198 Dr. Rankine on the Expansion of Saturated Vapours. 



perature. It is usually taken for granted that this quantity is 

 the same with the variation for one degree of temperature of 

 what is called the total heat of evaporation. 



"..... but I shall show that, according to the mechanical 

 theory of heat, these two quantities are not only distinct, but 

 in general of contrary signs/ 3 



(Then follows the investigation of a formula for the apparent 

 specific heat at saturation of a vapour which in practice may be 

 treated as perfectly gaseous, viz. 



*..*{,+„(,-;.£)}, 



in which & is the specific heat at constant volume, Nfc the ex- 

 cess of the specific heat at constant pressure above the specific 

 heat at constant volume, t the absolute temperature, and P the 

 pressure. After the formula comes the following passage) : — 



" For the vapours of which the properties are known, the nega- 

 tive terms of this expression exceed the positive at all ordinary 

 temperatures . . . ." 



In the paper of 1854, the expression corresponding to that 



in the preceding formula is K L > where K L is the mechanical 



r 



equivalent of the specific heat of the liquid from which the va- 

 pour comes, and an approximate value of r -r- Iv -j- ) (v 



beins the excess of the bulkiness or volume of a unit of weight 

 of the vapour above that of the liquid). 



This second expression is applicable to all vapours whether 

 perfectly gaseous or not ; and by supposing the vapour to be 

 perfectly gaseous, it becomes identical with the first expression. 

 The value of r at which the sign of the expression changes is 



of course = r^- 



I may add that the corresponding formula of Professor Clau- 

 sius, first published in 1850, indicates just as clearly that for 

 each vapour there must be a temperature at which the sign of 

 the specific heat, when the vapour is maintained at saturation, 

 changes from negative to positive (Abhandlungen iiber die 

 mechanische IVarmetheorie, page 38). 



The originality and importance of M. Hirn^s discovery, that 

 for some fluids the temperature in question lies within the limits 

 of temperatures attainable in ordinary experiments, are of course 

 not affected by the preceding statement. 

 I am, Gentlemen, 



Your most obedient Servant, 



Glasgow, February 12, 1866. W. J. Macquorx Kaxkixe. 



