324 



EXPLORATION GEOPHYSICS 



Position 2 



4>'= 300° 

 (Balance I) 



n\ - n'o = -a' sin 60° Ua - 2a' cos 60° Ury + b' sin 60° [/« + b' cos 60° Uy 



K84) 



<p" = 120° 

 (Balance II) 

 n"2 — n"o = — a" sin 60° Us — 2a" cos 60° Ux 



b" sin 60° Uxz — h" cos 60° Uy 



U85) 



Position 3 



<!>'= 60" 

 (Balance I) 



n\ — n'o — a' sin 60° C7a — 2a' cos 60° Uxy — b' sin 60° Uxz + b' cos 60° Uyz 



0" = 240° 

 (Balance II) 

 n"s — n"o =a" sin 60° [7a — 2a" cos 60° Uxy + b" sin 60° Uxz — b" cos 60° Uy 



Two of the unknowns can be found by forming the arithmetic mean of the deflec- 

 tions as indicated : 



^,^^n\ + n'. + n'. and >."o ^ ^"^ + ^^"^ + ^"^ 



O " 



Calling n'l — n'o = A'l ; n's — n'o = A'j/ n's — n'o = A's "j 



n"i — w"o = A"i ; ^"z — n"o = A"2 ; ^"s — n" o = A"3 j 



(86) 

 (87) 



Solution of the simultaneous equations for the gravity values can be accomplished by 

 using either Ai and As, or A2 and A3. The most simple and usable set of equations, 

 however, results from the Ai and A2 values and is as follows : 



Uxz = O ( A'2 - A'a) - S(A"2 - A"3) 



Uyz = P(A'2 + A'3) - S(A"2 + A"3) , 



[7a = -Q ( A'2 - A'3) + r( A"2 - A"3) ! 



2Uxv = -i?(A'2 + A'3) + r(A"2 + A"3) 



(88) 



Instrument Constants. — In Equation 88 the values O, P, Q, R, S, and T are 

 instrument constants which combine the constants a and b from both balances. The 

 relations involved are : 



P -o 



R=Q ' V3~ 



T=^ 

 b" 



(89) 



