Chap. 7] 



GRAVITATIONAL METHODS 



^^ = - V3(a"b"+aV0 [(^^^ + ^-'^ + b- (^-^' + -"'] 



^^" = a"b' + a'b" L'^' + V' ^"\ ■ 



For positions (1) and (3): 



181 



(7-52t) 



C/a = 



2U^ = 



V3(a 



_b^^ ITa'-l^' a"1 



(7-52i) 



It may happen that for some reason one beam of the double variometer 

 gets out of order. It is then possible to work with one beam only. How- 

 ever, more than three positions are required. For gradients only, obser- 

 vations are necessary in four positions, and for all derivatives five azimuths 

 are required. 



For observations in four azimuths, it is advisable to take the first 

 reading in the azimuth N 45° E. and rotate the instrument by 90° inter- 

 vals. Then, for beam I : 



(position 1) a = 225°: Ai' = sl'Ua + b' sin 45° f7„ - b' sin 45° Uyz 



(position 2) a = 315°: A2 = -eL'U^ + b' sin 45° C7„ + b' sin 45° Uy^ 



(position 3) a = 45°: A3 = a'U^ - b' sin 45° U„ + b' sin 45° [/„, 



(position 4) a = 135°: aI = -sl'Ua - b'sin 45° U„ - b' sin 45° Uy.. 



For beam II: 



(position 1) a= 45°: a'/ = a"C/A - b" sin 45° t/„ -\- b" sin 45° Uy, 



(position 2) a = 135°: A2 = -a"(7A - b" sin 45° f/x. - b" sin 45° Uy, 



(position 3) a = 225°: A3' = a"t/A + b" sin 45° U^, - h" sin 45° Uy, 



(position 4) a = 315°: a'/ = -&"Ua + b" sin 45° Ur, + b" sin 45° Uy,. 



