pendence with which he appropriated the doctrines of geometry. He belongs to the number of those special mathematical geniuses which the seventeenth century-as though a universal development of European humanity had pressed in that direction-produced in such surprising wealth. A nearer view of his achievements shows that almost everywhere mathematical work, marked alike by genius and application, is the active spirit that inspires everything. As early as 1664, Newton discovered his theory of fluxions, which he published twenty years later, when Leibniz was threatening to rob him of the honour of the discovery. Almost as long a time he carried with him the idea of gravitation; but while fluxions were immediately turned to brilliant account in his calculations, the proof of the unity between the falling motion of bodies. and the attraction of the heavenly bodies still needed a mathematical process of which the premisses were for some time unattainable. The calmness, however, with which Newton so long kept both great discoveries to himself, that he might make quiet use of the one, and that the other might ripen, deserves our admiration, and strikingly reminds us of the similar patience and fortitude of his great predecessor Copernicus. But in this also can we discern a great trait of Newton's character, that even after he was quite satisfied as to his discovery of the connection between the law of falling bodies and the elliptic orbits of the planets, and had the full calculations before him, he did not make a separate announcement of it, but incorporated it in his great work the " Principia" (1687), which treated so comprehensively all the mathematical and physical questions connected with gravitation, that Newton could justly give it the proud title of "The Mathematical Principles of Natural Philosophy."

Yet more important was another trait of a similar nature. We have already pointed out that Newton was very far indeed from perceiving in attraction, that fundamental force of all matter,' as the discoverer of which

he is now so much praised. Yet it is true that he had made the theory of some such universal attractive force necessary, by laying completely aside his unripe and vague conjectures as to the material cause of attraction, and kept strictly to what he could prove-the mathematical causes of the phenomena, supposing that there was some principle of approximation operating inversely as the square of the distance, let its physical nature be what it may.

We here reach one of the most important turning-points in the whole history of Materialism; and in order to set it in its true light, we must interject a few remarks on the real service rendered by Newton.

We have in our own days so accustomed ourselves to the abstract notion of forces, or rather to a notion hovering in a mystic obscurity between abstraction and concrete comprehension, that we no longer find any difficulty in making one particle of matter act upon another without immediate contact. We may, indeed. imagine that in the proposition, 'No force without matter,' we have uttered something very Materialistic, while all the time we calmly allow particles of matter to act upon each other through void space without any material link. From such ideas the great mathematicians and physicists of the seventeenth century were far removed. They were all in so far still genuine Materialists in the sense of ancient Materialism, that they made immediate contact a condition of influence. The collision of atoms or the attraction by hook-shaped particles, a mere modification of collision, were the type of all Mechanism and the whole movement of science tended towards Mechanism.

In two important points the mathematical formula of the laws had been reached before the physical explanation-the laws of Kepler, and the law of fall, discovered by Galilei; and thus these laws troubled the whole scientific world with the question of the cause-naturally

the physical, the mechanical cause-the cause to be explained from the collision of small particles—of the movement of falling and the motion of the heavenly bodies. In particular, for a long time before and after Newton, the cause of gravitation was a favourite subject of theoretical physics. In this universal sphere of physical speculation, the thought of the essential identity of both forces naturally lay very near; there was indeed, in the axioms of the Atomism of that time, but one single fundamental force in all the phenomena of nature! But this force operated under very various circumstances and shapes, and even then men had begun to be content no more with the bare possibilities of the Epikurean physics. They demanded the construction, the demonstration, the mathematical formula. In the consequent working out of this demand lies Galilei's superiority to Descartes, that of Newton and Huyghens to Hobbes and Boyle, who still found satisfaction in long-spun explanations of how the thing might be possible. In consequence of this effort on the part of Newton, it now again happened, and for the third time, that the mathematical construction went ahead of the physical explanation, and on this occasion the cir cumstance was to attain a significance unsuspected by Newton himself.

