ON THE ADIABATIC RELATIONS OF ETHYL OXIDE. 
185 
Let us assume that the equation to the isothermals of a gas can be written in the 
form 
/> = 6T — a, 
where h and a are functions of the volume onl 3 ^ Let us also assume that the equation 
for the adiabatic elasticity E can be put in the form 
E = pT - h, 
where g and h are functions of the volume only. Then, by eliminating T, and putting 
for E its value — ^that we have a linear differential equation for p of the 
first order, the independent variable being v. Idle integral of such an equation must 
be of the form 
p = 74 -j- y, 
where h is the constant of integration, while ip and y are functions of v only ; we see 
also that we must have i//'4 = — This equation determines a system of 
adiabatics by giving successively different values to I', and by taking two neighbouring- 
values, say k and h + dk, we obtain two adiabatics as near together as we please. Let 
Fio-. 6. 
now the pair of adiabatics be crossed by two isothermals at temperatures T and 
T -j- c7T, then the area of the infinitely small parallelogram formed must be inde¬ 
pendent of T by the Second Law- of Thermo-dynamics. 
Let ABCD in fig. 7 denote a magnified picture of this small parallelogram ; then. 
Fig. 7. 
b}- shearing the figure after the manner of Maxw-ell in obtaining his fourth thermo¬ 
dynamical relation {Joe. cit., p. 168), we obtain 
MDCCCXCVTI.—A. 2 B 
