814 



ELECTRICAL METHODS 



[Chap. 10 



depth are more effective the greater the length of the antenna. Changes 

 in antenna capacity are determined by measuring its wave length or 

 natural frequency by (1) a resonance (Fig. 10-129a) or (2) a heterodyne 

 method (Fig. 10-1296). 



In the first method, a push-pull oscillator of variable frequency and a 

 measuring circuit M with rectifier meter are coupled to the antenna circuit. 

 If the antenna is in resonance with the oscillator circuit, maximum energy 

 transfer occurs and the meter will indicate maximum current. The ac- 

 curacy obtainable with this circuit is c^X = 0.1 m and dC = 0.1 cm. 



'Mm 



P0^ 



L' 00000000^ 



9*8 



-'OWOOMOOO 



SOm 



Atftimt. 



Variable 

 OscUMor 



Fig. 10-129a. Oscillator cir- 

 cuit in capacity-resonance 

 method (after Stern). 



jfotidotd 

 Oscillottr 

 Telefhane 



Fig. 10-129b. Beat method for measuring 

 changes in antenna capacity (after Stern). 



More accurate is the heterodyne method illustrated in Fig. 10-1296. 

 The frequency of the beat note may be determined by comparison with a 

 fork or other frequency standard. The measurement consists of deter- 

 mining the capacity of the standard oscillator to bring about a definite 

 beat note. Its sensitivity may be adjusted to almost any desired value. 

 Since the beat note is Af = fs — fx , (with either frequency given by 

 / = 1 /27r -v/LC), where /s is the frequency of the standard oscillator and 

 fx the frequency of the antenna circuit, it is seen that with 1/2x\/L = p, 

 the change in frequency with change in capacity is df = — ^pC" dC. 

 Therefore, since p = /C^'^, the sensitivity is given hy df = — \f dC/C. 

 It can be increased by using a high frequency and a low capacity. How- 

 ever, it is preferable to increase the accuracy in the determination of the 

 beat frequency. Stem"^ states that with the circuit shown in Fig. 10-1296 

 the accuracy was ±0.03 cm in dC, which corresponds to an accuracy of 

 several decimeters for depths varying from 10 to 30 m. He applied the 

 capacity method to the measurement of thickness of glaciers. Consider- 

 able diflBculties were experienced in the field because of changes produced 



"* Gerl. Beitr., 23(3), 292-333 (1929). 



