,illustration3 ,wide ,world ,photos4 ,,dr4 ,,albert ,,einstein ,,in ,,his ,,study ,,at ,,berlin4 ,,easy ,,lessons ,,in ,,einstein ,a ,,discussion ,,of ,,the ,,more ,,intelligible ,,features ,,of ,,the ,,theory ,,of ,,relativity ,,by ,,edwin ,e4 ,,slosson1 ,m4,s41 ,ph4,d4 ,literary ,editor of ,the ,independent1 ,associate in the ,columbia ,school of ,journalism4 ,author of 8,great ,american ,universities10 8,major ,prophets of ,to-day10 8,six ,major ,prophets10 8,creative ,chemistry10 etc4 ,with an ,article by ,albert ,einstein and a ,bibliography ,,illustrated ,illustration ,,new ,,york ,,harcourt1 ,,brace ,,and ,,howe #aibj ,,copyright1 #aibj1 ,,by ,,harcourt1 ,,brace ,,and ,,howe1 ,,inc4 ,,the ,,quinn ,,boden ,,company ,,rahway1 ,n4 ,j4 ,deepest of all illusory ,appearances1 for hiding ,wonder1 as for many other ends1 are your two grand fundamental world-enveloping ,appearances1 ,space and ,time4--,,carlyle4 ,henceforth ,space in itself and ,time in itself sink into mere shadows and only a kind of union of the two can be maintained as self-existent4--,,minkowski4 ,a ,,prefatorial ,,dialogue 7,the ,purpose of which is to ,prevent the ,prospective ,reader from buying the ,book under ,false ,pretenses7 ,,scene3 ,a street car in uniform movement of translation in any direction4 ,,time3 ,the present4 ,the ,reader3 7looking over the top of a morning paper73 ,here's something queer--a whole page taken with a new discovery in physics--8,eclipse ,observations ,confirm ,einstein's ,theory of ,relativity40 ,anything about it in your paper8 ,the ,author3 ,yes4 ,here's a cartoon on it by ,mc,cutcheon4 ,the ,reader3 ,must be something to it then4 ,mc,cutcheon always knows what's news4 7,reads on with audible fragments7 8,most sensational discovery in the history of science0--8,greatest achievement of the human intellect0--8,upsets ,galileo1 ,newton1 and ,euclid0--8,revolution in philosophy and theology40 ,it looks as though ,i ought to know something about this1 doesn't it8 ,the ,author3 ,i think you will have to sometime4 ,and you might as well do it now and get it over with4 ,the ,reader3 7running down the column and hitting the high spots73 8,parallel lines meet0--8a man moving with the speed of light never grows old0--8gravitation due to a warp in space0--8length of a measuring stick depends upon direction of its motion0--8mass is latent energy0--8time as a fourth dimension0--why1 the man is crazy1 isn't he8 ,the ,author3 ,well1 definitions of insanity are so uncertain that it is not safe to say who is crazy4 ,but it seems there's method in his madness--otherwise how could he have hit upon the exact extent of the sun's attraction on light8 ,the ,reader3 7,picks up his paper and reads aloud with concentrated attention7 8,postulate ,i4 ,every law of nature which holds good with respect to a cordinate system ,k must also hold good for any other system ,k1 provided that ,k and ,k are in uniform movement of translation40 ,say1 do you know anything about this business8 ,the ,author3 ,well1 yes1 a little4 ,i have followed the controversy--at a safe distance--for a number of years4 ,the ,reader3 ,can you tell me in plain language what it is all about8 ,the ,author3 ,yes4 ,just that4 ,i can tell you what it is about1 though ,i can't tell you what it is4 ,einstein says that there are only twelve men in the world capable of understanding his latest paper4 ,the ,reader3 ,are you one of the twelve8 ,the ,author3 ,no1 nor the thirteenth4 ,but without plunging into the mathematics of it1 we might talk over some of the interesting aspects of the theory of relativity and in the end ,i could put you on track of the twelve so you could read up on the subject if you liked4 ,the ,reader3 ,all right4 ,that's fair4 ,this is a slow car anyhow4 ,go ahead4 ,the ,author3 7,see following pages7-- ,,easy ,,lessons ,,in ,,einstein 8,a warp in nature has been found1 ,no line is straight1 no circle round2 ,for ,isaac ,newton had unsound ,ideas of gravitation40 ,why is it that our newspapers are sending out their reporters to interview astronomers as well as actresses and devoting pages to speculations on the nature of space and time as well as on the state of the market8 ,it is--to get at the bottom of it--merely because a few photographs taken during the eclipse of the sun on ,may #bi1 #aiai1 by two telescopes1 one at ,sobral in northern ,brazil and the other on the island of ,principe off the west coast of ,africa1 showed an abnormal shift of less than one-#cbd1jjjth of a right angle in the position of the stars4 ,when these photograph films were laid over films taken before the eclipse it was found that the star-images about the darkened disk of the sun did not exactly coincide with the images when the sun was not in their midst4 ,measured with a micrometer the displacement of the stars from their ordinary positions was found to be #a4fj seconds of arc on the ,african plates and #a4ih seconds on the ,brazilian plates4 ,average these two observations and you get #a4gi4 ,this is extremely close to the #a4gc predicted by ,professor ,einstein of ,berlin and twice as large as the deflection calculated according to ,newton's law of gravitation which would be 4#hg of a second4 ,when the announcement of this result was made at the meeting of the ,royal ,society of ,london on ,november #f all eyes were turned toward ,sir ,oliver ,lodge1 for last ,february he had been rash enough to express the hope1 if not the prediction1 that the results of the eclipse expedition would support ,newton rather than ,einstein4 ,but instead of taking part in the discussion ,sir ,oliver got up and walked out4 ,it was suspected that he had 8gone off mad10 as we ,americans would put it1 because the starlight would not follow his preferred path4 ,but he put a stop to any such rumors by a letter to ,the ,times in which he explains that his departure was not due to any dissatisfaction with the universe but to the necessity of catching the #f o'clock train4 ,he frankly acknowledges that 8the eclipse result is a great victory for ,einstein2 the quantitative agreement is too close to allow much room for doubt0 but he adds 8a caution against a strengthening of great and complicated generalizations concerning space and time on the strength of this splendid result3 ,i trust that it may be accounted for1 with reasonable simplicity in terms of the ether of space40 ,this caution is wise1 but we cannot hold our breath till #aibb1 when the next eclipse comes1 to see if these observations are verified and we may in the meantime consider some of the implications of ,einstein's theory of relativity4 ,sir ,joseph ,thomson1 ,president of the ,royal ,society1 in making the momentous announcement in the session of the ,society1 said3 ,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 sustained 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 ,what is this theory of relativity and why is it so important8 ,the mathematics of it are too much for most of us1 but we can get some notion of it by a familiar illustration4 ,suppose you wake up some morning in a ,pullman berth and look out of the window to see where you are4 ,you find your view blocked by a passing train on the next track4 ,now if you do not feel any jar of your car and cannot catch sight of the landscape beyond the other train you cannot tell whether 7#a7 your train is moving forward and the other train is standing still1 or 7#b7 your train is standing still and the other train is moving backward1 or 7#c7 whether both trains are moving in opposite directions1 or 7#d7 whether both trains are moving in the same direction1 but your train faster4 ,it is obvious that the trains are getting past one another4 ,you can measure their speed of parting as accurately as you please4 ,but all you can perceive is the relative motion of the two trains4 ,you begin to wonder whether there is any such thing as absolute motion2 whether there is any real difference between rest and motion4 ,is there any possible way of telling whether your train is in motion or not if all you can see out of the window is some object that itself be moving8 ,suppose the windows were all curtained1 how could you find out whether you were moving forward or backward or standing still8 ,you discuss this curious question with your fellow passengers at the breakfast table and one of them makes the brilliant suggestion that it might be possible to determine the absolute motion of the car by reference to the air4 ,if the car is moving forward the air would stream from front to rear and the reverse if it were moving backward4 8,suppose10 says the ingenious experimentalist1 8that you stand at one end of the car and ,i at the other4 ,we will shout at each other alternately and time the passage of the sound with our stop watches4 ,since sound is carried by air waves it will take longer for the shout to go against the air current than with it1 and from that measurement it might be possible for us not only to determine which way the car is moving but how to calculate how fast it travels1 assuming1 of course1 that there is no wind blowing40 ,that strikes you as a crucial experiment1 but you point out one possible difficulty1 that the doors at the ends of the car may be closed and the air inside is being carried along with the car1 so no difference would be observable in the speed of the sound even though the car were moving4 8,all right10 replies your scientific friend1 8we will make a preliminary test to see if the enclosed air is carried along with the car1 and if we find that it is not then we will try the second experiment with the sound signals to see which way the air current is moving4 ,these two experiments must settle it1 for either the air is moving with the car or it is moving through the car4 ,can you conceive of any other possibility than these two80 ,no1 you cannot1 so you proceed to try the two experiments4 ,first you visit both ends of the car and find both doors open2 the air then is not being carried along with the car4 ,you turn then with confidence to the second experiment and you find1 of course1 that there is a difference in the speed of sound whether it moves with the air drift or against it4 ,there might1 ,i admit1 be practical difficulties in the way of carrying out such a delicate experiment on a moving train1 but we need not bother with them1 for probably the current of air through the car would be so strong as to blow your hat out of the back door and that would settle the question to your satisfaction--or at least it would settle the question in the affirmative4 ,but imagine your amazement if this second experiment should give negative results like the first one2 if you could detect no difference in time whether the sound was sent forward or back or across the car4 ,you would then have proved by experiment 7#a7 that the air did not move with the car and 7#b7 that the air did not move through the car4 ,you might suppose from this that your car is at rest1 but suppose the people on the other train passing yours tried the same experiments and got the same result1 namely1 that they1 too1 were at rest as regards the air4 ,you would then be in a quandary1 for your two indisputable experiments had apparently given contradictory results4 ,you might get out of it by saying that there was no air1 but if not what carried the sound waves--and the hat8 ,,contradictory ,,experiments ,now this is the quandary in which physicists have been in for the last thirty-three years4 ,is there any way of discovering absolute motion among the heavenly bodies8 ,we can observe and measure with great accuracy their relative motion4 ,the sun is seen to pass across the sky from east to west and man at first assumed that the earth was still and the sun went around it4 ,this is the natural and instinctive assumption1 for when you first glance out of your ,pullman window you get the impression that the other train is the moving one4 ,but for the last three hundred years it has been the fashion to assume the earth was moving and not the sun4 ,that assumption has the advantage of simplifying the calculations of the astronomers1 though ,i never could see why we should have to give up our simple notions of sunrise and sunset to save them a little trouble figuring4 ,the earth moves--if it does move--so quietly and silently that we feel no jar or engine-beat to tell us of its motion4 ,if the earth were perpetually shrouded by clouds could we find out its motion through space or even its rotation8 ,and do we actually get any proof on this point from observation of the heavenly bodies8 ,we see them moving about relatively to each other and we can represent their movements most easily by supposing that the moon goes around the earth and that the earth and the rest of the planets go around the sun4 ,but is this whole solar system in motion8 ,so it seems when we compare it with the stars4 ,but who knows if the solar system and all the visible stars are not altogether moving off through space at the rate of a mile or a thousand miles a second8 ,how can we tell unless we have something that is still and fixed to measure the motion by8 ,it seemed until recently that we had such a fixture1 the ether4 ,we know of the sun and stars only from the light that comes from them to us4 ,light1 as we can prove by simple experiments1 consists of wave motion4 ,now1 can you have wave motion without something to wave8 ,sound waves are conveyed by air but there is no air between the earth and the sun4 ,so as nothing could be found to fill this empty space scientists had to invent something to satisfy their sense of the fitness of things4 ,the ether was the product of their excogitations4 ,it was a ,british invention1 devised in the ,royal ,institution1 whence have come so many useful theories and discoveries4 ,the ether1 as ,salisbury said1 is simply the nominative of the verb 8to undulate40 ,it was conceived of as a sort of transparent jelly filling all space1 more rigid than any solid1 more frictionless than any fluid1 more easily penetrated than any gas4 ,it must be more elastic than steel and yet so rarefied that ordinary matter passes through it without the slightest effort4 ,the ether is supposed to slip between the particles of the rushing earth as the wind blows through the branches of a tree4 ,for many years after its invention the ether had nothing to do except to carry light about from one place to another4 ,but when the electro-magnetic waves of the wireless telegraph were produced something was needed also to carry them and this new task was laid upon the shoulders of the uncomplaining ether4 ,when ,rntgen discovered the ,x-rays1 whose waves are #aj1jjj times shorter than the shortest light waves1 these were turned over to the ether to run4 ,in fact1 it got so that whenever a physicist found any action that he could not explain by ordinary matter he said3 8,let the ether do it10 and that hypothetical substance apparently answered every purpose until it came to this question of relative motion4 ,now whatever we may think about the ether it would seem that if there is any such thing filling all 8empty0 space we might use it for measuring the motion of the earth through it as we did the air current in the car4 ,if the earth is really revolving around the sun the ether must be whizzing through its pores at the rate of about nineteen miles a second4 ,but wait--there is the possibility that the earth carries along with it in its flight through space a sort of atmosphere of ether as it does of air4 ,we must first get rid of this possibility by a preliminary experiment to see if a swiftly moving mass of matter does catch up and carry along with it a little of the ether4 ,this would cause a sort of an eddy or disturbance in the ether in the neighborhood of the moving mass as a boat disturbs the water4 ,for instance1 a ray of light passing close to a rapidly revolving wheel would be a little deflected and show a distorted image4 ,sir ,oliver ,lodge tried this experiment and got negative results4 ,that is1 moving matter does not disturb or carry with it the ether4 ,consequently1 it would seem1 we are left to the only other logical alternative1 that the ether drifts through matter and we should expect to detect this drift by measuring the speed of light in the direction of the earth's motion4 ,it ought to take longer for light to travel from one point to another if the earth meantime is moving away from the first point and it ought to take less time if the earth is moving toward it4 ,well1 ,michelson and ,morley tried this experiment--and also got negative results6 ,it did not make any difference whether the ray of light was sent in the direction of the earth's movement or the reverse or across the line1 it traveled invariably at the same speed1 #ahf1jjj miles a second4 ,here then were two unquestionable experiments apparently contradicting each other4 ,one proved that the ether did not travel with the earth4 ,the other proved that the ether did not stand still while the earth traveled through it4 ,now when we get contradictory answers to the questions we put to ,nature we must assume--unless ,nature is nonsensical--that we are asking nonsensical questions4 ,if in the trial of a pickpocket one witness swears that the thief did not run up the street and another witness that he did not run down the street the lawyer does not necessarily say that one of them must be a liar4 ,he meditates a moment and then it occurs to him that possibly the pickpocket did not move or that perhaps he disappeared into the third dimension by climbing up a fire-escape or dropping into a coalhole4 ,so with our ether quandary4 ,if the ether does not move and does not stand still perhaps there isn't any ether or perhaps there is a fourth dimension4 ,these are two conceivable ways out of the dilemma though they are not easy to accept1 either of them4 ,if there is no ether what carries the light waves8 ,if there is a fourth dimension in what direction does it lie8 ,but it is no harder to believe in or conceive of a fourth dimension than it is the ether1 and if the physicist finds that he needs it in his business he will have to have it4 ,einstein says that he needs a fourth dimension for his formulas4 ,,the ,,conundrum ,,of ,,the ,,ages ,for twenty-four hundred years philosophic thought has been concerned with the problem of the relation of space and time4 ,drop into any of the scientific societies of today and you will find them discussing whether space is finite or infinite1 whether there is any difference between rest and motion1 whether length is absolute or relative1 whether time and space have real existence1 which are the very questions discussed by ,pythagoras and ,zeno in the ,greek cities of ,asia ,minor4 ,now the time spent in these speculations has not been wasted1 although it has led to no definite conclusion1 for out of it have grown our mathematics and physics4 ,the ,wandering ,jew1 who is the only mortal having the privilege of attending the schools of the ,eleatics and those of the present day1 would observe one difference1 that modern scientists try to put their theories to the test of experiment wherever possible1 while the ancients were content with thinking them out4 ,of all the guesses that have been given to this riddle of the universe none has been more bold and revolutionary than that contained in a paper of four or five pages contributed in #aije to the ,annalen der ,physik by ,albert ,einstein4 ,the controversy it precipitated has not altogether been confined to the realm of pure reason1 for scientists are but human and as such are not entirely uninfluenced by patriotic prejudice4 ,in this brief paper he proposed a new theory of the universe based upon two postulates4 ,the first was the principle of relativity2 that all motion is relative4 ,this means1 for instance1 that we would never know the motion of a smoothly moving train if the windows were darkened and that we could never discover the forward movement of the earth if we could not see the heavenly bodies4 ,einstein's second postulate was that the velocity of light is independent of the motion of the source4 ,this is a hard one for our reason to swallow1 for it means that nothing can travel faster than light1 #ahf1jjj miles a second1 and that you cannot make light travel faster than that by giving it a swift send-off4 ,it is the same as saying that if a man standing on the cowcatcher of an engine threw a ball forward1 it would not make any difference with the velocity of the ball whether the train was running at full speed forward or backward or standing still4 ,but the experiments of the ,american physicists1 ,michelson and ,morley1 who measured the speed of light and found it the same whether the earth was moving toward the source of the ray or away from it1 or at right angles to its direction1 confirm ,einstein's second assumption4 ,if we accept ,einstein's two primary postulates and his later 8,principle of ,equivalence0 his theory clears up this ether-drift difficulty as well as various other riddles of the universe4 ,it explains the shifting of the orbit of ,mercury that ,newton's theory could never account for4 ,it foretold the deflection of light by the sun's gravitation that the observations on the eclipse of last ,may confirmed4 ,a third test1 the shifting of the lines of the solar spectrum toward the red end in a gravitational field1 has not been met4 ,such technical points concern only physicists and astronomers1 but ,einstein's relativity theory1 which two out of the three experiments support1 carries with it certain speculations as to time and space that are upsetting to current conceptions4 ,,paradoxes ,,of ,,relativity ,all three of ,newton's laws of motion are now questioned and the world is called upon to unlearn the lesson which ,euclid taught it that parallel lines never meet4 ,according to ,einstein they may meet4 ,according to ,newton the action of gravitation is instantaneous throughout all space4 ,according to ,einstein no action can exceed the velocity of light4 ,if the theory of relativity is right there can be no such thing as absolute time or way of finding whether clocks in different places are synchronous4 ,our yardsticks may vary according to how we hold them and the weight of a body may depend upon its velocity4 ,the shortest distance between two points may not be a straight line4 ,these are a few of the startling implications of ,einstein's theory of relativity4 ,if he had put it forward as a mere metaphysical fancy1 as a possible but unverifiable hypothesis1 it would have aroused mere idle curiosity4 ,but he deduced from it mathematical laws governing physical phenomena which could be put to the test of experiment4 ,they have been tested in these two crucial cases and prove to be true4 ,in the preceding pages we have discussed the question of the relativity of motion and seen how impossible it is to tell1 for instance1 whether a train or a ship you are on is moving or not unless you can compare it with something that you are 8sure0 is stationary4 ,but what are you sure is stationary8 ,nothing on earth surely1 for the earth compared with the 8fixed0 stars is spinning around at the rate of about a thousand miles an hour and rushing around the sun at the rate of nearly #gj1jjj miles an hour4 ,but are we sure the stars are fixed since we have nothing else to compare them with8 ,you may remember ,herbert ,spencer's illustration of the sea captain who was walking west on the deck of a ship sailing east at the same rate4 ,is he moving or not8 ,if you are in the same boat1 you say he is4 ,if you are on shore when the ship is passing you say he is standing still and 8marking time40 ,it all depends on the point of view4 ,now you may readily admit that all motion is relative1 not absolute1 and yet you may balk at the idea that space and time are also relative1 not absolute4 ,but motion is merely simultaneous change of position in space and time1 and why should we feel so certain about space and time when we have never seen either8 ,you may say1 for instance1 that you are sure your desk is so long4 ,but if ,i ask you how long you have to say as long as something else4 ,you may say it is a yard long4 ,but how long is a yard8 ,it is as long as some tape or stick marked 8one yard10 and this in turn has been taken from some other yardstick1 until you get back to the brass rod in ,london that is just as long as the distance from the tip of the nose of ,king ,henry ,i to the end of his royal thumb4 ,but such a standard of absolute measurement is unsatisfactory to everyone except an absolute monarchist4 ,but apart from the difficulty of the present inaccessibility of ,king ,henry's nose and thumb1 can we be confident that our yardstick keeps the same length while we are measuring with it8 ,we must admit indeed that it is longer on a summer day than on a winter day1 but can we be sure that it does not alter in length when we hold it upright or lay it horizontally8 ,or1 rather1 could we tell if it did change in length as it is changed in direction8 ,,are ,,you ,,sure ,,of ,,your ,,shape8 ,if you have ever been in any of those funny places at the amusement parks you will have noticed the convex mirrors there and how ridiculous they make other people look4 ,if you cannot afford the nickel necessary for the study of optics in such an establishment you can contemplate your reflection in the side of a shiny tin cup or can4 ,in a plane mirror you see a man who looks as you suppose yourself to be except that somehow you seem to have become left-handed4 ,but when you look into a convex cylindrical mirror set upright you see a man thinner than you 8really are40 ,look into the same mirror set horizontal and you see a man shorter than you 8really are40 ,you grin at the sight of such queer-looking creatures1 but you notice that they are equally amused at your shape4 ,now how are you going to prove to the men in the curved glasses that they are mere caricatures and that you are not really built on the plan of either of these images8 ,you naturally resort to measurement1 as a scientist should4 ,you cannot get into the mirror world to measure the tall man who pretends to represent you1 but you can explain to him in the sign language what you want him to do and he instantly complies4 ,you stand up a measuring rod at your side and show him that you are exactly #gb inches tall4 ,he also sets up a rod and that also reads #gb inches4 ,never mind1 let him use any kind of measure he likes1 you will catch him when it comes to measurement of width with the same stick4 ,you hold your rule across your shoulders and it reads #ah inches1 that is1 one-fourth your height4 ,but he also measures his width with his rule and makes it just the same1 #ah inches1 although as you see him he looks at least six times as high as he is broad4 ,illustration3 ,,the ,,measure ,,of ,a ,,man ,when the man in the middle looks at himself in a curved mirror he sees what he regards as a distorted image4 ,the image on the right is thinner and seems taller because it is reflected from a cylindrical surface set upright4 ,the image on the left is shorter and seems broader because it is reflected from a cylindrical surface set horizontally4 ,but if the man and his image are measured by scales in the real world and the mirror world they come out the same4 ,so1 too1 it would be impossible for us to find out if everything in the world were expanded or contracted in all directions4 ,in other words1 all measurements are relative4 ,according to ,einstein any body in movement is shortened in the direction of the line of motion while the transverse dimension remains the same4 ,if1 then1 a man is being carried headlong through space with a velocity approaching the speed of light he would be shortened like the man on the left4 ,if he were moving sideways he would be like the man on the right4 ,the man's image in a plane mirror seems to him symmetrical but reversed4 ,his right hand has somehow got over on his left side and vice versa4 ,such a transformation as the mirror seems to effect cannot be actually accomplished in ordinary space1 but would conceivably be possible in a space of four dimensions4 ,now you are sure he is cheating--must have some sort of telescoping rod that contracts and expands according to the way he holds it4 ,you point out to him that his measure is unreliable1 but to your surprise his gestures seem intended to convince you that you instead are using the elastic rule4 ,you shake your fist in his face--to which he responds with equal indignation--and then you turn to the squatty chap in the other mirror1 hoping he will be amenable to reason4 ,but he also measures himself as #gb inches high and #ah inches wide by his own rule4 ,if you try the still queerer-looking fellow in the concavo-convex mirror who is distorted in all sorts of ways you will find that his rule lengthens and shortens and bends just enough to make him as symmetrical a man as yourself4 ,and how can he be otherwise since he is the image of yourself8 ,you are therefore driven to doubt the invariableness of your own yardsticks4 ,suppose when you wake up tomorrow everything1 including all means of measuring1 is twice as big as it is today4 ,could you tell the difference8 ,would it make any difference8 ,would there be any difference8 ,is there any such thing as absolute distance8 ,are not all measurements relative8 ,such questions had from the earliest times occupied the attention of speculative philosophers1 but they passed from the realm of metaphysics to the realm of physics in #ahhf when ,michelson and ,morley made their famous experiment on the speed of light in various directions4 ,their object was to find out if the ether1 the hypothetical medium carrying the light waves1 was stationary and drifted back through the earth as the earth moved onward4 ,they devised an instrument of such delicacy that the stamp of a foot a hundred yards off would be noticeable4 ,a ray of light was divided into two parts2 one half was sent forward and back in the direction toward which that part of the earth where the experiment was made was moving at the time2 the other half was sent back and forth across the line of this motion4 ,but the two rays of light following different routes came back at the same instant and matched up exactly4 ,in order to correct for any inequality in the instrument1 ,michelson and ,morley turned it around so the arm that formerly pointed across the line of motion now pointed in the direction of that motion and the other arm pointed across1 but that made no difference4 ,the light traveled with the same velocity regardless of the motion of the earth4 ,this negative result was just as astonishing as if you should stand at a certain spot on the bank of a river half a mile wide and should send out two boats1 one to go up the river half a mile against the current and then back with the current and the other boat to go across the river and back4 ,if both boats should return at the same moment you would be puzzled to account for it4 ,one way of accounting for it would be that your measurement of the half-mile course upstream had been a little short4 ,this was the explanation of the ,michelson-,morley experiment given by the ,dutch physicist1 ,lorentz4 ,he suggested that the arm of the instrument shortened a trifle as it was turned from across the line of the earth's motion to the direction of that motion4 ,the amount of shrinkage necessary to compensate for the ether drift would be exceedingly small4 ,besides how could you measure the change in the length of the arm if the rule you laid alongside of it altered in the same proportion8 ,lorentz's explanation could not be disproved1 yet it was so upsetting to our ordinary ideas of the stability of matter that it was hard to accept4 ,einstein took ,lorentz's idea and made it one of the fundamental principles of his new theory of the universe and then deduced from this theory sundry very startling conclusions1 some of which could be--and have been--confirmed by experiment4 ,according to ,einstein the size and shape of any body depends upon the rate and direction of its movement4 ,for ordinary speeds the alteration is very slight1 but it becomes considerable at rates approaching the speed of light1 #ahf1jjj miles a second4 ,if1 for instance1 you could shoot an arrow from a bow with a velocity of #afj1jjj miles a second1 it would shrink to about half its length1 as measured by a man remaining still on earth4 ,a man traveling along with the arrow could discover no change4 ,no force could bring the arrow or even the smallest particle of matter to a motion greater than the speed of light1 and the nearer it comes to this limit the greater the force required to move it faster4 ,this means that the mass of a body1 instead of being absolute and unalterable as we have supposed1 increases with the speed of its movement4 ,newton's laws of dynamics are therefore valid only for matter in motion at such moderate speeds as we have to deal with in our experiments on earth and in our observations of the heavenly bodies4 ,when we come to consider velocities approximating that of light the ordinary laws of physics are subject to an increasing correction4 ,if a person calculates that he is attaining a speed faster than light he will seem to another observer to be moving the other way4 ,that is1 any motion above the speed of light is negative motion4 ,just as a tourist traveling more than #ab1jjj miles away from home in any direction will really be getting nearer home the farther he goes4 ,such speculations would not have bothered anybody twenty years ago1 for then the physicist did not have to handle any cases of such high speeds4 ,but when radium was discovered it was found that this metal was continuously throwing off particles of negative electricity with approximately the speed of light4 ,now if these electrons are not matter they are at any rate the material of which matter is made4 ,they can be detected and counted and tracked and deflected and speeded and weighed4 ,they are very real things1 perhaps the ultimate reality of all things1 yet their extreme velocity carries them out of ,newton's world and into ,einstein's4 ,,introducing ,,the ,,fourth ,,dimension ,now ,einstein's world1 as ,i said before1 differs from the world in which we are accustomed to live in many particulars4 ,it has four dimensions instead of three4 ,one of these dimensions may be time4 ,time1 too1 must be relative1 not absolute4 ,this is even harder to imagine than the relativity of space4 ,as some schoolboy said3 8,if there were no matter in the universe the law of gravitation would fall to the ground40 ,quite so4 ,,what ,,is ,,meant ,,by ,,dimensions ,no dimensions3 ,a mathematical point4 ,has position but no size4 ,represented by a dot4 ,like this 4 ,one dimension3 ,has length but no breadth4 ,made by moving a point along straight in any direction4 ,represented by a line4 ,like this ---- ,two dimensions3 ,a plane surface like this page4 ,has length and breadth but no thickness4 ,made by moving a line in a direction perpendicular to its length 7that is1 into the second dimension74 ,represented by two straight lines of indefinite length perpendicular to each other4 ,the lines are called axes and are labeled x and y4 ,the point where they meet1 the origin1 is marked ,o4 ,like this ,illustration ,three dimensions3 ,a solid like a cube4 ,has length1 breadth and thickness4 ,made by moving a plane in a direction perpendicular to the other two 7that is1 into the third dimension74 ,cannot be pictured on paper1 but is indicated by three axes1 x1 y1 and z1 of which x and y are on the plane of the page and z is supposed to be stuck up at right-angles to the other two4 ,stick a pin into the paper at the point ,o and you will have the third or z axis4 ,like this ,illustration ,four dimensions3 ,has length1 breadth1 thickness and extension into a fourth dimension1 say time4 ,made by moving a cube in a direction perpendicular to the other three 7that is1 into the fourth dimension74 ,cannot be pictured on paper1 but may be indicated by four axes1 x1 y1 z and t 7or u71 each at right-angles to the other three4 ,like this ,illustration ,more dimensions3 ,any desired number of dimensions can be worked out mathematically but with increasing difficulty because of the impracticability of diagrammatical representation4 ,we can generalize the idea by speaking of a 8geometry of n dimensions0 where n may stand for any number whatever from zero to infinity4 ,a line of a given length contains an infinite number of points4 ,a square of a given size contains an infinite number of lines4 ,a cube of a given size contains an infinite number of plane squares4 ,a tesseract 7four-dimensional cuboid7 of a given size contains an infinite number of solid cubes4 ,and what would there be left of space if you took everything out of it1 and what would become of time if nothing ever happened8 ,in other words are not space and time merely forms of thought1 the framework of ideas1 and if so cannot we fix them over to suit our need of new conceptions8 ,as a matter of fact we do4 ,we have constructed by the aid of ,euclid and his successors a geometry of three dimensions that works perfectly for all ordinary requirements and if we need a fourth dimension to accommodate these new astronomical and physical phenomena we will build on the necessary addition to our conception of space4 ,there was no use having a fourth dimension so long as we had nothing to put in it4 ,for ordinary earth measurements 7geometry7 such as laying out a town lot we only use two dimensions1 length and breadth4 ,we speak of 8flat ground0 and 8water-level0 regardless of the fact that all our 8straight0 lines on the earth's surface are really curves that come back to us after going #be1jjj miles or less4 ,it is only when measuring mile lengths that we have to correct for the curvature of the earth in the third dimension4 ,so if1 as seems probable1 we shall have to make allowance in astronomical measurements for the curvature of the universe in a fourth dimension it will merely mean a little labor to the astronomers and it will relieve their minds of some of their perplexities4 ,there is nothing more mystical or mysterious or 8psychical0 about a fourth dimension than about the other three4 ,a dimension is simply a measurable direction and we can use five dimensions or n dimensions if we need to4 ,it does not matter that we cannot 8see0 a figure in four dimensions even with our mind's eye4 ,actually we cannot see any figure of more or less than two dimensions3 we have to take the others on faith4 ,nobody can see the mathematician's point because it has no dimensions1 no size at all4 ,the schoolboy says3 8,let that be the point ,a10 and we let it be although what he is pointing at with his stick is not a point but a vast irregular splotch of white chalk on the blackboard4 ,so1 too1 we cannot see a mathematical line because it has only one dimension1 length and no breadth4 ,but set four lines at right angles to one another and we get a square4 ,this we can really see if the enclosed surface is of a different color such as a shadow or black print4 ,set six squares together at right angles and we get a cube4 ,this we cannot see in its entirety at one time4 ,all that we see when we look squarely at a cube is a square4 ,if we look at it from an angle we see what looks like a square with a couple of lozenges on the sides4 ,the retina of the eye is practically a plane surface1 so all we can get is a two-dimensional projection of a solid4 ,illustration3 ,,how ,,to ,,draw ,a ,,four-,,dimensional ,,figure ,the best way to get an idea of the construction of a cubical solid in four dimensions is to draw a diagram yourself and trace out in turn each of the eight cubes that inclose it4 ,i am indebted to ,k4 ,w4 ,lamson of ,barnard ,college for the following sketch and directions3 ,draw the four cordinate axes ,,ox1 ,,oy1 ,,oz1 ,,ou4 ,lay off the unit a#a;a#d on the ,x axis1 a#a;a#b on the ,y axis1 a#a;a#g on the ,z axis and a#a;b#a on the ,u axis4 ,draw the cube a#a;a#b;a#c;a#d;a#e;a#f;a#g;a#h on the three axes ,,xyz4 ,draw parallel to this the cube b#a;b#b;b#c;b#d;b#e;b#f;b#g;b#h on the ,u axis4 ,draw the cube a#a;a#b;a#c;a#d;b#a;b#b;b#c;b#d on the three axes ,,xyu4 ,this is partly drawn already4 ,draw parallel to this the cube a#g;a#h;a#e;a#f;b#g;b#h;b#e;b#f on the three axes ,,xyu4 ,this completes the figure4 ,there are four other cubes in the figure besides those described above3 ,the cube on the ,,xzu axes a#a;a#d;b#a;b#d;a#g;a#h;b#g;b#h and its opposite a#b;a#c;b#b;b#c;a#e;a#f;b#e;b#f4 ,the cube on the ,,yzu axes a#e;a#b;a#g;a#a;b#e;b#b;b#g;b#a and its opposite a#f;a#c;a#h;a#d;b#f;b#c;b#h;b#d4 ,the figure has3 #af corners1 #cb edges1 #bd bounding squares1 #h bounding cubes4 ,the heavy line a#a;b#f might be called the principal diagonal and makes an angle of #fj degrees with each of the four axes4 ,it is foreshortened in the sketch1 but its real length is twice that of one edge of the cube4 ,every line except this is on the outside of the four-dimensional figure4 ,illustration3 ,,the ,,tesseract ,a four-dimensional cube-like solid if transparent and looked at with one eye would appear something like this4 ,but it is obviously impossible