Having now endeavoured to do justice to the memory and the labours of the illustrious dead, whose names will be long preserved in the annals of discovery, we shall now attempt to give a short view of the exertions of the living, of those great men to whom science still looks with confidence for the extension of her empire.
The celebrated M. de la Grange, who has outlived most of his contemporaries, was born at Turin on the 25th of January 1736, and has enriched astronomy with some of the most splendid discoveries of which it can boast. This illustrious mathematician began his career by two profound papers on the vibration of musical strings, which were published in the memoirs of the Academy of Turin. When he was only 28 years of age, he carried off the prize offered the Academy of Sciences in 1764, for the best dissertation on the equality between the period of the moon and her rotation about her axis, and on the remarkable coincidence observed by Cassini between the nodes of her orbit and her equator. He found that, in consequence of the elongation of the diameter of the moon which is turned towards the earth, she is subject to an oscillation round her axis, which tends constantly to produce an equality between her primitive rotation and her periodical revolution. The theory of the satellites of Jupiter occupied also the at tention of La Grange, and he again obtained the prize of 1766, of which this theory was the subject. In ap plying the problem of three bodies to this point, by con sidering only the action of one satellite upon another, when revolving round Jupiter, as Bailly had done, the omission of the action of the other two satellites must lead to very inaccurate results. La Grange, however, has considered the question in its most general aspect : He has taken into account the mutual derangements of all the four satellites ; and has in fact resolved a problem of five bodies. He proposed to determine, from these derangements, the masses of the satellites ; and he has pointed out the limits between which these masses must be comprehended. The perturbation of the motion of comets was the subject of the prize given by the academy in 1780, and Llk Grange had the honour of obtaining it. The inequalities of Jupiter and Saturn, which had per plexed both Euler and La Grange, conducted the latter to one of the greatest and most interesting discoveries. By a new method, equally simple and rigorous, he has demonstrated, that the reciprocal action of the planets, and the deviation of their figures from the spherical form, can never produce any alteration in their mean motions or mean distances. All the inequalities in the
system are merely periodical. The planetary orbits change their inclination. Their eccentricities vary within certain limits ; but the greater axes of their orbits, and their periods round the sun, remain perpetually the same. Amid the multiplied derangements which affect the bodies of the planetary system, the general harmony is always apparent ; and the little disorders which have so long perplexed the ingenuity of astronomers, seem only to evince the permanence and stability of the whole. What a sublime view of the great arrangements of the universe ! What an affecting proof of the goodness and wisdom of its Author ! The contemporary of La Grange in this brilliant ca re.cr of discovery was the celebrated La Place,—a name which in this country we have been taught to calum niate, but which every friend of science will associate with her most noble efforts, when the days of prejudice and illiberal sentiment are past. The complete solution of the problem of the tides, which had been discussed with such ability by Euler, Maclaurin, and Bernoulli, was reserved for La Place. Regarding every particle of water as influenced by three forces, the action of the earth, the sun, and the moon, and as impelled by the •earth's diurnal motion, he has determined the nature of the oscillations excited in the fluid mass. He found the mean depth of the sea to be four leagues, and he has determined the altitude of the tides in different lati tudes, and in different positions of the sun and moon ;— thc difference between the consecutive tides,—and the time which elapses between high water and the culmi nation of the sun and moon. The great coincidence between this theor% and observations made at Brest, is an additional proof, if any were wanted, of the theory of universal gravitation. The curious subject of the equi librium of the sea has also occupied the attention of La Place, in order to discover whether any motion commu nicated to the mass of water which surrounds our globe will finally subside, or increase to such a magnitude as to raise the waters to the top of the highest mountains. From this investigation it appears, that the undulations in the ocean continually tend to diminish, and that the equilibrium of the sea is stable, if the density of its wa ters is below the mean density of the earth.