648 ELECTRICAL METHODS [Chap. 10 



ties and resistances to obtain balance, 



LojCo wCaJ 



Rx = \^ - 4t\ ■ r. -\-Rz-Ro, (lO-lSc) 



Rs — Ri 

 so that if Cx = 0, Rx = Rs — Ro • Also, 



1 Co 



a = CO ^ ^ . (10-13d) 



\Co CsJ 



+ w (Rs — Ro) 



A method for determining the ground resistivities by induction is ar- 

 ranged as follows.^ A circular loop is laid out flat on the ground in such 

 a manner that its radius may be varied. In its center a pick-up coil is 

 set up, likewdse in a horizontal position. The e.m.f. induced in it is 

 measured, in respect to amplitude and phase, with a compensator whose 

 pickup coil is connected to the primary loop. An amplifier and phone, 

 or meter, indicates the balance between induced current and compensation 

 current. The e.m.f. induced in the pickup coil (and therefore the field 

 H) is dependent on the current / of the frequency / flowing in the primary 

 loop with the radius R. If p is the resistivity of the medium within range, 



? = '^, (10-14) 



^ P 



where c is a constant. The depth penetration is assumed to be equal to 

 the diameter of the loop; hence, the resistivity measured may not be a 

 true but an apparent resistivity. Further details will be given in the 

 section on inductive methods (page 797). 



6. High-frequency methods. The frequencies employed here range from 

 10 to 100 kilocycles. Several years ago when this frequency band was 

 used extensively, the Radiore Company developed a bridge in which the 

 impedance of the specimen in one arm of the bridge was measured by 

 comparison with a known resistance with capacitance in parallel in the 

 other arm. 



Measurements of the ground characteristics at high frequencies in situ 

 may be made with a double wire Lecher system^ or with the single ground 

 wire of a high-frequency generator, buried at a shallow depth parallel with 

 the surface. The current (measured at various points with a thermo- 

 milliammeter) decreases with distance from the source since the waves die 

 out because of space damping. If the wire is long enough so that no re- 



6 J. Koenigsberger, Beitr. angew. Geophys., 3(4), 392 (1933); 4(2), 201' (1934). 

 See also pp. 782 and 796, this chapter. 



^M. Abraham, et al., Phys. Zeit., 20(7), 145 (1919). 



