335 



by the attractions of the Moon and Sun and by the centri 

 fugal force. These pressures must of course be taken into 

 account. 



It would be uninteresting to follow step by step the 

 process of the investigation : they are very long, and I shall 

 therefore confine myself to stating the results. Mr- 

 Hopkins * first considers the earth as a homogeneous 

 spheroidal shell filled with a homogeneous fluid of equal 

 density. The two surfaces of the shell are supposed to 

 have equal ellipticities. On these suppositions he cal 

 culates the disturbing forces, forms the differential equa 

 tions for the motion of the pole, integrates them, and by 

 interpretation arrives at the following results. 



&quot; 1. The precession will be the same, whatever be the 

 thickness of the shell as if the whole earth were homoge 

 neous and solid. 



&quot; 2. The lunar nutation will be the same as for the 

 homogeneous spheroid to such a degree of approximation 

 that the difference is inappreciable to observation. 



&quot; 3. The solar nutation will be sensibly the same as for 

 the homogeneous spheroid, unless the thickness of the 

 shell be very nearly of a certain value, something less 

 than one-fourth of the earth s radius, in which case the nu 

 tation might become much greater than for the solid sphe 

 roid. 



&quot; 4. In addition to the above motions of precession and 

 nutation, the pole of the earth would have a small circular 

 motion, depending entirely on the internal fluidity. The 

 radius of the circle thus described would be greatest when 

 the thickness of the shell would be least, but the inequality 

 thus produced would not for the smallest thickness of the 

 shell exceed a quantity of the same order as the solar 

 nutation, and for any but the most inconsiderable thick 

 ness of the shell be entirely inappreciable to observation.&quot; 



Thus it appears that the effect of these pressures between 



* Phil. Trans. 1839, 1840, 1842, 



