412 LECTURE XLIII. 



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 th 

 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 tb j 

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

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

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

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

 happens 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 retro- 

 grade motion of Jupiter's nodes on the ecliptic. 



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

 variation of its position, which is only discovered by a comparison of very 

 distant 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 

 partially fluid, to assume a spherical form : but their rotatory motion would 

 require, for the preservation of this form, an excess of attraction in the 

 equatorial parts, in order to balance the greater centrifugal force arising 

 from the greater velocity of their motion : but since the attractive force of 

 the sphere on the particles at an equal distance from its centre is every 

 where equal, the equatorial parts would necessarily recede from the axis, 

 until the greater number of particles, acting in the same column, compen- 

 sated for the greater effect of the centrifugal force. The form would thus 

 be changed from a sphere to an oblate or flattened spheroid ; and the sur- 

 face of a fluid, either wholly or partially covering a solid body, must as- 

 sume the same figure, in order that it may remain at rest. The surface of 

 the sea is therefore spheroidical, and that of the earth deviates so far only 

 from a spheroidical figure, as it is above or below the general level of the 

 sea. (Plate XXXIV. Fig. 486.) 



The actions of the sun and moon, on the prominent parts about the 

 earth's equator, produce a slight change of the situation of its axis, in the 

 same manner as the attractions of the other planets occasion a deviation 

 from the plane of its orbit. Hence arises the precession of the equinoxes, 

 or the retrograde motion of the equinoctial points, amounting annually to 

 about 50 seconds. The nutation of the earth's orbit is a small periodical 

 change of the same kind, depending on the position of the moon's nodes ; in 



