38 
T°. Conceive a medium of uniform density within a closed space, and 
possessing a constitution fulfilling the conditions required by these hy- 
potheses. Conceive within this medium a canal of finite and uniform 
section which returns into itself. There will then be nothing to prevent 
the part of the medium which is within this canal from yielding to any 
force tending to make it glide lengthways. Itis 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 fortzorz, that 
none will arise from those acting farther within it. Hence, the medium 
is a fluid. 
IT°. 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 be capable of retaining a constitution such as is supposed, the 
molecular forces must be 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. Now, 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 be 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 be 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. E 
adopted, exclude many continuous functions; thus, using F to denote the mutual action 
of two molecules, and 7 for the interval between them, if the law of force be such that 
73 F becomes infinite for = 0, the central elements of the integral will contribute unduly 
to it, so that such a value as— 
az a we 
where y is the coefficient of gravity, 4, B, &c., constants, and a a line of fixed length, 
is not admissible if the method of integration be retained; yet this law, and others like 
it, would, it is evident, lead to several of the most obvious properties of matter. 
* 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). 
