MAGNETIC METHODS 129 



and since tan"^ is small compared to 1 (for small 6) the above can be written 



S-So 



tan e — 



2/ 



since the design of the instrument is such that the maximum deflection angle is less than 

 2°, we can derive the relationship; 



S-So = 2f ^^-''''3^ (48) 



vi'gh 



If Si = the scale reading at one station and S^ the scale reading at 

 another station, corresponding to vertical intensity Zi and Z^ respectively 

 at the two stations, then 



2/MiZi^^ (49) 



m gh 



If£ = ff (50) 



is called the scale value of the instrument then 



Z,-Z2 = E(S,-S2), (51) 



or in words : the difference in vertical intensity at two stations is propor- 

 tional to the difference in scale readings at the two stations. Further details 

 are given in referencesf . 



Theory of Operation of Horizontal Magnetometer. — The Schmidt- 

 type horizontal component magnetometer is used to measure differences in 

 the horizontal component of the earth's field at different stations. The 

 same general arrangement of knife edge, blades, block and quartz bearings 

 is used. The magnetic blades, however, stand vertically and the instrument 

 is operated with the plane of rotation of the blades in the magnetic 

 meridian. 



Figure 55 shows the vector relationships of the various forces acting 

 upon the moving system. The vertical component of the earth's field acts 

 chiefly against the bearings and hence has a negligible rotational component 

 at the small angles of tilt utilized in the measurements. 



The magnetic component of the earth's field causes a torque, which may 

 be expressed by the following equation : 



but since 2pl = M 



Tm = 2Hpl cos e - 2Zpl sin 6 



Tm = MH cos e - MZ sin (52) 



t O. C. Lester, "A Simple Derivation of the Working Equations of Magnetic Variometers for 

 the Vertical and Horizontal Intensity." A.A.P.G. Bull, Vol. 12, p. 855, 1928. 



C. A. Heiland and W. E. Pugh, "Theory and Experiments Concerning a New Compensated 

 Magnetometer System," A.I.M.E. Tech. Pub. 482 July, 1932. 



C. A. Heiland, "Theory of Adolf Schmidt s Horizontal Field Balance," A.I.M.E. Geophysical 

 Volume, 1929, pp. 261-314. 



