GRAVITATIONAL METHODS 

 R is the radius of the earth at the equator. Hence, 



331 



M=u^^= 1 ^ [978.039 ( 1 + 0.0053 sin^ cf> - 0.000007 sin^ 2<^) ] 



1 



[978.039 (0.0053 sin 2<^) ] (approximately) 



6.38 • 108 

 = 8.15 sin 24, • 10-9 (approximately) (90) 



The planetary correction for the curvature is given hy the formula : * 

 [/a = 5.15£(1 + cos2c^) • 10-9 (91) 



Graphs showing the latitude effects are given in Figure 186. 



LATITUOe 



Fig. 186. — Effects of latitude on quantities measured by the torsion balance. (Courtesy of 



E. V. McCollum.) 



Topographic Corrections 



The magnitude of the topographic correction to be applied to the gravity 

 gradient depends on several factors. For example, the correction for a 

 small mass, say a boulder, would depend on : the horizontal distance and 

 the vertical distance of the boulder from the torsion balance, the dimensions 

 of the boulder, and its density relative to that of the surrounding media. 

 The effect of the small mass on the gravity gradient is a maximum if the 

 mass is situated within a space angle of 40° to 60° below or above the hori- 

 zontal plane through the balance, and the effect is substantially zero when 

 the small mass is either vertically below or level with the balance. 



Except in very refined work, the effect on the gradient is negligible for 

 irregularities of mass located within ±5° of the horizontal plane through 



* Compare also, H. Shaw and E. Lancaster Jones, "The Theory and Practical 

 Employment of the Eotvos Torsion Balance," Mining Magazine, July, 1927. 



