184 MR W. J. M. RANKINE ON THE 
To obtain the maximum eross effect, the steam must continue to act expan- 
sively until it reaches the pressure of condensation, so that P,=P,. The clear- 
ance must also be null, or c=0. Making those substitutions in the formula (47.), 
we find, for the maximum gross effect of unity of weight of water, evaporated 
under the pressure P, and liquefied under the pressure P,, 
1 (=) l-¢ 
1 a miedebry 
ie ( =e 2) ee) 
In order to calculate directly the heat which is converted into power in this 
operation, let r,, 7,, respectively represent the absolute temperatures of evapora- 
tion and liquefaction, and L, the latent heat of evaporation at the lower tempera- 
ture 7,; then the total heat of evaporation at 7,, starting from 7, as the fixed 
point, by Equation (33.), is 
H,, ,=L, +7305 Ky (7, —T,)- 
This is the heat communicated to the water in raising it from +, to 7, and evapo- 
rating it. Now a weight 1—m of the steam is liquefied during the expansion at 
temperatures varying from 7, to 7,, so that it may be looked upon as forming a 
mass of liquid water approximately at the mean temperature Ay and from 
which a quantity of heat, approximately represented by 
Ky (l—m) — 
must be abstracted, to reduce it to the primitive temperature r,. 
Finally, the weight of steam remaining, m, has to be liquefied at the tem- 
perature 7,, by the abstraction of the heat 
m Ly. 
The difference between the heat given to the water, and the heat abstracted 
from it, or 
H,, ,—Ky (1—m) 1572 ‘m Ly 
* (56.) 
2h Ke (305 -*5") @=4) 
is the heat which has disappeared, and ought to agree with the expression (55.) 
for the power produced, if the calculation has been conducted correctly. 
As a first example, I shall suppose unity of weight of water to be evaporated 
under the pressure of four atmospheres, and liquefied under that of half an atmo- 
sphere; so that the proper values of the coefficients and exponent are 
