CHAPTER I.

Early notions of Physical Astronomy,-Newton.-His first Researches on the subject of Gravitation.-Cause of his failure.-Correspondence with Hooke.-Resumption of his previous Researches.-Law of the Areas.-Motion of a Body in an Elliptic Orbit, the force tending to the focus.-Picard.-His Measurement of an Arc of the Meridian.Complete success of Newton's Investigation relative to the Action of the Earth upon the Moon. - His establishment of the principle of Gravitation in its widest generality.— Consequences he derived from it.-The Principia.-Account of the circumstances connected with its publication.-Halley, Hooke, Wren.-Synopsis of the subjects treated of in the Principia.—Laplace's opinion of its merits.

ATTEMPTS were made at an early period in the history of astronomy to account for the motions of the celestial bodies by means of some common principle. The Greeks, as might be expected, were the first people who invented a physical theory of the heavens; but the result of their speculations in this instance was totally unworthy of their high intellectual character. Conceiving that the constant succession of phenomena in the same order could only be effected by means of some material agency, they supposed each of the planets to be inclosed in a solid sphere of transparent structure, having the earth situate in the centre. The motion of the planet was then supposed to be accomplished by the revolution of the entire sphere in the direction of the planet's real motion, and with a velocity corresponding to its periodic time. In order to account for the various irregularities of its motion, each of the planets was provided with several spheres, which modified each other's effects; and at an immense distance beyond the planetary apparatus was situated the primum mobile, or sphere of the starry heavens, which revolved from east to west in twenty-four hours, carrying along with it all the fixed stars. It certainly affords a remarkable illustration of the proneness of the human mind to ascend from the phenomena of nature to some ulterior cause, that this monstrous theory should have commanded the assent of the learned world until the close of the sixteenth century. Aristotle introduced it into his system of philosophy, and by this means it came to be generally adopted as part of the ancient astronomy. We must not, however, confound this offspring of the imagination with the epicyclical theory of Hipparchus, which, although involving certain gratuitous principles, was notwithstanding framed in accordance with observation. The latter, in fact, was a pure mathematical theory, devised for the purpose of representing the motions of the planets, without reference to the physical cause of those motions; and, although incomplete in its structure, in so far as it took no cognizance of the distances of the planets, still, as it could be submitted to a rigorous calculus, it held out to astronomers the prospect of arriving at the true system of nature by means of a comparison of its results with those of observation. The history of the two theories presents us, indeed, with an instructive lesson of the value of an hypothesis which contains some elements of truth as contrasted with the inanity of a mere fiction of the mind. The mathematical theory, besides affording admirable scope for the inventive powers, had the advantage of enabling astronomers throughout a long course of ages to predict the places of the planets with tolerable accuracy; and, finally, was instrumental in conduct

ing Kepler to a knowledge of their real motions: the physical theory, on the other hand, continued during an equal period to mislead men's minds, without possessing the redeeming merit of forming a subject of intellectual exercise; and, when it was at length overthrown by the invincible force of reasoning based upon facts, it disappeared without leaving a single trace of its existence behind.

It is difficult to ascertain what were the real opinions of Copernicus relative to the physical constitution of the heavens. While engaged, however, in establishing the Pythagorean system of the world, he was led to use a remark which may be said to contain the earliest notion of the principle of gravitation. The Aristotelians had asserted that heavy bodies, to use their own phraseology, naturally tend towards the centre of the universe, and as observation showed that a similar tendency existed towards the centre of the earth, they hence concluded that the earth must be placed immoveable in the centre of the universe. Copernicus, however, remarked that the parts of matter had a natural appetency to congregate together and unite in the form of spheres, and that the constant tendency of bodies towards the centre of the earth was merely a sensible manifestation of this inherent quality of matter.

Tycho Brahé was not endowed with qualities favourable to speculation, but he deserves to be mentioned in the history of physical astronomy, on account of the effect of his researches in leading to the overthrow of the ancient theory of solid orbs. By means of a series of careful observations on the comet of 1577, he discovered that it was at least three times more remote from the earth than the moon is; whence it followed, since comets traverse the celestial regions in all directions, that the heavens could not be composed of a solid mechanism such as the Aristotelians had imagined.

