MOSSOTTI ON CAPILLARY PHENOMENA. 573 
liquid, and for planes of the same substance, the depressions or 
elevations a will be approximately in the inverse ratio of the 
distances between the planes. 
9. Equation («.) is one of those which mathematicians call an 
equation at the limit, and holds for the circumference of the free 
surface. To obtain the equation corresponding to any point of 
that surface, let us consider the equilibrium of a small cylindrical 
fluid column, which from the external surface proceeds to a 
greater depth than the two planes, then bends and rises verti- 
‘cally between the two planes at a sensible distance from them 
“_ figs. 3 and 4). As soon as it is near the surface suppose 
Fig. 3 
‘the column turns so as to terminate at the surface normally to 
it. The pressure on the external surface being supposed zero, 
the described column will not be subjected to any pressure at 
its extremity in this plane surface. The action of the molecules 
of the internal fluid which forms the channel in which the column 
is enclosed will also be zero till it comes within the neighbour- 
hood of the internal surface, since if we suppose this channel 
divided into so many rings, each ring will exercise two equal 
opposite forces on the mass of the fluid column. Thus, if we 
omit the consideration of the action at the free surface within the 
planes, the fluid column suffers only the hydrostatic pressure 
arising from gravity; and if we call z the difference in level 
between the internal and external extremity of the fluid column, 
8 the area of a section, A its density, the column will be urged 
by a force g A sz upwards or downwards, according as the 
height of the liquid outside is greater or less than that of the 
liquid between the planes. Now we have seen that the attrac- 
tion of the molecules in the free surface within the planes, com- 
