88 GRAVITATIONAL METHODS [Chap. 7 



with respect to the beam. If D is the couple produced by an outside 

 mass (or by the ''curvature" effect of the gravitational field), and G-(p is the 

 couple produced by the gravity compensator, then Tip = D -{- G(p. It is 

 seen that t, the torsional coefficient of the wire, is reduced to t — G = t' 

 by the action of the deflectors and that the balance becomes more sensitive. 

 The "apparent" torsion coefficient is given by 



r' = r- ^ (1 + 3 cos 2,A), (7-4) 



where K is the moment of inertia of the balance beam, M the deflector 

 mass, r tlie distance from the beam and \l/ the deflector angle from hori- 

 zontal. The difference between the extreme values of t (when ^ is 90° 

 and 0°) is 6kKM/r . With the arrangement used by Eotvos (very thin 

 wires, r = 0.15, ikf = 40 kg, r = 10 cm, and K = 20,000 C.G.S.) it is 

 possible even to overcompensate external gravity forces. The gravity 

 compensator is applicable in gravitational model experiments not only 

 with a curvature variometer but with a gradient variometer as well. 



The gravity multiplicator is essentially a gravity compensator for 

 "dynamic" measurements. The deflector positions are changed in syn- 

 chronism with the beam oscillations and thereby the beam amplitude is 

 gradually increased. 



IV. PRINCIPLES OF GRAVITATION AS APPLIED IN GRAVITY 



MEASUREMENTS 



As in all geophysical problems involving fields of force, the analysis of 

 the gravitational field makes extensive use of two parameters, the field 

 vector and the potential. The gravity field vector has the peculiarity 

 that its three space components are very unequal; the horizontal compo- 

 nents are small and the vertical component is almost equal to the total 

 vector. The force of gravity, that is, the pressure which Ig mass exerts 

 on its base, is measured in units of g • cm. see" , or dynes, and is numerically 

 but not physically equal to the acceleration of gravity measured in units 

 of cm.sec" , or "Gals." Convenient practical units are the milligal, or 

 10"^ Gal, and the microgal, or 10~^ Gal. Gravity varies from 9.78 m-sec~^ 

 at the equator to 9.83 m-sec~" at the pole. Gravity anomalies rarely 

 exceed 100 milligals. 



The potential of the gravity field is frequently employed in its analysis 

 since, contrarily to the vector, it is a scalar quantity. Its first negative 

 derivatives with respect to the coordinates represent the components of 

 gravity. The gravity potential at the earth's surface may be defined as 



" Named after Galileo. 