to depict a four-dimensional figure on a two-dimensional surface like this page4--,from 8,the ,fourth ,dimension ,simply ,explained10 ,munn and ,company1 ,n4 ,y4 ,since our two eyes present us slightly different pictures of an object we infer from these its size1 shape and distance1 but this is guesswork4 ,still we have a pretty clear idea of a cube although we have never seen it in its solidity4 ,but the attempt to visualize the hypercube1 the four-dimensional figure corresponding to the cube1 strains our imagination to the breaking point4 ,some mathematicians endowed with constructive imaginations of high power claim to have got by long hard thinking some sort of a shadowy and fleeting perception of it1 but their visions--if they are not imaginary--do not help out us ordinary folks4 ,but if we cannot imagine--that is1 image--the hypercube we know all about it1 even its name4 ,it is called the 8tesseract10 and it is bounded by eight cubes just as the cube is bounded by six squares and the square by four lines4 ,the tesseract has #bd square faces1 #cb edges and #af rightangular corners4 ,,time ,,as ,,the ,,fourth ,,dimension ,although we find it hard to conceive of a fourth dimension in space we have no such difficulty in case the fourth dimension is time4 ,in fact1 we use this idea all the while and could not get along without it4 ,to fix the position of any event requires four dimensions4 ,for instance1 a man is shot4 ,where8 ,at the corner of #gth ,avenue and #db;d ,street1 ,new ,york4 ,this fixes the place by two cordinates crossing at right angles in a plane4 ,but was it above or below this1 on the twentieth floor of the ,times ,building or in the ,subway8 ,knowing this fixes the third dimension1 but we have still to fix its position in a fourth dimension1 time4 ,was it today or last week and what hour8 ,if then we find out all four we can distinguish this shooting from any that may have occurred in other places at the same time or at other times in the same place4 ,or consider this simple illustration3 ,cut a strip of motion picture film into its separate scenes and pile them up in order till it is as high as it is broad4 ,you have then a cubical event4 ,two dimensions of the cube are spatial2 the third dimension is essentially temporal1 although in a spatial form4 ,if one of the films from the middle of the pack represents the present then the films below represent the past and those above the future4 ,the people on the picture you picked out know only of the scene there depicted though they may have a fading memory of the past and a dim anticipation of the future4 ,but to you who are outside of the film pack all the scenes are equally visible4 ,they are all present to you4 ,this is the way most ,christians have conceived of ,god1 as one to whom past and future form one eternal present1 so he sees simultaneously all things that have been1 are or will be4 ,if our pile of film were made up of snapshots taken one a day throughout a man's life we should see at one glance his growth from babyhood to boyhood1 to maturity and old age4 ,we could turn the leaves of his life backward or forward as we will4 ,some day perhaps we shall have stereo-movies1 scenes in three dimensions with time as the fourth4 ,this idea of time as a fourth dimension is not a new one4 ,in #aged d',alembert1 defining 8dimension0 in the ,encyclopedia1 wrote3 8,a brilliant man of my acquaintance believes that one may regard duration as a fourth dimension40 ,in #aijc ,minkowski worked out the idea in mathematical form4 ,h4 ,g4 ,wells1 always quick to catch up a new scientific theory to use as a plot for a story1 wrote in #ahie of 8,the ,time ,machine10 a vehicle by which a man could travel back and forth in time as he can travel east and west in a motor car4 ,in this he visits the future and finds mankind split into two species1 a subterranean working class living on--literally--a pleasure-loving leisure class4 ,in 8,the ,plattner ,case0 ,wells tells of a chemical professor who was by an explosion knocked into--not the middle of next week as we commonly say--but into the fourth dimension of space4 ,ten days later he was knocked back again into our world but the only evidence of the truth of his story was that his heart beat on the right side and he was left handed and otherwise reversed in a way that would be impossible in a space of three dimensions4 ,illustration3 ,in space of three dimensions we cannot make a right hand glove and a left hand glove look the same no matter how we turn them around4 ,but if we turn one glove inside out it will match the other except that the lining now appears on the outside4 ,illustration3 ,our two hands cannot be turned inside out so as to look the same in three dimensions1 though they might in four dimensions4 ,we can turn a glove inside out in three dimensions and so make it just like its mate of the other hand1 but we cannot turn a solid inside out except in four-dimensional space4 ,in another of his 8,thirty ,strange ,stories0 ,wells tells 8,the ,story of ,davidson's ,eyes40 ,while ,davidson was working in his ,london laboratory a lightning shock so affected his eyesight that he could not see the familiar objects about him which he could feel but looked instead at a ,south ,sea island on the opposite side of the globe4 ,this might be possible in a curved space of four dimensions although ,wells professes to pooh-pooh such an absurd suggestion while he ingeniously insinuates it4 ,george ,macdonald in his fantastic romance 8,lilith0 also introduces the fourth dimension4 ,points that are far apart if measured in three dimensions may be close together in the fourth4 ,we can readily understand this if time is the fourth dimension1 for events can happen at the same instant though thousands of miles apart4 ,but it is not impossible to conceive of the fourth dimension as spatial instead of temporal if we approach the problem from a simpler standpoint4 ,let us think of ourselves as living in a 8,flatland0 of two dimensions with no thought of a third4 ,there yet survive in enlightened ,america individuals who believe that 8the sun do move0 and who deny that the earth is 8round like a ball40 ,that is1 they do not recognize the curvature of the earth in the third dimension4 ,but if such an individual were to travel in a 8straight0 line westward over the 8level0 land and water he would1 much to his surprise1 come back to his starting point which he had left #be1jjj miles behind him4 ,illustration3 ,by movement in one dimension we cannot make the lines ,,ab and ,b,a coincide for if we drag ,b,a straight on to ,,ab the ends will not match4 ,but if we swing ,b,a around through the second dimension we bring it on ,,ab so the letters correspond4 ,illustration3 ,in space of two dimensions1 such as a table top1 we cannot bring these two triangles into the same position4 ,if we drag one straight over on to the other 7movement in one dimension7 they will not fit together4 ,if we swing one triangle around 7movement in two dimensions7 they still do not fit4 ,but if we take one triangle off the table and turn it over 7movement in the third dimension7 we can then lay it by the side of the other and they will match perfectly4 ,a ,,worm',s-,,eye ,,view ,,of ,,the ,,world ,illustration ,suppose yourself a worm--the ,bible says you are anyway--and crawling around on a sheet of paper4 ,with your vermicular mind you doubtless would take a superficial view of the universe and find it as impossible to imagine a third dimension as man does a fourth4 ,if in the course of your crawling you came across a triangle you might--if you were a measuring worm--pace it off and find that the distance from ,a to ,b was #h inches1 from ,b to ,c was #f inches and from this data1 if you knew the law of the hypothenuse1 you might calculate that the distance from ,a to ,c was #aj inches4 ,on measuring it you would find your prediction verified and so gain perfect confidence in your plane geometry4 ,but unbeknownst to you1 poor worm with your eyes fixed on the paper1 some man may have picked up the sheet and crumpled it up or rolled it over so that ,a and ,c are only one inch apart--in the third dimension4 ,the worm is right when he thinks the distance between these points is #aj inches3 so is the man right when he says it is one inch4 ,it depends on the point of view4 ,now in ,einstein's view something of this sort happens to our three-dimensional space when matter gets into it4 ,we know for instance that if you divide the circumference of any circle by the diameter the ratio figures out as #c4adae4 ,it has been calculated to #gjg decimal places but we can dispense with the rest of them and call the whole thing ,pi for short4 ,write it in ,greek as and it looks more learned4 ,now if you place a heavy particle1 say a lead bullet1 in the center of a circle the ratio of the diameter to the circumference1 according to ,einstein1 becomes a little less than ,pi1 for the circle has been warped1 so to speak1 into the fourth dimension by the strain of gravitation4 ,the difference in such a case is too small to be measurable by any known means1 but it is supposed to be an actual1 not an imaginary1 deviation from the geometrical law4 ,now the sun being a big heavy body must extend its gravitational strain for a considerable distance around and a ray of light passing through this crumpled up space would not be able to pursue a straight course4 ,and1 according to the eclipse observations1 it does not4 ,light like everything else follows 8the easiest way0 and this is not always the straight and narrow path4 ,a river takes the easiest1 not the shortest1 way to the sea and this leads it through many meanderings4 ,most of us1 ,i suppose1 have a mental image of ,newton's gravitation as a sort of rope by which the sun pulls the earth into its orbit when it is disposed to fly off on a tangent4 ,but from ,einstein's viewpoint we should rather think of the earth as picking its way as best it can through a space-and-time combination that has been strained and distorted by the power of the sun4 ,i visualize ,einstein's solar system as a spider web with the sun in the middle like the spider and the planets like flies trying to get around through the tangled strands4 ,but it is more complicated than that for each planet has its own lesser web of radiating influence to drag about with it wherever it goes4 ,newton's idea is simpler1 but unfortunately light at least seems to follow ,einstein's law1 not ,newton's4 ,that is why ,einstein is such a troublesome fellow4 ,if he would confine himself to metaphysical speculation nobody need bother about these strange notions of his4 ,but when he points how they can be proved and then ,british astronomers and ,american physicists find things according to his deductions he cannot be ignored4 ,the man does not seem to have that decent respect for the opinions of mankind that leads most of us to limit our logic to the sphere of common sense4 ,when he gets an idea in his head he follows it wherever it leads him even though he bumps up against ,euclid and ,newton and the rest of us4 ,for instance1 if you admit the second of his two fundamental postulates1 that the speed of light is constant1 regardless of the velocity of its source1 you are irresistibly led--unless you let go of his hand somewhere on the way--to the conclusion that time is a local affair2 that there is no way of telling by light signals whether two clocks at a distance are keeping the same time1 or whether two events at different places occur simultaneously4 ,you could not tell this even if you could shoot a watch from one place to the other with the speed of light1 for no matter how many seconds--or years--the watch might be on its way it would register the same time4 ,if instead of a watch a man could travel at that speed he would not grow old on the way4 ,according to ,einstein no man1 watch or any other material thing can travel with the speed of light1 for it would require an infinite force to give the smallest particle such a velocity4 ,but let us suppose that a hollow projectile holding a man1 such as ,jules ,verne and ,wells used on their voyages to the moon1 should be sent off into space with a velocity one twenty-thousandth less than light4 ,if at the end of a year the projectile should be caught like a comet by the gravitation of some star and be swung around and sent back to the earth1 the man on stepping out of his shell would be two years older but he would find the world two hundred years older4 ,this would be1 as ,professor ,langevin suggests in ,scientia1 #aiaa1 an interesting way to study history1 but it would be risky1 not to say impossible4 ,still ,french scientists1 like ,napoleon1 have no place in their dictionaries for so stupid a word as 8impossible0 and ,m4 ,esnault-,pelterie has figured out that a thousand pounds of radium would be sufficient to carry a man to ,venus in #ce hours if a hollow projectile could be fitted up like a rocket with the radium in the rear sending out a rapid fire of electrons4 ,,turning ,,time ,,backward ,to loosen up our conventional ideas of the fixity of time and space we may accept the aid of the scientific romancers4 ,camille ,flammarion1 the famous ,french astronomer1 wrote a fantastic little book called 8,lumen0 which tells of a man who died in #ahfd4 ,his soul flew straight to its heaven which was one of the planets of ,capella1 the largest star in the constellation ,auriga4 ,here he found the benevolent inhabitants of that sphere1 who were endowed with superhuman powers of sight1 watching with great distress the bloody scenes of the ,french revolution of #agic1 and wondering how it would come out4 ,to the visitor from the earth this was an old story1 to the people of ,alpha ,aurigae it was a present spectacle1 for the distance of the star was such that it took light #gb years to travel from the earth1 so they were #gb years belated in their observation of current events on our planet4 ,the spirit of the defunct ,parisian1 having the power of flying through empty space at any speed he chose1 found that he had thereby also acquired control of time and could hasten1 retard1 stop or reverse the course of events at will by simply varying his speed4 ,if he remained stationary1 scenes on the earth would unfold at their normal rate and in regular order4 ,if he traveled away from the earth with the speed of light everything seemed to stand still4 ,if he traveled faster than light he overtook the rays that had left the earth farther and farther back in the past so he saw through them events in the reverse order4 ,for instance when he looked down on ,waterloo he saw the battlefield strewn with corpses and ,napoleon walking toward ,waterloo backward pushing his horse by the bridle4 ,this is how the battle looked to the interspatial observer3 ,when my sight was sufficiently habituated to the scene1 ,i perceived some soldiers coming to life out of the eternal night1 and by a single effort standing up4 ,the dead horses revived like the dead cavaliers1 and the latter remounted them4 ,as soon as two or three thousand men had returned to life1 ,i saw them form unconsciously in line of battle4 ,the two armies took their places fronting one another1 and began to fight desperately with a fury that one might have taken for despair4 ,as the combat deepened on both sides1 the soldiers came to life more rapidly4444 ,at each gap made by the cannon in the serried ranks a group of resuscitated dead filled up the gaps immediately4 ,when the belligerents had spent the whole day in tearing one another to pieces with grape-shot1 with cannons and bullets1 with bayonets1 sabers and swords--when the great battle was over1 there was not a single person killed1 no one was even wounded2 even uniforms that before it were torn and in disorder were in good condition1 the men were safe and sound1 and the ranks in correct form4 ,the two armies slowly withdrew from one another1 as if the heat of the battle and all its fury had no other object than the restoration to life1 amid the smoke of the combat1 of the two hundred thousand corpses which had lain on the field a few hours before4 ,what an exemplary and desirable battle it was6 ,another literary curiosity on the same theme is 8,ignis0 by ,comte ,didier de ,chousy4 ,this tells of certain engineers who attempted to utilize the internal heat of the earth by running the waters of a lake into a deep boring4 ,the result was an explosion that blew off a piece of the planet4 ,but the passengers on this artificial asteroid on looking down through their well at the earth they had left could see the lake and city undisturbed and watch themselves at work as they were before the place blew up4 ,the explanation was that this fragment of the earth was projected into space more rapidly than the speed of light and so was catching up with the rays that had gone out before the explosion2 these rays1 of course1 carried the picture of earlier scenes4 ,but ,einstein would say that this story--as we might ourselves have suspected--must be fiction for according to his theory the speed of light is the absolute limit of motion1 the infinity of velocity1 which no material body may excel or attain4 ,he does not1 however1 say anything about the possible speed of a disembodied spirit such as ,flammarion employed in his imaginary exploration of space4 ,,the ,,metaphysics ,,of ,,the ,,movies ,but from such fantasies we can see that the order in which we view events depends upon how fast and in what direction we are moving and that past and future may be reversed to our vision4 ,this is easily made apparent by means of motion pictures4 ,if the film is reeled off in the wrong direction the action is reversed4 ,so we see divers rising gracefully out of the water and landing on the spring board4 ,newly hatched chickens1 dismayed at the sight of this unfriendly world1 calmly tuck themselves back into their broken shells which close in upon them4 ,when we have come to the close of a perfect ,thanksgiving ,day the obliging operator may give us an encore of the dinner reversed by running his machine backward4 ,then we see pieces of turkey politely picked out of the mouths of the diners with their forks and replaced upon the plates4 ,when these are passed back to the carver he puts the slices neatly in their places and the fowl is then sent back to the oven to be unroasted4 ,the cook then sticks on the feathers4 ,the hired man carries the turkey out to the chopping block where with one swift stroke he restores the head and the fowl runs off backwards4 ,this is just as correct as the ordinary order4 ,the sequence of events is the same4 ,cause and effect are linked together as firmly as before1 only they have exchanged places4 ,a scientist knowing nothing of our world except from watching such reversed motion pictures might deduce from them the same consistent and logical system of natural laws that we now have although some of them1 for instance1 the second law of thermo-dynamics1 would be reversed in form4 ,the motion-picture man has also the power to alter the speed of the passage of time as he will by turning the crank faster or slower4 ,sometimes he is quite too careless in the way he employs this prerogative4 ,if he is behind time on his schedule he will rush through a lazy siesta scene in a ,mexican plaza with all the fury of a ,mack ,sennett farce4 ,but this telescoping of time can be used to advantage as when he shows us the growth of a plant1 the unfolding of its flower and the ripening of its fruit1 all in fifteen minutes4 ,on the other hand motion may be slowed up by taking twice as many pictures a minute as usual and projecting them at the ordinary rate4 ,for instance1 if it is a dog jumping up to grab a piece of meat from his master's hand1 we see the dog rise slowly from the ground and1 while poised in mid-air1 eye the meat carefully to select the best point of attack1 then deliberately take it between his jaws and gradually descend4 ,now notice that this is just as true a picture of the dog's jump as any other4 ,the movie man has simply expanded time measurements as he expands space measurements when he shows us a close-up4 ,a close-up with a face covering a sixteen-foot screen is just as true as a smaller picture4 ,it is what we should always see if the lens of our eyes were a bit more convex4 ,we look through the small end of an opera-glass and objects seem magnified4 ,we look through the large end and objects seem minified4 ,this is not an illusion4 ,the opera-glass does actually enlarge or reduce what we see4 ,so1 too1 time intervals can be lengthened or shortened4 ,take a dose of hashish--no1 