ON THE 



INTERNAL STRUCTURE OF THE EARTH CONSIDERED AS AFFECTING 

 THE PHENOMENA OF FllECESSION AND NUTATION. 



TriE equations of precession and nutation are, as is well known, entirely indepen- 

 dent of any particular law of density, and are functions only of the absolute values 

 of the moments of inertia about the equatorial and polar axes A and 6',' and are 

 independent indeed of the figure of the earth, except so far as it affects the values 

 of these moments. 



Moreover, if the earth, instead of being solid throughout, is (as supposed by most 

 geologists) a solid shell inclosing a fluid nucleus, it is only necessary (leaving out 

 of consideration the pressure that may be exerted on the interior surface by the 

 fluid) that the shell should have these moments of inertia. Mr. Poinsot'^ has obtained 

 as the results of calculation for a homogeneous spheroid, values of precession and 



nutation identical with those of observation, by taking the ellipticity at , and 



Yi (the ratio of mass of moon to tliat of the earth), at -— . 



88 



We have, assuming a uniform density, indicating by a and h the equatorial and 

 axial radii, and by e the ellipticity : — 



C=J% «' Z^=(approx.) -% n ¥ (l+4e) 

 15 lo 



A=^.n («* i+a^ &')= A^i V- (l+3e) 

 If e is taken at ^^ ^ then — r= . But all meridian measurements of 



' I assume, of course, the equality of all moments of inertia. A, about the equatorial axes, and 

 overlook all questions as to the non-S3-ramctr3' of the earth with respect to its axis of figure or to the 

 equator; for, in fact, neither the rotation of the earth nor any observable celestial phenomena reveal it. 



' Connaissanec fles temps, 1858. 



5 January, 1872. ( 33 ) 



