300 Proceedings of the Poyal Society of Edinburgh. [Sess. 
transferred from the check to the pusher. We suppose that when the 
pusher is at p', and the check at c\ there is a sudden transference of 
the ball from the pusher to the check, and that the ball then remains in 
contact with the check until the latter arrives at c", when the ball is 
suddenly retransferred from the check to the pusher, which is now in the 
position p". 
From now on the ball remains in contact with the pusher until it 
lA/ 
crosses the crest of the slope, and again we suppose the ball quickly trans- 
ferred from the pusher to the check ; and so on. 
Previous to the first transference of the ball from pusher to check the 
centre of gravity of the vsystem lies at the intersection of the pivot axes. 
The shift of the ball brings about a movement of the centre of gravitjq 
and there is applied to the pivoted system a couple of moment mg{d — 2r), 
and so long as the ball remains in contact with the check the amount of 
this couple does not change. The direction in which the couple is applied 
goes round with the rotating system. After the second transference of 
