and the Molecular Forces of Fluids. 91 
hemisphere fc e above that of the hemisphere fae, and is 
ad 
effective in the direction b a. “These two resultants must be 
equal. But as a é is small compared to 6 d, the attraction 
on 6 will differ little from the attraction on a. And as the 
latter must be just equal to the repulsion of the hemisphere 
ps, whose radius = a 6, it follows that this repulsion is 
very little greater than the difference of the repulsions of fc e 
and fae. That this may be the case, there must be a rapid 
variation of density at a, and at the same time, on account 
of the feebleness of the attractive resultant, a small variation 
at d. The repulsion on any particle will thus be chiefly 
owing to the action of the particles in its immediate neigh- 
bourhood, and be increased but little by the action of the 
more remote particles within the sphere of activity. The law 
of repulsion will be one of rapid diminution with the increase 
of distance from the repelling molecule; and the depth to 
which the superficial variation of density is considerable, will 
be less than the radius of the sphere of activity of the repul- 
sive force, and therefore much less than that for the attractive 
force. And if the variation of density is inconsiderable at 4, 
d fortiori it will be so at all points intermediate to 5 and d. 
When, therefore, it is required to investigate any effect due 
to the molecular attractions of fluids, the superficial variation 
of density may be neglected, if the suppositions on which the 
foregoing reasoning is founded be correct; and by treating 
the fluid as incompressible, the repulsive force will be taken 
account of with the same kind of approximation as when, in 
problems on the common theory of fluids, a change of pres- 
sure is supposed to be unaccompanied by a change of density. 
According to these views Laplace’s hypotheses suffice for a 
theory of capillary attraction, and any theory which, like that 
of M. Poisson, leaves the laws of the attractive and repulsive 
forces perfectly arbitrary, would seem to be not inconsistent 
with Laplace’s, but inclusive of it. 
N2 
