Thus 



and Resistance of Straight Conductors. 393 



in accordance with Ohm's law, and 



l/= W + 4tt/^ 



y 3 y 



If a=0, the first term in (43) disappears, and we get a sim- 

 plified result which should agree with one found previously 

 (13). We may compare them by replacing y with 2?rr. The 

 apparent discrepancy that the self-induction by (13) is twice 

 as great as by (43) depends merely upon a slight difference 

 in the way of reckoning. The result in (13) refers to a double 

 length I, one part from -the outgoing and the other from the 

 return conductor. 



At the other extreme, when p is very great, a simple result 

 again applies. In that case {e mh + e~ mh ) \ (e mb — e~ mb ) may be 

 replaced by unity, and (38) becomes 



dV . n 4:ira ' . ■ ., GV{2ir^pp) 



-j- =ipC 1- (1 +i) * ?±r± . 



dz r y y 



w _ W(2irfipp) (U) 



y ' .' 



L , _ 47TOZ + W(2irfip) , 45 x 



y y^p 



These formulae show that the resistance increases without 

 limit with p, being proportional to \/p, and that the self- 

 induction diminishes towards the limit 4=iral/y. If a be zero, 

 that is if the insulating layer be infinitely thin, the self-in- 

 duction diminishes without limit as p increases, being propor- 

 tional to p~K Another important point is that when p is great 

 enough, the values of B/ and 1/ are independent of b, the 

 thickness of the strips. The meaning of this is, of course, 

 that, under such circumstances, the currents concentrate 

 themselves more and more towards the inner parts, in the 

 endeavour to diminish the effective self-induction. 



The distribution of current in the extreme case, where it is 

 not limited by the thinness of the strips, is readily expressed . 

 We have in general 



W ~ ~~~Z e mb__ e -mb > * * * (^") 



becoming, when b = oo, 



was —*-»(*-•> (47) 



