Wave Propagation over Parallel Wires. 



617 



we get, after rearrangement and simplification, the following 

 infinite series for the tangential and normal components 

 of the magnetic force in the dielectric at the surface of 

 wire #1 : — 



Re = -Bj/a-cosfl (B 2 /« 2 -2 ) 



-cosl^(B 3 /a 3 + 1 1 ! (a/,)S 1 ) 

 -cos a^(B 4 /a*~2-j {a/c)' 2 X 2 J 



(22) 



H r = sin0(B 2 /a 2 + l o ) 



+ sin 20 ( B./a 8 --^. (a/c) 2,) 



+ sin3^(B 4 /a 4 + | ! (aA') 2 S 2 



(23) 



In these expressions the X's denote the following infinite 

 series : — 



X = B 1 /.-B 2 /c 2 4-B 3 /c 3 -- ..., 



X! - Bi/c^B^ 2 * 3B 3 /c 3 -4B 4 /6- 4 - . . . , 



t 2 = 1 . 2 . B^ -2.3. B 2 /c 2 + 3.4. B 3 /c 3 - 



^ . (n + 1^! (n + 2)! 



^ (24) 



From (10), (15), and (17) the tangential and normal 

 components of the magnetic force at the surface of the wire 

 are, in terms of the internal solution and the current I in 

 the wire : 



K e = {ill a) ( 1 + X±, h , cos + p-, h 2 cos 20 + . . . V (25) 



H, = (2I/a)(l/f Jo')(JA sin 6 + 2J 2 h 2 sin 20+ . . .), (26) 



where the argument of the Bessel functions J . . . J« and 

 J '. . . J n ' is % = ai\/4:7rXfJLip. 



The boundary condition of the continuity of H^ at the 



