and its Application to the Molecular Motions of Gases. 



1 d c h _ 1 d c h 



u\ 1 ~ u d log u 

 - du 

 u 



d c \ogu , d w ii J w logw 



and —r- —u 



dc 



45 



d c h 

 du 



— u 



dw dw 



by which they are transformed into 



dc 



d c h 



d log u 



d c h 



dw 



dw 



dji 

 dc 



d w h 

 dc 



dJi 



<?«, logw 



d loo- u dc 



(56) 



If, in the first of these two equations, instead of h and log u we 

 employ the expressions given in (53) and (54), we obtain 



dji 



dlogu \ ) 



(as it must be, according to the theorem of the mean ergal); and 

 accordingly the second of the two preceding equations can be 

 written in the following simplified form : — 



dji 

 dc 



dji 

 dc 



w 



d w log u 

 dc 



In an entirely corresponding manner we get : — 

 dJi 



d\o>%e 



= 2w, 



djc _ d w k _ 9 d w lo£ 

 dc dc dc 



d c (h- 



• IV 



d log i 



di(h — w) 

 dc 



2w, 



d w (h—w) 

 dc 



2w 



d w log 

 dc 



(58) 



(59) 



(60) 



Equations (53) refer to only one coordinate-direction ; but 

 from them the corresponding equations for all three directions 

 can be forthwith derived, which determine the quantities U, E, 

 and U — T as functions of w { , w 2 , w 3 , c ]} c 2 , c 3 . In order 

 that the formulae we obtain may not be too long, we will 

 first give to the second of the equations (53) the following 



