Ether , Light, and Matter. 941 



drift v is inclined at angle 6 to the ray, and if the conse- 

 quent aberration angle between ray and wave-normal is e, 

 so that 



sin 6 v _ 



the resultant velocity is 



V = V cos e + v cos 0, 



and the path of the ray between any two points A and B is 

 determined by 



r-J 



as . . 



=tt7 =a minimum, 



A V 



whicli can be written, without approximation, 



rn. Tcose C B v cos# j /1N 



So if v cos = d<j>/ds (that is if the drift has a velocity 

 potential </>) the second term — the only one obviously con- 

 taining 6 — is proportional to 4 > b~4 > a an ^ i s independent of 

 path. In other words, the time is unaffected by the drift, 

 to the first order of v/V. 



In another medium, V becomes Y/fi, and, if v becomes 

 v/fju 2 in accordance with Fresnel's law, the same velocity 

 potential (/> still holds good, And this accounts for the 

 negative results of a large number of last century's experi- 

 ments with prisms and water-filled telescopes, &c, some of 

 which are described in ' Nature,' vol. xlvi. p. 500. 



Even proceeding to the second order of drift velocity, 

 only the first term of (1) is effective — at least so long as 

 the drift is constant ; because for a closed contour, such 

 as is required for any feasible interference experiment, the 

 second term vanishes. The necessary condition may not 

 be satisfied under the peculiar conditions of destruction of 

 substance and failure of the continuity equation ; hence 

 perhaps McLaren's caution. But a second order effect, depen- 

 dent on cos e, would be expected, even in a uniform drift ; 

 for the duration of the drifted to-and-fro journey in any 

 direction, compared with the time of the same journey when 

 everything is stagnant, is, by (1) 



T' _ cos_e _ y'(l-a 2 sin 2 <9) 



T-i-y- i-a 2 ; • • • w 



an expression which may be regarded as the simplest 

 theoretical summary of Michelson's experiment. For in 

 Phil. Mag. S. 6. Vol. 41. No. 246. June 1921. 3 Q 



