History of Western Philosophy - Bertrand Russell [303]
Newton (1642–1727) achieved the final and complete triumph for which Copernicus, Kepler, and Galileo had prepared the way. Starting from his three laws of motion—of which the first two are due to Galileo—he proved that Kepler's three laws are equivalent to the proposition that every planet, at every moment, has an acceleration towards the sun which varies inversely as the square of the distance from the sun. He showed that acceleration towards the earth and sun, following the same formula, explains the moon's motion, and that the acceleration of falling bodies on the earth's surface is again related to that of the moon according to the inverse square law. He defined 'force' as the cause of change of motion, i.e. of acceleration. He was thus able to enunciate his law of universal gravitation: 'Every body attracts every other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.' From this formula he was able to deduce everything in planetary theory: the motions of the planets and their satellites, the orbits of comets, the tides. It appeared later that even the minute departures from elliptical orbits on the part of the planets were deducible from Newton's law. The triumph was so complete that Newton was in danger of becoming another Aristotle, and imposing an insuperable barrier to progress. In England, it was not till a century after his death that men freed themselves from his authority sufficiently to do important original work in the subjects of which he had treated.
The seventeenth century was remarkable, not only in astronomy and dynamics, but in many other ways connected with science.
Take first the question of scientific instruments.2 The compound microscope was invented just before the seventeenth century, about 1590. The telescope was invented in 1608, by a Dutchman named Lippershey, though it was Galileo who first made serious use of it for scientific purposes. Galileo also invented the thermometer—at least, this seems most probable. His pupil Torricelli invented the barometer. Guericke (1602–86) invented the air pump. Clocks, though not new, were greatly improved in the seventeenth
century, largely by the work of Galileo. Owing to these inventions, scientific observation became immensely more exact and more extensive than it had been at any former time.
Next, there was important work in other sciences than astronomy and dynamics. Gilbert (1540–1603) published his great book on the magnet in 1600. Harvey (1578–1657) discovered the circulation of the blood, and published his discovery in 1628. Leeuwenhoek (1632–1723) discovered spermatozoa, though another man, Stephen Hamm, had discovered them, apparently, a few months earlier; Leeuwenhoek also discovered protozoa or unicellular organisms, and even bacteria. Robert Boyle (1627–91) was, as children were taught when I was young, 'the father of chemistry and son of the Earl of Cork'; he is now chiefly remembered on account of 'Boyle's Law', that in a given quantity of gas at a given temperature, pressure is inversely proportional to volume.
I have hitherto said nothing of the advances in pure mathematics, but these were very great indeed, and were indispensable to much of the work in the physical sciences. Napier published his invention of logarithms in 1614. Co-ordinate geometry resulted from the work of several seventeenth-century mathematicians, among whom the greatest contribution was made by Descartes. The differential and integral calculus was invented independently by Newton and Leibniz; it is the instrument for almost all higher mathematics. These are only the most outstanding achievements in pure mathematics; there were innumerable others of great importance.
The result of the scientific work we have been considering was that the