( 596 ) 



a e «"" 



X = -— ,,+ t^'■■"»'+^,.-"•or . . . . (16) 



By means of this formula we can calculate, for a definite instant 

 t, the mean value x for a large number of molecules, all acted on 

 by the same electric force ae'>>'. Noav, for each molecule, the con- 



stants C\ and Cj are determined by the values of X and — immediately 



after the last blow, i. e. by the values x„ and I -— I existing at 



the time t — 19-, if & is the interval that has elajised since that blow. 



We shall suppose that immediately after a blow all directions of 



the displacement and tlie velocity of the electron are equally pro- 



fdx\ 

 bable. Then the mean values ot x„ and — are 0, and we shall 



find the exact value of x, if in the determination of C\ and C\, we 



dx . , , . 



suppose X and — to vanisii at tiie tmie t — &. 



dt 



In this way, (16) becomes 



ae«"'' I 1 /. >t\ ., ,„ 1 /, n\ ., , ^=.) 



From this X is found, if, after multiplying by -e ' dd^, we inte- 



T 



grate from & ^ to 9- ^ oo . If ?« is an imaginai'y constant, we have 



00 & 



1 r «s — 1 



I e ' dd' = 



1 — ?<T 



Hence, after some transformations, 



— fl © 



/ 1 \ iinn 



(17) 



If this is compared with (15), it appears that, on account of the 

 blows, the phenomena will bo the same as if there were a resistance 

 determined by 



.» = ?^, (Ï8) 



T 



and an elastic force having for its coelTiicient 



(/)=/+^ (19) 



