,from ,,newton to ,,einstein ,changing ,conceptions of ,,the ,,universe ,,by ,,benjamin ,,harrow1 ,ph4,d4 ,,second ,,edition1 ,,revised ,,and ,,enlarged ,with ,articles by ,prof4 ,einstein1 ,prof4 ,j4 ,s4 ,ames 7,johns ,hopkins71 ,sir ,frank ,dyson 7,astronomer ,royal71 ,prof4 ,a4 ,s4 ,eddington 7,cambridge7 and ,sir ,j4 ,j4 ,thomson 7,president of the ,royal ,society7 ,portraits and ,illustrations ,,new ,,york ,d4 ,,van ,,nostrand ,,company ,eight ,warren ,street #aibj ,,preface ,einstein's contributions to our ideas of time and space1 and to our knowledge of the universe in general1 are of so momentous a nature1 that they easily take their place among the two or three greatest achievements of the twentieth century4 ,this little book attempts to give1 in popular form1 an account of this work4 ,as1 however1 ,einstein's work is so largely dependent upon the work of ,newton and ,newton's successors1 the first two chapters are devoted to the latter4 ,b4 ,h4 ,,preface ,,to ,,second ,,edition ,the preparation of this new edition has made it possible to correct errors1 to further amplify certain portions of the text and to enlarge the ever-increasing bibliography on the subject4 ,photographs of ,professors ,j4 ,j4 ,thomson1 ,michelson1 ,minkowski and ,lorentz are also new features in this edition4 ,the explanatory notes and articles in the ,appendix will1 ,i believe1 present no difficulties to readers who have mastered the contents of the book4 ,they are in fact popular expositions of various phases of the ,einstein theory2 but experience has shown that even popular expositions of the theory need further popular introductions4 ,i wish to take this opportunity of thanking ,prof4 ,einstein1 ,prof4 ,a4 ,a4 ,michelson of the ,university of ,chicago1 ,prof4 ,j4 ,s4 ,ames of ,johns ,hopkins ,university1 and ,professor ,g4 ,b4 ,pegram of ,columbia ,university for help in various ways which they were good enough to extend to me4 ,prof4 ,j4 ,s4 ,ames and the editor of ,science have been kind enough to allow me to reprint the former's excellent presidential address on ,einstein's theory1 delivered before the members of the ,american ,physical ,society4 ,b4 ,h4 ,,table ,,of ,,contents ,,page ,i4 ,newton #a ,,ii4 ,the ,ether and ,its ,consequences #bg ,,iii4 ,einstein #da ,,iv4 ,appendix #ha ,time1 ,space and ,gravitation1 by ,prof4 ,einstein #hh ,einstein's ,law of ,gravitation1 by ,prof4 ,j4 ,s4 ,ames #ic ,the ,deflection of light by ,gravitation and the ,einstein ,theory of ,relativity1 by ,sir ,frank ,dyson1 ,prof4 ,a4 ,s4 ,eddington and ,sir ,j4 ,j4 ,thomson #aab ,,newton ,newton was the greatest genius that ever existed4--,lagrange1 one of the greatest of ,french mathematicians4 ,the efforts of the great philosopher were always superhuman2 the questions which he did not solve were incapable of solution in his time4--,arago1 famous ,french astronomer4 ,,einstein ,this is the most important result obtained in connection with the theory of gravitation since ,newton's day4 ,einstein's reasoning is the result of one of the highest achievements of human thought4--,sir ,j4 ,j4 ,thomson1 president of the ,british ,royal ,society and professor of physics at the ,university of ,cambridge4 ,it surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge4 ,the revolution introduced into the physical conceptions of the world is only to be compared in extent and depth with that brought about by the introduction of the ,copernican system of the universe4--,prof4 ,max ,planck1 professor of physics at the ,university of ,berlin and winner of the ,nobel ,prize4 ,i ,,newton ,in speaking of ,newton we are tempted to paraphrase a line from the ,scriptures3 ,before ,newton the ,solar ,system was without form1 and void2 then ,newton came and there was light4 ,to have discovered a law not only applicable to matter on this earth1 but to the planets and sun and stars beyond1 is a triumph which places ,newton among the super-men4 ,what ,newton's law of gravitation must have meant to the people of his day can be pictured only if we conceive what the effect upon us would be if someone--say ,marconi--were actually to succeed in getting into touch with beings on another planet4 ,newton's law increased confidence in the universality of earthly laws2 and it strengthened belief in the cosmos as a law-abiding mechanism4 ,newton's ,law4 ,the attraction between any two bodies is proportional to their masses and inversely proportional to the square of the distance that separates them4 ,this is the concentrated form of ,newton's law4 ,if we apply this law to two such bodies as the sun and the earth1 we can state that the sun attracts the earth1 and the earth1 the sun4 ,furthermore1 this attractive power will depend upon the distance between these two bodies4 ,newton showed that if the distance between the sun and the earth were doubled the attractive power would be reduced not to one-half1 but to one-fourth2 if trebled1 the attractive power would be reduced to one-ninth4 ,if1 on the other hand1 the distance were halved1 the attractive power would be not merely twice1 but four times as great4 ,and what is true of the sun and the earth is true of every body in the firmament1 and1 as ,professor ,rutherford has recently shown1 even of the bodies which make up the solar system of the almost infinitesimal atom4 ,this mysterious attractive power that one body possesses for another is called gravitation1 and the law which regulates the motion of bodies when under the spell of gravitation is the law of gravitation4 ,this law we owe to ,newton's genius4 ,newton's ,predecessors4 ,we can best appreciate ,newton's momentous contribution to astronomy by casting a rapid glance over the state of the science prior to the seventeenth century--that is1 prior to ,newton's day4 ,ptolemy's conception of the earth as the center of the universe held undisputed sway throughout the middle ages4 ,in those days ,ptolemy was in astronomy what ,aristotle was in all other knowledge3 they were the gods who could not but be right4 ,did not ,aristotle say that earth1 air1 fire and water constituted the four elements8 ,did not ,ptolemy say that the earth was the center around which the sun revolved8 ,why1 then1 question further8 ,questioning was a sacrilege4 ,copernicus 7#adgc-aedc71 however1 did question4 ,he studied much and thought much4 ,he devoted his whole life to the investigation of the movements of the heavenly bodies4 ,and he came to the conclusion that ,ptolemy and his followers in succeeding ages had expounded views which were diametrically opposed to the truth4 ,the sun1 said ,copernicus1 did not move at all1 but the earth did2 and far from the earth being the center of the universe1 it was but one of several planets revolving around the sun4 ,the influence of the church1 coupled with man's inclination to exalt his own importance1 strongly tended against the acceptance of such heterodox views4 ,among the many hostile critics of the ,copernican system1 ,tycho ,brahe 7#aedf-afja7 stands out pre-eminently4 ,this conscientious observer bitterly assailed ,copernicus for his suggestion that the earth moved1 and developed a scheme of his own which postulated that the planets revolved around the sun1 and planets and sun in turn revolved around the earth4 ,the majority applauded ,tycho2 a small1 very small group of insurgents had faith in ,copernicus4 ,the illustrious ,galileo 7#aefd-afdb7 belonged to the minority4 ,the telescope of his invention unfolded a view of the universe which belied the assertions of the many1 and strengthened his belief in the ,copernican theory4 ,it 7the ,copernican theory7 explains to me the cause of many phenomena which under the generally accepted theory are quite unintelligible4 ,i have collected arguments for refuting the latter1 but ,i do not venture to bring them to publication4 ,so wrote ,galileo to his friend1 ,kepler4 ,i do not venture to bring them to publication4 ,how significant of the times--of any time1 one ventures to add4 ,galileo did overcome his hesitancy and published his views4 ,they aroused a storm4 ,look through my telescope1 he pleaded4 ,but the professors would not2 neither would the body of ,inquisitors4 ,the ,inquisition condemned him3 ,the proposition that the sun is in the center of the earth and immovable from its place is absurd1 philosophically false and formally heretical2 because it is expressly contrary to the ,holy ,scriptures4 ,and poor ,galileo was made to utter words which were as far removed from his thoughts as his oppressors' ideas were from the truth3 ,i abjure1 curse and detest the said errors and heresies4 ,the truth will out4 ,others arose who defied the majority and the powerful ,inquisition4 ,most prominent of all of these was ,galileo's friend1 ,kepler4 ,though a student of ,tycho1 ,kepler did not hesitate to espouse the ,copernican system2 but his adoption of it did not mean unqualified approval4 ,kepler's criticism was particularly directed against the ,copernican theory that the planets revolve in circles4 ,this was boldness in the extreme4 ,ever since ,aristotle's discourse on the circle as a perfect figure1 it was taken for granted that motion in space was circular4 ,nature is perfect2 the circle is perfect2 hence1 if the sun revolves1 it revolves in circles4 ,so strongly were men imbued with this perfection1 that ,copernicus himself fell victim4 ,the sun no longer moved1 but the earth and the planets did1 and they moved in a circle4 ,radical as ,copernicus was1 a few atoms of conservatism remained with him still4 ,not so ,kepler4 ,tycho had taught him the importance of careful observation1--to such good effect1 that ,kepler came to the conclusion that the revolution of the earth around the sun takes the form of an ellipse rather than a circle1 the sun being stationed at one of the foci of the ellipse4 ,to picture this ellipse1 we shall ask the reader to stick two pins a short distance apart into a piece of cardboard1 and to place over the pins a loop of string4 ,with the point of a pencil draw the loop taut4 ,as the pencil moves around the two pins the curve so produced will be an ellipse4 ,the positions of the two pins represent the two foci4 ,kepler's observation of the elliptical rotation of the planets was the first of three laws1 quantitatively expressed1 which paved the way for ,newton's law4 ,why did the planets move in just this way8 ,kepler tried to answer this also1 but failed4 ,it remained for ,newton to supply the answer to this question4 ,newton's ,law of ,gravitation4 ,the ,great ,plague of #afff drove ,newton from ,cambridge to his home in ,lincolnshire4 ,there1 according to the celebrated legend1 the philosopher sitting in his little garden one fine afternoon1 fell into a deep reverie4 ,this was interrupted by the fall of an apple1 and the thinker turned his attention to the apple and its fall4 ,it must not be supposed that ,newton discovered gravity4 ,apples had been seen to fall before ,newton's time1 and the reason for their return to earth was correctly attributed to this mysterious force of attraction possessed by the earth1 to which the name gravity had been given4 ,newton's great triumph consisted in showing that this gravity1 which was supposed to be a peculiar property residing in the earth1 was a universal property of matter2 that it applied to the moon and the sun as well as to the earth2 that1 in fact1 the motions of the moon and the planets could be explained on the basis of gravitation4 ,but his supreme triumph was to give1 in one sublime generalization1 quantitative expression to the motion regulating heavenly bodies4 ,let us follow ,newton in his train of thought4 ,an apple falls from a tree #ej yards high4 ,it would fall from a tree #ejj yards high4 ,it would fall from the highest mountain top several miles above sea level4 ,it would probably fall from a height much above the mountain top4 ,why not8 ,probably the further up you go the less does the earth attract the apple1 but at what distance does this attraction stop entirely8 ,the nearest body in space to the earth is the moon1 some #bdj1jjj miles away4 ,would an apple reach the earth if thrown from the moon8 ,but perhaps the moon itself has attractive power8 ,if so1 since the apple would be much nearer the moon than the earth1 the probabilities are that the apple would never reach the earth4 ,but hold6 ,the apple is not the only object that falls to the ground4 ,what is true of the apple is true of all other bodies--of all matter1 large and small4 ,now there is the moon itself1 a very large body4 ,does the earth exert any gravitational pull on the moon8 ,to be sure1 the moon is many thousands of miles away1 but the moon is a very large body1 and perhaps this size is in some way related to the power of attraction8 ,but then if the earth attracts the moon1 why does not the moon fall to the earth8 ,a glance at the accompanying figure will help to answer this question4 ,we must remember that the moon is not stationary1 but travelling at tremendous speed--so much so1 that it circles the entire earth every month4 ,now if the earth were absent the path of the moon would be a straight line1 say ,,mb4 ,if1 however1 the earth exerts attraction1 the moon would be pulled inward4 ,instead of following the line ,,mb it would follow the curved path ,,mb'4 ,and again1 the moon having arrived at ,b'1 is prevented from following the line ,b',c1 but rather ,b',c'4 ,so that the path instead of being a straight line tends to become curved4 ,from ,kepler's researches the probabilities were that this curve would assume the shape of an ellipse rather than a circle4 ,the only reason1 then1 why the moon does not fall to the earth is on account of its motion4 ,were it to stop moving even for the fraction of a second it would come straight down to us1 and probably few would live to tell the tale4 ,newton reasoned that what keeps the moon revolving around the earth is the gravitational pull of the latter4 ,the next important step was to discover the law regulating this motion4 ,here ,kepler's observations of the movements of the planets around the sun was of inestimable value2 for from these ,newton deduced the hypothesis that attraction varies inversely as the square of the distance4 ,making use of this hypothesis1 ,newton calculated what the attractive power possessed by the earth must be in order that the moon may continue in its path4 ,he next compared this force with the force exerted by the earth in pulling the apple to the ground1 and found the forces to be identical6 ,i compared1 he writes1 the force necessary to keep the moon in her orb with the force of gravity at the surface of the earth1 and found them answer pretty nearly4 ,one and the same force pulls the moon and pulls the apple--the force of gravity4 ,further1 the hypothesis that the force of gravity varies inversely as the square of the distance had now received experimental confirmation4 ,the next step was perfectly clear4 ,if the moon's motion is controlled by the earth's gravitational pull1 why is it not possible that the earth's motion1 in turn1 is controlled by the sun's gravitational pull8 that1 in fact1 not only the earth's motion1 but the motion of all the planets is regulated by the same means8 ,here again ,kepler's pioneer work was a foundation comparable to reinforced concrete4 ,kepler1 as we have seen1 had shown that the earth revolves around the sun in the form of an ellipse1 one of the foci of this ellipse being occupied by the sun4 ,newton now proved that such an elliptic path was possible only if the intensity of the attractive force between sun and planet varied inversely as the square of the distance--the very same relationship that had been applied with such success in explaining the motion of the moon around the earth6 ,newton showed that the moon1 the sun1 the planets--every body in space conformed to this law4 ,the earth attracts the moon2 but so does the moon the earth4 ,if the moon revolves around the earth rather than the earth around the moon1 it is because the earth is a much larger body1 and hence its gravitational pull is stronger4 ,the same is true of the relationship existing between the earth and the sun4 ,further ,developments of ,newton's ,law of ,gravitation4 ,when we speak of the earth attracting the moon1 and the moon the earth1 what we really mean is that every one of the myriad particles composing the earth attracts every one of the myriad particles composing the moon1 and vice versa4 ,if in dealing with the attractive forces existing between a planet and its satellite1 or a planet and the sun1 the power exerted by every one of these myriad particles would have to be considered separately1 then the mathematical task of computing such forces might well appear hopeless4 ,newton was able to present the problem in a very simple form by pointing out that in a sphere such as the earth or the moon1 the entire mass might be considered as residing in the center of the sphere4 ,for purposes of computation1 the earth can be considered a particle1 with its entire mass concentrated at the center of the particle4 ,this viewpoint enabled ,newton to extend his law of inverse squares to the remotest bodies in the universe4 ,if this great law of ,newton's found such general application beyond our planet1 it served an equally useful purpose in explaining a number of puzzling features on this planet4 ,the ebb and flow of the tides was one of these puzzles4 ,even in ancient times it had been noticed that a full moon and a high tide went hand in hand1 and various mysterious powers1 were attributed to the satellite and the ocean4 ,newton pointed out that the height of the water was a direct consequence of the attractive power of the moon1 and1 to a lesser extent1 because further away1 of the sun4 ,one of his first explanations1 however1 dealt with certain irregularities in the moon's motion around the earth4 ,if the solar system would consist of the earth and moon alone1 then the path of the moon would be that of an ellipse1 with one of the foci of this ellipse occupied by the earth4 ,unfortunately for the simplicity of the problem1 there are other bodies relatively near in space1 particularly that huge body1 the sun4 ,the sun not only exerts its pull on the earth but also on the moon4 ,however1 as the sun is much further away from the moon than is the earth1 the earth's attraction for its satellite is much greater1 despite the fact that the sun is much huger and weighs far more than the earth4 ,the greater pull of the earth in one direction1 and a lesser pull of the sun in another1 places the poor moon between the devil and the deep sea4 ,the situation gives rise to a complexity of forces1 the net result of which is that the moon's orbit is not quite that of an ellipse4 ,newton was able to account for all the forces that come into play1 and he proved that the actual path of the moon was a direct consequence of the law of inverse squares in actual operation4 ,the ,principia4 ,the law of gravitation1 embodying also laws of motion1 which we shall discuss presently1 was first published in ,newton's immortal ,principia 7#afhf74 ,a selection from the preface will disclose the contents of the book1 and1 incidentally1 the style of the author3 444 ,we offer this work as mathematical principles of philosophy2 for all the difficulty in philosophy