288 PHYSICS: A. G. WEBSTER 
In order to obtain the expression for the energy for such a gas, we make use 
of the equation 
u = j^i^T^-pyv + c^rj, (9) 
in which we have now to put 
bp ^ bjp, v) I b{T, v) 
bT b(x,y)/ b{x,y) 
We have now to make use of equations (6) in which, replacing the usual, 
thermal notation, and now using x and y for the arbitrary parameters, 
T = To=^2x V - To<p'iy) - x'<p'(y), 
p = <p(y) - x<p'{y), (10) 
7) = x-\-y, 
bx oy bx by 
^ = ± 2 V- T,<p'{y) - 2 xAy), 
bx 
by ^ (p\y) 
so that finally 
..p . X ( -2<pCy)+x<p'\y) ^ 
\\(To=^2x V- To^\y) - xWy) ) \ , — / \ 
^ (p \.y) ^ 
(11) 
X 
(bv , , . 1 , ^ ^bT , , bT , 
J dx-{- — dy>-\-CA —dx-{- — - dy 
(.ox dy ) (.ox by 
I have also integrated the equation for the case that the difference of the 
specific heats is a linear function of the temperature, but this seems not neces- 
sary in the light of present experimental data. 
