109 
1917-18.] Studies in Clocks and Time-keeping, 
where 
n'jn = 1+ . . . — J ( K l n ) tan (y 4- JS) .... (24) 
If y-f^d is positive, that is to say, if the middle of the maintenance follows 
the vertical position of the pendulum, the escapement error is positive. 
(2) Pallet Friction in Graham Escapement . — Shortly after the main- 
tenance is over, the scape-wheel tooth and train lock upon the opposite 
dead face of the pallet, which is carried by the |)endulum along with it. 
The locking takes place a little way up the face of the pallet, and the 
friction is therefore not quite equal in the two phases of the tooth ascend- 
ing and descending the dead face. The diagram shows this, and also 
indicates the positions of locking and unlocking relative to the maintenance 
just considered. It is clear that the chief effect of such a disturbance will 
be in the second harmonic and therefore of no importance. So far as it 
appears in the first harmonic, the zeroes are just beyond A, A'. It is there- 
fore evident that it will unite well with the chief part of the maintenance 
and have little effect upon time-keeping. 
(3) Chronometer Escapement. — This escapement has been applied to 
clocks by Messrs Dent, the sidereal standard at Greenwich and a replica 
— - - 
: y ^ _ ^ ] 
~ ~ ~ 
- - 
V A 1 \ \ 1 I 
T T 1 — \ t — -l — 
B A 8/ a' e. 
Fig. 10. 
of it at Brussels (Uccle Observatory) being fitted with it. I shall treat 
it as the case of an impulse, given every 2 secs., say, R = A from T = y — \$ 
to T = y + -|d, and zero elsewhere. 
We have 
R = 2A/-7r[J8 + sinJS . cos (r — y) + . . .] 
whence 
x = 2A(7 r?i 2 ) _1 [^8 + ( ?i/k ) sin IS cos y sin r + -J sin S cos 2 (r — y) + . . . ] 
and 
n'/n = 1 + . . . - b(K/n) tan y .... (25) 
If the middle of the maintenance follows the lowest point of the pendulum 
the escapement error is positive, n increasing with the arc. 
(4) Contact Roller upon Pendulum . — Electric contact for a chronograph 
is sometimes made by attaching a small roller to the pendulum, which 
strikes upon a jewel supported by a light spring at each semi-oscillation, 
and throwing it aside, brings it into contact with another piece and so 
closes a circuit. The chief blow upon the pendulum occurs just before 
its lowest point. 
