This fourth volume covers the period which was probably the most varied of Newton’s whole career. The Principia had already established Newton as the world’s foremost mathematician and natural philosopher. In spite of the abstruse nature of the mathematical treatment adopted in its pages, the first edition was rapidly exhausted and, within a very few years, Newton was being urged to consider the preparation of the second edition. This was to contain, inter alia, his further researches upon the motion of the Moon, the solar system, and the behaviour of the comets. Not until 1694, however, did his thoughts upon this project assume definite shape. To carry out his plan, he had need of the most accurate observations available, and for these he turned to the Observatory at Greenwich, where John Flamsteed had been installed as King’s Astronomer. So came about that close association between the two men which was to last for many years, though not without frequent interruptions.