Theory of Surface Forces. 419 
and on substituting the value of: p in (10) we find by 
integrating, 
\ 2 f 2 l f dY\* u 
p 
'1 
If R denotes a value between the minimum and maximum 
values of the radii of the spheres, which limit the capillary 
layer, we may write 
r 
■-"-i-sKar)* • • • < 13 > 
Now we have for the cohesion respectively in the direction 
of the lines of force and perpendicular to this direction* : 
a" X (f dY \ 2 V2 1 
When further ^ and jo 2 denote respectively the hydrostatic 
pressures in the same directions we have also f : 
S 2 — S, = pi— p 2 - 
Hence : 
1 /dVV 
The total departure from the law of Pascal being the 
surface-tension H o£ Laplace, we have thus : 
H== 4^J 1 (ar) <tt= 5iJ I l3ir) <a ' 
and equation (13) becomes 
Pv—Pl=-JJT. ( 13 «) 
By the aid of (12) we can write therefore the equations of 
Lord Kelvin in the form : 
Vi+f/ 2H \ 
*■-* i> 2 W-(*iW)' R | 
and ' * ' * ( U ) 
t> 2 + < 2H 
^ _i?1 W2+% '-( Wl + V) ■ R / 
* Phil. Mag. Dec. 1906, p. 564. 
t Phil. Mag. Dec. 1906, p. 564. The hydrostatic pressure p 1 is therefore 
in the direction of the radius of the capillary layer. 
