MAGNETIC METHODS 97 



of an earth inductor ; occasionally, however, a dip circle is employed. The 

 dip circle comprises a magnetized needle, which is supported so that it 

 is free to swing in a vertical plane, and a circle graduated in degrees. 

 An axle passes through the center of gravity of the magnetized needle 

 and terminates in small pivots which rest on pivot bearings. The angle 

 of dip may be read directly ofif the vertical graduated circle which is 

 concentric with the axis of rotation of the needle, provided this axis is 

 perpendicular to the plane on the magnetic meridian. If the needle does 

 not swing in the plane of the magnetic meridian, measurements must be 

 made for two orientations of the instrument at right angles to each 

 other. From these two readings, /„ and x'oo-a). the true dip angle i 

 can be calculated by the formula 



cinHa + ctn^f (90— a) = ctn^i 



Earth Inductors. — The earth inductor may be used to determine the 

 inclination of the earth's magnetic field, any component of the earth's 

 magnetic field, or the direction of the magnetic meridian.* 



Various designs have been suggested. The operating principle of all 

 of them, however, is essentially similar to that of a small dynamo. When 

 a coil of wire is rotated in a magnetic field so as to cut magnetic lines 

 of force, an E.M.F. is induced in the coil. The magnitude of the induced 

 E.M.F. depends on the number of magnetic lines of force which are 

 cut by the coil and may be expressed by an equation of the form : 



^ 2NHA 

 E = 



where ^ 



E = the average E.M.F, induced in the coil on rotating it through one- 

 half turn. 

 A^ = the number of turns of wire in the coil. 



H = component of the earth's magnetic field parallel to the axis of ro- 

 tation of the coil. 

 A = area of the coil. 

 T = time for one-half turn. 



The induced E.M.F. creates a flow of current when the circuit is closed. 

 The magnitude of this current is determined by the induced potential and 

 the impedance of the coil and auxiliary circuit. 



Evidently, when the plane of the coil is parallel to the magnetic field, 

 no lines of magnetic force are cut, and the induced E.M.F. and current 

 are zero. Hence, to determine the magnetic inclination with an earth 

 inductor, it is only necessary to measure the angle of inclination of the 

 brush assembly system making contact with the commutator of the coil 

 when no current flows as the coil is rotated. 



* For a detailed description of the theory of the standard earth inductor used for 

 inclination measurements see N. E. Dorsey, "The Theory of the Earth Inductor as an 

 Inclinometer," Terr. Mag. 18 (l) pp. 1-37, 1937. 



