PENDULUM OBSERVATIONS. 13 
image of the slit coincides with one of the cross wires. A shutter, 
worked by an electromagnet, moves across the slit. This shutter also 
carries a slit, and the adjustments are such that in one position the two 
slits are in the same horizontal line, and the light can pass through; in 
any other position of the shutter itis obscured. The electromagnet is 
actuated by means of a current which passes through the clock, and is 
broken once a second. Thus, the shutter oscillates once a second, in 
time with the clock, and once a second an instantaneous beam of light 
is emitted from the slit and reflected by the pendulum, appearing as 
a flash coincident with the cross wire. 
When the pendulum is moving the apparent position of the flash 
will depend on the position of the pendulum when the reflection 
occurs. If the pendulum is vibrating exactly in half-seconds it will 
have completed exactly two vibrations in the interval (one second) 
between two flashes, and the flash will always occupy the same posi- 
tion on the field. If the period of the pendulum is slightly less or 
slightly greater than half a second the position of the flash will shift 
on the field. If it be watched, it will be found to move gradually to 
one side of the cross wire and then to come back, until after a certain 
number of seconds it again coincides with the cross wire; it then 
continues to move to the opposite side of the wire, and after another 
interval reverses its direction and crosses the wire again, now moving 
as at first. In taking the observations it is necessary to observe 
transits both from right to left and from left to right. 
The time which it is required to measure accurately is the interval 
between two consecutive transits of the cross wire in the same direction. 
This we shall call the coincidence interval. Now we know that at the 
beginning and end of the coincidence interval the pendulum was in 
exactly the same position. During the interval, then, it has com- 
pleted a whole number of swings. ‘If it had been a half-second pen- 
dulum exactly, this number would have been twice the number of 
seconds in the interval. If the period is slightly greater than half a 
second the pendulum falls behind the clock at each swing, and at the 
end of the coincidence period it has fallen behind by exactly one 
swing. Thus, if the coincidence interval be s seconds, we arrive at the 
result that in s seconds the pendulum has executed 2 s — 1 swings. 
Thus, the complete period of the pendulum is seconds. 
8 
2s—1 
If the period of the pendulum be less than half a second it will, 
during the coincidence period, gain on the clock, and the complete 
period of the pendulum will be eal seconds. 
In the pendulums supplied to the Expedition the first formula 
