128 EXPLORATION GEOPHYSICS 



blocks and blades, is to position the center of gravity of the magnetic 

 system at a point below and on the south (pole) side of the axis of rota- 

 tion or knife edge. 



m — total mass of magnetic system in grams. (Note change in the meaning of m 

 as here used in relation to m as used previously for pole strength.) 



g = acceleration due to gravity in cm. per sec. per sec. 

 2 / = distance between magnetic poles of system. 



a ■=. horizontal displacement and h = vertical displacement of center of gravity of 

 the system from its axis of rotation, in cm., when 6 = 0°. 



p = pole strength of system c.g.s. units. 

 M = 2 pi z= magnetic moment of system. 



Z = vertical component of the magnetic field, gammas. 

 Pz ^ pZ := force on pole due to vertical component of earth's field. 



6 = deflection angle of system. 

 Wi = temperature coefficient adjustment weight. 

 Wo = latitude adjustment weight. 

 Ws = sensitivity adj ustment weight. 



The torque Tz on the magnet system due to the vertical magnetic component Z, 

 is given by the equation : 



Tz = (2 pi) Z cos e 



However, 2 pi = M = magnetic moment of the magnetic system from which we 

 can write : 



T^ = M Z cos e (46) 



which is the torque due to the vertical component of the earth's magnetic field, when 

 the magnetic system is oriented with its axis in the plane of the magnetic meridian, 

 and horizontal. 



The torque due to gravity Tg, opposes the magnetic torque Tz. The gravitational 

 torque Tg may be expressed by 



Tg = m'ga cos 6 + m'gh sin (46a) 



When the magnetic moment equals the gravity moment, the system will come to 

 equilibrium, and then Tz = Tg or 



MZ cos 6 = m'ga cos 6 + m'gh sin 6 



from which may be derived 



, n MZ — m'ga .,-. 



tan e = , ^ (47) 



mgh 



To convert the angular deflection of the magnetic system into scale deflection it is 

 seen that 



tan 2 ^ = "^ ~ ^'' 



f 



where 9 = the angle of tilt of the system 



S = scale reading corresponding to this deflection 



So = scale reading corresponding to ^ = 0°, or when the axis of the system is 

 horizontal, 

 f = the focal length of the objective lens of the telescope. 



But, from trigonometry, 



2 tan e 



tan 2 61 = ■ 



1— tan^ e 



