664: Mr. Gr. A. Schott on Radiation from Moving Systems 



rmal to d 



1 + ZU/C 



If of. be the angle made by the normal to dS' with r 1 , we 

 have 



cos a = l\' + mu! + nv ] = — _. 



\/l + 2ZU/C + U7C* 



If dS' subtend the solid angle ofo> at we have 



dS' = sec ol .r f2 dco. 

 Hence 



dS = cos a d$'=? J2 d(D, 



R=~rr(l + ZU/C)(T' 2 + F 2 y^ ft ,. . . . (8) 



This equation expresses the rate at which the moving 

 system (X) loses energy by radiation at time t, in terms of 

 the field in the system of reference (%') at the time t', corre- 

 sponding to the time t — r+^L in the moving system. In 



this respect it differs from the expressions given by Abraham *, 

 which express it in terms of the state of the moving system 

 at the time t. 



§ 9. We shall now find the reaction of the sether on the 

 moving system due to radiation. 



According to the theory developed by Lorentz and by 

 Abraham t the electromagnetic force on all the charges 

 contained within the fixed surface S is the sum of (1) a 

 surface integral 



Y~ (T [2E(\X + fiY + vZ) - JJn . (X 2 + Y 2 + Z 2 ) 



+ 2H(\L +/*M + vN) - JJn . (L 2 + M 2 + N 2 )]dS, 



where, as before, (X, yu, v) are the direction cosines of the 

 outward normal to the element d$, and JJn is a unit vector 

 along that normal ; and 

 (2) a volume integral 



^jjMi.dxdydz, 



extended over the whole space enclosed by the whole surface S. 



The quantity P/C 2 is the electromagnetic momentum per 



unit volume ; the integral (2) is the rate of decrease of the 



* Luc. cit. p. 278. 



t Lorentz " Elektronentheorie," Mathematische Encyklopadie, vol. xiv. 

 p. 161. 



