66

This illustrious philosopher, who contributed more than any other mortal ever did towards enlarging the domain of human knowledge, appears to have been quite unconscious of any difference between himself and ordinary inquirers of nature. Alluding to his discoveries in a letter to Dr. Bentley, he says, If I have done the public any service this way, it is due to nothing but industry and patient thought." In fact, it was only by the most strenuous contention of mind, and the sternest subjection of the will, that even Newton was enabled to penetrate into the more recondite parts of the system of the world. One of his biographers has remarked * that, during the two years he was engaged in preparing the Principia, he lived only to calculate and think. Oftentimes lost in the contemplation of those grand objects to which it relates, he acted unconsciously, his thoughts appearing to take no cognizance of the ordinary concerns of life. Frequently, when rising in the morning, he would be arrested by some new conception, and would remain for hours seated on his bedside in a state of complete abstraction. He would even have neglected to take sufficient nourishment if he had not been reminded by others of the time of his meals. Speaking of the mode by which he arrived at his discoveries, he said, "I keep the subject constantly before me, and wait till the first dawnings open slowly by little and little into a full and clear light." On another occasion, when some of his friends were complimenting him on the great results he had achieved, he replied: I know not what the world will think of my labours, but to myself it seems to me that I have been but as a child playing on the sea-shore; now finding some pebble rather more polished, and now some shell rather more agreeably variegated than another, while the immense ocean of truth extended itself unexplored before me." What a lesson of humility is here conveyed to those explorers of nature who cannot congratulate themselves on the discovery even of such shells and pebbles as those which adorn the cabinet of the Principia.

་

Newton died on the 20th March, 1727, at the advanced age of eighty-five years. Unlike some of his illustrious predecessors, he continued throughout his long career to receive the honours due to his exalted genius, and his death was deplored as a national calamity. His funeral obsequies were performed with the ceremonies usually confined to persons of royal birth. His body lay in state in the Jerusalem Chamber, and was subsequently interred in Westminster Abbey, his pall having been borne by six peers. A monument was erected over his remains, the inscription upon which concludes with the following suitable words: "Sibi gratulentur mortales, tale tantumque extitisse humani generis decus."+

for this purpose, any more than we should be warranted in inferring from Fermat's theory of Maxima and Minima, or Barrow's Method of Tangents, that either of these mathematicians had discovered the Differential Calculus. The probability is, that in this, as in many other instances, Newton solved the problem merely en passant, attending less to the means than the end to be obtained by them.

Biot. Biographie Universelle.-See also Life of Newton, L. U.K.

+ Let mortals congratulate themselves that so great an ornament of the human race has existed.

CHAPTER III.

Circumstances which impeded the early progress of the Newtonian Theory. Its reception in England. - Reception on the Continent.-Huygens, Leibnitz.-Researches in Analysis and Mechanics.-Their influence on Physical Astronomy.-Problem of Three Bodies.—Motion of the Lunar Apogee.—Clairaut.—Lunar Tables.—Mayer.

NOTWITHSTANDING the multitude of sublime discoveries by which the theory of gravitation was first announced to the world, no attempt was made to develope the views of its immortal founder, during the first half century that elapsed after the publication of the Principia. The seductive speculations of Descartes had already taken a firm hold of men's minds, and had been introduced as a branch of scientific study into the principal universities of Europe. Independently of this circumstance, the profound and intricate reasoning, which Newton was compelled to adopt in the Principia, formed a serious impediment to the early dissemination of his doctrines. As the questions considered in that immortal work were generally of the kind which required the aid of the higher geometry for their complete investigation, only a very small number of mathematicians were qualified to appreciate the evidence upon which the conclusions of the author were founded. The methods also which he employed in expounding his discoveries were almost wholly the creation of his own genius, and it was necessary to study them with deep attention in order to become familiar with their real character. Hence it is easy to understand why the severe doctrines of the Principia continued long to be neglected, while the more accommodating principles of the Cartesian theory met with universal favour.

The country which gave birth to Newton may in some degree be considered an exception to these remarks. The Principia, upon its first appearance, was read with admiration by the most eminent mathematicians of the day; and the sublime truths announced in it were enthusiastically embraced by the more intelligent classes of the community. The university of St. Andrews, in Scotland, has the honour of being the first Academic Institution which admitted the Newtonian theory as a subject of study. In 1690, James Gregory, the celebrated mathematician who was then professor of philosophy in that university, published a thesis containing twenty-five positions, twenty-two of which are said to have formed a compendium of the Principia. The same principles were introduced into the university of Cambridge under the auspices of Dr. Samuel Clarke, the personal friend of Newton. Whiston first expounded them from the chair, in the year 1699. They were also taught at Oxford by Keil, as early as the year 1704.

