116 - 



be expressed in terms of the actual orientation of that arm, /?„ , and 

 the error associated with that arm, e„ , that is introduced by the 

 metal mass of the cradle: 



6 ■ = e + e 



"^ " (6.1) 



Since the compasses were placed upon each arm at about the same 



distance from the center of the instrument, and if one assumes that 



the effect of the metal mass upon the compass readings is the same 



for each arm (i.e., radially inward), then the errors associated with 



each of two collinear arms should be equal and opposite in sense. 



(See Figure VI-A) . Accordingly, the sum of the errors associated 



with the reading for each arm should equal zero; 



4 



I ^n = ° (6.2) 



n=l 



If one expresses the actual orientation of each arm in terms of the 

 orientation of the arm with the smallest value of apparent direction. 

 Equation 6.1 may be written as: 



(6.3a) 



^4' = ^3 -^ ^°° ■*■ U (6.3b) 



