42 Prof. R. Clausius on the Theorem of the Mean Ergal, 

 the result is _2 



C— lok n 



From this equation another can easily be derived, in which k is 

 presented as a function of w ; and if we at the same time take 

 into consideration that h = k—iv, we obtain : — 



2 R n ~ l 



Jcz=w-\ w n -4-2- 



n c 



2/3 



2 tt-2 





, 2 £ «z» n n*-2/3 2 ^z_ 2 



A= W™ +2 s 5-W n + ... 



w c n 6 c l 



_ 2/3 5ZJ" , ^ 2 -2/3 2 2Lz* 

 h—w— — w+ - — w » +2' — s 5-w » +. . . . 



(53) 



We will in like manner express also the three quantities be- 

 longing to k, h, and h — w, viz. e, u, and t, or, still better, their 

 logarithms, as functions of w. In order, first, to determine i, 

 we employ the first of the equations (30), and put therein for k 

 the expression given in the first of the equations (53), by which 



we get 



_ir n-1 B _I 3rc-4/3 2 _ 2 1 



i = 2V2cw *\}-—^ „+____„, . + ...J. 



If from this we derive the equation for log i, considering that 

 we can put 



e = 2mivi and u = 2mwi~, 

 and accordingly 



log e = log i + log 2mw and log u = 2 log i + log 2m w, 

 we get 



rc-1 



logi=log(2 v / 2^ 2 )-^ 

 (n«-2)(n-2) ff 



i *" 



2n 3 



-o ^ 



+ . 



I 71-18 _2 

 log e = log (W2mav*) — ~^— ~ ™ n 



(n*-2){n-2) j3 s 



(54) 



2n 3 



log ?i= log (16mc 2 ) —2 



i# » +., 



n-1 /3 



«; 



(n*-2)(n-2)j8 a _? 



3 9 tc -j- . . , 



