83 
1917-18.] Studies in Clocks and Time-keeping. 
The work done on the pendulum, IV, in each impulse, is now constant, 
and not subject to any compensating deduction when V and the arc are 
greater. It is clear that <fi should be reduced as nearly as possible to zero ; 
any irregularity in it will produce a change in I. If <fi = 0, IV is inde- 
pendent of the angle of the wedge ; a narrow wedge is then to be preferred, 
for this concentrates the impulse more upon the vertical position of the 
pendulum, diminishing the effect of any irregularities upon the epoch, as 
explained below, and approaching more nearly than perhaps any other 
case to the ideal free pendulum. 
We can compare this with the case of a circular pallet or roller, con- 
sidered in Case 1, if we take, for example, 1—15°, 0 = 12° in Case 3. The 
arcs during which contact takes place between impulse piece and pallet are 
in the ratio h tan i : a sin y. Making the whole impulse I the same for 
both, this ratio becomes : 
y . . 30° 45° 60° 75° 90° 
ratio . . . -055 d80 ’397 ’703 F000. 
Hence the proportion of the swing of the pendulum which is entirely free is 
distinctly greater for the wedge-shaped pallet, and could be made greater 
still if friction were reduced by introducing a small roller where the impulse 
piece makes contact with the pallet. 
The third clock I shall describe is Cottingham's clock with Gill’s 
escapement. Gill described this escapement in principle in Brit. Associa- 
tion Report, 1880, p. 56, from which tig. 4, p. 84, is taken, and some 
experiments were made to realise it. Several years after, while at the 
Cape, he carried it out with elaborate detail, but the clock was not a 
success, and, I understand, is not at present running. In principle the 
escapement is identical with Tiede’s and Knoblich’s escapements, described 
in Astronomische Nachricliten, Bd. 69, pp. 55-59 (1867). Foerster describes 
the performance of the former, in 1878,* and mentions that it had been 
running for a year and three-quarters, and exhibited an admirable rate. 
He also mentions that the idea was the same as in a clock constructed 
by Liais much earlier, in 1854. But of these anticipations Gill and 
Cottingham were not aware. The principle is indeed the same, but the 
details, upon which in practice all depends, present little resemblance. 
Cottingham’s clock in its present form is unilateral, giving one impulse 
every 2 secs. The crutch consists of a frame of three rods mutually at 
right angles. The first serves as pivot axis, the pivoting being done by 
two needle-points resting in agate cuts. This axis is carefully allined with 
the axis of rotation of the pendulum passing through the middle of the 
* A.N., Bd. 91, No. 2182. 
