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

Rh 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,

These equations, along with