( 676 ) 



cos'ntk.QFê'dê 



and the total sum of all the Q terms is got from this l>y an inte- 

 gration which we may extend from § = — x to §=-[-ao. Conse- 

 qnently, the sum of those Q terms will not be altered, if, in each of 

 them, we replace §'/, by 



W=fl'^''d^ (22) 



This expression l)eing the same whatever be the particnlar valne 

 of cos^ ntk, the snm in (20) at once becomes 



1^^^ [cos' Ht/,] (23) 



k 



Again, since the instants t^, t^, . . . . are nnifonnly distributed at 

 distances that are verv small parts o( llie peiiod — , the sum will 

 remaiji the same, if in every term we write \ instead of co.s' ntk. 

 The number of terms being — , we lind for (23) 



2t* 



and for (20) 





We have by (21) and (22) 



S3 . 



I 



hence, replacing r bv — , we lind 



u 





24r:t'c'3r^ 24:Jt'c'dr 



and for the emission (14), in so far as it is due to the one kind of 

 electrons that has been considered 



n^e'NluA , 

 to (J) d )i. 



This value must still be multiplied by 2 because we may apply 

 to tlie second of the components (6) the same reasoning as to the 

 first component, and the total radiation from the plate may obviously 

 be considered as the sum of all the values corresponding to the 



