4- 7 4- S' 'T 
REDUCTION OF PENDULUM OBSERVATIONS. 125 
These apply to Washington, the initial station. For any 
other station the correction is 
\ 9 *_ 288.1 
X g t + 273.1 29 
where K is the coefficient for Washington, g w is gravity at 
Washington, g is gravity at any other station, t is the tem¬ 
perature centigrade, and P is the barometer in inches. 
In the application of these formulae differential correc¬ 
tions are first applied to reduce to a mean pressure and 
temperature. The mean swing is then brought to one ab¬ 
solute atmosphere and to 15° centigrade, which corresponds 
to one absolute unit of temperature. Either of two methods 
may be employed to refer the time of oscillation to the chro¬ 
nometer or clock. If a clock is used, coincidences are gen¬ 
erally observed. With a chronometer, the successive transits 
of the end of the pendulum across the vertical at the lowest 
point are registered electrically on the chronograph. For¬ 
merly 100 transits were observed at the beginning and end of 
a swing, besides taking 40, at intervals of an hour, during 
the swing, in order to count correctly the whole number of 
oscillations made. This, however, is pushing the observa¬ 
tions to a point far beyond the necessary accuracy. The 
probable error of the mean of 40 transits is for an experi¬ 
enced observer only s ’002, as far as observation is concerned. 
This would give an uncertainty for one oscillation in a 
swing of 4 or 5 hours of 2 in the seventh place, and for 1J 
hours, the shortest swings, with heavy end up, of less than 
one in the sixth place. In regard to the intermediate trans¬ 
its, inasmuch as the object is only to guard against losing 
two whole oscillations (since, if transits are always begun 
with the pendulum moving in the same direction, any mis¬ 
count must involve the loss of an even number of beats) 
it is quite sufficient to take one or two transits only. This 
lessening of the number of observed transits very mate¬ 
rially shortens the work of the chronographic method, and no 
significant error can arise therefrom. 
