,the ,einstein ,theory of ,relativity ,a ,concise ,statement by ,prof4 ,h4,a4 ,lorentz of the ,university of ,leyden ,,note ,whether it is true or not that not more than twelve persons in all the world are able to understand ,einstein's ,theory1 it is nevertheless a fact that there is a constant demand for information about this much-debated topic of relativity4 ,the books published on the subject are so technical that only a person trained in pure physics and higher mathematics is able to fully understand them4 ,in order to make a popular explanation of this far-reaching theory available1 the present book is published4 ,professor ,lorentz is credited by ,einstein with sharing the development of his theory4 ,he is doubtless better able than any other man--except the author himself--to explain this scientific discovery4 ,the publishers wish to acknowledge their indebtedness to the ,new ,york ,times1 ,the ,review of ,reviews and ,the ,athenaeum for courteous permission to reprint articles from their pages4 ,professor ,lorentz's article appeared originally in ,the ,nieuwe ,rotterdamsche ,courant of ,november #ai1 #aiai4 ,,introduction ,the action of the ,royal ,society at its meeting in ,london on ,november #f1 in recognizing ,dr4 ,albert ,einstein's theory of relativity has caused a great stir in scientific circles on both sides of the ,atlantic4 ,dr4 ,einstein propounded his theory nearly fifteen years ago4 ,the present revival of interest in it is due to the remarkable confirmation which it received in the report of the observations made during the sun's eclipse of last ,may to determine whether rays of light passing close to the sun are deflected from their course4 ,the actual deflection of the rays that was discovered by the astronomers was precisely what had been predicted theoretically by ,einstein many years since4 ,this striking confirmation has led certain ,german scientists to assert that no scientific discovery of such importance has been made since ,newton's theory of gravitation was promulgated4 ,this suggestion1 however1 was put aside by ,dr4 ,einstein himself when he was interviewed by a correspondent of the ,new ,york ,times at his home in ,berlin4 ,to this correspondent he expressed the difference between his conception and the law of gravitation in the following terms3 ,please imagine the earth removed1 and in its place suspended a box as big as a room or a whole house1 and inside a man naturally floating in the center1 there being no force whatever pulling him4 ,imagine1 further1 this box being1 by a rope or other contrivance1 suddenly jerked to one side1 which is scientifically termed 'difform motion'1 as opposed to 'uniform motion4' ,the person would then naturally reach bottom on the opposite side4 ,the result would consequently be the same as if he obeyed ,newton's law of gravitation1 while1 in fact1 there is no gravitation exerted whatever1 which proves that difform motion will in every case produce the same effects as gravitation4 ,i have applied this new idea to every kind of difform motion and have thus developed mathematical formulas which ,i am convinced give more precise results than those based on ,newton's theory4 ,newton's formulas1 however1 are such close approximations that it was difficult to find by observation any obvious disagreement with experience4 ,dr4 ,einstein1 it must be remembered1 is a physicist and not an astronomer4 ,he developed his theory as a mathematical formula4 ,the confirmation of it came from the astronomers4 ,as he himself says1 the crucial test was supplied by the last total solar eclipse4 ,observations then proved that the rays of fixed stars1 having to pass close to the sun to reach the earth1 were deflected the exact amount demanded by ,einstein's formulas4 ,the deflection was also in the direction predicted by him4 ,the question must have occurred to many1 what has all this to do with relativity8 ,when this query was propounded by the ,times correspondent to ,dr4 ,einstein he replied as follows3 ,the term relativity refers to time and space4 ,according to ,galileo and ,newton1 time and space were absolute entities1 and the moving systems of the universe were dependent on this absolute time and space4 ,on this conception was built the science of mechanics4 ,the resulting formulas sufficed for all motions of a slow nature2 it was found1 however1 that they would not conform to the rapid motions apparent in electrodynamics4 ,this led the ,dutch professor1 ,lorentz1 and myself to develop the theory of special relativity4 ,briefly1 it discards absolute time and space and makes them in every instance relative to moving systems4 ,by this theory all phenomena in electrodynamics1 as well as mechanics1 hitherto irreducible by the old formulae--and there are multitudes--were satisfactorily explained4 ,till now it was believed that time and space existed by themselves1 even if there was nothing else--no sun1 no earth1 no stars--while now we know that time and space are not the vessel for the