Ill 
1917—18.] Studies in Clocks and Time-keeping. 
Cottingham. — In the running of this clock, 1917 July to December, the 
crutch was picked up on the right of the vertical at 2T *5 and dropped upon 
return on the left of the vertical at 14T5. 
M = 77 kg. 
The couple exerted by the crutch on the pendulum (as measured 
Dec. 1) is equal to the weight of 1*73 gr., with an arm of 2*1 cm. 
This follows the pendulum over 2D5 + 1475 = 36 r , every 2 secs. 
Hence 
W/M{ri 2 + . . . } = 173 x 2d x 981 x ( 1 8'/3438')/7 *7 x 10 3 x 10 4 . 
Also from a series of observations, 
K /n = 0-50 x IQ- 4 . 
That is to say, expressing a in ', 
a 2 = (2 /ttw 2 ) x 2 x 10 4 X 1-73 X 2-1 x 981 x 18 x 3438/7*7 x 10 7 , 
or 
a = 6T. 
The observed semi-arc described is 60'. 
The angles y, 8 of page 105 are given by 
2a siny = 43', 2a sin (8 - y) = 29', 
or 
y = 21°, 8 = 35°. 
Inspecting the formula for x, p. 105, it is easily seen that the calculation 
of a above is simply the same as that for the coefficient of sin r in the 
expression for x. 
Synchronome. — The work done upon the pendulum during 1 sec. is, 
by p. 81, 
mfa{ 1 - cos y) 2 (l + \ cos y), 
so that the formula gives 
a 2 = (2/Trn 2 )(n/K)mfa(l - cos y) 2 (l + J cos y)/M{d 2 + . . .}. 
According to the measures 
K /n = 0-76 x 10“ 4 , 
a = 0’32 cm., 
M = 7 0 kg. 
The value of mf has been varied during the running, viz. mf=l' 00, 
0'85, 0'55 gr.-wt. respectively. The value of y cannot be observed with any 
precision but appears to be in the neighbourhood of 60° ; it will, of course, 
increase as mf is diminished. 
