304 
PHYSICS: A. G. WEBSTER 
Proc. N. a. 
From the second law of thermodynamics, introducing the integrating 
factor 1/T and the entropy 5, we have 
T dx dy T dx T dy 
from which we get in a similar manner : 
dC^bT _bCybT ^ ^ ^ (C, - Cy) dT c)7 
By a combination of these two equations we get 
(C, -Cy) — ~ 
bx by b{x,y) 
which is equation (3) of my paper quoted above. 
These are all the equations that we can get from the laws of thermody- 
namics and since any function has two partial derivatives for and Cyy 
there will be four, which to be sure are connected by two equations. It 
is, I think, obvious that two equations are not sufficient. At any rate, 
let us proceed to an examination of the equation of state suggested by M. 
LeChatelier. If we have: 
X = p, y = V, T = pjiv) = xfiy), 
we at once obtain 
OX oy oxoy 
And accordingly in the equation of the first law we have 
^f'iy) -/W^ + (C, - Cy)f'{y) = 1. (3) 
OX oy 
and in the equation of the second law 
xf{y) ^ - fiy) ^ + {C,- C,)f{y) = (C, - Q/'M. (4) 
OX oy 
We accordingly obtain the relations between the two specific heats : 
xfiy) ^ - Ay) ^-^ = 0, (5) 
OX oy 
C,- Cy = — . (6) 
From (6) we get 
Substituting this value in equation (5) we obtain 
(>y ay p 