On the continent, all the great mathematicians were unanimous in their hostility to the Newtonian theory. Huygens, although he generally speaks of Newton in terms of profound admiration, was so strongly impressed with his own peculiar notions of gravity, that he failed to appreciate the force of the reasoning by which the doctrines of his contemporary were supported. He admitted the mutual gravitation of the planets and satellites according to the law of the inverse square of the distance; but he could not be persuaded to extend the same principle to the material molecules of which the several bodies are composed. He had adopted

Descartes' notion of a vortex, to explain the descent of bodies at the earth's surface; but in order to account for their invariable tendency to the centre of the earth, and not to the axis, he supposed the ethereal medium composing the vortex to circulate round the earth in all directions. In accordance with these views, he considered the force of gravity to be equally intense at all equal distances from the centre of the earth; and his investigation of the figure of the latter was founded simply on the statical relation connecting the absolute value of gravity with the centrifugal force generated by the diurnal motion. Alluding in one of his works to Newton's researches relative to the figure of the earth, he says that they are based upon a principle which appears to him inadmissible, inasmuch as it supposes that all the particles of matter attract each other; but this he contends to be an unfounded assumption, which cannot be reconciled with the established laws of mechanics. On another occasion his language, though more cautious, is decidedly hostile to the doctrines of the English philosopher. Newton," says he, "believes that the space between the celestial bodies is void; or at least that the fluid pervading it is so rare as not to affect the motions of the planets; but, if this were true, my explanation of light and gravity would be entirely overthrown." It is interesting to remark the sound views by which this distinguished philosopher was guided when his mind was not wholly under the influence of his own favourite notions. In course of some allusions to the Cartesian theory, he thus expresses his deliberate opinion respecting the merits of that celebrated fiction. "The entire system of Descartes, concerning comets, planets, and the origin of the world, rests upon so weak a foundation, that I wonder how the author of it took the trouble of arranging so many reveries. We should have achieved a great step if we succeeded in forming a clear idea of what really exists in nature, but we are still very far from having attained that end."*

66

Leibnitz and John Bernouilli were equally conspicuous in their opposition to the Newtonian theory. In 1689 Leibnitz published a physical dissertation in the Leipsic acts, in which he explained the motions of the planets by means of an ethereal fluid, somewhat after the manner of Descartes. By the aid of several arbitrary assumptions, he succeeded in shewing the possibility of an elliptic motion in a vortex, and hence deduced the law of the inverse square of the distance; but it is remarkable that, although he was indebted to Newton for the suggestion of this law, he merely incidentally mentions the name of the English philosopher in connexion with it; and appears to be totally ignorant of the Principia, although two years had passed since it was published. "I see," says he that this law has been already deduced by the celebrated geometer, Isaac Newton, as appears from an account of it given in the Leipsic acts, but I am unacquainted with the mode by which he arrived at it."

In France, the Cartesian philosophy, as may naturally be supposed, was for a long time even more popular than in any other country. Cassini, and Maraldi, persisted till their deaths in rejecting the theory of gravitation; and their example was generally followed by contemporary astronomers. The earliest historical recognition of Newton's principles in France, is contained in a memoir by Louville, which appeared in the volume of the Academy of Sciences for the year 1720. The motion of a

Kosmotheoros sive de Terris Celestibus earumque natura conjecturæ. 4to, Hage,

body in an elliptic orbit is there explained by means of two forces-the one a momentary impulse directed along the tangent; the other a continuous force tending towards the focus of the ellipse. Maupertius was the first astronomer of France who undertook a critical defence of the theory of gravitation. In his treatise on the figures of the celestial bodies, which appeared in the year 1732, he compared together the theories of Descartes and Newton, and concluded by expressing a strong opinion in favour of that of the latter philosopher. The person, however, who contributed most to the general diffusion of the doctrines of gravitation in France, was unquestionably Voltaire. In 1738 that celebrated writer published a brief but very luminous exposition of Newton's most important discoveries in optics and astronomy. Being written in a popular style, this little work soon found its way into all ranks of society; and from the time of its first appearance we may date the triumph of Newton's principles over those of his once redoubtable rival.

