422 Journal of the Asiatic Society of Bengal. [{N.S., XIV, 
i=T : a it 
+ \\\ (X,,u+ Y,v+Z,w)dS dt — \\\\ 2W dQ dt, 
t=o a Fe ae 
-where 
2W= Xx ln + Vy Cyy + Zz Cog + Xy Cy y + Xz lng + V2 eye (3). 
Denoting by 7' the time-average of kinetic energy per unit 
volume, and by W the time-average of the — energy 
per unit volume, we have 
[=F 
\\\r—m eeal\\\ p(Xu+ Yor Zw) dt. da 
% t=o 
_i f 2 Je 4). 
a\\\ eae +v* + w’) be ( 
2: we now take a closed volume 2 aiid W,T i 
pa ae values over time as well as over space, We § 
t= 
w-7-\(\\ p (Xu + Yu + Zw) do dt 
t=o 
* 307 “(| oo + ¥,0+Zqw) a dt (5). 
e/ 
Since if 7 be sufficiently cas the function Sw +0 +i) 
will have the same value at the beginning ihe end of . 
process if the motion be vibratory, for then 7 will conta 
large number of periods. 
_ 3 The analogy of. theorem (5) to Clausius’s Nie 
Theorem is quite evident. Accord ding to the virial thee 
we have 
—T=}335 2X +y¥ +22, 
where T = kinetic ber of particles 
cnt voluine, energy of the number ol pa 
within 
* es Al. 
' Vide Jeans’ Dynamical Theory of Gases, Second Edition, page | 
