Voiv. 6, 1920 
PHYSICS: A. G. WEBSTER 
305 
bc,_bc,^ r 
f dx dy 
a partial differential equation of the first order for C^, which is of the 
form 
bx by 
if we put, 
dy dy\f) 
This is immediately integrated by Lagrange's method, if we write 
dx _ dy _ dz dx _ ^ _ 
P ~ Q ~ R' ^ dlogf ~ ~ ^ ~ 
dy{f) 
dy 
We obtain two particular integrals, in which we are to put 
u ^ xf — T = const., V — = const., v = (p{u), 
where (p is an arbitrary function. We thus obtain finally 
C, = l/f'(v) + v(J), = viT) (9) 
and we find that neither of the specific heats is constant or independent 
of the pressure, nor is their difference constant, although it is independent 
of the pressure. Such a gas has no cohesion pressure, but does not in 
general have a zero Joule-Kelvin effect. If, on the contrary, we take a 
gas subject to the equation, 
T = vg(p) 
which has a zero Joule-Kelvin effect, we have a similar conclusion, inter- 
changing p and V. 
If, on the other hand, one of our variables is the absolute temperature, 
we are to write, 
dO = C,dT + L,dx (10) 
where is the latent heat for constant x. We then obtain from the first 
law 
bU ^ bv bU ^ bv 
■ — ^^x ~ P — > — ^x ~ P » 
bx bx bT bT 
bC, bL, b{p, v) 
and from the second, 
bx bT b{x, T) 
bS _ dS _ 
bx ~ y df~ Y 
bC. bL. L. 
(11) 
