so 



Chap. 10] ELECTRICAL METHODS 649 



flection occurs at the end, the decrease of the current with distance is 

 given by 



7, = U-e-f^ (10-15a) 



Assuming further that the displacement current is negligible, the damp- 

 ing coefl&cient may be written 



Y = 2ir V7^ , (10-156) 



that is, damping increases with frequency / and ground conductivity a. 



It is seen that /j; = /o/e when x^ = l/y. Hence, x^ = j^r \/ ~r ^ 



that 



a = -^T- (10-15c) 



4irrce/ 



if Xe denotes the distance at which the current has dropped to — - of its 

 value at the source. 



F, Methods for the Determination of Dielectric Constants 



Since the capacity of a condenser is proportional to the dielectric con- 

 stant of the medium within, most laboratory methods for the determina- 

 tion of the dielectric constant make use of the difference in the capacity 

 of a condenser with and without the substance. (1) The change in capac- 

 ity may be measured directly by the resonance method. (2) The more 

 common procedure, however, is to determine the impedance of a specimen 

 by a substitution method. (3) The ratio of the reactive and conductive 

 components may be determined by the phase-shift method. (4) Dielectric 

 soil properties may be studied by an analysis of the ellipse of polarization 

 of surface radio waves. 



1. Resonance method. In all laboratory methods for the determination 

 of soil properties at radio frequencies, a soil condenser is applied, con- 

 sisting of two concentric cylinders separated by an insulator (Fig. 10-1 5a). 

 Most measurements consist of, or are equivalent to, determining the 

 geometric capacity Co of this condenser and comparing it with its capacity 

 when filled with soil (Cs). 



In the resonance method (Fig. 10-156) a source of RF is coupled to a 

 circuit containing the secondary of a mutual inductance in parallel with a 

 variable condenser Ca and the soil condenser Cs. The voltmeter V in- 

 dicates a maximum at the point of resonance. The soil condenser is first 

 removed and the condenser Ca is so adjusted that resonance is obtained. 

 Assume that its capacity is then C The soil condenser is then inserted 



