circle to represent the moon's orbit and calculates by what amount the moon ought to fall toward the earth in a minute, assuming that its distance from the earth is that given in the books. In his own words he finds the figures "to answer pretty nearly," But this does not satisfy him; to a mind like Newton's "pretty nearly" is as bad as "not at all," so he lays aside his papers until more exact data are at hand. He has, however, made the first stage of the journey toward the goal. This was in the plague year, 1666. As soon as the university is again convened, Newton returns to Cambridge and for a number of years is engrossed in the study of optics. In 1672 he is momentarily reminded of the problem while editing a revised edition of Varenius's "Geography." In this he gives the accepted value for the earth's degree sixty-one and one half miles. This was probably the value Newton used in his calculations of 1666 and which fitted "pretty well," as he said. In 1679-80 Newton has an unwilling and one-sided correspondence with Hooke relating to the theory of projectiles, and in which the subject of gravity is involved.
We may be sure that during these years Newton had many times analyzed the grand problem of solar gravity and had carefully noted just what was involved therein. We may even venture to note what must have been his thoughts. If, he would say to himself, it be gravity that rules the motion of the moon, then I must prove the following:
1. Gravity must act on all kinds of matter alike, for the earth is a composite body, and presumably the moon also.
2. We know with a fair degree of accuracy that the moon is sixty-one earth-radii from us, but to make any calculation, this distance must be known in feet. Hence it is important that measurements of the size of the earth be made with the greatest care.
3. The same law should extend to the planets also, but the planetary orbits are ellipses, hence I must prove that the ellipse is a possible or necessary orbit under such a law of force.
4. I must determine some point from which measurements of distance between earth and moon are to be made, e. g., shall it be from the centers of these bodies? Also, does the same law of force hold good over the whole distance, or is it modified as the surface of the earth or moon is approached?
Whether or no Newton set the matter in orderly array, it is clear from his papers and letters that each of these points was considered. Thus he proves the first point by an exhaustive series of experiments on pendulums in which he varies the material of which the pendulum is made, proving clearly, "by experiments made with the greatest accuracy, the quantity of matter in bodies to be proportional to their weights." The converse must also be true—the weight or pull of gravity on bodies is proportional to their mass or quantity of mat-