Gilbert, an English philosopher of great merit, who flourished towards the close of the sixteenth century, was one of the first persons who arrived at general notions on the subject of gravitation. His researches on magnetism, pursued in strict accordance with the principles of the inductive philosophy, were much esteemed by Kepler and Galileo, both of whom profess to have been greatly indebted to him for their views on that subject. In his treatise on the magnet, published in 1600, he explains the influence of the earth upon the moon by comparing the former to a great loadstone. He announces his opinions, however, much more explicitly in his posthumous work on the "New Philosophy," which first appeared about the middle of the seventeenth century. In this treatise, he asserts that the earth and moon act upon each other like two magnets; but he considers the influence of the earth to be greater than that of the moon, on account of its superior mass. It is important to note his explanation of the mode in which the two bodies affect each other. "It is not," says he, "so as to make the bodies unite like two magnets, but that they may go on in a continuous course." In another part of the same work, he ascribes the tides partly to the influence of the moon. "The moon," says he, "does not act on the seas by its rays or its light. How then? Certainly by the common effort of the bodies, and (to explain it by something similar) by their magnetic attraction." He seems to have been more perplexed in accounting for the ebb of the tide than for its flow. In order to explain this part of the phenomenon, he assumes

⚫ De Mundo Nostro Sublunari, Philosophia Nova, Amstelodami, 1651.

that, besides the waters of the ocean, the earth contains subterranean humours and spirits, which are drawn out by the attraction of the moon; and, when that body has retired, are then absorbed again into the bowels of the earth. "The moon," says he, "attracts not so much the sea as the subterranean spirits and humours, and the interposed earth has no more power of resistance than a table or any other dense body has to resist the force of a magnet."

The preceding remarks of Gilbert contain unquestionably one of the earliest traces which is to be found among the writings of modern authors, of the notion of an attractive force acting between the bodies of the solar system. The moon's attractive influence upon the earth is naturally enough suggested by the phenomenon of the tides; but the influence of the earth upon the moon is mixed up with a great deal of error and confusion. It appears to him to be indicated not by the revolution of the moon in a curvilinear orbit round the earth, but by her accompanying that body in a continuous course round the sun. In fact the principle of terrestrial attraction is suggested by the notion of the earth dragging the moon along with her in her annual orbit. Finding himself utterly unable to account for the mutual attraction of the earth and moon, without the continual approach and ultimate union of the two bodies, he attempts to get rid of the difficulty by shifting his hypothesis, or, in other words, by asserting that the effects resulting from the mutual influence of the two bodies is not similar to the effects of magnetic attraction. Although Gilbert, therefore, deserves much credit for the sagacity with which he recognised, to a certain extent, the principle of gravitation, his ideas of it are so vague and inconsistent, that his speculations cannot be said to rise above the merit of mere conjectures.

Kepler, in the introduction to his " Astronomia Nova," published in 1609, announces the mutual gravitation of matter in very remarkable terms. He asserts, as Copernicus had already done, that bodies do not tend towards the centre of the earth, because it is the centre of the universe, but because it is the centre of a round body of the same nature with themselves. If two stones were situated in space beyond the influence of a third body, they would approach towards each other like two magnetic needles, and would meet in an intermediate point, each passing through a space proportional to the comparative mass of the other. If the moon and earth were not retained by their animal force, or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon would fall to the earth through the other fiftythree parts, and they would there meet. If the earth should cease to attract the waters to itself, all the waters of the sea would be raised, and would flow to the body of the moon.

These remarks are indeed very striking, and show how profoundly their illustrious author could penetrate into the secrets of nature; but we should not be justified in attaching to them all the importance due to a distinct. recognition of the principle of gravitation. In his ideas and reasoning he coincides with Gilbert, except that he extends the principle of gravitation to the whole material universe. The difficulty which Gilbert experienced in accounting for the constant separation of the moon and earth, notwithstanding their mutual attraction, occurs with its full force to Kepler. The latter, however, gets over it not as Gilbert had done, by assuming a principle inconsistent with his previous ideas on the subject, but by supposing the terrestrial attraction to be neutralized by the animal force

C

of the moon or some other equivalent. It is clearly possible to establish any principles whatever, if we are at liberty to have recourse to such assumptions in support of our reasoning. It will be remarked that Kepler does not seek to explain how the motion of the moon in her orbit is continually kept up; he doubtless assigned this task to the animal force. which regulated the distance between the two bodies. The difficulty of accounting for the motion of a body in its orbit, by means of a centripetral force, occurs to him perpetually throughout the Astronomia Nova in course of his speculations on the physical cause of the planetary motions. In attempting to explain the phenomena of these motions by means of a force emanating from the sun, he is now compelled, like Gilbert, to introduce a principle totally at variance with his previous notions of gravitation; for he imagines that the planet requires to be continually impelled in its orbit by the solar force. To meet this view of the case, he supposes the sun to revolve from west to east, upon an axis perpendicular to the plane of the ecliptic, and to send forth continually magnetic rays, which attract the planet in a direction transverse to the line joining it and the sun.

