With regard, then, to this part of the discovery, that the force of the sun follows the inverse duplicate proportion of the distances, we see that several other persons were on the verge of it at the same time with Newton; though he alone possessed that combination of distinctness of thought and power of mathematical invention, which enabled him to force his way across the barrier. But another, and so far as we know, an earlier train of thought, led by a different path to the same result; and it was the convergence of these two lines of reasoning that brought the conclusion to men’s minds with irresistible force. I speak now of the identification of the force which retains the moon in her orbit with the force of gravity by which bodies fall at the earth’s surface. In this comparison Newton had, so far as I am aware, no forerunner. We are now, therefore, arrived at the point at which the history of Newton’s great discovery properly begins. ~Additional material in the [3rd edition].~ [399]
CHAPTER II.
The Inductive Epoch of Newton.—Discovery of the Universal Gravitation of Matter, according to the Law of the Inverse Square of the Distance.
IN order that we may the more clearly consider the bearing of this, the greatest scientific discovery ever made, we shall resolve it into the partial propositions of which it consists. Of these we may enumerate five. The doctrine of universal gravitation asserts,
1. That the force by which the different planets are attracted to the sun is in the inverse proportion of the squares of their distances;
2. That the force by which the same planet is attracted to the sun, in different parts of its orbit, is also in the inverse proportion of the squares of the distances;
3. That the earth also exerts such a force on the moon, and that this force is identical with the force of gravity;
4. That bodies thus act on other bodies, besides those which revolve round them; thus, that the sun exerts such a force on the moon and satellites, and that the planets exert such forces on one another;
5. That this force, thus exerted by the general masses of the sun, earth, and planets, arises from the attraction of each particle of these masses; which attraction follows the above law, and belongs to all matter alike.
The history of the establishment of these five truths will be given in order.
1. Sun’s Force on Different Planets.—With regard to the first of the above five propositions, that the different planets are attracted to the sun by a force which is inversely as the square of the distance, Newton had so far been anticipated, that several persons had discovered it to be true, or nearly true; that is, they had discovered that if the orbits of the planets were circles, the proportions of the central force to the inverse square of the distance would follow from Kepler’s third law, of the sesquiplicate proportion of the periodic times. As we have seen, Huyghens’ theorems would have proved this, if they had been so applied; Wren knew it; Hooke not only knew it, but claimed a prior knowledge to Newton; and Halley had satisfied himself that it was at [400] least nearly true, before he visited Newton. Hooke was reported to Newton at Cambridge, as having applied to the Royal Society to do him justice with regard to his claims; but when Halley wrote and informed Newton (in a letter dated June 29, 1686), that Hooke’s conduct “had been represented in worse colors than it ought,” Newton inserted in his book a notice of these his predecessors, in order, as he said, “to compose the dispute.”[25] This notice appears in a Scholium to the fourth Proposition of the Principia, which states the general law of revolutions in circles. “The case of the sixth corollary,” Newton there says, “obtains in the celestial bodies, as has been separately inferred by our countrymen, Wren, Hooke, and Halley;” he soon after names Huyghens, “who, in his excellent treatise De Horologio Oscillatorio, compares the force of gravity with the centrifugal forces of revolving bodies.”