ROYAL IRISH ACADEMY. 
211 
potlieses. Conceive within this medium a canal of finite and uniform 
section which returns into itself. There will then he nothing to prevent 
the part of the medium which is within this canal from yielding to any 
force tending to make it glide lengthways. It is evident from hypotheses 
(4) and (5) that no obstacle to this motion will arise from the molecular 
forces acting on the superficial portions of the canal, and, a fortiori , that 
none will arise from those acting farther within it. Hence, the medium 
is a fluid. 
11°. Again, conceive the medium within the closed space to consist of 
two parts of different densities in contact with one another. Then, in order 
that it may he capable of retaining a constitution such as is supposed, the 
molecular forces must he such as will make the part of greater density 
diffuse into the other. For the sphere of action round some molecules will 
consist of two segments of unequal density. How, a segment of the 
greater density must exert either a greater attraction on the central mo¬ 
lecule than an equal and similarly situated segment of less density or a 
greater repulsion. For if it exerted neither, it would follow, from 
hypotheses (3), (4), and (5), that the density might he increased or de¬ 
creased to any extent without opposition from the molecular forces,— 
a state of things wholly unknown in nature. Again, it cannot have a 
greater attraction; for it would follow that, even if the conditions at 
the surface of a uniform medium could he such as to establish a state of 
equilibrium, this equilibrium could only be unstable; so that on the 
most trifling inequality of density occasioned by a deranging cause, the 
parts of less density would flow into those of greater ; so that the whole 
medium would ultimately collapse into one or more points, or until some 
forces not consistent with the hypotheses came into play; or else it would 
get into a state of permanent internal motion inconsistent with hypo¬ 
thesis (1). The only remaining alternative,* that the segment of greater 
density exercises a greater repulsion, leads to no such impossible results. 
It might only require the parts of greater density to flow towards those 
of less, and thus make a state of uniform density one of stable equili¬ 
brium with a pressure against the containing vessel. Hence the medium 
is an elastic fluid or a gas. 
111°. Hext let the medium be of uniform density within a closed 
space, and imagine any plane crossing this space; then the pressure per 
square inch of the part of the medium lying on one side of this plane 
against the part lying on the other side may be seen to be a function of 
the density as follows :—Let m be a molecule sufficiently near to the plane 
on one side to be within the range of molecular repulsion of particles 
lying at the other side, and describe round m a sphere including all the 
molecules which act on it. Part of this sphere will, therefore, lie beyond 
the plane, and from hypotheses (3), (4), and (5), we find that the action 
on m arising from that segment of the sphere will vary directly as the 
density; since to alter the density is the same thing as to increase or 
* A less attraction or repulsion from a segment of greater density has not been con¬ 
sidered, since it is at once inconsistent with hypothesis (3). 
