292 



EXPLORATION GEOPHYSICS 



torsion balance is shown in Figure 152. fF is a calibrated torsion wire of 

 very small diameter, terminating in a support carrying a small mirror and 

 an aluminum bar of negligible mass. A small weight is fastened to one end 

 of the bar, and a similar weight is suspended from a fine wire on the other 

 end. The angular deflection of the suspended system is measured with the 

 aid of a telescope by observing the shift of a scale image reflected by the 

 mirror. The torque T required to rotate the swinging system (balance 

 beam, weights, and mirror) through an angular deflection 6, with a torsion 

 constant of t, is 



The working equation of the torsion balance will be determined there- 

 fore by an expression for T in terms of the parameters measured at a par- 

 ticular station and the instrumental constants of the balance. 



The gravity force which turns the beam against the torsional resistance 

 of the wire may be divided into two parts, viz. : 



1, The force arising from 



LINES OF GRAVITATIONAL FORCE 



<r 



(a) 



i PLUMB 

 LINE 



<r 



FLAT BEDS — 



LINES OF GRAVITATIONAL FORCE 



(b) 



TORSION 

 BALANCE 



the curvature of the equipoten- 

 E_Qu.iP0TEN_TiAL tial surface passing through 

 the center of gravity of the 

 balance beam, called the curva- 

 ture quantity, and 



— :^^ 2. The force arising from 



■^-^=^^ —_ the convergence of the equi- 



---' " ' potential surfaces passing 



through the hanging weighf 



mass and through the mass on 



EQuiPqjEjLTiAL the end of the beam. This is 



SURFACE 



called the gradient of gravity. 



■VV///,V,V//A\V///.' 1 



Curvature of Lines of 

 Force of Gravity. — Consider 

 the direction of the lines of 

 force of gravity for a restricted 

 portion of the earth's surface 

 where there is no discontinuity 

 in density in the subsurface 

 and where the beds making up 

 the geological section are flat. 

 In such an ideal case, the di- 

 rection and intensity of the lines of gravitational force would be the 

 same at each of a series of closely spaced points across such an area. The 

 lines of force would be parallel to each other and their direction would 

 be shown by the direction of a plumb line. (See Figure 153a.) No forces 

 would act to produce a twist on a torsion balance placed in such a force 



Fig. 153.— (a) Illustrating conditions of lines of 

 force of gravity and an equipotential surface at right 

 angles to it, for flat uniform beds in a local area, (b) 

 Torsion balance placed in such a field experiences no 

 twisting force. Direction of force lines shown by plumb 

 line. 



