SPECIFIC HEATS OF SOME COMPOUND GASES. 569 
draw the isothermal curve accurately. Hence the vapour-density determinations in 
some cases give a rather irregular curve, but when the divergences are so great as to 
leave much doubt how the curve should be drawn, I have made a separate determi- 
nation of the relative densities in the way described under ethyl chloride in my 
former paper. 
The column headed 8 in the tables below, gives the ratio of the rates of increase 
with rise of temperature of the internal energy of the molecule and its kinetic energy 
of translation. . 
The usual equation connecting 8 and y, viz., 
7 S@=m> 
is deduced on the assumption that the gas is perfect, for it neglects the change of 
potential energy due to separation of the molecules on expansion, and assumes that 
pv is proportional to ¢. 
For air and a few other gases this is a matter of no consequence, but when we come 
to vapours not far removed from saturation, it is necessary to use a better formula, or 
at least to find whether the error made by using the old one is serious compared with 
the experimental error. 
Since, to a first approximation, pv is equal to Rt, we may write the characteristic 
equation in the form 
(DO == I SG, DO) ns 2 es 6 eb 2 2 (N), 
where f is so small that its square and the squares of its differential coefficients can 
be neglected. 
Now we know from thermodynamics that 
GC, = ©, = t(dpldt)y (didi) is. kyu oh Le) 
and from equation (1) we get by differentiating at constant volume and pressure 
respectively 

a _ R+ dfldt 




dt},  v—df|dp 
du\ _R+df{dt 
Gi » p— afidv 
Hence 
Ce ¢ (Rh + df/dty 
y "(p= adfidv) (v = af dp) 
eRe il ay i ay 2 df 
~ po G+75¢+ v apt R ak 
MDCCCXCV.—A. 4D 