universe1 but could not exist at all if there were no contents1 namely1 no sun1 earth and other celestial bodies4 ,this special relativity1 forming the first part of my theory1 relates to all systems moving with uniform motion2 that is1 moving in a straight line with equal velocity4 ,gradually ,i was led to the idea1 seeming a very paradox in science1 that it might apply equally to all moving systems1 even of difform motion1 and thus ,i developed the conception of general relativity which forms the second part of my theory4 ,as summarized by an ,american astronomer1 ,professor ,henry ,norris ,russell1 of ,princeton1 in the ,scientific ,american for ,november #bi1 ,einstein's contribution amounts to this3 ,the central fact which has been proved--and which is of great interest and importance--is that the natural phenomena involving gravitation and inertia 7such as the motions of the planets7 and the phenomena involving electricity and magnetism 7including the motion of light7 are not independent of one another1 but are intimately related1 so that both sets of phenomena should be regarded as parts of one vast system1 embracing all ,nature4 ,the relation of the two is1 however1 of such a character that it is perceptible only in a very few instances1 and then only to refined observations4 ,already before the war1 ,einstein had immense fame among physicists1 and among all who are interested in the philosophy of science1 because of his principle of relativity4 ,clerk ,maxwell had shown that light is electro-magnetic1 and had reduced the whole theory of electro-magnetism to a small number of equations1 which are fundamental in all subsequent work4 ,but these equations were entangled with the hypothesis of the ether1 and with the notion of motion relative to the ether4 ,since the ether was supposed to be at rest1 such motion was indistinguishable from absolute motion4 ,the motion of the earth relatively to the ether should have been different at different points of its orbit1 and measurable phenomena should have resulted from this difference4 ,but none did1 and all attempts to detect effects of motions relative to the ether failed4 ,the theory of relativity succeeded in accounting for this fact4 ,but it was necessary incidentally to throw over the one universal time1 and substitute local times attached to moving bodies and varying according to their motion4 ,the equations on which the theory of relativity is based are due to ,lorentz1 but ,einstein connected them with his general principle1 namely1 that there must be nothing1 in observable phenomena1 which could be attributed to absolute motion of the observer4 ,in orthodox ,newtonian dynamics the principle of relativity had a simpler form1 which did not require the substitution of local time for general time4 ,but it now appeared that ,newtonian dynamics is only valid when we confine ourselves to velocities much less than that of light4 ,the whole ,galileo-,newton system thus sank to the level of a first approximation1 becoming progressively less exact as the velocities concerned approached that of light4 ,einstein's extension of his principle so as to account for gravitation was made during the war1 and for a considerable period our astronomers were unable to become acquainted with it1 owing to the difficulty of obtaining ,german printed matter4 ,however1 copies of his work ultimately reached the outside world and enabled people to learn more about it4 ,gravitation1 ever since ,newton1 had remained isolated from other forces in nature2 various attempts had been made to account for it1 but without success4 ,the immense unification effected by electro-magnetism apparently left gravitation out of its scope4 ,it seemed that nature had presented a challenge to the physicists which none of them were able to meet4 ,at this point ,einstein intervened with a hypothesis which1 apart altogether from subsequent verification1 deserves to rank as one of the great monuments of human genius4 ,after correcting ,newton1 it remained to correct ,euclid1 and it was in terms of non-,euclidean geometry that he stated his new theory4 ,non-,euclidean geometry is a study of which the primary motive was logical and philosophical2 few of its promoters ever dreamed that it would come to be applied in physics4 ,some of ,euclid's axioms were felt to be not necessary truths1 but mere empirical laws2 in order to establish this view1 self-consistent geometries were constructed upon assumptions other than those of ,euclid4 ,in these geometries the sum of the angles of a triangle is not two right angles1 and the departure from two right angles increases as the size of the triangle increases4 ,it is often said that in non-,euclidean geometry space has a curvature1 but this way of stating the matter is misleading1 since it seems to imply a fourth dimension1 which is not implied by these systems4 ,einstein supposes that space is ,euclidean where it is sufficiently remote from matter1 but that the presence of matter causes it to