CHAP. II., 2.] 



PHYSICAL ASTRONOMY LAGRANGE. 



15 



quainted. The range of insight which man has ac- 

 quired into the past and future history of the uni- 

 verse throughout periods, compared to which, the 

 whole existence of his species is but a span, enhances 

 our admiration of the reasoning power which can 

 attain to knowledge so high and excellent. And the 

 sublimity of the contemplation is increased when we 

 recollect that these recondite truths are all conse- 

 quences of a law so simple as that of gravity. Ob- 

 servation will reveal only to a late posterity the se- 

 cular modifications of the planetary orbits which geo- 

 metry now predicts to us. Some of the ellipses will 

 elongate, whilst others tend to become circles ; their 

 planes will vary in inclination, but ultimately be 

 stayed within the limit which human sagacity had 

 predicted myriads of years before. "These," says a 

 French analyst, "are the pendulums of eternity, which 

 beat ages whilst ours beat seconds." And amidst 

 all these variations, subject to law and to impass- 

 able limits, the Major Axes of the orbits preserve a 

 stedfast uniformity, or are subject only to transient 

 fluctuations ; and thus permanence arises in the midst 

 of change, and the perfection of the system is demon- 

 strated by the very nature of the disturbances which 

 seemed at one time inevitably to limit its duration. 

 (55.) It remains to add, in closing this interesting 



Poisson's discussion, that Lagrange himself had not quitted the 

 toe theory ^ e ^ t> e f re his able disciple and follower, Poisson, 

 pursued the inquiry of the stability of the system, 

 and the permanency of the major axes particularly, 

 to a degree of approximation not before attempted. 

 He included the perturbations of the second order, 

 or those which arise by correcting the elements for 

 the disturbances first found, and including the effects 

 of the correction in the modification of the perturba- 

 tions themselves. These also are subject to the 

 same laws as found by Laplace and Lagrange for 

 lower degrees of approximation ; and as MM. de 

 Pontecoulant and Leverrier have confirmed the result 

 (at least for all the larger planets of the system), we 

 may conclude it to be a truth as firmly established as 

 any negative fact can be, that our system is arranged 

 for a duration apparently indefinite ; that if the planets 

 cease to roll, and the sun and moon to do their 

 office in enlightening the world, it must be in all 



(56.) 



probability by an interposition of Almighty power, 

 as direct and immediate as the creative energy by 

 which they were launched into space, and (our earth at 

 least) peopled with successive racesof animated beings.' 



We have, in the commencement of this section, 

 disclaimed the intention of entering at large upon the Lagrange's 

 history of Lagrange' s discoveries. They fell more pro- otn .!f 

 perly under the scope of the preceding Dissertation, 

 and an able summary and enumeration of his writings 

 by no less competent a person than Dr Thomas Young 

 will be found in the alphabetical part of this Encyclo- 

 paedia. I will only add, that while scarcely a topic 

 in physical astronomy, or in pure mathematics , failed 

 to receive important additions from his pen, his 

 memoirs on the Libration of the Moon, his solution 

 of several problems of Sound and vibrating strings, 

 and his methods of computing the perturbations of 

 Comets, are amongst his contributions to science, 

 most vividly remembered and most justly admired as 

 models of analytical ability. He himself is stated 

 to have preferred, amongst all his papers, one in the 

 Turin Memoirs of 1784, on the Integral Calculus. 2 



With reference to the Lunar Libration, Lagrange (57.) 

 confirmed the singular conclusion of Newton, that the Libration 

 moon is a spheroid, having three unequal axes, the 

 longest of which is always approximately directed to 

 the earth, and the shortest is her axis of rotation. 

 In consequence of this, the moon, of necessity, re- 

 volves on her axis in the exact time that she circu- 

 lates round the earth (supposing that at any time 

 these periods were nearly, though not absolutely, 

 coincident), and is subject (as Newton had divined) 

 to a species of oscillation upon her axis, owing to the 

 line of the earth's attraction not always coinciding 

 (in consequence of the moon's irregular motion in 

 longitude) with the moon's greatest diameter. This 

 constitutes a physical libration, as inequalities in lon- 

 gitude, by enabling us to see more or less of the 

 lunar hemisphere diametrically opposed to us, con- 

 stitute an optical libration, or apparent to-and-fro 

 motion on her axis. In this investigation Lagrange 

 first used the combination of D'Alembert's Principle 

 with that of Virtual Velocities, afterwards fully ex- 

 panded in the Mecanique Analytique? 



Lagrange was happy in passing his days with (58.) 



1 No reasonable doubt exists as to the stability of the planetary system to which our earth belongs, as it is at present consti- 

 tuted. To what extent the laws of order which we observe in it might be transgressed with impunity, it is more difficult to say. 

 The investigations of Laplace and Lagrange assume the motion of the planets in one direction, and their moderate excentri- 

 cities and inclinations, as conditions of the guarantee of stability. But it does not appear by any means certain that all these 

 conditions are essential, and consequently the argument which has been sometimes employed, that the concurrence of many in- 

 dependent circumstances were requisite to the stability of the system, is at least incomplete. Compare Laplace, Systdme du 

 Monde, edit. 1824, vol. ii., p. 29, and Herschel's Outlines of Astronomy, art. (669). 



2 It is No. 17 in the enumeration of his papers in the article LAGBANGE in the Encyclopaedia. 



3 Very recently (1854), M. Hansen of Gotha, a most eminent living authority, has somewhat modified the received opinion M. Hansen 

 respecting the moon's figure. He finds that the presumed ellipticity of the moon in the direction of the radius of her orbit is on the 

 not justified by observations, which ought to show a slight variation in her horizontal diameter when the libration presents to moon 'ft 



us our satellite in a slightly varied aspect. And he infers from an elaborate investigation of the lunar observations, that her figure, 

 centre of figure does not coincide with her centre of gravity, but lies about 31 English miles nearer to us than the latter. M. 

 Hansen adds that the existence of such a protuberance of the moon's body relatively to the centre of gravity on the side which 

 we can alone view, would account for the apparent absence of water and air, which may abound upon the opposite side. 

 Astronomical Society's Notices, vol. xv., p. 13. 



