662 Mr. G. A. Schott on Radiation from Moving Systems 



Let P be the point (a?, y, z), 

 the position o£ the system at 

 time t, the distance OP being 

 supposed large compared with the 

 largest dimension of the system 

 and with the wave-length. 



The disturbance (6), (7), which 

 exists at P at time t, was emitted 

 at a previous time t, when the 

 system was at E, such that 



EP = C(*-t), 



EO = U(*-t) = ?EP. 



Let EP = /o, and let its direction cosines be (X, ja, v). 

 Let P' be the point (V, y f , z'), so that NP' = /<:NP; then 

 OP' = /, and (I, m, n) are the direction cosines of OP'. 

 We easilv find 



X = 



z+u/c 



1 + ZU/C 



Km 



Kn 



P = 



1 + ZU/C 1 + /U/C 



P =(1 + ITJ/C)- 



Thus equations (7) express the fact that P is along the 

 ray EP, and that its magnitude is 



f U\ 2 



Equations (6) give 



XL + YM:+ZN=XX+/ A Y + vZ=\L + /xM-fvN=0, 



X2 + Y 2 H-Z 2 = L 2 + M 2 + N 2 =^ 2 (l + Z^y(T /2 4-P /2 ). 



These express the facts that the electric and* magnetic forces 

 are perpendicular to each other and to the ray EP, and that 

 they are equal to each other. 



The wave surface, which at time t passes through P, is the 

 sphere whose centre is E and radius EP. 



§ 8. We require to solve three problems : 



(1) To find the rate at which the system of electrons 

 loses energy by radiation. 



(2) To find the radiation pressure on it, that is, the 



reaction due to the aether on account of radiation. 



(3) To find the radiant energy received per second by a 



fixed surface exposed to the radiation. 

 It might be supposed that (1) was simply (3) treated for a 

 surface completely enclosing the system ; but this is not so, 