Although Physical Astronomy may be considered as almost stationary during the period we have been considering, there were causes in silent operation which contributed powerfully to its future developement. Since the time of its invention, by Newton and Leibnitz, the infinitesimal analysis continued to be assiduously cultivated by the most eminent mathematicians of Europe, and was rapidly advancing to a high state of perfection. Without the aid of this powerful instrument of research, it would have been impossible to determine with precision the minute irregularities which take place in the motions of the planets in virtue of their mutual attraction. Newton, in his investigations, had applied the ancient geometry with almost superhuman address; but he appeared to have utterly exhausted its resources, and no other course remained for his successors than to devise other methods of greater fertility and more easy application. Leibnitz, and the two Bernouillis, by means of their brilliant researches in the new calculus, were unconsciously promoting this desirable end. These eminent analysts little imagined, while sneering at the theory of gravitation, that their own labours were destined to become subservient in reconciling its most minute consequences with the observed motions of the celestial bodies, and thereby in placing it for ever beyond the reach of cavil. The researches in mechanics, which engaged the attention of geometers during this period, also exercised a favourable influence in preparing men's minds for the consideration of the great questions relating to the system of the world. This branch of science appeared to offer an unlimited field of original speculation, until D'Alembert*, in 1740, discovered a general principle by means of which every question of motion was immediately reducible to a corresponding one of equilibrium. The statical equations being easily formed, the difficulties attending all such researches henceforth assumed a purely analytical character. It is not improbable that this important generalization had the effect of directing the attention of geometers to physical astronomy, which now presented the most inviting field of study.

The success which attended Newton's efforts to explain the phenomena of the system of the world, by the principle of universal gravitation, was well calculated to encourage his followers to engage in similar researches. Not only did he give a complete theory of the motion of two bodies revolving under the influence of their mutual attraction, but, with un

* Born at Paris, 1717; died in 1783.

rivalled sagacity, he also traced the various disturbing effects produced by the action of a third body upon either of them, and even actually computed several of the more important inequalities in the moon's motion. He did not attempt to investigate the effects of the mutual attraction of the planets, but he clearly perceived that the elliptic motion of each would in consequence be more or less deranged; and he especially remarked that the action of Jupiter on Saturn, when these two planets were in conjunction, attained such a magnitude that it could not be overlooked *. In one important instance Newton signally failed in reconciling his theory with observation. We allude to his attempt to determine the motion of the lunar apogee, on which occasion he obtained a result equal only to half the quantity which observation assigned. This discordance was naturally considered as offering a serious objection to the Newtonian theory; for the evection, which is the largest inequality in the moon's longitude, after the elliptic inequality, depends, to a certain extent, on the motion of the apogee, and therefore it still remained inexplicable by the principle of gravitation.

Euler appears to have been the first geometer who attempted the developement of physical astronomy beyond the point at which the founder of it had left it. In 1745 he investigated the perturbations of the moon, and in the following year he constructed new lunar tables based upon his researches; but, as he employed few observations in determining the maximum values of the inequalities, his tables did not present a marked superiority over those in actual use. About the same time Clairaut† and D'Alembert, two of the first geometers of France, undertook the investigation of the lunar perturbations without any knowledge of each other's intentions.

The Academy of Sciences of Paris having offered their prize of 1748, for an investigation of the irregularities of Jupiter and Saturn, Euler composed a memoir on the subject, which he transmitted to the Academy in the month of July, 1747. The two geometers above mentioned, naturally imagining that their eminent contemporary might anticipate them in their researches, took the precaution of communicating the result of their labours to the Academy before the time appointed for the award of the prize. Clairaut lodged his memoir in the hands of the Secretary on the 9th of November, 1747, and D'Alembert on the 15th of the same month. In all the three memoirs, the perturbing action of the celestial bodies was investigated by an analytical process. Clairaut mentions that he first endeavoured to calculate the lunar inequalites after the manner of Newton; but, having been soon stopped by insuperable difficulties, he decided upon having recourse to analysis alone in all his researches.

The subject, even when so treated, is one of astonishing intricacy; but,

* Newton remarked that when Jupiter and Saturn are in conjunction, the action of Jupiter upon Saturn is to the action of the sun upon the same planet, as I to 211: "whence," says he, "there arises, in each conjunction with Jupiter, a derangement of Saturn's orbit, which is so sensible, as to be the cause of embarrassment to astronomers." Princip., b. iii. prop 13. Euler, however, discovered by analysis that the corresponding derangement of Jupiter is about six times greater, although the action of Saturn upon that planet is to the action of the sun only as 1 to 500. This remark of Euler's," says Laplace, "shows us that we ought not to adopt, but with extreme reserve, the most plausible appearances so long as they are not verified by decisive proofs." Méc. Cél., tome v. p. 302.

+ Born at Paris, 1713; died, 1765.

Born at Basle, 1707; died at St. Petersburg, 1783.