488 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
If a be the density of the liquid 
we have also 
v = 
N — £ 
pQ = £; 
hence the value of L for the solid and liquid equals 
f (A0 + R0 log + (N - f) cfi + 0 %dv - th - (N - () «v 
Let us suppose that the mass of the vapour is increased by S£; then, since L is 
stationary, 
ctL ^ 
si = 0 ’ 
the temperature remaining constant. Hence we have 
he + -&e\og^--Re+i;Ke l -j]!-c i e-\f e -w l + th = (,. . (ie) 
When the mass of the vapour increases by S£, the mass of the liquid diminishes by 
the same amount, so that the volume of the liquid diminishes by S|/cr, and therefore, 
since the liquid and vapour are supposed to be contained in a vessel of constant 
volume, the volume of the liquid increases by the same amount, so that 
dQ_ 1 
d£ a 
and equation (16) becomes 
Ae + neiog^-ue^i-^j-c.d-^e^-w. + w^o; . . ( 17 ) 
or if, for brevity, we write 
s —_j _, 
R <r dd ' R R 
p = p 0 ^ e -P/<r e ^-WEfl ; .(18) 
or, since p/cr is very small, we have approximately, writing p 0 ' for p 0 e ? , 
p = p 0 ' 
(19) 
[The quantity most closely related to w 1 — w. 2 is the latent heat of evaporation, but 
the two quantities are not necessarily identical, for — w 2 is the excess of the 
intrinsic potential energy of unit mass of the vapour over that of unit mass of the 
liquid at the same temperature. The latent heat, however, at this temperature is 
