remarks, "that if attraction existed, it would decrease as the square of the distance." The influence of gravity was still more distinctly developed by Borelli, a Neapolitan philosopher, who published ǹ 1666 a work on Jupiter's satellites.* In this work he maintains, that all the planets perform their motions round the sun according to a general law; that the satellites of Jupiter and of Saturn move round their primary planets in the same manner as the moon does round the earth, and that they all revolve round the sun, which is the only source of any virtue, and that this virtue attaches them, and unites them so that they cannot recede from their centre of action.† Our countryman Dr. Robert Hooke seems to have devoted much of his attention to the cause of the planetary motions. On the 21st March, 1666, he read to the Royal Society an account of a series of experiments for determining if bodies experience any variation in their weight at different distances. from the centre of the earth. His experiments, as Hooke himself saw, were by no means satisfactory, and hence he was led to the ingenious idea of measuring the force of gravity by observing, at different altitudes, the rate of a pendulum clock. About two months afterward, he exhibited to the Society an approximate representation of the forces which retain the planets in their orbits, in the paths described by a circular pendulum impelled with dif Theorica Medicearum planetarum ex causis physicis deducta. Flor. 1666, 4to. †M. Delambre maintains that these views of Borelli are only those of Kepler slightly modified. Newton and Huygens have attached to them a greater value. The last of these philosophers remarks, "Refert Plutarchus, fuisse jam olim qui putaret ideo manere lunam in orbe suo, quod vis recedendi a terra, ob motum circularem, inhiberetur pari vi gravi. tatis, qua ad terram accedere conaretur. Idemque ævo nostro, non de luna tantum sed et planetis ceteris statuit Alphonsus Borellus, ut nempe primariis eorum gravitas esset solem versus; lunis vero ad terram Jovem ac Saturnum quos comitantur."-Huygen, Cosmotheor, lib ii.; Opera, t. ii. p. 720. ferent degrees of force; but though this experiment illustrated the production of a curvilineal motion, by combining a tangential force with a central power of attraction, yet it was only an illustration, and could not lead to the true cause of the planetary motions. At a later period, however, viz. in 1674, Hooke resumed the subject in a dissertation entitled "An Attempt to prove the Motion of the Earth from Observation," which contains the following remarkable observations upon gravity: "I shall hereafter explain a system of the world differing in many particulars from any yet known, answering in all things to the common rules of mechanical motions. This depends upon three suppositions: first, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, whereby they attract, not only their own parts, and keep them from flying from them, as we may observe the earth to do, but that they also do attract all the other celestial bodies that are within the sphere of their activity, and consequently, that not only the sun and moon have an influence upon the body and motion of the earth, and the earth upon them, but that Mercury, Venus, Mars, Jupiter, and Saturn, also, by their attractive powers, have a considerable influence upon its motion, as in the same manner the corresponding attractive power of the earth hath a considerable influence upon every one of their motions also. second supposition is this, that all bodies whatsoever that are put into a direct and simple motion will so continue to move forward in a straight line, till they are, by some other effectual powers, deflected, and sent into a motion describing a circle, ellipsis, or some other more compounded curve line. The third supposition is, that those attractive powers are so much the more powerful in operating by how much the nearer the body wrought upon is to their own centres. Now, what these several degrees are 1 The have not yet experimentally verified; but it is a notion which, if fully prosecuted, as it ought to be, will mightily assist the astronomers to reduce all the celestial motions to a certain rule, which I doubt will never be done without it. He that understands the nature of the circular pendulum and circular motion will easily understand the whole of this principle, and will know where to find directions in nature for the true stating thereof. This I only hint at present to such as have ability and opportu nity of prosecuting this inquiry, and are not wanting of industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand, which I would first complete, and therefore cannot so well attend it. But this I do not promise the undertaker, that he will find all the great motions of the world to be influenced by this principle, and that the true understanding thereof will be the true, perfection of astronomy." This passage, which has been considered as a remarkable one by the philosophers of every country. has, we think, been misapprehended by M. Delambre, when he asserts that every thing which it contains "is to be found expressly in Kepler."* * Hist. de l'Astronomie aux Dix-huitieme Siècle, p.9. CHAPTER XI. The first Idea of Gravity occurs to Newton in 1666-His first Specalations upon it-Interrupted by his Optical Experiments- Heresumes 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 Principia-His Principles of Natural Philosophy-Proceedings of the Royal Society on this Subject-The Principia appears in 1687-General Account of it, and of the Discoveries it contains-They meet with great Opposition, owing to the Prevalence of the Cartesian System-Account of the Reception and Progress of the Newtonian Philosophy in foreign Countries-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 wer 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 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 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 |