Theory of Heat to the Study of Volatile Liquids. 479 



We can thus calculate, by means of the numbers and Tables 

 furnished by M. Regnault, two essential elements of the pro- 

 blem : — (1) the heat absorbed in A by the volatilization of the 

 liquid, minus the heat restored by the return of the liquid 

 from the temperature t' to t° ; (2) the work expended, by the 

 action of the pump B, to obtain the compression of the vapour 

 from the pressure P to P' 20 . 



Each of these two equations is completely independent of 

 the other ; and one of them gives a quantity of calories, the 

 other a quantity of kilogrammetres. 



The problem has not hitherto been stated in this form ; and 

 yet it is the natural method for arriving at the discovery of 

 the connexion that may exist between the quantities which 

 have been supposed to be entirely independent and without 

 any intimate relation between them. 



For the calculations we will adopt the following symbols : — 

 t° } temperature of the refrigerant A ; t f , temperature of the 

 condenser C ; -%%-£, the coefficient of dilatation of the gases ; 

 P, the maximum tension of the vapours at t° ; P / , the maxi- 

 mum tension of the vapours at t r ; T, the work done by the 

 pump B ; c, the specific heat of the liquid ; S, density of the 

 vapour at 0°, referred to that of the air ; 1*293 kilog., weight 

 of a cubic metre of air ; 10333 kilog. = atmospheric pressure 

 on a square metre ; X, the latent heat of the liquid at t°. 



We will suppose that the laws of Mariotte and Gay-Lussac 

 apply rigorously, which is not strictly correct for ail vapours. 

 We make the calculation for 1 kilog. of liquid. 



1st. The work T. 

 The work is produced by the compression of the vapour at 

 t° when it is made to pass from the pressure P to the pressure 

 P'. By calculation we find for T : — 



10333 (274 + O ^ (f) n\ 



T kilogrammetres = - - * * * \ A v 



1-293 8x274 



The expression M p ) represents the Napierian logarithm of 



the quotient of the pressures ; it is introduced into this for- 

 mula by integrating the work between the limits P and P'. 



2nd. The heat absorbed in the refrigerant A. 

 For 1 kilogramme of liquid, we have 



\ — c (f — t) = heat absorbed in A, in calories. . . (II.) 

 Note that these two equations have not one letter in com- 

 mon; they represent two totally different orders of facts. 



