SKCT. III. MEAN MOTION AND MAJOR AXIS. 19 



turbation ; but still, a comparatively permanent change 

 is effected 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 between the variation 

 of the eccentricity 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 incli- 

 nations and eccentricities in a state of perpetual variation. 

 It makes the major axis of all the orbits continually re- 

 volve, and causes, on an average, 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 phe- 

 nomenon of great complexity, extending through un- 

 known ages. At the present time the inclinations of all 

 the orbits are decreasing, but so slowly, that the incli- 

 nation 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 axis 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. 



It is true that, according to theory, the radial disturb- 

 ing force should permanently alter the dimensions of all 

 the orbits, and the periodic times of all the planets, to a 

 certain degree. For example, the masses of all the 



