and the distance of the surface from the centre, that is, the radius of the earth; and, squaring these numbers, the inverse proportion would be that of the spaces fallen through, in one second, by the moon, and by a body at the surface of the earth. If, then, this calculated result agreed with the result actually observed, his conjecture would be verified; and the very same force of gravity which causes bodies to fall near the earth, would be that which causes the moon to fall, or, in other words, to be deflected from a rectilinear course, and to describe her orbit about the earth. In this calculation, Newton took for the radius of the earth that value which resulted from the measurement of the length of a degree, according to the determination of Norwood and others, before mentioned, the best known at that time. The result of the calculation did not fulfil Newton's anticipation. Hence, with real, philosophic love of truth, he modified his suppositions to accord with the result: and concluded that, though gravitation is in part the cause of the moon's motion, yet, some other, as yet unknown, cause conspires with it to produce the effect.

On his return to Cambridge, his attention, as we have already seen, was fully occupied with other subjects; and, not having brought his speculation on gravity to any satisfactory termination, he carefully concealed his ideas; and probably dismissed the subject from his thoughts for some time.

Meanwhile we have already noticed the approaches which had been made by several philosophers, but especially by Hooke, towards the theory of gravitation. And it was by some speculations of this eminent man (now secretary to the Royal Society) that Newton's attention was recalled to the subject. In 1679, Newton addressed a letter to him, in reply to some queries proposed by the society, in which he suggested, that, if the earth be really in motion, it would be actually evince by the circumstance, that a body let fall from a great height (since, by virtue of its elevation, it participates in a velocity greater than that of bodies on the surface)

will not fall exactly in a perpendicular line, but will deviate towards the east. Hooke entered upon the subject both experimentally and theoretically: he verified the fact, and improved upon the theory, by showing that the deviation ought to be a little to the south-east, the direction of gravity being (except at the equator) oblique to the earth's axis of rotation. This topic being discussed, led to the further question, in what line the body would descend. Newton, it appears, had inferred that it would be a species of spiral, owing to the resistance of the air. Hooke alleged that in vacuo it ought to be a portion of an ellipse, but he assigned no reason or proof of this. Nor could he do so afterwards, when earnestly pressed, both by Halley and Wren, to give a demonstration. It was about this time that his other speculations, to which we have before referred, on gravity, &c., were communicated to the Royal Society. It is probable that, at this time, Newton had succeeded in investigating some of those dynamical problems respecting elliptic motion, to which we have before adverted. Still, these were mere abstract speculations, the lofty exercises of a mathematical genius of the highest order, but which, as it yet seemed, were not to be recognised in nature; so far, that is, as the accuracy of observation had then extended.

But upon what did the insufficiency of Newton's calculated result depend? Might not the numerical values assumed be open to question? The orbit and distance of the moon were so well ascertained, by the long-continued labours of astronomers, that with respect to them there could be little doubt. Not so the magnitude of the earth. We have already seen how slow was the advance to accuracy, in obtaining this result from the measurement of arcs of the meridian. The more accurate determination of Picard had, however, now been effected; and his recent result became the subject of discussion at a meeting of the Royal Society, in June, 1682. Newton, being present, felt, of course, a degree of interest in the discussion, totally unsuspected by the bystanders.

Noting down Picard's value of the earth's radius, he hurried home, and, having substituted this number in his former proportion, and proceeded a little way in the calculation, he was utterly unable to carry it on, from the overpowering excitement of its anticipated termination. He requested a friend to finish it for him; and the result was, a perfect accordance of the force which acts upon the moon, with the force of gravity at the earth's surface, diminished in the exact ratio of the squares of the distances.

General View of the System.

This one grand result sufficed as a clue to the whole mechanism of the planetary system. Newton now devoted himself to follow up the ideas which this conclusion suggested, in connection with the deductions he had already made with respect to the dynamical laws of central forces. The great inductive laws of Kepler had shown that those relations obtain, at least, to a great degree of exactness, between the distances and periods of all the planets, the forms of their orbits, and the equable description of areas which, on abstract dynamical principles, ought to belong to bodies freely revolving about a common centre of force, from which the diminution of that force takes place, in proportion to the squares of the distances. This accordance was exhibited in the system of the primary planets round the sun, and even yet more palpably in the small systems of satellites round Jupiter and Saturn; and, lastly, but not least, in the motion of the moon round the earth. This last case, in fact, was the key to the others. Equable description of areas, as we have observed, was the test or index of a centre of force. But that centre might be an empty point of space. In the case of the earth and moon, the centre of force was at the centre of the earth; and that particular physical property which we find belonging to particles of matter on the earth's surface, and which we call gravity, or weight,

was proved to be the very same which affects the moon. Its identity was defined by the actual observed diminu.. tion of its intensity as we ascend in the atmosphere, and its precise agreement with the diminished force with which it was proved to act on the moon. Does it, then, asked Newton, act between every two particles of matter throughout the universe? Is there (without any physical hypothesis as to the modus operandi) a real tendency to approach each other, with an intensity inversely as the square of the distance actually existing and operating throughout the planetary system? To this question the accumulating testimony of the observed phenomena, as examined by Newton and his successors, to the present day, has been giving the answer. The force of the argument depends upon the collective proofs which all the facts, in their several ways, minister to the truth of the great principle of gravitation.

In a system of bodies, connected by this sort of attractive influence, and revolving about their common centre of gravity, if one body were considerably greater than the other, the common centre of gravity might fall within the mass of the greater body, and even be situated sensibly in its centre. Thus, the centre of the earth was seen to be, at once situated in the centre of force of the moon's orbit, and, the actual source of the physical force of gravitation. In the same way it followed that Jupiter and Saturn were, in like manner, actual sources of gravitating influence to their satellites, as well as situated in the centres of force of their orbits. In like manner, therefore, the centre of the sun, by virtue of the universal observance of the same law, of the inverse squares of the distances, was the source of gravitating influence to all the planets, as well as the point in space to which the equable description of areas, in all their orbits, pointed as the centre of force. Among the various remarkable applications which Newton made of this truth, none are, perhaps, at first sight, more striking, or even seem more incredible, to a person unacquainted with the subject, than the determination of the actual

densities, or specific gravities, of the matter of which the several planets are composed. Yet the principle on which they are found, is no other than that by which the intensity of the earth's gravitation on the moon is ascertained. Gravity is nothing else than weight, proportional to the quantity of matter; and density is measured by the quantity of matter and the magnitude.

But this same principle of the mutual attraction between all particles of matter throughout the universe, and the law of gravitation, inversely as the square of the distance, and directly proportional to the mass or quantity of matter, was yet found to be applicable to a different class of phenomena, and susceptible of proof from other facts in the system of the world, of which they afforded an explanation. Such were the tides; the general facts of which were investigated by Newton, to a sufficient extent to evince, at least, the general applicability of his principles. He showed that they were due to the joint action of the sun and moon, and even estimated the amount to which the tide ought to rise from theory, supposing its course uninterrupted by continents, and the depth uniform. No theory, it is evident, can accurately agree with facts modified by circumstances so widely different as the actual cases are from these suppositions; but still there is a very near accordance between Newton's result and the average height of the tide in the main ocean.

The waters of the sea having a free motion, which the solid parts of the globe have not, are able to obey the impulse of attraction to a certain extent, limited by their terrestrial gravitation. According to the relative positions of the two luminaries, the resulting effect of their two attractions, conspiring or opposing, produces a greater or less rise in the waters, as each portion comes successively under its influence; and a corresponding rise at the opposite point, since the water on that side, being farther from the sun or moon, is less attracted than the earth, which is thus, as it were, drawn away