Chap. 71 



GRAVITATIONAL METHODS 



183 



(1) a = 0^ n'l - no = 2si"U^ + h"Uy, 



(2) a = 72°; n^ - n'o = a" sin 36° C/a - 2a" cos 36° U^y 



+ b" cos 72° Uy, - h" sin 72° U, 



(3) « = 144°; 7H - no = &" sin 36° U^ + 2a" cos 72° f/^v 



- b" cos 36° Uy^ - b" sin 36° U, 



(4) a = 216°; w'/ - n'o = a" sin 36° lU + 2a" cos 72° t/.„ 



- b" cos 36° Uy, + b" sin 36° f/, 



(5) a = 288°; n',' - no' = a" sin 36° U^ - 2a" cos 36° U^ 



4- b" cos 72° Uy^ + b" sin 72° U,> 



For beam I reverse only the signs for gradients. 

 Hence, for beam II : 



U^z = r [M(n5 - nz) + N(w4 - na)] 

 b 



Uyz = ^ [P(n6 + 712 - 2ni) - 0(n4 + na - 2ni)] 

 b 



j7a = -- [N(n5 - na) - M(n4 - na)] 



2f/:.„ = - [0(w5 + n2 - 2ni) - P(n4 + na - 2ni)], 

 a 



} (7-54o) 



where 



M = 

 N = 

 O = 

 P = 



sin 72' 



2 - cos 72° + cos 36° 



sin 36° 



2 - cos 72° + cos 36° 



1 + cos 36° 



or 0.38042 

 or 0.23511 



5(cos 72° + cos 36°) 



1 - cos 72° 

 5(cos 72° + cos 36°) 



or 0.32361 

 or 0.12361. 



With the foregoing coefficients, the instrument constants a and b may 

 be combined for convenience in calculation. Equations (7-54a) contain 



