GRAVITATIONAL METHODS 283 



are recorded photographically on a strip of film on which is also recorded 

 the beats of the pendulum at the field station. 



If the times of swing (half periods) of the base pendulum and the 

 field pendulum are exactly the same, the marks on the film which corre- 

 spond to the beats of the two pendulums will coincide or lie on a straight 

 line. If the times of swing are not exactly the same, the marks will be 

 displaced with respect to one another. After a certain number of vibrations 

 of the base pendulum, the marks due to the two pendulums will again 

 coincide. This forms a coincidence, as in the case discussed previously. The 

 number of oscillations of the base pendulum (which, in effect, functions 

 like the chronometer previously considered) can be read directly from the 

 photographic film. 



Corrections. — -A number of corrections must be applied to the period 

 of oscillation of a pendulum. Corrections are made for the following 

 effects: (1) infinitesimal arc of swing, (2) temperature, (3) pressure, 

 (4) true sidereal time, (5) inflexible support. 



As the details of determining and applying these corrections vary con- 

 siderably with different pendulum apparatus they will not be presented. 

 However the order of magnitude of the above corrections will show their 

 relative importance. 



Arc of swing. An error of 0.4 mm. in observing the initial arc of swing of the 

 pendulum, or of 0.8 mm. in observing the final arc, produces an error of 0.001 dyne in 

 the computed value oi g. These figures apply to the Coast and Geodetic equipment 

 shown in Figure 135. 



Temperature. In the same equipment an error of 0.6° C. in temperature with 

 bronze pendulums and of 0.9° C. with invar pendulums makes an error of 0.001 dyne 

 mg. 



Pressure. An error of 3 mm. of mercury column in the mean pressure inside the 

 receiver may cause, as in the above cases, 0.001 error in g. This figure applies to invar 

 pendulums. 



Chronometer rate. The rate at which the chronometer used to determine the 

 period gains or loses per 24 hours must be considered. Accuracy in timing is in fact 

 the crux of pendulum gravity measurements. An error of 0.04 sec. in the observed 

 daily rate of the chronometer, reduced to sidereal time, may bring about an error of 

 0.001 in gravity value calculated. 



Flexure of the pendulum support. Observations with pendulums show that 

 practically all so-called "rigid" supports have a certain flexibility. When a pendulum 

 swings it communicates motion to the receiver in which it is housed and to the support, 

 causing them to oscillate. This oscillation in turn afifects the observed period of the 

 pendulum. 



Flexure of the support can be measured by an apparatus operating on the principle 

 of the interferometer. This device consists of a lamp and lens properly set up to 

 furnish a beam of sodium or other monochromatic light. A glass plate is arranged so 

 as to separate the beam into two parts, one transmitted and the other reflected by the 

 plate. Two mirrors are provided, one in the path of each beam, and a telescope for 

 observing the resulting image. One of tlie mirrors is mounted on the pendulum receiver 

 and the other on an independent support in front of it. When the difi^erent parts of 



