166 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
That this quantity is almost always positive appears from the following consider- 
ations. The latent heat of evaporation L is in general capable of being represented 
approximately by an expression of this form : 
L — a — b(r—x) (74.) 
(For water, a = 7 96° Centigr. X K w = 1,106,122 ft. lb.; & = 0‘695 X K w = 965*772 ft. lb. 
per Centigrade degree.) 
Hence the second factor in equation (73.) is nearly equal to 
Now 
ai S\~ T q) 17 1 , ‘I - 
( Tl -.,.(T S -*r Ki - hy p- los ^ 
T, —X 
X* 
(75.) 
hyp. log 
T,— X T T, 
Therefore the expression (75.) is positive so long as 
exceeds K L , the specific heat of the liquid. . . . (75 a.) 
For Water, this condition is fulfilled for all temperatures lower than 523^° Centi- 
grade (at which t 1 —k= 7 96° Centigrade) ; and there is reason to believe that it is 
fulfilled also for other fluids at those temperatures at which their vapours can be 
used for any practical purpose. 
To determine the proportion of the fluid which is liquefied by a given expansion 
under pressure, we have the following formula, deduced from equation (58.) : — 
n= 
tV-Vc 
v'i—v 
(76.) 
As a numerical example, we may take the case of art. (44.), where saturated steam 
at 140° Centigrade is supposed to be expanded under pressure until its temperature 
falls to 40° Centigrade. The volume of one pound of water and steam at the end of 
the expansion has already been found to be 
V c =258‘l cubic feet. 
While, according to the table in article (38.), the volume of a pound of steam at that 
temperature is 
«4=313’56 cubic feet. 
Consequently the fraction liquefied by the expansion is 
313 - 56 - 258-1 55'46 
n ~ 313 - 56 - 0 - 016 - 313 - 544 - 0 1 
This conclusion was arrived at contemporaneously and independently, by M. 
Clausius and myself, about four years since. Its accuracy was subsequently called 
in question, chiefly on the ground of experiments, which show that, steam, after being 
expanded by being “ wire-drawn,” that is to say, by being allowed to escape through 
a narrow orifice, is' super-heated, or at a higher temperature than that of liquefaction 
at the reduced pressure. Soon afterwards, however, Professor William Thomson 