don't--,i should say1 if you did take a dose you would find that your perception of duration was prolonged4 ,if while under the influence of the drug you drop a book it will seem an hour getting to the ground4 ,de ,quincey describes such experiences in his 8,confessions of an ,opium ,eater40 ,but without entering into such abnormal states we all know by everyday experience how time flies or lags according to the number of our sensations4 ,bergson's philosophy is built upon the distinction between the idea of duration as experienced by all of us and the idea of time as established by the physicists for comparative measurements4 ,we live in deeds not years2 in thoughts not breaths2 ,in feelings not in figures on a dial4 --,festus4 ,for all we know an ephemeral insect that dies in a day may live a longer life than a ,galapagos turtle that exists for two centuries4 ,what ,mark ,twain said about classical music applies also to science2 8,it is not so bad as it sounds40 ,the thing that the chemist calls 8sodium chloride0 other folks call 8salt0--and so does he when he is off duty4 ,don't let the scientist bluff you by his polysyllabic propensity4 ,just try to see what he means by such language4 ,now what these new-fashioned non-,euclidean geometricians call 8the four-dimensional space-time continuum0 is essentially the same system of reference as you have used ever since you could toddle4 ,minkowski did not invent it4 ,everybody thinks that way unless he is an idiot4 ,each one of us has had to build up his own philosophy of the universe long before we went to school1 mostly before we could talk4 ,we had to study geometry while we were in our cradles--worse than that we had to work out a practical system of geometry for ourselves without the help of ,euclid or anyone else4 ,we had to excogitate a system of relationship between the sights and sounds and touches that came to us before we could get along in the world4 ,probably we all solve this riddle of the universe in about the same way although since there is no way of directly comparing notes we cannot be sure about that4 ,,the ,,egocentric ,,theory ,,of ,,the ,,universe ,but the framework that we construct to hold everything outside of ourselves is essentially of the following form3 ,you are the center of your universe4 ,everything and every event that you are considering is related to you here and now4 ,starting from this1 your point of place and time1 you imagine eight straight lines stretching out toward infinity in eight directions as divergent as possible4 ,these lines--call them destinations or directions or dimensions or cordinates as you please--consist of four opposing pairs1 right and left1 up and down1 forward and back1 future and past4 ,somewhere along or between these four dimensional lines that cross in your brain you can find a place for anything that you need2 your pencil1 the discovery of ,america1 the sun and next ,friday4 ,you can connect up all these things by lines which may represent changes1 that is the tracks of movements in space and time4 ,to connect the pencil in your hand with the discovery of ,america you would have to count back #dbh years on the time line and measure off on the east-west and north-south lines whatever distance you may be from ,san ,salvador--not to consider the motion of the earth4 ,anything that exists1 that is to say1 persists1 is moving along the time dimension at what appears to be a uniform rate4 ,of course you can1 if you like1 conceive of time itself as a stream flowing through things4 ,since all motion is relative1 that way of looking at it is just as 8true0 as the other4 ,but it is simpler and more sensible to think of things moving through a stationary time just as we think of them moving through a stationary space4 ,a material point that is at rest1 such as the dot of an i on this page1 7we continue to disregard the motion of the earth7 is not moving about in space but is moving forward in time4 ,its track then is a straight line along the time dimension4 ,that is1 a material point is a line in the fourth dimension4 ,if you move the page to the right the forward movement of the dot of the i in the time dimension is combined with the sideways motion in a single slanting line4 ,if you move the page simultaneously upward1 rightward and backward the track of the point is a line combining the movement in all four dimensions4 ,such a track of a point moving through space and time is called its 8world-line40 ,it is a continuity of one dimension4 ,any event is the point of intersection of one or more such world lines and we can never observe anything except such intersections4 ,that is to say1 everything happens somewhere and sometime4 ,a picture flashed on a cinema screen has three dimensions4 ,it is1 say1 #aj feet long and #f feet high and lasts of a second1 but it has no thickness4 ,a man necessarily has four dimensions4 ,he may measure from #bd to #gb inches in one dimension1 from #h to #ah inches in the second1 from #d to #i inches in the third and #gj years in the fourth4 ,after all1 the idea of the relativity of time ought to be easier to accept than that of space for it is in accord with experience instead of contrary to it4 ,we drop off to sleep and wake the next instant if we credit our personal perceptions4 ,why should we believe the sun and the clock in preference to ourselves8 ,bergson bases his whole philosophy upon the distinction between duration as it is felt by the individual while he is living through it and time as it is employed by the physicist in his calculations4 ,the latter conception1 physical time1 is1 as ,bergson says1 a mere invention of man and virtually a fourth dimension of space1 so he concludes3 ,to sum up2 every demand for explanation in regard to freedom comes back1 without our suspecting it1 to the following question3 8,can time be adequately represented by space80 ,to which we answer3 ,yes1 if you are dealing with time flown2 ,no1 if you speak of time flowing4#a ,past and future are alike to the physicist1 differing only in direction1 like east and west4 ,but to the living person they are altogether different things4 ,for man rolls up his past1 as a tourist his rug1 and carries it with him wherever he goes4 ,that is why ,wells's 8,time ,machine0 and the reversed reels of the movies are so funny4 ,there is nothing absurd about running a wheel backward but there is about running a man backward4#b ,the physicist feels no reluctance about turning the stream of time backward for all physical phenomena are reversible under the proper conditions4 ,if we interpret the universe as merely matter in motion and imagine at a certain instant that every individual particle reverses its motion and goes in just the opposite direction at the same speed1 then the whole history of the world would be renacted in the opposite order and the earth would return to its primeval nebul4 ,in ,wells's story1 8,the ,new ,accelerator10 a professor invents an elixir that speeds up the rate of living a thousandfold4 ,a person taking a dose of it sees people as wax figures apparently motionless in the midst of violent action4 ,falling objects seem to stand still in the air4 ,the music of a band is reduced to 8a low-pitched1 wheezy rattle0 or 8the slow muffled ticking of some monstrous clock40 ,but in compensation for this the accelerated drug-fiend could watch at leisure the slow flapping of a bee's wings4 ,but even ,wells with his seven-league-boots imagination finds it difficult to keep ahead of the march of science4 ,what he then saw only with his mind's eye we can actually observe4 ,by moving the accelerating lever on your phonograph toward the ,s end of the scale you can slow up the tune and lower its pitch until it becomes inaudible as music4 ,the new ,path ultra-rapid camera can take pictures at the rate of #afj to the second4 ,when these are projected on the screen at the usual rate of #af to the second all movement takes place ten times slower than in actual life4 ,this gives opportunity for the study in detail of the action of a ballplayer pitching a curve or of the wing motion of a humming bird or of the splash of a marble falling into water or of the flight of a bullet4 ,we can magnify motion or minify it as much as we will4 ,the cinematograph owes its origin the desire of ,senator ,leland ,stanford to study the movement of a horse's legs so as to find out why one racer went faster than another4 ,such playful flights of the scientific imagination as ,wells and ,flammarion indulge in and such freaks of projection as the camera man amuses us with are of use to those of us who find difficulty in translating a mathematical formula into terms of everyday life4 ,there is no better place to study metaphysics than in the world of the flickering screen1 for there man has complete control of time and space4 ,he can enlarge and reduce any object4 ,he can hasten1 retard or reverse any action4 ,he can throw upon the screen at the same time events happening months and miles apart4 ,therefore to those of us who have had the advantage of an education in the movies1 ,einstein's ideas of the relativity of time and space do not seem startling or inconceivable4 ,kant not only conceived the possibility of more than three dimensions but believed in the probability of it4 ,his argument is based on greater insight into the intentions of the ,almighty than we of this day would claim3 8,if it is possible that there be developments of other dimensions in space1 it is also very probable that ,god has somewhere produced them4 ,for ,his works have all the grandeur and variety that can possibly be conceived40 ,in this temporal1 spatial and material world of ours reality requires that the four dimensions should hang together4 ,but at an infinite distance from all matter this fourfold combination would be dissolved into a three-dimensional space and a one-dimensional time4 ,in that extra-mundane realm time ceases to flow1 gravitation no longer drags downward1 matter is non-existent1 light is immovable and change is impossible4#c ,thus the new mathematics leads to a state curiously like the conventional conception of heaven4 ,we talk as our forefathers did about 8the ends of the earth0 but we know that one might start from his home and walk forever in any direction without coming to an end of it4 ,but though the earth's surface is infinite in the sense of endless1 yet one never can get more than #h1jjj miles away from home where'er he may roam4 ,if a man stood on the top of the highest mountain on earth and aimed a level gun in any direction1 the bullet1 if it could be given sufficient velocity to counteract the influence of gravity1 would go around the world and hit him in the back of the head4 ,or if light were sufficiently deflected by gravitation to follow a level line around the earth--another absurd assumption--the man looking through a level telescope in any direction could see how his hair was combed in the back4 ,such happenings1 though impossible1 are not inconceivable but are logical consequences of our knowledge that the world is round and that what we call straight or level lines as measured on plain or sea are really great circles around a center four thousand miles below4 ,now is it not also conceivable that the lines we call straight in astronomical space may also have an imperceptible curvature in some unknown fourth dimension8 ,if this curve is closed like the circumferences of the earth a ray of light pursuing a straight course in a certain direction might eventually return upon its track1 even though not refracted or reflected by the matter it passes through or by4 ,a telescope of unlimited power pointed into space at a tangent might then show the observer his own back1 if light were transmitted instantaneously1 but1 since it is not and since the curvature of space1 if there be any1 is exceedingly minute1 what the observer would see1 assuming that the earth had come back to its former position1 might be the scenes of some geological age millions of years ago4 ,,non-,,euclidean ,,geometry ,the idea that space itself may be curved and that the axioms and assumptions on which our geometry since the time of ,euclid have been based1 may not be absolutely and exactly and eternally and universally true has been diligently studied during the last fifty years4 ,the ,russian ,lobatchewsky1 the ,hungarian ,bolyai and the ,german ,riemann have developed systems of geometry by starting from premises the opposite of those of ,euclid and these systems are just as logical and consistent with themselves as the ordinary or ,euclidean geometry4 ,these non-,euclidean geometries were at first commonly regarded as mere freaks of the mathematical imagination1 but they have already proved valuable in leading to a reconsideration of the fundamental principles of our thinking and1 if ,einstein is right1 they may be necessary to explain physical phenomena4 ,it is hard for the mathematician to discover anything useless4 ,a distinguished ,american mathematician in announcing a new theorem exclaimed3 8,and thank ,heaven1 no possible use can ever be found for it40 ,but1 whatever it was1 he made a rash boast for nowadays the mechanic treads on the heels of the mathematician and uses imaginary quantities1 actual only in the fourth dimension1 like -#a1 in figuring out the winding of his dynamo4 ,readers whose mathematical faculty is weak or undeveloped and who like something concrete with 8human interest0 in it will find what they want in 8,flatland by ,a ,square10 a book published in ,boston in #ahia4 ,the author1 who turned out to be the ,reverend ,edwin ,abbott1 tells of a land in only two dimensions4 ,the ruling class consisted of polygons1 the bourgeoisie of squares and equilateral triangles1 the lower class of isosceles triangles of narrow base1 while the criminals had more irregular forms and the women were mere needles4 ,since all were confined to a surface1 four lines set in a square made a tight prison4 ,the inhabitants of ,flatland1 even the aristocratic and intellectual individuals who had so many sides as to be almost circular1 could not conceive of a third dimension from which a person like ourselves could look down and see at a glance the insides of their houses1 their safes and their bodies just as a being in the fourth dimension could see the insides of ours4 ,the narrator1 that is1 ,a ,square of ,flatland1 visits as a missionary the land of two dimensions where all the people lie in a line and refuse to believe in anything outside it and finally he encounters and endeavors to convert a solitary point of no dimensions but finds him1 as we should expect1 an incorrigible solipsist4 ,we should all of us have been familiar with the fourth dimension for years if ,slade had not turned out a trickster4 ,slade was an ,american medium--the original of ,browning's 8,mr4 ,sludge0--who fooled ,professor ,zllner by giving him what purported to be experimental evidence of the fourth dimension4 ,zllner was a distinguished ,german physicist1 ,professor of ,astronomy in the ,university of ,leipzig1 old1 near-sighted1 pre-disposed to spiritualism1 and unskilled in legerdemain4 ,any proofs that ,zllner asked for1 ,slade was usually able at the next sance to produce4 ,all the things that one might do in four dimensions but could not do in three were forthcoming by the obliging spirits whom ,slade had at call4 ,illustration3 ,in space of one dimension 7a straight line7 there could be neither bend1 loop nor knot in a string4 ,illustration3 ,in space of two dimensions 7a flat surface7 a double bend could be made in the string but no loop or knot could be made4 ,illustration3 ,but if we raise one string 7into the third dimension7 and lay it over the other like this3 ,illustration3 ,we get a loop but cannot form a knot without using the ends4 ,illustration3 ,a knot like this cannot be made in a string so long as the ends are held by the hands4 ,but if we could use a fourth dimension we could tie such a knot as easily as we made a bend by the use of the second dimension and a loop by the use of the third4 ,if such a knot could be tied in a string so held it would be experimental evidence of the existence of four-dimensional space4 ,zllner tied the ends of a string together and sealed them on the table top1 letting the loop hang down under the table out of sight4 ,he then asked to have a single knot tied in the string and the spirits tied four4 ,zllner also reports that the coins he put into a sealed box were taken out and writing produced inside sealed slates4 ,on the basis of these experiments ,zllner wrote a volume on 8,transcendental ,physics0 to prove the existence of another world in the fourth dimension4 ,but when ,slade tried his tricks in ,london he was caught at them by ,professor ,e4 ,ray ,lankester4 ,he was convicted of deception with intent to defraud in the ,bow ,street ,police ,court and sentenced to three months' imprisonment with hard labor4 ,nowadays the apparatus for ,slade's famous slate-writing trick can be purchased at any conjurer's shop4 ,it is vain to expect anything scientific to come out of the sance room where the alleged phenomena are not reproducible under specified conditions but appear only occasionally and under circumstances prescribed by the medium who always may be and often is proved to be a sleight-of-hand--or sleight-of-foot--performer4 ,the fourth dimension which ,einstein and other scientists are now considering is not conceived of as the abode of departed spirits1 a spare room for ghostly visitants1 but merely as a new factor in a mathematical formula4 ,it offers us no hope of ever being able to take coin out of a closed safe or put coin into an unopened coconut but it does promise to explain certain optical phenomena which1 though rare and minute1 are yet open to the observation of anybody1 be he skeptical or credulous4 ,,some ,,simple ,,examples ,lisbon lies nearly straight east of ,new ,york but when a ship captain wants to go to ,lisbon he does not sail straight east but sets his course a little northward in the beginning and a little southward toward the end and so gets there quicker than if he had followed a line of latitude4 ,draw his course on a flat map and you would think he was taking a roundabout route1 but trace it on a globe and you will see that he is following a great circle1 the geodetic line1 which is the shortest distance between any two points on the earth's surface4 ,an airman looking down on a rocky1 hilly1 woody country sees it as a flat plain and if he watched a hunter returning home with his bag of game would wonder that he did not go straight instead of wandering around in such an irregular way4 ,yet the hunter1 being tired1 is taking what is for him the shortest way home as he dodges rocks and circumambulates the hills4 ,the easiest way is the shortest way4 ,a river in its desire to reach the sea always takes the shortest possible way4 ,its meanderings are not meaningless but determined by a law as rigid as a law of geometry1 that is1 the law of gravitation which prevents the river from taking a short cut over the hill4 ,if you look at a landscape over a heated plain or bonfire or through uneven glass you will see that the image is distorted and confused because the rays of light are refracted and entangled as they pass through this unequal medium4 ,yet each ray is going just as straight as it can toward your eye4 ,now to such familiar cases where a ray of light is bent out of its straight course by the uneven density of the air or glass through which it passes ,einstein has added another and unsuspected effect1 namely1 that light is likewise deflected in passing through a strong gravitational field such as the vicinity of a large body like the sun4 ,it has long been known that the displacement of the earth in space and time 7that is to say1 its motion7 causes an apparent displacement of the stars in space4 ,the astronomer does not point his telescope straight at a star4 ,if he did1 he would not see it1 for1 owing to the forward motion of the earth1 the telescope moves out of range of the rays that otherwise would have reached it4 ,illustration3 ,everyone knows that a ray of light is bent out of its straight course as it passes from the air into a denser medium like water or glass1 and that this deflection apparently shifts the position of the object from which the light comes4 ,einstein's theory and the ,british eclipse observations prove1 what was not known before1 that a ray of light as it passes through the gravitational field of a large body like the sun1 is also perceptibly bent out of its straight course and likewise makes an apparent shift