284 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
So long as the halls are constrained to move on the plate h after the 
manner described, the average speed of recovery is constant, and in no way 
depends on the inclination of the pivoted system to the vertical. It is 
important also to notice, in connection vdth what follows, that the speed 
of recovery does not depend on the speed of rotation of the erector. That 
the rate of recovery should not depend on the erector speed may seem 
puzzling, but the reason will be apparent from consideration of fig. 16 . 
Here, instead of two balls, a series is employed. When the pivoted 
system is upright — -that is, when the plate h is horizontal — let the balls 
move round on the plate with uniform speed in the circle abcea. If distri- 
buted evenly they will apply no couple about the pivots. If the pivoted 
system is inclined about P2P2’ ^ upwards, a downwards, then with the 
direction of spin of the gyroscope, and that of the rotation of the balls on 
the plate, clockwise as seen from above, to cause the pivoted system to 
approach the vertical on the pivots P2P2 > couple must be applied to the 
system tending to move b downwards and P upwards. If the balls can 
now be constrained to move uniformly in the path abcdefa, such a couple 
is obtained, and obviously the moment of the couple does not depend on 
