172 MR W. J. M. RANKINE ON THE 
equal to that consumed during the evaporation; for as the sum of the expansive 
and compressive powers, and of those dependent on molecular arrangement during 
the whole process, is equal to zero, so must the sum of the quantities of heat 
absorbed and evolved. 
The heat of liquefaction, at a given temperature, is therefore equal to that 
of evaporation, with the sign reversed. 
(18.) If to the latent heat of evaporation at a given temperature, is added the 
quantity of heat necessary to raise unity of weight of the liquid from a certain 
fixed temperature (usually that of melting ice) to the temperature at which the 
evaporation takes place, the result is called the total heat of evaporation from the 
fixed temperature chosen. 
According to the theory of Carnot, this quantity is called the constituent 
heat of vapour ; and it is conceived, that if liquid at the temperature of melting 
ice be raised to any temperature and evaporated, and finally brought in the state 
of vapour to a certain given temperature, the whole heat expended will be equal 
to the constituent heat corresponding to that given temperature, and will be the 
same, whatsoever may have been the intermediate changes of volume, or the tem- 
perature of actual evaporation. 
According to the mechanical theory of heat, on the other hand, the quantity 
of heat expended must vary with the intermediate circumstances ; for otherwise 
no power could be gained by the alternate evaporation and liquefaction of a fluid 
at different temperatures. 
(19.) The law of the latent and total heat of evaporation is immediately 
deducible from the principle of the constancy of the total vs viva in the two forms 
of heat and expansive power, when the body has returned to its primitive density 
and temperature, as already laid down in Article 7. 
That principle, when applied to evaporation and liquefaction, may be stated 
as follows :— 
Let a portion of fiuid in the liquid state be raised from a certain temperature 
to a higher temperature : let it be evaporated at the higher temperature: let the 
vapour then be allowed to expand, being maintained always at the temperature 
of saturation for its density, until it is restored to the original temperature, at 
which temperature let it be liquefied :—then the excess of the heat absorbed by the 
fluid above the heat given out, will be equal to the expansive power generated. 
To represent those operations algebraically,—let the lower absolute tempe- 
rature be 7, :—the volume of unity of weight of liquid at that temperature, v,, and 
that of vapour at saturation, V,: let the pressure of that vapour be P,: the latent 
heat of evaporation of unity of weight, L,; and let the corresponding quantities 
for the higher absolute temperature 7,, be v,, V,, P,, L,. Let K, represent the 
mean apparent specific heat of the substance in the liquid form between the tem- 
peratures r, and r,. Then,— 
