As science has been developed, the domain of quantity has everywhere
encroached on that of quality, till the process of scientific inquiry
seems to have become simply the measurement and registration of
quantities, combined with a mathematical discussion of the numbers
thus obtained. It is this scientific method of directing our
attention to those features of phenomena which may be regarded as
quantities which brings physical research under the influence of
mathematical reasoning. In the work of the Section we shall have
abundant examples of the successful application of this method to the
most recent conquests of science; but I wish at present to direct your
attention to some of the reciprocal effects of the progress of science
on those elementary conceptions which are sometimes thought to be
beyond the reach of change.
If the skill of the mathematician has enabled the experimentalist to
see that the quantities which he has measured are connected by
necessary relations, the discoveries of physics have revealed to the
mathematician new forms of quantities which he could never have
imagined for himself.
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