seems to consist in this--from the phenomena of motions to investigate the forces of nature1 and then from these forces to demonstrate the other phenomena2 and to this end the general propositions in the first and second book are directed4 ,in the third book we give an example of this in the explication of the system of the world2 for by the propositions mathematically demonstrated in the first book1 we there derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets4 ,then1 from these forces1 by other propositions which are also mathematical1 we deduce the motions of the planets1 the comets1 the moon and the sea4 ,i wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles2 for ,i am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies1 by some causes hitherto unknown1 are either mutually impelled towards each other1 and cohere in regular figures1 or are repelled and recede from each other4444 ,at this point we may state that neither ,newton1 nor any of ,newton's successors including ,einstein1 have been able to advance even a plausible theory as to the nature of this gravitational force4 ,we know that this force pulls a stone to the ground2 we know1 thanks to ,newton1 the laws regulating the motions due to gravity2 but what this force we call gravity really is we do not know4 ,the mystery is as deep as the mystery of the origin of life4 ,prof4 ,einstein1 writes ,prof4 ,eddington1 has sought1 and has not reached1 any ultimate explanation of its that is1 gravitation cause4 ,a certain connection between the gravitational field and the measurement of space has been postulated1 but this throws light rather on the nature of our measurements than on gravitation itself4 ,the relativity theory is indifferent to hypotheses as to the nature of gravitation1 just as it is indifferent to hypotheses as to the nature of light4 ,newton's ,laws of ,motion4 ,in his ,principia ,newton begins with a series of simple definitions dealing with matter and force1 and these are followed by his three famous laws of motion4 ,the nature and amount of the effort required to start a body moving1 and the conditions required to keep a body in motion1 are included in these laws4 ,the ,fundamentals1 mass1 time and space1 are exhibited in their various relationships4 ,of importance to us particularly is that in these laws1 time and space are considered as definite entities1 and as two distinct and widely separated manifestations4 ,we shall see that in ,einstein's hands a very close relationship between these two is brought about4 ,both ,newton and ,einstein were led to their theory of gravitation by profound studies of the mathematics of motion1 but as ,newton's conception of motion differed from ,einstein's1 and as1 moreover1 important discoveries into the nature of matter and the relationship of motion to matter were made subsequent to ,newton's time1 we need not wonder that the two theories show divergence2 that1 as we shall see1 ,newton's is probably but an approximation of the truth4 ,if we confine our attention to our own solar system1 the deviation from ,newton's law is1 as a rule1 so small as to be negligible4 ,newton's laws of motion are really axioms1 like the axioms of ,euclid3 they do not admit of direct proof2 but there is this difference1 that the axioms of ,euclid seem more obviously true4 ,for example1 when ,euclid informs us that things which are equal to the same thing are equal to one another1 we have no hesitation in accepting this statement1 for it seems so self-evident4 ,when1 however1 we are told by ,newton that the alteration of motion is ever proportional to the motive force impressed1 we are at first somewhat bewildered with the phraseology1 and then1 even when that has been mastered1 the readiness with which we respond will probably depend upon the amount of scientific training we have received4 ,every body continues in its state of rest or of uniform motion in a straight line1 unless it is compelled to change that state by forces impressed thereon4 ,so runs ,newton's first law of motion4 ,a body does not move unless something causes it to move2 to make the body move you must overcome the inertia of the body4 ,on the other hand1 if a body is moving1 it tends to continue moving1 as witness our forward movement when the train is brought to a standstill4 ,it may be asked1 why does not a bullet continue moving indefinitely once it has left the barrel of the gun8 ,because of the resistance of the air which it has to overcome2 and the path of the bullet is not straight because gravity acts on it and tends to pull it downwards4 ,we have no definite means of proving that a body once set in motion would continue moving1 for an indefinite time1 and along a straight line4 ,what ,newton meant was that a body would continue moving provided no external force acted on it2 but in actual practise such a condition is unknown4 ,newton's first law defines force as that action necessary to change a state of rest or of uniform motion1 and tells us that force alone changes the motion of a body4 ,his second law deals with the relation of the force applied and the resulting change of motion of the body2 that is1 it shows us how force may be measured4 ,the alteration of motion is ever proportional to the motive force impressed1 and is made in the direction of the right line in which that force is impressed4 ,newton's third law runs--,to every action there is always opposed an equal reaction4 ,the very fact that you have to use force means that you have to overcome something of an opposite nature4 ,the forward pull of a horse towing a boat equals the backward pull of the tow-rope connecting boat and horse4 ,many people1 says ,prof4 ,watson1 find a difficulty in accepting this statement 444 since they think that if the force exerted by the horse on the rope were not a little greater than the backward force exerted by the rope on the horse1 the boat would not progress4 ,in this case we must1 however1 remember that1 as far as their relative positions are concerned1 the horse and the boat are at rest1 and form a single body1 and the action and reaction between them1 due to the tension on the rope1 must be equal and opposite1 for otherwise there would be relative motion1 one with respect to the other4 ,it may well be asked1 what bearing have these laws of ,newton on the question of time and space8 ,simply this1 that to measure force the factors necessary are the masses of the bodies concerned1 the time involved and the space covered2 and ,newton's equations for measuring forces assume time and space to be quite independent of one another4 ,as we shall see1 this is in striking contrast to ,einstein's view4 ,newton's ,researches on ,light4 ,in #affe1 when but #bc years old1 ,newton invented the binomial theorem and the infinitesimal calculus1 two phases of pure mathematics which have been the cause of many a sleepless night to college freshmen4 ,had ,newton done nothing else his fame would have been secure4 ,but we have already glanced at his law of inverse squares and the law of gravitation4 ,we now have to turn to some of ,newton's contributions to optics1 because here more than elsewhere we shall find the starting point to a series of researches which have culminated so brilliantly in the work of ,einstein4 ,newton turned his attention to optics in #afff when he proved that the light from the sun1 which appears white to us1 is in reality a mixture of all the colors of the rainbow4 ,this he showed by placing a prism between the ray of light and a screen4 ,a spectrum showing all the colors from red to violet appeared on the screen4 ,another notable achievement of his was the design of a telescope which brought objects to a sharp focus and prevented the blurring effects which had occasioned so much annoyance to ,newton and his predecessors in all their astronomical observations4 ,these and other discoveries of very great interest were brought together in a volume on optics which ,newton published in #agjd4 ,our particular concern here is to examine the views advanced by him as to the nature of light4 ,that the nature of light should have been a subject for speculation even to the ancients need not surprise us4 ,if other senses1 as touch1 for example1 convey impressions of objects1 it is true to say that the sense of sight conveys the most complete impression4 ,our conception of the external world is largely based upon the sense of sight2 particularly so when we deal with objects beyond our reach4 ,in astronomy1 therefore1 a study of the properties of light is indispensable4 #a ,but what is this light8 ,we open our eyes and we see2 we close our eyes and we fail to see4 ,at night in a dark room we may have our eyes open and yet we do not see2 light1 then1 must be absent4 ,evidently1 light does not wholly depend upon whether our eyes are open or closed4 ,this much is certain3 the eye functions and something else functions4 ,what is this something else8 ,strangely enough1 ,plato and ,aristotle regarded light as a property of the eye and the eye alone4 ,out of the eye tentacles were shot which intercepted the object and so illuminated it4 ,from what has already been said1 such a view seems highly unlikely4 ,far more consistent with their philosophy in other directions would have been the theory that light has its source in the object and not in the eye1 and travels from object to eye rather than the reverse4 ,how little substance the ,aristotelian contribution possesses is immediately seen when we refer to the art of photography4 ,here light rays produce effects which are independent of any property of the eye4 ,the blind man may click the camera and produce the impression on the plate4 ,newton1 of course1 could have fallen into no such error as did ,plato and ,aristotle4 ,the source of light to him was the luminous body4 ,such a body had the power of emitting minute particles at great speed1 and these when coming in contact with the retina produce the sensation of sight4 ,this emission or corpuscular theory of ,newton's was combated very strongly by his illustrious ,dutch contemporary1 ,huyghens1 who maintained that light was a wave phenomenon1 the disturbance starting at the luminous body and spreading out in all directions4 ,the wave motions of the sea offer a certain analogy4 ,newton's strongest objection to ,huyghens' wave theory was that it seemed to offer no satisfactory explanation as to why light travelled in straight lines4 ,he says3 ,to me the fundamental supposition itself seems impossible1 namely that the waves or vibrations of any fluid can1 like the rays of light1 be propagated in straight lines1 without a continual and very extravagant bending and spreading every way into the quiescent medium1 where they are terminated by it4 ,i mistake if there be not both experiment and demonstration to the contrary4 ,in the corpuscular theory the particles emitted by the luminous body were supposed to travel in straight lines4 ,in empty space the particles travelled in straight lines and spread in all directions4 ,to explain how light could traverse some types of matter--liquids1 for example--,newton supposed that these light particles travelled in the spaces between the molecules of the liquid4 ,newton's objection to the wave theory was not answered very convincingly by ,huyghens4 ,today we know that light waves of high frequency tend to travel in straight lines1 but may be prevented from doing so by gravitational forces of bodies near its path4 ,but this is ,einstein's discovery4 ,a very famous experiment by ,foucault in #ahec proved beyond the shadow of a doubt that ,newton's corpuscular theory was untenable4 ,according to ,newton's theory1 the velocity of light must be greater in a denser medium 7such as water7 than in a lighter one 7such as air74 ,according to the wave theory the reverse is true4 ,foucault showed that light does travel more slowly in water than in air4 ,the facts were against ,newton and in favor of ,huyghens2 and where facts and theory clash there is but one thing to do3 discard the theory4 ,some ,facts about ,newton4 ,newton was a ,cambridge man1 and ,newton made ,cambridge famous as a mathematical center4 ,since ,newton's day ,cambridge has boasted of a ,clerk ,maxwell and a ,rayleigh1 and her ,larmor1 her ,j4 ,j4 ,thomson and her ,rutherford are still with us4 ,newton entered ,trinity ,college when he was #ah and soon threw himself into higher mathematics4 ,in #affi1 when but #bg years old1 he became professor of mathematics at ,cambridge1 and later represented that seat of learning in ,parliament4 ,when his friend ,montague became ,chancellor of the ,exchequer1 ,newton was offered1 and accepted1 the lucrative position of ,master of the ,mint4 ,as president of the ,royal ,society ,newton was occasionally brought in contact with ,queen ,anne4 ,she held ,newton in high esteem1 and in #agje she conferred the honor of knighthood on him4 ,he died in #agbg4 ,i do not know1 wrote ,newton1 what ,i may appear to the world1 but1 to myself1 ,i seem to have been only like a boy playing on the seashore1 and directing myself in now and then finding a smoother pebble or a prettier shell than ordinary1 whilst the great ocean of truth lay all undiscovered before me4 ,such was the modesty of one whom many regard as the greatest intellect of all ages4 ,,references ,an excellent account of ,newton may be found in ,sir ,r4 ,s4 ,ball's ,great ,astronomers 7,sir ,isaac ,pitman and ,sons1 ,ltd41 ,london74 ,sedgewick and ,tyler's ,a ,short ,history of ,science 7,macmillan1 #aiah7 and ,cajori's ,a ,history of ,mathematics 7,macmillan1 #aiag7 may also be consulted to advantage4 ,the standard biography is that by ,brewster4 ,,ii ,,the ,,ether ,,and ,,its ,,consequences ,huyghens' wave theory of light1 now so generally accepted1 loses its entire significance if a medium for the propagation of these waves is left out of consideration4 ,this medium we call the ether4 #b ,huyghens' reasoning may be illustrated in some such way as this3 ,if a body moves a force pushes or pulls it4 ,that force itself is exemplified in some kind of matter--say a horse4 ,the horse in pulling a cart is attached to the cart4 ,the horse in pulling a boat may not be attached to the boat directly but to a rope1 which in turn is attached to the boat4 ,in common cases where one piece of matter affects another1 there is some direct contact1 some go-between4 ,but cases are known where matter affects matter without affording us any evidence of contact4 ,take the case of a magnet's attraction for a piece of iron4 ,where is the rope that pulls the iron towards the magnet8 ,perhaps you think the attraction due to the air in between the magnet and iron8 ,but removing the air does not stop the attraction4 ,yet how can we conceive of the iron being drawn to the magnet unless there is some go-between8 some medium not readily perceptible to the senses perhaps1 and therefore not strictly a form of matter8 ,if we can but picture some such medium we can imagine our magnet giving rise to vibrations in this medium which are carried to the iron4 ,the magnet may give rise to a disturbance in that portion of the medium nearest to it2 then this portion hands over the disturbance to its neighbor1 the next portion of the medium2 and so on1 until the disturbance reaches the iron4 ,you see1 we are satisfying our sense-perception by arguing in favor of action by actual contact rather than some vague action at a distance2 the go-between instead of being a rope is the medium called the ether4 ,foucault's experiment completely shattered the corpuscular theory of light1 and for want of any other more plausible alternative1 we are thrown back on ,huyghens' wave theory4 ,it will presently appear that this wave theory has elements in it which make it an excellent alternative4 ,in the meantime1 if light is to be considered as a wave motion1 then the query immediately arises1 what is the medium through which these waves are propagated8 ,if water is the medium for the waves of the sea1 what is the medium for the waves of light8 ,again we answer1 the medium is the ether4 ,what ,is ,this ,ether8 ,balloonists find conditions more and more uncomfortable the higher they ascend1 for the density of the air 7and therefore the amount of oxygen in a given volume of air7 becomes less and less4 ,meteorologists have calculated that traces of the air we breathe may reach a height of some #bjj miles4 ,but what is beyond8 ,nothing but the ether1 it is claimed4 ,light from the sun and stars reaches us via the ether4 ,but what is this ether8 ,we cannot handle it4 ,we cannot see it4 ,it fails to fall within the scope of any of our senses1 for every attempt to show its presence has failed4 ,it is spirit-like in the popular sense4 ,it is ,lodge's medium for the souls of the departed4 ,helmholtz and ,kelvin tried to arrive at some properties of this hypothetical substance from a careful study of the manner in which waves were propagated through this ether4 ,if1 as the wave theory teaches us1 the ether can be set in motion1 then according to laws of mechanics1 the ether has mass4 ,if so it is smaller in amount than anything which can be detected with our most accurate balance4 ,further--and this is a difficulty not easily explained--if this ether has any mass1 why does it offer no detectable resistance to the velocity of the planets in it8 ,why is not the velocity of the planets reduced in time1 just as the velocity of a rifle bullet decreases owing to the resistance of the air8 ,lodge1 in arguing in favor of an ether1 holds that its presence cannot be detected because it pervades all space and all matter4 ,his favorite analogy is to point out the extreme unlikelihood of a deep-sea fish discovering the presence of the water with which it is surrounded on all sides2--all of which tells us nothing about the ether1 but does try to tell us why we cannot detect it4 #c ,in short1 answering the query at the head of this paragraph1 we may say that we do not know4 ,waves ,set up in ,this ,ether4 ,the waves are not all of the same length4 ,those that produce the sensation of sight are not the smallest waves known1 yet their length is so small that it would take anywhere from one to two million of them to cover a yard4 ,curiously enough1 our eye is not sensitive to wave lengths beyond either side of these limits2 yet much smaller1 and much larger waves are known4 ,the smallest are the famous ,x-rays1 which are scarcely one ten-thousandth the size of light waves4 ,waves which have a powerful chemical action--those which act on a photographic plate1 for example--are longer than ,x-rays1 yet smaller than light waves4 ,waves larger than light waves are those which produce the sensation of heat1 and those used in wireless telegraphy4 ,the latter may reach the enormous length of #e1jjj yards4 ,x-ray1 actinic1 or chemically active ray1 light ray1 heat ray1 wireless ray--they differ in size1 yet they all have this in common3 they travel with the same speed 7#ahf1jjj miles per second74 ,the ,electromagnetic ,theory of ,light4 ,powerful support to the conception that space is pervaded by ether was given when ,maxwell discovered light to be an electromagnetic phenomenon4 ,from purely theoretical considerations this gifted ,english physicist was led to the view that waves could be set up as a result of electrical disturbances4 ,he proved that such waves would travel with the same velocity as light waves4 ,as air is not needed to transmit electrical phenomena--for you can pump all air out of a system and produce a vacuum1 and electrical phenomena will continue--,maxwell was forced to the conclusion that the waves set up by electrical disturbances and transmitted with the same velocity as light1 were enabled to do so with the help of the same medium as light1 namely1 the ether4 ,it was now but a step for ,maxwell to formulate the theory that light itself is nothing but an electrical phenomenon1 the sensation of light being due to the passage of electric waves through the ether4 ,this theory met with considerable opposition at first4 ,physicists had been brought up in a school which had taught that light and electricity were two entirely unrelated phenomena1 and it was difficult for them to loosen the shackles that bound them to the older school4 ,but two startling discoveries helped to fasten attention upon ,maxwell's theory4 ,one was an experimental confirmation of ,maxwell's theoretical deduction4 ,hertz1 a pupil of ,helmholtz1 showed how the discharge from a ,leyden jar set up oscillations1 which in turn gave rise to waves in the ether1 comparable1 in so far as velocity is concerned1 to light waves1 but differing from the latter in wave length1 the ,hertzian waves being much longer4 ,at a later date these waves were further investigated by ,marconi1 with the result that wireless messages soon began to be flashed from one place to another4 ,just as there is a close connection between light and electricity1 so there is between light and magnetism4 ,the first to point out such a relationship was the illustrious ,michael ,faraday1 but we owe to ,zeeman the most extensive investigations in this field4 ,if we throw some common salt into a flame1 and1 with the help of a spectroscope1 examine the spectrum produced1 we are struck by two bright lines which stand out very prominently4 ,these lines1 yellow in color1 are known as the ,d-lines and serve to identify even minute traces of sodium4 ,what is true of sodium is true of other elements3 they all produce very characteristic spectra4 ,now ,zeeman found that if the flame is placed between a powerful magnet1 and then some common salt thrown into the flame1 the two yellow lines give place to ten yellow lines4 ,such is one of the results of the effect of a magnetic field on light4 ,the ,electron4 ,the ,zeeman effect led to several theories regarding its nature4 ,the most successful of these was one proposed by ,larmor and more fully treated by ,lorentz4 ,it has already been pointed out that the only difference between wireless and light waves is that the former are much longer1 and1 we may now add1 their vibrations are much slower4 ,light and wireless waves bear a relationship to one another comparable to the relationship born by high and low-pitched sounds4 ,to produce wireless waves we allow a charge of electricity to oscillate to and fro4 ,these oscillations1 or oscillating charges1 are the cause of such waves4 ,what charges give rise to light waves8 ,lorentz1 from a study of the ,zeeman effect1 ascribed them to minute particles of matter1 smaller than the chemical atom1 to which the name electron was given4 ,the unit of electricity is the electron4 ,electrons in motion give rise to electricity1 and electrons in vibration1 to light4 ,the ,zeeman effect gave ,lorentz enough data to calculate the mass of such electrons4 ,he then showed that these electrons in a magnetic field would be disturbed by precisely the amount to which ,zeeman's observations pointed4 ,in other words1 the assumption of the electron fitted in most admirably with ,zeeman's experiments on magnetism and light4 ,in the meantime1 a study of the discharge of electricity through gases1 and1 later1 the discovery of radium1 led1 among other things1 to a study of beta or cathode rays--negatively charged particles of electricity4 ,through a series of strikingly original experiments ,j4 ,j4 ,thomson ascertained the mass of such particles or corpuscles1 and then the very striking fact was brought out that ,thomson's corpuscle weighed the same as ,lorentz's electron4 ,the electron was not merely the unit of electricity but the smallest particle of matter4 ,the ,nature of ,matter4 ,all matter is made up of some eighty-odd elements4 ,oxygen1 copper1 lead are examples of such elements4 ,each element in turn consists of an innumerable number of atoms1 of a size so small1 that #cjj million of them could be placed alongside of one another without their total length exceeding one inch4 ,john ,dalton more than a hundred years ago postulated a theory1 now known as the atomic theory1 to explain one of the fundamental laws in chemistry4 ,this theory started out with an old ,greek assumption that matter cannot be divided indefinitely1 but that1 by continued subdivision1 a point would be reached beyond which no further breaking up would be possible4 ,the particles at this stage ,dalton called atoms4 ,dalton's atomic hypothesis became one of the pillars upon which the whole superstructure of chemistry rested1 and this because it explained a number of perplexing difficulties so much more satisfactorily than any other hypothesis4 ,for nearly a century ,dalton stood as firm as a rock4 ,but early in the nineties some epoch-making experiments on the discharge of electricity through gases were begun by a group of physicists1 particularly ,crookes1 ,rutherford1 ,lenard1 ,roentgen1 ,becquerel1 and1 above all1 ,j4 ,j4 ,thomson1 which pointed very clearly to the fact that the atoms are not the smallest particles of matter at all2 that1 in fact1 they could be broken up into electrons1 of a diameter one one-hundred-thousandth that of an atom4 ,it remained for the illustrious ,madame ,curie to confirm this beyond all doubt by her isolation of radium4 ,here1 as ,madame ,curie showed1 was an element whose atoms were actually breaking up under one's very eyes1 so to speak4 ,so far have we advanced since ,dalton's day1 that ,dalton's unit1 the atom1 is now pictured as a complex particle patterned after our solar system1 with a nucleus of positive electricity in the center1 and particles of negative electricity1 or electrons1 surrounding the nucleus4 ,all this leads to one inevitable conclusion3 matter is electrical in nature4 ,but now if matter and light have the same origin1 and matter is subject to gravitation1 why not light also8 ,so reasoned ,einstein4 ,summary4 ,newton's studies of matter in motion led to his theory of gravitation1 and1 incidentally1 to his conception of time and space as definite entities4 ,as we shall see1 ,einstein in his theory of gravitation based it upon discoveries belonging to the post-,newtonian period4 ,one of these is ,minkowski's theory of time and space as one and inseparable4 ,this theory we shall discuss at some length in the next chapter4 ,other important discoveries which led up to ,einstein's work are the researches which culminated in the electron theory of matter4 ,the origin of this theory may be traced to studies dealing with the nature of light4 ,here again ,newton appears as a pioneer4 ,newton's corpuscular theory1 however1 proved wholly untenable when ,foucault showed that the velocity of light in water is less than in air1 which is the very reverse of what the corpuscular theory demands1 but which does agree with ,huyghens' wave theory4 ,but ,huyghens' wave theory postulated some medium in which the waves can act4 ,to this medium the name ether was given4 ,however1 all attempts to show the presence of such an ether failed4 ,naturally enough1 some began to doubt the existence of an ether altogether4 ,huyghens' wave theory received a new lease of life with ,maxwell's discovery that light is an electromagnetic phenomenon2 that the waves set up by a source of light were comparable to waves set up by an electrical disturbance4 ,zeeman next showed that magnetism was also1 closely related to light4 ,a study of ,zeeman's experiments led ,lorentz to the conclusion that electrical phenomena are due to the motion of charged particles called electrons1 and that the vibrations of these electrons give rise to light4 ,the conception of the electron as the very fundamental of matter was arrived at in an entirely different way3 from studies dealing with the discharge of electricity through gases and the breaking up of the atoms of radium4 ,if matter and light have the same origin1 and if matter is subject to gravitation1 why not light also8 ,,references ,for the general subject of light the reader must be referred to a rather technical work1 but one of the best in the ,english language3 ,edwin ,edser1 ,light for ,students 7,macmillan1 #aijg74 ,the nature of matter and electricity is excellently discussed in several books of a popular variety4 ,the very best and most complete of its kind that has come to the author's attention is ,comstock and ,troland's ,the ,nature of ,matter and ,electricity 7,d4 ,van ,nostrand ,co41 #aiai74 ,two other very readable books are ,soddy's ,matter and ,energy 7,henry ,holt and ,co47 and ,crehore's ,the ,mystery of ,matter and ,energy 7,d4 ,van ,nostrand ,co41 #aiag74 ,,iii ,,einstein ,this is the most important result obtained in connection with the theory of gravitation since ,newton's day4 ,einstein's reasoning is the result of one of the highest achievements of human thought4 ,these words were uttered by ,sir ,j4 ,j4 ,thomson1 the president of the ,royal ,society1 at a meeting of that body held on ,november #f1 #aiai1 to discuss the results of the ,eclipse ,expedition4 ,einstein another ,newton--and this from the lips of ,j4 ,j4 ,thomson1 ,england's most illustrious physicist6 ,if ever man weighed words carefully it is this ,cambridge professor1 whose own researches have assured him immortality for all time4 ,what has this ,albert ,einstein done to merit such extraordinary praise8 ,with the world in turmoil1 with classes and races in a death struggle1 with millions suffering and starving1 why do we find time to turn our attention to this ,jew8 ,his ideas have no bearing on ,europe's calamity4 ,they will not add one bushel of wheat to starving populations4 ,the answer is not hard to find4 ,men come and men go1 but the mystery of the universe remains4 ,it is ,einstein's glory to have given us a deeper insight into the universe4 ,our scientists are ,huxley's agnostics3 they do not deny activities beyond our planet2 they merely center their attention on the knowable on this earth4 ,our philosophers1 on the other hand1 go far afield4 ,some of them soar so high that1 like one poet's opinion of ,shelley1 the bubble bursts4 ,einstein1 using the tools of the scientist--the experimentalist--builded a skyscraper which ultimately reached the philosophical school4 ,his rle is the rle of alcohol in causing water and ether 7the ansthetic7 to mix4 ,ether and water will mix no better than oil and water1 without the presence of alcohol2 in its presence a uniform mixture is obtained4 ,the ,object of the ,eclipse ,expedition4 ,einstein prophesied that a ray of light passing near the sun would be pulled out of its course1 due to the action of gravity4 ,he went even further4 ,he predicted how much out of its course the ray would be deflected4 ,this prediction was based on a theory of gravitation which ,einstein had developed in great mathematical detail4 ,the object of the ,british ,eclipse ,expedition was either to prove or disprove ,einstein's assumption4 ,the ,result of the ,expedition4 ,einstein's prophecy was fulfilled almost to the letter4 ,the ,significance of the ,result4 ,since ,einstein's theory of gravitation is intimately associated with certain revolutionary ideas concerning time and space1 and1 therefore1 with ,fundamentals of the ,universe1 the net result of the expedition was to strengthen our belief in the validity of his new view of the universe4 ,it is our intention in the following pages to discuss the expedition and the larger aspects of ,einstein's theory that follow from it4 ,but before we do so we must have a clear idea of our solar system4 ,our ,solar ,system4 ,in the center of our system is the sun1 a flaming mass of fire1 much bigger than our own earth1 and very1 very far away4 ,the sun has its family of eight planets--of which the earth is one--which travel around the sun2 and around some of the planets there travel satellites1 or moons4 ,the earth has such a satellite1 the moon4 ,now we have good reasons for believing that every star which twinkles in the sky is a sun comparable to our own1 having also its own planets and its own moons4 ,these stars1 or suns1 are so much further away from us than our own sun1 that but a speck of their light reaches us1 and then only at night1 when1 as the poets would say1 our sun has gone to its resting place4 ,the distances between bodies in the solar system is so immense that1 like the number of dollars spent in the ,great ,war1 the number of miles conveys little1 or no impression4 ,but picture yourself in an express train going at the average rate of #cj miles an hour4 ,if you start from ,new ,york and travel continuously you would reach ,san ,francisco in #d days4 ,if you could continue your journey around the earth at the same rate you would complete it in #ce days4 ,if now you could travel into space and to the moon1 still with the same velocity1 you would reach it in #cej days4 ,having reached the moon1 you could circumscribe it with the same express train in #h days1 as compared to the #ce days it would take you to circumscribe the earth4 ,if instead of travelling to the moon you would book your passage for the sun you1 or rather your descendants1 would get there in #cej years1 and it would then take them #aj additional years to travel around the sun4 ,immense as these distances are1 they are small as compared to the distances that separate us from the stars4 ,it takes light which1 instead of travelling #cj miles an hour1 travels #ahf1jjj miles a second1 about #h minutes to get to us from the sun1 and a little over #d years to reach us from the nearest star4 ,the light from some of the other stars do not reach us for several hundred years4 ,the ,eclipse of the ,sun4 ,now to return to an infinitesimal part of the universe--our solar system4 ,we have seen that the earth travels around the sun1 and the moon around the earth4 ,at some time in the course of these revolutions the moon must come directly between the earth and the sun4 ,then we get the eclipse of the sun4 ,as the moon is smaller than the earth1 only a portion of the earth's surface will be cut off from the sun's rays4 ,that portion which is so cut off suffers a total eclipse4 ,this explains why the eclipse of ,may1 #aiai1 which was a total one for ,brazil1 was but a partial one for us4 ,einstein's ,assertion ,re-stated4 ,einstein claimed that a ray of light from one of the stars1 if passing near enough to the surface of the sun1 would be appreciably deflected from its course2 and he calculated the exact amount of this deflection4 ,to begin with1 why should ,einstein suppose that the path of a ray of light would be affected by the son8 ,newton's law of gravitation made it clear that bodies which have mass attract one another4 ,if light has mass--and very recent work tends to show that it has--there is no reason why light should not be attracted by the sun1 or any other planetary body4 ,the question that agitated scientists was not so much whether a ray of light would be deviated from its path1 but to what extent this deviation would take place4 ,would ,einstein's figures be confirmed8 ,of the bodies within our solar system the sun is by far the largest1 and therefore it would exert a far greater pull than any of the planets on light rays coming from the stars4 ,under ordinary conditions1 however1 the sun itself shines with such brilliancy1 that objects around it1 including rays of light passing near its surface1 are wholly dimmed4 ,hence the necessity of putting our theory to the test only when the moon covers up the sun--when there is a total eclipse of the sun4 ,a ,graphical ,representation4 ,imagine a star ,a1 so selected that as its light comes to us the ray just grazes the sun4 ,if the path of the ray is straight--if the sun has no influence on it--then the path can be represented by the line ,,ab4 ,if1 however1 the sun does exert a gravitational pull1 then its real path will be ,,ab'1 and to an observer on the earth the star will have appeared to shift from ,a to ,a'4 ,what the ,eclipse ,expedition ,set ,out to ,do4 ,photographs of stars around the sun were to be taken during the eclipse1 and these photographs compared with others of the same region taken at night1 with the sun absent4 ,any apparent shifting of the stars could be determined by measuring the distances between the stars as shown on the photographic plates4 ,three ,possibilities ,anticipated4 ,according to ,newton's assumption1 light consists of corpuscles1 or minute particles1 emitted from the source of light4 ,if this be true these particles1 having mass1 should be affected by the gravitational pull of the sun4 ,if we apply ,newton's theory of gravitation and make use of his formula1 it can be shown that such a gravitational pull would displace the ray of light by an average amount equal to #j4ge 7seconds of angular distance47 #d ,on the other hand1 where light is regarded as waves set in motion in the ether of space 7the wave theory of light71 and where weight is denied light altogether1 no deviation need be expected4 ,finally there is a third alternative3 ,einstein's4 ,light1 says ,einstein1 has mass1 and therefore probably weight4 ,mass is the matter light contains2 weight represents pull by gravity4 ,light rays will be attracted by the sun1 but according to ,einstein's theory of gravitation the sun's gravitational pull will displace the rays by an average amount equal to #a4ge 7seconds of angular distance74 ,the ,expeditions4 ,that science is highly international1 despite many recent examples to the contrary1 is evidenced by this ,british ,eclipse ,expedition4 ,here was a theory propounded by one who had accepted a chair of physics in the university of ,berlin1 and across the ,english ,channel were ,germany's mortal enemies making elaborate preparations to test the validity of the ,berlin professor's theory4 ,the ,british ,astronomical ,society began to plan the eclipse expedition even before the outbreak of the ,great ,war4 ,during the years that followed1 despite the destinies of nations which hung on threads from day to day1 despite the darkest hours in the history of the ,british people1 our ,english astronomers continued to give attention to the details of the proposed expedition4 ,when the day of the eclipse came all was in readiness4 ,one expedition under ,dr4 ,crommelin was sent to ,sobral1 ,brazil2 another1 under ,prof4 ,eddington1 to ,principe1 an island off the west coast of ,africa4 ,in both these places a total eclipse was anticipated4 ,the eclipse occurred on ,may #bi1 #aiai4 ,it lasted for six to eight minutes4 ,some #ae photographs1 with an average exposure of five to six seconds1 were taken4 ,two months later another series of photographs of the same region were taken1 but this time the sun was no longer in the midst of these stars4 ,the photographs were brought to the