22 BELL SYSTEM TECHNICAL JOURNAL 



and £j is a wa\'e function which in the conductor satisfies the two- 

 dimensional wave equation 



In addition, E^ and F are connected with the conductor current I 

 by the relations 



/= X ^ E4S, 



X here denoting the conductivity of the conductor. 



It follows at once that the determination of F and E^ from (28)-(31) 

 is a generalization of the two-dimensional potential problem involved 

 in the determination of $ from (24)-(26) ; it may be precisely stated 

 as follows: 



The function F satisfies Laplace's equation 



everywhere outside the n conductors. Inside the jth conductor the 

 electric force EJ satisfies the two-dimensional wave equation 



{i^^ + w)^-'^ '■'"''' (i=1.2, •••«) (33) 



while at the surface of the jth conductor 



A TT - -At?; 



^F= -f^~Ei, U=U2,---n) 

 onj jij oUj 



(34) 



and 



ixniwlj = (p ~ FdTj, ( j = 1, 2, • • • n). (35) 



Just as equations (24)-(26) uniquely detennine $ as a linear function 

 oi Qi ' • • Qn, so equations (32)-(35) uniquely determine the potential 

 function F in the dielectric and the electric intensities .E^^^^ • • • £2^"^ 

 in the n conductors as linear functions of the conductor currents; thus 



F = /i(.v, y)Ii + /2(.v, t)/2 + • • • + /„(.v, v)/„, (36) 



