22 INVARIABLE PLANE. SECT. III. 



2 42', the terrestrial equator, which is inclined to it at 

 an angle of 23 27' 34"- 69, will never coincide with the 

 plane of the ecliptic : so there never can be perpetual 

 spring (N. 79). The rotation of the earth is uniform ; 

 therefore day and night, summer and winter, will con- 

 tinue their vicissitudes while the system endures, or is 

 undisturbed by foreign causes. 



" Yonder starry sphere 

 Of planets and of fix'd, in all her wheels 

 Resembles nearest mazes intricate, 

 Eccentric, intervolved, yet regular, 

 Then most, when most irregular they seem." 



The stability of our system was established by La 

 Grange: "a discovery," says Professor Playfair, "that 

 must render the name forever memorable in science, 

 and revered by those who delight in the contemplation 

 of whatever is excellent and sublime." After Newton's 

 discovery of the mechanical laws of the elliptical orbits 

 of the planets, La Grange's discovery of their periodical 

 inequalities is, without doubt, the noblest truth in physi- 

 cal 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 difficulty was in part obviated, and 

 the principle for accomplishing 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 center of gravity of the system, 

 about which the whole oscillates within very narrow 

 limits, and that this plane will always remain parallel to 

 itself, 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 unconnected with any other. The position of 

 the plane is determined by this property that, if each 

 particle in the system be multiplied by the area de- 

 scribed upon this plan in a given time, by the projection 

 of its radius vector about the common center of gravity 

 of the whole, the sum of all these products will be a 