famous ,greenwich ,observatory1 near ,london1 and the astronomers and mathematicians began their laborious measurements and calculations4 ,on ,november #f1 at the meeting of the ,royal ,society1 the result was announced4 ,the ,sobral expedition reported #a4ih2 the ,principe expedition #a4fb4 ,the average was #a4h4 ,einstein had predicted #a4ge1 ,newton might have predicted #j4ge1 and the orthodox scientists would have predicted #j4 ,there could now no longer be any question as to which of the three theories rested on a sure foundation4 ,to quote ,sir ,frank ,dyson1 the ,astronomer ,royal3 ,after a careful study of the plates ,i am prepared to say that there can be no doubt that they confirm ,einstein's prediction4 ,a very definite result has been obtained that light is deflected in accordance with ,einstein's law of gravitation4 #e ,where ,did ,einstein ,get ,his ,idea of ,gravitation8 ,in #aije ,einstein published the first of a series of papers supporting and extending a theory of time and space to which the name the theory of relativity had been given4 ,these views as expounded by ,einstein came into direct conflict with ,newton's ideas of time and space1 and also with ,newton's law of gravitation4 ,since ,einstein had more faith in his theory of relativity than in ,newton's theory of gravitation1 ,einstein so changed the latter as to make it harmonize with the former4 ,more will be said on this subject4 ,let not the reader misunderstand4 ,newton was not wholly in the wrong2 he was only approximately right4 ,with the knowledge existing in ,newton's day ,newton could have done no more than he did2 no mortal could have done more4 ,but since ,newton's day physics--and science in general--has advanced in great strides1 and ,einstein can interpret present-day knowledge in the same masterful fashion that ,newton could in his day4 ,with more facts to build upon1 ,einstein's law of gravitation is more universal than ,newton's2 it really includes ,newton's4 ,but now we must turn our attention very briefly to the theory of relativity--the theory that led up to ,einstein's law of gravitation4 ,the ,theory of ,relativity4 ,the story goes that ,einstein was led to his ideas by watching a man fall from a roof4 ,this story bears a striking similarity to ,newton and the apple4 ,perhaps one is as true as the other4 #f ,however that may be1 the principle of relativity is as old as philosophical thought1 for it denies the possibility of measuring absolute time1 or absolute space4 ,all things are relative4 ,we say that it takes a long time to get from ,new ,york to ,albany2 long as compared to what8 long1 perhaps1 as compared to the time it takes to go from ,new ,york ,city to ,brooklyn4 ,we say the ,white ,house is large2 large when compared to a room in an apartment4 ,but we can just as well reverse our ideas of time and distance4 ,the time it takes to go from ,new ,york to ,albany is short when compared to the time it takes to go from ,new ,york to ,san ,francisco4 ,the size of the ,white ,house is small when compared to the size of the city of ,washington4 ,let us take another illustration4 ,every time the earth turns on its axis we mark down as a day4 ,with this as a basis1 we say that it takes a little over #cfe days for the earth to complete its revolution around the sun1 and our #cfe days we call a year4 ,but now consider some of our other planets4 ,with our time as a basis1 it takes ,jupiter or ,saturn #aj hours to turn on its axis1 as compared to the #bd hours it takes the earth to turn4 ,saturn's day is less than one-half our day1 and our day is more than twice ,saturn's--that is1 according to the calculations of the inhabitants of the earth4 ,mercury completes her circuit around the sun in #hh days2 ,neptune1 in #afd years4 ,mercury's year is but one-fourth ours1 ,neptune's1 #afd times ours4 ,and observers at ,mercury and ,neptune would regard us from their standard of time1 which differs from our standard4 ,you may say1 why not take our standard of time as the standard1 and measure everything by it8 ,but why should you8 ,such a selection would be quite arbitrary4 ,it would not be based on anything absolute1 but would merely depend on our velocity around the sun4 ,these ideas are old enough in metaphysics4 ,einstein's improvement of them consists not merely in speculating about them1 but in giving them mathematical form4 ,the ,origin of the ,theory of ,relativity4 ,a train moves with reference to the earth4 ,the earth moves with reference to the sun4 ,we say the sun is stationary and the earth moves around the sun4 ,but how do we know that the sun itself does not move with reference to some other body8 ,how do we know that our planetary system1 and the stars1 and the cosmos as a whole is not in motion8 ,there is no way of answering such a question unless we could get a point of reference which is fixed--fixed absolutely in space4 ,we have already alluded to our view of the nature of light1 known as the wave theory of light4 ,this theory postulates the existence of an all-pervading ether in space4 ,light sets up wave disturbances in this ether1 and is thus propagated4 ,if the ocean were the ether1 the waves of the ocean would compare with the waves set up by the ether4 ,but what is this ether8 ,it cannot be seen4 ,it defies weight4 ,it permeates all space4 ,it permeates all matter4 ,so say the exponents of this ether4 ,to the layman this sounds very much like another name for the ,deity4 ,to ,sir ,oliver ,lodge it represents the spirits of the departed4 ,to us1 of importance is the conception that this ether is absolutely stationary4 ,such a conception is logical if the various developments in optics and electricity are considered4 ,but if absolutely stationary1 then the ether is the long-sought-for point of reference1 the guide to determine the motion of all bodies in the universe4 ,the ,famous ,experiment ,performed by ,prof4 ,michelson4 ,if there is an ether1 and a stationary ether1 and if the earth moves with reference to this ether1 the earth1 in moving1 must set up ether currents--just as when a train moves it sets up air currents4 ,so reasoned ,michelson1 a young ,annapolis graduate at the time4 ,and forthwith he devised a crucial experiment the explanation of which we can simplify by the following analogy3 ,which is the quicker1 to swim up stream a certain length1 say a hundred yards1 and back again1 or across stream the same length and back again8 ,the swimmer will answer that the up-and-down journey is longer4 #g ,our river is the ether4 ,the earth1 if moving in this ether1 will set up an ether stream1 the up stream being parallel to the earth's motion4 ,now suppose we send a beam of light a certain distance up this ether stream and back1 and note the time2 and then turn the beam of light at right angles and send it an equal distance across the stream and back1 and note the time4 ,how will the time taken for light to travel in these two directions compare8 ,reasoning by analogy1 the up-and-down stream should take longer4 ,michelson's results did not accord with analogy4 ,no difference in time could be detected between the beam of light travelling up-and-down1 and across-and-back4 ,but this was contrary to all reason if the postulate of an ether was sound4 ,must we then revise our ideas of an ether8 ,perhaps after all there is no ether4 ,but if no ether1 how are we to explain the propagation of light in space1 and various electrical phenomena connected with it1 such as the ,hertzian1 or wireless waves8 ,there was another alternative1 one suggested by ,larmor in ,england and ,lorentz in ,holland1--that matter is contracted in the direction of its motion through the ether current4 ,to say that bodies are actually shortened in the direction of their motion--by an amount which increases as the velocity of these bodies approaches that of light--is so revolutionary an idea that ,larmor and ,lorentz would hardly have adopted such a viewpoint but for the fact that recent investigations into the nature of matter gave basis for such belief4 ,matter1 it has been shown1 is electrical in nature4 ,the forces which hold the particles together are electrical4 ,lorentz showed that mathematical formulas for electrical forces could be developed which would inevitably lead to the view that material bodies contract in the direction of their motion4 #h ,but this is ridiculous1 you say2 if ,i am shorter in one direction than in another ,i would notice it4 ,you would if some things were shortened and others were not4 ,but if all things pointing in a certain direction are shortened to an equal extent1 how are you going to notice it8 ,will you apply the yard stick8 ,that has been shortened4 ,will you pass judgment with the help of your eyes8 ,but your retina has also contracted4 ,in brief1 if all things contract to the same amount it is as if there were no contraction at all4 ,lorentz's ,plausible ,explanation ,really ,deepens the ,mystery4 ,the startling ideas just outlined have opened up several new vistas1 but they have left unanswered the two problems we set out to solve3 whether there is an ether1 and if so1 what is the velocity of the earth in reference to this ether8 ,lorentz maintains that there is an ether1 but the velocities of bodies relative to it must forever remain a mystery4 ,as you change your position your distances change2 you change2 everything about you changes accordingly2 and all basis for comparison is lost4 ,nature has entered into a conspiracy to keep you ignorant4 ,einstein ,comes upon the ,scene4 ,einstein starts with the assumption that there is no possible way of identifying this ether4 ,suppose we ignore the ether altogether1 what then8 #i ,if we do ignore the ether we no longer have any absolute point of reference2 for if the ether is considered stationary the velocity of all bodies within the ether may be referred to it2 any point in space may be considered a fixed point4 ,if1 however1 there is no ether1 or if we are to ignore it1 how are we to get the velocity of bodies in space8 ,the ,principle of ,relativity4 ,if we are to believe in the causal relationship between only such things as lie within the realm of observation1 then observation teaches us that bodies move only relative to one another1 and that the idea of absolute motion of a body in space is meaningless4 ,einstein1 therefore1 postulates that there is no such thing as absolute motion1 and that all we can discuss is the relative motion of one body with respect to another4 ,this is just as logical a deduction from ,michelson's experiment as the attempt to explain ,michelson's anomalous results in the light of an all-pervading ether4 ,consider for a moment ,newton's scheme4 ,this great pioneer pictured an absolute standard of position in space relative to which all velocities are measured4 ,velocities were measured by noting the distance covered and dividing the result by the time taken to cover the distance4 ,space was a definite entity2 and so was time4 ,time1 said ,newton1 flows evenly on1 independent of aught else4 ,to ,newton time and space were entirely different1 in no way to be confounded4 ,just as ,newton conceived of absolute space1 so he conceived of absolute time4 ,from the latter standard of reference the idea of a simultaneity of events at different places arose4 ,but now if there is no standard of reference1 if the ether does not exist or does not function1 if two points ,a and ,b cannot be referred to a third1 and fixed point ,c1 how can we talk of simultaneity of events at ,a and ,b8 #aj ,in fact1 ,einstein shows that if all you can speak about is relative motion1 then one event which takes say one minute on one planet would not take one minute on another4 ,for consider two bodies in space1 say the planets ,venus and the earth1 with an observer ,b on ,venus and another ,a on the earth4 ,b notes the time taken for a ray of light to travel from ,b to the distance ,m4 ,a on the earth has means of observing the same event4 ,b records one minute4 ,a is puzzled1 for his watch records a little more than one minute4 ,what is the explanation8 ,granting that the two clocks register the same time to start with1 and assuming further ,einstein's hypothesis that the velocity of light is independent of its source1 the difference in time is due to the fact that the planet ,venus moves with reference to the observer on the earth2 so that ,a in reality does not measure the path ,,bm and ,,mb1 but ,,bm' and ,m',b'1 where ,,bb' represents the distance ,venus itself has moved in the interval4 ,and if you put yourself in ,b's position on ,venus the situation is exactly reversed4 ,all of which is simply another way of saying that what is a certain time on one body in space is another time on another body in space4 ,there is nothing definite in time4 ,prof4 ,cohen's ,illustration4 ,further bewildering possibilities are clearly outlined in this apt illustration3 ,if when you are going away on a long and continuous journey you write home at regular intervals1 you should not be surprised that with the best possible mail service your letters will reach home at progressively longer intervals1 since each letter will have a greater distance to travel than its predecessor4 ,if you were armed with instruments to hear the home clock ticking1 you would find that as your distance from home keeps on increasing1 the intervals between the successive ticks 7that is1 its seconds7 grow longer1 so that if you travelled with the velocity of sound the home clock would seem to slow down to a standstill--you would never hear the next tick4 ,precisely the same is true if you substitute light rays for sound waves4 ,if with the naked eye or with a telescope you watch a clock moving away from you1 you will find that its minute hand takes a longer time to cover its five-minute intervals than does the chronometer in your hand1 and if the clock travelled with the velocity of light you would forever see the minute hand at precisely the same point4 ,that which is true of the clock is1 of course1 also true of all time intervals which it measures1 so that if you moved away from the earth with the velocity of light everything on it would appear as still as on a painted canvas4 ,your time has apparently come to a standstill in one position and is moving in another6 ,all this seems absurd enough1 but it does show that time alone has little meaning4 ,minkowski's ,conclusion4 ,the relativity theory requires that we thoroughly reorganise our method of measuring time4 ,but this is intimately associated with our method of measuring space1 the distance between two points4 ,as we proceed we find that space without time has little meaning1 and vice versa4 ,this leads ,minkowski to the conclusion that time by itself and space by itself are mere shadows2 they are only two aspects of a single and indivisible manner of coordinating the facts of the physical world4 ,einstein incorporated this time-space idea in his theory of relativity4 ,how ,we ,measure a ,point in ,space4 ,suppose ,i say to you that the chemical laboratory of ,columbia ,university faces ,broadway2 would that locate the laboratory8 ,hardly1 for any building along ,broadway would face ,broadway4 ,but suppose ,i add that it is situated at ,broadway and #aagth ,street1 south-east8 there could be little doubt then4 ,but if1 further1 this laboratory would occupy but part of the building1 say the third floor2 then the situation would be specified by naming ,broadway1 #aagth ,street ,s4 ,e41 third floor4 ,if ,broadway represents length1 #aagth ,street width1 and third floor height1 we can see what is meant when we say that three dimensions are required to locate a position in space4 ,the ,fourth ,dimension4 ,a point on a line may be located by one dimension2 a point on a wall requires two dimensions2 a point in the room1 like the chemical laboratory above ground1 needs three4 ,the layman cannot grasp the meaning of a fourth dimension2 yet the mathematician does imagine it1 and plays with it in mathematical terms4 ,minkowski and ,einstein picture time as the fourth dimension4 ,to them time occupies no more important position than length1 breadth1 or thickness1 and is as intimately related to these three as the three are to one another4 ,h4 ,g4 ,wells1 the novelist1 has beautifully caught this spirit when in his novel1 ,the ,time ,machine1 he makes his hero travel backwards and forwards along time just as a man might go north or south4 ,when the man with his time machine goes forward he is in the future2 when he goes backwards he is in the past4 ,in reality1 if we stop to think a minute1 there is no valid reason for the non-existence of a fourth dimension4 ,if one1 two and three dimensions1 why not four--and five and six1 for that matter8 ,theoretically at least there is no reason why the limit should be set at three4 ,however1 our minds become sluggish when we attempt to picture dimensions beyond three2 just as an extraordinary effort on our part is needed to follow ,einstein when he juggles with space and time4 ,our difficulty in imagining four dimensions may be likened to the difficulty two-dimensioned beings would experience in imagining us1 beings of the conventional three dimensions4 ,suppose these two-dimensional beings were living on the surface of the earth2 what could they see8 ,they could see nothing below and nothing above the surface4 ,they would see shifting surfaces as we walked about1 but being sensitive to length and breadth only1 and not to height1 they could gain no notion whatsoever of what we really look like4 ,it is thus with us when we attempt to picture four-dimensional space4 ,perhaps the analogy of the motion picture may help us somewhat4 ,as everybody knows1 these motion pictures consist of a series of photographs which are shown in rapid succession on the screen4 ,each photograph by itself conveys a sensation of space1 that is1 of three dimensions2 but one photograph rapidly following another conveys the sensation of space and time--four dimensions4 ,space and time are interlinked4 ,the ,time-space ,idea ,further ,developed4 ,we have already alluded to the fact that objects in space moving with different velocities build up different time intervals4 ,thus the velocity of the star ,arcturus1 if compared with reference to the earth1 moves at the rate of #bjj miles a second4 ,its motion through space is different from ours4 ,objects which1 according to ,lorentz1 contract in the direction of their motion to an extent proportional to their velocity1 will contract differently on the surface of ,arcturus than on the earth4 ,our space is not ,arcturus' space2 neither is ,arcturus' time our time4 ,and what is true of the discrepancies existing between the space and time conceptions of the earth and ,arcturus is true of any other two bodies in space moving at different velocities4 ,but is there no relationship existing between the space and time of one body in the universe as compared to the space and time of another8 ,can we not find something which holds good for all bodies in the universe8 ,we can4 ,we can express it mathematically4 ,it is the concept of time and space interlinked2 of time as the fourth dimension1 length1 breadth and thickness being the other three2 of time as one of four co-ordinates and at right angles to the other three 7a situation which requires a terrific stretch