tion 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 ( 16321723)
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 consequence of the scientific work we have been considering was that the outlook of
educated men was completely transformed. At the beginning of the century, Sir Thomas Browne
took part in trials for witchcraft; at the end, such a thing would have been impossible. In
Shakespeare's time, comets were still portents; after the publication of Newton Principia in 1687,
it was known that he and Halley had calculated the orbits of certain comets, and that they were as
obedient as the planets to the law of gravitation. The reign of law had established its hold on
men's imaginations, making such things as magic and sorcery incredible. In 1700 the mental
outlook of educated men was completely modern; in 1600, except among a very few, it was still
largely medieval.
In the remainder of this chapter I shall try to state briefly the philosophical beliefs which appeared
to follow from seventeenth