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CHAPTER XI.

The first Idea of Gravity ocours to Neuton in 1666-His first Specu.

lations upon it-Interrupted by his Optical Experiments-He resumes the Subject in consequence of a Discussion with Dr. HookeHe discovers the true Law of Gravity and the Cause of the Planetary Motions--Dr. Halley urges him to publish his PrincipiaHis Principles of Natural Philosophy--Proceedings of the Royal Society on this Subject--The Principia appears in 1637-General Account of it, and of the Discoveries it contains--They meet with great Opposition, owing to the Prevalence of the Cartesian System-Accinint of the Reception and Progress of the Newtonian Philosophy in foreign Coun: tries-- Account of its Progress and Establishment in England.

Such is a brief sketch of the labours and lives of those illustrious men who prepared the science of astronomy for the application of Newton's genius. Copernicus had determined the arrangement and general movements of the planetary bodies: Kepler had proved that they moved in elliptical orbits; that their radii vectores described arcs proportional to the times; and that their periodic times were related to their distances. Galileo had added to the universe a whole system of secondary planets; and several astronomers had distinctly referred the motion of the heavenly bodies to the power of attraction,

In the year 1666, when the plague had driven Newton from Cambridge, 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 towards 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 tops of the highest mountains as at the bottom of the deepest mines, he conceived it highly probable, that it must extend much farther than was usually supposed. No sogner 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 at a given distance from the centre of 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

* “ But for the duplicate proportion, I gathered it from Kepler's theorem about twenty years ago."--Newton's Letter to Halley, July 14, 1686.

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 supposed that each degree of latitude contained sixty 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 onesixth greater than that which 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 in 1666, his attention was occupied with those optical discoveries of which we have given an account in a preceding chapter; but he had no sooner brought them to a close than his mind reyerted to the great subject of the planetary motions. Upon the death of Olden. burg in August, 1678, Dr. Hooke was appointed secretary to the Royal Society ; and as this learned body had requested the opinion of Newton about a system of physical astronomy, he addressed a letter, to Dr. Hooke on the 28th November, 1679. In this letter he proposed a direct experiment for verifying the motion of the earth, viz. 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 exactly a vertical

* Whiston Asserts that this cause was supposed by Newton to be something analogous to the vortices of Descartes. - See Whiston's Me

the vortices of Descariposed by Newton to he

moirs of himself

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 the idea thus casually suggested, and Dr. Hooke was appointed to put it to the test of experiment. Being thus led to consider the subject more attentively, he wrote to Newton, that wherever the direction of gravity was oblique to the axis on which the earth revolved, that is, in every part of the earth exs cept 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 December, 1679.* Newton had erronea ously 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 eccentric ellipse in vacuo, and an ellipti-spiral, if the body moved in a resisting medium.f

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, as he himself informs us in his letter to Halley, I to discover “ the theorem by which he afterward examined the ellipsis," 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. * Waller's Life of Hooke, p. 22.

Ibid. 1 July 27, 1686, Biog. Brit. p. 2662.

But though Newton had thus discovered the true cause of all the celestial inotions, 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 the meridian, executed by M. Picard in 1679, 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 calculation of 1665, 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 on the calculation. In this state of mind he intrusted 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

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