Time would fail me if I were to attempt to illustrate by examples the
scientific value of the classification of quantities. I shall only
mention the name of that important class of magnitudes having
direction in space which Hamilton has called vectors, and which form
the subject-matter of the Calculus of Quaternions, a branch of
mathematics which, when it shall have been thoroughly understood by
men of the illustrative type, and clothed by them with physical
imagery, will become, perhaps under some new name, a most powerful
method of communicating truly scientific knowledge to persons
apparently devoid of the calculating spirit.

The mutual action and reaction between the different departments of
human thought is so interesting to the student of scientific progress,
that, at the risk of still further encroaching on the valuable time of
the Section, I shall say a few words on a branch of physics which not
very long ago would have been considered rather a branch of
metaphysics. I mean the atomic theory, or, as it is now called, the
molecular theory of the constitution of bodies.

Not many years ago if we had been asked in what regions of physical
science the advance of discovery was least apparent, we should have
pointed to the hopelessly distant fixed stars on the one hand, and to
the inscrutable delicacy of the texture of material bodies on the
other.

Indeed, if we are to regard Comte as in any degree representing the
scientific opinion of his time, the research into what takes place
beyond our own solar system seemed then to be exceedingly unpromising,
if not altogether illusory.