304 EXPLORATION GEOPHYSICS 



lations of the balance beam from being transmitted to the suspension prism. The 

 balance beam can be locked by turning a knob. 



The balance beam can be viewed through a glass window by removing the screw 

 caps at the ends of the tube. The torsion head is provided with a horizontal slide and 

 a fine vertical and azimuth adjustment. In addition, the height adjustment screw is 

 hollow which permits a considerable increase in the length of the torsion wire without 

 a corresponding increase in the overall height of the instrument. 



To decrease the observation time, tungsten wires having a torsion coefficient of 

 T= 1.2 c. g. s. units are used. The sensitivity is 0.1 Eotvos units per 0.1 scale division 

 of the graduated plate. 



Torsion Balance Theory- 

 Forces Acting on the Torsion Balance Due to the Gradient of 

 Gravity. — A small section taken between two converging equipotential 

 surfaces is shown in Figure 165, where U2 is the gravity potential on the 



upper surface and Ui that on the lower 



'^TZtU surface, g' and g are the values of the 



force of gravity on the U2 surface at 



"^ ^ two points separated by the distance ds. 



■}—r As previously shown g^ is greater than 



_^__ jk_. 



■t 



- __ g ; (see Figure 159 and Equation 34). 

 Fig. 165-Showing the curvature of the The angle of Convergence between 



lines of force of gravity and two equipoten- the tWO SUrfaCCS, for the SCCtion taken, 



tial surfaces U2 and Ui vi'hich converge at . . , ,. . 1 



the angle e. g and g' = gravity force along is e, and T IS the radlUS of CUrvatUrC of 



dh and dh', and dh and dh' = the distance it- r r r •, i-ni 



between the surfaces measured vertically the ImeS of JOTCe OJ gravity. 1 he SUr- 



curvature^oftheTravity *force Hne^s^ '"^ ° faccs are Spaced apart the amount dh' 



and dh at the points g' and g respec- 

 tively. The distance ds is in a horizontal direction, h is measured vertically 

 downward. 



It is a general proposition that g = —dU/ds, which indicates that the 

 force of gravity is the maximum potential gradient in the vertical direction. 

 (dh is the vertical direction, along a line of force of gravity, which defines 

 that direction or the direction of a plumb line, while the minus sign indicates 

 that the force of gravity, or potential gradient, is directed toward decreas- 

 ing potential.) 



It then follows, that the difference in potential between equipotential 

 surfaces, such as those of Figure 165, is dU = +^ dh since dh is measured 

 in —s direction. Applying this to points g' and g, it follows that dU (at g') 

 = g' dh', and dU (at g) = g dh. As noted, the value of dU (or Af/) is 

 everywhere the same between two adjacent equipotential surfaces so that 



g' dh' = g dh 

 and 



g'/g = dh/dh' (35) 



We are, however, concerned with the curvature of the lines of force of 

 gravity from the vertical. From Figure 165, the gravity force g' equals g 

 plus the rate of change of gravity in the direction s (along the equipotential 



