Experiments with Alternating Currents. 233 



To eliminate any possible errors due to the self-induction of 

 the bridge-wire, the resistance of the standard arm was always 

 varied until the reading of the bridge was not far from the 

 middle of the wire. 



I no longer employed a tuning-fork as interrupter, but 

 used an apparatus discussed in Addendum II., which enabled 

 me to obtain any number of breaks per second up to 500. 



To explain the fact, discovered by himself, that a bismuth 

 wire in a strong magnetic field has apparently a higher 

 resistance when measured with a telephone and an alternating 

 current than with a galvanometer and constant current, 

 Lenard frames the bold hypothesis that it is not the frequency 

 of by far the greater part of the alternating current that has 

 to do with the increased resistance, but accidental (so to 

 speak) oscillations with a frequency of about 10,000. 



With the bismuth spiral in a strong field absolute silence 

 is never obtained in the telephone, but there is a decided 

 minimum noise of a nondescript character. 



No differences of resistance could be detected with fre- 

 quencies between 60 and 500. 



It is well known that an alternating current tends to travel 

 along the surface of a conductor, especially when the con- 

 ductor is magnetic ; the result is that the resistance for an 

 alternating current is greater than for a steady one. 



Let I be the length of a straight wire, R the resistance to 

 steady currents, p/2ir the frequency of vibration, //, the mag- 

 netic permeability for circumferential magnetization, E/ the 



resistance to alternating currents ; then if ^S * 3 sma ll> 



R = R i 1+ 12 sr - 185 bt / ap P rox -* 



° r R-RJl+^ffi} roughly, 



-n/i + 1 ^ 2 \ 



w T here r = resistance per unit length. 



In the case of a copp'er wire 1 millim. in diameter, where 

 fi=l, the increase of resistance with an alternating current 

 of frequencv 10,000 equals about one tenth. 



The formula becomes unworkable when ^f is large ; 



but it seems probable that if a current of 10,000 exists side 



by side with one of 100, the use of sufficient iron wire of 



sufficient diameter would enable us to diminish the strength of 



* Lord Rayleigh, Phil. Mag. vol. xxi. 1886, p. 387. 



