placed; and the secondary ones might describe fi gures of the same kind round their respective primaries, without being disturbed by the continual motion of the centres of their revolutions. That if the force which retained each of them in their orbits was like that of gravity, and directed towards the sun, they would each of them describe equal areas in equal times. That if this attractive power of the sun, like all other qualities which are diffused in rays from a centre, diminished in the same proportion as the squares of the distances increased, their mo tions would be swiftest when nearest the sun, and slowest when farthest off from him, in the same proportion in which by observation they are discovered to be; and that, upon the same supposition of this gradual diminution of their respective gravities, their periodic times would bear the same proportion to their distances which Kepler and Cassini had established betwixt them*."

213. Nor was this all; for he not only endeavoured to shew that gravity might be the connecting principle of the planetary movements, but he proved that it really was so. Galileo had shewn that when a stone is projected, it is deflected from the rectilinear path into a parabola, in consequence of the gravity of the stone towards the earth. To shew that the moon is retained in its orbit by the force of gravity, Newton shewed that it was continually bent from the tangent of its orbit, in the same manner as Galileo shewed the deflection of the path of the stone, projected near the surface of the earth: that both these motions are directed to the same point, and agree in quantity: that, if the moon were to approach to the surface of the earth, the force by which it is retained in its orbit, would make it descend through the same space towards the centre of the earth, as an heavy body would fall through by its gravity in the same time; and that if a stone

* Dr. Adam Smith's History of Astronomy,

could be carried to the distance of the moon, and there projected with a sufficient velocity, it would revolve round the earth like a moon, in consequence of the same cause which bends its motion into a curve when projected near the earth's surface. Similar methods of reasoning were applied to all the planets; and as it appeared that the revolutions of the primary planets round the sun, and those of the satellites of jupiter and saturn round their primaries, are phenomena of the same kind with the revolution of the moon about the earth; likewise, as the centripetal powers of the primary are directed towards the centre of the sun, and those of the satellites towards the centre of their respective primaries; and lastly, as all these powers are reciprocally as the squares of the distances from the centres; it was safely concluded that the cause was the same in all, and therefore that the gravitation of matter is universally extended.

214. This system of Newton is the only one which accounts, in a satisfactory manner, for the various irregularities which astronomers have observed in the heavens. It assigns a reason why the centres of the revolutions of the planets are not precisely in the centre of the sun, but in the common centre of gravity of the sun and the planets: it is applied with peculiar success to the solution of the irregularities in the motion of the moon, and to the deviations from regularity in the motions and orbits of the various primaries and secondaries: that which had puzzled all preceding philosophers even to guess at the cause, namely, the precession of the equinoxes, has been explained on the principles of Newton, and calculations applied to the theory, the conclusions resulting from which correspond very accurately with the ob servations of astronomers: and other phenomena which have been discovered since the time of Newton, have met with a ready solution by a just appli

cation of his principles. So that, although gravity be an occult cause, as was at firft objected against it, yet, as in all the consequences deduced from it, the reasoning flowed from its effects without entering into the contemplation of causes, it must be acknowledged, that by making the phenomena of gravity the subject of physical consideration, Newton performed the most essential service to philosophy and as his system has now acquired the most universal empire that was ever established in philosophy, we shall conceive ourselves fully justifiable in adopting his principles in every subsequent part of this work, where they will assist us in our en quiries.

CHAPTER VIII.

On the Truth of the Copernican System, as improved by Kepler and Newton.

ART. 215. IN deducing the laws by which the motions of the celestial bodies were regulated, as attempted to be shewn in the faint sketch given at the end of the last chapter, it is manifest that Newton must have directed his enquiries agreeably to the principles of the soundest reasoning. His rules of philosophising are, indeed, excellent; and, as they may often be of considerable utility in developing the causes of many natural appearances, they are here inserted.

216. RULE I. More causes of natural things are not to be admitted, than are both true and sufficient to explain the phænomena.

RULE II. Therefore to the same natural effects we must always assign, as far as possible, the same

causes.

RULE III. The qualities of bodies which admit neither retention nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

RULE IV. In Experimental Philosophy, proposi tions collected from the phænomena by induction are to be deemed (notwithstanding contrary hypotheses) either exactly or very nearly true, till other phænomena

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occur, by which they may be rendered either more accurate, or liable to exceptions.

217. The first of these rules is founded upon the principle, that in Nature nothing is done in vain, but all is simple, and there are no traces of superfluous causes of things. The second naturally results from it; for no person who allowed that simplicity reigned in the operations of Nature, would ascribe respiration in man and in animals to different causes; or would feel a difficulty in admitting that the cause of the descent of stones was the same in America as in Europe. The third is consistent with the principle of analogy, agreeably to which the far greater part of Human actions are regulated: by this rule, because extension, divisibility, hardness, mobility, gravity, the vis inertiæ, &c. are found in all bodies which fall under our cognizance, we conclude that they are original and universal properties of all bodies whatever. The fourth rule must, of necessity, be admitted, otherwise arguments by induction might at any time be destroyed by mere hypotheses, and reason would be subdued by fancy.

218. If the truth of the general laws of motion and gravity (as laid down by the authors on mechanics) be granted, and their truth has repeatedly been demonstrated both by theory and by actual experiments; we may, by a natural combination of these laws of motion, with the rules just given, be nearly as fully persuaded of the truth of the Copernican System, with the improvements of Kepler and Newton, as we should be by the most direct demonstration. Perhaps the only objection which can now be urged with any force, against this system, is drawn from the supposed impossibility of the earth's motion; for if once it be admitted that the earth is not fixed and immoveable, the mind will readily assent to every other part of this system. Now, it is manifest from constant observation, that either the earth