Page:Reflections on the Motive Power of Heat.djvu/201

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 operation 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

$v=v'+{\frac {H}{k}}.$

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 abscissæ of the curve at the instants of the second and fourth operations respectively, when the temperature is t, we have

$x=v-\sigma v,\quad x'=v'-\sigma v',$

and, therefore, by the preceding equations,

$x={\frac {1-\sigma }{k}}\{H+c(S-t)W\},$

(a)

$x'={\frac {1-\sigma }{k}}c(S-t)W.$

(b)

These equations, along with

$y=y'=p,$

(c)