220 



DISCOVERY 



as both authors indicate, hes in the success of the attempt 

 to secure for the inhabitants of rural districts a fullness 

 of hfe and interest, upon lines which each suggests, to 

 counter the attractions of the conditions of life in a town. 



E. N. Fallaize. 



A POPULAR EXPOSITION OF EINSTEIN'S 

 THEORY 



The Theory of Relativity and its Influence on Scientific 

 Thought. By A. S. Eddington, M.A., F.R.S. 

 (Clarendon Press, Oxford, 2S.) 



Professor Eddington 's " Romanes Lecture " is as good 

 a Romanes as we have heard or read, and we are giving 

 two somewhat lengthy extracts from it in the hope that 

 they will send readers to the original. The first describes 

 a deduction from Einstein's theory not usually mentioned 

 in popular expositions of it ; the second draws an interest- 

 ing comparison between a flat earth and a flat world. 



I will conclude this part of the argument with an 

 experimental application wliich illustrates the power of 

 Einstein's method. Much study has of late been given 

 to electrons moving with very high speeds ; for example, 

 the particles shot off from radio-active substances are 

 negative • electrons wliich sometimes attain speeds of 

 100,000 miles a second. It is found by experiment that 

 the rapid motion produces an increase of mass of these 

 particles. I want to show that the theory of relativity 

 gives a very simple explanation of just how this increase 

 of mass occurs. But I must first remark that an explana- 

 tion had been previously given which had generally 

 been accepted as satisfactory. The phenomenon was 

 actually predicted by J. J. Thomson before relativity 

 was thought of ; because, assuming that the mass of a 

 particle is of electrical origin, an application of Max- 

 well's equations shows that it ought to increase vnth 

 velocity. But the precise law of increase cannot be 

 predicted on tliis basis, since various plausible assump- 

 tions lead to slightly different results. . . . Einstein 

 takes us straight to the root of the mystery, and he clears 

 up one point which was misleading, if not actually wrong, 

 in the older explanation. The change of mass does not 

 in any way depend on whether the mass is of electrical 

 origin or not ; it arises simply from the fact that mass 

 IS a relative quantity depending by its definition on the 

 relative quantities length and time. Let us look at the 

 ^ particle from its own point of view ; it is j ust an 

 ordinary electron in no way different from any other. 

 " But it is travelling unusually rapidly ? " " That," says 

 the electron, " is a matter of opinion. So far as I am 

 aware I am at rest, if the word ' rest ' has any meaning. 

 In fact I was just contemplating with amazement your 

 extraordinary speed of 100,000 miles a second with which 

 you are shooting past me." Of course our motion is of 

 no particular concern to the electron, and it will not 

 modify its condition on oui account, so it keeps its mass, 

 radius, electric field, etc., equal to the standard constants 

 applying to electrons in general. These terms are relative, 

 and refer therefore to some particular frame of space 



and time — clearly the frame appropriate to an electron 

 in self-contemplation, viz. the one with respect to which 

 it is at rest. But this frame is not the usual geocentric 

 frame to which we refer quantities such as length, time, 

 and mass ; there is a difference of 100,000 miles a second 

 between our station of observation and that of the 

 particle in self-contemplation. It is a mere matter 

 of geometry to discover what the (3 particle's lengths 

 and times become when referred to the partitions which 

 we have drawn across the world. But when we calculate 

 the consequential change of mass resulting from the 

 changes of length and time, we find that it should be 

 increased in precisely the proportion indicated by the 

 most refined experiments. 



The ancients believed that the earth was flat. The 

 small portion of its surface with wliich they were cliiefly 

 concerned could be represented without serious distor- 

 tion on a flat map. As more distant countries were added, 

 it would be natural to think that they also could be 

 included in the flat map. You have all seen such maps 

 of the world, e.g. Mercator's projection, and you will 

 remember how Greenland appears enormously exaggerated 

 in size. Now those who adhered to the flat-earth theory 

 must hold that the flat map gives the true size of 

 Greenland. How then would they explain that travellers 

 in that country reported that the distances were much 

 shorter ? They would, I suppose, invent a theory that 

 a demon resided in that country who helped travellers 

 on their way, making the journeys appear much shorter 

 than they " really " were. No doubt the scientists would 

 preserve their self-respect by using some Graeco-Latin 

 polysyllable instead of the word " demon," but that 

 must not disguise from us the fact that they " really " 

 were appealing to a deus ex niachina. 



The name demon is rather suitable, however, because 

 he has the impish characteristic that we cannot pin him 

 down to any particular locality. We might equally 

 well start our flat map with its centre in Greenland ; 

 then it would be found that journeys there were quite 

 normal, and that the activities of the demon were dis- 

 turbing travellers in Europe. We now recognise that 

 the true explanation is that the earth's suiface is curved ; 

 and the demoniacal complications appeared because we 

 were forcing the earth's surface into an inappropriate 

 flat frame which distorts the simphcity of things. 



What has happened in the case of the earth has hap- 

 pened also in the case of the world, and a similar revolu- 

 tion of thought is needed. An observer, say at the centre 

 of the earth, finds that there is a frame of space and 

 time — a flat or Euclidean frame — in wliich he can locate 

 tilings happening in his neighbourhood without distorting 

 their natural simplicity. There is no gravitation, no 

 tendency of bodies to fall, so long as the observer con- 

 fines his observations to his immediate neighbourhood. 

 He extends this frame of space and time to greater 

 distances, and ultimately to the earth's surface, where 

 he encounters the phenomenon of falling apples. This 

 new phenomenon must be accounted for, so he invents 

 a deus ex machina which he calls gravitation, to whose 



