NEWTON'S DEMONSTRATION. 193 demonstration. Furthermore, the elliptical motion had not been considered. Any other curve would, thus far, have served as well as the ellipse, provided its two extremities had shown an equal curvature. The remaining portion of the demonstration, the measurement of the solar action throughout the extent of the orbit, is to be obtained only by transcendental analysis. The process is necessary for carrying on the comparison of the solar action and the centrifugal force; and the theory of the curvature of the ellipse is required. Huyghens made a near approach to the principle of this great process; but it could not be completed without the aid of the differential analysis, of which Newton was the inventor, as well as Leibnitz. By the aid of this analysis, the force of the solar action in all parts of the orbit is easily Newton's estimated, in various ways; and it is found to vary inversely to the square of the distance, and that it is independent of the direction. the same method shows, in accordance with Kepler's third law, that the action varies in proportion to distance alone; so that the sun acts upon all the planets alike, whatever may be their dimensions, their distance only being the circumstance to be considered. Thus Newton completed his demonstration of the fundamental law that the solar action is, in every case, proportionate, at the same distance, to the mass of the planet; in the same way that, by the identity of the fall of all terrestrial bodies in a vacuum, or by the precise coincidence of their oscillations, proof had already been obtained of the proportion between their weight and their masses. We thus see how the three laws of Kepler have concurred in establishing, according to the rules of rational mechanics, this fundamental law of nature. The first shows the tendency of all the planets towards the sun; the second shows that this tendency, the same in every direction, changes with the distance from the sun, inversely to its square; and the third teaches that this action is always simply proportionate, the distance being equal, to the mass of each planet. In accordance with the laws of Kepler, which relate to the whole interior of our system, the same theory applies to the connection between the satellites and their planets. Newton thought it necessary to complete his demonstra I. tion by presenting it in an inverse manner; that is, by determining à priori the planetary motions which must result from such a dynamic law. The process brought him back, as it must do, to Kepler's laws. Besides furnishing some means of simplifying the study of these motions, this labour proved that, whereas, by Kepler's laws, the orbit might have had more figures than one, the ellipse was the only one possible under the Newtonian law. Old difficulty explained. It was once a great perplexity to some people, which others could not satisfactorily explain, that when the planet is travelling towards its aphelion we cannot say that it tends towards the sun. But the difficulty arose out of the use of inappropriate language. The question is, not whether the planet is nearer to the sun than it lately was, but whether it is nearer than it would have been without the force that sends it forward. It is always tending towards the sun to the utmost that is allowed by the other force to which it is subjected. The orbit is always concave towards the sun; and it would evidently have been insurmountable if the trajectory could have been convex. In the same way, when a bomb ascends, its weight is not suspended or reversed: it always tends towards the earth, and is, in fact, falling towards it more rapidly every moment, even if ascending, because it is every moment further below the point at which it would have been but for the action of the earth upon it; and its trajectory is always concave to the ground. Term Attraction inadmissible. I have thus far carefully avoided giving any name to the tendency of the planets towards the sun, and of the satellites towards the planets. To call it attraction would be misleading; and we, in truth, can know nothing of its nature. All that we know is that these bodies are connected, and that their effect upon each other is mathematically calculable. It is by quite another property of Newton's great discovery that this effect is explained, in the true sense of the word,— that is, comprehended from its conformity with the ordinary phenomena which gravity continually produces on the surface of our globe. Let us now see what this property of the discovery is. EXTENT OF THE DEMONSTRATION. 195 If the earth had no We owe a great deal to the moon. satellite, we might calculate the celestial motions by the rules of dynamics, but we could not connect them with those which are under our immediate observation. It is the moon which affords this connection by enabling us to establish the identity of its tendency towards the earth with weight, properly so called; and from this knowledge, we have risen to the view that the mutual action of the heavenly bodies is nothing else than weight properly generalized; or, putting it the other way, that weight is only a particular case of the general action. The case of the moon is susceptible of the most precise testing. The data are known; and by dynamical analysis, the intensity of the action of the earth upon the moon is exactly ascertainable. We have only to suppose the moon close to the earth, with the due increase of this intensity, inversely to the square of the distance, and compare it with the intensity of weight on the earth, as manifest to us by the fall of bodies, or by the pendulum. A coincidence between the two amounts to proof; and we have, in fact, mathematical demonstration of it. It was in pursuing this method of