506 ON THE OSCILLATIONS OF A ROTATING ELLIPSOIDAL SHELL. 
The direction-cosines of the instantaneous axis referred to the principal axes of the 
shell Ox), Oy,, Oz, are 
0, — 06, 6, + of, 
SS Sa Ns 
@ @ 5 
or 
— 26] * in, +96) + ve +44) |sin Oe +) 
26| Hat 4a) + Vat ge) eos (Mt +6), 1: 
therefore, relatively to the shell, the instantaneous axis describes a cone in period 27/h. 
This motion would ensue if the shell were started rotating about an axis not 
coincident with its principal axis, and it is analogous to the motion of a rigid body 
under no forces when slightly disturbed from a motion of pure rotation about a 
principal axis. 
