its stimulationby the attracting bodies are concerned, may always be described inthe same way--i. E. , through comparisons of the same general form, as we again and again give certain values to the numbers that markthe sphere of gravitation. (For the sake of simplification I heredisregard the fact that Einstein desires that also the way in whichtime is measured and represented by figures shall have no influenceupon the central value of the comparisons. ) Whether this aim could be attained was a question of mathematicalinquiry. It really was attained, remarkably enough, and, we may say, tothe surprise of Einstein himself, although at the cost of considerablesimplicity in the mathematical form; it appeared necessary for thefixation of the field of gravitation in one or the other point inspace to introduce no fewer than ten quantities in the place of theone that occurred in the example mentioned above. In this connection it is of importance to note that when we excludecertain possibilities that would give rise to still greater intricacy, the form of comparison used by Einstein to present the theory isthe only possible one; the principle of the freedom of choice inco-ordinates was the only one by which he needed to allow himself tobe guided. Although thus there was no special effort made to reach aconnection with the theory of Newton, it was evident, fortunately, at the end of the experiment that the connection existed. If weavail ourselves of the simplifying circumstance that the velocitiesof the heavenly bodies are slight in comparison with that of light, then we can deduce the theory of Newton from the new theory, the"universal" relativity theory, as it is called by Einstein. Thusall the conclusions based upon the Newtonian theory hold good, asmust naturally be required. But now we have got further along. TheNewtonian theory can no longer be regarded as absolutely correct in allcases; there are slight deviations from it, which, although as a ruleunnoticeable, once in a while fall within the range of observation. Now, there was a difficulty in the movement of the planet Mercurywhich could not be solved. Even after all the disturbances caused bythe attraction of other planets had been taken into account, thereremained an inexplicable phenomenon--i. E. , an extremely slow turningof the ellipsis described by Mercury on its own plane; Leverrier hadfound that it amounted to forty-three seconds a century. Einsteinfound that, according to his formulas, this movement must reallyamount to just that much. Thus with a single blow he solved one ofthe greatest puzzles of astronomy. Still more remarkable, because it has a bearing upon a phenomenon whichformerly could not be imagined, is the confirmation of Einstein'sprediction regarding the influence of gravitation upon the courseof the rays of light. That such an influence must exist is taughtby a simple examination; we have only to turn back for a moment tothe following comparison in which we were just imagining ourselvesto make our observations. It was noted that when the compartment isfalling with the acceleration of 981 the phenomena therein will occurjust as if there were no attraction of gravitation. We can then seean object, A, stand still somewhere in open space. A projectile, B, can travel with constant speed along a horizontal line, withoutvarying from it in the slightest. A ray of light can do the same; everybody will admit that in each case, if there is no gravitation, light will certainly extend itself in arectilinear way. If we limit the light to a flicker of the slightestduration, so that only a little bit, C, of a ray of light arises, or if we fix our attention upon a single vibration of light, C, whilewe on the other hand give to the projectile, B, a speed equal to thatof light, then we can conclude that B and C in their continued motioncan always remain next to each other. Now if we watch all this, notfrom the movable compartment, but from a place on the earth, then weshall note the usual falling movement of object A, which shows us thatwe have to deal with a sphere of gravitation. The projectile B will, in a bent path, vary more and more from a horizontal straight line, and the light will do the same, because if we observe the movementsfrom another standpoint this can have no effect upon the remainingnext to each other of B and C. DEFLECTION OF LIGHT The bending of a ray of light thus described is much too light on thesurface of the earth to be observed. But the attraction of gravitationexercised by the sun on its surface is, because of its great mass, morethan twenty-seven times stronger, and a ray of light that goes close bythe superficies of the sun must surely be noticeably bent. The rays ofa star that are seen at a short distance from the edge of the sun will, going along the sun, deviate so much from the original direction thatthey strike the eye of an observer as if they came in a straight linefrom a point somewhat further removed than the real position of thestar from the sun. It is at that point that we think we see the star;so here is a seeming displacement from the sun, which increases in themeasure in which the star is observed closer to the sun. The Einsteintheory teaches that the displacement is in inverse proportion to theapparent distance of the star from the centre of the sun, and that fora star just on its edge it will amount to 1'. 