olution with the discovery of Harvey, a contemporary of
Newton.

The seventeenth century, with Descartes' application of algebra to
geometry, and Newton's and Leibnitz's invention of the differential and
integral calculus, improved our methods of calculation to such a point
that summary methods of vastly greater comprehensiveness and elasticity
can be applied to any problem of which the elements can be measured. The
mere improvement in the method of describing the same things (cf. e.g. a
geometrical problem as written down by Archimedes with any modern
treatise) was in itself a revolution. But the new calculus went much
farther. It enabled us to represent, in symbols which may be dealt with
arithmetically, any form of regular movement.

As movement is universal, and the most obvious external manifestation of
life itself, the hopes of a mathematical treatment of all phenomena are
indefinitely enlarged, for all fresh laws or forms might conceivably be
expressed as differential equations. So to the vision of a Poincare the
human power of prediction appears to have no assignable theoretical
limit.

The seventeenth century which witnessed this momentous extension of
mathematical methods, also contains the cognate foundation of scientific
physics. Accurate measurement began to be applied to the phenomena of
light and heat, the expansion of gases, the various changes in the forms
of matter apart from life. The eighteenth century which continued this
work, is also and most notably marked by the establishment of a
scientific chemistry. In this again we see a further extension of
accurate measurement: another order of things different in quality began
to be treated by a quantitative analysis. Lavoisier's is the greatest
name. He gave a clear and logical classification of the chemical
elements then known, which served as useful a purpose in that science,
as classificatory systems in botany and zoology have done in those
cases. But the crucial step which established chemistry, a step also due
to Lavoisier, was making the test of weight decisive. 'The balance was
the _ultima ratio_ of his laboratory.' His first principle was that the
total weight of all the products of a chemical process must be exactly
equal to the total weight of the substances used. From this, and rightly
disregarding the supposed weight of heat, he could proceed to the
discovery of the accurate proportions of the elements in all the
compounds he was able to a