( 41fi ) 



amplitude ii, aotiiit!,' iii (lio dii-cclioii of' OY, lliis may l)c found hv a 

 reasoiiiiig' siniihir (o lliat we have used iii §^\ 12 and 13. Let us 

 suppose for a iDOinent au electrouiotive force of the sauie direction 

 and inteusitv to exist in an element of volume s of the aether Jiear 

 the point F. The amplitude of the electric force ^'.^ in the aether 

 immediately before the plate will then be (cfr. 38) 



and thai of the current ^,^ in the plate 



«J n'' s g 



If follows from this that, if the element s in the plate is the seat 

 of an electromotive force Ol'^^, with amplitude <l^, the current 

 (è*^. =r <i\. at the point P will have this same value. The amplitude 

 of the electric force (?., will be 



a„ n S '/ <7 



// = ~ ■— = - \/2k S a, (in 



4jt f^ r cr 



and the corresponding radiation across the element to' 



1 ,, , k^a^ci^oi'dn 



— ch to ^^^ — . 



2 cr'' 



This leads immediately to the expression (42). 



§ 16. We are now in a position to form an idea of the state ef 

 radiation in a system of bodies of any kind. After having divided 

 them into elements of volume s, and after having determined the 

 principal directions at every point, we conceive in eacli element the 

 electromotive forces whose amplitudes are determined by (40) and 

 ^41), the phases of all these forces being wholly independent of each 

 other. In representing to ourselves the state of things obtained in this 

 way, we must keep in mind : 



1*^ that the principal directions and the coefficients «i, a^, «j 

 will, in general, change from point to point and will depend on the 

 frequency n. 



2"*^i'" . that for each frequency n or rather for each interval dn of 

 frequencies, we must assume electromotive forces of the intensity we 

 have deiined in what precedes, all these forces existing simultaneously. 



We shall now show that, if the temperature is uniform throughout 

 the system, the condition for the equilibrium of radiation will be 

 fultilled in virtue of our assumptions. Of course, it will suffice to 

 prove this [>roposition for a single interval of frequencies d n. 



