270 RECENT EESE ARCHES OX THE 



of its transverse axis. For, if tlie motions of the perihelia of Jupiter 

 and Saturn were very nearly the same, the action of Jupiter on the 

 eccentricity of Saturn's orbit would be at its maximum value <luring- 

 very loiij;- periods of time, and thereby produce great and permanent 

 changes in the value of that element. But, in the existing conditions, 

 the rapid motion of Saturn's orbit prevents such an accumulation of 

 perturbation, and any increase of eccentricity is soon changed into a 

 corresponding diminution. The same remark is also applicable to the 

 perturbations of the forms of the orbits of Jupiter and Uranus by the 

 disturbing action of Saturn ; for the secular variations of Jupiter's 

 orbit depend almost entirely upon the influence of Saturn, because the 

 planet IS^eptune is too remote to produce much disturbance, and the 

 mean disturbing influence of Uranus on the eccentricity of Jupiter's 

 orbit is identically equal to nothing, b\^ reason of the relation which 

 always exists between the perihelia of their orbits. We may here observe 

 that the eccentricity of the orbit of Saturn always increases, while that 

 of Jupiter diminishes, and vice versa. 



The consequences which result from the mutual relations which alwaj'S 

 exist between the nodes of Jupiter and Saturn, on the invariable plane 

 of the planetary system, are no less interesting or remarkable with re- 

 spect to the position of the orbit of Uranus than those which result 

 from the permanent relation between the perihelia of Jupiter and Uranus 

 are with respect to the form of the orbit of Saturn. The mean disturbing 

 for^e of Saturn on the inclination of the orbit of Uranus is aljout four 

 times that of Jupiter ; but as these two planets always act on the inclina- 

 tions in opposite directions, it follows that the joint action of the two 

 planets is equivalent to the action of a single planet at the distance of 

 Saturn and liaving about three-fourths of his mass; so that the orbit of 

 Uranus might attain a considerable inclination from the superior action 

 of Saturn if allowed to accumulate during the lapse of an unlimited 

 time, at its maximum rate of variation depending on the action of this 

 planet. But such an accumulation of perturbation is rendered forever 

 impossible by reason of the comparatively rapid motion of the nodes of 

 Jupiter and Saturn, with respect to that of Uranus, on the invariable 

 l)lane. By reason of this rapid motion, the secular changes of the inclina- 

 tion of the orbit of Uranus pass through a complete cycle of values in 

 the period of 50,300 years. The correspoiuling cycle of perturbation in 

 the eccentricity of Saturn's orbit is (>!),1-J:0 years. It is the rapid 

 motion of the orbit with respect to tlie forces in the one case, and 

 the rapid motion of the forces with respect to the orbit, in the other, 

 tliat gives permanence of form and position to the orbits of Saturn and 

 Uranus. 



The mean angular distance between the perihelia of Jupiter and 

 Uranus is exactly- 180^ ; but the conditions of the variations of these 

 elements are sufficiently elastic to allow of a considerable deviation on 

 each side of their mean positions. The perihelion of Jupiter may difler 