become slightly non-,euclidean--the more matter there is in the neighborhood1 the more space will depart from ,euclid4 ,by the help of this hypothesis1 together with his previous theory of relativity1 he deduces gravitation--very approximately1 but not exactly1 according to the ,newtonian law of the inverse square4 ,the minute differences between the effects deduced from his theory and those deduced from ,newton are measurable in certain cases4 ,there are1 so far1 three crucial tests of the relative accuracy of the new theory and the old4 7#a7 ,the perihelion of ,mercury shows a discrepancy which has long puzzled astronomers4 ,this discrepancy is fully accounted for by ,einstein4 ,at the time when he published his theory1 this was its only experimental verification4 7#b7 ,modern physicists were willing to suppose that light might be subject to gravitation--i4e41 that a ray of light passing near a great mass like the sun might be deflected to the extent to which a particle moving with the same velocity would be deflected according to the orthodox theory of gravitation4 ,but ,einstein's theory required that the light should be deflected just twice as much as this4 ,the matter could only be tested during an eclipse among a number of bright stars4 ,fortunately a peculiarly favourable eclipse occurred last year4 ,the results of the observations have now been published1 and are found to verify ,einstein's prediction4 ,the verification is not1 of course1 quite exact2 with such delicate observations that was not to be expected4 ,in some cases the departure is considerable4 ,but taking the average of the best series of observations1 the deflection at the sun's limb is found to be #a4ih''1 with a probable error of about #f per cent41 whereas the deflection calculated by ,einstein's theory should be #a4ge''4 ,it will be noticed that ,einstein's theory gave a deflection twice as large as that predicted by the orthodox theory1 and that the observed deflection is slightly larger than ,einstein predicted4 ,the discrepancy is well within what might be expected in view of the minuteness of the measurements4 ,it is therefore generally acknowledged by astronomers that the outcome is a triumph for ,einstein4 7#c7 ,in the excitement of this sensational verification1 there has been a tendency to overlook the third experimental test to which ,einstein's theory was to be subjected4 ,if his theory is correct as it stands1 there ought1 in a gravitational field1 to be a displacement of the lines of the spectrum towards the red4 ,no such effect has been discovered4 ,spectroscopists maintain that1 so far as can be seen at present1 there is no way of accounting for this failure if ,einstein's theory in its present form is assumed4 ,they admit that some compensating cause may be discovered to explain the discrepancy1 but they think it far more probable that ,einstein's theory requires some essential modification4 ,meanwhile1 a certain suspense of judgment is called for4 ,the new law has been so amazingly successful in two of the three tests that there must be some thing valid about it1 even if it is not exactly right as yet4 ,einstein's theory has the very highest degree of aesthetic merit3 every lover of the beautiful must wish it to be true4 ,it gives a vast unified survey of the operations of nature1 with a technical simplicity in the critical assumptions which makes the wealth of deductions astonishing4 ,it is a case of an advance arrived at by pure theory3 the whole effect of ,einstein's work is to make physics more philosophical 7in a good sense71 and to restore some of that intellectual unity which belonged to the great scientific systems of the seventeenth and eighteenth centuries1 but which was lost through increasing specialization and the overwhelming mass of detailed knowledge4 ,in some ways our age is not a good one to live in1 but for those who are interested in physics there are great compensations4 ,,the ,,einstein ,,theory ,,of ,,relativity ,a ,concise ,statement by ,prof4 ,h4 ,a4 ,lorentz1 of the ,university of ,leyden ,the total eclipse of the sun of ,may #bi1 resulted in a striking confirmation of the new theory of the universal attractive power of gravitation developed by ,albert ,einstein1 and thus reinforced the conviction that the defining of this theory is one of the most important steps ever taken in the domain of natural science4 ,in response to a request by the editor1 ,i will attempt to contribute something to its general appreciation in the following lines4 ,for centuries ,newton's doctrine of the attraction of gravitation has been the most prominent example of a theory of natural science4 ,through the simplicity of its basic idea1 an attraction between two bodies proportionate to their mass and also proportionate to the square of the distance2 through the completeness with which it explained so many of the peculiarities in the movement of the bodies making up the solar system2 and1 finally1 through its universal validity1 even in the case