Chessin — On the Motion of Gyroscopes. 27 



^If 



l/d+ b sin^ 6 dO 

 (17) '^ = \a L/ (cos ^ — cos v) (?i — cos d) 







and remark that 



i 



yd-\-b^m^e dd 



y/(cos 6 — cos 7}) (n — cos 6) 



l/d + bsm^0 dd 



p 



I v/(cos ^ — cos v) {n — cos 6) 



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 



dt 



it = ±^^2^~ 



l~a i/d + bsm'd dd 



e 



sin 2 t/cos 6 — cos rj 



and shows that the axis of the torus approaches assymptotically 

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

 ■deviation (t?) from ZZ\ where the sign of 6' changes, this 

 sign remains unchanged throughout the motion, and if Tj de- 

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

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

 OZ, we find that 



Vd^-b^xn^d dd I ad i_d 



dd_ 







sm_ 



2 



4. e. T, = oo . 



