en
separately developed, the one partly in connection with astronomy, the
other solely by analysing terrestrial movements; now join in the
investigations of Newton to create a true theory of the celestial
motions. And here, also, we have to notice the important fact that, in
the very process of being brought jointly to bear upon astronomical
problems, they are themselves raised to a higher phase of development.
For it was in dealing with the questions raised by celestial dynamics
that the then incipient infinitesimal calculus was unfolded by Newton
and his continental successors; and it was from inquiries into the
mechanics of the solar system that the general theorems of mechanics
contained in the _Principia_,--many of them of purely terrestrial
application--took their rise. Thus, as in the case of Hipparchus, the
presentation of a new order of concrete facts to be analysed, led to the
discovery of new abstract facts; and these abstract facts having been
laid hold of, gave means of access to endless groups of concrete facts
before incapable of quantitative treatment.

Meanwhile, physics had been carrying further that progress without
which, as just shown, rational mechanics could not be disentangled. In
hydrostatics, Stevinus had extended and applied the discovery of
Archimedes. Torricelli had proved atmospheric pressure, "by showing that
this pressure sustained different liquids at heights inversely
proportional to their densities;" and Pascal "established the necessary
diminution of this pressure at increasing heights in the atmosphere:"
discoveries which in part reduced this branch of science to a
quantitative form. Something had been done by Daniel Bernouilli towards
the dynamics of fluids. The thermometer had been invented; and a number
of small generalisations reached by it. Huyghens and Newton had made
considerable progress in optics; Newton had approximately calculated the
rate of transmission of sound; and the continental mathematicians had
succeeded in determining some of the laws of sonorous vibrations.
Magnetism and electricity had been considerably advanced by Gilbert.
Chemistry had got as far as the mutual neutralisation of acids and
alkalies. And Leonardo da Vinci had advanced in geology to the
conception of the deposition of marine strata as the origin of fossils.
Our present purpose does not require that we should give particulars.
All that it here concerns us to do is to illustrate the _consensus_
su