MOTIVE POWER OF HEAT. 177 



and t, and W the weight of the entire mass,, in 

 pounds, we have 



kv'=c(S-t)W. 



Again, the circumstances during the second oper- 

 ation are such that the mass of liquid and vapor 

 possesses H units .of heat more than during the 

 fourth; and consequently, at the instant of the 

 second operation, when the temperature is t, the 

 volume v of the vapor will exceed v' by an amount 

 of which the latent heat is H, so that we have 



* '='+? ' 



40. Now, at any instant, the volume between 

 the piston and its primitive position is less than 

 the actual volume of vapor by the volume of the 

 water evaporated. Hence, if x and x' denote the 

 abscissae of the curve at the instants of the second 

 and fourth operations respectively, when the tem- 

 perature is t, we have 



x = v (TV, x'= v' vv' , 

 and, therefore, by the preceding equations, 



. . (a) 

 .. (b) 



These equations, along with y = y' = p, . . (c) 



