30 ACTION OF PLANETS ON THE SATELLITES. [SECT. in. 



much as 8 -37 ; so that the conjunctions do not happen exactly 

 in the same points of the orbits till after a period of 850 

 years ; and, in consequence of this small advance, the planets 

 are brought into such relative positions, that the inequality, 

 which seemed to threaten the stability of the system, is com- 

 pletely compensated, and the bodies, having returned to the 

 same relative positions with regard to one another and the 

 sun, begin a new course. The secular variations in the ele- 

 ments of the orbit increase the period of the inequality to 918 

 years (N. 84). As any perturbation which affects the mean 

 motion affects also the major axis, the disturbing forces tend 

 to diminish the major axis of Jupiter's orbit and increase 

 that of Saturn's during one half of the period, and the con- 

 trary during the other half. This inequality is strictly pe- 

 riodical, since it depends upon the configuration (N. 85) of 

 the two planets ; and theory is confirmed by observation, 

 which shows that, in the course of twenty centuries, Jupiter's 

 mean motion has been accelerated by about 3 23', and Saturn's 

 retarded by 5 13'. Several instances of perturbations of this 

 kind occur in the solar system. One, in the mean motions 

 of the Earth and Venus, only amounting to a few seconds, 

 has been recently worked out with immense labour by Pro- 

 fessor Airy. It accomplishes its changes in 240 years, and 

 arises from the circumstance of thirteen times the periodic 

 time of Yenus being nearly equal to eight times that of the 

 Earth. Small as it is, it is sensible in the motions of the 

 Earth. 



It might be imagined that the reciprocal action of such 

 planets as have satellites would be different from the influ- 

 ence of those that have none. But the distances of the sa- 

 tellites from their primaries are incomparably less than the 

 distances of the planets from the sun, and from one another. 

 So that the system of a planet and its satellites moves nearly 

 as if all these bodies were united in their common centre of 

 gravity. The action of the sun, however, in some degree 

 disturbs the motion of the satellites about their primary. 



