MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
157 
vapour corresponding 1 to the absolute temperature r ; and, unity of weight being the 
quantity of the aggregate under consideration, let v be the volume corresponding to 
complete liquefaction, v' that corresponding to complete evaporation, and V the actual 
volume at any time; let n be the proportion of liquid, and 1— n that of vapour, cor- 
responding to the aggregate volume V ; then 
V — nv -f- ( 1 — n)v' (58.) 
and V may have any value not less than v nor greater than v' , while P and r remain 
constant; the proportion of liquid, n, being regulated according to the foregoing 
equation. 
(37-) Proposition XVI. — Problem. The density of a liquid and of its vapour, when 
in contact at a given temperature, being given, and the isothermal lines of the aggregate ; 
it is required to determine the latent heat of evaporation of unity of weight of the fluid. 
(Solution.) The densities of the liquid and of its vapour, are respectively the re- 
ciprocals of the volumes of total liquefaction and total evaporation of unity of weight, 
above-mentioned. In fig. 20, let the abscissae Ov, Ov' represent these volumes, and 
the equal ordinates, vA, v'B, the pressure corresponding to the given temperature; 
Fig. 20. 
so that AB parallel to OX is the isothermal line of the aggregate for that tempera- 
ture. Suppose two curves of no transmission, AM, BN, to be drawn from A and B 
respectively, and indefinitely prolonged towards X ; then the indefinitely-prolonged 
area MABN represents the mechanical equivalent of the latent heat sought ; and 
this area is to be computed in the following manner. Draw a second isothermal 
line ab indefinitely near to AB, at an interval corresponding to the indefinitely-smali 
difference of temperature dr ; then, ultimately, 
dr : t—k : : area AB ba : area MABN ; 
or. symbolically, 
dP 
L=latent heat of evaporation = (r— k) (y' — v). 
(59.) 
This is simply the application of Propositions I. and II. to the aggregateof a liquid 
and its vapour, mutatis mutandis. 
