These two discoveries are known as Kepler's First and Second Laws. His Third Law connects all the planets together. It was known that the outer planets not only take longer to revolve round the Sun than the inner, but that their actual motion in space is slower, and Kepler found that this actual speed of motion is inversely as the square root of its distance from the Sun; or, if the square of the speed of a planet be multiplied by its distance from the Sun, we get the same result in each case. This is usually expressed by saying that the cube of the distance is proportional to the square of the time of revolution. Thus the varying rate of motion of each planet in its orbit is not only subject to a single law, but the very different speeds of the different planets are also all subject to a law that is the same for all. Thus the whole of the complicated machinery of Ptolemy had been reduced to three simple laws, which at the same time represented the facts of observation much better than any possible development of the Ptolemaic mechanism. On his discovery of his third law Kepler had written: "The book is written to be read either now or by posterity--I care not which; it may well wait a century for a reader, as God has waited 6000 years for an observer." Twelve years after his death, on Christmas Day 1642 (old style), near Grantham, in Lincolnshire, the predestined "reader" was born. The inner meaning of Kepler's three laws was brought to light by ISAAC NEWTON. {30} CHAPTER III THE LAW OF GRAVITATION The fundamental thought which, recognised or not, had lain at the root of the Ptolemaic system, as indeed it lies at the root of all science, was that "like causes must always produce like effects." Upon this principle there seemed to the ancient astronomers no escape from the inference that each planet must move at a uniform speed in a circle round its centre of motion. For, if there be any force tending to alter the distance of the planet from that centre, it seemed inevitable that sooner or later it should either reach that centre or be indefinitely removed from it. If there be no such force, then the planet's distance from that centre must remain invariable, and if it move at all, it must move in a circle; move uniformly, because there is no force either to hasten or retard it. Uniform motion in a circle seemed a necessity of nature.