GRAVITATIONAL METHODS 



337 



mark on the rod can be set at the H.I. (or height of instrument) of the 

 surveying instrument used. 



The divisions of the rod below the zero point are painted red, indicating 

 positive elevation differences, and the divisions above the zero mark are 

 painted black, indicating negative elevation differences. These elevation 

 differences are entered in the form with the 

 corresponding sign on the basis noted, as plus 

 where the ground rises and as minus where it 

 is lower than at the instrument station. In or- 

 der to obtain a proper value for the density of 

 the soil at the station, this quantity is measured 

 by the methods previously described. A ter- 

 rain can be surveyed in something less than 

 half an hour by an energetic crew. 



Computations 



The differences in elevation measured on 

 the 8 points of each circle (or out-distance) 

 are labeled Z and given a subscript indicating 

 the azimuth on which they were taken, in 

 accordance with the system of numbering 

 shown in Figure 187. For example, Zx is the 

 elevation difference in north azimuth, Zg the 

 difference in the N. 45° E. azimuth, Z3 that 

 in the east azimuth, etc., with the Z values 

 referring to a circle of given radius being 

 considered together. 



ADJUSTABLE 

 FOOT 



Fig. 188. — Showing a conve- 

 nient form of metric rod for ter- 

 rain correction survey. Rod has 

 an adjustable foot so that the 

 height of the instrument can be 

 set at the zero on the rod. 



In the terrain computation, the coefffcient b indicates the effect of the 

 terrain on the east-west gradient or Uy^. As shown in the equation follow- 

 ing, Z3 is positive and Z7 negative, and Z2, Z^, Zg and Zg enter the computa- 

 tion proportionately to the sin of 45° (0.707). (See also Equation 96.) 



Since Zi and Z5 are height differences in the north and south azimuths 

 respectively (directly north or south of the torsion balance), they will have 

 no effect and do not enter the equation. 



(« Uy,) : b = 0.707 (Z, + Zi-Ze- Z^) + Z^-Z, 



(98) 



The coefficient c gives the terrain effect on the north-south gradient, and 

 therefore Zi is positive and Z5 negative. Z^, Zg, Z^ and Zg enter in pro- 

 portion to the sin 45°. Z3 and Z7 do not affect the north-south gradient. 



(^ U^,) : c = 0.707 (Z2 + Zs-Zi- Ze) + Z,-Z, (99) 



In a similar manner the terrain effects for the curvature values relate 



