SECT, in.] IKVAKIABLE PLANE. 27 



The stability of our system was established by La Grange : 

 " a discovery," says Professor Playfair, " that must render 

 the name for ever memorable in science, and revered by 

 those who delight in the contemplation of whatever is excel- 

 lent and sublime." After Newton's discovery of the me- 

 chanical laws of the elliptical orbits of the planets, La 

 Grange's discovery of their periodical inequalities is, with- 

 out doubt, the noblest truth in physical astronomy ; and, in 

 respect of the doctrine of final causes, it may be regarded as 

 the greatest of all. 



Notwithstanding the permanency of our system, the secular 

 variations in the planetary orbits would have been extremely 

 embarrassing to astronomers when it became necessary to 

 compare observations separated by long periods. The diffi- 

 culty was in part obviated, and the principle for accomplish- 

 ing it established, by La Place, and has since been extended 

 by M. Poinsot. It appears that there exists an invariable 

 plane (N. 80), passing through the centre of gravity of the 

 system, about which the whole oscillates within very narrow 

 limits, and that this plane will always remain parallel to it- 

 self, whatever changes time may induce in the orbits of the 

 planets, in the plane of the elliptic, or even in the law of 

 gravitation ; provided only that our system remains uncon- 

 nected with any other. The position of the plane is deter- 

 mined by this property that, if each particle in the system 

 be multiplied by the area described upon this plane in a given 

 time, by the projection of its radius, vector about the common 

 centre of gravity of the whole, the sum of all these products 

 will be a maximum (N. 81). La Place found that the plane 

 in question is inclined to the ecliptic at an angle of nearly 

 1 34' 15", and that, in passing through the sun, and about 

 midway between the orbits of Jupiter and Saturn, it may be 

 regarded as the equator of the solar system, dividing it into 

 two parts, which balance one another in all their motions. 

 This plane of greatest inertia, by no means peculiar to the 

 solar system, but existing in every system of bodies sub- 



