Theory of Heat to the Study of Volatile Liquids. 481 



Of these two hypotheses, therefore, the first is based on a 

 deduction resting upon the similar physical state of liquids, the 

 second on the principle of equality of return. 



If the second hypothesis were not verified, we might com- 

 bine two reversible cycles, Carnot's and that supplied by a 

 volatile liquid ; the difference of the two would be represented 

 by the transformation of a certain quantity of surrounding 

 heat into mechanical work. In fact, Carnot's cycle proves 

 that, given a quantity of heat Q disposable at temperatures 

 t' and t, we can always transform into work a quantity 



Q= 2fer? oalories - 



In the cycle represented in our figure 1, we dispose in the 

 condenser of a quantity of heat of which the minimum is 



Q=\ at a temperature t! ; 



we can therefore always derive from it a motive force given 

 by the expression 



if-— t 

 T=A y , x 433" 5 mechanical heat-equivalents. 



If this quantity be greater than T derived from equation L, 

 we shall evidently have disposable work which will be ex- 

 pressed by the combination of the two cycles, or T / — T, and 

 which will be derived from surrounding sources of heat. 



Introducing our two hypotheses into equations I. and II., 

 re have the following relations : — 



Our equation II. may be represented by 



X— c(f— t) = Q, heat absorbed in A. 



If we calculate by means of Carnot's cycle the work which 

 nust be expended in order to derive a quantity of heat Q at 

 ;he temperature t and make it pass into t' , it is given by the 

 xpression 



deducing this equation, and denoting by E the mechanical 

 quivalent of the heat, we get 



97A-L/ =kilogrammetres required. 



We now equate this work obtained by Carnot's cycle with 

 hat which we found for the cycle of a volatile liquid, and 

 Phil. Mag. S. 5. Vol. 1. No. 6. June 1876. 2 K 



