August ii, 192 i] 



NATURE 



749 



or against a discrepancy due to the observer's 

 motion, in the measured 186,330 miles a second. 

 In a to-and-fro journey there is complete com- 

 pensation for any possible discrepancy in speed 

 so far as small quantities of the first order, in- 

 volving the ratio m/c, are concerned. The only 

 outstanding discrepancy to be expected is of the 

 second order of minutiae ; and that, as many of us 

 think, is systematically neutralised by the 

 FitzGerald-Lorentz contraction, which, though it 

 is a consequence of the electrical theory of matter, 

 is stigmatised as an unreal contrivance, a mere 

 invented refuge, by the philosophers above re- 

 ferred to. 



Relativity has only to do with second-order 

 effects ; it essentially depends on ds-, the square 

 of a small interval; but the statement above 

 quoted is not entirely about second-order effects ; 

 it relates to the first order — to a journey in one 

 direction — and would require for direct verifica- 

 tion an observation of the difference in the time 

 of a single journey, when the observer is moving 

 (a) with, (b) against, an aether stream. 



The nearest approach to a measurement of this 

 kind that might conceivably be made would be 

 a vastly improved determination of the velocity 

 of light by a method based on the observation of 

 some periodic feature in Jupiter's satellites during 

 the course of Jupiter's year. To make a deter- 

 mination possible at all, the earth must be moving 

 either to or from Jupiter at the time — it does not 

 matter which — and the chance of obtaining a posi- 

 tive result depends on the varying angle which 

 the line joining earth and Jupiter makes with 

 the sun's way, or rather with the direction of 

 locomotion of the solar system through the aether, 

 whatever that direction may be. 



But I think it is generally agreed — subject, 

 however, to the opinion of the chief authority on 

 those motions. Prof. R. A. Sampson — that the 

 gravitational theory of the satellites, perturbed 

 as they are by each other as well as by the 

 oblateness of Jupiter, is not yet nearly perfect 

 enough to enable us to decide the question 

 whether the velocity of light deduced from their 

 eclipses is dependent on the season of Jupiter's 

 year, — in other words, whether light appears to 

 reach us with the same speed when we are looking 

 at Jupiter down-stream as it does when we are 

 looking at him up-stream (see Phil. Trans., 1893, 

 vol. clxxxiv., pp. 746, 779, and 785). For we 

 have no means of determining the instant at 

 which the light starts from Jupiter ; all that we 

 can really observe is the time that hght takes 

 to transit the distance travelled by the earth in 

 the interval between two eclipses. 



Apart from all astronomical observation, how- 

 ever, it has been claimed that the rather recent 

 pair of experiments of Prof. Majorana, with 

 moving mirrors {Phil. Mag., February, 1918, 

 p. 163, and January, 1919, p. i45)> do 

 establish the thesis that the observed velo- 

 city of Hght is independent of the relative 

 motion of observer; but they, too, are ob- 



XO. 2702, VOL. 107] 



servations made on a to-and-fro journey, and, 

 therefore, for the present purpose, are beside the 

 mark. If light were a projectile, it could be hit 

 forward by a moving mirror, like a cricket ball, 

 but no one can suppose that any kind of impact 

 can alter the subsequent velocity of waves through 

 a medium, nor is it to be supposed that motion 

 of a source can affect the travelling rate of waves 

 which it has emitted and abandoned. 



More Careful Discussion of Doppler Effect. 



Motion of the source does not affect velocity, 

 but if a moving source emits waves at constant 

 frequency n, the wave-length ought to be different 

 in different directions 6, and this modified wave- 

 length, 



y _ccos( + ucos6 

 n 

 can be observed by a fixed observer, and, when 

 compared with the normal X^cjn, is called the 

 Doppler effect. The small aberration angle e, 

 between ray and normal to wave-front, is defined 

 by c sin e — It sin = 0. 



If, however, the source is fixed in the aether, 



and only an observer is moving, the velocity and 



the wave-length are both quite normal; but the 



-frequency with which the waves are encountered 



by the observer will depend on the speed and 



direction of his own motion. Consequently there 



is again an observable Doppler effect expressed 



as 



, c cos € + u cos B 

 n= ^ , 



to be compared with n^cjX. 



Hence if an observer steadily chases a source, 

 keeping a fixed distance between them, the two 

 effects- — -the real wave-elongation and the ap- 

 parent frequency increase — neutralise each other 

 exactly whatever the direction of joint motion, 

 because nX'=n'\. So drift through a medium 

 produces no trace of a Doppler effect. 



Nevertheless, the two types of effect — one with 

 source only moving, the other with receiver only 

 moving — are not identical ; they are the same 

 when both are moving in the same direction, so 

 as to be relatively at rest, but not the same when 

 they are moving relatively to each other. For, 

 writing ufc as a, and taking the case of 

 relative recession between source and receiver, we 

 get, for the observed frequency ratio, — 

 if it be the source only which is moving, 



n X cos e + a COS B 

 while if it be the receiver only which is moving, 



Hence 



— = cos f-a cos 

 n 



n" is not equal to «', but 



— = cos'^ 6 — a* cos- 6 

 n 



= I — a- sin^ 6- cr cos* B 



which is the square of the usual FitzGerald con- 



