126 
PRESTON. 
The counting of the oscillations is a comparatively easy 
matter when the period is known to within less than one 
ten thousandth of a second, because the uncertainty in that 
case cannot accumulate to be more than about half a second 
in a couple of hours, which will always enable us to decide 
between the two contiguous even numbers. This does not 
consider the changes arising from changes of temperature; 
but they are not usually enough to throw doubt on the 
number of oscillations. At one station, however, which has 
already been cited, the range of temperature was so great 
that it was necessary to consider it in making the count. 
At the Lick observatory, on the contrary, all conditions were 
so perfect that intermediate transits were unnecessary. The 
time computed for the duration of a swing of 15,000 oscil- 
h m s 
lations for pendulum No. 3 was 4 0 33.7, and the observed 
duration was never more than one-tenth of a second differ¬ 
ent from this. Here obviously there was no necessity for 
intermediate transits at all, in order to count the oscillations. 
The swings were made to consist of exactly 15,000 oscil¬ 
lations. A sounder near the observer gave the seconds from 
the clock, which was in another building. The minute was 
known from a sidereal watch compared daily with the clock. 
This enabled the observer to terminate the swing at exactly 
the end of the 15,000th oscillation, the moving pendulum 
being followed by the eye and the clock-beats by the ear. 
As before stated, when the calculated time had elapsed, the 
pendulum was always found within a tenth of its ampli¬ 
tude from the lowest point. The determination of the ap¬ 
proximate period of oscillation is accomplished by taking 
transits at short intervals near the end of a swing. For 
the first and shortest interval the number of vibrations is 
actually counted from the chronograph. The first approxi¬ 
mation will then be in error by a fractional part of the error 
commuted in the terminal observations, and the error of the 
deduced period will vary inversely as the number of inter¬ 
mediate oscillations. Then, knowing the uncertainty of a 
single oscillation, it is easily seen how long the next interval 