in the position of its source1 the star4--,from ,black ,davis' 8,practical ,physics40 ,published by ,the ,macmillan ,company4 ,if you have ever tried to shoot a bird on the wing1 or1 better1 a prairie-dog from a train you will get the idea4 ,or1 if you have not had this experience1 you have doubtless watched the raindrops running down a car window and have noticed that when the rain is falling straight down the drops strike the pane on a slant when the car is moving forward4 ,the faster the car moves the greater the deviation from the perpendicular4 ,if the train runs backward the rain-streaks slant in the opposite direction4 ,if then you should be asked to point out the direction of the cloud from which the rain is coming you would--unless you knew and made allowance for the movement of the train--point in a line with the streaks on the pane1 sometimes backward1 sometimes forward1 but not straight upward where the raincloud really is4 ,now the astronomer is on a moving train1 the earth1 which is rushing around a ring about #ahf1jjj1jjj miles across4 ,consequently every star appears to wabble around in a little ellipse and the astronomer has to aim his telescope1 now on one side1 then on the other1 of the real position of the star in order to bring it on the cross-hairs of his object glass4 ,this apparent displacement of the stars is known as 8the aberration of light0 was explained by ,fresnel in #ahah--to everybody's satisfaction until recently--on the assumption that all space is filled with an immovable medium1 the ether1 which transmits the rays of light in straight lines in the form of wave motion1 and that the earth moves through the ether without displacing it1 somewhat as an airplane moves through still air4 ,but the aviator knows how fast he is moving by the current of air streaming back in his face4 ,why then1 since the ether is in perfect repose1 could we not determine the absolute motion of the earth through space by measuring the drift of the ether as it streams through the pores of the earth8 ,light appears to afford us a means of measuring such a drift of the ether through matter1 if there be such4 ,since light is conveyed by the ether we should naturally expect it to take less time to travel a certain distance if the receiving instrument is carried toward the source of the light by the earth motion than if it is being carried away from it4 ,this question was put to the crucial test by two ,american physicists1 ,michelson and ,morley1 who devised an instrument so delicate that it could detect differences of one-#be1jjj1jjjth of an inch in the path of a light ray4 ,but although this delicacy was ten times greater than was necessary to detect the ether drift1 if there were any1 no evidence of such drift could be discovered4 ,,the ,,eclipse ,,observations ,in the history of science the year #aiai is likely to be known1 not as the year of the overthrow of the ,german ,empire1 but as the year of the overthrow of ,newton's law of gravitation4 ,the ,british astronomers who went to ,africa to observe the eclipse of the sun ,may #bi1 #aiai1 came back with the proof that a ray of light passing close by the sun is bent out of its straight course4 ,the photographs taken during the six minutes when the sun was shadowed show the surrounding stars in different positions from where they are seen when the sun's disk is not in their midst4 ,this is the second time that ,einstein has scored over ,newton4 ,the first was in regard to the orbit of ,mercury4 ,if the sun and ,mercury were alone in the universe the planet1 according to ,newton's law1 would revolve forever around the sun in the same elliptical track4 ,but the presence of the other planets makes ,mercury deviate from this regular route so the ellipse it describes is never quite the same but slowly shifts around so that in the course of centuries its longer diameter would be pointing in a different direction4 ,calculating by ,newton's law1 the influence exerted by the other planets astronomers found that it would shift the orbit of ,mercury #ecb seconds of arc in a century4 ,but when they took observations on ,mercury they found that its orbit was shifting at the rate of #egd seconds4 ,the discrepancy between observation and theory1 #db seconds1 is thirty times greater than could be accounted for by errors of instruments or observation4 ,but according to ,einstein's theory1 if the sun and ,mercury were alone in space with no other planets interfering1 the orbit of ,mercury would not remain the same1 but would advance at the rate of #dc seconds a century4 ,this1 as the reader will observe1 is in substantial agreement with the discrepancy which has for two centuries puzzled astronomers1 since it was inexplicable on the ,newtonian theory4 ,the electro-magnetic theory of light1 thought out by ,clerk ,maxwell forty-five years ago1 has proved to be an excellent guide to research and led to many practical applications1 such as wireless telegraphy4 ,according to this theory the miles-long ,marconi waves1 the infinitesimal waves that we feel as heat or see as light and the still more minute waves of the ,x-rays are movements of the same sort1 though differing in length1 and all travel at the same speed in space of #ahf1jjj miles a second4 ,it was one of the implications of ,maxwell's theory1 though it was not perceived until later1 that light and all such waves must exercise a certain pressure upon a body against which they strike1 just as a jet of water from a fireman's hose pushes against the side of a house4 ,the pressure of light is so exceedingly slight that it had never been noticed1 but it has been actually detected and measured by ,professors ,e4 ,f4 ,nichols of ,yale and ,g4 ,f4 ,hull of ,dartmouth4 ,the sunshine falls upon the earth with a force of #afj tons4 ,both theory and experiment have shown that a beam of light has inertia or mass1 that is to say1 a beam of light pushes like a water jet1 and it has now been proved1 by the eclipse expedition1 that the pull of gravity deflects a beam of light as it does a water jet4 ,that is to say1 a beam of light has weight1 is attracted by gravity4 ,this deflection of a beam of light by gravity is extremely small1 but photographs taken during the recent total eclipse of the sun show that star beams that passed near the sun are bent out of a straight path4 ,illustration3 ,the eclipse expedition found that the stars seen about the sun appear slightly shifted from the positions they occupy on a map of the same region of the sky when the sun is not in their midst4 ,this shows that a ray from a star is refracted or bent as it passes close to the sun and confirms ,einstein's theory that light is affected by gravitation4 ,the observed angle of deflection agrees closely with that predicted by ,einstein but is twice as great as that required by ,newton's theory of gravitation4 ,in this diagram of course the angle of the deflected ray and the size of the sun and earth relative to distance are greatly exaggerated4 ,a better illustration of the eclipse observation than ,i could word is given by ,sir ,oliver ,lodge in his interesting article on 8,the ,new ,theory of ,gravitation0 in ,the ,nineteenth ,century of ,december1 #aiae1 from which ,i therefore quote3 ,take a fine silk thread of indefinite length1 and stretch it straight over the surface of a smooth table or floor4 ,imagine a star at one end of the thread1 and an eye at the other2 and let the thread typify one of the rays of light emitted in all directions by the star1 viz4 the ray emitted in the direction of the observing eye4 ,now take a halfpenny or an ,american quarter1 place it on the table close to the thread1 so that the eye end of the thread is ten feet away2 and then push the halfpenny gently forward1 till it has displaced the thread the barely perceptible amount of one thousandth of an inch4 ,the eye looking along the thread will now see that the ray is no longer absolutely straight2 in other words1 the star whose apparent position is determined by that ray will appear slightly shifted4 ,the scale is fixed by the size of the halfpenny1 whose diameter1 one inch1 is used to represent the ,sun's diameter of #hjj1jjj miles4 ,the ten-foot distance between eye and ,sun practically supposes that the eye is on the ,earth1 which would be a spot one hundredth of an inch in diameter1 or about the size of this full stop4 ,as for the distance of the star1 at the other far end of the thread1 that does not matter in the least3 but1 on this scale1 it may be interesting to note that one of the nearest stars1 about eight light-years away1 would require the thread to be a thousand miles long4 ,the ray is now bent or deflected as it passes the neighborhood of the ,sun on its long journey1 so that it is out of place one thousandth of an inch at a distance of ten feet2 and the effect of this tilt of the ray1 upon the observer1 is to make him just able to see a star upon the ,sun's #8limb' when it is really behind it1 or to make him see a star slightly further off the #8limb' or rim of the ,sun than it really is4 ,the shift of one thousandth of an inch at a distance of ten feet corresponds to an angle of one and three-quarter seconds of arc1 which is just the optical shift that actually ought to occur1 according to ,einstein1 when a ray from a star nearly grazes the ,sun's limb on its way to a telescope2 and this is the optical shift which we now know does occur4 ,that may be taken as the definite result of the recent eclipse observations4 ,the effect1 both in magnitude and direction1 had been predicted four years before1 on the strength of a mathematical investigation1 by ,professor ,einstein4 ,the images of two stars1 one on each side of the sun's disk1 will apparently be crowded a little apart when the sun comes between them4 ,a star that would be just eclipsed by the edge of the sun's disk if its rays came straight may still be visible since the rays are curved4 ,in other words we can 8see around a corner0 as every good teacher is said to do4 ,if the sun were encircled by a ring of stars1 or a nebula1 like a halo1 the circle of light would be contracted as it passed the sun and would come to a focus at a place seventeen times the distance of ,neptune1 or #dg1fjj1jjj1jjj miles beyond the sun4 ,the observations made by the ,british expeditions during the eclipse of ,may #bi1 #aiai1 were not altogether satisfactory4 ,at ,principe1 on account of a cloud that drifted by at an inopportune time1 only a few photographs could be obtained4 ,at ,sobral one of the object glasses gave distorted plates1 but the other gave a very good series of seven star images4 ,these when measured at the ,greenwich ,observatory gave the following figures which are in accordance with those calculated by ,einstein's formula3 ,,radial ,,displacement ,,of ,,stars ,,in ,,seconds ,,of ,,angle ,as observed by the ,british astronomers3 4#bj 4#cb 4#ef 4#ed 4#hd 4#ig #a4jb ,as predicted by ,einstein3 4#cb 4#cc 4#dj 4#ec 4#ge 4#he 4#hh ,this is regarded by the astronomers of the ,british ,eclipse ,expedition as sufficiently close to confirm ,einstein's law but those who hesitate to accept so far-reaching and subversive a theory on the basis of these few minute measurements may hold their judgment in suspense until #aibb when the next solar eclipse1 visible in ,australia1 takes place4 ,or possibly some means may be found to take star photographs close to the sun while shining4 ,our ,california mountain observatories may be of service in this since they are perched above much of the dust and mist and denser air that cause a strong light to irradiate and fog the photographic plate4 ,doubtless1 too1 the old photographs of earlier eclipses will now be got out to see if they contain any stars suitable for measuring4 ,some of the opponents of ,einstein suggest that the observed deflection of the starlight may be due to a solar atmosphere that refracts the rays like our earthly air4 ,but it is hardly probable that an enveloping atmosphere sufficiently dense and so far-extending as to produce such an effect would have remained unobserved and it is highly improbable that the density of such an atmosphere should have just the density and decrease with the distance at just the rate to produce the deflection predicted by ,einstein's calculation4#d ,the discovery is rather disconcerting to astronomers1 for all their calculations for the last three hundred years have been based upon the assumption that light travels in straight lines at even speed through empty space or1 what is the same thing1 through the ether4 ,if now light is pulled aside by gravitation as it goes by a solid body the rays from a distant star having to pass through the tangled throng of the ,milky ,way might travel a very devious route and the star would appear to us to be located in a different place from where it really is4 ,in fact it is possible that a star which we see double may actually be single but that rays starting out from it in different directions may be so deflected by passing near other stars that when they reach us they appear to come from different points of space and so appear to us as twin stars4 ,there may1 too1 be dead or dark stars on the way whose existence we cannot discern and allow for4 ,now those of us who are not astronomers are not much concerned over a discrepancy of a few hundredths of a second in the measurement of an angle by the telescope4 ,we do not care much where ,mercury will be five centuries hence1 for we do not know quite where it is now4 ,if astronomers made the laws of ,nature instead of merely discovering them we might be afraid that at their next congress they might repeal ,newton's law of gravitation and send us all flying off into space4 ,but fortunately they have no such power and even though they should all become adherents of ,einstein's most revolutionary theories1 ,newton's laws of mechanics and ,euclid's laws of geometry would remain as true as they ever were1 not perhaps absolutely and universally true1 as we have assumed1 but sufficiently accurate for all practical purposes4 ,deviations from them can only become detectable when we come to consider movements as swift as light waves or electrons4 ,how a heavy object can alter space relations may be seen from this simple illustration3 ,stretch a sheet of rubber over a hoop like a drumhead4 ,it is now level and flat and if parallel lines are drawn across it in two directions so as to divide it up into squares like a checkerboard all these lines are straight and equidistant and all the squares are of equal size4 ,a row of worms1 starting in an even rank and crawling along the parallel lines across the drumhead1 would keep even all the way4 ,now lay a bullet on the center of the drumhead4 ,the rubber sags down and stretches1 most in the middle1 least at the edges4 ,the 8parallel0 lines are no longer equidistant4 ,the squares are no longer equal4 ,the lines are no longer of the same length4 ,if now we repeat our worm race we shall find that those worms following lines close to the weight have to go down hill and up again and so travel a greater distance to traverse the same number of squares than those following lines nearer the edge which lie comparatively flat and are nearly as short as before4 ,consequently the worms will be slowed up in proportion to their nearness to the center and the row of their heads will be swung around at an angle to their former frontage4 ,we might 8explain0 this by assuming that the worms on seeing the bullet to one side were drawn by their curiosity a little toward it1 those nearest of course being drawn the most4 ,or if we had got beyond this crude animistic method of explanation we might assume that the bullet was attached to the head of each worm by an invisible lariat which being pulled by the bullet drew the worms more or less to one side1 the shorter the lariat the stronger the pull4 ,or if we had outgrown this crude mechanical method of explanation we might assume the existence of a 8force0 in the lead which in some mysterious manner attracts the heads of the worms inversely as the square of their distance4 ,but instead of inventing a wormhead psychology or an invisible cord or an incomprehensible force is it not simpler to consider the space between and to suppose that the lines to be traversed are lengthened in the neighborhood of the weight8 ,now these four successive methods of explanation have been used to account for gravitation4 ,first it was assumed by the ancient ,babylonians and ,hebrews that the sun and stars were living beings1 gods or angels1 moving of their own volition around the earth1 or at least that each was guided in its orbit by its particular god or angel4 ,the later ,greeks of ,ptolemy's time supposed the heavenly bodies to be set in concentric crystal spheres and so revolved2 ,i presume by somebody turning a crank behind the scenes4 ,then came ,newton and said3 8,let's discard the ,ptolemaic spheres and all mechanical connection and assume a force of gravitation attracting all bodies in proportion to their masses and inversely proportional to the squares of the distances separating them40 ,now comes ,einstein and says3 8,let's discard this hypothetical force and simply assume that the field of time and space traversed by a moving body is altered if there is another body in the vicinity40 ,in ,einstein's view gravitation is not a force2 it is a distortion of space and time in the presence of matter4 ,a comet sweeping past the sun cannot pursue a straight course1 as it could in interstellar space1 but follows a curved path about the sun which is for the comet the shortest way it can go under the circumstances4 ,so1 too1 a row of light waves coming from a distant star keeps an even front as they pass through empty space but as they come close to the sun they find their paths impeded1 or1 we may say1 stretched4 ,those going nearest the sun are slowed up the most2 those farthest off the least4 ,consequently the wavefront is slued around a bit and the direction of the ray is slightly altered4 ,if now light waves have difficulty getting past the sun we should expect that they would experience like difficulty getting away from the sun4 ,they would be slowed up a bit by its gravitational pullback4 ,the frequency would be reduced2 the interval of time between wave-crests lengthened4 ,this means1 in the case of sound1 lowering the pitch4 ,touch your finger to the turntable of your phonograph and you flat the tone4 ,in the case of light1 it means change of color toward the red4 ,this effect1 according to ,einstein1 should be1 but has not been1 observed4 8,if ,einstein's third prediction is verified10 says ,sir ,oliver ,lodge1 8,einstein's theory will dominate all higher physics and the next generation of mathematical physicists will have a terrible time of it4 ,for university courses and for all practical purposes we shall have the ,galilean and ,newtonian dynamics but they will reign as a limited monarchy and sooner or later the ,einstein physics cannot fail to influence every intelligent man4 ,if these complications are to come into science we must leave them to the younger men4 ,i hope that gravitation1 now that it has begun to interact with light1 will begin to give up its secrets1 but in my time ,i must be content to get secrets out dynamically and leave transcendental methods to others40 ,one ,english scientist1 ,thomas ,case1 writes to ,the ,times to protest that it would have been in much better taste for the ,royal ,society to have adjourned its discussion 8before bringing into question the reputation of ,newton1 who was ,president of the ,royal ,society for the last twenty-five years of his life and raised the society to the acme of its fame40 ,,who ,,is ,,einstein8 ,albert ,einstein was born in ,germany in #ahgd4 ,he early showed the bent of his genius and at the age of twelve1 when his fellow pupils were plodding along with their daily tasks1 he was plunging through works of higher mathematics borrowed from his teacher4 ,he was only eighteen when he conceived the outlines of his theory and ten years later it was ready to give to the world4 ,he left ,germany for ,switzerland at the age of sixteen and became naturalized as a ,swiss citizen4 ,his first academic position was the ,professorship of ,mathematical ,physics at the ,zrich ,polytechnic4 ,then the founding of the ,kaiser ,wilhelm ,academy for ,research at ,berlin gave him opportunity to work out his theories undisturbed by other duties4 ,shortly before the war he was called to ,berlin to succeed the famous ,dutch physicist1 ,professor van't ,hoff in the ,academy4 ,the object of this institution was the