306 Proceedings of the Koyal Society of Edinburgh. [Sess. 
(fig. 28) (the device is supposed to be inclined to the vertical wholly about 
the pivots ^ 2 ^ 2 )’ i^evolves through a half turn with the erector, its amount 
remaining constant meanwhile, and goes out of existence at B ; simul- 
taneously with its disappearance it reappears at A, revolves as before, to 
go out of existence at B ; and so on. The lines a represent the couple 
for a few of the directions in which it acts in the course of the half turn 
which it executes. 
When the inclination of the pivoted system to the vertical has reached 
a limiting value, which value depends, as already explained, on the design 
and speed of the erector, the radial motion of the ball ceases. But the 
balls are allowed a small 
amount of clearance when 
situated in the outer compart- 
ments of the slots (fig. 17), 
and the erection of the device 
continues after the manner 
described above for the erector 
illustrated in fig. 26. The 
inclination of the pivoted 
system to the vertical being 
now very small, the transfer- 
ence of a ball from its pusher 
to its check takes place in 
the neighbourhood of c, and 
the re transference from the 
check to the pusher at D. 
As a consequence, a couple (represented by h) comes into, existence at c, 
revolves with the erector to D, and goes out of existence, to be succeeded 
by a couple of equal moment which appears at c simultaneously with the 
disappearance of the former couple at D ; and so on until the erection of the 
device is complete. In each case, it will be seen readily from the figure, the 
direction of the integral couple is such as to erect the pivoted system about 
the pivots P 2 P 2 ’ ^^d it turns therefore almost wholly about the pivots p 2 P^z- 
The erection is accompanied by little, if any, turning on the pivots PiPi . 
In constructing the above diagram the convention has been adhered to 
according to which the line which represents a moment is drawn towards 
the observer when the moment has a counter-clockwise direction as viewed 
by him. 
In the construction of the double erector illustrated in figs. 24 and 25 
the slots which limit the freedom of the balls are so constructed that, for 