of the imagination to visualize74 ,the four dimensions are sufficient to co-ordinate the time-space relationships of all bodies in the cosmos1 and hence have a universality which is totally lacking when time and space are used independently of one another4 ,the four components of our time-space are up-and-down1 right-and-left1 backwards-and-forwards1 and sooner-and-later4 ,strain and ,distortion in ,space4 ,the four-dimensional unit has been given the name world-line1 for the world-line of any particle in space is in reality a complete history of that particle as it moves about in space4 ,particles1 we know1 attract one another4 ,if each particle is represented by a world-line these world-lines will be deflected from their course owing to such attraction4 ,imagine a bladder representing the universe1 with lines on it representing world-lines4 ,now squeeze the bladder4 ,the world-lines are bent in various directions2 they are distorted4 ,this illustrates the influence of gravity on these world-lines2 it is the strain brought about due to the force of attraction4 ,the distorted bladder illustrates even more1 for it is a true representation of the real world4 ,how ,einstein's ,conception of ,time and ,space ,led to a ,new ,view of ,gravitation4 ,in our conventional language we speak of the sun as exerting a force on the earth4 ,we have seen1 however1 that this force brings about a distortion or strain in world-lines2 or1 what amounts to the same thing1 a distortion or strain of time and space4 ,the sun's force1 the force of any body in space1 is the force due to gravity2 and these forces may now be treated in terms of the laws of time and space4 ,the earth1 ,prof4 ,eddington tells us1 moves in a curved orbit1 not because the sun exerts any direct pull1 but because the earth is trying to find the shortest way through a space and time which have been tangled up by an influence radiating from the sun4 #aa ,at this point ,newton's conceptions fail1 for his views and his laws do not include strains in space4 ,newton's law of gravitation must be supplanted by one which does include such distortions4 ,it is ,einstein's great glory to have supplied us with this new law4 ,einstein's ,law of ,gravitation4 ,this appears to be the only law which meets all requirements4 ,it includes ,newton's law1 and cannot be distinguished from it if our experiments are confined to the earth and deal with relatively small velocities4 ,but when we betake ourselves to some orbits in space1 with a gravitational pull much greater than the earth's1 and when we deal with velocities comparable to that of light1 the differences become marked4 ,einstein's ,theory ,scores ,its ,first ,great ,victory4 ,in the beginning of this chapter we referred to the elaborate eclipse expedition sent by the ,british to test the validity of ,einstein's new theory of gravitation4 ,the ,british scientists would hardly have expended so much time and energy on this theory of ,einstein's but for the fact that ,einstein had already scored one great victory4 ,what was it8 ,imagine but a single planet revolving about the sun4 ,according to ,newton's law of gravitation1 the planet's path would be that of an ellipse--that is1 oval--and the planet would travel indefinitely along this path4 ,according to ,einstein the path would also be elliptical1 but before a revolution would be quite completed1 the planet would start along a slightly advanced line1 forming a new ellipse slightly in advance of the first4 ,the elliptic orbit slowly turns in the direction in which the planet is moving4 ,after many years--centuries--the orbit will be in a different direction4 ,the rapidity of the orbit's change of direction depends on the velocity of the planet4 ,mercury moving at the rate of #cj miles a second is the fastest among the planets4 ,it has the further advantage over ,venus or the earth in that its orbit1 as we have said1 is an ellipse1 whereas the orbits of ,venus and the earth are nearly circular2 and how are you going to tell in which direction a circle is pointing8 ,observation tells us that the orbit of ,mercury is advancing at the rate of #egd seconds 7of arc7 per century4 ,we can calculate how much of this is due to the gravitational influence of other planets4 ,it amounts to #ecb seconds per century4 ,what of the remaining #db seconds8 ,you might be inclined to attribute this shortcoming to experimental error4 ,but when all such possibilities are allowed for our mathematicians assure us that the discrepancy is #cj times greater than any possible experimental error4 ,this discrepancy between theory and observation remained one of the great puzzles in astronomy until ,einstein cleared up the mystery4 ,according to ,einstein's theory the mathematics of the situation is simply this3 in one revolution of the planet the orbit will advance by a fraction of a revolution equal to three times the square of the ratio of the velocity of the planet to the velocity of light4 ,when we allow mathematicians to work this out we get the figure #dc1 which is certainly close enough to #db to be called identical with it4 ,still ,another ,victory8 ,einstein's third prediction--the shifting of spectral lines toward the red end of the spectrum in the case of light coming to us from the stars of appreciable mass--seems to have been confirmed recently 7,march1 #aibj74 ,the young physicists in ,bonn1 writes ,prof4 ,einstein to a friend1 have now as good as certainty 7so gut wie sicher7 proved the red displacement of the spectral lines and have cleared up the grounds of a previous disappointment4 ,summary4 ,velocity1 or movement in space1 is at the basis of ,einstein's work1 as it was at the basis of ,newton's4 ,but time and space no longer have the distinct meanings that they had when examined with the help of ,newton's equations4 ,time and space are not independent but interdependent4 ,they are meaningless when treated as separate entities1 giving results which may hold for one body in the universe but do not hold for any other body4 ,to get general laws which are applicable to the cosmos as a whole the ,fundamentals of ,mechanics must be united4 ,einstein's great achievement consists in applying this revised conception of space and time to elucidate cosmical problems4 ,world-lines1 representing the progress of particles in space1 consisting of space-time combinations 7the four dimensions71 are strained or distorted in space due to the attraction that bodies exhibit for one another 7the force of gravitation74 ,on the other hand1 gravitation itself--more universal than anything else in the universe--may be interpreted in terms of strains on world-lines1 or1 what amounts to the same thing1 strains of space-time combinations4 ,this brings gravitation within the field of ,einstein's conception of time and space4 ,that ,einstein's conception of the universe is an improvement upon that of ,newton's is evidenced by the fact that ,einstein's law explains all that ,newton's law does1 and also other facts which ,newton's law is incapable of explaining4 ,among these may be mentioned the distortion of the oval orbits of planets round the sun 7confirmed in the case of the planet ,mercury71 and the deviation of light rays in a gravitational field 7confirmed by the ,english ,solar ,eclipse ,expedition74 ,einstein's ,theories and the ,inferences to be ,drawn from ,them4 ,einstein's theories1 supported as they are by very convincing experiments1 will probably profoundly influence philosophic and perhaps religious thought1 but they can hardly be said to be of immediate consequence to the man in the street4 ,as ,i have said elsewhere1 ,einstein's theories are not going to add one bushel of wheat to war-torn and devastated ,europe1 but in their conception of a cosmos decidedly at variance with anything yet conceived by any school of philosophy1 they will attract the universal attention of thinking men in all countries4 ,the scientist is immediately struck by the way ,einstein has utilized the various achievements in physics and mathematics to build up a co-ordinated system showing connecting links where heretofore none were perceived4 ,the philosopher is equally fascinated with a theory1 which1 in detail extremely complex1 shows a singular beauty of unity in design when viewed as a whole4 ,the revolutionary ideas propounded regarding time and space1 the brilliant way in which the most universal property of matter1 gravitation1 is for the first time linked up with other properties of matter1 and1 above all1 the experimental confirmation of several of his more startling predictions--always the finest test of scientific merit--stamps ,einstein as one of those super-men who from time to time are sent to us to give us a peep into the beyond4 ,some ,facts about ,einstein ,himself4 ,albert ,einstein was born in ,germany some #de years ago4 ,at first he was engaged at the ,patent ,bureau in ,berne1 and later became professor at the ,zrich ,polytechnic4 ,after a short stay at ,prague ,university he accepted one of those tempting ,akademiker professorships at the university of ,berlin--professorships which insure a comfortable income to the recipient of one of them1 little university work beyond1 perhaps1 one lecture a week1 and splendid facilities for research4 ,a similar inducement enticed the chemical philosopher1 ,van 't ,hoff1 to leave his ,amsterdam1 and the ,swedes came perilously near losing their most illustrious scientist1 ,arrhenius4 ,einstein published his first paper on relativity in #aije1 when not more than #cj years old4 ,of this paper ,planck1 the ,nobel ,laureate in physics this year1 has offered this opinion3 ,it surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge4 ,the revolution introduced into the physical conceptions of the world is only to be compared in extent and depth with that brought about by the introduction of the ,copernican system of the universe4 ,einstein published a full exposition of the relativity theory in #aiaf4 ,during the momentous years of #aiad-ai1 ,einstein quietly pursued his labors4 ,there seems to be some foundation for the belief that the ways of the ,german ,high ,command found little favor in his eyes4 ,at any rate1 he was not one of the forty professors who signed the famous manifesto extolling ,germany's aims4 ,we know for a fact1 writes ,dr4 ,o4 ,a4 ,rankine1 of the ,imperial ,college of ,science and ,technology1 ,london1 that ,einstein never was employed on war work4 ,whatever may have been ,germany's mistakes in other directions1 she left her men of science severely alone4 ,in fact1 they were encouraged to continue in their normal occupations4 ,einstein undoubtedly received a large measure of support from the ,imperial ,government1 even when the ,german armies were being driven back across ,belgium4 ,quite recently 7,june1 #aibj7 the ,barnard ,medal of ,columbia ,university was conferred on him in recognition of his highly original and fruitful development of the fundamental concepts of physics through application of mathematics4 ,in acknowledging the honor1 ,prof4 ,einstein wrote to ,president ,butler that 444 quite apart from the personal satisfaction1 ,i believe ,i may regard your decision to confer the medal upon him as a harbinger of a better time in which a sense of international solidarity will once more unite scholars of the various countries4 ,,references ,for those lacking all astronomical knowledge1 an excellent plan would be to read the first #dj pages of ,w4 ,h4 ,snyder's ,everyday ,science 7,allyn and ,bacon71 in which may be found a clear and simple account of the solar system4 ,this could be followed with ,bertrand ,russell's chapter on ,the ,nature of ,matter in his little volume1 ,the ,problems of ,philosophy 7,henry ,holt and ,co474 ,here the reader will be introduced to the purely philosophical side of the question--quite a necessary equipment for the understanding of ,einstein's theory4 ,of the non-mathematical articles which have appeared1 those by ,prof4 ,a4 ,s4 ,eddington 7,nature1 volume #aja1 pages #ae and #cd1 #aiah7 and ,prof4 ,m4 ,r4 ,cohen 7,the ,new ,republic1 ,jan4 #ba1 #aibj7 are the best which have come to the author's notice4 ,other articles on ,einstein's theory1 some easily comprehensible1 others somewhat confusing1 and still others full of noise and rather empty1 are by ,h4 ,a4 ,lorentz1 ,the ,new ,york ,times1 ,dec4 #ba1 #aiai 7since reprinted in book form by ,brentano's1 ,new ,york1 #aibj72 ,j4 ,q4 ,stewart1 ,scientific ,american1 ,jan4 #c1 #aibj2 ,e4 ,cunningham1 ,nature1 volume #ajd1 pages #ced and #cgd1 #aiai2 ,f4 ,h4 ,loring1 ,chemical ,news1 volume #aab1 pages #bbf1 #bcf1 #bdh1 and #bfj1 #aiae2 ,e4 ,b4 ,wilson1 ,scientific ,monthly1 volume #aj1 page #bag1 #aibj2 ,j4 ,s4 ,ames1 ,science1 volume #ea1 page #bec1 #aibj #ab2 ,l4 ,a4 ,bauer1 ,science1 volume #ea1 page #cja 7#aibj71 and volume #ea1 page #eha 7#aibj72 ,sir ,oliver ,lodge1 ,scientific ,monthly1 volume #aj1 page #cgh1 #aibj2 ,e4 ,e4 ,slosson1 ,independent1 ,nov4 #bi1 ,dec4 #ac1 ,dec4 #bj1 ,dec4 #bg1 #aiai 7since collected and published in book form by ,harcourt1 ,brace and ,howe72 ,isabel ,m4 ,lewis1 ,electrical ,experimenter1 ,jan41 #aibj2 ,a4 ,j4 ,lotka1 ,harper's ,magazine1 ,march1 #aibj1 page #dgg2 and ,r4 ,d4 ,carmichael1 ,new ,york ,times1 ,march #bh1 #aibj4 ,einstein himself is responsible for a brief article in ,english which first appeared in the ,london ,times1 and was later reprinted in ,science1 volume #ea1 page #h1 #aibj 7see the ,appendix74 ,a number of books deal with the subject1 and all of them are more or less mathematical4 ,however1 in every one of these volumes certain chapters1 or portions of chapters1 may be read with profit even by the non-mathematical reader4 ,some of these books are3 ,erwin ,freundlich1 ,the ,foundations of ,einstein's ,theory of ,gravitation 7,university ,press1 ,cambridge1 #aibj74 7,a very complete list of references--up to ,feb41 #aibj--;is also given72 ,a4 ,s4 ,eddington1 ,report on the ,relativity ,theory of ,gravitation for the ,physical ,society of ,london 7,fleetway ,press1 ,ltd41 ,london1 #aibj72 ,r4 ,c4 ,tolman1 ,theory of the ,relativity of ,motion 7,university of ,california ,press1 #aiag72 ,e4 ,cunningham1 ,relativity and the ,electron ,theory 7,longmans1 ,green and ,co41 #aiae72 ,r4 ,d4 ,carmichael1 ,the ,theory of ,relativity 7,john ,wiley and ,sons1 #aiac72 ,l4 ,silberstein1 ,the ,theory of ,relativity 7,macmillan1 #aiad72 and ,e4 ,cunningham1 ,the ,principle of ,relativity 7,university ,press1 ,cambridge1 ,england1 #aiad74 ,to those familiar with the ,german language ,einstein's book1 ber die spezielle und die allgemeine ,relativittstheorie 7,friedr4 ,vieweg und ,sohn1 ,braunschweig1 #aibj71 may be recommended4 #ac ,the mathematical student may be referred to a volume incorporating the more important papers of ,einstein1 ,minkowski and ,lorentz3 ,das ,relativittsprinzip1 7,b4 ,g4 ,teubner1 ,berlin1 #aiac74 ,einstein's papers have appeared in the ,annalen der ,physik1 ,leipzig1 volume #ag1 page #acb1 #aije1 volume #di1 page #gfj1 #aiaf1 and volume #ee1 page #bda1 #aiah4 ,,appendix ,note #a 7page #ba7 ,on this earth there is indeed a tiny corner of the universe accessible to other senses than the sense of sight3 but feeling and taste act only at those minute distances which separate particles of matter when 'in contact3' smell ranges over1 at the utmost1 a mile or two1 and the greatest distance which sound is ever known to have traveled 7when ,krakatoa exploded in #ahhc7 is but a few thousand miles--a mere fraction of the earth's girdle4--,prof4 ,h4 ,h4 ,turner of ,oxford4 ,note #b 7page #bg7 ,huyghens and ,leibniz both objected to ,newton's inverse square law because it postulated action at a distance1--for example1 the attractive force of the sun and the earth4 ,this desire for continuity in physical laws led to the supposition of an ether4 ,we may here anticipate and state that the reason which prompted ,huyghens to object to ,newton's law led ,einstein in our own day to raise objections to the ether theory4 ,in the formulation of physical laws1 only those things were to be regarded as being in causal connection which were capable of being actually observed4 ,and the ether has not been actually observed4 ,the idea of continuity implies distances between adjacent points that are infinitesimal in extent2 hence the idea of continuity comes in direct opposition with the finite distances of ,newton4 ,the statement relating to causal connection--the refusal to accept an ether as an absolute base of reference--leads to the principle of the relativity of motion4 ,note #c 7page #cj7 ,sir ,oliver ,lodge goes to the extreme of pinning his faith in the reality of this ether rather than in that of matter4 ,witness the following statement he made recently before a ,new ,york audience3 ,to my mind the ether of space is a substantial reality with extraordinarily perfect properties1 with an immense amount of energy stored up in it1 with a constitution which we must discover1 but a substantial reality far more impressive than that of matter4 ,empty space1 as we call it1 is full of ether1 but it makes no appeal to our senses4 ,the appearance is as if it were nothing4 ,it is the most important thing in the material universe4 ,i believe that matter is a modification of ether1 a very porous substance1 a thing more analogous to a cobweb or the ,milky ,way or something very slight and unsubstantial1 as compared to ether4 ,and again3 ,the properties of ether seem to be perfect4 ,matter is less so2 it has friction and elasticity4 ,no imperfection has been discovered in the ether space4 ,it doesn't wear out2 there is no dissipation of energy2 there is no friction4 ,ether is material1 yet it is not matter2 both are substantial realities in physics1 but it is the ether of space that holds things together and acts as a cement4 ,my business is to call attention to the whole world of etherealness of things1 and ,i have made it a subject of thirty years' study1 but we must admit that there is no getting hold of ether except indirectly4 ,i consider the ether of space1 says ,lodge1 in conclusion1 the one substantial thing in the universe4 ,and ,lodge is certainly entitled to his opinion4 ,note #d 7page #ea7 ,for the benefit of those readers who wish to gain a deeper insight into the relativity principle1 we shall here discuss it very briefly4 ,newton and ,galileo had developed a relativity principle in mechanics which may be stated as follows3 ,if one system of reference is in uniform rectilinear motion with respect to another system of reference1 then whatever physical laws are deduced from the first system hold true for the second system4 ,the two systems are equivalent4 ,if the two systems be represented by xyz and x'y'z'1 and if they move with the velocity of v along the x-axis with respect to one another1 then the two systems are mathematically related thus3 x' x - vt1 y' y1 z' z1 t' t1 and this immediately provides us with a means of transforming the laws of one system to those of another4 ,with the development of electrodynamics 7which we may call electricity in motion7 difficulties arose which equations in mechanics of type 7#a7 could no longer solve4 ,these difficulties merely increased when ,maxwell showed that light must be regarded as an electromagnetic phenomenon4 ,for suppose we wish to investigate