MOSSOTTI ON CAPILLARY PHAZNOMENA. 571 
-will acquire an intermediate degree of rarefaction, and will there- 
fore be endowed with an intermediate force of tension. If we 
‘call © the diminution in the force of tension, produced on the 
contiguous stratum of fluid by the action of the planes, T — © 
will be the expression for the force of tension of that stratum. 
At the point of junction of the free surface with the surface 
contiguous to the planes, the passage from one to the other will 
be along a curve of very great curvature. The resultant of the 
attractions on a small prism in the free surface will not be any 
longer normal to it, since this resultant will be influenced by the 
action of the planes, and the tension will pass rapidly from the 
value which it has at the free surface to that which it has along 
the planes. At a scarcely perceptible distance from the extre- 
mities of the arc of junction the forces will again act in a direc- 
tion normal to the surface, and the two tensions will be constant. 
Now since the resultant of the actions of the planes upon each 
molecule of the are of junction is clearly always perpendicular 
to those planes, and on the other hand the internal part of the 
fluid varies in density only so as to resist the actions which take 
place at its surface, we may compare the equilibrium of the arc 
of junction to that of a portion of catenary of variable density 
acted upon by gravity in a direction perpendicular to the planes, 
and we know that in this case the tension at the lowest point, 
Y and the part of the tension at the extremity of the curve resolved 
; perpendicular to the direction of gravity, must be equal for equi- 
librium. The part of the tension at the free surface resolved 
vertically must therefore be equal to the tension at the stratum 
contiguous to the planes; and if we call the angle between the 
planes and the tangent to the free surface at the upper extremity 
of the arc of junction, we shall have for our first equation 
Poa T sy Oasoxia woven) 
Now T — © being constant for the same liquid and for planes 
of the same substance, » must also be constant, whatever be the 
free surface of the fluid. 
A force of contraction equal to T — © will act also on the other 
side contiguous to the other plane, and the free surface will be 
drawn down by these tensions until the hydrostatic pressure 
arising from the weight of the fluid at a higher level externally 
be such as to counteract them. 
If we call P the weight of fluid that would fill the space be- 
tween the planes up to a level with the external fluid, that is the 
