Chap. 8] MAGNETIC METHOD 321 



If the needle is not suspended in its center of gravity, a moment due to 

 gravity must be added. If e is the distance of the center of gravity from 

 the axis, 



Di = —emg cos r? sin t. (8-17a) 



If e subtends the angle f with the x direction and if the horizontal and 

 vertical projections of e are a = e cos f and d = — e sin ^, respectively, 



D2 = —mg sin i (a cos 77 + c? sin 77). (8-176) 



In the equilibrium position D =^ Di -\- D2 = Q so that 



MH sin a cos t + MZ sin i + mqa sin t /r. .^x 



tan 77 = —^ -^-^^-^ • (8-18) 



MH cos a — mgd sm t 



This formula is fundamerital for all magnetic balances. 



B. Prospecting Magnetometers 



1. In the Schmidt vertical magnetometer (Fig. 8-18) a magnetic system is 

 balanced on a knife edge at right angles to the magnetic meridian. Its 

 inclination is measured by means of a mirror attached to the system, in 

 conjunction with an autocollimation telescope system. The center of 

 gravity is on the south side below the pivot, and is usually readjusted so 

 that the balance system is horizontal in the area under investigation. The 

 balance system is surrounded by an aluminum case containing copper 

 dampers, thermometers, and levels. The case, in turn, is protected by a 

 cork-lined case to reduce the effects of abrupt temperature changes. The 

 magnetic system is supported by a bridge with two quartz bearings. Three 

 points on a movable arm fit three grooves on the underside of the system, 

 the vertical motion of the arm being controlled by an arresting lever from 

 the outside. 



The instrument is fastened to the tripod head by means of three pegs 

 on the bottom of the case. In all models up to 1935, deflections were read 

 by observing the relative displacement of two scale images. The scale 

 had forty divisions, of which the 0-, 20-, and 40-scale divisions were marked 

 by heavier lines which were used as "indices." Some users adjusted the 

 system to read 20 at a base station and used this reading as so that subse- 

 quent readings gave directly the positive or negative anomalies. In the 

 optical system of the newer models the scale has 60 divisions. Mounted 

 to the side of this scale is a glass plate with 3 index lines; the double scale 

 image is avoided and the range is 120 scale divisions. A teleobjective 

 lens now gives twice the focal length compared with the earlier models.- 

 If there is any doubt in which direction the scale of an older type mag- 