of the far-distant planetary systems1 it compelled the admiration of all4 ,but1 while the skill of the mathematicians was devoted to making more exact calculations of the consequences to which it led1 no real progress was made in the science of gravitation4 ,it is true that the inquiry was transferred to the field of physics1 following ,cavendish's success in demonstrating the common attraction between bodies with which laboratory work can be done1 but it always was evident that natural philosophy had no grip on the universal power of attraction4 ,while in electric effects an influence exercised by the matter placed between bodies was speedily observed--the starting-point of a new and fertile doctrine of electricity--in the case of gravitation not a trace of an influence exercised by intermediate matter could ever be discovered4 ,it was1 and remained1 inaccessible and unchangeable1 without any connection1 apparently1 with other phenomena of natural philosophy4 ,einstein has put an end to this isolation2 it is now well established that gravitation affects not only matter1 but also light4 ,thus strengthened in the faith that his theory already has inspired1 we may assume with him that there is not a single physical or chemical phenomenon--which does not feel1 although very probably in an unnoticeable degree1 the influence of gravitation1 and that1 on the other side1 the attraction exercised by a body is limited in the first place by the quantity of matter it contains and also1 to some degree1 by motion and by the physical and chemical condition in which it moves4 ,it is comprehensible that a person could not have arrived at such a far-reaching change of view by continuing to follow the old beaten paths1 but only by introducing some sort of new idea4 ,indeed1 ,einstein arrived at his theory through a train of thought of great originality4 ,let me try to restate it in concise terms4 ,,the ,,earth ,,as ,a ,,moving ,,car ,everyone knows that a person may be sitting in any kind of a vehicle without noticing its progress1 so long as the movement does not vary in direction or speed2 in a car of a fast express train objects fall in just the same way as in a coach that is standing still4 ,only when we look at objects outside the train1 or when the air can enter the car1 do we notice indications of the motion4 ,we may compare the earth with such a moving vehicle1 which in its course around the sun has a remarkable speed1 of which the direction and velocity during a considerable period of time may be regarded as constant4 ,in place of the air now comes1 so it was reasoned formerly1 the ether which fills the spaces of the universe and is the carrier of light and of electro-magnetic phenomena2 there were good reasons to assume that the earth was entirely permeable for the ether and could travel through it without setting it in motion4 ,so here was a case comparable with that of a railroad coach open on all sides4 ,there certainly should have been a powerful ether wind blowing through the earth and all our instruments1 and it was to have been expected that some signs of it would be noticed in connection with some experiment or other4 ,every attempt along that line1 however1 has remained fruitless2 all the phenomena examined were evidently independent of the motion of the earth4 ,that this is the way they do function was brought to the front by ,einstein in his first or special theory of relativity4 ,for him the ether does not function and in the sketch that he draws of natural phenomena there is no mention of that intermediate matter4 ,if the spaces of the universe are filled with an ether1 let us suppose with a substance1 in which1 aside from eventual vibrations and other slight movements1 there is never any crowding or flowing of one part alongside of another1 then we can imagine fixed points existing in it2 for example1 points in a straight line1 located one meter apart1 points in a level plain1 like the angles or squares on a chess board extending out into infinity1 and finally1 points in space as they are obtained by repeatedly shifting that level spot a distance of a meter in the direction perpendicular to it4 ,if1 consequently1 one of the points is chosen as an original point we can1 proceeding from that point1 reach any other point through three steps in the common perpendicular directions in which the points are arranged4 ,the figures showing how many meters are comprized in each of the steps may serve to indicate the place reached and to distinguish it from any other2 these are1 as is said1 the co-ordinates of these places1 comparable1 for example1 with the numbers on a map giving the longitude and latitude4 ,let us imagine that each point has noted upon it the three numbers that give its position1 then we have something comparable with a measure with numbered subdivisions2 only we now have to do1 one might say1 with a good many imaginary measures in three common perpendicular directions4 ,in this system of co-ordinates the numbers that fix the