Chap. 101 



ELECTRICAL METHODS 



813 



_^ 



02 



0.4 0.6 



08 



1.0 



ing for water. In Russia, 

 Petrowsky tried the quarter- 

 wave procedure for the location 

 of ore bodies but nothing definite 

 is known about results obtained. 

 It is noted that neither theory 

 nor the model experiments dis- 

 cussed above make allowance for 

 the absorption ; therefore, the re- 

 flected energy may be less than 

 assumed, which would make the 

 maxima and minima less distinct. 

 The absorption would increase 

 with an increase in conductivity 

 and frequency. 



2. The capacity method is based 

 on the fact that the capacity of an antenna and therefore the natural 

 frequency of an oscillator is dependent on the distance and electrical prop- 

 erties of bodies in its vicinity. Assume a long cylindrical conductor of 

 the length I and radius r in a medium with the dielectric constant kq , 

 stretched out parallel with the surface of an infinite medium of the die- 

 lectric constant k at the distance d. Then the antenna capacity is 





Fig. 10-128a. Theoretical variation of 

 electrical field strength with distance of 

 reflecting sheet (after Hummel). 



c = 



K{sl 



( loge ^ + —T— log. , 



5) 



(10-69a) 



This expression is composed of the capacity of the conductor and that of 

 an image at depth 2d, the reflection factor being {k — kq)/{k -f kq). For 

 K = 0, and Ko = 1 (antenna in air), eq. (10-69a) becomes 



c 



I 



2 log 



2d 



(10-696) 



OZ 



0.4 06 



08 



to 



1.2 



Fig. 10-1286. Experimental curve, determined by 

 varying distance of sheet (after Hummel). See also 

 preceding figure. 



It is seen that the ele- 

 vation of the antenna 

 above the interface is 

 the predominant factor; 

 hence, this method has 

 been proposed for the 

 measurement of the 

 height of planes and 

 dirigibles. Changes in 



