ELECTRICAL TRANSMISSION ALONG WIRES 19 



tangential to the conductor surface; My is therefore the normal com- 

 ponent of M at the surface of the conductor and must there be con- 

 tinuous. Ez and {dldx)Es are also continuous. Consequently, we 

 must have by equating My as given by (13) and (14), 



the subscript e indicating the value of (dldy)M2 outside the conductor. 

 But from the expression for Ex, as given by (14), this is precisely the 

 condition that makes Ex = at the surface of the conductor. Conse- 

 quently we arrive at the very important proposition that, subject to 

 the approximations involved in (13), the tangential component of E in 

 the xy- plane vanishes at the conductor surfaces. 



We shall now find it convenient to express the field in the dielectric 

 in accordance with (8) in terms of the wave functions F, $, 0. Writing 



= ^-exp {iwt — 7s), (16) 



d satisfies the differential equation 



dx^ dy 



.2 + 572^= i^'-y')e. (17) 



Now, in the dielectric, iP- and 7^ are both exceedingly small quantities 

 which are nearly equal, so that v^ — y^ is the difference of two very 

 small and nearly equal quantities. We therefore replace it by zero, 

 so that 



(£+$)^ = «- ('«) 



6 is therefore a two-dimensional potential function. Consequently 

 a conjugate two-dimensional potential function yp exists, such that 



d-x^^d-y"^' 

 dy dx 



Writing 



equations (8) become 



^ = ^-exp (icot — yz). 



Mx = ^{F-y^), 



