ox THE ADIABATIC RELATIONS OF ETHYL OXIDE. 
187 
then 
h'jh - C6 = f/t//. 
Substituting for “^7 write this 
l/jh -Cb= ~ g/bv, 
so that 
g = Cb'^v — b'v. 
As long as there is no assumption made about the connection between g and b, 
this equation simply gives g in terms of b. The adiabatics we have drawn, however, 
were the result of further assuming that gjb is equal to a constant; and if this 
condition is introduced, we find that the form of b is restricted. Let us denote 
by y, the constant value of gjb, theu 
b'jb^ + gjbH = C, or 5762 + yjbv = C. 
Put 1/6 = u, and we have 
(lujdv — yujx' = ~ C. 
This equation is easily integrated, and we obtain 
so that 
V + ev^ 
where E, and e are constants at our disposal. 
If we confine ourselves to volumes which lie between 70 and 4, the values of 6 may 
be roughly reproduced by means of the above formula, taking care to give suitable 
values to R and e. But if, in such a formula, we were to attempt to extrapolate to 
large volumes, the result would be that we should obtain values of 6 totally at 
variance with experiment. This shows us once more the need of restricting our 
formulae entirely to those portions of the field that have been experimentally 
investigated. 
Appendix. 
Experiments with Liquid Ether. 
In experimenting with liquid ether, the apparatus and method of working were 
similar in every respect to what has already been described. 
The volume of 1 grm. of the ether was, as before, not directly determined, but was 
2 B 2 