same as ,carnegie had when he founded his institution for scientific research at ,washington1 which was to seek out the exceptional man wherever he may be found and set him at his peculiar tasks4 ,at ,berlin ,einstein receives a salary of #d1ejj and has nothing to do but sit and think4 ,this he continued to do all through the five years of war and revolution as quietly and persistently as ,kant at ,knigsberg during the wars and revolutions of a century before4 ,or as ,archimedes at the siege of ,syracuse who was absorbed in drawing geometrical figures in the sand--his blackboard--when a ,roman soldier ran him through with a spear4 ,on two occasions he took part in the world-struggle going on about his study1 both actions greatly to his credit4 ,in the beginning he refused to sign the manifesto of the ,german men of science denying all the charges against ,germany1 and at the time of the armistice he signed an appeal in favor of the revolution4 ,he is an ardent ,zionist and has promised to aid the ,hebrew university which is to be founded at ,jerusalem4 ,according to tradition1 ,isaac ,newton was led to his theory of gravitation by observing an apple falling from a tree in his garden4 ,the newspaper correspondents start a similar tradition by reporting that ,einstein got his theory of gravitation by observing a man falling from the roof of a building in ,berlin4 ,now a man has the advantage of an apple in that he is able to tell his sensations4 ,when ,dr4 ,einstein1 who had seen the accident from his library window in the top story of a neighboring apartment house1 reached the spot he found the man had hit upon a pile of soft rubbish and had escaped almost without injury4 ,asked how it felt to fall he told ,dr4 ,einstein that he had no sensation of downward pull at all4 ,this led ,dr4 ,einstein to consider whether the relativity theory1 which he had applied only to the case of uniform motion in a straight line1 could not be extended to difform or accelerated motion by gravitation4 ,so the special relativity theory which he had enunciated in #aije developed ten years later into a generalized relativity theory 7,verallgemeinerten ,relativittstheorie74 ,,how ,,to ,,lose ,,weight ,a man falling out of an airplane is obeying a natural impulse1 namely1 the force of gravitation4 ,so long as he does not resist he is free as air1 light as a feather1 and altogether comfortable4 ,he can look down with complacency and contempt on the poor mortals below him who are trying to stand up against this natural impulse and laboriously dragging one foot after another as they crawl about the earth when they might be flying through space without effort as he is4 ,it is only when he tries to stop his free fall by bumping against the ground that he gets into trouble on account of gravitation4 ,it was in this way that the ,calvinists1 who were a sort of mathematical theologians1 conceived of the fall of man4 ,the sinner is simply obeying the force of natural depravity1 namely1 moral gravity1 and so long as he is conscienceless and does not consider his inevitable end he has no knowledge of the moral law and is quite happy in his downfall4 ,a person falling freely loses all his weight4 ,his hat does not press down on his head4 ,his feet do not press down on his shoes4 ,if he lets go of his walking-stick it does not 8fall down0 at his feet4 ,it stands upright and simply travels along with him4 ,for1 as ,galileo showed when he dropped his big and little cannon ball off the ,leaning ,tower of ,pisa1 all bodies fall with the same speed4 ,if he were in a falling elevator with an opaque door he would not know he were falling unless he surmised it from the absence of gravitation as evidenced by his own feeling of lost weight and the queer behavior of the objects in the car4 ,he might fall all his life and never find it out4 ,the law of gravitation is like criminal law2 you don't feel it till you come into conflict with it4 ,or if our illustration requires too tall a skyscraper1 let us imagine that a comet as it flies by knocks a chip off the earth with a group of people on it4 ,this terrestrial fragment1 cast loose in space1 gets caught by the attractive force of some gigantic and distant star and falls toward it with ever-increasing velocity for thousands of years4 ,the inhabitants of this errant orb would never know it from their own feelings or any observations they could make on their own little world4 ,does that seem incredible to you8 ,then tell me how do you know but this our world is such a planet and together with the solar system has been falling for thousands of years toward some center of attraction8 ,astronomers1 indeed1 say that we are moving at tremendous speed toward ,canis ,major1 in other words that the world is going to the dogs4 ,all this means that uniformly accelerated motion1 such as gravitation imparts to a freely falling body1 is1 like uniform translatory motion1 a question of relativity and cannot be discovered by an observer carried along by such movement4 ,the idea that uniform translation1 like the moving train we have considered1 is merely relative motion1 is an old idea and not hard to understand or accept4 ,but when we try to extend the principle of relativity to acceleration1 that is1 to a rate of motion that is continuously increased or retarded1 we get a new and revolutionary conception of the universe and are drawn into some very startling conclusions4 ,einstein took this step five years ago and that is what has caused the present excitement4 ,for ,einstein when he once gets hold of an idea follows it wherever it leads him with the undaunted determination of a ,nantucket sailor towed by a harpooned whale4 ,it was a whale of an idea that he harpooned in #aiae and it carried him into strange waters4 ,it led directly to a contradiction or correction of one of the two fundamental postulates which he had laid down as the foundation of his theory of the universe in #aije1 namely1 that the velocity of light in space is a constant4 ,but he promptly abandoned this idea with cheerful nonchalance in favor of the new notion that the velocity of light is affected by gravitation4 ,a ,,substitute ,,for ,,gravity ,let us then follow ,einstein and apply his ,principle of ,equivalence to accelerated motion and see what it leads to4 ,imagine yourself shut up inside a closed chamber1 like an elevator car1 somewhere out in space away from the gravitational forces of the earth or sun4 ,suppose this chamber to be rising with a constantly increasing velocity4 ,we can1 if we want to be definite about it1 assume that the chamber is a big shell pulled up by a cable coiling around a conical windlass that hauls it up faster all the time4 ,or we can assume that it is propelled from behind by the continuous backfire of explosives1 like the rocket which ,professor ,goddard proposes to send to the moon4 ,all we need is some force1 not gravitation1 capable of giving the chamber every second an additional velocity of thirty-two feet a second4 ,now the point is that if you were in such an upward-moving chamber you would not know but what you were resting on the earth4 ,everything would behave exactly the same4 ,if you now weigh one hundred and fifty pounds on the scales1 that is1 if your shoe soles press down with that force1 the floor of the rising chamber would press upward with that same force and you would not know the difference4 ,if you let loose a ball from your hand the floor would rise up to meet it and it would appear to fall4 ,if you threw the ball upward with a velocity greater than the velocity of the chamber at the moment1 the ball would rise1 but since the velocity of the chamber was constantly increasing the floor would gain on the ball and catch up with it4 ,this would look to you just the same as when on earth you threw a ball into the air and it fell back to the ground1 drawn1 as you are accustomed to think1 by 8the force of gravitation40 ,but here we have no 8force10 but merely a mode of motion4 ,under such circumstances it would seem that all ,nature conspired to keep you in the dark4 ,you appeal to the ether1 that supposedly stable and stationary medium that fills all space1 but that also fails you4 ,you try the ,michelson-,morley experiment to see if you are moving through the ether or at rest on the earth but your apparatus expands or contracts just enough to deceive you4 ,you now try observing horizontal rays of light but they seem to bend2 that is1 a beam of sunshine entering a pinhole on one side of your camera obscura will not strike the wall at a spot exactly opposite but a little below it1 if you have instruments sufficiently delicate to show this4 ,you try vertical rays of light in this fashion3 ,you examine with the spectroscope rays of light coming from two sources below 7behind7 your instrument1 one at a distance and the other nearer4 ,now since you are moving away with increasing speed1 the light from the farther source will have to take longer strides to catch up4 ,or in other words1 its frequency will be reduced and it will be shoved toward the red end of the spectrum where the longer waves are4 ,you will have noticed that when a whistling train rushes past the train you are on1 the whistle as it comes toward you is raised in pitch 7decreased wave-length7 and as it recedes from you is lowered in pitch 7increased wave-length74 ,now1 says ,einstein to himself1 if my ,principle of ,equivalence is correct and there is no difference between 7#a7 weight and 7#b7 the accelerated upward movement of an observer1 then all the optical effects that ,i have thought out in the second case must apply to the first1 that is1 to gravitation4 ,it must follow that a ray of light passing through a gravitational field will be bent out of its course as though it were attracted by the heavy body4 ,this prediction has been verified4 ,it must further follow that light proceeding from a heavy body like the sun or a star will be held back or slowed up by the attraction of gravitation1 and the spectral lines will be displaced toward the left as compared with the same lines in the spectrum of an earthly light4 ,now such displacement has been observed in stellar spectra but it does not seem to be of the right value to satisfy ,einstein's equation and it has not been observed in sunlight4 ,the remarkable thing about it is that ,einstein1 by following a line of reasoning somewhat like that which ,i have crudely outlined1 not merely supplied an explanation for phenomena that had been observed but could not be explained 7such as the discrepancy in the orbit of ,mercury7 but he provided in advance the explanation for phenomena that had never been observed until he directed attention to it 7such as the deflection of starlight by the sun74 ,sir ,oliver ,lodge says of this3#e ,before ,einstein's prediction nothing of the kind had been seen1 nothing of the kind had been looked for1 nor1 so far as it is known1 had such an amount of deflection been suspected4 ,whatever may ultimately be thought of the validity of ,einstein's views as a whole it is evident that he has worked out a mathematical method of unprecedented power and wide usefulness4 ,professor ,bumstead of ,yale says3 ,einstein's theory is important in that it exemplifies a method which is in many respects new in theoretical physics and which may prove to be a very powerful method for advancing scientific knowledge4 ,there was no idea that the prediction of the bending of light would fix up ,mercury's perihelion and incidentally explain a two-century old astronomical difficulty4 ,that came straight out of a blue sky4 ,,mechanical ,,versus ,,mathematical ,,minds ,we sometimes hear it said that 8,einstein has overthrown ,newton's theory of gravitation40 ,that is impossible because ,newton did not have any theory of gravitation4 ,he merely laid down the law of gravitation4 ,he told how bodies behaved toward their neighbors2 he did not tell why4 ,newton was not content with the idea of action at a distance through empty space and he tried to explain gravitation by the pressure of the ether on material bodies but he was not satisfied with the results and did not publish them4 ,in the #bcd years since many men have tried their hands at devising some sort of machinery that will 8explain0 gravitation4 ,for human beings are like ,toddie of 8,helen's ,babies0 and want to have the watch opened so they can 8see the wheels go wound40 ,at least ,anglo-,saxons have that desire4 ,poincar1 the ,french physicist1 said this is the distinction between the ,anglo-,saxon and ,latin minds2 the former are uneasy until they can imagine a mechanical model to represent natural phenomena1 the latter are satisfied with a mathematical formula expressing the action4 ,the ether1 which was invented to explain light1 also required 8explanation40 ,lord ,kelvin imagined it to consist of spinning tops which have a sort of mobile stability4 ,sir ,oliver ,lodge has filled it with a complicated structure of interlocking geared wheels to account for electro-magnetic action4 ,these are typical ,anglo-,saxon modes of thinking4 ,on the other hand1 ,einstein1 who1 in spite of his ,hebrew blood and ,german training1 has preminently what ,poincar claims as the ,latin temperament1 does not have any use for the ether and does not care at all whether he can 8picture0 the fourth dimensions on paper or not4 ,now some of us are excessively ,anglo-,saxon in our attitude toward mathematics4 ,it is with a fellow-feeling for such folks that ,i have filled this little volume with such crude and absurd analogies as trains and elevators and projectiles flying through space and ,coney ,island mirrors4 ,to the mathematically minded such illustrations are not simplifications but complications1 not representations but caricatures4 ,mathematics is the proper language of physics as the five-barred staff is the proper language of music4 ,ask a musician to explain a symphony in plain everyday ,english and he cannot do it1 though he carry the ,oxford ,dictionary in his head4 ,he can have the music played for us or he can show us the printed score but he could never convey it in ordinary language however long he might be willing to talk or we to listen4 ,but we must not do the musician or the mathematician the injustice to suspect that his notions are hazy or absurd because he cannot explain 7i4e4 translate7 them to us4 ,nor should we assume that the new ideas1 because they are more difficult for us to grasp1 are necessarily more complicated or extravagant than the old4 ,a friend of mine who is familiar with both tells me that ,einstein's papers are easier reading than ,newton's 8,principia40 ,the aim of science is simplification through generalization and this is the widest generalization yet attempted4 ,it promises to bring gravitation into relationship with other forces4 ,one great generalization1 the law of the conservation of energy worked out by ,joule and others in the forties1 brought heat and work and chemical power all into one simple system4 ,clerk ,maxwell in the seventies brought together in one beautiful formulation all the diverse phenomena of light1 electricity and magnetism4 ,but gravitation has always stood out against any such league of natural forces4 ,it refused to come into the combine4 ,it remained unique1 independent1 irreducible1 unalterable and inexplicable4 ,everything else is correlated and interactive4 ,heat destroys magnetism1 magnetism produces electricity2 electricity dissolves chemical combination2 chemical combination produces heat2 heat causes motion2 motion makes magnetism2 magnetism produces heat2 and so on in endless round1 each affecting all the others4 ,different substances behave very differently2 one is more easily heated than another2 some are readily magnetized or electrified1 others are not so susceptible2 certain elements rush into each others' arms1 others cannot be forced into combination4 ,but gravitation seemed indifferent to all these things2 it showed no prejudices or preferences4 ,it attracted with equal force all sorts of substances1 no matter whether they were hot or cold1 shiny or black1 moving or still1 electrified or magnetized or neither4 ,other forces and effects too required time for action at a distance4 ,sound travels at the rate of #a1ajj feet a second in ordinary air4 ,light travels at the rate of #ahf1ccg miles a second in a vacuum4 ,but the force of gravity seemed not to require any time but to be everywhere1 acting all the while1 and nothing could shield it off or shut it out or in any way interfere with it4 ,the substance or mass of a body as measured by its weight 7the gravitational pull of the earth7 was always identical with its mass as measured by its inertia 7its resistance to being set in motion74 ,all the energies are interchangeable4 ,all other forces could be reduced or increased1 annulled or brought into effect at will4 ,not so gravitation4 ,any bodies of a certain mass placed at a certain distance apart are always drawn by the same attraction4 ,that is1 gravitation is affected by nothing except geometrical relationships4 ,this naturally leads us to suspect that gravitation is nothing but a geometrical relationship1 that it is somehow a peculiarity of space itself4 ,if so1 our demand of the physicist that he show us gravitation1--drag out this mysterious force from its hiding-place and let us see it--is altogether irrational4 ,it is like a blind man hunting in a dark cellar at midnight for a black cat that isn't there4 ,the geometrician tells us that the internal angles of any triangle are equal to two right angles4 ,shall we ask him1 what is the force that makes it so8 ,shall we refuse to ride on a trolley car until the electrician can answer our persistent question2 8but what is electricity80 ,when we ask such a question we are really asking him to tell us what electricity is not4 ,to show us what electricity is he can keep his mouth shut and simply point to the dynamo that produces it1 the wire that conveys it and the motor that consumes it4 ,but what we secretly mean is that he show us a mechanical model that imperfectly imitates some of the actions of electricity or a mathematical formula that will calculate its effects4 ,now ,einstein seems in the way of making gravitation the foundation of a new system of geometry4 ,instead of 8explaining0 gravitation in terms of something else he will explain other things in terms of gravitation1 or rather of his space-time manifold of which gravitation is one of the properties4 ,einstein's law of gravitation proves to be more accurate than ,newton's law1 but the correction is trifling except in rare cases4 ,but ,einstein's theory of gravitation is fundamental and far-reaching and if it is substantiated it will revolutionize physics and radically affect our ordinary conceptions of the universe4 ,the verification of a prediction does not necessarily prove the truth of the hypothesis that led to the prediction4 ,many a scientific discovery has come out of a false assumption4 ,just as a miner may reopen an abandoned gold mine or work over his dump heap to get more out of it1 so scientists often return to an old theory which they had abandoned for a more fruitful hypothesis4 ,,the ,,weight ,,of ,,light ,it is interesting to see that our modern physicists show a disposition to adopt a corpuscular or emission theory of light not unlike the conception which ,newton steadfastly and vainly defended against the undulatory theory4 ,professor ,thomson1 of ,cambridge1 reminds us that the crucial experiment between the two theories was the test made by ,bennet in #agib to determine if light exerted any pressure on a body when it struck it as it would if light consisted of minute particles driven straight forward with great velocity4 ,bennet found no such pressure and the corpuscular theory was regarded as disproved4 ,but it was later found that the undulatory theory also involved such a pressure1 and recent experimenters have proved and measured it4 ,as ,professor ,thomson says3 ,it is perhaps fortunate that ,bennet had not at his command more delicate apparatus4 ,had he discovered the pressure of light1 it would have shaken confidence in the undulatory theory and checked that magnificent work at the beginning of the last century which so greatly increased out knowledge of optics4 ,of course any modern form of the emission theory of light must account1 as ,newton's did not1 for such phenomena as interference and polarization1 which are so satisfactorily handled by the undulatory theory4 ,that is1 it must combine the best features of both4 ,professor ,thomson shows that only an exceedingly small fraction of the