436 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, 
and, therefore, 
Log, H, = wal? dV — ~ log, V +f (7) + constant. 
J (7) is easily found to be =— log. + for a perfect gas, and being independent of 
the density, is the same for all substances in all conditions; Hence we find (the 
integrals being so taken that for a perfect gas they shall = O) 
Ne M dp 1 
= ea Saas zy) Se 
@ilog,H, M fd?p 1 
i) ae: Fi hala 
@log. H, Mdp 1 
dtdV htdt KV 


and, therefore, 
0 Q= (t-k) {or (sr + [7aev) +dv. Ph : . (25.) 
is the variation of latent heat, expressed in terms of the pressure, volume, and 
temperature ; to which if the variation of sensible heat, 6 Q=% 07, be added, the 
complete variation of heat, 6Q+0Q=6. Q, in unity of weight of the substance, 
corresponding to the variations 6 V and O7 of volume and temperature, will be 
ascertained. 
It is obvious that equation (25), with its consequences, is applicable to any 
mixture of atoms of ae ne substances in equilibrio of pressure and temperature ; 

for in that case r, oe and $ 772 are the same for each substance. We have only 
to substitute for 24 ai the following expression :— 

hy by hy My. y 
ny M, + 7, Moe 
where 7,, 7,, &c., are the proportions of the different ingredients in unity of weight 
of the mixture, so that n,+n,+&c.=1. 
Equation (25) agrees exactly with equation (6) in the first section of my 
original paper on the Theory of the Mechanical Action of Heat. It is the funda- 
mental equation of that theory; and I shall now proceed to deduce the more 
important consequences from it. 
(10.) Equivalence of Heat and Expansive Power. Jov.x’s Law.—From the 
variation of the heat communicated to the body, let us subtract the variation of 
the expansive power given out by it, or 
POV={p+s(V) } OV 
The result is the variation of the total power exercised upon or communicated to 
* This coefficient corresponds to — iz in the notation of my previous paper on the Mechanical 
K 
Action of Heat. 

