( 673 ) 



§ 6. Wo have now to raU'uljitc tho coofticionl ^/,„ by means of 



(13). After lia\ ing- siihsliliiled in llie iiile<i'i-al the value (7), wc may 



still take for its limits and »>, proNided we reckon the time from 



/' 

 an instant, precedin^i»- hv the interval — the moment from which it 



(■ 



has heen reckoned till now. Thus: 



1 r r '/", 



nt . ~ (It 



~[\h 



2jtc'd7' |_ J (It 



u 

 or, after integration by parts, since sin nt vanishes at the limits, 



a,,i z= ^ e I cos nt . u, dt (15) 



2 ^ 0^ i-^ 7- L J J ^ ^ 







The sum in these expressions relates to all the electrons in the 

 part a>A of the plate and it is by reason of the immense number 

 of these particles that a delinite value may be assigned to ii^m- 



We shall begin by detei-mining ^/%„ and the amount of the radiation 

 in the supposition that there are only free electrons of one kind (§ 3), 

 We shall write if = NioL. for their number, e for the charge of 

 each of then», and we shall further simplify the problem by supposing 

 that the molecular velocity ii, the same for all the electrons, is not 

 altered l)y the collisions and that all the paths between two successive 

 impacts have exactly the same length /. Then, the time 



_ I 



H 



will also ha\e a delinite length. , 



§ 7. Let t^, t^, t^, . . . be a series of instants, between and ih, at 

 intervals t from each other. Then it is clear that, if we fix our 

 attention on the positions of a single electron at these instants, we 

 shall have one poijit on each of tlie sides of the zigzag-line described 

 by this particle. 



Now we may in the fu-st place determine the integral in (J 5) for 

 the la[)se of time during which an electron travels over the side of 

 the zigzag-line on which it is found at the time ti^. As the length 



. 2^ 

 T ot this interval is much shorter than the period — of the factor 



n 



cos nt, we may write for the integral 



ros iitf^. . r u^ (16) 



It is clear that we shall obtain the sum in (15), for the <^ electrons, 



