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AT present physical astronomy rests entirely on the general law of the mutual attraction, which all parts of matter exercise on each other. The name of system is commonly given to this law; but it is a very improper term, as universal gravitation is now a demonstrated truth, though we may be allowed to employ it for the sake of brevity, and to avoid circumlocution.
I shall begin with a concise account of the manner, in which the celestial motions were formerly explained; I shall then make known the means, by which Newton was led to the discovery of the grand engine of attraction; and I shall afterward relate the principal applications made of it.
The ancients rarely employed the test of experi ment in natural philosophy, where however it is indispensable for, the means by which nature acts being almost always unknown to us, we have no resource but that of studying and comparing their effects. Swayed by the spirit of system, in the worst sense of the word, and more eager to display their conjectures and opinions, than ambitious of the solid glory to be obtained by first instructing themselves through the medium of an uninterrupted and eritical observation of phenomena; into their explana
tions of these they introduced substantial forms, oc cult qualities, &c.; viz. words devoid of meaning, and contrived to give free scope to all the freaks of imagination.
Des Cartes felt, that such a mode of philosophizing was only a perpetual source of false reasoning and erroneous consequences. He was desirous of explaining every thing by means of matter and motion, without admitting in bodies any other properties, than those which are essential to them. With this view he laid down as a principle, that all bodies are composed of the same elements: that their constitution, both internal and external, depends solely on certain simple figures of their constituent parts: and that, when these primordial figures are once known, nothing more is necessary, but to extend and follow their combinations, in the different accidents of rest and motion, to which bodies are subject.
This commencement was rational, and indicated views, which might have led to very useful truths, if directed by experience. But soon embarrassed by the number and variety of phenomena to be explained, as well as dazzled by some imperfect experiments, and fancying himself capable of divining others by the mere strength of his genius, des Cartes admitted in the constituent parts of matter arbitrary magnitudes and configurations, with motions and situations for which no cause existed, except the necessities of his system. He imagined invisible fluids, of extreme tenuity, agitated by secret motions, penetrating the pores of bodies without experiencing any resistance, and always obedient, if I may so express myself, to the
Moon passes through in a given time, in one minute for instance: 2dly, the centripetal force of the Moon, or the quantity of the force with which it is attracted toward the Earth, in one minute; this being evidently a third proportional to the diameter of the lunar orbit, and the arc which it describes in a minute.
The result of all these calculations is, that the quantity of the Moon's deviation from the tangent, or approach to the Earth, in one minute, is about 16 feet. And as we know by experience, that heavy bodies at the surface of the Earth fall sixteen feet in a second, or 3600 times 16 feet in a minute, we perceive, that from the Earth to the Moon gravitation is not uniform, but that it has diminished in the ratio of 3600 to 1, or of the square of sixty to the square of one, that is as the square of the distance between the Earth and Moon to the square of the Earth's radius. This is the first instance of that celebrated law of the gravitation of the celestial bodies in the inverse ratio of the squares of their distances.
Before I proceed any farther, I cannot refrain from pointing out a new and striking mark of the slowness, with which human knowledge advances. In 1673, fifteen years before Newton's book appeared, Huygens had given the properties of the centrifugal and centripetal forces in the circle in thirteen propositions. Had he applied this theory to the rotatory motion of the Earth round it's axis, and to the motion of the Moon round the Earth, he would have discovered the law of the Moon's gravitation toward the Earth. In fact, according to propositions
11 and 111 combined together, the centrifugal force of the Moon is to the centrifugal force at the surface of the Earth, as the square of the space, which the Moon traverses in a minute, divided by 60, is to the square of the space, which a point on the surface of the Earth traverses in a minute, divided by one: and according to proposition v, combined with the ordinary theory of the fall of heavy bodies, the centrifugal force of a point on the surface of the Earth is to the force of gravity at this surface, as 1 to 289. Now if we multiply these two proportions term by term, and perform the calculations pointed out, we shall find the centrifugal force of the Moon to be to the force of gravity at the Earth's surface, as 1 to 3600; which is the conclusion of Newton. But Huygens did not make this application, and the honour of having discovered the law of the gravitation of the planets, and confirming it by calculation, belongs to the english geometrician.
When Newton had discovered the law of the gravitation of the Moon toward the Earth, it was not difficult for him equally to determine the tendencies of the primary planets toward the Sun, and those of the satellites toward their primary planets. Here the elements of the calculations were furnished by the laws of Kepler.
The primary planets describe ellipses round the Sun, which occupies one of their foci; and in a similar manner the satellites describe ellipses round their primaries. Now by the first law of Kepler, the times employed in passing through the parts. of any orbit are as the areas included between the longer
different orders, which he issued to them as circumstances required. Lastly from suppositions to suppositions he preceded to the conception of those famed vortices, or immense currents of ethereal matter, which he made to carry the planets, as a river carries a boat. His disciples were neither less daring, nor more fortunate, than himself. Obliged to give up several essential points of his system, they substituted instead of them, on every occasion, new hypotheses, as fragile and precarious as those of their masNotwithstanding so many exertions made to prop it up, this vast edifice has almost wholly crumbled to pieces.
Newton, wisely rejecting the illusions of imagination, studied Nature in herself, and at length divined her secret by dint of research and meditation. Profound skill in geometry, and the theory of central forces discovered by Huygens, enabled the learned englishman to discover the law of the force, which retains the Moon in it's orbit round the Earth, or which occasions this satellite to gravitate constantly toward it's primary planet. He then extended this law to all the bodies of our planetary system. Such was nearly the gradation of his ideas on this vast subject.
We see that a cannon ball, impelled by the explosion of a charge of powder, falls at a distance so much the greater, as the impulse of the explosion is more powerful. Farther, the theory of Huygens informs us, that, if the ball, acted upon by a uniform gravitation constantly directed toward the centre of the Earth, were projected horizontally with a velocity equal