Resistance of Compound Conductors. 489 



reed 8*9. These are, as usual, in terms of the scale of the 

 apparatus. The absolute resistance to steady currents 



centim. 



R = -230xl0 9 



sec. 



In this example, the change of resistance (in the ratio 

 1*89 : 1) is so great that no use can be made of the approxi- 

 mate formula quoted above, but we must revert to the original 

 series. In the notation employed in the paper referred to, if 

 <f>(x) denote the function *, 



x 2 x n 



1 + x + p ^ 2 2 "*" •••"*" ]2 2 2 , n 2 ~*~ " ' " '> 



the resistance to variable currents (B/) , and the self-induction, 

 I/, are given by 



R + ^R ~R A+ P(ipWB.y ' '-' " {) 



so that the real part of the fraction (/>/<// gives the ratio R//R. 

 By calculation from the series I find 



T^Scl= ~f5g:- X iS - 1-8906+ix 1-5859, 



(p\ixo'26bO) — 1'0297 + zx 1*6662 



in which the first term on the right agrees sufficiently nearly 

 with the observed value ot R'/R. We may conclude that 



pZ/*/R=5'2365, 

 whence 



^ = 99-5. 



In order to give an idea of the degree of accuracy with which 

 fju is determined by the observed value of R'/R, it may be 

 worth while to record another numerical result, viz. : — 



PmSS) =^6-Hxl-6544. 



In these calculations it is assumed that the increase in R, 

 observed when variable currents are substituted for steady 

 ones, is due simply to a less favourable distribution of current 

 over the section. If there were sensible hysteresis in the 

 magnetic changes, R would be still further increased. I 

 believe, however, that under such magnetizing forces as were 

 at play in these experiments, there is no important hysteresis, 

 and that /x may be treated as sensibly constant. 



The increased self-induction and resistance of an iron wire, 



* The relation of cfi to Bessel's function of order zero is expressed by 



<K*)=j (2*y#). 



