that mathematical methods are, as yet, not so largely employed.
But these sciences are far less highly developed, far less exact
and systematic, that is to say, far less scientific, at present,
than is either physics or chemistry. However, the application of
statistical methods promises good results, and there are not wanting
generalisations already arrived at which are expressible mathematically;
Weber's Law in psychology, and the law concerning the arrangement
of the leaves about the stems of plants in biology, may be instanced
as cases in point."[1]


[1] Quoted from a lecture by the present writer on "The Law of
Correspondences Mathematically Considered," delivered before The
Theological and Philosophical Society on 26th April 1912, and
published in _Morning Light_, vol. xxxv (1912), p. 434 _et seq_.


The Pythagorean doctrine of the Cosmos, in its most reasonable form,
however, is confronted with one great difficulty which it seems incapable
of overcoming, namely, that of continuity. Modern science, with its
atomic theories of matter and electricity, does, indeed, show us that
the apparent continuity of material things is spurious, that all material
things consist of discrete particles, and are hence measurable in
numerical terms. But modern science is also obliged to postulate an
ether behind these atoms, an ether which is wholly continuous, and hence
transcends the domain of number.[1] It is true that, in quite recent
times, a certain school of thought has argued that the ether is also
atomic in constitution--that all things, indeed, have a grained structure,
even forces being made up of a large number of quantums or indivisible
units of force. But this view has not gained general acceptance, and it