Mr. W. J. M. Rankine on the Mechanical Action of Heat. 117 



(15.) Besides the conditions of constant volume and constant 

 pressure^ there is a third condition in which it is of importance 

 to know the apparent specific heat of an elastic fluid, namely, 

 the condition of vapour at saturation, or in contact with its 

 liquid. 



The apparent specific heat of a vapour at saturation is the 

 quantity of heat which unity of weight of that vapour receives 

 or gives out, while its tempei'ature is increased by one degree, 

 its volume being at the same time compressed so as to bring it 

 to the maximum pressure corresponding to the increased tem- 

 perature. 



It has been 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. Such is, indeed, 

 the case according to the theory of Caruot ; 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. 



I shall for the present consider such vapours only as may be 

 treated in practice as perfect gases, so as to make the first of the 

 equations (20) applicable. 



It has been shown that the logarithm of the maximum elas- 

 ticity of a vapour in contact with its hquid may be represented 

 by the expression 



logP = «-^-4- 



The coefficients a, /S, 7 being those adapted for calculating 



the common logarithm of the pressure, I shall use the accented 



letters a', /3', <^ to denote those suited to calculate the hyperbolic 



logarithm, beins: equal respectively to the former coefficients 



X 2-3025851. 



Then for vapoui' at saturation, 



-=^:.?i... .... ,0, 



Making this substitution in the general equation (21), we find 

 the following value for the apparent specific heat of perfectly 

 gaseous vapour at saturation : — 



K,=..P-=.(,.N.X-)T 



=4l.N(l-lf)} ^. . (30, 



"CnMVN"^ T tV' 

 (16.) For the vapours of which the properties are known, the 



