SECT. III. INVARIABLE PLANE. 23 



The plane of the ecliptic itself, though assumed to be fixed at 

 a given epoch for the convenience of astronomical computation, is 

 subject to a minute secular variation of 45"'7, occasioned by the 

 reciprocal action of the planets. But, as this is also periodical, 

 and cannot exceed 2 42', the terrestrial equator, which is inclined 

 to it at an angle * of 23 27' 28"'29, 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 continue 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 for ever memorable in science, and revered by those who 

 delight in the contemplation of whatever is excellent and sub- 

 lime." After Newton's discovery of the mechanical laws of the 

 elliptical orbits of the planets, that of their periodical inequali- 

 ties, by La Grange, is, without doubt, the noblest truth in the 

 mechanism of the heavens ; 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 com- 

 pare observations separated by long periods. The difficulty was 

 in part obviated, and the principle for accomplishing it esta- 

 blished, 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 itself, whatever changes time may 

 induce in the orbits of the planets, in the plane of the ecliptic, 

 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 described upon this plane in a 

 * The obliquity given in the text is for the year 1858. 



