518 LECTURE XLIII. 



but Newton first demonstrated the same proportion with respect to elliptic 

 orWts, and showed that the time of revolution in an ellipsis is equal to the 

 time of revolution in a circle, of which the diameter is equal to the greater 

 axis of the ellipsis, or the semidiameter to the mean distance of the planet. 



The universality of the laws of gravitation, as applied to the different 

 planets, shows also that the matter, of which they are composed, is equally 

 subjected to its power; for if any of the planets contained a portion of an 

 inert substance, requiring a force to put it in motion, and yet not liable to 

 the force of gravitation, the motion of the planet would be materially dif- 

 ferent from that of any other planet similarly situated. 



The deviations of each planet from the plane of its orbit, and the motions 

 of its nodes, or the points in which the orbit intersects the plane of the 

 ecliptic, as well as the motions of the aphelion, or the point where the orbit 

 is remotest from the sun, have also been deduced from the attractions of the 

 other planetary bodies; but the calculations of the exact quantities of these 

 perturbations are extremely intricate. In general, each of the disturbing 

 forces causes the nodes to have a slight degree of retrograde motion ; but on 

 account of the peculiar situation of the orbits of Jupiter and Saturn, it hap- 

 pens that the retrograde motion of Jupiter's node, on the plane of the orbit 

 of Saturn, produces a direct motion on the ecliptic, so that the action of 

 Saturn tends to lessen the effect of the other planets in causing a retrograde 

 motion of Jupiter's nodes on the ecliptic. 



The secular diminution of the obliquity of the ecliptic, or that slow vari- 

 ation of its position, which is only discovered by a comparison of very dis- 

 t^mt observations, is occasioned by the change of position of the earth's orbit, 

 in consequence of the attractions of the other planets, especially of Jupiter. 

 It has been calculated that this change may amount, in the course of many 

 ages, to 10" or 11*, with respect to the fixed stars; but the obliquity of the 

 ecliptic to the equator can never vary more than two or three degrees, since 

 the equator will follow, in some measure, the motion of the ecliptic. 



The mutual attraction of the particles of matter, composing the bulk of 

 each planet, would naturally dispose them, if they were either wholly or 



