Theory of Surface Forces. 129 
h of a plane capillary layer may be expressed by 
7 3H 
where H is the ordinary constant of Laplace, and p L the 
pressure of the vapour. I£ we accept the equation of state 
of van der Waals for the homogeneous phase, we have for 
this temperature * 
while the proportion between the specific volume v 2 of the 
vapour and that of the liquid is about 19. Hence (see 
equation (19)): 
„ . 19 2H' 19 2H' 4H' f99 , 
Ja.. = circa -^ . - = TT! .TTT" = o tt"". • (22) 
18 p Y 18 oH 3 H v J 
2h 
Xow the radius of the bubble of vapour must be at least 
the average distance between two molecules, and because 
this distance has in the vapour a value of the order of the 
radius of the sphere of action, the cohesion of the vapour 
being practically null, we see that in the formula (22) the 
minimum value of Rr is of the same order as h, and H' must 
therefore be also of the same order of greatness as H, then 
h, the thickness of the capillary layer, is of the order of the 
sphere of action. 
The curve A r3 6 corresponds to the other limit. The 
radius of the corresponding spherical drop of liquid is given 
bv the formula: 
R = Vl + Vl " 2R " (231 
W denotes the departure from the law of Pascal, i\ and 
u 2 are respectively the abscissa of H and K in fig. 1, and 
Vj" and t: 2 " the abscissa of A 6 and P. If the radius of the 
spherical drop of liquid has a measurable value we have : 
H"=H. 
Every point of the part PK (fig. 7) of the theoretical 
isotherm we have thus brought in connexion with a spherical 
drop of liquid. If C 5 is the considered point, the ordinate 
and the abscissa of this point give respectively the pressure 
p v of the vapour which surrounds the drop and the recip- 
rocal value of the density of the vapour. The pressure pi of 
the liquid in the interior of the drop is given by the ordinate 
of A 5 , for which the thermodynamical potential has the same 
* J. D. van der Waals, Kontinuitat &c. p. 105 (1899). 
Phil. Mag. B. 6. Vol. 15. Xo. 88. April 1908. 2 G 
