SECT. II I. MEAN MOTION AND MAJOll AXIS. 19 



manent change is effected in the inclination, which is not com- 

 pensated 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 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 reaction of the whole 

 system are 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 per- 

 petual variation. It makes the major axes of all the orbits con- 

 tinually revolve, 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 phenomenon of great 

 complexity, extending 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 per- 

 manently independent of secular changes. They are so connected 

 by Kepler's law, of the squares of the periodic times being pro- 

 portional 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 disturbing 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 planets revolving within the orbit 

 of any one, such as Mars, by adding to the interior mass, increase 

 the attracting force of the sun, which, therefore, must contract 

 the dimensions of the orbit of that planet, and diminish its 

 periodic time ; whilst the planets exterior to Mars's orbit must 