ether is concerned in the forward movement of light1 in other words1 8the wave front must be more analogous to bright specks on a dark ground than to a uniformly illuminated surface40 ,he does not1 however1 go so far as ,planck in regarding it as proved that radiant energy of all kinds has a unit or atomic structure1 the color of the light depending on the size of these particles4 ,the discovery of the pressure of a beam of light has led to some startling conclusions4 ,for example1 what shall be done with ,newton's law that action and reaction are equal8 ,when a gun is fired the kick of the gun is balanced by the momentum of the projectile4 ,when a reflector throws a beam of light into space1 the kick of it is there all right but where is the projectile1 if light is merely the undulation of an imponderable fluid8 ,we may suppose that the light strikes some dark body out in space1 transmits its impulse to that and ,newton's laws is satisfied1 but it may be a long time before such a body is encountered and it may never be3 at any rate a law that remains in a state of innocuous desuetude for several thousand years is not good for much4 ,we must then assume that light has mass since it has inertia and momentum4 ,but if light has mass it must have weight2 that is1 it must be attracted by gravitation4 ,the eclipse observations confirmed this deduction4 ,newton would have expected something of this1 for he says in his ,opticks3#f ,query #a4--;,do not ,bodies act upon ,light at a distance1 and by their action bend its ,rays1 and is not this action 7caeteris paribus7 strongest at the least distance8 ,the observed deflection of light due to the sun's gravitation is greater than ,newton would have anticipated but it would have been still more disconcerting to the nineteenth-century physicists1 for in giving up ,newton's emission theory they had come to regard light as merely a form of motion in a weightless medium1 the ether4 ,disembodied energy1 like heat and light in ethereal space1 was regarded as having no mass or weight4 ,twentieth-century physicists are coming to the opposite view1 that the mass of a body is the measure of its internal energy4 ,if so1 mass is not constant but changes with composition1 temperature1 structure1 electrification and motion4 ,as ,einstein himself expresses it3 ,it is evident that it is not possible to attribute an absolute sense to the notion of acceleration1 no more than to the notion of velocity4 ,it is only possible to speak of the acceleration of a material point in connection with a body taken as the body of reference4 ,it follows from this that there is no sense in attributing to a body a 8resistance to acceleration0 in the absolute sense1 like the resistance of inertia in the classical mechanics4 ,further1 this resistance of inertia ought to be so much the greater when there is1 in the neighborhood of the body1 more inert masses not in accelerated movement4 ,on the other hand1 this resistance ought to disappear when these masses participate in the acceleration of the body4 ,now it is altogether remarkable that the equations of the gravitational field contain these different aspects of the resistance of inertia1 which one might call the relativity of inertia4 ,the progress of science is continually toward a dematerialization of matter4 ,physical analysis resolves the crude1 heavy1 solid stuff that our senses show us into finer and finer particles farther and farther apart until these practically disappear into mere points of irradiating influence4 ,first the mass is divided into the molecule and this again into the atom1 assumed1 at the time it was invented1 to be the ultimate unit of matter4 ,but recently the atom has been shown to be a sort of solar system1 but more complex1 composed of hundreds of electrons1 corpuscles of electricity1 whose radius is calculated to be #a_/aj1jjj1jjj1jjj1jjj of a centimeter 7a centimeter is so ---- long74 8,but the size of the centers of disturbance1 which in ,einstein's theory are associated with matter1 bears to the size of the electron about the same proportion as the size of the smallest particle visible under the most powerful microscope to that of the earth itself40#g ,the old axiom was1 8matter cannot act where it is not40 ,the new version might rather read3 8matter cannot act except where it is not40 ,that is to say1 attention is now directed to the space surrounding a material body or electrical corpuscle4 ,although we laymen are not concerned with the niceties of astronomical measurements there is an aspect of this conflict of theories that does interest us4 ,the theory of ,newton or1 to go back further1 of ,galileo1 that the earth moves around the sun1 altered profoundly the philosophical and religious beliefs of the world1 and the theory of ,einstein is much more far-reaching and revolutionary in its metaphysical implications than the former4 ,professor ,planck1 who has just received the ,nobel ,prize for his discoveries in physics1 said of ,einstein's first paper3 ,it surpasses in boldness everything previously suggested in speculative natural philosophy and even in the philosophical theories of knowledge4 ,non-,euclidean geometry is child's play in comparison4444 ,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 ,copernican system of the universe4 ,,mutable ,,theories ,,and ,,stable ,,facts ,there is a feeling very prevalent among the general public interested in such things that the foundations of modern science are being swept away by the recent discoveries4 ,the layman has been led to believe that such laws as gravitation1 the conservation of matter and the immutability of the elements are the most certain and absolute truths of science4 ,but now he hears reputable men of science talk calmly about the decay of matter and the transformation of one element into another1 and gravely consider a theory which makes invalid ,newton's three laws of motion4 ,it surprises1 even shocks1 him1 as much as it would to have a convention of bishops discuss the question of whether there is a ,god1 or the ,supreme ,court agree to set aside the ,constitution of the ,united ,states1 or a congress of physicians resolve that all medicine does more harm than good4 ,he knows that the mere broaching of such heretical views in these assemblies would be met with a storm of indignation and that all the weapons of contempt1 ridicule and even personal spite would be directed against the rash innovator4 ,therefore he is astonished and puzzled to see that in the scientific world these revolutionary theories are received with interest and even pleasure1 and in the criticism to which they are subjected there is scarcely a trace of animosity4 ,and he does not see why men of science who have accepted doctrines apparently contradictory to their former teachings do not appear shamefaced and apologetic before the public1 like augurs whose tricks had been exposed4 ,the difficulty of the layman arises from his not understanding how a scientist looks at his science2 not realizing how firmly he holds to its facts and how loosely he holds to its theories4 ,the scientist never bothers his head with the question whether a particular theory is true or false4 ,he considers it simply as more or less useful1 more or less adequate1 succinct and comprehensive4 ,a theory is merely a tool1 and he drops one theory and picks up another at will and without a thought of inconsistency1 just as a carpenter drops his saw and picks up his chisel4 ,he will say that the earth moves around the sun one moment1 and the next will revert to the theory of ,chaldean astronomers1 because it is more convenient1 and say 8the sun rises40 ,really1 the new discoveries are not so upsetting to science as they appear to the general public4 ,unexpected and revolutionary as they are1 no page of millions that record the experiments and observations of science is invalidated4 ,no man's work is proved wrong4 ,revolutions in science do not destroy2 they extend4 ,in the reaction of public opinion toward any novel and revolutionary idea there are three stages observable4 #a4 ,that it is not true4 #b4 ,that it is not new even if it is true4 #c4 ,that it does not make any difference anyhow4 ,the first is merely the natural and instinctive reaction against any disturbing intellectual innovation4 ,it is a flat denial inspired by that unconscious neophobia or xenophobia that possesses all of us more or less4 ,the second stage is the effort at compromise in which usually both the advocates and opponents of the new idea coperate by endeavoring to prove that it is not so novel and unprecedented as was at first assumed but fits in very fairly with our accepted notions1 in fact may be regarded as a supplement or even a natural development of them4 ,the third stage1 like the second1 is designed as an attempt to disarm opposition by allaying alarm in the conservative mind4 ,the second line of argument has a good deal of validity1 for even the most startling and original idea will be found on closer examination to have its roots deep in the ground of the past and to have been approximately anticipated many times before4 ,the third line of argument also contains some truth for we find everyday life does go on in much the same way1 although it may seem that the foundations have been knocked from under our mental1 moral or social universe by some new notion4 ,yet as the popular mind gradually accepts and adapts itself to the novel conception we generally find that its influence is even more far-reaching than was at first anticipated4 ,in the case of the ,copernican theory it took about two centuries for the controversy to pass through the three stages and the mind of the public to become readjusted to the new conception of the earth's revolution4 ,in the case of the ,darwinian theory of evolution the process was accomplished in about fifty years4 ,the ,einstein theory is more subversive of ordinary ideas than either of the others so it would naturally take longer to soak in4 ,but the modern mind seems to be subject to acceleration and we see in the two months since the notion has been sprung upon the public that all three of the lines of argument are appearing at once and so the controversial period may run its course in five years though it will be longer before its indirect influence upon our fundamental philosophy and habits of thought are fully felt4 ,,scientific ,,versus ,,legal ,,laws ,in all such discussions we must bear in mind that 8law0 in the scientific sense of the word means1 not a commandment or a rule1 but merely a way of working4 ,it is a concise description of how things behave4 ,there are no laws in ,nature2 there are only laws of ,nature2 that is to say1 laws drawn out of ,nature 7or1 if you prefer ,latin to ,anglo-,saxon1 laws deduced from ,nature7 by man for his own convenience in thinking4 ,physical laws are therefore essentially psychological2 mere memory schemes1 calculating machines4 ,the law of gravitation is no more gravity than the funny wriggles that my stenographer is making in her notebook are the sounds ,i am uttering4 ,to change geometries does not require any such effort as to change cars4 ,it means merely changing our minds4 ,but this is harder for some of us than it ought to be4 ,here is where the theory of relativity will be of use to us4 ,poincar1 the ,french mathematician1 cousin of the late ,president1 said3 8,these two propositions1 #8the earth turns round' and #8it is more convenient to suppose the earth turns round' have the same meaning4 ,there is nothing more in the one than in the other40 ,if ,galileo and his inquisitors had understood the ,principle of ,relativity it might have saved them both trouble2 the former temporary imprisonment and the latter everlasting disgrace4 ,a revolution in science is simply a change in mental attitude4 ,maybe a political revolution is no more4 ,it is disconcerting to the layman to be told1 first1 that matter consists of solid round atoms in empty space2 next1 that it is made of mere particles of electricity and negative at that2 then that it is constituted out of strains in the ether2 again1 that the atoms are bubbles in the ether2 and finally1 that there is not any ether4 ,but these various hypotheses are like the crayon strokes that an artist makes about a figure he is trying to draw4 ,they are all attempts at preliminary sketches for mental pictures of natural phenomena4 ,we do not call the geographers inconsistent and contradictory because one colors ,massachusetts red on the map and another colors it green4 ,all scientific hypotheses are put to the pragmatic test of which works the best in unlocking the secrets of ,nature4 ,is 8wheat0 or 8sesame0 the magic word8 ,whether we call a dog 8,fido0 or 8,towser0 depends not on which name is shorter or sounds better but on which the dog answers to4 ,if gravitation comes to heel better when we say 8,einstein0 than when we say 8,newton10 all right1 we'll change4 ,i trust that these frivolous illustrations will not lead my readers to accuse me of treating gravity with levity4 ,the layman--and with him must be included all those who have merely learned science but not used it--talks a great deal about 8the laws of ,nature10 which he regards as abstract1 immutable1 universal and eternal edicts1 part of which are transcribed into the textbooks4 ,to the working scientist they are only more or less convenient formulas2 in the ultimate analysis only mnemonic symbols for stringing together facts to make them easier to handle1 like vibgyor1 for the spectrum colors4 ,he knows that most of them are limited in their scope and only approximate in their accuracy4 ,his chief delight is in discovering these limitations and irregularities4 ,he regards these 8laws0 with no awe or reverence4 ,he has no attachment for any of them--unless it happens to be one that he has formulated himself4 ,if he finds a new hypothesis that works better he throws the old one aside as he does his old model dynamo1 or keeps it around as handy still for doing some of the common work of the laboratory4 ,it is1 to recur to our example1 just as 8true10 using the word in its ordinary sense1 to say that the sun goes around the earth as to say that the earth goes around the sun1 for all motion is relative1 and we can regard either body as the stationary one or both as moving1 as we choose4 ,when we say that the statement that the earth moves around the sun is the 8true0 one1 we merely mean that it is the more convenient form of expression1 for on this hypothesis the paths of the earth and the other planets become circles 7or more accurately speaking1 irregular and eccentric spirals7 while on the other and older hypothesis their paths are very complicated and difficult to handle mathematically4 ,the theory that the earth moves is not only simpler than that of a stationary earth1 but it is wider in its scope4 ,it explains more1 that is1 it connects up with other knowledge1 such as the flattening at the poles4 ,copernicus1 then1 did not discover a new fact about the solar system4 ,he only invented a lazier way of thinking about it4 ,the man of science invents an hypothesis whenever he needs one in his business4 ,it is to him merely a new tool1 a novum organum4 ,if there is not an ether it would be necessary to create one4 ,so he did it4 ,he had to have a noun for the verb 8undulate40 ,when he had created it he saw it was not good4 ,the properties with which he endowed it were self-contradictory1 and it refused either to move with the earth or to pass through it4 ,but these theoretical inconsistencies do not bother the physicist much4 ,in spite of them the ether is a handy thing to have about the laboratory4 ,the scientist does not abandon a theory because it has inconsistencies any more than he divorces his wife because she has inconsistencies4 ,certainly the physicist did not consider himself presumptuous in thus inventing ether for his own convenience4 ,he knew that the ordinary man had in the same way invented 8matter0 long ago for his own convenience4 ,it is a crude1 inadequate and impossible idea1 this nave conception of matter as something solid1 heavy1 hard1 inert1 indestructible1 impenetrable1 colored and surfaced2 but it is good enough for part of the people all of the time and for all of the people part of the time4 ,the physicist himself uses it for everyday4 ,only in his rigorous moments does he come down to bed-rock and say1 with ,poincar1 8,mass is a co-efficient which it is convenient to introduce into calculations40 ,but when the physicist thus reduces matter to a small italic m some people are sure to say that he is denying the existence of matter4 ,what would they say about ,riemann who considers matter to be holes in the ether8 ,a definition is a different thing from a denial4 ,there are people among us who deny the existence of matter and they call themselves 8,scientists10 too1 but they are not the ones who are devoting their days and nights to the study of the workings of matter in order to make it the servant of man4 ,a professor of chemistry would not think of asking his students if the atomic theory is true any more than he would ask them if the atomic theory is blue4 ,he does not care whether they believe the atomic theory or not4 ,he only wants them to be able to use the atomic theory for getting certain valuable results4 ,consequently1 he watches with interest and without apprehension the progress of discovery in radio-activity which is undermining the old conception of the atom4 ,he would be glad to get rid of the atomic theory if he could find something better because after all it is a clumsy thing and will not hold half the facts he wants to put into it4 ,he would have no more hesitation about dropping it than he has in setting down one beaker to pick up a larger one when what he has in the first is frothing over4 ,he does not want to spill anything1 but he does not care what vessel it is in4 ,revolutions in science never go backward and they differ from political revolutions in that nothing worth saving is lost in transition4 ,the new theory must always include all that the old one does and more4 ,in their struggle for existence1 formulas fight like snakes2 the one that can swallow the other beats4 ,now a four-dimensional universe can take in a three-dimensional universe and have space to spare for whatever the narrower conception could not include so it seems likely to prevail4 ,we now know how to sympathize with those poor frightened people who lived in the times of ,copernicus and ,galileo when they were told that the solid earth on which they stood was not supported by anything1 but whirling about and rushing around through empty space and that half the time they hung with their heads down over immeasurable space with nothing to hold on to4 ,but they got used to it in time and lived happily ever after4 ,so may we4 ,for the benefit of those who want to get their information at first hand ,i append an article by ,dr4 ,einstein himself which appeared in the ,london ,times of ,december #ac1 #aiai1 and in ,science of ,january #f1 #aibj3 ,,time1 ,,space1 ,,and ,,gravitation ,by ,dr4 ,albert ,einstein ,i respond with pleasure to your ,correspondent's request that ,i should write something for the ,times on the ,theory of ,relativity4 ,after the lamentable breach in the former international relations existing among men of science1 it is with joy and gratefulness that ,i accept this opportunity of communication with ,english astronomers and physicists4 ,it was in accordance with the high and proud tradition of ,english science that ,english scientific men should have given their time and labor1 and that ,english institutions should have provided the material means1 to test a theory that had been completed and published in the country of their enemies in the midst of war4 ,although investigation of the influence of the solar gravitational field on rays of light is a purely objective matter1 ,i am none the less very glad to express my personal thanks to my ,english colleagues in this branch of science2 for without their aid ,i should not have obtained proof of the most vital deduction from my theory4 ,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 mechanical1 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 ,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 cordinates4 ,the laws of mechanics of ,galileo and ,newton can be formulated only by using a system of cordinates4 ,the state of motion of a system of cordinates cannot be chosen arbitrarily if the laws of mechanics are to hold good 7it must be free from twisting and from acceleration74 ,the system of cordinates 