90 The Rev. J. Challis on Capillary Attraction 
ments have not succeeded in establishing even the existence 
of such a variation. 
The object of the following remarks is to show, in the first 
place, that capillary phenomena will be little affected by the 
superficial variation of density, when the molecular attraction 
is feeble compared to the repulsion, and the sphere of attrac- 
tive activity great compared to that of the repulsive activity ; 
and then to give a reason for supposing the molecular forces 
of fluids to be of this nature, by showing that such an hypo- 
thesis will account for their fluzdity. 
The constitution of fluids is here assumed to be molecular, 
and the molecules are conceived to be held in places of equi- 
librium by attractive and repulsive forces, which near the 
boundaries of the fluids necessarily produce a variation of com- 
pression. The condition of equilibrium of the molecules at 
the free surface requires the extent of action of the attractive 
force to be greater than that of the repulsive, while experience 
shows that the sphere of molecular activity is of insensible 
magnitude. With respect to any point at a sensible distance 
from the surface, if we conceive a plane to pass through it, 
the resultant of the repulsions it is subject to from the action 
of the particles on one side of the plane will be perpendicular 
to the plane, and equal and opposite to the resultant from the 
action of the particles on the other side. The same may be 
said of the attractions. But the attractive resultant may be 
very different from the repulsive resultant. The ratio of the 
two may be taken as the measure of the proportion of the 
attractive to the repulsive action of the fluid. Let us now 
assume the attractive action to be very feeble compared to the 
repulsive, but to have a much larger sphere of activity, and 
consider what will result from this hypothesis. 
Conceive m an to represent the projection of the plane 
surface of the fluid on the plane of the paper; abcd, a 
normal to the surface; a b, the radius of the sphere of re- 
pulsive activity, and } d the same for the attractive force. 
Let the spherical surface afc e be described with centre 
6 and radius 6 a; and m d n, a portion of a spherical surface, 
with centre 6 and radius bd. The former surface includes 
all the atoms which exert a sensible repulsive force on an atom 
at b, and the space between this surface and the latter in- 
cludes all the atoms whose attractions are sensible at the 
same point. The resultants both of the attractive and re- 
pulsive forces on 6 will be in the normal acd. The attrac- 
tive resultant is the excess of the action of hdkecf above 
that of mafh and »aek, and takes effect in the direction 
bc. The repulsive resultant is the excess of the action of the 
