750 



NATURE 



[August ii, 1921 



traction. The relativity doctrine, in order to 

 avoid recognising- any such difference, would pre- 

 sumably distribute this factor between the two 

 expressions, making them 



X'_cos e + acos 6 

 n" _ cos € - a cos 6 . 



SO that there shall be equality between n"\' and 

 n\, and then it is impossible to tell to which body 

 the motion belongs. 



Note that the introduced $ factor cannot in 

 this case be attributed to a FitzGerald contrac- 

 tion of the grating — if a grating is used as the 

 measuring instrument, — for the aspect of the 

 grating to the incident light, and therefore to 

 the motion under examination, is normal, not 

 tangential. But the law of reflection is interfered 

 with by the motion, in a way investigated in Phil. 

 Trans, for 1893 (vol. clxxxiv. , A, pp. 793-800), and 

 the result is to give a modified deviation which 

 will be interpreted as part of the Doppler effect. 

 The discrepancy is reckoned, on p. 798 loc. cit., 

 for any incidence angle i and any drift angle <^, as 

 a- cos^ i sin 2 {i—cp); so it is a maximum for 

 normal incidence and »for a drift direction making 

 45° with the ray. 



This might readily have the average value ^o^ 

 needed to replace the ordinary $ factor, but in so 

 far as it yields a factor depending on the angle (f> 

 its changes seem amenable to observation. 



In the same Phil. Trans, paper I show (p. 787) 

 that the Doppler effect observed by a moving 

 grating is really an aberration effect, due to the 

 motion being partly across the diffracted rays, 

 although the incident ray may be along the drift. 

 For a grating must deviate in accordance with 

 wave-length, whether it be moving or stationary, 

 so far as first order is concerned. 



But the question arises, What happens when the 

 grating is drifting partly in its own plane 

 (^=90°) and thereby suffering a FitzGerald 

 contraction? 



The answer seems to be that the extra aberra- 

 tion due to this drift will just compensate the 

 second-order Doppler effect otherwise to be ex- 

 pected from the ostensibly narrower-ruled grating. 

 There are certain possibilities here, however, 

 which need looking into. 



Summary of this Portion. 



The Einstein formulation seems to justify itself 

 by results, and may be supposed to strengthen 

 the claims of any philosophy suggested by it, as 

 well as to establish the explicit assumptions on 

 which the theory is based; but we should be 

 careful to perceive that justification is of this sub- 

 sequent inferential order, and that it is not pri- 

 marily the outcome of experiment — certainly not 

 of any old unexplained measurements. The whole 

 thing depends on the law that we postulate for the 

 composition of velocities. When two velbcities in 

 the same direction are compounded, is the result- 

 NO. 2702, VOL. 107] 



ant velocity u + v, or is it really uv^ Einstein's 



assumption led to the latter as a physical truths 

 and if that is right it is algebraically undeniable 

 that if one of the component velocities is c, the 

 resultant will be c also ; and any such criterion 

 as my old experiment (1892-97) with rotating 

 discs, whereby it was sought to observe a pos- 

 sible difference between c + v and c — v, cannot 

 give any positive result. Nor can it, by giving 

 the result zero, prove that v is o, because, as a 

 matter of simple algebra, if w = c, no sort of v 

 can make any difference, not even if it be infinite. 



So also Michelson's experiment can show 

 nothing, nor can any velocity compounded with 

 the velocity of light exhibit itself in any way, if 

 that is the true law of composition of velocities in 

 general. 



But why into this composition formula should 

 there enter the velocity of light? If, for instance, 

 the composition is between a ship and a tide, or 

 a satellite and a planet, or the usual railway train 

 and embankment, one cannot avoid the question,. 

 What on earth has the speed of light to do 

 with it? any more than the speed of sound or of 

 a messenger boy, or whatever agent it is which 

 brings information to an observer. It is true 

 that the law of composition is essential to the 

 principle of relativity, but when we are engaged 

 in establishing that principle it is scarcely fair to 

 assume it. 



The curious law of composition is deduced from 

 the Lorentz transformation of space and time to 

 other co-ordinates, 



and in the establishment of these equations it is 

 assumed that all observers have the same value of 

 c, or that x- — cH^ is invariant. 



1 apprehend that for this transformation, treated 

 as formal correspondence, there is a good deal to 

 be said, so that any law deduced from it may be 

 true with all its consequences ; but it is surely a 

 mistake to say that the measured velocity of light 

 has been experimentally proved constant. So far 

 as the velocity of light is concerned, the reason- 

 ing is circular. I suggest that it is also danger- 

 ous to adopt a mode of exposition which denies 

 reality to the FitzGerald contraction. Still more 

 is it premature to assume, as more than a tem- 

 porary conclusion, that no phenomenon demon- 

 strating our motion through the aether of space 

 can ever be discovered ; which carries with it the 

 implied suggestion that the inability is because 

 such a medium does not exist ; so that not only 

 can all motion be treated undynamically as a 

 purely geometrical or kinematic relation, but so 

 also that in absolute truth there is no difference 

 discernible between a dog wagging its tail and 

 the tail wagging the dog. Kinematically, it is 

 as easy to take the apple as standard of reference 

 as it is to take the earth, but physically and ener- 