It is hardly necessary to state that this opinion of the planets being kept revolving by a force continually whirling them round in their orbits is not only at direct variance with the character of a gravitating force, but is also inconsistent with the fundamental principles of motion. It must be admitted that there was more of truth in Ross's words than he could perhaps justly take credit for, when he asserted that "Kepler's opinion, that the planets are moved round by the sunne, and that this is done by sending forth a magnetic virtue, and that the sunbeames are like the teethe of a wheele taking hold of the planets, are senselesse crotchets fitter for a wheeler or a miller than a philosopher."*

Kepler might have formed more accurate ideas on the physical cause of the planetary motions, if the science of mechanics had been more advanced in his time; but it is surprising that, although he constantly strove throughout his researches on the planet Mars, as detailed by him in the Astronomia Nova, to connect the varying motion of the planet with a force emanating from the sun, he nowhere speculates so judiciously on that force as in the introduction to his work; and at the conclusion of his labours he inspires no more confidence in his reader respecting the reality of the force than he did at the commencement of them. In fact, it is to the extraordinary tenacity with which he clung to the idea of a solar force acting somehow on the planets, and his strong conviction that their motions were regulated by fixed laws, that we must ascribe the brilliant result of his researches, rather than to any clear perception either of the nature of the force or of its mode of operation.

It is difficult to say whether Gilbert or Kepler was first led to speculate on the physical theory of the celestial motions. Kepler's earliest notions on the subject are to be found in his "Mysterium Cosmographicum," which was published in 1596. Gilbert's "Treatise on the Magnet" appeared in 1600, and he died in 1608, leaving behind him his posthumous work, which was published only in 1651. It is clear from the nature of Gilbert's ideas, which turn entirely upon the magnet, that they could not have been suggested to him by Kepler's speculations. It is equally certain that the latter was not indebted to any person for his opinion

The New Planet no Planet, or the Earth no Wandering Star, 4to., London, 1646. See also Life of Kepler.-L. U.K.

relative to the existence of some physical principle directing the motions. of the planets. When, however, he attempted at a subsequent period of his researches to devise a consistent theory of the solar force, he adopted the views of Gilbert by assuming it to be a modified form of magnetism. This appears from his great work, the "Astronomia Nova,"* wherein he cites the opinion of Gilbert while proceeding to frame his theory of a whirling force.

Galileo, by means of his admirable researches on mechanics, contributed in a high degree towards the formation of more distinct ideas on the subject of curvilinear motion. The principle of mutual gravitation does not seem, however, to have found any favour with him, for he censures Kepler on account of his opinion relative to the attraction of the earth by the moon. He admitted the attraction of the moon by the earth, but he by no means formed a distinct conception of the mode in which the force of gravity in this case operates. "The parts of the earth," says he, "have such a propensity to its centre, that when it changes its place, although they may be very distant from the globe at the time of the change, yet must they follow. An example similar to this is the perpetual sequence of the Medicean stars, although always separated from Jupiter. The same may be said of the moon obliged to follow the earth."

The earth's attraction is here evidently inferred from the moon constantly attending her in her annual orbit round the sun. It might, however, be concluded from the same phenomenon, with equal shew of reason, that the moon attracts the earth; for the moon cannot be said to follow the earth any more than the earth can be said to follow the moon, since, in fact, both bodies, while revolving round the sun, revolve also continually round their common centre of gravity. The grand fact which leads to the establishment of the action of the earth upon the moon, consists in the revolution of the latter in a curvilinear orbit which is concare with respect to the earth. It has been sometimes said that Kepler only required a more complete knowledge of the laws of motion in order to have demonstrated the existence of the principle of gravitation. Here, however, we have a philosopher equal in sagacity to Kepler-who had successfully analyzed the phenomenon of curvilinear motion in one of its manifestations at least, and who moreover had access to the opinions of Kepler on the subject of gravitation; still, notwithstanding all these advantages, he failed to recognise the existence of an attractive force, either in the motion of the moon round the earth, or in the motions of the planets round the sun. This circumstance ought to render us cautious in attaching an undue value to mere sagacious surmises unsupported by legitimate proof, and in ascribing to individuals any credit for discoveries which are not the actual result of their own labours.

We do not propose to make any further allusion to Descartes' theory of vortices, beyond the few words we have already said respecting it in the introduction to this work. No doubt, we think, can exist that this celebrated fiction exercised a most pernicious influence in retarding the progress of sound mechanical ideas relative to celestial physics. Like the theory of solid orbs, it at length utterly disappeared before the advancing light of true science, after continuing for nearly a century to

• Astronomia Nova, cap. xxxv., p. 176.

+ Dialago sopra i due Massimi Sistemi del Mondo.-Firenze, 1632. See also Life of Galileo.-L. U. K.