616 On Propagation of Electric Oscillations. 



We may write this 



2/ 



-c 2 log(~Ac 2 ) = 



n 



(h being the constant inside the bracket); 



2hf 



■he 2 log (-he 2 ) = 



n 



Therefore, using Sommerfeld's approximate solution as 

 stated in § 4 above, 



—hc 2 = -@, 



n 



c 2 = ©"^ (32) 



n 



So that, i£ we neglect the slow variation of ©, the solution is 

 independent of h. 



To tind a measure of the effect of the n leads under dis- 

 cussion, we may compare them with a single wire of the same 

 material. For this we have by (8), a ! being the radius, and 

 f the corresponding constant, 



- C Mog(-^ C 2 )=2/' 



c 2 = ®.2f (33) 



Therefore if the single wire is to produce the same effect 

 as the n wires, we must have 



Referring to (10), we see that when k 2 a is large this gives 

 a'=na ; 



when k a is small, 



a '- = na . 



In other words, when the skin-effect is marked the n wires 

 produce the same effect on the waves as a single wire of n 

 times the perimeter ; but when the currents are not concen- 

 trated on the surface, but occupy the whole section, the 

 n wires can be replaced by a single wire of n times the area. 

 This result was of course to be expected from geneial con- 

 siderations. The same approximate method of treatment 

 might be applied to equation (26) above. 



Queen's College, Belfast. 

 19th October, 1900. 