75 (1. 75 seconds). This isapproximately the thousandth part of the apparent diameter of the sun. Naturally, the phenomenon can only be observed when there is a totaleclipse of the sun; then one can take photographs of neighboring starsand through comparing the plate with a picture of the same part ofthe heavens taken at a time when the sun was far removed from thatpoint the sought-for movement to one side may become apparent. Thus to put the Einstein theory to the test was the principal aim ofthe English expeditions sent out to observe the eclipse of May 29, one to Prince's Island, off the coast of Guinea, and the other toSobral, Brazil. The first-named expedition's observers were Eddingtonand Cottingham, those of the second, Crommelin and Davidson. Theconditions were especially favorable, for a very large number ofbright stars were shown on the photographic plate; the observers atSobral being particularly lucky in having good weather. The total eclipse lasted five minutes, during four of which it wasperfectly clear, so that good photographs could be taken. In thereport issued regarding the results the following figures, which arethe average of the measurements made from the seven plates, are givenfor the displacements of seven stars: 1''. 02, 0''. 92, 0''. 84, 0''. 58, 0''. 54, 0''. 36, 0''. 24, whereas, according to the theory, the displacements should have amounted to:0''. 88, 0''. 80, 0''. 75, 0''. 40, 0''. 52, 0''. 33, 0''. 20. If we consider that, according to the theory the displacements mustbe in inverse ratio to the distance from the centre of the sun, thenwe may deduce from each observed displacement how great the sidewaysmovement for a star at the edge of the sun should have been. As themost probable result, therefore, the number 1''. 98 was found fromall the observations together. As the last of the displacements givenabove--i. E. , 0''. 24 is about one-eighth of this, we may say that theinfluence of the attraction of the sun upon light made itself feltupon the ray at a distance eight times removed from its centre. The displacements calculated according to the theory are, just becauseof the way in which they are calculated, in inverse proportion to thedistance to the centre. Now that the observed deviations also accordwith the same rule, it follows that they are surely proportionatewith the calculated displacements. The proportion of the first andthe last observed sidewise movements is 4. 2, and that of the two mostextreme of the calculated numbers is 4. 4. This result is of importance, because thereby the theory is excluded, or at least made extremely improbable, that the phenomenon ofrefraction is to be ascribed to, a ring of vapor surrounding thesun for a great distance. Indeed, such a refraction should cause adeviation in the observed direction, and, in order to produce thedisplacement of one of the stars under observation itself a slightproximity of the vapor ring should be sufficient, but we have everyreason to expect that if it were merely a question of a mass ofgas around the sun the diminishing effect accompanying a removalfrom the sun should manifest itself much faster than is really thecase. We cannot speak with perfect certainty here, as all the factorsthat might be of influence upon the distribution of density in a sunatmosphere are not well enough known, but we can surely demonstratethat in case one of the gasses with which we are acquainted were heldin equilibrium solely by the influence of attraction of the sun thephenomenon should become much less as soon as we got somewhat furtherfrom the edge of the sun. If the displacement of the first star, whichamounts to 1. 02-seconds were to be ascribed to such a mass of gas, thenthe displacement of the second must already be entirely inappreciable. So far as the absolute extent of the displacements is concerned, itwas found somewhat too great, as has been shown by the figures givenabove; it also appears from the final result to be 1. 98 for the edgeof the sun--i. E. , 13 per cent, greater than the theoretical valueof 1. 75. It indeed seems that the discrepancies may be ascribed tofaults in observations, which supposition is supported by the factthat the observations at Prince's Island, which, it is true, did notturn out quite as well as those mentioned above, gave the result, of 1. 