Theory of Surface Forces. 423 
Now we have (see above) for every point of the capillary 
layer : 
1 /dV\ 2 
Hence , ,, , dp Y ~ 
Pi > P^ anc * * nus always ~~ > U. 
For a capillary layer, which limits a bubble of vapour, the 
hydrostatic pressure p± increases therefore continually in the 
direction : liquid-vapour. The value pi of p x in the homo- 
geneous phase of the liquid is presented in fig. (4) by the 
ordinate of the point A, and the value p v in the homogeneous 
phase of the vapour by 'the ordinate of the point C. If 
PB is the tangent at a point B of the curve ABC, we have 
PW = BWcota = (p 1 - i?2 ; : d p =1R. 
' dk 
Fig 4. 
Aocis 
In the same manner, as I have demonstrated for a plane 
capillary layer *, we may prove that the curve, which represents 
the potential V of the attractive forces between the volume- 
elements as a function of h, has only one point of inflexion, 
or that -— - has only one maximum value. Because -yr 
. 1 /dV\* . dh 
is proportionate to =p(-?r- ) {see equation (15)}, the curve, 
which presents p Y as a function of h, must therefore have 
likewise a point of inflexion and the p 1 — /i-curve has thus 
a form as the curve ABC in fig. 4, The equation (15) 
may be written : 
d Pl _ 1 /^V\ 2 2dh 
dv ~~ 4:7rf\dh J 'Rdv' 
* Phil. Mag-. Oct. 1907, p. 517. 
