Chap. 8] MAGNETIC METHOD 323 



_, MK sin a cos I + MZ sin i + mga sin i ,r, -.^x 



s - So = 2f r-p= — -, ^ . (8-19) 



MR cos a — mga sm i 



In the normal operating position, a = 7r/2 or 3t/2, i = 7r/2, and d and a 

 are negative. Then 



. - ,. = ^MZ-mga 



mga 



If a reading s corresponding to a vertical intensity Z has been obtained at 

 one locality and a reading s' at another with the vertical intensity Z' , 

 the difference in the readings 



mga 

 Hence, AZ = As-m^d/2tM = AZ = Asc, if 



is the scale value of the instrument. Eq. (8-20) may also be written 



Z — — • ^a J , so that 



Til 



e(s - So) = Z - —.ga = Z - Zo. (8-23) 



It is seen that (m/M)-ga is the vertical intensity for which the system 

 is adjusted. 



If the instrument deviates from the correct azimuth by the angle 8, a 

 change in scale value takes place and 



Ci = Co H 2f ~ • (8-24a) 



Hence, the deflection decreases when the instrument is rotated to the 

 north of the K-W position and if the reading is greater than 20. For a 

 reading less than 20, the deflection increases. If the instrument is rotated 

 to the south, the readings increase if greater than 20, and decrease when less 

 than 20. For small misorientations (up to 10°) the error cancels out in 

 two diametrically opposite (Aa = 180°) positions. 



If the instrument is tilted, the effect is an optical one in the E-W, and 

 an earth-magnetic one in the N-S direction because the horizontal intensity 

 becomes effective. Whether the errors produced thereby cancel in the 

 mean of the two operating positions depends entirely on whether the tilt 

 is produced by a wrong setup on the tripod head or by an inchnation of 

 the axis of rotation of the latter. An E-W component of tilt of the axis 