the motion of a source of light 7which may be the equivalent of the motion of the earth with reference to the sun7 with respect to the velocity of the light it emits--a typical example of the study of moving systems--how are we to coordinate the electrodynamical and mechanical elements8 ,or1 again1 suppose we wish to investigate the velocity of electrons shot out from radium with a speed comparable to that of light1 how are we to coordinate the two branches in tracing the course of these negative particles of electricity8 ,it was difficulties such as these that led to the ,lorentz-,einstein modifications of the ,newton-,galileo relativity equations 7#a74 ,the ,lorentz-,einstein equations are expressed in the form3 x' fracx-vtsqrt#a-;fracv#b;c1 y' y1 z' z1 t' fract-fracvc#b;cdot xsqrt#a-;fracv#b;c#b1 c denoting the velocity of light in vacuo 7which1 according to all observations1 is the same1 irrespective of the observer's state of motion74 ,here1 you see1 electrodynamical systems 7light and therefore ray velocities such as those due to electrons7 are brought into play4 ,this gives us ,einstein's special theory of relativity4 ,from it ,einstein deduced some startling conceptions of time and space4 ,note #e 7page #ee7 ,the velocity 7v7 of an object in one system will have a different velocity 7v'7 if referred to another system in uniform motion relative to the first4 ,it had been supposed that only a something endowed with infinite velocity would show the same velocity in all systems1 irrespective of the motions of the latter4 ,michelson and ,morley's results actually point to the velocity of light as showing the properties of the imaginary infinite velocity4 ,the velocity of light possesses universal significance2 and this is the basis for much of ,einstein's earlier work4 ,note #f 7page #ef7 ,euclid assumes that parallel lines never meet1 which they cannot do of course if they be defined as equidistant4 ,but are there such lines8 ,and if not1 why not assume that all lines drawn through a point outside a given line will eventually intersect it8 ,such an assumption leads to a geometry in which all lines are conceived as being drawn on the surface of a sphere or an ellipse1 and in it the three angles of a triangle are never quite equal to two right angles1 nor the circumference of a circle quite pi times its diameter4 ,but that is precisely what the contraction effect due to motion requires4 7,dr4 ,walker7 ,note #g 7page #eg7 ,einstein had become tired of assumptions4 ,he had no particular objection to the ether theory beyond the fact that this ether did not come within the range of our senses2 it could not be observed4 ,the consistent fulfilment of the two postulates--'action by contact' and causal relationship between only such things as lie within the realm of observation see ,note #b combined together is1 ,i believe1 the mainspring of ,einstein's method of investigation4444 7,prof4 ,freundlich74 ,note #h 7page #ei7 ,that the conception of the simultaneity of events is devoid of meaning can be deduced from equation 7#b7 see ,note #d4 ,we owe the proof to ,einstein4 ,it is possible to select a suitable time-coordinate in such a way that a time-measurement enters into physical laws in exactly the same manner as regards its significance as a space measurement 7that is1 they are fully equivalent symbolically71 and has likewise a definite coordinate direction4444 ,it never occurred to anyone that the use of a light-signal as a means of connection between the moving-body and the observer1 which is necessary in practice in order to determine simultaneity1 might affect the final result1 i4e41 of time measurements in different systems4 7,freundlich74 ,but that is just what ,einstein shows1 because time-measurements are based on simultaneity of events1 and this1 as pointed out above1 is devoid of meaning4 ,had the older masters the occasion to study enormous velocities1 such as the velocity of light1 rather than relatively small ones--and even the velocity of the earth around the sun is small as compared to the velocity of light--discrepancies between theory and experiment would have become apparent4 ,note #i 7page #fg7 ,how the special theory of relativity 7see ,note #d7 led to the general theory of relativity 7which included gravitation7 may now be briefly traced4 ,when we speak of electrons1 or negative particles of electricity1 in motion1 we are speaking of energy in motion4 ,now these electrons when in motion exhibit properties that are very similar to matter in motion4 ,whatever deviations there are are due to the enormous velocity of these electrons1 and this velocity1 as has already been pointed out1 is comparable to that of light2 whereas before the advent of the electron1 the velocity of no particles comparable to that of light had ever been measured4 ,according to present views all inertia of matter consists only of the inertia of the latent energy in it2 444 everything that we know of the inertia of energy holds without exception for the inertia of matter4 ,now it is on the assumption that inertial mass and gravitational pull are equivalent that the mass of a body is determined by its weight4 ,what is true of matter should be true of energy4 ,the special theory of relativity1 however1 takes into account only inertia 7inertial mass7 but not gravitation 7gravitational pull or weight7 of energy4 ,when a body absorbs energy equation #b 7see ,note #d7 will record a gain in inertia but not in weight--which is contrary to one of the fundamental facts in mechanics4 ,this means that a more general theory of relativity is required to include gravitational phenomena4 ,hence ,einstein's ,general ,theory of ,relativity4 ,hence the approach to a new theory of gravitation4 ,hence the setting up of a differential equation which comprises the motion of a body under the influence of both inertia and gravity1 and which symbolically expresses the relativity of motions4444 ,the differential law must always preserve the same form1 irrespective of the system of coordinates to which it is referred1 so that no system of coordinates enjoys a preference to any other4 7,for the general form of the equation and for an excellent discussion of its significance1 see ,freundlich's monograph1 pages #bg-cc47 ,,time1 ,,space1 ,,and ,,gravitation #ad ,by ,prof4 ,albert ,einstein ,there are several kinds of theory in physics4 ,most of them are constructive4 ,these attempt to build a picture of complex phenomena out of some relatively simple proposition4 ,the kinetic theory of gases1 for instance1 attempts to refer to molecular movement the mechanical thermal1 and diffusional properties of gases4 ,when we say that we understand a group of natural phenomena1 we mean that we have found a constructive theory which embraces them4 ,theories of ,principle4--,but in addition to this most weighty group of theories1 there is another group consisting of what ,i call theories of principle4 ,these employ the analytic1 not the synthetic method4 ,their starting-point and foundation are not hypothetical constituents1 but empirically observed general properties of phenomena1 principles from which mathematical formul are deduced of such a kind that they apply to every case which presents itself4 ,thermodynamics1 for instance1 starting from the fact that perpetual motion never occurs in ordinary experience1 attempts to deduce from this1 by analytic processes1 a theory which will apply in every case4 ,the merit of constructive theories is their comprehensiveness1 adaptability1 and clarity1 that of the theories of principle1 their logical perfection1 and the security of their foundation4 ,the theory of relativity is a theory of principle4 ,to understand it1 the principles on which it rests must be grasped4 ,but before stating these it is necessary to point out that the theory of relativity is like a house with two separate stories1 the special relativity theory and the general theory of relativity4 ,since the time of the ancient ,greeks it has been well known that in describing the motion of a body we must refer to another body4 ,the motion of a railway train is described with reference to the ground1 of a planet with reference to the total assemblage of visible fixed stars4 ,in physics the bodies to which motions are spatially referred are termed systems of coordinates4 ,the laws of mechanics of ,galileo and ,newton can be formulated only by using a system of coordinates4 ,the state of motion of a system of coordinates can not be chosen arbitrarily if the laws of mechanics are to hold good 7it must be free from twisting and from acceleration74 ,the system of coordinates employed in mechanics is called an inertia-system4 ,the state of motion of an inertia-system1 so far as mechanics are concerned1 is not restricted by nature to one condition4 ,the condition in the following proposition suffices2 a system of coordinates moving in the same direction and at the same rate as a system of inertia is itself a system of inertia4 ,the special relativity theory is therefore the application of the following proposition to any natural process3 ,every law of nature which holds good with respect to a coordinate system ,k must also hold good for any other system ,k' provided that ,k and ,k' are in uniform movement of translation4 ,the second principle on which the special relativity theory rests is that of the constancy of the velocity of light in a vacuum4 ,light in a vacuum has a definite and constant velocity1 independent of the velocity of its source4 ,physicists owe their confidence in this proposition to the ,maxwell-,lorentz theory of electro-dynamics4 ,the two principles which ,i have mentioned have received strong experimental confirmation1 but do not seem to be logically compatible4 ,the special relativity theory achieved their logical reconciliation by making a change in kinematics1 that is to say1 in the doctrine of the physical laws of space and time4 ,it became evident that a statement of the coincidence of two events could have a meaning only in connection with a system of coordinates1 that the mass of bodies and the rate of movement of clocks must depend on their state of motion with regard to the coordinates4 ,the ,older ,physics4--,but the older physics1 including the laws of motion of ,galileo and ,newton1 clashed with the relativistic kinematics that ,i have indicated4 ,the latter gave origin to certain generalized mathematical conditions with which the laws of nature would have to conform if the two fundamental principles were compatible4 ,physics had to be modified4 ,the most notable change was a new law of motion for 7very rapidly7 moving mass-points1 and this soon came to be verified in the case of electrically-laden particles4 ,the most important result of the special relativity system concerned the inert mass of a material system4 ,it became evident that the inertia of such a system must depend on its energy-content1 so that we were driven to the conception that inert mass was nothing else than latent energy4 ,the doctrine of the conservation of mass lost its independence and became merged in the doctrine of conservation of energy4 ,the special relativity theory which was simply a systematic extension of the electro-dynamics of ,maxwell and ,lorentz1 had consequences which reached beyond itself4 ,must the independence of physical laws with regard to a system of coordinates be limited to systems of coordinates in uniform movement of translation with regard to one another8 ,what has nature to do with the coordinate systems that we propose and with their motions8 ,although it may be necessary for our descriptions of nature to employ systems of coordinates that we have selected arbitrarily1 the choice should not be limited in any way so far as their state of motion is concerned4 7,general theory of relativity47 ,the application of this general theory of relativity was found to be in conflict with a well-known experiment1 according to which it appeared that the weight and the inertia of a body depended on the same constants 7identity of inert and heavy masses74 ,consider the case of a system of coordinates which is conceived as being in stable rotation relative to a system of inertia in the ,newtonian sense4 ,the forces which1 relatively to this system1 are centrifugal must1 in the ,newtonian sense1 be attributed to inertia4 ,but these centrifugal forces are1 like gravitation1 proportional to the mass of the bodies4 ,is it not1 then1 possible to regard the system of coordinates as at rest1 and the centrifugal forces as gravitational8 ,the interpretation seemed obvious1 but classical mechanics forbade it4 ,this slight sketch indicates how a generalized theory of relativity must include the laws of gravitation1 and actual pursuit of the conception has justified the hope4 ,but the way was harder than was expected1 because it contradicted ,euclidian geometry4 ,in other words1 the laws according to which material bodies are arranged in space do not exactly agree with the laws of space prescribed by the ,euclidian geometry of solids4 ,this is what is meant by the phrase a warp in space4 ,the fundamental concepts straight1 plane1 etc41 accordingly lose their exact meaning in physics4 ,in the generalized theory of relativity1 the doctrine of space and time1 kinematics1 is no longer one of the absolute foundations of general physics4 ,the geometrical states of bodies and the rates of clocks depend in the first place on their gravitational fields1 which again are produced by the material system concerned4 ,thus the new theory of gravitation diverges widely from that of ,newton with respect to its basal principle4 ,but in practical application the two agree so closely that it has been difficult to find cases in which the actual differences could be subjected to observation4 ,as yet only the following have been suggested3 #a4 ,the distortion of the oval orbits of planets round the sun 7confirmed in the case of the planet ,mercury74 #b4 ,the deviation of light-rays in a gravitational field 7confirmed by the ,english ,solar ,eclipse expedition74 #c4 ,the shifting of spectral lines towards the red end of the spectrum in the case of light coming to us from stars of appreciable mass 7not yet confirmed74 ,the great attraction of the theory is its logical consistency4 ,if any deduction from it should prove untenable1 it must be given up4 ,a modification of it seems impossible without destruction of the whole4 ,no one must think that ,newton's great creation can be overthrown in any real sense by this or by any other theory4 ,his clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built4 ,,einstein',s ,,law ,,of ,,gravitation #ae ,by ,prof4 ,j4 ,s4 ,ames ,johns ,hopkins ,university 444 ,in the treatment of ,maxwell's equations of the electromagnetic field1 several investigators realized the importance of deducing the form of the equations when applied to a system moving with a uniform velocity4 ,one object of such an investigation would be to determine such a set of transformation formul as would leave the mathematical form of the equations unaltered4 ,the necessary relations between the new space-coordinates1 those applying to the moving system1 and the original set were of course obvious2 and elementary methods led to the deduction of a new variable which should replace the time coordinate4 ,this step was taken by ,lorentz and also1 ,i believe1 by ,larmor and by ,voigt4 ,the mathematical deductions and applications in the hands of these men were extremely beautiful1 and are probably well known to you all4 ,lorentz' paper on this subject appeared in the ,proceedings of the ,amsterdam ,academy in #aijd4 ,in the following year there was published in the ,annalen der ,physik a paper by ,einstein1 written without any knowledge of the work of ,lorentz1 in which he arrived at the same transformation equations as did the latter1 but with an entirely different and fundamentally new interpretation4 ,einstein called attention in his paper to the lack of definiteness in the concepts of time and space1 as ordinarily stated and used4 ,he analyzed clearly the definitions and postulates which were necessary before one could speak with exactness of a length or of an interval of time4 ,he disposed forever of the propriety of speaking of the true length of a rod or of the true duration of time1 showing1 in fact1 that the numerical values which we attach to lengths or intervals of time depend upon the definitions and postulates which we adopt4 ,the words absolute space or time intervals are devoid of meaning4 ,as an illustration of what is meant ,einstein discussed two possible ways of measuring the length of a rod when it is moving in the direction of its own length with a uniform velocity1 that is1 after having adopted a scale of length1 two ways of assigning a number to the length of the rod concerned4 ,one method is to imagine the observer moving with the rod1 applying along its length the measuring scale1 and reading off the positions of the ends of the rod4 ,another method would be to have two observers at rest on the body with reference to which the rod has the uniform velocity1 so stationed along the line of motion of the rod that as the rod moves past them they can note simultaneously on a stationary measuring scale the positions of the two ends of the rod4 ,einstein showed that1 accepting two postulates which need no defense at this time1 the two methods of measurements would lead to different numerical values1 and1 further1 that the divergence of the two results would increase as the velocity of the rod was increased4 ,in assigning a number1 therefore1 to the length of a moving rod1 one must make a choice of the method to be used in measuring it4 ,obviously the preferable method is to agree that the observer shall move with the rod1 carrying his measuring instrument with him4 ,this disposes of the problem of measuring space relations4 ,the observed fact that1 if we measure the length of the rod on different days1 or when the rod is lying in different positions1 we always obtain the same value offers no information concerning the real length of the rod4 ,it may have changed1 or it may not4 ,it must always be remembered that measurement of the length of a rod is simply a process of comparison between it and an arbitrary standard1 e4g41 a meter-rod or yard-stick4 ,in regard to the problem of assigning numbers to intervals of time1 it must be borne in mind that1 strictly speaking1 we do not measure such intervals1 i4e41 that we do not select a unit interval of time and find how many times it is contained in the interval in question4 7,similarly1 we do not measure the pitch of a sound or the temperature of a room47 ,our practical instruments for assigning numbers to time-intervals depend in the main upon our agreeing to believe that a pendulum swings in a perfectly uniform manner1 each vibration taking the same time as the next one4 ,of course we cannot prove that this is true1 it is1 strictly speaking1 a definition of what we mean by equal intervals of time2 and it is not a particularly good definition at that4 ,its limitations are sufficiently obvious4 ,the best way to proceed is to consider the concept of uniform velocity1 and then1 using the idea of some entity having such a uniform velocity1 to define equal intervals of time as such intervals