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 suffices3 a system of cordinates 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--8,every law of nature which holds good with respect to a cordinate system ,k must also hold good for any other system ,k1 provided that ,k and ,k are in uniform movement of translation40 ,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 cordinates1 that the mass of bodies and the rate of movement of clocks must depend on their state of motion with regard to the cordinates4 ,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 theory1 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 cordinates be limited to systems of cordinates in uniform movement of translation with regard to one another8 ,what has nature to do with the cordinate systems that we propose and with their motions8 ,although it may be necessary for our descriptions of nature to employ systems of cordinates 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 cordinates 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 cordinates 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 ,euclidean 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 ,euclidean geometry of solids4 ,this is what is meant by the phrase 8a warp in space40 ,the fundamental concepts 8straight10 8plane10 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 systems 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 toward 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 forever retain their significance as the foundation on which our modern conceptions of physics have been built4 ,a final comment4 ,the description of me and my circumstances in ,the ,times shows an amusing feat of imagination on the part of the writer4 ,by an application of the theory of relativity to the taste of readers1 today in ,germany ,i am called a ,german man of science1 and in ,england ,i am represented as a ,swiss ,jew4 ,if ,i come to be regarded as a bte noire1 the descriptions will be reversed1 and ,i shall become a ,swiss ,jew for the ,germans and a ,german man of science for the ,english6 ,,footnotes3 ,footnote #a3 ,bergson3 8,time and ,free ,will10 p4 #bba4 ,footnote #b3 ,bergson in his 8,laughter0 traces all humor back to this fundamental absurdity of making a man act mechanically4 ,footnote #c3 8,we can thus say that all these paradoxical phenomena 7or rather negations of phenomena7 which have been enumerated above can only happen after the end or before the beginning of eternity0 7,de ,sitter74 ,footnote #d3 ,if you insist upon seeing just what is the difference between ,einstein's and ,newton's laws of gravitation here it is as given in ,the ,scientific ,monthly of ,january1 #aibj3 ,any particle or light pulse moves so that the integral of ds between the two points of its path 7in four dimensions7 is stationary where 7according to ,einstein7 ds#b -7#a - #bm_/r7-#a;dr#b-r#b d #b 7#a - #bm_/r7dt or 7according to ,newton7 ds#b dr#b - r#b d #b 7#a - #bm_/r7dt ,these expressions are in polar cordinates for a particle of gravitational mass m4 ,the new factor introduced by ,einstein is1 as shown above1 #a_/a-7bm_/r7 ,footnote #e3 ,nineteenth ,century1 ,december1 #aiai4 ,footnote #f3 ,quoted by ,eddington in ,contemporary ,review1 ,december1 #aiai4 ,footnote #g3 ,sir ,joseph ,thomson in ,nature1 ,december #d1 #aiai4 ,and finally ,,if ,,you ,,want ,,to ,,read ,,more ,,about ,,the ,,einstein ,,theories ,for the non-mathematical reader3 ,,abbott1 ,,edwin4 ,flatland1 by ,a ,square4 ,boston1 #ahia4 ,an amusing way of leading up to the fourth dimension4 ,,campbell1 ,,norman4 ,the ,commonsense of ,relativity4 ,philosophical ,magazine1 ,april1 #aiaa4 ,,carr1 ,,wildon4 ,the ,metaphysical ,implications of the ,theory of ,relativity4 ,philosophical ,review1 ,jan41 #aiae4 ,,carus1 ,,paul4 ,the ,principle of ,relativity4 ,chicago3 ,open ,court ,publishing ,co41 #aiac4 ,,comstock1 ,d4 ,f4 ,the ,principle of ,relativity4 ,science1 ,may #bj1 #aiaj1 vol4 #ca1 p4 #gfg4 ,,cunningham1 ,e4 ,einstein's ,relativity ,theory of ,gravitation4 ,nature1 ,dec4 #d1 #aa1 and #ah1 #aiai4 ,an interesting non-mathematical discussion of the latest phases of the theory4 ,,eddington1 ,a4 ,s4 ,einstein's ,theory of ,space and ,time4 ,contemporary ,review1 ,dec1 #aiai4 ,good popular article4 ,,eddington1 ,a4 ,s4 ,gravitation4 ,scientific ,american ,supplement1 ,july #f and #ac1 #aiah4 ,an excellent popular explanation by the leading ,british disciple of ,einstein4 ,,einstein1 ,a4 ,time1 ,space1 and ,gravitation4 ,science1 ,garrison1 #aibj1 ,jan4 #c1 n4s41 vol4 #ea1 p4 #h-aj4 ,my ,theory4 ,living ,age4 ,boston1 #aibj1 vol4 #cjd1 p4 #da-c1 ,jan4 #c4 ,,flammarion1 ,,camille4 ,lumen4 ,new ,york3 ,dodd1 ,mead and ,co41 #ahig4 ,contains nothing about ,einstein but presents the relativity of time in fantastic form4 ,,keyser1 ,c4 ,j4 ,concerning the ,figure and the ,dimensions of the ,universe of ,space4 ,science1 ,june #ac1 #aiac4 ,,lodge1 ,,sir ,,oliver4 ,the ,new ,theory of ,gravity4 ,nineteenth ,century1 ,dec41 #aiai4 ,the ,ether versus ,relativity4 ,fortnightly ,review1 ,jan41 #aibj4 ,admirable article by a courteous opponent4 ,,poincar1 ,,henri4 ,science and ,method2 also contained in ,the ,foundations of ,science4 ,new ,york3 ,the ,science ,press1 #aiac4 ,,russell1 ,,bertrand4 ,the ,relativity ,theory of ,gravitation4 ,english ,review1 ,dec41 #aiai4 ,a clear explanation by one of the foremost of ,british philosophers4 ,,thomson1 ,j4 ,deflection of ,light by ,gravitation and the ,einstein ,theory of ,relativity4 ,scientific ,monthly1 ,garrison1 ,n4 ,y41 #aibj1 vol4 #aj1 p4 #gi-he1 ,jan4 ,,various ,,writers4 ,the ,fourth ,dimension ,simply ,explained4 ,new ,york3 ,munn and ,co41 #aiaj4 ,the essays submitted for a prize offered by the ,scientific ,american4 ,twenty-two mathematicians try their best to justify the title and if they do not succeed it is not their fault4 ,,wetzel1 ,,reinhard ,a4 ,the ,new ,relativity in ,physics4 ,science1 ,new ,york1 #aiac4 ,new ser41 vol4 #ch1 pp4 #dff-dgd4 ,explains the relativity of time with diagrams and references to the literature4 ,other articles of general interest may be found in3 ,science3 ,july #af1 #aiji2 ,may #bj1 #aiaj2 ,june #bj1 #aiac2 ,april #bd1 #aiad2 ,dec4 #e1 #aiai4 ,scientific ,american ,supplement3 ,april #g1 #aiag2 ,dec4 #ag1 #aiaj4 ,london ,nation3 ,nov4 #ad and ,dec4 #bg1 #aiai4 ,london ,times3 ,nov4 #h1 #ah1 and #be1 ,dec4 #d and #ai1 #aiai4 ,london ,nature3 ,almost every number in ,nov41 ,dec41 #aiai1 ,jan41 ,feb41 #aibj4 ,new ,york ,times3 ,nov4 #g and #af1 ,dec4 #ba1 #aiai4 ,new ,york ,sun3 ,nov4 #aj1 #aiai4 ,the ,new ,republic3 ,jan4 #ba1 #aibj4 ,for the mathematical reader3 ,,einstein1 ,,albert4 ,bases physiques d'une thorie de la gravitation4 ,socit ,astronomique de ,france4 ,bulletin1 ,paris1 #aiag1 ,tome #ca1 pp4 #djg-daa4 ,die formale ,grundlage der allgemeinen ,relativittstheorie4 ,kniglich ,preussischen ,akademie der ,wissenschaften4 ,sitzungsberichte1 ,berlin1 #aijd 7,juli-,dez471 pp4 #ajcj-ajhe4 ,die ,grundlagen der allgemeinen4 ,relativittstheorie4 ,annalen der ,physik1 ,leipzig1 #aiaf1 ,band #di1 ,folge #d1 p4 #gfi4 ,ist die ,trgheit eines ,korpers von seinem ,energieinhalt abhngig8 ,annalen der ,physik1 ,leipzig1 #aije1 ,band #ah1 ,folge #d1 pp4 #fci-fdd4 ,lichtgeschwindigkeit und ,statik des ,gravittionsfeldes4 ,annalen der ,physik1 ,leipzig1 #aiab1 ,band #ch1 ,folge #d1 pp4 #cee-cfi4 ,prinzipielles zur allgemeinen ,relativittstheorie4 ,annalen der ,physik1 ,leipzig1 #aiah1 ,band #ee1 ,folge #d1 pp4 #bda-bdd4 ,uber das ,relativittsprinzip und die aus demselben gezogenen ,folgerungen4 ,jahrbuch der ,radioaktivitt und ,elektronik1 ,leipzig1 #aijh1 ,band #d1 pp4 #daa-dfb4 ,uber den ,einfluss der ,schwerkraft auf die ,ausbreitung des ,lichtes4 ,annalen der ,physik1 ,lypzig1 #aiaa4 ,band #ce1 pp4 #hih-ijh4 ,uber die ,mglichkeit einer neuen ,prfung des ,relativittsprinzips4 ,annalen der ,physik1 ,leipzig1 #aijg1 ,band #bc1 pp4 #aig-bjh4 ,uber die vom ,relativittsprinzip geforderte ,trgheit der ,energie4 ,annalen der ,physik1 ,leipzig1 #aijg1 ,band #bc1 ,folge #d1 pp4 #cga-chd4 ,uber einen die ,erzeugung und ,verwandlung des ,lichtes betreffendes heuristischen ,gesichtspunkt4 ,annalen der ,physik1 ,leipzig1 #aije1 ,band #ag1 ,folge #d1 pp4 #acb-adh4 ,zum gegenwrtigen ,stande des ,gravittionsproblems4 ,physikalische ,zeitschrift1 ,leipzig1 #aiac1 ,band #ad1 pp4 #abdi-abff4 ,zum ,relativitts ,problem4 ,scientia1 ,bologna1 #aiad1 vol4 #ae1 pp4 #ccg-dh4 ,zur ,elektrodynamik bewegter ,korper4 ,annalen der ,physik1 ,leipzig1 #aije1 ,band #ag1 ,folge #d1 pp4 #hia-iba4 ,zur ,theorie der ,lichterzeugung und ,lichtabsorption4 ,annalen der ,physik1 ,leipzig1 #aijf1 ,band #bj1 ,folge #d1 pp4 #aii-bjf4 ,spielen ,gravitationsfelder im ,aufbau der materiellen ,elementarteilchen eine wesentliche ,rolle8 ,sitz4 ,preuss4 ,akad4 ,wiss41 ,april #aj1 #aiai4 ,,einstein1 ,,albert1 and ,,marcel ,,grossman4 ,entwurf einer verallgemeinerten ,relativittstheorie und einer ,theorie der ,gravitation4 ,zeitschrift fr ,mathematik und ,physik1 ,leipzig1 #aiad1 ,band #fb1 pp4 #bbe-bfa4 ,,einstein1 ,,lorentz and ,,minkowski4 ,relativittsprinzip1 ,das4 ,eine ,sammlung von ,abhandlungen4 ,mit ,anmerkungen von ,a4 ,sommerfeld und ,vorwort von ,o4 ,blumenthal4 ,leipzig3 ,b4 ,g4 ,teubner1 #aiac1 #hi p4 7,fortschritte der mathematischen ,wissenschaften in ,monographien1 ,heft #b47 ,a reprint of these three famous fundamental papers4 ,,abraham1 ,m4 ,die neue ,mechanik4 ,scientia1 ,bologna1 #aiad1 vol4 #ae1 pp4 #h-bg4 ,nochmals ,relativitt und ,gravitation4 ,bemerkungen zu ,a4 ,einsteins ,erwiderung4 ,annalen der ,physik1 ,leipzig1 #aiab1 ,folge #d1 vol4 #ci1 pp4 #ddd-ddh4 ,,backlund1 ,a4 ,v4 ,zusammenstellung einer ,theorie der klassischen ,dynamik und der neuen ,gravittionstheorie von ,einstein4 ,arkiv fr mathematik1 astronomie1 och fysik1 ,stockholm1 #aiai1 ,band #ad1 no4 #aa1 #fd seite4 ,,bateman1 ,h4 ,general ,relativity ,theory4 ,phil4 ,mag41 ,feb41 #aiji1 vol4 #cg4 ,applies the theory to life and mind4 ,,brillouin1 ,,marcel4 ,propos ,sceptiques au ,sujet du ,principe de ,relativit4 ,scientia1 ,bologna1 #aiac1 vol4 #ac1 pp4 #aj-bf4 ,,brose1 ,,henry ,l4 ,einstein's ,theory of ,relativity 7non-math4 form74 ,lecture published in pamphlet by ,b4 ,h4 ,blackwell4 ,noted in ,english ,mechanic1 ,dec4 #ai1 #aiai4 ,,carmichael1 ,,robert ,,daniel4 ,the ,theory of ,relativity4 ,mathematical ,monographs1 no4 #ab4 ,new ,york3 ,john ,wiley1 #aiac4 ,,cobb1 ,,charles ,w4 ,relativity4 ,journal of ,philosophy1 ,psychology1 and ,scientific ,method1 ,jan4 #ah1 #aiag4 ,,conway1 ,a4 ,w4 ,relativity4 ,edin4 ,math4 ,tracts1 no4 #c1 ,london1 #aiac4 ,,crommelin1 ,a4 ,c4 ,d4 ,results of the ,total ,solar ,eclipse of ,may #bi and the ,relativity ,theory4 ,science1 vol4 #ej1 pp4 #eah-ebj4 ,sci4 ,amer4 ,supp41 ,dec4 #f1 #aiai4 ,,cunningham1 ,e4 ,report on the ,relativity ,theory of ,gravitation4 ,london1 ,green1 #aiae4 ,,dezuani1 ,,armando4 ,equilibrio relativo ed equazioni gravitazionali di ,einstein nel caso stazionario4 ,il nuovo cimento1 ,pisa1 #aiai1 vol4 #ah1 pp4 #e-be1 ,july1 #aiai4 ,,donder1 ,t4 ,,de4 ,gravitational ,tensors of ,einstein's ,theory4 ,science ,abstracts1 ,april #cj1 #aiai4 ,,droste1 ,j4 ,the ,field of ,moving ,centers in ,einstein's ,theory of ,gravitation4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiaf1 vol4 #ai1 pp4 #ddg-dge4 ,the ,field of a ,single ,center in ,einstein's ,theory of ,gravitation and the ,motion of a ,particle in that ,field4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiaf1 vol4 #ai1 pp4 #aig-bah4 ,,eddington1 ,a4 ,s4 ,report on the ,relativity ,theory of ,gravitation4 ,london3 ,fleetway ,press1 #aiah4 #ia p4 ,the only account of ,einstein's latest theory in ,english4 ,,eddington1 ,a4 ,s41 and ,,others4 ,the ,deflection of ,light by ,gravitation and the ,einstein ,theory of ,relativity4 ,the ,report of the ,british ,eclipse ,expedition to the ,royal ,society4 ,scientific ,monthly1 ,jan41 #aibj4 ,,grossman1 ,,marcel4 ,dfinitions1 mthodes et problmes mathmatiques relatifs la thorie de la gravitation4 ,archives des ,sciences ,physiques et ,naturelles1 ,genve1 ,jan4-,juin1 #aiad1 #d priode1 ,tome #cg1 pp4 #ac-ai4 ,,guillaume1 ,e4 ,theory of ,relativity4 ,archives des ,sciences1 ,dec41 #aiah1 vol4 #df4 ,,humm1 ,r4 ,j4 ,energy ,equations of ,general ,theory of ,relativity4 ,annalen der ,physik1 #aiai1 vol4 #eh4 ,,huntington1 ,,edward ,v4 ,a new approach to the theory of relativity4 ,festschrift ,heinrich ,weber4 ,leipzig1 #aiab1 pp4 #adg-afi4 ,,ishiwara1 ,,jun4 ,zur relativistischen ,theorie der ,gravitation4 ,tohoku ,imperial ,university4 ,science reports1 ser4 #a1 ,sendai1 ,japan1 vol4 #d1 pp4 #aaa-afj4 ,,kafka1 ,h4 ,tensor ,analysis4 ,annalen der ,physik1 #aiai1 vol4 #eh1 pp4 #a-ed4 ,,kottler1 ,,friedrich4 ,uber die physikalischen ,grundlagen der einsteinschen ,gravittionstheorie4 ,annalen der ,physik1 ,leipzig1 #aiah1 ,band #ef1 ,folge #d1 pp4 #djh-dfb4 ,,larmor1 ,j4 ,essence of ,physical ,relativity4 ,nat4 ,acad4 ,sci4 ,proc41 vol4 #d1 ,nov41 #aiah4 ,,laue1 ,,rd4 ,m4 ,das ,relativittsprinzip4 ,braunschweig1 #aiaa4 #bjh p4 ,,lecornu1 ,l,,on4 ,la ,mcanique4 ,paris3 ,flammarion1 #aiji4 ,,lorentz1 ,h4 ,a4 ,considerations lmentaires sur le principe de relativit4 ,revue gnrale des sciences1 ,paris1 #aiad4 ,tome #be1 pp4 #agi-ahf4 ,la gravitation4 ,scientia4 ,bologna1 #aiad1 vol4 #f1 pp4 #bh-ei4 ,das ,relativittsprinzip4 #aiad4 ,la ,gravitation4 ,scientia1 ,bologna1 #aiad1 vol4 #af1 pp4 #bh-ei4 ,on ,einstein's theory of gravitation4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag-ah1 vol4 #ai1 pp4 #acda-acfi2 vol4 #bj1 pp4 #b-cd4 ,on ,hamilton's principle in ,einstein's theory of gravitation4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag1 vol4 #ai1 pp4 #gea-gfe4 ,,lunn1 ,,arthur ,c4 ,some functional equations in the theory of relativity4 ,american ,mathematical ,society4 ,bulletin1 ,lancaster1 ,pa41 #aiai1 vol4 #bf1 pp4 #bf-cd4 ,,michelson1 ,a4 ,a41 and ,,morley1 ,e4 ,w4 ,the ,relative ,motion of the ,earth and the ,luminiferous ,ether4 ,american ,journal of ,science1 #ahhg1 vol4 #cd1 p4 #ccc4 ,see also3 ,astro-,physical ,journal1 vol4 #cg1 pp4 #ajj-aic4 ,the report of the crucial experiments that upset the idea of a stationary ether4 ,,minkowski1 ,,hermann4 ,relativittsprinzip4 ,jahresbericht der ,deutschen ,mathematiker-,vereinigung4 ,leipzig1 #aiae1 ,band1 #bd1 pp4 #abda-abdd4 ,,nordstr,m1 ,,gunnar4 ,einstein's theory of gravitation and ,herglotz's mechanics of continua4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag1 vol4 #ai4 ,,nordstr,m1 ,g4 ,on the ,energy of the ,gravitation ,field in ,einstein's ,theory4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiah1 vol4 #bj1 pp4 #abch-abde4 ,,palatini1 ,a4 ,la ,teoria di ,relativit nel suo ,sviluppo ,storieo4 ,scientia1 ,nov4 and ,dec41 #aiai 7in ,italian and ,french74 ,,planck1 ,,max4 ,zur ,dynamik bewegter ,systeme4 ,kniglich ,preussischen ,akademie der ,wissenschaften4 ,sitzungberichte1 ,berlin1 #aijg1 pp4 #edb-egj4 ,his theory4 ,,petzoldt1 ,j4 ,does the ,relativity ,theory ,exclude the ,reality of ,space and ,time8 ,deutsche ,phys4 ,gesell41 ,dec4 #cj1 #aiah4 ,,ritz1 ,w4 ,la gravitation4 ,scientia1 ,bologna1 #aiji1 vol4 #e1 pp4 #aeb-afe4 ,,rufus1 ,,carl4 ,relativity in astronomy4 ,popular ,astronomy1 ,northfield1 ,minn41 #aiah1 vol4 #bf1 pp4 #afj-afe4 ,,silberstein1 ,l4 ,the ,theory of ,relativity4 ,london3 ,macmillan1 #aiad1 #ib p4 ,,sitter1 ,w4 ,,de4 ,on ,einstein's theory of gravitation1 and its astronomical consequences4 ,royal ,astronomical ,society4 ,monthly ,notices1 ,london1 #aiae-ah1 vol4 #gf1 pp4 #fii-gbh2 vol4 #gg1 pp4 #aee-ahd2 vol4 #gh1 pp4 #c-bh4 ,on the relativity of rotation in ,einstein's theory4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag1 vol4 #ai1 pp4 #ebg-ecb4 ,on the relativity of inertia4 ,remarks concerning ,einstein's latest hypothesis4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag1 vol4 #ai1 pp4 #abag-abee4 ,planetary motion and the motion of the moon according to ,einstein's theory4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiaf1 vol4 #ai1 pp4 #cfg-cha4 ,further ,remarks on the ,solutions of the ,field-equations of ,einstein's ,theory of ,gravitation4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiah1 vol4 #bj1 pp4 #acji-acab4 ,,st4 ,,john1 ,,charles ,,edward4 ,the principle of generalized relativity and the displacement of the ,fraunhofer lines toward the red4 ,carnegie ,institution of ,washington4 ,contributions of the ,mount ,wilson ,solar ,observatory1 ,washington1 vol4 #g1 no4 #ach4 ,,treslin1 ,j4 ,the equations of the theory of electrons in a gravitation field of ,einstein deduced from a variation principle4 ,koninklijke ,akademie van ,wetenschappen4 ,proceedings1 ,amsterdam1 #aiag1 ,band #ai1 pp4 #hib-hif4 ,,tunzelman1 ,g4 ,w4 ,,de4 ,relativity ,theory4 ,science ,progress1 #aiai1 vol4 #ac4 ,,weyl1 ,h4 ,eine neue ,erweiterung der ,relativittstheorie4 ,annalen der ,physik1 #aiai1 vol4 #ei1 pp4 #ajj-abc4 ,raum1 ,zeit1 ,materie4 ,springer4 #aiah4 ,zur ,gravittionstheorie4 ,annalen der ,physik1 #aiag1 vol4 #ed1 pp4 #aag-ade4 ,,wilson1 ,,edwin ,,bidwell4 ,generalized cordinates1 relativity1 and gravitation4 ,astrophysical ,journal1 ,chicago1 #aiag1 vol4 #de1 pp4 #bdd-bec4 ,,wilson1 ,,william4 ,relativity and gravitation4 ,physical ,society of ,london4 ,proceedings1 ,london1 #aiai1 vol4 #ca1 pp4 #fi-gg4 ,,wilson and ,,lewis4 ,the ,time-,space ,manifold4 ,proceedings of the ,american ,academy of ,arts and ,sciences1 ,nov41 #aiab1 vol4 #dh1 pp4 #chi-ejf4 ,,thanks ,most of the mathematical references cited above have been borrowed bodily from the book list prepared by ,miss ,mary ,e4 ,todd of the ,science ,room of the ,new ,york ,public ,library and published in the ,library ,journal4 ,as soon as the ,einstein craze struck ,new ,york these books were placed on a long table and it has been difficult to find a seat at this table1 day or evening1 ever since4 ,at ,cambridge ,university when ,professor ,eddington lectured on the ,einstein theory the students waiting for the opening of the hall doors formed a cue extending half-way across ,trinity ,great ,court4 ,it is unusual in any university to have 8standing room only0 at a lecture on mathematical physics4 ,about half of the present volume appeared in ,the ,independent of ,november #bi1 ,december #g1 #ac1 and #bj1 #aiai1 and ,i am indebted to ,hamilton ,holt1 the editor1 and to ,karl ,v4 ,s4 ,howland1 the publisher of that magazine1 for the privilege of reprinting them in book form4 ,i am further grateful to several professors of physics1 mathematics1 astronomy and philosophy who have been kind enough to criticize and correct this material1 but since it would not be fair to hold them responsible for my personal views and unconventional language ,i shall have to express my thanks to them in private4 ,,index ,bergson1 ,henri1 #dg1 #ea1 #eb ,carlyle1 iv ,curvature of space1 #bf1 #ce1 #ch1 #if ,eclipse observations1 #b1 #fe1 #gb ,einstein1 ,albert ,postulates of1 #ac1 #hc1 #aaa ,theory of time1 #aji ,theory of gravitation1 #ci1 #eh1 #gf1 #hj1 #hf1 #ic1 #if1 #aji ,life of1 #gh ,works of1 #aaf1 #aag ,equivalence1 principle of1 #ad1 #hc1 #hf ,ether1 #h1 #aa1 #hh1 #ajf ,flammarion1 ,camille1 #dj ,flatland1 #ce1 #eg ,fourth dimension1 #bd1 #cd1 #di ,gravitation1 #fh1 #gd1 #gg1 #hj1 #hf1 #ij ,laws1 natural1 #ajb1 #aji ,light1 deflection of ray1 #aa1 #fb1 #gi1 #he ,light1 pressure of1 #fg1 #ic ,lodge1 ,sir ,oliver1 #b1 #fh1 #ge1 #hg1 #hh ,lorentz1 #bb1 #aaa1 #aab1 #aah ,macdonald1 ,george1 #cd ,maxwell1 ,clerk1 #fg1 #aaa1 #aab ,mercury1 orbit of1 #ad1 #ff ,michelson and ,morley experiment1 #aa1 #ba1 #bb1 #he ,minkowski1 iv1 #ah ,mirror1 images1 #ah ,motion picture illustrations1 #ca1 #dd1 #df1 #ej1 #ec ,newton1 #ae1 #bc1 #ci1 #ff1 #gf1 #gi1 #hg1 #ij1 #ie ,non-,euclidean geometry1 #cj1 #dh1 #eg1 #aab ,planck1 #ih1 #aba ,poincar1 ,h41 #hh1 #ajg ,relativity of measurements1 #ae1 #bj1 #bf ,relativity of motion1 #d1 #h1 #ae1 #bc ,relativity of time1 #ae1 #bd1 #dg1 #ea ,slade1 #eh1 #fj ,spectrum1 shifting of lines of1 #ad1 #gg1 #he ,theories1 reception of new1 #ih1 #aja ,theory of relativity1 #b1 #ae ,thomson1 ,sir ,joseph1 #c1 #ic1 #id1 #ie ,time as fourth dimension1 #cj1 #cb1 #di ,time1 reversal of1 #da1 #dd ,wells1 ,h4 ,g41 #cb1 #cd1 #dj1 #eb ,zllner1 #eh1 #fj ,,transcriber',s ,,notes ,simple typographical errors have been silently corrected2 unbalanced quotation marks were remedied when the change was obvious1 and otherwise left unbalanced4 ,punctuation and spelling were made consistent when a predominant preference was found in the original book2 otherwise they were not changed4 ,inconsistent hyphens left as printed4