position of one or the other of the bodies may now be read off at any moment4 ,this is the means which the astronomers and their mathematical assistants have always used in dealing with the movement of the heavenly bodies4 ,at a determined moment the position of each body is fixed by its three co-ordinates4 ,if these are given1 then one knows also the common distances1 as well as the angles formed by the connecting lines1 and the movement of a planet is to be known as soon as one knows how its co-ordinates are changing from one moment to the other4 ,thus the picture that one forms of the phenomena stands there as if it were sketched on the canvas of the motionless ether4 ,,einstein',s ,,departure ,since ,einstein has cut loose from the ether1 he lacks this canvas1 and therewith1 at the first glance1 also loses the possibility of fixing the positions of the heavenly bodies and mathematically describing their movement--i4e41 by giving comparisons that define the positions at every moment4 ,how ,einstein has overcome this difficulty may be somewhat elucidated through a simple illustration4 ,on the surface of the earth the attraction of gravitation causes all bodies to fall along vertical lines1 and1 indeed1 when one omits the resistance of the air1 with an equally accelerated movement2 the velocity increases in equal degrees in equal consecutive divisions of time at a rate that in this country gives the velocity attained at the end of a second as #iha centimeters 7#cb4b feet7 per second4 ,the number #iha defines the acceleration in the field of gravitation1 and this field is fully characterized by that single number2 with its help we can also calculate the movement of an object hurled out in an arbitrary direction4 ,in order to measure the acceleration we let the body drop alongside of a vertical measure set solidly on the ground2 on this scale we read at every moment the figure that indicates the height1 the only co-ordinate that is of importance in this rectilinear movement4 ,now we ask what would we be able to see if the measure were not bound solidly to the earth1 if it1 let us suppose1 moved down or up with the place where it is located and where we are ourselves4 ,if in this case the speed were constant1 then1 and this is in accord with the special theory of relativity1 there would be no motion observed at all2 we should again find an acceleration of #iha for a falling body4 ,it would be different if the measure moved with changeable velocity4 ,if it went down with a constant acceleration of #iha itself1 then an object could remain permanently at the same point on the measure1 or could move up or down itself alongside of it1 with constant speed4 ,the relative movement of the body with regard to the measure should be without acceleration1 and if we had to judge only by what we observed in the spot where we were and which was falling itself1 then we should get the impression that there was no gravitation at all4 ,if the measure goes down with an acceleration equal to a half or a third of what it just was1 then the relative motion of the body will1 of course1 be accelerated1 but we should find the increase in velocity per second one-half or two-thirds of #iha4 ,if1 finally1 we let the measure rise with a uniformly accelerated movement1 then we shall find a greater acceleration than #iha for the body itself4 ,thus we see that we1 also when the measure is not attached to the earth1 disregarding its displacement1 may describe the motion of the body in respect to the measure always in the same way--i4e41 as one uniformly accelerated1 as we ascribe now and again a fixed value to the acceleration of the sphere of gravitation1 in a particular case the value of zero4 ,of course1 in the case here under consideration the use of a measure fixed immovably upon the earth should merit all recommendation4 ,but in the spaces of the solar system we have1 now that we have abandoned the ether1 no such support4 ,we can no longer establish a system of co-ordinates1 like the one just mentioned1 in a universal intermediate matter1 and if we were to arrive in one way or another at a definite system of lines crossing each other in three directions1 then we should be able to use just as well another similar system that in respect to the first moves this or that way4 ,we should also be able to remodel the system of co-ordinates in all kinds of ways1 for example by extension or compression4 ,that in all these cases for fixed bodies that do not participate in the movement or the remodelling of the system other co-ordinates will be read off again and again is clear4 ,,new ,,system ,,or ,,co-,,ordinates ,what way ,einstein had to follow is now apparent4 ,he must--this hardly needs to be said--in calculating definite1 particular cases make use of a chosen system of co-ordinates1 but as he had no means of limiting his choice beforehand and in general1 he had to reserve full liberty of action in this respect4 ,therefore he made it his aim so to arrange the theory that1 