GRAVITATIONAL METHODS 319 



The value of ^r is about 1000 or 10^ dynes; g times the differential 

 curvature in units of 10~^- gives R in units of 10~^, Since the field 

 measurements of R are not accurate within a few per cent, the numerical 

 value of R in Eotvos units (or 1 X 10""^ dynes) is used. 



The values of curvature for R actually measured in the field commonly 

 range from 5 to 50 Eotvos units. Large values of R are much more common 

 than large values of the gradient. 



A torsion balance with a hanging weight is acted upon by two moments 

 of force, Ml and Mg. The rest position of the balance system represents 

 a balance between these moments and the resistance to twist of the torsion 

 wire in the instrument. Since the torsion coefficient of this wire is known, 

 a means is thus available for measuring these moments. 



Ml arises from the forces acting on the instrument due to the gradient 

 of gravity and is composed of a N-S component Uxz and an E-W component 

 Uyz. Mg arises from the forces acting on the instrument due to the curv- 

 ature conditions of the equipotential surface of gravity passing through 

 the center of gravity of the instrument. The curvature quantity is also 

 made up of two components, namely U^ (the N-S component) and 2Uxy 

 (the E-W component). 



COMPUTATION OF GRAVITY DATA FROM TORSION 

 BALANCE RECORDS 



Methods of Observing Deflections of the Beam. — In the torsion 

 balance with a hanging weight, the sum of the gradient moment Mi and 

 the curvature moment M^ is balanced by the twist of the torsion wire at 

 equilibrium. With t = the torsion coefficient of the torsion wire and a = 

 the angle of deflection of the beam, when equilibrium has been reached, 

 we have 



Ta = Ml + Ms 



The deflection can be measured by a telescope and graduated scale, 

 utilizing the mirror on the stem of the balance beam. This system is shown 

 in Figure 180. The distance / (focal length of the telescope lens) is in scale 

 divisions. 



With no forces acting on the torsion balance there would be no deflection. 

 A reading of no represents this torsionless position of the beam. If a 

 deflection angle a of the beam is observed, the change in scale reading 

 corresponds to the double angle or 2a, designated by a scale reading of n. 

 Where D = f : 



n — no = 2 a D (71) 



A second method of observing balance beam deflections is to place a 

 lens of focal length / in front of the balance beam mirror. A source of light 

 and a photographic plate are both set at the distance of the focal length 

 from the lens, as is shown in Figure 181. 



