When mechanics had reached the point to which Galileo brought it—­when the simple laws of force had been disentangled from the friction and atmospheric resistance by which all their earthly manifestations are disguised—­when progressing knowledge of physics had given a due insight into these disturbing causes—­when, by an effort of abstraction, it was perceived that all motion would be uniform and rectilinear unless interfered with by external forces—­and when the various consequences of this perception had been worked out; then it became possible, by the union of geometry and mechanics, to initiate physical astronomy.  Geometry and mechanics having diverged from a common root in men’s sensible experiences; having, with occasional inosculations, been 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 subsisting in this stage of growth, and afterwards.  Let us look at a few cases.