as are required for the entity to traverse equal lengths4 ,these last we have already defined4 ,what is required in addition is to adopt some moving entity as giving our definition of uniform velocity4 ,considering our known universe it is self-evident that we should choose in our definition of uniform velocity the velocity of light1 since this selection could be made by an observer anywhere in our universe4 ,having agreed then to illustrate by the words uniform velocity that of light1 our definition of equal intervals of time is complete4 ,this implies1 of course1 that there is no uncertainty on our part as to the fact that the velocity of light always has the same value at any one point in the universe to any observer1 quite regardless of the source of light4 ,in other words1 the postulate that this is true underlies our definition4 ,following this method ,einstein developed a system of measuring both space and time intervals4 ,as a matter of fact his system is identically that which we use in daily life with reference to events here on the earth4 ,he further showed that if a man were to measure the length of a rod1 for instance1 on the earth and then were able to carry the rod and his measuring apparatus to ,mars1 the sun1 or to ,arcturus he would obtain the same numerical value for the length in all places and at all times4 ,this doesn't mean that any statement is implied as to whether the length of the rod has remained unchanged or not2 such words do not have any meaning--remember that we can not speak of true length4 ,it is thus clear that an observer living on the earth would have a definite system of units in terms of which to express space and time intervals1 i4e41 he would have a definite system of space coordinates 7x1 y1 z7 and a definite time coordinate 7t72 and similarly an observer living on ,mars would have his system of coordinates 7x'1 y'1 z'1 t'74 ,provided that one observer has a definite uniform velocity with reference to the other1 it is a comparatively simple matter to deduce the mathematical relations between the two sets of coordinates4 ,when ,einstein did this1 he arrived at the same transformation formul as those used by ,lorentz in his development of ,maxwell's equations4 ,the latter had shown that1 using these formul1 the form of the laws for all electromagnetic phenomena maintained the same form2 so ,einstein's method proves that using his system of measurement an observer1 anywhere in the universe1 would as the result of his own investigation of electromagnetic phenomena arrive at the same mathematical statement of them as any other observer1 provided only that the relative-velocity of the two observers was uniform4 ,einstein discussed many other most important questions at this time2 but it is not necessary to refer to them in connection with the present subject4 ,so far as this is concerned1 the next important step to note is that taken in the famous address of ,minkowski1 in #aijh1 on the subject of ,space and ,time4 ,it would be difficult to overstate the importance of the concepts advanced by ,minkowski4 ,they marked the beginning of a new period in the philosophy of physics4 ,i shall not attempt to explain his ideas in detail1 but shall confine myself to a few general statements4 ,his point of view and his line of development of the theme are absolutely different from those of ,lorentz or of ,einstein2 but in the end he makes use of the same transformation formul4 ,his great contribution consists in giving us a new geometrical picture of their meaning4 ,it is scarcely fair to call ,minkowski's development a picture2 for to us a picture can never have more than three dimensions1 our senses limit us2 while his picture calls for perception of four dimensions4 ,it is this fact that renders any even semi-popular discussion of ,minkowski's work so impossible4 ,we can all see that for us to describe any event a knowledge of four coordinates is necessary1 three for the space specification and one for the time4 ,a complete picture could be given then by a point in four dimensions4 ,all four coordinates are necessary3 we never observe an event except at a certain time1 and we never observe an instant of time except with reference to space4 ,discussing the laws of electromagnetic phenomena1 ,minkowski showed how in a space of four dimensions1 by a suitable definition of axes1 the mathematical transformation of ,lorentz and ,einstein could be described by a rotation of the set of axes4 ,we are all accustomed to a rotation of our ordinary cartesian set of axes describing the position of a point4 ,we ordinarily choose our axes at any location on the earth as follows3 one vertical1 one east and west1 one north and south4 ,so if we move from any one laboratory to another1 we change our axes2 they are always orthogonal1 but in moving from place to place there is a rotation4 ,similarly1 ,minkowski showed that if we choose four orthogonal axes at any point on the earth1 according to his method1 to represent a space-time point using the method of measuring space and time intervals as outlined by ,einstein2 and1 if an observer on ,arcturus used a similar set of axes and the method of measurement which he naturally would1 the set of axes of the latter could be obtained from those of the observer on the earth by a pure rotation 7and naturally a transfer of the origin74 ,this is a beautiful geometrical result4 ,to complete my statement of the method1 ,i must add that instead of using as his fourth axis one along which numerical values of time are laid off1 ,minkowski defined his fourth coordinate as the product of time and the imaginary constant1 the square root of minus one4 ,this introduction of imaginary quantities might be expected1 possibly1 to introduce difficulties2 but1 in reality1 it is the very essence of the simplicity of the geometrical description just given of the rotation of the sets of axes4 ,it thus appears that different observers situated at different points in the universe would each have their own set of axes1 all different1 yet all connected by the fact that any one can be rotated so as to coincide with any other4 ,this means that there is no one direction in the four-dimensional space that corresponds to time for all observers4 ,just as with reference to the earth there is no direction which can be called vertical for all observers living on the earth4 ,in the sense of an absolute meaning the words up and down1 before and after1 sooner or later1 are entirely meaningless4 ,this concept of ,minkowski's may be made clearer1 perhaps1 by the following process of thought4 ,if we take a section through our three-dimensional space1 we have a plane1 i4e41 a two-dimensional space4 ,similarly1 if a section is made through a four-dimensional space1 one of three dimensions is obtained4 ,thus1 for an observer on the earth a definite section of ,minkowski's four-dimensional space will give us our ordinary three-dimensional one2 so that this section will1 as it were1 break up ,minkowski's space into our space and give us our ordinary time4 ,similarly1 a different section would have to be used to the observer on ,arcturus2 but by a suitable selection he would get his own familiar three-dimensional space and his own time4 ,thus the space defined by ,minkowski is completely isotropic in reference to measured lengths and times1 there is absolutely no difference between any two directions in an absolute sense2 for any particular observer1 of course1 a particular section will cause the space to fall apart so as to suit his habits of measurement2 any section1 however1 taken at random will do the same thing for some observer somewhere4 ,from another point of view1 that of ,lorentz and ,einstein1 it is obvious that1 since this four-dimensional space is isotropic1 the expression of the laws of electromagnetic phenomena take identical mathematical forms when expressed by any observer4 ,the question of course must be raised as to what can be said in regard to phenomena which so far as we know do not have an electromagnetic origin4 ,in particular what can be done with respect to gravitational phenomena8 ,before1 however1 showing how this problem was attacked by ,einstein2 and the fact that the subject of my address is ,einstein's work on gravitation shows that ultimately ,i shall explain this1 ,i must emphasize another feature of ,minkowski's geometry4 ,to describe the space-time characteristics of any event a point1 defined by its four coordinates1 is sufficient2 so1 if one observes the life-history of any entity1 e4g41 a particle of matter1 a light-wave1 etc41 he observes a sequence of points in the space-time continuum2 that is1 the life-history of any entity is described fully by a line in this space4 ,such a line was called by ,minkowski a world-line4 ,further1 from a different point of view1 all of our observations of nature are in reality observations of coincidences1 e4g41 if one reads a thermometer1 what he does is to note the coincidence of the end of the column of mercury with a certain scale division on the thermometer tube4 ,in other words1 thinking of the world-line of the end of the mercury column and the world-line of the scale division1 what we have observed was the intersection or crossing of these lines4 ,in a similar manner any observation may be analyzed2 and remembering that light rays1 a point on the retina of the eye1 etc41 all have their world-lines1 it will be recognized that it is a perfectly accurate statement to say that every observation is the perception of the intersection of world-lines4 ,further1 since all we know of a world-line is the result of observations1 it is evident that we do not know a world-line as a continuous series of points1 but simply as a series of discontinuous points1 each point being where the particular world-line in question is crossed by another world-line4 ,it is clear1 moreover1 that for the description of a world-line we are not limited to the particular set of four orthogonal axes adopted by ,minkowski4 ,we can choose any set of four-dimensional axes we wish4 ,it is further evident that the mathematical expression for the coincidence of two points is absolutely independent of our selection of reference axes4 ,if we change our axes1 we will change the coordinates of both points simultaneously1 so that the question of axes ceases to be of interest4 ,but our so-called laws of nature are nothing but descriptions in mathematical language of our observations2 we observe only coincidences2 a sequence of coincidences when put in mathematical terms takes a form which is independent of the selection of reference axes2 therefore the mathematical expression of our laws of nature1 of every character1 must be such that their form does not change if we make a transformation of axes4 ,this is a simple but far-reaching deduction4 ,there is a geometrical method of picturing the effect of a change of axes of reference1 i4e41 of a mathematical transformation4 ,to a man in a railway coach the path of a drop of water does not appear vertical1 i4e41 it is not parallel to the edge of the window2 still less so does it appear vertical to a man performing manoeuvres in an airplane4 ,this means that whereas with reference to axes fixed to the earth the path of the drop is vertical2 with reference to other axes1 the path is not4 ,or1 stating the conclusion in general language1 changing the axes of reference 7or effecting a mathematical transformation7 in general changes the shape of any line4 ,if one imagines the line forming a part of the space1 it is evident that if the space is deformed by compression or expansion the shape of the line is changed1 and if sufficient care is taken it is clearly possible1 by deforming the space1 to make the line take any shape desired1 or better stated1 any shape specified by the previous change of axes4 ,it is thus possible to picture a mathematical transformation as a deformation of space4 ,thus ,i can draw a line on a sheet of paper or of rubber and by bending and stretching the sheet1 ,i can make the line assume a great variety of shapes2 each of these new shapes is a picture of a suitable transformation4 ,now1 consider world-lines in our four-dimensional space4 ,the complete record of all our knowledge is a series of sequences of intersections of such lines4 ,by analogy ,i can draw in ordinary space a great number of intersecting lines on a sheet of rubber2 ,i can then bend and deform the sheet to please myself2 by so doing ,i do not introduce any new intersections nor do ,i alter in the least the sequence of intersections4 ,so in the space of our world-lines1 the space may be deformed in any imaginable manner without introducing any new intersections or changing the sequence of the existing intersections4 ,it is this sequence which gives us the mathematical expression of our so-called experimental laws2 a deformation of our space is equivalent mathematically to a transformation of axes1 consequently we see why it is that the form of our laws must be the same when referred to any and all sets of axes1 that is1 must remain unaltered by any mathematical transformation4 ,now1 at last we come to gravitation4 ,we can not imagine any world-line simpler than that of a particle of matter left to itself2 we shall therefore call it a straight line4 ,our experience is that two particles of matter attract one another4 ,expressed in terms of world-lines1 this means that1 if the world-lines of two isolated particles come near each other1 the lines1 instead of being straight1 will be deflected or bent in towards each other4 ,the world-line of any one particle is therefore deformed2 and we have just seen that a deformation is the equivalent of a mathematical transformation4 ,in other words1 for any one particle it is possible to replace the effect of a gravitational field at any instant by a mathematical transformation of axes4 ,the statement that this is always possible for any particle at any instant is ,einstein's famous ,principle of ,equivalence4 ,let us rest for a moment1 while ,i call attention to a most interesting coincidence1 not to be thought of as an intersection of world-lines4 ,it is said that ,newton's thoughts were directed to the observation of gravitational phenomena by an apple falling on his head2 from this striking event he passed by natural steps to a consideration of the universality of gravitation4 ,einstein in describing his mental process in the evolution of his law of gravitation says that his attention was called to a new point of view by discussing his experiences with a man whose fall from a high building he had just witnessed4 ,the man fortunately suffered no serious injuries and assured ,einstein that in the course of his fall he had not been conscious in the least of any pull downward on his body4 ,in mathematical language1 with reference to axes moving with the man the force of gravity had disappeared4 ,this is a case where by the transfer of the axes from the earth itself to the man1 the force of the gravitational field is annulled4 ,the converse change of axes from the falling man to a point on the earth could be considered as introducing the force of gravity into the equations of motion4 ,another illustration of the introduction into our equations of a force by a means of a change of axes is furnished by the ordinary treatment of a body in uniform rotation about an axis4 ,for instance1 in the case of a so-called conical pendulum1 that is1 the motion of a bob suspended from a fixed point by string1 which is so set in motion that the bob describes a horizontal circle and the string therefore describes a circular cone1 if we transfer our axes from the earth and have them rotate around the vertical line through the fixed point with the same angular velocity as the bob1 it is necessary to introduce into our equations of motion a fictitious force called the centrifugal force4 ,no one ever thinks of this force other than as a mathematical quantity introduced into the equations for the sake of simplicity of treatment2 no physical meaning is attached to it4 ,why should there be to any other so-called force1 which like centrifugal force1 is independent of the nature of the matter8 ,again1 here on the earth our sensation of weight is interpreted mathematically by combining expressions for centrifugal force and gravity2 we have no distinct sensation for either separately4 ,why then is there any difference in the essence of the two8 ,why not consider them both as brought into our equations by the agency of mathematical transformations8 ,this is ,einstein's point of view4 ,granting1 then1 the principle of equivalence1 we can so choose axes at any point at any instant that the gravitational field will disappear2 these axes are therefore of what ,eddington calls the ,galilean type1 the simplest possible4 ,consider1 that is1 an observer in a box1 or compartment1 which is falling with the acceleration of the gravitational field at that point4 ,he would not be conscious of the field4 ,if there were a projectile fired off in this compartment1 the observer would describe its path as being straight4 ,in this space the infinitesimal interval between two space-time points would then be given by the formula ds#b dx#ba dx#bb dx#bc dx#bd1 where ds is the interval and x#a1 x#b1 x#c1 x#d are coordinates4 ,if we make a mathematical transformation1 i4e41 use another set of axes1 this interval would obviously take the form ds#b g#aa;dx#bcc g#bb;dx#bb g#cc;dx#bc g#dd;dx#bd #b;g#ab;dx#a;dx#b rmetc41 where x#a1 x#b1 x#c and x#d are now coordinates referring to the new axes4 ,this relation involves ten coefficients1 the coefficients defining the transformation4 ,but of course a certain dynamical value is also attached to the g's1 because by the transfer of our axes from the ,galilean type we have made a change which is equivalent to the introduction of a gravitational field2 and the g's must specify the field4 ,that is1 these g's are the expressions of our experiences1 and hence their values can not depend upon the use of any special axes2 the values must be the same for all selections4 ,in other words1 whatever function of the coordinates any one g is for one set of axes1 if other axes are chosen1 this g must still be the same function of the new coordinates4 ,there are ten g's defined by differential equations2 so we have ten covariant equations4 ,einstein showed how these g's could be regarded as generalized potentials of the field4 ,our own experiments and observations upon gravitation have given us a certain knowledge concerning its potential2 that is1 we know a value for it which must be so near the truth that we can properly call it at least a first approximation4 ,or1 stated differently1 if ,einstein succeeds in deducing the rigid value for the gravitational potential in any field1 it must degenerate to the ,newtonian value for the great majority of cases with which we have actual experience4 ,einstein's method1 then1 was to investigate the functions 7or equations7 which would satisfy the mathematical conditions just described4 ,a transformation from the axes used by the observer in the following box may be made so as to introduce into the equations the gravitational field recognized by an observer on the earth near the box2 but this1 obviously1 would not be the general gravitational field1 because the field