338 EXPLORATION GEOPHYSICS 



to elevation differences on given azimuths as shown by the following 

 equations : 



(^ U^y) •.d = Z,-Zj, + Ze-Zs (100) 



{-=iU^) \ e = Z,- Zs + Z,- Z, (101) 



It is apparent that elevation differences in the azimuths 1, 3, 5, and 7, 

 or north, east, south and west, do not affect the east-west curvature 

 quantity. 



The coefficients h, c, d, and e are computed for every circle (or out- 

 distance where rod readings are taken). They are given subscripts relating 

 to the circle involved ; for example, bi represents the correction effect for 

 the first or 1.5 meter circle, and b^ that for the out-distance of the second 

 or 3 m., etc. 



The operations indicated in Equations 98 to 101 result in a numerical 

 value for b, c, d, and e for a given circle. For example, the amount oi bi 

 might be + 1.4 for the 1.5 meter ring, and for ei for the same out-distance 

 the value might be —7. (See sample computation sheet.) 



As gravity effects are inversely proportional, in general, to the inverse 

 square of the distance, it follows that elevation differences on the circles 

 nearer the station will exert more influence than will those which are 

 farther away. This is "weighted" by proper constants for the b, c, d and e 

 values. 



As shown by the terrain correction form, the value for bi above (repre- 

 senting the 1.5 zone) is multiplied by the factor 0.59. For the 3-meter ring 

 the factor is 0.161, and for 5 meters it is .0577. These factors are the same 

 for the north-south and for the east-west gradient effects. A different set 

 of factors applies to the curvature quantities with a value of 0.8255 for 

 the 1.5 band, 0.49 for the 3-meter, and 0.3357 for the 5-meter zones, etc., 

 as indicated on the form. Both the north-south and the east-west curvature 

 effects take the same set of factors. These factors are the values K referred 

 to in Equation 97 and are valid for a torsion balance positioned with its 

 center of gravity 90 centimeters above the ground surface. 



The terrain effects on the curvature quantities are considerably greater 

 than on the gradients, as indicated by factors of 0.8255 for the 1.5 meter 

 zone on the curvature and 0.59 for the gradient. This means that the curva- 

 ture quantities are influenced more by terrain effects than are the gradients. 

 This fact must be considered during interpretation of the results. 



An example illustrating the preceding discussion on the terrain cor- 

 rection is given in the sample calculation on page 339. To save space, this 

 correction is not complete, as the corrections should be carried out until 

 the effects from the farther rings are small with respect to the curvature 

 effects. The corrections are in Eotvos units, and from the sample terrain 

 correction sheet are entered on the plate calculation form, in the box at the 

 lower left. 



