of Electrons, and the Spectrum of Canal Rays. 663 



because the energy of the aether inside this surface is conti- 

 nually changing on account of the motion of the system. 



E is as before the position of 

 the system at time t, APB the 

 wave emitted at E, for the time t. 

 F is the position of the system at 

 time r + dr, CD the wave emitted 

 at JF, for the time t. 



The energy radiated by the 

 system during the interval dr is 

 the energy contained between the 

 two waves AB, CD; since they are not concentric, this 

 energy requires a different interval of time, dt, to pass each 



point P of AB. Since t = r + ~, we have 







dt 



= dr(l + f\ =dr(l- Scos AEP). 



N ° W cosAEP = X=i±^; hence dl= M 



1 + /U/C — . 1+/U/C 



Let dS be an element of area of the wave AB at P. The 

 energy which crosses d& during time dt is, by (7), 



(\V+/iQ + v'R)dSdt= ^(1 + ZU/C)(T' 2 +P ,2 )^S. 



Hence the rate at which the system radiates energy is 



R=^. 1 f(l + /U/C)(T' 2 + P' 2 )rfS. 



Since T', P' are given for the system (20 it is convenient 

 to transform the integral to this system. Let d& correspond 

 to c?S, and let (A/, p', v 1 ) be its direction cosines. 



(20 being derived from (2) by stretching every line 

 parallel to Ox in the ratio k : 1, every area parallel to the yz 

 plane is unaltered, while every area parallel to Ox is increased 

 in the ratio *c : 1. Hence we have 



XdS =\'d&', ^S --= k>W, vdS = K V 'd$. 



These equations give at once 



Z + U/C , m ,_ n 



va + azU/C + tP/C*' yH-2m/C + U 2 /C 2 ' vA-!-2/U/C + U 2 /C* 



v / l + 2/U/C+U 2 /C 2 



