78 
Proceedings of the Royal Society of Edinburgh. [Sess. 
as the vertical position, being the position in which no bending remains 
in the spring, and hence the scape-wheel tooth is able to slide upon the 
pallet. From the unlocking position to the locking position the pendulum 
is not free but under the control of the maintenance, being in connection 
with the anchor and train. As already said, it begins this part of its 
motion by swinging with the spring straight, rolling upon the knife-edges 
that support the cock. Then the cock is moved by the scape-wheel back 
to its vertical position and locked. The two operations together may be 
considered as constituting the maintenance, and discussed jointly in their 
effect upon the motion of the pendulum. 
I am not concerned in the present paper with numerical details of 
clocks more than is necessary to make the application of theory clear, and 
so will merely mention that according to my measures for the clock Riefler 
it is found approximately : — 
Total semi-arc executed by pendulum ..... 100' 
Arc described from unlocking at the vertical position during 
the time the scape-wheel is sliding down pallet . . . 20' 
Arc described while train is moving freely up to point when 
anchor is brought into contact with lift-face of scape- wheel 10' 
Arc described from beginning of lift until anchor is brought 
back and locked in vertical position ..... 20' 
So that the supplementary arc during which the pendulum 
moves freely is ........ 50' 
The first three of these portions of the whole arc are considered to 
cover the “ maintenance ” ; it is true that during the second the pendulum 
is free from the train, but it is not swinging upon its spring at the time 
but upon the knife-edges that support the cock, and this must be considered 
as introducing a disturbance. It may be remarked before leaving the 
matter that this highly peculiar arrangement of hanging the pendulum from 
a rocking cock in place of a fixed one does not in any sense introduce a second 
period into the system, such as might be expected from a double pendulum. 
The construction has in fact no second period, being, in a strict dynamical 
sense, unstable, because the knife-edges are below the point at which they 
support the spring. 
I shall next describe the essential features of the Synchronome move- 
ment. It is described in detail in the patent specification, 9527, W. H. 
Shortt, 1915, from which the figure is taken. The pendulum is linked 
permanently with a piece which may be called the crutch. The crutch is 
the piece which unlocks the maintenance and receives its impulse. Its axis 
is an arbor parallel to the axis of oscillation of the pendulum (but not 
