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BELL SYSTEM TECHNICAL JOURNAL 



the flexibility of bridges of type 1, obtained by their unequal ratio 

 arms. On the other hand, the use of substitution to measure the 

 resistance or conductance component of the unknown has many ad- 

 vantages, the principal one being that it allows the choice of a type 

 of bridge which will give directly the reactance component of the 

 unknown in terms of an adjustable resistance and then by use of 

 the substitution method to balance the resistance or conductance 

 of the unknown by means of a second adjustable resistance, thus 

 obtaining the ideal method of balance, using two adjustable re- 

 sistances. 



For the purpose of illustration, the case of the measurement of an 

 inductive impedance may be taken. In general, the most desirable 

 method would be to balance the reactance by means of series resistance. 

 This can be done by means of the bridges of Figs. 2e or 2g. Choosing 

 Fig. 2e as the preferred form, the bridge would normally take the 

 form of Fig. 3a. 



Fig. i—{a) Bridge of type 2 for measuring self-inductance, {b) The same bridge 

 modified by the use of partial substitution. 



For normal operation, Cad and Rad would be the adjustable 

 standards. The series inductance of the unknown would be given 

 directly as KRad, while the series resistance would be given as K/Cad- 

 This measurement of the series resistance requires an adjustable 

 capacitance and a computation due to the reciprocal relation. Now 

 suppose a fixed value for Cad were used and an adjustable resistance 

 standard Rs placed in series with Zx, giving the form of Fig. 3b, in 

 which Rad and Rs are the adjustable standards. If terminals Zx are 

 short circuited, the conditions for balance are Rs = K/Cad and 



