660 Mr. Gc A. Schott on Radiation from Moving Systems 



All the operations are supposed to be performed in the 

 system S'. 



The values of <£', A' are given by the usual integrals 



where r' is the distance from the point (V, y' z r ), at which 

 the field is required for time t', to the element dg drj' d£, f ; the 

 square bracket denotes that the quantity inside is to be taken 



. r' . 



for the element d^dr/dX^ at the time t' — p, which is the time 



of emission of the disturbance due to that element. 



It should be noticed that the field is the same as if the 

 system (2') were at rest as a whole, except that E' involves 



an additional term p-V-F'. This term only vanishes when 



all the charges are at rest relative to one another. In our 

 case it is present, because we are dealing with systems of 

 electrons in orbital motion. 



§ 6. We shall only require the field at a distance from the 

 system of electrons large compared with its largest linear 

 dimension. </>', A' are the sums of periodic expressions of 



fur r'/C) 



the form — r-* — -' where r' is the distance measured from 



r 



any convenient origin in the system. If we neglect quantities 



of relative order — , where X is the wave-length, we may 

 write 



A I ^ A = *' A=_ LA 



-dr' C ht" &*' r' V c s*" ' ' ' 



where (I, m, n) are the direction cosines of r' . Hence 



div.A'=- 1^ pF + roG' + tiH'). 

 \j ot 



We shall find it convenient to transform to polar co- 

 ordinates- (V, y <f>) in the system (S')« For polar axis 

 choose any convenient line fixed in this system, and for initial 

 plane the plane through this axis and Ox. Let the direction 

 cosines of the axis be (a, b, c) } those of the radius vector (V,, 



