CHAPTER V.

Newton's first speculations on Gravity. He discovers the true law of Gravity and the cause of the Planetary Motions. His principles of Natural Philosophy. His "Principia" appears in 1687. Account of

it and the Discoveries it contains. They meet with great opposition. The reception of the Newtonian Philosophy. Doctrine of Infinite Quantities. Discovers the Binomial Theorem. Doctrine of Fluxions. His Mathematical Tracts. His Universal Arithmetic. Account of the celebrated Controversy respecting the Invention of Fluxions.

WHEN the plague had driven Newton from Cambridge, in 1666, he was sitting alone in the garden at Woolsthorpe, and reflecting on the nature of gravity, that remarkable power which causes all bodies to descend to the centre of the earth. As this power is not found to suffer any sensible diminution at the greatest distance from the earth's centre to which we can reach, being as powerful at the summit of the highest mountain as at the bottom of the deepest mine, he conceived it highly probable that it must extend much farther than was usually supposed. No sooner had this happy conjecture occurred to his mind than he considered what would be the effect of its extending as far as the moon. That her motion must be influenced by such a power, he did not for a moment doubt; and a little reflection convinced him that it might be sufficient for retaining that luminary in her orbit round the earth. Though the force of gravity suffers no sensible diminution at those small distances from the earth's centre at which we can place ourselves, yet he thought it very possible that, at the distance of the moon, it might differ much in strength from what it is on the earth. In order to form some estimate of the degree of its diminution, he considered that if the moon be

retained in her orbit by the force of gravity, the primary planets must also be carried round the sun by the same power; and by comparing the periods of the different planets, with their distances from the sun, he found that if they were retained in their orbits by any power like gravity, its force must decrease in the duplicate proportion, or as the squares of their distances from the sun. In drawing this conclusion, he supposed the planets to move in orbits perfectly circular, and having the sun in their centre. Having thus obtained the law of the force by which the planets were drawn to the sun, his next object was to ascertain if such a force emanating from the earth, and directed to the moon, was sufficient, when diminished in the duplicate ratio of the distance, to retain her in her orbit. In performing this calculation, it was necessary to compare the space through which heavy bodies fall in a second of time at a given distance from the earth, viz., at its surface, with the space through which the moon, as it were, falls to the earth in a second of time while revolving in a circular orbit. Being at a distance from books when he made this computation, he adopted the common estimate of the earth's diameter, then in use among geographers and navigators, and each degree of latitude contained 60 English miles. In this way he found that the force which retains the moon in her orbit, as deduced from the force which occasions the fall of heavy bodies to the earth's surface, was one-sixth greater than what is actually observed in her circular orbit. This difference threw a doubt upon all his speculations; but unwilling to abandon what seemed to be otherwise so plausible, he endeavoured to account for the difference of the two forces, by supposing that some other cause must have been united with the force of gravity in producing so great a velocity of the moon in her circular orbit. As this new cause, however, was beyond the reach of observation, he discontinued all further inquiries into

the subject, and concealed from his friends the speculations in which he had been employed.

After his return to Cambridge his attention was occupied with those optical discoveries which we have already noticed; but he had no sooner brought them to a close than his mind reverted to the subject of the planetary motions. Upon the death of Oldenburg, in 1678, Doctor Hooke was appointed secretary to the Royal Society; and as this distinguished body had requested the opinion of Newton about the system of physical astronomy, he addressed a letter to the secretary, on the 28th of November, 1679, in which he proposed a direct experiment 'for verifying the motion of the earth, namely, by observing whether or not bodies that fall from a considerable height descend in a vertical direction, for if the earth were at rest, the body would describe a vertical line, whereas if it revolved round its axis, the falling body must deviate from the vertical line towards the east. The Royal Society attached great value to this idea, and appointed Dr. Hooke to put it to the test of experiment. Being thus led to consider the subject more attentively, he wrote to Newton, that where ever the direction of gravity was oblique to the axis on which the earth revolved, that is, in every part of the earth except the equator, falling bodies should approach to the equator, and the deviation from the vertical, in place of being exactly to the east, as Newton maintained, should be to the south-east of the point from which the body began to move. Newton acknowledged that this conclusion was correct in theory, and Dr. Hooke is said to have given an experimental demonstration of it before the Royal Society, in 1679. Newton had erroneously concluded, that the path of the falling body would be a spiral; but Dr. Hooke, on the same occasion on which he made the preceding experiment, read a paper to the Society in which he proved that the path of the body would be an eccen

tric ellipse in the vacuo, and an elliptic spiral, if the body moved in a resisting medium.

This correction of Newton's error, and the discovery that a projectile would move in an elliptical orbit when under the influence of a force varying in the inverse ratio of the square of the distance, led Newton to discover the theorem by which he afterwards examined the ellipses," and to demonstrate the celebrated proposition, that a planet acted upon by an attractive force varying inversely as the squares of the distances, will describe an elliptical orbit in one of whose foci the attractive force resides.

But though Newton had thus discovered the true cause of all the celestial motions, he did not yet possess any evidence that such a force actually resided in the sun and planets. The failure of his former attempt, to identify the law of falling bodies, at the earth's surface, with that which guided the moon in her orbit, threw a doubt over all his speculations, and prevented him from giving any account of them to the public.

An accident, however, of a very interesting nature, induced him to resume his former inquiries, and enabled him to bring them to a close. In June, 1682, when he was attending a meeting of the Royal Society of London, the measurement of a degree of meridian, executed by M. Picard, became the subject of conversation. Newton took a memorandum of the result obtained by the French astronomer, and having deduced from it the diameter of the earth, he immediately resumed his former calculations, and began to repeat it with these new data, In the progress of the calculation, he saw that the result which he had formerly expected, was likely to be produced, and he was thrown into such a state of nervous irritability, that he was unable to carry it on. In this state of mind, he entrusted it to one of his friends, and he had the high satisfaction of finding his former views amply realized. The force of gravity which regulated the fall

of bodies at the earth's surface, when diminished as the square of the moon's distance from the earth, was found to be almost exactly equal to the centrifugal force of the moon, as deduced from her observed distance and velocity.

The influence of such a result upon such a mind may be more easily conceived than described. The whole material universe was spread out before him ;the sun with all his attending planets-the planets with all their satellites-the comets wheeling in every direction in their eccentric orbits, and the systems of the fixed stars stretching to the remotest limits of space. All the varied and complicated movements of the heavens, in short, must have been at once presented to his mind as the necessary result of that law which he had established in reference to the earth and the moon.

After extending this law to the other bodies of the system, he composed a series of propositions on the motion of the primary planets about the sun, which were sent to London about the end of 1683, and were soon afterwards communicated to the Royal Society.

About this period other philosophers had been occupied with the same subject. Sir Christopher Wren had many years before endeavoured to explain the planetary motions "by the composition of a descent towards the sun, and an impressed motion; but he at length gave it over, not finding the means of doing it. In January, 1684, Dr. Halley had concluded that the centrepital force decreased in the reciprocal proportion of the squares of the distances, and having one day met Sir Christopher Wren and Dr. Hooke, the latter affirmed that he had demonstrated upon that principle all the laws of the celestial motions. Dr. Halley confessed that his attempts were unsuccessful, and Sir Christopher, in order to encourage the inquiry, offered to present a book of forty shillings value, to