414 Mr. Rankine on the Hypuihetus of Molecular Vortices, 

 and therefore 



3Q'=(.-«){a..(-^./g.v).av.|}.(.5) 



is the variation of latent heat, expressed in terms of the pressure, 

 volume, and temperature; to which, if the variation of sensible 

 heat, 8Q = h^T, be added, the complete variation of heat, SQ + 

 gQ' = 8 . Q, in unity of weight of the substance, corresponding 

 to the variations 8V and St of volume and temperature, will be 

 ascertained. 



The only spccitic coefficient in the above formula has the fol- 

 lowing value : — 



^=Nfe« (25 A) 



It is obvious that equation (25), with its consequences, is 

 applicable to any mixture of atoms of different substances in 



. dp 



equilibrio of pressure and temperature ; for m that case t, -t-, 



and -r^ are the same for each substance. We have onlv to sub- 



stitute for -^ the following expression, — 



n,^+«2^ + &c.=«.2(nNfe), . . (25 B) 



where Uy, n^, &c. are the proportions of the diflPerent ingredients 

 in unity of weight of the mixture, so that ny + 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 fundamental equation of that theory, 

 and I shall now proceed to deduce the more important conse- 

 quences from it. 



(10.) Equivalence of Heat and Expansive Poiver. Joule's 

 Law. — From the variation of the heat communicated to the body, 

 let lis subtract the variation of the expansive power given out by 

 it, or 



PSV={;;+/(V)}SV. 



The result is the variation of the total power exercised upon, or 

 communicated to, unity of weight of the substance, supposing 

 that there is no chemical, electrical, magnetic, or other action 

 except heat and pressure ; and its value is 



8>F = 8Q+SQ'-PSV=8T.{fe + ^(i-^,)+(T-«/^^v} 



+ 8V.{(T-«)| -;;-/(¥)} (26) 



This expression is obviously an exact differential, and its in-. 



