

Use of Mutual Inductometers. 499 



The most useful case of this is when the ratio arms are 

 equal, i. e. <7 = 1, and then these equations reduce to 



P = Q (2) 



and L 2 -L 1 + N = 2(m + M) (3) 



The best arrangement is to make L 2 = L X permanently in 

 the inductometer, and then the unknown inductance is given 

 directly by 



N = 2(m + M) (4). 



When Lj and L 2 are the upper and lower fixed coils in the 

 inductometer, the reading of the instrument is m + M and thus 

 N = 2 x Reading, and thus is read directly. The sensitivity 

 of the bridge is here much greater than when L 2 consists of 

 a separate balancing coil. 



§3. Measurement of Effective Resistance, 



If an alternating current at n ~ per second having an 

 effective value I in flowing through a circuit wastes energy 

 in it at the rate of R/ I 2 watts (including losses due to eddy 

 currents, magnetic and dielectric hysteresis, &c), then R' is^ 

 called the Effective Resistance of the circuit (for frequency n). 

 In general it increases with the frequency, and when tele- 

 phonic frequencies (500 to 2000 — per sec.) are reached, it 

 may often become very much larger than the ohmic resistance. 

 As its value governs the loss of energy, it is of the utmost 

 importance in telephone work to be able to measure it with 

 accuracy. In former papers already cited I have shown how 

 it can be directly measured by a mutual inductance bridge 

 simultaneously with the effective self inductance of the 

 circuit. When the bridge has equal ratio arms which can 

 be interchanged to ensure that they are identical, the method 

 is free from serious error ; but if unequal ratio arms have to 

 be employed, large errors may arise from the very small but 

 unavoidable self inductances of these arms. The importance 

 of this in the simple self-inductance bridge was pointed out 

 lately by Giebe *, and upon his mathematical result he based 

 his ingenious method of measuring very small inductances. 



I have applied similar treatment to the somewhat more 

 complicated case of the mutual inductance bridge as 

 follows. 



* Ami. der Physik, p. 941 (24), 1907. 



2K2 