proof that Newton evinced that philosophical severity which we find so interesting in the anecdote of his long delay, because he could not establish the coincidence, while confident that he had discovered the fact. He failed for want of an accurate measurement of a degree on the earth's surface; and he put aside this important part of his great. conception till Picard's measurement of the earth enabled him to establish his demonstration. Extent of the demonstration. The identity of weight and the moon's tendency towards the earth places the whole of celestial mechanics in a new light. It shows us the motions of the stars as exactly like that of projectiles which we have under our immediate observation. If we could start our projectiles with a sufficient and continuous force, we should, except for the resistance of the air, find them the models of the planetary system: or, in other words, astronomy has become to us an artillery problem, simplified by the absence of a resisting medium, but complicated by the variety and plurality of weights.—If our observation of weight on our globe has helped us to a knowledge of planetary relations, our celestial observations have in turn taught us the law of the variation of weight, imperceptible in terrestrial phenomena. Men had always conceived weight to be an inalterable property of bodies, finding that no metamorphosis,-not even from life to death,-made any change in the weight of a body, while it remained entire. This was the one particular in which men might suppose they had found the Absolute. In a moment, the Newtonian demonstration overthrew this fast-rooted notion, and showed that weight was a relative quality,—not under the circumstances in which it had hitherto been observed, but under the new one,- the position of the observed body in the system,—its distance from the centre of the earth. The human mind could hardly have sought out this fact directly: but, once revealed in the course of astronomical study, the verification easily followed; and experiments on our globe, in the vertical direction, and yet more in the horizontal, have established the reality of the law, by experiments too delicate, from the necessity of the case, to be appreciable, if we had not known beforehand what differences must be found to exist. Term Gravitation unobjectionable. It is to express briefly the identity between weight and the accelerating force of the planets that the happy term Gravitation has been devised. This term has every merit. It expresses a simple fact, without any reference to the nature or cause of this universal action. It affords the only explanation which positive science admits; that is, the connection between certain less known facts and other better known facts. Since the creation of this term, there has been no excuse for the continued use of the word attraction. It is desirable to avoid pedantry in language; but it is of high importance to preserve pure the positive character of so fundamental a conception as this, by using a term which expresses exactly what we know, and dismissing one which assumes what is purely fanciful, and wholly incorrect. Attraction is a drawing towards. Now, when we draw anything towards us, the distance is of no importance: the same force draws the same body with equal ease three feet or thirty feet, which is directly contradictory to the facts of gravitation. Our business is with PRIMARY AND SECONDARY GRAVITATION. 197 the fact of the action, and not at all with its nature. It was the use of this metaphysical term, it now appears, which occasioned the opposition that the Newtonian theory encountered so long, and especially in France. Descartes had, by laborious efforts, banished the notions of occult qualities, which he perceived to be so fatal to science; and in this theory of attraction, his followers saw a falling back into the old metaphysical delusions. We perceive this in the writings of John Bernouilli and Fontenelle: and it appears that the clear and positive scientific intellect of France did good service in stripping off from the sublime discovery of Newton the metaphysical appearance which obscured its reality for a time. One more consideration remains to be ad- Gravitation is verted to. We have regarded the heavenly that of molebodies thus far as points, without reference cules. to their forms and dimensions. But as it is proved that the intensity of the action of the sun on the planets, and of the planets on their satellites, is proportioned to the mass of the body acted upon, it is clear that the force operates directly only on molecules, which are all independently affected by it; and equally, their distance being the same. The gravitation of molecules is therefore the only real one; and that of masses is simply its mathematical result. In the mathematical study of motions however it is necessary to have a conception of a single force, instead of such an infinity of elementary actions: and hence arises that preliminary part of celestial mechanics which consists in compounding in one result all the mutual gravitation of the molecules of two stars. Newton founded this portion, with all the rest; and the two theorems which he established for the purpose still remain the commonest expression of this important theory. He proved that if the stars were truly spherical, and their strata were homogeneous, the gravitation of their particles would be so balanced that the bodies might be treated as points, in the study of their motions of translation. But the irregularity of their forms, however slight, must be considered in the theory of their rotations, to which these theorems cease to be applicable. For any other form than the sphere, the problem becomes very complicated; and the analytical difficulties can be |