102 ON THE MAGNITUDE OF THE SOLAR SYSTEM. 



particle of tlie earth is attracted both by the sun and by the moon, bnt 

 in conseqnence of the poUir flattening- the resultant of these attractions 

 passes a little to one side of the earth's center of gravity. Thus a 

 couple is set up, which, by its action upon the rotating earth, causes 

 the axis thereof to describe a surface which may be called a fluted cone, 

 with its apex at the earth's center. A top spinning with its axis 

 inclined describes a similar cone, except that the flutings are absent 

 and the apex is at the point upon which the spinning occurs. For con- 

 venience of computation we resolve this action into two components, 

 and we name that which produces the cone the luni-solar precession, 

 and that which produces the flutings the nutation. In this i>lienomenon 

 the i)art played by the sun is comparatively small, and by eliminating 

 it we obtain a relation between the luni solar precession, the nutation, 

 and the moon's parallax which can be used to verify and correct the 

 observed values of these quantities. 



In the preceding paragraph we have seen that the relation between 

 the quantities there considered depends largely ui>oii tlie flattening of 

 tlie earth, and thus we are led to inquire how and with wliat degree 

 of accuracy that is determined. There are five methods — viz, one geo- 

 detic, one gravitational, and three astronomical. The geodetic method 

 depends upon measurements of the length of a degree on various parts 

 of the earth's surface; and with the data hitherto accumulated it lias 

 proved quite unsatisfactory. The gravitational method consists in 

 determining the length of the seconds pendulum over as great a range 

 of latitude as possible, and deducing therefrom the ratio of the earth's 

 polar and equatorial semidiameters by means of Clairaut's theorem. 

 The pendulum experiments show that the earth's crust is less dense on 

 mountain plateaus than at the seacoast, and thus for the first time we 

 are brought into contact with geological considerations. The first 

 astronomical nu'thod consists in observing tlie moon's i)arallax from 

 various points on the earth's surface; and as these parallaxes are noth- 

 ing else than the angular semidiameter of the eartli at tlie respective 

 points, as seen from the moon, they afford a direct measure of the flat- 

 tening. The second and third astronomical methods are based upon 

 certain perturbatn^ns of the moon which depend upon the figure of the 

 earth, and should give extremely accurate results; but unfortunately 

 very great difliculties oppose themselves to the exact measurenuMit of 

 the i^erturbations. There is also an astronomico-geological method 

 which can not yet be regarded as conclusive on account of our lack of 

 knowledge respecting the law of density which prevails in the interior 

 of the earth. It is based upon the fact that a certain function of the 

 earth's moments of inertia can be determined from the observed values 

 of the coetticients of precession and nutation, and could also be deter- 

 mined from the figure and dimensions of the earth if we knew the exact 

 distribution of matter in its interior. Our present knowledge on that 

 subject is limited to a superficial layer not more than 10 miles thick. 



