and the Molecular Forces of Fluids. 93 
the fluid incompressible, we may employ the common equa- 
tion of the equilibrium of fluids, viz. dp = e@(Xd2+Ydy 
+Z ds), in questions relating to capillarity. 1t is well known 
that this equation determines the resultant of the forces acting 
on any particle at the surface to be perpendicular to the sur- 
face. 
Let ANQ be the projection on the plane of the paper of 
a fluid surface near its contact with a plane solid surface, 
supposed to be projected into the straight and vertical line 
AB. Drawa tangent AT at A. The resultant of the forces 
acting on a particle at A will be 
perpendicular to AT. Conceive a 
plane perpendicular to the plane of 
the paper to pass through A, and 
to make an angle 6 with AB; and 
another plane, similarly situated, to 
make an angle +89 with the same 
line. Then 20 being indefinitely 
small, the attraction of the fluid 
between the planes on A will vary 
as0$. Let it = qg24, and let the 
angle TAB = ¢. The total at- 
traction of the fluid between the 
planes A T and AB on A, will in 
the vertical direction be fg d 4 cos 4 
[from 6 = 0 to 6 = ¢], or g sing; and in the horizontal di- 
rection, fgd 4 sin 6 [from 6 = 0 to § = ¢], or g (l— cos¢). 
The resultant of the solid’s attraction, which will be in the 
horizontal direction, will be found by putting gq! for g, and 
180° for ¢ in the last expression, and will consequently be 
2q'. The resultant of the attraction of the portion Q AT 
between the surface and the tangent plane will be nearly in 
the direction AT. Calling it £, and the force of gravity g, 
the whole attraction in AB =g+q sing+é cos ¢, and 
that in the horizontal direction = 2 q'—g (1—cos¢) —k sing. 
Since the resultant of these is perpendicular to A T, their 
ratio = tan ¢, from which equality we readily obtain 
(2q'~— 9) sing = gceoso+h. 
Now, for all fluids capable of hanging in drops of sensible 
thickness from the horizontal surface of the solid, 2¢q' is 
greater than q; and considering the small extent of activity of 
the molecular forces, both g' and g must be exceedingly 
greater than gravity. Also if ¢ be an angle of considerable 
magnitude, “ must be much smaller than the left side of the 
