4:12f Mr. Rankine on the Hypothesis of Molecular Vortices, 



^-^Cmpdxdydz. 

 The sum of such actions upon all the particles in unity of 

 weight is equal in amount, and opposite in sign, to the variation 

 of latent heat ; that is to say, 



8Q!=^jyy^pB(fidxdydz (23) 



To determine the value of the variation Scj), let it he divided 

 into two parts, thus : — 



where A0 = (^ — ^,. 



First. With respect to 8(p^, it is obvious, that because, accord- 

 ing to equations (6, 7), 



]\IV = /tMV f^\^^^ -^ d(b, 

 we must have 



8Y=kYB(}>, and Bc{>,= ^. 

 Hence the first part of the integral (23) is 



To determine the second part of the integral, we have the 

 condition, that the quantity of atomic atmosphere enclosed 

 within each surface at which A<p has some given value is inva- 

 riable j that is to say. 



1 





Hence 

 BA(f> 



kp.MYe"^^^ — 

 a), 



The value of the second part of the integral (23) is now found 

 to be 



