The philosophers of all ages had recognized the connection between the phenomena of the tides and the position of the moon. The College of Jesuits at Coimbra, and subsequently Antonio de Dominis and Kepler, distinctly referred the tides to the attraction of the waters of the earth by the moon; but so imperfect was the explanation which was thus given of the phenomena that Galileo ridiculed the idea of lunar attraction, and substituted for it a fallacious explanation of his own. That the moon is the principal cause of the tides is obvious from the well-known fact that it is high water at any given place about the time when she is in the meridian of that place; and that the sun performs a secondary part in their production may be proved from the circumstance that the highest tides take place when the sun, the moon, and the earth are in the same straight line; that is, when the force of the sun conspires with that of the moon; and that the lowest tides take place when the lines drawn from the sun and moon to the earth are at right angles to each other; that is, when the force of the sun acts in opposition to that of the moon. By comparing the spring and neap tides Newton found that the force with which the moon acted upon the waters of the earth was to that with which the sun acted upon them as 4.48 to 1; that the force of the moon produced a tide of 8.63 feet; that of the sun, one of 1.93 feet; and both of them combined, one of 10-1/2 French feet, a result which in the open sea does not deviate much from observation. Having thus ascertained the force of the moon on the waters of our globe, he found that the quantity of matter in the moon was to that in the earth as 1 to 40, and the density of the moon to that of the earth as 11 to 9. The motions of the moon, so much within the reach of our own observation, presented a fine field for the application of the theory of universal gravitation. The irregularities exhibited in the lunar motions had been known in the time of Hipparchus and Ptolemy. Tycho had discovered the great inequality, called the "variation," amounting to 37', and depending on the alternate acceleration and retardation of the moon in every quarter of a revolution, and he had also ascertained the existence of the annual equation. Of these two inequalities Newton gave a most satisfactory explanation.