The theory of the plenum is associated with the doctrine of
mathematical continuity, and its mathematical methods are those of the
Differential Calculus, which is the appropriate expression of the
relations of continuous quantity.

The theory of atoms and void leads us to attach more importance to the
doctrines of integral numbers and definite proportions; but, in
applying dynamical principles to the motion of immense numbers of
atoms, the limitation of our faculties forces us to abandon the
attempt to express the exact history of each atom, and to be content
with estimating the average condition of a group of atoms large enough
to be visible. This method of dealing with groups of atoms, which I
may call the statistical method, and which in the present state of our
knowledge is the only available method of studying the properties of
real bodies, involves an abandonment of strict dynamical principles,
and an adoption of the mathematical methods belonging to the theory of
probability. It is probable that important results will be obtained
by the application of this method, which is as yet little known and is
not familiar to our minds. If the actual history of Science had been
different, and if the scientific doctrines most familiar to us had
been those which must be expressed in this way, it is possible that we
might have considered the existence of a certain kind of contingency a
self-evident truth, and treated the doctrine of philosophical
necessity as a mere sophism.

About the beginning of this century, the properties of bodies were
investigated by several distinguished French mathematicians on the
hypothesis that they are systems of molecules in equilibrium. The
somewhat unsatisfactory nature of the results of these investigations
produced, especially in this country, a reaction in favour of the