( 419 ) 

 to (46) and (47) and taking the real parts 



a Ö n' r' — .v^ ( r 



^x — 7 1 • i"— cos 7l\t - 



^ 71 r V r \ V 



vr,, r=z .-^ COS n\ t , ^z = — 



fi -^— • IjWO /t I C/ I J ^w~ — 



4:jtrv^ r^ V V J 4jrrv 



— cos w I t 



-9' 



rtSn z f '>'\ , a^ti y ( 7 



^x = , .n,/ == - (05 71 It , S;>. = — — ^ (05 n ' ' 



The electric and magnetic force being known, the tlovv of energy 

 through the sphere may be calculated by means of (23). Its value is 



a' S^ 



71 



12ji^v' ' ' ' ^^^^ 



If we perform a similar calculation in the assumption of a magne- 

 tomotive force with amplitude a, acting in the space S, the result is 



a' S» 7i' 



12 Jiqv' ^^^^ 



§ 18. Let P be a point of the body L mentioned at the beginning 

 of the preceding paragraph, / an arbitrarily chosen direction and let 

 us seek the amplitude ((^/) of the electric current, or rather the 

 square of the amplitude, produced by the radiating bodies, confining 

 ourselves to the interval of frequencies (hi. 



We shall divide the bodies into elements of volume s and we shall 

 denote, for one of these elements lying at the point Q, by h one of 

 the principal directions, by ah the coefficient relating to it, and by 

 ük (cfr. (45) ) the amplitude of the electromotive force acting in that 

 direction. 



The amplitude (^/) produced by this force at the point Pis equal 

 to the amplitude of the current ^h, existing in the element s, if an 



electromotive force (Jg/ , having the amplitude -^ is applied to an 



element of volume S of the aether near P. In order to express myself 

 more l)rietly, I shall understand by A the radiation that would be 

 excited by an electromotive action at the j^oint P in the direction 

 / of such intensity that the product (^ei) ^ has the value 1. The 

 amplitude {^i) in P, of which we have just spoken, will be found 

 if we multiply by au s the value which, in that state, (^/j) would 

 have in the element s. Hence 



/ff ^. . c2 /rc^ . S2 7i'c'kmS d7i ((n^q)^ 



(34 Jt^ c^ k chi A 

 wk, (50) 



