Theory of Heat to the Steam-engine. 



255 



place. If the vessel has to be compressed, then the assumption 

 that at the commencement it contained no liquid could not be 

 made, because in such a case the vapour would not remain at a 

 maximum density, but would become over-heated by the heat 

 generated through compression. During expansion, however, 

 not only does the vapour remain at a maximum density, but a 

 part of it is actually condensed ; and it is the diminution of m 

 consequent thereon which is exhibited in the Table. The initial 



temperature is supposed to be 150^ C, and the values of ^ are 



given which correspond to the periods when, by expansion, the 



temperature is reduced to 125°, 100°, &c As before, in 



order to distinguish it from the absolute temperature T, the tem- 

 perature counted from the freezing-point is represented by t. 



16. In order to express the relation which exists between the 

 volume V and the temperature, we must employ the equa- 

 tion (6), i, e. 



v=:mu + Mo: 



The magnitude a herein involved, which represents the volume 

 of a unit of weight of liquid, changes very little with the tempe- 

 rature; and these small changes may be the more safely neglected, 

 because the whole value of <t is very small in comparison to u ; 

 we shall consequently consider o", as well as the product Mo-, as 

 constant. The product mu therefore alone remains to be deter- 

 mined. For this purpose we have only to substitute the value 

 of r, as given in equation (VI), in equation (VII), and we obtain 



mu 



dp ( dp\ Mc, T .^.^^,. 



dp 



The differential coefficient -~^ which here appears, is to be con- 

 sidered as known, p itself being given as a function of the tem- 

 perature. Hence the product mu is determined by this equation, 

 and by the addition of Mcr the required value of v will also result 

 from it. 



The same assumptions being made as before, the following 



Table shows a series of values of the fraction — calculated from 

 this equation. For the sake of comparison are also appended 



