(55.) 
Poisson’s 
addition to 
the theory. 
Cuar. II., § 2.) 
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. 
It remains to add, in closing this interesting 
discussion, that Lagrange himself had not quitted the 
field before 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 apparentlyindefinite ; that ifthe planets 
cease to roll, and the sun and moon to do their 
office in enlightening the world, it must be in all 
PHYSICAL ASTRONOMY—LAGRANGE. 
813 
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 races of animated beings.’ 
We have, in the commencement of this section, 
(56.) 
disclaimed the intention of entering at large upon the Lagrange’s 
history of Lagrange’s discoveries. They fell more pro- 
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- 
pedia. 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.? 
With reference to the Lunar Libration, Lagrange 
other 
writings. 
(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 aspecies 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 Mécanique Analytique.’ 
Lagrange was happy in passing his days with 
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- 
dent circu 
were requisite to the stability of the system, is at least incomplete. Compare Laplace, Systéme 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 LAGRANGE in the Encyclopedia. 
3 Very recently (1854), M. Hansen of Gotha, a most eminent living authority, has somewhat modified the received opinion M, Hansen 
ing 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's 
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. 
of the 
Moon. 
(58.) 