changes as one moves over the surface of the earth4 ,a solution found1 therefore1 as just indicated1 would not be the one sought for the general field2 and another must be found which is less stringent than the former but reduces to it as a special case4 ,he found himself at liberty to make a selection from among several possibilities1 and for several reasons chose the simplest solution4 ,he then tested this decision by seeing if his formul would degenerate to ,newton's law for the limiting case of velocities small when compared with that of light1 because this condition is satisfied in those cases to which ,newton's law applies4 ,his formul satisfied this test1 and he therefore was able to announce a law of gravitation1 of which ,newton's was a special form for a simple case4 ,to the ordinary scholar the difficulties surmounted by ,einstein in his investigations appear stupendous4 ,it is not improbable that the statement which he is alleged to have made to his editor1 that only ten men in the world could understand his treatment of the subject1 is true4 ,i am fully prepared to believe it1 and wish to add that ,i certainly am not one of the ten4 ,but ,i can also say that1 after a careful and serious study of his papers1 ,i feel confident that there is nothing in them which ,i can not understand1 given the time to become familiar with the special mathematical processes used4 ,the more ,i work over ,einstein's papers1 the more impressed ,i am1 not simply by his genius in viewing the problem1 but also by his great technical skill4 ,following the path outlined1 ,einstein1 as just said1 arrived at certain mathematical laws for a gravitational field1 laws which reduced to ,newton's form in most cases where observations are possible1 but which led to different conclusions in a few cases1 knowledge concerning which we might obtain by careful observations4 ,i shall mention a few deductions from ,einstein's formul4 #a4 ,if a heavy particle is put at the center of a circle1 and1 if the length of the circumference and the length of the diameter are measured1 it will be found that their ratio is not pi 7#c4adaei74 ,in other words the geometrical properties of space in such a gravitational field are not those discussed by ,euclid2 the space is1 then1 non-,euclidean4 ,there is no way by which this deduction can be verified1 the difference between the predicted ratio and pi is too minute for us to hope to make our measurements with sufficient exactness to determine the difference4 #b4 ,all the lines in the solar spectrum should with reference to lines obtained by terrestrial sources be displaced slightly towards longer wave-lengths4 ,the amount of displacement predicted for lines in the blue end of the spectrum is about one-hundredth of an ,angstrom unit1 a quantity well within experimental limits4 ,unfortunately1 as far as the testing of this prediction is concerned1 there are several physical causes which are also operating to cause displacement of the spectrum-lines2 and so at present a decision can not be rendered as to the verification4 ,st4 ,john and other workers at the ,mount ,wilson ,observatory have the question under investigation4 #c4 ,according to ,newton's law an isolated planet in its motion around a central sun would describe1 period after period1 the same elliptical orbit2 whereas ,einstein's laws lead to the prediction that the successive orbits traversed would not be identically the same4 ,each revolution would start the planet off on an orbit very approximately elliptical1 but with the major axis of the ellipse rotated slightly in the plane of the orbit4 ,when calculations were made for the various planets in our solar system1 it was found that the only one which was of interest from the standpoint of verification of ,einstein's formul was ,mercury4 ,it has been known for a long time that there was actually such a change as just described in the orbit of ,mercury1 amounting to #egd'' of arc per century2 and it has been shown that of this a rotation of #ecb'' was due to the direct action of other planets1 thus leaving an unexplained rotation of #db'' per century4 ,einstein's formul predicted a rotation of #dc''1 a striking agreement4 #d4 ,in accordance with ,einstein's formul a ray of light passing close to a heavy piece of matter1 the sun1 for instance1 should experience a sensible deflection in towards the sun4 ,this might be expected from general consideration of energy in motion2 energy and mass are generally considered to be identical in the sense that an amount of energy ,e has the mass ,e#a;c#b where c is the velocity of light2 and consequently a ray of light might fall within the province of gravitation and the amount of deflection to be expected could be calculated by the ordinary formula for gravitation4 ,another point of view is to consider again the observer inside the compartment falling with the acceleration of the gravitational field4 ,to him the path of a projectile and a ray of light would both appear straight2 so that1 if the projectile had a velocity equal to that of light1 it and the light wave would travel side by side4 ,to an observer outside the compartment1 e4g41 to one on the earth1 both would then appear to have the same deflection owing to the sun4 ,but how much would the path of the projectile be bent8 ,what would be the shape of its parabola8 ,one might apply ,newton's law2 but1 according to ,einstein's formul1 ,newton's law should be used only for small velocities4 ,in the case of a ray passing close to the sun it was decided that according to ,einstein's formula there should be a deflection of #a''4ge whereas ,newton's law of gravitation predicted half this amount4 ,careful plans were made by various astronomers1 to investigate this question at the solar eclipse last ,may1 and the result announced by ,dyson1 ,eddington and ,crommelin1 the leaders of astronomy in ,england1 was that there was a deflection of #a''4i4 ,of course the detection of such a minute deflection was an extraordinarily difficult matter1 so many corrections had to be applied to the original observations2 but the names of the men who record the conclusions are such as to inspire confidence4 ,certainly any effect of refraction seems to be excluded4 ,it is thus seen that the formul deduced by ,einstein have been confirmed in a variety of ways and in a most brilliant manner4 ,in connection with these formul one question must arise in the minds of everyone2 by what process1 where in the course of the mathematical development1 does the idea of mass reveal itself8 ,it was not in the equations at the beginning and yet here it is at the end4 ,how does it appear8 ,as a matter of fact it is first seen as a constant of integration in the discussion of the problem of the gravitational field due to a single particle2 and the identity of this constant with mass is proved when one compares ,einstein's formul with ,newton's law which is simply its degenerated form4 ,this mass1 though1 is the mass of which we become aware through our experiences with weight2 and ,einstein proceeded to prove that this quantity which entered as a constant of integration in his ideally simple problem also obeyed the laws of conservation of mass and conservation of momentum when he investigated the problems of two and more particles4 ,therefore ,einstein deduced from his study of gravitational fields the well-known properties of matter which form the basis of theoretical mechanics4 ,a further logical consequence of ,einstein's development is to show that energy has mass1 a concept with which every one nowadays is familiar4 ,the description of ,einstein's method which ,i have given so far is simply the story of one success after another2 and it is certainly fair to ask if we have at last reached finality in our investigation of nature1 if we have attained to truth4 ,are there no outstanding difficulties8 ,is there no possibility of error8 ,certainly1 not until all the predictions made from ,einstein's formul have been investigated can much be said2 and further1 it must be seen whether any other lines of argument will lead to the same conclusions4 ,but without waiting for all this there is at least one difficulty which is apparent at this time4 ,we have discussed the laws of nature as independent in their form of reference axes1 a concept which appeals strongly to our philosophy2 yet it is not at all clear1 at first sight1 that we can be justified in our belief4 ,we can not imagine any way by which we can become conscious of the translation of the earth in space2 but by means of gyroscopes we can learn a great deal about its rotation on its axis4 ,we could locate the positions of its two poles1 and by watching a ,foucault pendulum or a gyroscope we can obtain a number which we interpret as the angular velocity of rotation of axes fixed in the earth2 angular velocity with reference to what8 ,where is the fundamental set of axes8 ,this is a real difficulty4 ,it can be surmounted in several ways4 ,einstein himself has outlined a method which in the end amounts to assuming the existence on the confines of space of vast quantities of matter1 a proposition which is not attractive4 de,sitter has suggested a peculiar quality of the space to which we refer our space-time coordinates4 ,the consequences of this are most interesting1 but no decision can as yet be made as to the justification of the hypothesis4 ,in any case we can say that the difficulty raised is not one that destroys the real value of ,einstein's work4 ,in conclusion ,i wish to emphasize the fact1 which should be obvious1 that ,einstein has not attempted any explanation of gravitation2 he has been occupied with the deduction of its laws4 ,these laws1 together with those of electromagnetic phenomena1 comprise our store of knowledge4 ,there is not the slightest indication of a mechanism1 meaning by that a picture in terms of our senses4 ,in fact what we have learned has been to realize that our desire to use such mechanisms is futile4 ,,the ,,deflection ,,of ,,light ,,by ,,gravitation ,,and ,,the ,,einstein ,,theory ,,of ,,relativity4 #af ,sir ,frank ,dyson the ,astronomer ,royal ,the purpose of the expedition was to determine whether any displacement is caused to a ray of light by the gravitational field of the sun1 and if so1 the amount of the displacement4 ,einstein's theory predicted a displacement varying inversely as the distance of the ray from the sun's center1 amounting to #a''4ge for a star seen just grazing the sun4444 ,a study of the conditions of the #aiai eclipse showed that the sun would be very favorably placed among a group of bright stars--in fact1 it would be in the most favorable possible position4 ,a study of the conditions at various points on the path of the eclipse1 in which ,mr4 ,hinks helped us1 pointed to ,sobral1 in ,brazil1 and ,principe1 an island off the west coast of ,africa1 as the most favorable stations4444 ,the ,greenwich party1 ,dr4 ,crommelin and ,mr4 ,davidson1 reached ,brazil in ample time to prepare for the eclipse1 and the usual preliminary focusing by photographing stellar fields was carried out4 ,the day of the eclipse opened cloudy1 but cleared later1 and the observations were carried out with almost complete success4 ,with the astrographic telescope ,mr4 ,davidson secured #ae out of #ah photographs showing the required stellar images4 ,totality lasted #f minutes1 and the average exposure of the plates was #e to #f seconds4 ,dr4 ,crommelin with the other lens had #g successful plates out of #h4 ,the unsuccessful plates were spoiled for this purpose by the clouds1 but show the remarkable prominence very well4 ,when the plates were developed the astrographic images were found to be out of focus4 ,this is attributed to the effect of the sun's heat on the coelostat mirror4 ,the images were fuzzy and quite different from those on the check-plates secured at night before and after the eclipse4 ,fortunately the mirror which fed the #d-;inch lens was not affected1 and the star images secured with this lens were good and similar to those got by the night-plates4 ,the observers stayed on in ,brazil until ,july to secure the field in the night sky at the altitude of the eclipse epoch and under identical instrumental conditions4 ,the plates were measured at ,greenwich immediately after the observers' return4 ,each plate was measured twice over by ,messrs4 ,davidson and ,furner1 and ,i am satisfied that such faults as lie in the results are in the plates themselves and not in the measures4 ,the figures obtained may be briefly summarized as follows3 ,the astrographic plates gave #j''4ig for the displacement at the limb when the scale-value was determined from the plates themselves1 and #a''4dj when the scale-value was assumed from the check plates4 ,but the much better plates gave for the displacement at the limb #a''4ih1 ,einstein's predicted value being #a''4ge4 ,further1 for these plates the agreement was all that could be expected4444 ,after a careful study of the plates ,i am prepared to say that there can be no doubt that they confirm ,einstein's prediction4 ,a very definite result has been obtained that light is deflected according to ,einstein's law of gravitation4 ,professor ,a4 ,s4 ,eddington ,royal ,observatory ,mr4 ,cottingham and ,i left the other observers at ,madeira and arrived at ,principe on ,april #bc4444 ,we soon realized that the prospect of a clear sky at the end of ,may was not very good4 ,not even a heavy thunderstorm on the morning of the eclipse1 three weeks after the end of the wet season1 saved the situation4 ,the sky was completely cloudy at first contact1 but about half an hour before totality we began to see glimpses of the sun's crescent through the clouds4 ,we carried out our program exactly as arranged1 and the sky must have been clearer towards the end of totality4 ,of the #af plates taken during the five minutes of totality the first ten showed no stars at all2 of the later plates two showed five stars each1 from which a result could be obtained4 ,comparing them with the check-plates secured at ,oxford before we went out1 we obtained as the final result from the two plates for the value of the displacement of the limb #a''4f #j4c4444 ,this result supports the figures obtained at ,sobral4444 ,i will pass now to a few words on the meaning of the result4 ,it points to the larger of the two possible values of the deflection4 ,the simplest interpretation of the bending of the ray is to consider it as an effect of the weight of light4 ,we know that momentum is carried along on the path of a beam of light4 ,gravity in acting creates momentum in a direction different from that of the path of the ray and so causes it to bend4 ,for the half-effect we have to assume that gravity obeys ,newton's law2 for the full effect which has been obtained we must assume that gravity obeys the new law proposed by ,einstein4 ,this is one of the most crucial tests between ,newton's law and the proposed new law4 ,einstein's law had already indicated a perturbation1 causing the orbit of ,mercury to revolve4 ,that confirms it for relatively small velocities4 ,going to the limit1 where the speed is that of light1 the perturbation is increased in such a way as to double the curvature of the path1 and this is now confirmed4 ,this effect may be taken as proving ,einstein's law rather than his theory4 ,it is not affected by the failure to detect the displacement of ,fraunhofer lines on the sun4 ,if this latter failure is confirmed it will not affect ,einstein's law of gravitation1 but it will affect the views on which the law was arrived at4 ,the law is right1 though the fundamental ideas underlying it may yet be questioned4444 ,one further point must be touched upon4 ,are we to attribute the displacement to the gravitational field and not to the refracting matter around the sun8 ,the refractive index required to produce the result at a distance of #ae' from the sun would be that given by gases at a pressure of #a_/fj to #a_/bjj of an atmosphere4 ,this is of too great a density considering the depth through which the light would have to pass4 ,sir ,j4 ,j4 ,thomson ,president of the ,royal ,society 444 ,if the results obtained had been only that light was affected by gravitation1 it would have been of the greatest importance4 ,newton1 did1 in fact1 suggest this very point in his ,optics1 and his suggestion would presumably have led to the half-value4 ,but this result is not an isolated one2 it is part of a whole continent of scientific ideas affecting the most fundamental concepts of physics4444 ,this is the most important result obtained in connection with the theory of gravitation since ,newton's day1 and it is fitting that it should be announced at a meeting of the society so closely connected with him4 ,the difference between the laws of gravitation of ,einstein and ,newton come only in special cases4 ,the real interest of ,einstein's theory lies not so much in his results as in the method by which he gets them4 ,if his theory is right1 it makes us take an entirely new view of gravitation4 ,if it is sustained that ,einstein's reasoning holds good--and it has survived two very severe tests in connection with the perihelion of mercury and the present eclipse--then it is the result of one of the highest achievements of human thought4 ,the weak point in the theory is the great difficulty in expressing it4 ,it would seem that no one can understand the new law of gravitation without a thorough knowledge of the theory of invariants and of the calculus of variations4 ,one other point of physical interest arises from the discussion4 ,light is deflected in passing near huge bodies of matter4 ,this involves alterations in the electric and magnetic field4 ,this1 again1 implies the existence of electric and magnetic forces outside matter--forces at present unknown1 though some idea of their nature may be got from the results of this expedition4 ,,notes #a ,see ,note #a at the end of the volume4 #b ,see ,note #b4 #c ,see ,note #c4 #d ,a circle--in our case the horizon--is measured by dividing the circumference into #cfj parts2 each part is called a degree4 ,each degree is divided into #fj minutes1 and each minute into #fj seconds4 #e ,see page #aac4 #f ,see ,note #d4 #g ,see ,note #e4 #h ,see ,note #f4 #i ,see ,note #g4 #aj ,see ,note #h4 #aa ,see ,note #i4 #ab ,see page #ic4 #ac ,this has since been translated into ,english by ,dr4 ,lawson and published by ,methuen 7,london74 ,since the above has been written two excellent books have been published4 ,one is by ,prof4 ,a4 ,s4 ,eddington1 ,space1 ,time and ,gravitation 7,cambridge ,univ4 ,press1 #aibj74 ,the other1 somewhat more of a philosophical work1 is ,prof4 ,moritz ,schlick's ,space and ,time in ,contemporary ,physics 7,oxford ,univ4 ,press1 #aibj74 ,though published as early as #ahig1 ,bertrand ,russell's ,an ,essay on the ,foundations of ,geometry 7,cambridge ,univ4 ,press1 #ahig7 contains a fine account of non-,euclidean geometry4 #ad ,republished by permission from ,science4 #ae ,presidential address delivered at the ,st4 ,louis meeting of the ,physical ,society1 ,december #cj1 #aiai4 ,republished by permission from ,science4 #af ,from a report in ,the ,observatory1 of the ,joint ,eclipse ,meeting of the ,royal ,society and the ,royal ,astronomical ,society1 ,november #f1 #aiai4