Theory of Surface-Forces. 421 
This theorem may also be demonstrated without the aid of 
a special potential function in the following manner : — 
We divide the capillary layer (that may be limited by a 
arbitrary surface) into volume -elements by a system of 
orthogonal surfaces, of which one is presented by a surface 
of equal density. Every element, such as ABCD A'B'O'D' 
7A. 
must be in equilibrium under the action of the hydrostatic 
pressures round about this element*. Let R x and E 2 
denote respectively the radii of curvature of the elements AB 
and BO of the lines of curvature on a surface of equal density, 
while a. and /3 be the angles AMB and BXC. Further, we 
indicate the hydrostatic pressures respectively in a direction 
perpendicular to the surfaces of equal densities and parallel 
to these surfaces by p x and p 2 , while the differential A A' of 
the normal MA is denoted by dli. The pressures on the faces 
BCC'B' and ADD'A' are thus ^ x surface BCC'B' =^ 2 £R 2 dA 
and the pressures on the faces ABB 'A' and DCC'D': p ? aR t dh. 
The components of these hydrostatic pressures in the direction 
of the normal through the middle of ABCD are thus : 
p 2 /3B. 2 dh sin \ol and p 2 aB. 1 dh sin ^/3. 
For the pressures on the elements of surface ABCD and 
A'B'CD', we have 
pycflL^ . /3R 2 and U + & dh ) u(R, + dh) . /3(B 3 + dh) . 
* Gravitation is not considered. 
