G10 Prof. W. B. Morton on some Cases of Propagation 

 The equation then reduces to 



„ , b k^ J (* o a) , 



C log — = - — -^7-, — r =/. . . • 



a k 2 a J 1 [k 2 a) 



(12 



This agrees with Mie's result, neglecting jj and higher 



powers. It will be seen that a simple equation for c 2 replaces 

 the transcendental form treated by Sommerfeld. 



§ 6. Equation for the most General Case. 



It is clear that we can apply the same method to the most 

 general case, on the understanding that the mutual distances 

 of the wires are all large in comparison with their radii. We 

 shall have a different pair of constants {d,D) for each wire. 

 The continuity of magnetic force for each wire will give 



l L — ^i a Kl( Cg ) (19\ 



D~ ktfJ^ay l } 



the constants k l} fa, a having now different values for the 

 different wires. 



The lengthwise electric force inside the wire is as before, 



^^=^j$t Kl(M) hy (13) 



c 2 faa J^faa) 



<? 



Distinguishing the wires by subscripts, we get for the first 

 Avire 



D 1 ^=D 1 K K) + D 2 K ( c ^ 2 )H-D 3 K (e^)+ . (14) 



&125 ^i3j & c « being the mutual distances. 

 For shortness write 



Ko(cai)=1 °g 7 ^ =:Al 

 Ko(^i2) = Bi2, and so on. 

 The equation giving c for the system is 



(15) 



-£ 



B 15 



B J3 



B i3 



B 2 3 



= 0. 



(In) 



