and its Application to the Molecular Motions of Gases, 39 



order to obtain 



i 



■=4m\/2k(c—0k »j 



1 V^l 



If we multiply this by -=■ c 2 % and represent the product 



m4sV 2 

 on the left-hand side by a single letter, putting 



p n ~ 2 

 V= 7=c~*-, (39) 



we can give it the form 



V =(kc n y2[l-I3{kc n )~n]. . . . (40) 



7j is here represented as a function of kc n ; and we can proceed 

 with this equation as we did with (32), in order to represent kc n as 

 a function of rj • and thus we get 



kc n = v *(l + 2/3 V - 2 n + ?^>y4 + . . .). . (41) 



We can therefore thus express the result sought : — If^ denotes 

 a function the form of which is determined by the equation 



then 



r 2 q,„ A. 4 \ 



^(,) = ,^i + 2/3 ,— + ^L_j* / sy- » + ,..], . (42) 



*=<-"* tV ¥ ) (43) 



Further, by employing the value found for k } the following 

 value of w can be deduced from equations (30) : — 



/ <e n ~ 2 \ 



1 _ n ^ \m~W2 ° 2 / ,aa\ 



w = s c w e . ♦ , (44) 



A de 



In order, lastly, to exhibit h as a function of u, we multiply 

 the first two of equations (30) into one another, whence arises 



_s(, 



pck n + 



n n 



By putting herein, according to the signification of u, 



•2 u 



2m 

 and then dividing the equation by 8c 2 , we get 



»— 1 * n — 2 -* 



16mc 2 