no matter how the choice was made1 the phenomena of gravitation1 so far as its effects and its stimulation by the attracting bodies are concerned1 may always be described in the same way--i4e41 through comparisons of the same general form1 as we again and again give certain values to the numbers that mark the sphere of gravitation4 7,for the sake of simplification ,i here disregard the fact that ,einstein desires that also the way in which time is measured and represented by figures shall have no influence upon the central value of the comparisons47 ,whether this aim could be attained was a question of mathematical inquiry4 ,it really was attained1 remarkably enough1 and1 we may say1 to the surprise of ,einstein himself1 although at the cost of considerable simplicity in the mathematical form2 it appeared necessary for the fixation of the field of gravitation in one or the other point in space to introduce no fewer than ten quantities in the place of the one that occurred in the example mentioned above4 ,in this connection it is of importance to note that when we exclude certain possibilities that would give rise to still greater intricacy1 the form of comparison used by ,einstein to present the theory is the only possible one2 the principle of the freedom of choice in co-ordinates was the only one by which he needed to allow himself to be guided4 ,although thus there was no special effort made to reach a connection with the theory of ,newton1 it was evident1 fortunately1 at the end of the experiment that the connection existed4 ,if we avail ourselves of the simplifying circumstance that the velocities of the heavenly bodies are slight in comparison with that of light1 then we can deduce the theory of ,newton from the new theory1 the universal relativity theory1 as it is called by ,einstein4 ,thus all the conclusions based upon the ,newtonian theory hold good1 as must naturally be required4 ,but now we have got further along4 ,the ,newtonian theory can no longer be regarded as absolutely correct in all cases2 there are slight deviations from it1 which1 although as a rule unnoticeable1 once in a while fall within the range of observation4 ,now1 there was a difficulty in the movement of the planet ,mercury which could not be solved4 ,even after all the disturbances caused by the attraction of other planets had been taken into account1 there remained an inexplicable phenomenon--i4e41 an extremely slow turning of the ellipsis described by ,mercury on its own plane2 ,leverrier had found that it amounted to forty-three seconds a century4 ,einstein found that1 according to his formulas1 this movement must really amount to just that much4 ,thus with a single blow he solved one of the greatest puzzles of astronomy4 ,still more remarkable1 because it has a bearing upon a phenomenon which formerly could not be imagined1 is the confirmation of ,einstein's prediction regarding the influence of gravitation upon the course of the rays of light4 ,that such an influence must exist is taught by a simple examination2 we have only to turn back for a moment to the following comparison in which we were just imagining ourselves to make our observations4 ,it was noted that when the compartment is falling with the acceleration of #iha the phenomena therein will occur just as if there were no attraction of gravitation4 ,we can then see an object1 ,a1 stand still somewhere in open space4 ,a projectile1 ,b1 can travel with constant speed along a horizontal line1 without varying from it in the slightest4 ,a ray of light can do the same2 everybody will admit that in each case1 if there is no gravitation1 light will certainly extend itself in a rectilinear way4 ,if we limit the light to a flicker of the slightest duration1 so that only a little bit1 ,c1 of a ray of light arises1 or if we fix our attention upon a single vibration of light1 ,c1 while we on the other hand give to the projectile1 ,b1 a speed equal to that of light1 then we can conclude that ,b and ,c in their continued motion can always remain next to each other4 ,now if we watch all this1 not from the movable compartment1 but from a place on the earth1 then we shall note the usual falling movement of object ,a1 which shows us that we have to deal with a sphere of gravitation4 ,the projectile ,b will1 in a bent path1 vary more and more from a horizontal straight line1 and the light will do the same1 because if we observe the movements from another standpoint this can have no effect upon the remaining next to each other of ,b and ,c4 ,,deflection ,,of ,,light ,the bending of a ray of light thus described is much too light on the surface of the earth to be observed4 ,but the attraction of gravitation exercised by the sun on its surface is1 because of its great mass1 more than twenty-seven times stronger1 and a ray of light that goes close by the superficies of the sun must surely be noticeably bent4 ,the rays of a star that are seen at a short distance from the edge of the sun will1 going along the sun1 deviate