( «rx^ ) 



of metal wire willi a radius li and tlie wire to liave a eirciilar 

 section with a radius /•, then we have i z=z .t r'' N er and 



nr'2jtRNmv^ 2R m 



(jrr' Nevy r' Ne"- 



Supposing r to be small compared with R we may calculate L 

 for this circuit from the formula of Kirchhoff: 



L — 2jtR\l{ — J — 1,75 . 



The number N being probably diiferent for different metals, L' 

 also appears to depend on the kind of metal of which the circuit 

 consists, whereas L only depends upon the geometrical properties 

 of the circuit. On the other hand we see that L' lias a constant value 

 for a given wire, independent of the way in which the wire is wound 

 to a coil, whereas L depends in a high degree upon the way of coiling. 



The ratio — will therefore in diiferent cases have a very different 



value. We shall try to get an idea of what order this quantity can 



be, and inquire whether we are always justified in neglecting L' 



compared with L. To this purpose we can make use of the value 



of Ne, which has been calculated by .1. J. Thomson ') for bismuth. 



From the xalue of the resistance and from the variability of the 



resistance in the magnetic Held Thomson deduces that the value of 



e 

 Ne for bismuth amounts to about Ü,1J. If we put = 1,865.10" 



we 



find 



L —- . 10-6 



Metals with a greater conductivity will probably have a higher 

 value for xV. Thomson estimates the value of N for copper or silver 

 to be several thousands of times larger than for bismuth. 



We obtain the same result by starting from the values 



N, = 0,69 . 10^^ N, = 0,46 . 10'^ 



for the numbers of positive and of negative particles per cm^, which 

 have been derived by Dkude ") from the behaviour of bismuth in 



1) J. J. Thomson. Rapports présenlés au congres de physique a Paris, 111. 

 p. 145. 1900. 



2j Drude. Ann. der Phys. IV l-'olge. 3. p. 388. 1900. 



^j Edw. B. Kosa and Louis Cohen. Bulletin of the Bureau of Standards. Vol. 4. 

 No. 1. Reprint No. 75. 



