ON THE LAWS OF GRAVITATION. 519 



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 Adhere 

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

 greater number pf particles, acting in the same column, compensated 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 surface of a fluid, 

 cither wholly or partially covering a solid body, must assume the same 

 figure, in order that it may remain at rest. The surface of the sea is there- 

 fore spheroidical, and that of the earth deviates so far only from a spheroi- 

 dical figure, as it is above or below the general level of the sea. (Plate 

 XXXI V. Fig. 436.) 



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

 trograde 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 notles; in conse- 

 quence of which, according to Dr. Bradley's original observations, the pole 

 of the equator describes in the heavens a little ellipsis, of which the diameters 

 are 16 and 20 seconds. The same cause is also concerned in modifying the 

 secular variation of the obliquity of the ecliptic; and on the other hand, this 

 variation has a considerable effect on the apparent precession of the equi- 

 noxes. On account of the different quantity of the precession at different 

 times, the actual length of the tropical year is subjected to a slight varia- 

 tion; it is now 4 or 5 seconds shorter than it was in the time of Hipparchus. 

 The utmost change, that can happen from this cause, amounts to 43 seconds. 



The exact computation of the moon's motion is one of the most difficult, as 

 Hrell as the most important problems in astronomy; but it is easy to under- 

 stand, in general, how the dilierence in the quantity and direction of the 

 sun's actions ofi the moon and earth, may cause such a derangement of the 



