146 
PROFESSOR HUGH L. CALLEXDAR ON 
calculates the densities and proportions of the two ingredients on the' assumption 
that each constituent follows the Mendeleeff law of expansion, or that the density 
is a linear function of the temperature. He thus finds that 1 gramme of water at 
0° C. consists of liquid 3HoO, density ’88, ’375 gramme ; liquid 2H. : 0, density 1‘09, 
’625 gramme. The latent heat of fusion of trihydrol, 16 calories, is calculated on 
the assumption that it would expand ’0366 on fusing, wdiich is the mean expansion 
on fusion deduced from a number of metals. The remainder of the latent heat of 
fusion of ice is supposed to be made up of the heat ot dissociation of ‘625 trihydrol 
into dihydrol, and the solution of the remaining fraction - 375 in the dihydrol. As 
a starting-point for the explanation of the variation of the specific heat, he assumes 
that the specific heat of dihydrol is l’OO at 200° C., at which temperature water 
contains ’167 of trihydrol. Taking “the usual rate of variation of the specific heat 
of a liquid as T per cent, per degree,” he finds - 83 for the specific heat of pure 
dihydrol at 0° C. He takes that of trihydrol to be '6 with a similar rate of increase, 
and explains the remainder of the specific heat of water as due to the heat of 
dissociation of trihydrol and of solution in dihydrol, which he calculates on the 
above assumed values of the specific heats. 
It is more natural to regard the high specific heat of water as due to internal work 
done against molecular forces, and as being closely related to the decrease of the 
latent heat of vaporization with rise of temperature. Whatever assumptions are 
made with regard to the molecular constitution of water, it was proved by Rankeste 
(in a slightly different form), in 1849, that the rate of decrease of the latent heat 
dhfdd was equal to the difference between the specific heat of water s K , and that of 
steam S* at constant pressure. 
dh/dd = S s — s K .(14). 
This is accurately and necessarily true if we assume that steam may be regarded 
as an ideal gas of constant specific heat, which is probably justifiable at low pressures. 
At higher pressures, it is necessary to make allowance for the co-aggregation of the 
steam molecules, which may be effected to a high degree of approximation by the 
method which I have explained (‘ Roy. Soc. Proc.,’ Nov., 1900). If we write h for 
the total heat of water from 0° C. (without assuming the specific heat to be constant), 
we obtain the relation, 
L - L 0 = S 0 (0 — 6» 0 ) - (n + 1) {cp - c 0 p 0 ) - h . . . . (15), 
where S 0 is the limiting value of S* at zero pressure, and c represents the defect of 
the actual volume of the steam from the ideal volume R 6/p. This defect of volume 
is independent of the pressure p, but varies inversely as the nth power of the 
absolute temperature 6. It is clear that the rate of diminution of the latent heat is 
