MUTUAL IMPEDANCE OF GROUNDED WIRES 173 



in the first of which the double primes indicate the components of 

 the secondary field. 



The expressions for the field intensities in terms of the Hertzian 

 vector components may now be written out by equations (2) and (3) 

 and are as follows: 



CO dy 



CO 



dz dx 



ic .aiij; 



CO oy 



„ ,„ . s /an. , an. 



E = .Af^' + ^Hi 



" dy\dx dz 



dz \ OX dz 



(6) 



The proper general solution of (1) for the components of the second- 

 ary fields is of the following form: 



/•CO 



n = cos «<^ I (f{ti)e'"-\- g(u)e-''')Jn{ni)du. (7) 



X 



where a^ = ti^ -\- 7^ and cos = - . 



r 



The boundary conditions at 2 = and z = — h consist in the 



continuity of the tangential {x, y) components of H and E. The 



equations arising from the boundary conditions can be simplified by 



differentiation or integration with respect to x or j' (which is possible 



by virtue of (7)) , and are taken in the following convenient form: 



z= 0: 



To'no, = Ti'ni,, (8) 





dUdx I dlitiz ^ dUu . ^Ilia ,. „s 



dx dz dx dz 



To^Ho^r = 70-ni,; (11) 