64, somewhat lower than Einstein's figure. (The observations made with a second instrument at Sobral gave aresult of 0. 93, but the observers are of the opinion that because ofthe shifting of the mirror which reflected the rays no value is tobe attached to it. ) DIFFICULTY EXAGGERATED During a discussion of the results obtained at a joint meeting ofthe Royal Society and the Royal Astronomical Society held especiallyfor that purpose recently in London, it was the general opinion thatEinstein's prediction might be regarded as justified, and warm tributesto his genius were made on all sides. Nevertheless, I cannot refrain, while I am mentioning it, from expressing my surprise that, accordingto the report in The Times there should be so much complaint aboutthe difficulty of understanding the new theory. It is evident thatEinstein's little book "About the Special and the General Theory ofRelativity in Plain Terms, " did not find its way into England duringwartime. Any one reading it will, in my opinion, come to the conclusionthat the basic ideas of the theory are really clear and simple; it isonly to be regretted that it was impossible to avoid clothing them inpretty involved mathematical terms, but we must not worry about that. I allow myself to add that, as we follow Einstein, we may retainmuch of what has been formerly gained. The Newtonian theory remainsin its full value as the first great step, without which one cannotimagine the development of astronomy and without which the secondstep, that has now been made, would hardly have been possible. Itremains, moreover, as the first, and in most cases, sufficient, approximation. It is true that, according to Einstein's theory, because it leaves us entirely free as to the way in which we wish torepresent the phenomena, we can imagine an idea of the solar systemin which the planets follow paths of peculiar form and the rays oflight shine along sharply bent lines--think of a twisted and distortedplanetarium--but in every case where we apply it to concrete questionswe shall so arrange it that the planets describe almost exact ellipsesand the rays of light almost straight lines. It is not necessary to give up entirely even the ether. Many naturalphilosophers find satisfaction in the idea of a material intermediatesubstance in which the vibrations of light take place, and theywill very probably be all the more inclined to imagine such a mediumwhen they learn that, according to the Einstein theory, gravitationitself does not spread instantaneously, but with a velocity that atthe first estimate may be compared with that of light. Especially informer years were such interpretations current and repeated attemptswere made by speculations about the nature of the ether and aboutthe mutations and movements that might take place in it to arriveat a clear presentation of electro-magnetic phenomena, and also ofthe functioning of gravitation. In my opinion it is not impossiblethat in the future this road, indeed abandoned at present, will oncemore be followed with good results, if only because it can lead to thethinking out of new experimental tests. Einstein's theory need not keepus from so doing; only the ideas about the ether must accord with it. Nevertheless, even without the color and clearness that the ethertheories and the other models may be able to give, and even, we can feel it this way, just because of the soberness inducedby their absence, Einstein's work, we may now positively expect, will remain a monument of science; his theory entirely fulfillsthe first and principal demand that we may make, that of deducingthe course of phenomena from certain principles exactly and to thesmallest details. It was certainly fortunate that he himself put theether in the background; if he had not done so, he probably wouldnever have come upon the idea that has been the foundation of allhis examinations. Thanks to his indefatigable exertions and perseverance, for he hadgreat difficulties to overcome in his attempts, Einstein has attainedthe results, which I have tried to sketch, while still young; he isnow 45 years old. He completed his first investigations in Switzerland, where he first was engaged in the Patent Bureau at Berne and later as aprofessor at the Polytechnic in Zurich. After having been a professorfor a short time at the University of Prague, he settled in Berlin, where the Kaiser Wilhelm Institute afforded him the opportunity todevote himself exclusively to his scientific work. He repeatedlyvisited our country and made his Netherland colleagues, among whom hecounts many good friends, partners in his studies and his results. Heattended the last meeting of the department of natural philosophy ofthe Royal Academy of Sciences, and the members then had the privilegeof hearing him explain, in his own fascinating, clear and simple way, his interpretations of the fundamental questions to which his theorygives rise.