Resistance of Compound Conductors. 485 



steady currents was 16*79. To periodic currents of fre- 

 quency 1050 the resistance was just perceptibly greater, viz. 

 16*85, which increased a little further (17*15) when the 

 secondary was closed. The closing of the secondary left the 

 self-induction sensibly unaffected at 21°*2. The much slighter 

 influence of the secondary here observed is due mainly to the 

 higher resistance of the iron as compared with copper. A 

 calculation carried out as before gives 



p 2 W _ ma 

 R 2 +p 2 L 2 ' 



agreeing pretty well with the proportional change observed 

 in the resistance. The corresponding change in self-induc- 

 tion would be barely sensible. 



In the case where the primary and secondary circuits are 

 similar (S = R, N = L), Maxwell's general formulae may be 

 written in the form 



(5) 



R'-R ^ L-L^ p 2 W 



R " L ~R 2 +j9 2 L 2; ' ' 



and we may note two extreme cases. When p is small, or, 

 more fully expressed, when the period of vibration is long in 

 comparison with the time-constant of either circuit, viz. L/R, 

 the reaction of the secondary currents is of small importance. 

 On the other hand, when p is large, the right-hand member 

 of (5) approaches to the form M 2 /L 2 • and this again does 

 not differ much from unity when the two circuits consist of a 

 double coil of non-magnetic wire. Under such circumstances 

 the reaction of the secondary tends to destroy the self-induction 

 and to double the resistance of the primary. 



Being desirous of investigating an example approximating 

 to the second extreme, I prepared a double coil of stouter 

 wire than the preceding. The diameter was about *08 inch, 

 and the length of each wire was 318 inches. There were 

 20 (double) turns, so that the mean diameter of the coil, 

 wound as compactly as possible, was about 5 inches. The 

 resistance of each wire was about *05 ohm. 



The coefficient of mutual induction was determined by 

 comparison of the self-induction (L) of one wire with that of 

 the two wires connected oppositely in series, viz. (2L — 2M). 

 In this way it appeared that 



M = 43°*l = 43*l x 1553 centim. 



The interrupter was the reed, of frequency 1050. 



Observation showed that the closing of the secondary 

 diminished the self-induction from 44°*4 to 3°*4. The re- 



Phil. Mag. S. 5. Vol. 22. No. 139. Dec. 1886. 2 L 



