Page images
PDF
EPUB

the exactness necessary. Besides, he had neglected the attraction of Saturn, which however bears a sensible proportion to that of Jupiter, since the quantity of matter in that planet is about a third of the quantity in this. The attraction of the Earth also has a perceptible influence on the motion of the comet. Every thing therefore invited the geometricians, who had treated the perturbations of the planets with so much success, to examine those of the comets according to the same principles.

Clairaut was the first, who applied his solution of the problem of three bodies to the motion of comets, and in particular to that of Halley's. In his calculations he employed the attractions of both Jupiter and Saturn. This new problem had it's peculiar difficulties. In the motion of the planets the orbits are but little eccentric, and their inclination with respect to each other is small; but in that of the comets the radius vector varies considerably, and the orbit of the comet may make a very great angle with that of the perturbing planet. These differences necessarily alter the nature of some of the means to be employed in the two cases for arriving at converging formule. Clairaut however surmounted the difficulties attached to the motion of comets, at least in a great measure. Having nearly completed his calculations, he announced at a public meeting of the academy of sciences, on the 14th of november, 1758, that the comet of 1682 would appear in the beginning of 1759, and pass it's perihelion about the 15th of april.

This excited the attention and curiosity of the blic. As soon as the comet was seen, which was

in the beginning of january, the news, adroitly spread through the principal societies in Paris, where Clairaut had many friends, brought his name into the highest repute; the greater part considered him as the sole author of the prediction of the comet's return; and the voice of the learned few, who maintained the rights of Halley, was not heard. Some of Clairaut's pupils, a little too jealous of their master's honour, went so far as to say, that the solution of the problem of three bodies had a particular advantage over all others, which rendered it alone easily applicable to the motion of comets.

This assertion, which Clairaut had the weakness tacitly to support, was an unpardonable injustice toward Euler and d'Alembert. Euler, solely occupied by the question itself, on which he composed an excellent piece, that shared the prize of the Academy of Petersburg in 1762 with one of Clairaut's, took no notice of it. D'Alembert, living in the midst of the vortex of Paris, could not preserve the same indifference. He showed, not only that Clairaut's analytical solution was destitute of the exclusive advantage ascribed to it, but that it was even incomplete, or at least very inconvenient for use, and of little accuracy in certain parts of the orbit of the comet. He even carried his criticism still farther; and, tracing the solution up to it's very principles, he pointed out essential defects in it, even with regard to the motion of the planets. At the same time he treated the problem of comets by a very simple and complete method, free from every objection. Too fond, however, of speculative researches, and averse to the la

[blocks in formation]

borious task of numerical computations, he allowed the glory of rendering a great practical service to astronomy, to be ravished from him on this occasion, as he did on many others.

Clairaut, much less fertile in analytical discoveries, but more dexterous in seizing the means of exciting public applause, of which he was extremely covetous, commonly directed his pursuit toward objects, of which many could appreciate the results, if not the theory. He laboured his performances with the greatest care, and seldom failed to give them all the perfection of which they were susceptible. Accordingly he enjoyed, even during his lifetime, a very high reputation. His gentle disposition, his politeness, and the extreme care he took to wound the vanity of no one, made him greatly sought after in the World. Unfortunately for the sciences he was too compliant in this respect: engaged at supper parties, keeping late hours, and leading a way of life, which he would fain have reconciled with his ordinary labours, but could not, his health was impaired, and he died while yet young, though he was naturally of a good constitution.

D'Alembert, confident of his own superiority, disdained the praise that is echoed by one person after another, without being felt. An excellent man, a tender and compassionate friend, a generous benefactor, he possessed all the essential virtues. The faults, with which he is reproached, arose from a fund of gayety and jocularity, to which he sometimes gave himself up, without listening to the dictates of prudence or moderation. He dismissed with a cold reception the

flatterers,

would say,

flatterers, or troublesome visitors, who came to pay their court to him. I had rather be uncivil,' he than be pestered with such men.' Never asking a favour from a man in power, he reserved to himself the privilege of making them feel the keenness of his wit, when they merited it, and which he was very capable of exercising. With such principles, and such conduct, he made himself a multitude of enemies. Some men of letters, of mean and jealous dispositions, could not forgive him for endeavouring to share their labours and their laurels. They would have respected in him the great geometrician alone; but they endeavoured to pull down a rival author: and as he attained not perhaps the first rank as a writer, envy endeavoured to persuade the world, that he had not done this in any thing else. Such reasoning, however, was flimsy sophistry; and it would have been more just to conclude, that this transition from the thorns of the higher geometry to the flowers of literature marked the flexibility of a genius of the first order, whose principal talent was for the mathematical sciences.

While the learned were employed on the problem of three bodies, d'Alembert resolved another, which required him to create a mechanism in some respects new. The object was, to assign the physical cause, that produces the precession of the equinoxes, and the nutation of the Earth's axis, according to the newtonian system.

Observations had taught, that the axis of the Earth has a circular motion round the poles of the ecliptic,

contrary

contrary to the order of the signs; and that it likewise experiences a libration with respect to the plane of the ecliptic, which is accomplished during one revolution of the lunar nodes. It was known also, that the globe of the Earth is not spherical, but forms an oblate spheroid. Now, if we inscribe in the terrestrial spheroid a sphere, which has for it's diameter the axis of revolution of the spheroid, we shall perceive, that, on account of the reciprocal inclinations of the ecliptic and the equator, the Sun, or Moon, does not exert equal attractions on two corresponding points of the spheroidal crust, which constitutes the excess of the spheroid over the inscribed sphere. Hence it follows, that the force resulting from all the attractions of these two celestial bodies does not pass, unless accidentally, through the centre of gravity of the terrestrial spheroid; and consequently it will occasion the axis of the Earth, to have a certain motion with regard to the plane of the ecliptic. This motion is composed at every instant of the mean retrograde motion of the equinoctial points, and the libration of the axis of the Earth with respect to the plane of the ecliptic. It remains then to be subjected to a precise calculation, at least as far as the imperfection of analysis will allow.

Newton, employing as axioms certain propositions, of which some were not sufficiently evident in themselves, and others deviated a little from the truth, made nevertheless such an adroit and happy combination of the forces by which he supposed the axis of the Earth must be affected, that he found the mean

quantity

« PreviousContinue »