﻿the Rigidity of the Earth. 219 



Prof. Newcomb begins with the remark that the condition 

 for the possibility of the 427 days' period is, that the pole of 

 the principal axis shall be at a distance from the North Pole 

 [that is from the point which would be the pole of rotation 

 and inertia if the perturbation did not exist] equal to f of the 

 distance between the pole of rotation and the North Pole. 

 (See fig. 1.) Thus the pole of rotation R revolves in nearly 



Fiff.l. 



'O 



P, the North Pole. _ 



P', pole of the principal axis. 



R, pole of rotation. 



O, centre of inertia. 



305 days about the pole of inertia P', but this latter and also 



R revolve about the North Pole in 427 days. The little 



circle is rolling on the greater. 



The precise statement of the problem is the following : — 

 The equations of motion relatively to axes revolving with 



angular velocities p, q, r are of course : 



Suppose that the body is elastic, that ,v , y , z are the coordi- 

 nates of particles belonging to their undisturbed positions, 

 suppose that f, 77, f are the displacements, suppose that the 

 revolving axes are fixed relatively to the coordinates x ,y ,z , 

 then x , ?/ , z are constants, and as 



y =3/0 +v, 



-j-j reduces to — |, and so on. 



Further, neglecting f, 77, f in comparison with ,r , y , z , 



