_René Descartes_ was born at La Haye in Touraine, 1596, and died at Stockholm in 1650. He did important work in mathematics, physics, anatomy, and philosophy. Was greatest as a philosopher and mathematician. At the age of twenty-one he served as a volunteer under Prince Maurice of Nassau, but spent most of his later life in Holland. His famous _Discourse on Method_ appeared at Leyden in 1637, and his _Principia_ at Amsterdam in 1644; great pains being taken to avoid the condemnation of the Church. Descartes's main scientific achievement was the application of algebra to geometry; his most famous speculation was the "theory of vortices," invented to account for the motion of planets. He also made many discoveries in optics and physiology. His best known immediate pupils were the Princess Elizabeth of Bohemia, and Christina, Queen of Sweden. He founded a distinct school of thought (the Cartesian), and was the precursor of the modern mathematical method of investigating science, just as Galileo and Gilbert were the originators of the modern experimental method. LECTURE VI DESCARTES AND HIS THEORY OF VORTICES After the dramatic life we have been considering in the last two lectures, it is well to have a breathing space, to look round on what has been accomplished, and to review the state of scientific thought, before proceeding to the next great era. For we are still in the early morning of scientific discovery: the dawn of the modern period, faintly heralded by Copernicus, brought nearer by the work of Tycho and Kepler, and introduced by the discoveries of Galileo--the dawn has occurred, but the sun is not yet visible. It is hidden by the clouds and mists of the long night of ignorance and prejudice. The light is sufficient, indeed, to render these earth-born vapours more visible: it is not sufficient to dispel them. A generation of slow and doubtful progress must pass, before the first ray of sunlight can break through the eastern clouds and the full orb of day itself appear.