274 EXPLORATION GEOPHYSICS 



the two axes and the parallelism of the two axes, and (3) degree of per- 

 fection with which friction is eliminated. In use, the accuracy is chiefly 

 dependent upon the accuracy of time measurement. The most accurate 

 measurements of the absolute value of g are believed to be those of 

 Kiihnen and Furtwangler at Potsdam in 1898-1904 which had a probable 

 error of three parts in a million.! Such accuracy of measurement cannot 

 be achieved in field measurements and recourse generally is had to relative 

 gravity measurements. 



The Determination of the Relative Force of Gravity 

 with a Pendulum 



For small amplitudes of swing and when using the same pendulum for 

 determining the relative force of gravity at various stations, a simple rela- 

 tionship exists. The period of vibration (T) of a given pendulum of length 

 (I) varies with the value of the force of gravity (g) at the station, in accord- 

 ance with Equation 23. 



T = 27rV- 



' g 



in which T = seconds ; / = cm. ; g = dynes/mass = cm./sec^. 



g = -^T (24) 



Comparative Gravity Measurements. — Relative determinations of 

 gravity are made by firs.t calibrating the pendulum by observing its period 

 of oscillation at the Washington gravity base or some other base where the 

 absolute value of gravity has been determined, and then observing the 

 period of the same pendulum at the various field stations where readings 

 are to be made. The value of gravity at the base and at each field station 

 is inversely proportional to the square of the period of oscillation of the 

 pendulum at the two stations ; where subscript b = base and n = new 

 station, with other symbols as already defined, 



ffb T 2 ' ^" 7^ 2 



■'6 ^ n 



f=^or<7. = 2^ (25) 



Comparative determinations are largely used in geodetic work. They 

 can be made with an accuracy ± 0.0004 dynes or better, and more rapidly 

 than absolute determinations. 



Development of Gravity Work in the United States. — Active inter- 

 est in gravity determinations by pendulum began in 1873 under the United 



t Handbuch der Geophysik, Vol. 1, p. 753 



