﻿924 Mr. E. Buckingham on th 



m on t/ie 



By equation (2) the effect of all these n arrivals is to increase 

 the period in the ratio 



r n a = (l + /3cos0) M = l + n/9cos<k. . . (5) 



the remaining terms being of higher orders in j3. Inserting 

 the value of n from (4) we have 



r n = 1 + ^ cos 2 6 sin 6 dd> ; 



and since pets is the infinitesimal increase of volume, Ar, 

 which occurs within the time t as a result of the motion M, 

 this last equation may be written in the form 



< = l+-2^ cousin <^. ... (6) 



So far we have considered only the directions between <f> 

 and <£> -f- def), but meanwhile the given element of energy has 

 also been arriving a large number of times at every other 

 possible angle between and ir/2, and equation (6), with the 

 appropriate value of (f>, is applicable to every such angle. 

 The total effect of all the arrivals at all possible angles will 

 therefore be to change the period in the ratio given by the 

 product of all the expressions of the form (6) for all values 

 of cj) ; and dropping terms of higher order in ft, the value of 

 this product will be 



IT 



t 1 Av C 2 2 ... 7, -, , 1 Av ,-. 



+ 2 V 1 cos </> sm </># = 1 +g~ • • • (0 



If we go on to treat the effects of the departures, the 

 reasoning will be found to be the same all the way through, 

 with the mere substitution of -v/r for (/>, and the total effect 

 will be found, as before, to be to increase the period in the 



ratio 1 -f . Hence the combined result of the two sets 



b v 



of effects, which have in reality been occurring alternately, 



is to increase the period of every element of the radiation in 



the ratio 



T + AT/ lArX'.lA* 



Replacing the period by the wave-length we therefore have 



AX _ 1 Av , m 



A 3 v 



