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



neglected. Denote averages taken in this way by a bar 

 over the symbol of the quantity averaged, e. g. R. During 

 this process the coordinate (f> disappears at the same time as t 

 from the expressions for T' 2 , V 2 , in virtue of assumption (B). 

 (2) Put dco = sin d0 dty ; note that 



I —a cos + \/l — d 2 sin 0cos<£, 



m = b cos — sin cos (f) -\ -— — sin sin <b, 



A/1 — o 2 VI — a- 



n = c cos v=-=- sin cos 6 ; = sin sin <f>. 



Integrate from <f> = to 2tt and from 6 = to 7r. 

 (8), (13) give 



^ = R' = ic\\T 2 + V ,2 )r' 2 sin 6d0. . . (14) 

 For shortness write 



R.=1C I \T /2 + P 2 y 2 .P.(cos0)sin0d0 (15) 

 Jo 



with the usual notation of zonal harmonics. We note that 

 Hi is identically zero for odd values of i, because T /2 , P /2 do 

 not change when ir — 6 is put for 0. 

 (9), (12) give 



4U _ , 1 



X= " J[C^Vh * R + i P ^ • *2 } , 



r =-whv^ h -^ (16) 



u 



Cx/C 2 -!?' 



Z= — „ / ^, TT ,«r'.E 2 . 



L 1 + 1U 2 /C 2 ~ 2U 2 ^ 



The radiation pressure F does work on the moving system 

 (%) at the rate W= —VX; hence 



^ a(c 2 - u») {ff+'i p »W • *»}» • • • ( 18 ) 



With respect to equations (10), (11) of § 10 the integration 



