Prof. Challis on a Theory of Molecular Forces. 89 
no law of force which is not a mathematical deduction, by means 
of hydrodynamical equations, from the assumed dynamical pro- 
perty of the medium that its pressure is proportional to its den- 
sity. The history of physical science seems to show that theo- 
retical investigation proceeds in but one course, that of deducing 
quantitative laws, by means of solutions of equations, from 
known or hypothetical principles. For example, by the solu- 
tions of the first order of differential equations, the Jaw of vis 
viva is deduced from dynamical principles known by experiment, 
and from D’Alembert’s principle. By the same class of equa- 
tions, Kepler’s laws are readily deduced from certain hypotheses 
respecting the force of gravity. In the latter instance, one of the 
hypotheses is, that gravity varies inversely as the square of the 
distance from the centre of emanation. As this hypothesis may 
also be called a quantitative Jaw, it may, according to these views, 
be presumed to be itself deducible from ulterior principles by 
means of a higher order of equations. This is what I have 
attempted to do in a communication to the Philosophical Maga- 
zine for December 1859. 
If this course of investigation applies to one kind of force, it 
is reasonable to suppose that it applies to all. It is a matter of 
demonstration that a theory of molecular forces cannot be con- 
structed on the hypothesis that the forces vary according to some 
law of the distance from individual material particles, unless the 
law be such that the force changes sign with the distance, so as 
to become attractive after being repulsive. But if force be a 
virtue resident in the particle, it must. at its origin be either 
attractive or repulsive, and it seems impossible to conceive how 
by emanation to a distance it can change its quality. This diffi- 
culty, as will be shown, is not encountered in a theory of mole- 
cular forces, which deduces their laws from the dynamical action 
of an elastic medium. 
Again, on the same principles it is not permitted to ascribe to 
the ultimate atoms of matter any variable quantitative proper- 
ties. Accordingly I assume in the following theory, as I have 
done heretofore, that, while different atoms may be of different 
magnitudes, their magnitudes and forms are constant, and that 
all have the same intrinsic inertia. The property of constancy 
of form might be otherwise expressed by saying that the atoms 
are infinitely hard. Further, | make the more particular hypo- 
thesis, that all atoms have the form of a sphere. It would be 
contrary to these principles to ascribe to an atom the property 
of elasticity, because, from what we know of this property by 
experience, it is quantitative, and, being most probably depend- 
ent on an aggregation of atoms, may admit of explanation by a 
complete theory of molecular forces. 
