Ckessin — On the Motion of Gyroscopes. 27 



4j; 



, , l/d-\- b sin^ d dO 



(17) 



(cos 6 — cos -q) (n — cos 6) 







and remark that 



i 



Vd + b sin2 e de 



V^(cos 6 — cos T}) (n — cos 6) 



>/rf + 6sin'<9 de 



X 



il/(cos 6 — cos Ti) (n — cos^) 

 -V 



we find that the oscillations of the axis of the torus are iso- 

 chronic and that the period of a complete oscillation is 4t. 



B. n = 1. 



Equation (15) becomes 



I a i/d + bsiu'^e dS 

 sin a i/cos 6 — cos rj 



and shows that the axis of the torus approaches assymptoticaJly 

 to the position OZ. In fact, after the moment of maximum 

 deviation (ij) from ZZ'y where the sign of d' changes, this 

 sign remains unchanged throughout the motion, and if t^ de- 

 note the time required for the passing of the;axis of the torus 

 from the position of maximum deviation (17) to the position 

 OZf we find that 



la I Vd + bem^e dd \ ad Cd 



J sin 21/COS e-coQv \^^Bm j J sii 



de_ 

 



sin_ 

 2 



«. e. T, = 00 . 