so much from the original direction that they strike the eye of an observer as if they came in a straight line from a point somewhat further removed than the real position of the star from the sun4 ,it is at that point that we think we see the star2 so here is a seeming displacement from the sun1 which increases in the measure in which the star is observed closer to the sun4 ,the ,einstein theory teaches that the displacement is in inverse proportion to the apparent distance of the star from the centre of the sun1 and that for a star just on its edge it will amount to #a'4ge 7#a4ge seconds74 ,this is approximately the thousandth part of the apparent diameter of the sun4 ,naturally1 the phenomenon can only be observed when there is a total eclipse of the sun2 then one can take photographs of neighboring stars and through comparing the plate with a picture of the same part of the heavens taken at a time when the sun was far removed from that point the sought-for movement to one side may become apparent4 ,thus to put the ,einstein theory to the test was the principal aim of the ,english expeditions sent out to observe the eclipse of ,may #bi1 one to ,prince's ,island1 off the coast of ,guinea1 and the other to ,sobral1 ,brazil4 ,the first-named expedition's observers were ,eddington and ,cottingham1 those of the second1 ,crommelin and ,davidson4 ,the conditions were especially favorable1 for a very large number of bright stars were shown on the photographic plate2 the observers at ,sobral being particularly lucky in having good weather4 ,the total eclipse lasted five minutes1 during four of which it was perfectly clear1 so that good photographs could be taken4 ,in the report issued regarding the results the following figures1 which are the average of the measurements made from the seven plates1 are given for the displacements of seven stars3 #a''4jb1 #j''4ib1 #j''4hd1 #j''4eh1 #j''4ed1 #j''4cf1 #j''4bd1 whereas1 according to the theory1 the displacements should have amounted to3 #j''4hh1 #j''4hj1 #j''4ge1 #j''4dj1 #j''4eb1 #j''4cc1 #j''4bj4 ,if we consider that1 according to the theory the displacements must be in inverse ratio to the distance from the centre of the sun1 then we may deduce from each observed displacement how great the sideways movement for a star at the edge of the sun should have been4 ,as the most probable result1 therefore1 the number #a''4ih was found from all the observations together4 ,as the last of the displacements given above--i4e41 #j''4bd is about one-eighth of this1 we may say that the influence of the attraction of the sun upon light made itself felt upon the ray at a distance eight times removed from its centre4 ,the displacements calculated according to the theory are1 just because of the way in which they are calculated1 in inverse proportion to the distance to the centre4 ,now that the observed deviations also accord with the same rule1 it follows that they are surely proportionate with the calculated displacements4 ,the proportion of the first and the last observed sidewise movements is #d4b1 and that of the two most extreme of the calculated numbers is #d4d4 ,this result is of importance1 because thereby the theory is excluded1 or at least made extremely improbable1 that the phenomenon of refraction is to be ascribed to1 a ring of vapor surrounding the sun for a great distance4 ,indeed1 such a refraction should cause a deviation in the observed direction1 and1 in order to produce the displacement of one of the stars under observation itself a slight proximity of the vapor ring should be sufficient1 but we have every reason to expect that if it were merely a question of a mass of gas around the sun the diminishing effect accompanying a removal from the sun should manifest itself much faster than is really the case4 ,we cannot speak with perfect certainty here1 as all the factors that might be of influence upon the distribution of density in a sun atmosphere are not well enough known1 but we can surely demonstrate that in case one of the gasses with which we are acquainted were held in equilibrium solely by the influence of attraction of the sun the phenomenon should become much less as soon as we got somewhat further from the edge of the sun4 ,if the displacement of the first star1 which amounts to #a4jb-seconds were to be ascribed to such a mass of gas1 then the displacement of the second must already be entirely inappreciable4 ,so far as the absolute extent of the displacements is concerned1 it was found somewhat too great1 as has been shown by the figures given above2 it also appears from the final result to be #a4ih for the edge of the sun--i4e41 #ac per cent1 greater than the theoretical value of #a4ge4 ,it indeed seems that the discrepancies may be ascribed to faults in observations1 which supposition is supported by the fact that the observations at ,prince's ,island1 which1 it is true1 did not turn out quite as well as those mentioned above1 gave the result1 of #a4fd1 somewhat lower than ,einstein's