7i8 



NATURE 



[August 4, 192 1 



Once the transformations 



with their correlative 



'<'-"?) 



x=^{x'-k-uf) 



are introduced, the coefficient /3 is self-defined as 

 ^^[c^-u'^)z=.c'^^ and results flow in thick and fast. 

 Thus if we seek to superpose a velocity dx' jdi' , or 

 V, on the speed ii, and reckon the result as dx/dt, 

 or w, working mechanically on the above two 

 equations, we do not find, as we might expect, 

 7v = u + v, but 



u + v 

 , uv ' 



This appears to have nothing to do with the 

 )3 factor, but to depend only on the second term 

 in the expression for t. \Ve must remember, how- 

 ever, that without the )8 factor we could not write 

 the reciprocal equations, which permit simple re- 

 versal of sign in v if it is opposed to u. The 

 consequences of this law of composition of velo- 

 cities are astonishing, and include among them 

 the uniqueness and maximal character of the velo- 

 city c. 



Conjirmatiou. 



The Einstein assumptions have never been 

 directly ascertained by experiment. They are not 

 the result of experiment at all ; they are a reasoned 

 type of hypothesis, and any provisional confirma- 

 tion must be derived from the legitimacy of the 

 conclusions which, from them and their extensions, 

 the far-reaching genius of Einstein has shown to 

 be attainable. Briefly we may cite the general 

 type of confirmations, including those of his com- 

 pleter theory, thus : — 



The velocity of light inside transparent matter, 

 being less than its value in free space, is aff^ected 

 by its motion in the way Eresnel predicted and 

 Fizeau confirmed. The equations give this result 

 without the need of Fresnel's theory. 



Even outside great masses of matter the velo- 

 city is now discovered to be slightly affected (still 

 diminished, never increased) in a second-order 

 way that Einstein predicted and astronomers con- 

 firmed. Starlight is deflected by this gravitational 

 refractivity. 



Not only so. The neighbourhood of a very 

 large mass of matter introduces secondary higher- 

 order effects into the aether in such a way as to 

 affect not its luminiferous properties only, but its 

 gravitational structure too ; and the consequence 

 is that the orbit of a planet sufficiently near the 

 sun behaves, not exactly in accordance with the 

 laws of particle dynamics in empty space, but with 

 a slight modification, depending on the squares of 

 small quantities, such as the general principle of 

 relativity enabled Einstein to calculate. And, as 

 everyone knows, an outstanding discrepancy — 

 though one detected only through the extreme re- 

 finement of astronomy — was thus triumphantly 

 removed from the planet Mercury, the only planet 

 near enough to the sun to be sensibly affected. 

 NO. 2701, VOL. 107] 



Thus, then, the general mathematical trend of 

 ideas on which the principle was founded may be 

 claimed as confirmed in this ex post facto manner ;. 

 but many varieties of expression, and attempts to 

 interpret the principle philosophically, are far from 

 establishment still. 



Alternative Modes of Statement. 



If we take up an agnostic position, we cannot 

 say — and Prof. Einstein seems to agree — that, as 

 a deduction from experiment, any philosophic or 

 metaphysical position is really proven. What we 

 can definitely say is that certain statements are 

 consistent with all the experirrients hitherto made, 

 but we cannot say that every other mode of state- 

 ment is ruled out. In nearly every case — prob- 

 ably in every case — the result of experiment caa 

 be expressed otherwise. Thus, for instance, my 

 experiment with the rotating discs (Phil. Trans., 

 vol. clxxxiv., 1893) showed that their motion 

 neither added nor subtracted anything, nor 

 affected the vel(x:ity of light in their immediate 

 neighbourhood, although their circumference; 

 was travelling at a speed almost sufficient 

 to tear the steel asunder, and although an ex- 

 ceedingly minute alteration in the speed of light 

 could have been observed ; but this negative result 

 can be expounded, and indeed was expounded, by 

 saying that the aether — the vehicle of light — is not 

 carried forward or perturbed at all by the adja- 

 cent moving matter. And that is part of an en- 

 tirely rational aether theory of the atomic structure 

 of matter. 



The famous Michelson-Morley experiment, 

 again, wherein no result is found, although the 

 apparatus must be immersed in a relative aether 

 stream, can be, and was, explained by saying that 

 everv solid body suffers a FitzGerald-Lorentz de- 

 formation due to its motion relative to that stream. 



Again, the most important Fizeau experiment, 

 one which did yield a positive result, because here 

 light was travelling through and inside trans- 

 parent moving matter, and so was accelerated and 

 retarded by a measurable amount — not, indeed, 

 beyond the velocity c, but beyond the velocity 

 c/n, where n is the index of refraction — this result 

 was explained, and by Fresnel anticipated, by 

 assuming (crudely) that a given proportion of the 

 aether clung to moving matter and was trans- 

 ported with it, or (less crudely) that the presence of 

 matter so modified or loaded the aether as not only 

 to retard the light considerably in any case, but 

 to retard it difi'erently when in motion than when 

 at rest. Electrically, this comes out with complete 

 clarity, because the loading property — the matter- 

 caused modification of the aether constants fi and 

 K— really does belong to the matter, and travels 

 with it. 



So in every instance which had been already 

 explored an explanation was forthcoming, and 

 had been accepted as sufficiently plausible and 

 satisfactory ; but it was a different explanation in 

 each case. Not differing so as to be inconsistent 

 —they were all consistent with a certain view of 



