650 



ELECTRICAL METHODS 



[Chap. 10 



and the air condenser is re-adjusted to the value C" to give voltage reso- 

 nance. Since Cs = C" — C, the dielectric constant is given by k = (C" — 

 C')/Co , where Co is the geometric capacity of Cs. This method also 

 furnishes the conductance component or the equivalent damping factor 

 by an analysis of the shape of the resonance curve, by varying the con- 

 denser Ca in steps and observing the corresponding voltages on either side 

 of and at the resonance point. If Ci and d are two condenser readings 

 obtained on either side of the resonance point where the voltage is ^ of 

 the maximum e.m.f., and if AC is the difference of these two readings, the 

 phase shift of the resultant in respect to the conductive component is 

 given by 



2C, 



tan <p = 



AC 



(10-16) 



According to eq. (10-lOc) the phase shift is tan (p = ku/^ttg. In the 

 equivalent circuit (Fig. 10-1 5c) the reactance component of the current 



Jll fc. 



I, 



w 



Cg = Ko^e 



J? = 



AAAA- 

 / 



(o) 



(b) 



4n<rCe 



(c) 



Fig. 10-15. (a) Soil condenser. (6) Resonance method of determining dielectric 

 constants of soils, (c) Reactive and conductive components through soil condenser. 

 (Adapted from Ratcliffe and White.) 



Ic is controlled by the effective capacity of the soil condenser, or Cg = 

 kCq , whereas the conductive component is given by the resistance R = 

 l/47ro-Co. Hence, by substitution, R = 2/ajAC. The method of deter- 

 mining the conductive component from the decrement of the response 

 curve furnishes good jesults only for comparatively high frequencies, of 

 the order of 0.2 to 5 megacycles.* 



2. Substitution method. In this method the impedance of the soil speci- 

 men is determined^ by substituting for the coil condenser a simulating 

 unit consisting of a resistance with a condenser in parallel. These are 

 varied until the same resonant output voltage is obtained. A tuned cir- 

 cuit loosely coupled to an oscillator and provided with a beat oscillator 

 and low-frequency detecting unit may be used in these measurements as 

 shown in Fig. 10-16. From the resistance and capacitance components 



8 J. A. Ratcliffe and F. W. G. White, Phil. Mag., 10, 667 (1930). 



9 C. B. Feldman, I.R.E. Proc, 21, 764-801 (June, 1933). 



