WAVE I'ROPAC.n ION 541 



Whence, in the ground 



n,= -^ f \/fx--\-ia .F(fx). cos x/x.ey'^^^^+^^dfji, (2) 



tcoJo 



IIy=l f fji. Fiix). sin Xfx.e'-^i^^+^dii, (3) 



loo Jo 



it being understood that v^O. The function F(iJ.) in the preceding 

 formulas is to be determined 1)\' the boundary conditions. 



In the dielectric, IIx and Ily ma\' be regarded as composed of two 

 components; thus 



IIy=IIyP'^Hy', 



where ///, /// designate the field due to the current / in the wire, and 

 Hx', Hy the field of the ground current. 



Neglecting axial displacement currents in the dielectric, and as- 

 suming that the wire is of sufficiently small radius so that the distri- 

 bution of current over its cross section is symmetrical, we have 



H.' = ^^.2I, (4) 



P 



/// = 5i^'. 2/, (5) 



P 



where p' = \/x^ -\-{y — h) -, 



cos 9' = ^, (6) 



P 



sin Q'^x/p'. 

 The secondary magnetic field IIx , Hy is taken as 



' 0(m)cos xii.e-yf'dix, (7) 







Hy'^-i <t>{iJi)s\n xp..e-yHix. (8) 



Jo 



At the surface of separation v = 0, IIx^, Ily? are expressible as the 

 P^ourier integrals 



IIx'' = 21 COS xfx.e-^f'dp, (9) 



•/o 



Ily'' = 21 f sin xp.e-'-f'dix. (10) 



