VARIATION OF MOLECULAR SURFACE-ENERGY WITH TEMPERATURE. 657 
5. Complete Equation expre-'ising the relation hetiveen Molecular Surface-energy and 
TempeixUure. 
All the previous woi’k has been on the assumption that the rectilinear equation of 
yyi ~ k{t — d) holds for the substances examined. But it was mentioned on p. 651 
that near the critical point this simple relation no longer holds. There can be little 
doubt that as the liquid reaches a higher and higher temperature its surface is 
exposed to a more vigorous bombardment from the gaseous molecules. The molecular 
volume, and therefore the molecular surface, is rapidly increasing near the critical 
point; and the surface-tension, as well as the surface-energy, decreases less rapidly as 
the critical point is approached than at lower temperatures. The force required to" 
extend a surface is less decreased by unit rise of temperature at high than at low 
temperatures. Here we have no analogy to guide us, for gases have never been 
investigated where p approximates to zero, the volume of one gramme being kept 
constant, or in other words, we know nothing of the behaviour of gases near the 
absolute zero of temperature. 
It is, moreover, possible that the distribution of molecules on the surface of a liquid 
at high temperatures is different from that in its interior ; and as we have no clear 
idea of the condition of matters at the surface of a liquid, we can form no theory 
which would conduct us to a reasonable, and not'' empirical form of equation. 
It was necessary, therefore, to seek for some expression which would represent this 
deviation as a function either of molecular surface or of temperature, and Mr. Bose- 
Innes has kindly assisted us in this. The expression 
y (Mv)^ = KT — fcd {1 — ] 0”^^) 
reproduces the results with considerable accuracy. At high temperatures, i.e., where 
T is small, the correction becomes of importance ; and at temperatures lower than 
the critical temperature by 25° or 30°, the correction becomes insignificant. The 
results near the critical temperature are reproduced for ethyl oxide, methyl formate, 
ethyl acetate, and benzene in the following table :— 
4 V 
MDCCCXCIII.—A. 
