22 MEAN MOTION AND MAJOR AXIS. [SECT. in. 



disturbing body, whose motion has not hitherto been taken 

 into the account, so that perturbation compensates pertur- 

 bation ; but still a comparatively permanent change is ef- 

 fected in the inclination, which is not compensated till the 

 nodes have accomplished a complete revolution. 



The changes in the inclination are extremely minute (N. 

 75), compared with the motion of the nodes, and there is the 

 same kind of inseparable connection between their secular 

 changes that there is bet ween the variation of the excentricity 

 and the motion of the major axis. The nodes and inclinations 

 vary simultaneously, their periods are the same, and very great . 

 The nodes of Jupiter's orbit, from the action of Saturn alone, 

 require 36,261 years to accomplish even a tropical revolution. 

 In what precedes, the influence of only one disturbing body 

 has been considered ; but, when the action and re-action of 

 the whole system is taken into account, every planet is acted 

 upon, and does itself act, in this manner, on all the others ; 

 and the joint effect keeps the inclinations and excentricities 

 in a state of perpetual variation. It makes the major axes 

 of all the orbits continually revolve, and causes, on an ave- 

 rage, a retrograde motion of the nodes of each orbit upon 

 every other. The ecliptic (N. 71) itself is in motion from 

 the mutual action of the earth and planets, so that the 

 whole is a compound phenomenon of great complexity, ex- 

 tending through unknown ages. At the present time the 

 inclinations of all the orbits are decreasing, but so slowly, 

 that the inclination of Jupiter's orbit is only about six 

 minutes less than it was in the age of Ptolemy. 



But, in the midst of all these vicissitudes, the length of 

 the major axes and the mean motions of the planets remain 

 permanently independent of secular changes. They are so 

 connected by Kepler's law, of the squares of the periodic 

 times being proportional to the cubes of the mean distances 

 of the planets from the sun, that one cannot vary without 

 affecting the other. And it is proved, that any variations 

 which do take place are transient, and depend only on the 

 relative positions of the bodies. 



