THK OVKOSCOPK. 65 



attraction of gravitation. The path would be the unstable 

 horizontal path of the theoretical gyroscope already referred 

 to as resulting when the initial velocity is equal to the critical 

 velocity. The rotational velocity continues to decrease, how- 

 ever, and consequently the gyroscopic force also decreases, 

 becoming now too weak to sustain the horizontal motion. 

 The path of the axis hence inclines slightly downward. The 

 axis gains velocity by the fall, a result which has the effect of 

 preventing the deviating force from decreasing as rapidly as 

 otherwise. The inclined course of the axis continues hence- 

 forth, the velocity gained by the fall being insufficient to 

 compensate for the continual loss of velocity of rotation of 

 the wheel. The mass of the wheel in falling also supplies the 

 energy necessary to overcome the friction of the pivot and the 

 atmospheric resistance. The subsequent path of the axis 

 winds slowly downward, the rotational velocity becoming less 

 and less and the velocity of the axis greater. The final result 

 would be that the wheel would stop rotating and the apparatus 

 swing around the pivot at a low level, sustained only by cen- 

 trifugal force, provided the axis did not slip off the pivot or 

 the wheel strike the standard. Within certain limits this hel- 

 ical path is stable and restores itself after a disturbance, since 

 no matter how often interfered with the same factors which 

 produced it are always at work to restore it. This result is in 

 striking contrast with that obtained with the theoretical instru- 

 ment, as in that case the stable path was the nutating one. 



The slowing down of the wheel being the most prominent 

 feature in the action of the practical gyroscope, it follows that 

 under ordinary circumstances this downward non-nutating 

 helical path will be the one ordinarily met with. 



(b) Turn now to the effect of friction in opposing the 

 orbital motion. It will be seen that the opposing force due to 

 this cause, acting horizontally, combines with the gravita- 

 tional force, producing a primar>^ couple constantly directed 

 downward and slightly backward. This, as we have seen 

 before, will continually cause the orbital motion to be directed 



