614 Mr. J. R. Carson on 



These equations are satisfied if we introduce a function V 

 which satisfies the equation 



.and then derive E^ and E y from V in accordance with 

 E, = -£v, 



"l^ 



J >J 



}(ow, at the surfaces of the wires the tangential electric force 

 in the plane XY, which is continuous, is very small compared 

 with the normal component. Consequently very small error 

 is introduced if in determining V it is taken as constant 

 over the circumferences of the wires in the plane XY. 

 It follows at once that 



V = V «<**-^, . ' (14) 



where V is the electrostatic potential and the surfaces of the 

 wires are equipotential surfaces. The determination of E z 

 and E y in the dielectric is therefore reduced to a two- 

 dimensional electrostatic problem, in w r hich the surfaces 

 of the two wires are equipotential surfaces. 



The solution of our problem — namely, the determination 

 of 7 and the coefficients A . . . A n and B x . . . B„ of equations 

 (8) and (12) — is obtained by formulating and satisfying the 

 boundary conditions which obtain at the surfaces of the 

 wires. These are that the tangential electric and magnetic 

 forces are continuous. The current distribution in the 

 wire, which carries with it its alternating current resistance, 

 is, however, determinable by a less general statement of the 

 boundary conditions ; namely, that the tangential magnetic 

 forces and the normal magnetic induction are continuous. 

 With the current distribution in the wire determined, the 

 propagation factor y is determined without difficulty, as is 

 shown subsequently. 



Before proceeding with the determination of the co- 

 efficients A ...A» of equation (8), the alternating current 

 resistance of the wire will be formulated. Let the value 

 of p! at the surface of wire #1 be denoted by 



f = bi^i = ia ^ 4:7r\tiip, 

 A„ = /* n A (n= 1, 2, 3 ...). 



