Chap. 7] 



GRAVITATIONAL METHODS 



177 



By combination of (7-48^) and (7-48t), 



dy' 

 so that by substituting (a — X) for jS and considering eq. (7-48/) 



r'2 ax'2 cos2X\a?/2 aa;V' 



(7-4 



r/a^t/ a^c/\ X . o ^ a't.^ „ 1 



Da = X 



(7-506) 



Fig. 7-60. Gradient and curvature effects on balance beam as functions of azmiuth. 



where d'^U/dy'^ - d'^U/dx^ = C7a is the so-called north and 2 d^U/dxdy = 

 2Uxy the east component of the curvature values. The equation indicates 

 that the curvature effects are proportional to the double azimuth, while the 

 gradient effects are porportional to the azimuth itself (see Fig. 7-60). 



In the equilibrium position, T(p = Di + D2, where t is the torsional 

 coefficient of the wire and ^ the angle of deflection. The beam deflection 

 is measured by mirror (attached to the beam), graduated scale, and tele- 

 scope, or by photographic recording. In both cases, an "autocollimation" 

 method is applied with the "objective" lens in front of the balance-beam 

 mirror. If n is the reading corresponding to a deflection ^, and no (torsion- 