And thus that great generalisation, celebrated by its connection with the story of the fall of the apple,57 was by no means the most important feature in Newton's discovery. Apart from the influence of the theory we have just mentioned, we have here again sufficient traces to show that the idea of an extension of gravity into space was not far away. Nay, the thought had already occurred 57 Comp. Whewell's Hist. of the Induct. Sci., ii. 166 foll. From this it appears that so much may be taken from Newton's own communications, according to a tolerably credible tradition coming through Pemberton and Voltaire-that so early as the year 1666, in his twenty-fourth year,

as he sat alone in a garden, he reflected upon gravity, and inferred that as gravity still operates at the greatest distances from the centre of the earth of which we have any knowledge, it must therefore influence the motion of the moon.

to the ancients that the moon would fall to the earth it it were not kept suspended by the force of its revolution.58 Newton was acquainted with the composition of forces,59 and so it lay directly in his path to carry that idea further into the theory-that the moon does actually fall towards the earth. From this falling motion and a forward motion in the direction of the tangent results the orbit of the moon. Regarded as the personal achievement of a great scientific power, the thought here was less important in itself than the criticism brought to bear upon the thought. Newton, as is well known, laid his calculations aside, because the result gave no exact agreement with the motion of the moon.60 Without wholly giving up his main notions, Newton seems to have sought an explanation of the difference in the operation of some other influence to him unknown; but as he could not complete his demonstration without an exact knowledge of this disturbing force, the whole matter remained for a time in abeyance. Later, as all the world knows, Picard's measurement of the degree (1670), proved that the earth was greater than had hitherto been supposed, and the correction of this factor supplied the desired accuracy to Newton's calculations.

59 Comp. Dühring, Krit. Gesch. der allg. Principien der Mechanik, Berlin, 1873, p. 175. Ib. p. 18o foll., are noteworthy expressions of Copernicus and Kepler. See moreover in Whewell, Hist. Induct. Sci., ii. 150, the views of Borelli. It must also be observed that Descartes in his Vortical Theory found also the mechanical cause of gravity; so that the idea of the unity of both phenomena was at that time commonly taught. Dühring justly observes that the true problem was to bring the vague idea of an approximation or 'full' of the heavenly bodies into agreement with Galilei's mathematically definite notion of the fall of terrestrial bodies. These forerunners constantly show how near was the actual syn

thesis, and we have shown in the text how Atomism must have furthered this synthesis. But Newton's merit lay in this, that he turned the universal thought into a mathematical problem, and, above all, that he effected a brilliant solution of the problem.

59 In this respect Huyghens especially had done very much by way of preparation, while the first beginnings of the correct theory are here again to be traced to Galilei. Comp. Whewell, Hist. Induct. Sci., ii. 80 foll.; Dühring, p. 163 foll. 188.

60 Whewell, Hist. Induct. Sci., ii. 168, with which, however, must be compared, as to the story of the beginning of the calculation, Hettner, Literatarg, d. 18 Jahrh., i. 123.

Of great importance, not only for this demonstration, but also especially for its far-reaching consequences, was Newton's assumption that the gravitation of a planet is only the sum of the gravitation of all its individual portions. From this immediately flowed the inference that the terrestrial bodies gravitate towards each other; and further, that even the smallest particles of these masses attract each other. So arose the first foundation of molecular physics. But here the generalisation itself lay so near that it was within immediate reach of every supporter of the Atomistic or corpuscular theory. The effect of the whole could not be other than the sum of the effects of its constituent portions. If we suppose, however, that even Atomism must have made this doctrine impossible, because it bases everything upon the collision of the atoms while it is here a question of attraction, we only confound once more what, since Kant and Voltaire, has been currently called the doctrine of Newton with Newton's real view of these things.

We must here recollect the modification of Atomism made by Hobbes. The 'relativity' of the conception of an atom bore its physical fruits in the more decided distinction between the ether and 'ponderable' matter. There can be bodies, according to Hobbes, which are so small as to be incognisable by our senses, and which in a certain relation may justly be termed 'atoms.' At the same time, others may be supposed to exist by the side of these, which, compared with them, are microscopically small, and by the side of these again others still smaller, and so on to infinity. Physics begin by using the first member of this chain, in order to resolve the original constituents of all bodies into heavy atoms; that is, atoms subject to gravitation; and then to assume other particles, infinitely finer atoms, without weight, and yet material, subject to the same laws of collision, of motion, and so on. In these was sought the cause of gravity, and no prominent physicist at that time thought of any other kind of