(14) 
and X, Y perpendicular to one another in the principal 
plane of the system, also fixed in space. 
NAS ON 
R 
The position of ABC relatively to XYZ may be defi- 
ned by the Eulerian angles %, #0, 9 as shown in the 
annexed figure. If p, q, r are the components of angu- 
lar velocity of the Earth about the axes À, B, C; and if 
A, À, C are the moments of inertia about the same axes, 
the equations of motion are 
dp dq dr 
— —= — C LS À — — CEA L C—— 0. 
ÿ dt mor dt À )p? dt 2 
These equations have to be modified 1f we take account 
of the elastic yielding of the Earth to centrifugal force. 
Supposing that a spherical planet of the same mass, law 
of internal density, and elastieity as the actual Earth were 
made to rotate with the same angular velocity as the 
actual Earth, it would become strained under the influence 
of centrifugal force. This spherical planet being ideal, 
we may further suppose that the materials of which it is 
