422 Dr. G. Bakker on the 
When we substitute |a for sin \a. and \$ for sin ^/3, the 
equation of equilibrium may be written : 
i/3R 2 p 2 dh + uj3U lP2 dh= (p L + ^ dh ^a(Rj + dh)/3(R 2 + dh) -p^/SR^ 
Neglecting the infinitely small of higher order and omitting 
the common factors dh, a and ft, we find : 
p 2 U 2 +p 2 R 1 =p 1 R l +PiR 2 - Jj^ RiR 2 ■ • 
or 
~3?-Cft-A)(i + i). • • (16.) 
For a capillary layer which has the form of a spherical 
shell, we have thus : 
dh ~ U ' ^ U) 
If we consider the positive in the direction : liquid-vapour, 
equation (17) corresponds to a spherical drop of liquid, sur- 
rounded by vapour ; for, in fig. 3, we have considered dh 
positive in a direction opposite to the direction of the radius 
of curvature. The equation (16 a) may be expressed as the 
following general theorem : 
The gradient of the hydrostatic pressure pj in a direction 
normal to the surfaces of equal density in a point of an arbitrary 
capillary layer is equal to the product of the departure from the 
law of Pascal and the curvature of the surface of equal 
density, that passes through the considered point. 
If the curvature is null and the capillary layer therefore 
plane, we have properly : 
dp 1 _ 2(p x —p 2 ) _ n 
dh ~ oo 
or p x = constant = pressure of the vapour. 
For a capillary layer, which limits a spherical bubble of 
vapour, we have already found : 
£-**?* o*> 
Integrating the equation (16), we find immediately the 
theorem of Lord Kelvin : 
2 f 2 2H 
p v -pi= g (Pi—P2)dh= --g-. 