figure4 7,the observations made with a second instrument at ,sobral gave a result of #j4ic1 but the observers are of the opinion that because of the shifting of the mirror which reflected the rays no value is to be attached to it47 ,,difficulty ,,exaggerated ,during a discussion of the results obtained at a joint meeting of the ,royal ,society and the ,royal ,astronomical ,society held especially for that purpose recently in ,london1 it was the general opinion that ,einstein's prediction might be regarded as justified1 and warm tributes to his genius were made on all sides4 ,nevertheless1 ,i cannot refrain1 while ,i am mentioning it1 from expressing my surprise that1 according to the report in ,the ,times there should be so much complaint about the difficulty of understanding the new theory4 ,it is evident that ,einstein's little book ,about the ,special and the ,general ,theory of ,relativity in ,plain ,terms1 did not find its way into ,england during wartime4 ,any one reading it will1 in my opinion1 come to the conclusion that the basic ideas of the theory are really clear and simple2 it is only to be regretted that it was impossible to avoid clothing them in pretty involved mathematical terms1 but we must not worry about that4 ,i allow myself to add that1 as we follow ,einstein1 we may retain much of what has been formerly gained4 ,the ,newtonian theory remains in its full value as the first great step1 without which one cannot imagine the development of astronomy and without which the second step1 that has now been made1 would hardly have been possible4 ,it remains1 moreover1 as the first1 and in most cases1 sufficient1 approximation4 ,it is true that1 according to ,einstein's theory1 because it leaves us entirely free as to the way in which we wish to represent the phenomena1 we can imagine an idea of the solar system in which the planets follow paths of peculiar form and the rays of light shine along sharply bent lines--think of a twisted and distorted planetarium--but in every case where we apply it to concrete questions we shall so arrange it that the planets describe almost exact ellipses and the rays of light almost straight lines4 ,it is not necessary to give up entirely even the ether4 ,many natural philosophers find satisfaction in the idea of a material intermediate substance in which the vibrations of light take place1 and they will very probably be all the more inclined to imagine such a medium when they learn that1 according to the ,einstein theory1 gravitation itself does not spread instantaneously1 but with a velocity that at the first estimate may be compared with that of light4 ,especially in former years were such interpretations current and repeated attempts were made by speculations about the nature of the ether and about the mutations and movements that might take place in it to arrive at a clear presentation of electro-magnetic phenomena1 and also of the functioning of gravitation4 ,in my opinion it is not impossible that in the future this road1 indeed abandoned at present1 will once more be followed with good results1 if only because it can lead to the thinking out of new experimental tests4 ,einstein's theory need not keep us from so doing2 only the ideas about the ether must accord with it4 ,nevertheless1 even without the color and clearness that the ether theories and the other models may be able to give1 and even1 we can feel it this way1 just because of the soberness induced by their absence1 ,einstein's work1 we may now positively expect1 will remain a monument of science2 his theory entirely fulfills the first and principal demand that we may make1 that of deducing the course of phenomena from certain principles exactly and to the smallest details4 ,it was certainly fortunate that he himself put the ether in the background2 if he had not done so1 he probably would never have come upon the idea that has been the foundation of all his examinations4 ,thanks to his indefatigable exertions and perseverance1 for he had great difficulties to overcome in his attempts1 ,einstein has attained the results1 which ,i have tried to sketch1 while still young2 he is now #de years old4 ,he completed his first investigations in ,switzerland1 where he first was engaged in the ,patent ,bureau at ,berne and later as a professor at the ,polytechnic in ,zurich4 ,after having been a professor for a short time at the ,university of ,prague1 he settled in ,berlin1 where the ,kaiser ,wilhelm ,institute afforded him the opportunity to devote himself exclusively to his scientific work4 ,he repeatedly visited our country and made his ,netherland colleagues1 among whom he counts many good friends1 partners in his studies and his results4 ,he attended the last meeting of the department of natural philosophy of the ,royal ,academy of ,sciences1 and the members then had the privilege of hearing him explain1 in his own fascinating1 clear and simple way1 his interpretations of the fundamental questions to which his theory gives rise4