574 MOSSOTTI ON CAPILLARY PHA NOMENA. 
bined with its curvature, gives rise to a force which urges thé 
portion of the fluid column normal! to the said surface inwards 
or outwards, according as the surface is convex or concave. This 
force is measured at every point by ” @ being the radius of 
curvature. For the equilibrium of the column then we must have 
the equation 
gAsz+t+ 2 = 0. 
The ordinate z being reckoned positive, when measured upwards 
from the external level, we must take ¢ positive or negative, ac- 
cording as the free surface is concave or convex. 
The considerations which have led us to this equation do not 
depend on the supposition that the surface is cylindrical: if they 
extend therefore to the more general case of any surface what- 
ever, keeping in mind that then the force perpendicular to the 
internal surface, which acts on the portion of the fluid column 
normal to it, is measured by the tension multiplied by the sum 
of the inverse radii of curvature of two sections perpendicular to 
each other, we shall have, calling g! the second radius of curvature, 
1 1 
Asz=s.T(245 3 
- bien t 
2 
If we put =A = = t being a constant quantity for every fluid, 
the above equation may be put under the simpler form, 
2=5($ +3): bade 
The two formule («.) and (8.), of which the former refers to the 
circumference, the latter to any point of the free surface, form 
the basis of the whole theory of capillary action. The applica- 
tion of these equations to the various cases requires only some. 
processes of integral calculus, of no great difficulty to any one 
who has acquired practice in it. As we do not wish to do more 
than set forth the mechanical principles on which the theory 
is founded, and give a precise idea of the manner in which 
capillary phenomena are produced, we shail only add (note 2, 
p- 576) the formule which Poisson has deduced for some prin 
cipal cases in his Théorie de ?_ Action Capillaire, in order that th 
reader may find them ready should he wish to apply them. 
