DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
489 
the amount of work required to convert unit mass of liquid into vapour. If the 
kinetic energy of unit mass of the liquid is the same as that of unit mass of the gas 
at the same temperature, the latent heat will equal w 1 — w 2 , but if the kinetic 
energies are different, then, since the latent heat equals the difference between the 
sum of the kinetic and potential energies, it will not equal w 1 — wy]* 
In the above work we have assumed that the vapour obeys Boyle’s Law. If we 
assume that the relation between pressure, density and temperature is that given by 
van der Waals’ formula 
R# a 
P ~ v - b ~ v 2 ’ 
where v is the reciprocal of the density, and a and b constants, we may show, in a 
way similar to that by which we established equation (16), that, when the vapour is 
in equilibrium with the fluid, 
B 6 log 
+ a p 
110 
1 - bp 
dp 
dd 
— w x + Wo = 0 ; 
or, since p/cr is very small, we may write this equation as 
+ 2 ap —- R0 bp — L0 — (w x — w 2 ) = 0, 
( 20 ) 
neglecting b 2 , and writing L for a number of constant terms. 
§ 7. The method just given enables us to calculate readily the effect of slight 
changes in the physical conditions on the vapour-pressure. Let us take, first, the 
effect of surface-tension. If the shape of the liquid is such that the area of its free 
surface changes when any of it evaporates, then we must take into account the 
energy due to the surface-tension. Let us suppose that the liquid is a spherical drop, 
whose radius is a ; then we must add to the expression for the mean potential energy 
of the liquid the term 47ra 2 T, where T is the surface-tension of the liquid. In this 
case, using the same notation as before, and assuming Boyle’s Law, we have 
P(iQ\ 
dp 
L = I ( ke + B0 log ^=j + (N - ( ) J g dv — # Wl — (N — () w s — WT; 
and the equation got by making the value of L stationary for a small change in £ is 
A9 4- R0 log ^ - R<9 + R 0^-c x d--J - w x + - 877-aT ^ = 0 ; (21) 
MDCCCLXXX VII. —A. 
* Paragraph substituted October, 1887. 
3 R 
