GRAVITY MEASUREMENTS. 
35 
employed for this purpose. The pendulum whose coefficients 
were desired was swung successively under the various con¬ 
ditions to be investigated, while in another room a second 
pendulum whose period was known was swung simultane¬ 
ously under uniform conditions. By suitable electric con¬ 
nections the same chronometer was used in observing both 
pendulums and its rate deduced from the observations with 
the second pendulum. With this rate correction applied, the 
periods of the first pendulum were obtained entirely free 
from the irregularities of rate of chronometer. This same 
method, which obviates the necessity for time observations, 
has been applied successfully in this country and elsewhere 
for comparing gravity at two distant stations telegraphically 
connected. 
The following are the corrections in seconds that were 
applied in reducing to standard conditions: 
Arc correction = — 
PM sin (<p 4- (p f ) sin (<p — <p ') 
32 log sin <p — log sin <p' 1 
where Pis period in seconds, M is modulus of common loga¬ 
rithmic system, <p and <p f are initial and final semi-arcs. 
Temperature correction = + 0.00000419 (15— T), 
where T is observed temperature in degrees centigrade. 
Pressure correction = + 0.000000101 
Pr 
1+.00367 T° 
] 
where Pr is observed pressure in millimeters, and T is tem¬ 
perature. 
Rate correction = 0.00001157 R P, 
where P is period and R is "daily rate on sidereal time in 
seconds, + if losing, — if gaining. 
Flexure correction = — 0.00000065 D, 
where D is the observed movement of the knife-edge in 
microns when a force of 1.5 kilograms is applied horizontally 
in the plane of oscillation. 
The flexure coefficient used as derived from experiment 
differs slightly from that deduced from the theoretical for- 
