326 BOOK OF MATHEMATICAL PROBLEMS. 



and if <*>,, <o f , o> 8 be the angular velocities of the sphere about 

 these directions, 



7/3 



<!>! = 0, a<o a sin 6 = w, aa> a = 6 . 



Clt 



1543. A rough sphere, radius a, rolls in a spherical bowl of 

 radius a + b in a state of steady motion, the normal making an 

 angle a with the vertical : prove that the time of small oscillations 

 about this position is 



/( 76cosa ) 

 V 15#(1 +3 cos 8 a)J* 



