502 Mr. A. Campbell on the 



contrary, for the effective resistance T the correction may 

 become very important, since co 2 is large even for moderate 

 frequencies. For example, let 11 = 99, S = l, P — Pi = 20, 

 M = l millihenry, Z = 10 microhenries, \=1 microhenry, and 

 n = 1000 — per sec, giving a> 2 =40 x 10 6 . 

 Then we have 



T = P -Pi + 3-6=:23-6 ohms, 



while X=100M~3-6xl0- 6 



= 0-1-3-6 Xl0- 6 henry. 



Thus the small inductances I and X affect the measurement 

 of the effective resistance T by as much as 15 per cent., while 

 the self inductance X is only affected by 3' 6 parts in 100,000. 



This example shows how much more difficult it usually is 

 to measure effective resistance than self inductance. The 

 difficulty is got over, however, if we can make RA = SZ 

 (i.e. <r\=l), for then the terms involving I and X disappear 

 and we have 



X=(l + <r)M (16) 



and T=P -P 1 (17) 



To ensure that RA = SZ, or in other words that the pro- 

 portional arms have self inductances in the ratio of their 

 resistances, is not a very easy matter. The following is the 

 best method that I have tried. A coil (A) is constructed of 

 highly stranded wire to give moderately high self inductance 

 (say 0'1 henry) with as high effective insulation resistance 

 as possible *. Its distributed capacity k, which should be as 

 small as possible, may be measured by connecting it through 

 a thermoammeter to a small variable condenser and adjusting 

 the latter to give resonance with an alternating current of 

 known frequency (2000 to 10,000 ~ per sec.) in a loosely 

 coupled neighbouring coil. If K be the reading of the variable 

 condenser in mfds., and L the inductance in henries of the 

 coil (A), then n v /(K + &)L = 159'3, and so k can be found. 

 It is well known that the effective resistance T' and induc- 

 tance X' are given by Dolezalek's formulas, 



X / =X(l + 2a> 2 L£) (18) 



and T' = T(l + a> 2 L&), (19) 



where X and T are the values if k were absent (in this case 

 the values for very low frequency). 



* See ' Electrician/ Dec. 10, 1909. 



