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of Edinburgh, Session 1869 - 70 . 
great in comparison with their magnitudes, and that these particles 
attract each other,—the sphere, however, of their attraction extend¬ 
ing to a distance infinitesimally small in comparison with the 
observed disturbances of the fluid-level. 
The accommodation of this theory to the actual phenomena is 
accomplished by long operations, comprehensible only by those 
who are familiar with the higher calculus. The object of the pre¬ 
sent paper is to examine this theory in the light afforded by a 
general knowledge of the leading law r s of mechanical science. For 
this purpose, the author proceeds to analyse the ordinary pheno¬ 
mena of the rise of water round a piece of clean glass which has 
been plunged into it. Assuming a fluid particle situated upon the 
inclined surface, he observes that, according to the hypothesis of 
an infinitesimally small sphere of attraction, this particle is beyond 
the direct influence of the glass; the only other influences to which 
it is subjected are gravitation and the attraction by the adjacent 
fluid particles. 
Now, according to this same hypothesis, the particle is attracted 
by that part of the fluid which is within a small sphere described 
around it; but the curved surface, having its radius of curvature 
infinitely greater than the radius of this sphere, may be regarded 
as flat within the range of attraction, and therefore the solicita¬ 
tion, to which the particle is exposed, must be exerted in a direc¬ 
tion normal to the surface. By a more minute examination, the 
author shows that, if the radius of the sphere of attraction be 
reckoned as a differential of the first order, any deviation from nor¬ 
mality must belong to the third order of differentials—that is, 
must be of an order infinitesimally smaller than the infinitesimally 
small sphere of attraction. 
Thus the only two solicitations to which the particle can be 
subjected are, the attraction of the fluid exerted in a direction 
normal to the surface, and gravitation. Now, it is impossible that 
the resultant of these two solicitations can be normal to the sur¬ 
face; but no fluid can be in repose if the attraction exerted upon a 
particle at its surface be not normal to that surface, wherefore, the 
author of the paper concludes, the infinitesimally-small-sphere-of- 
attraction-hypothesis is untenable. 
On considering the hypothesis of attraction generally, the author 
