MUTUAL IMPEDANCE OF GROUNDED WIRES 175 



The boundary conditions for the ::-components may be satisfied by 

 taking n = 1 in equation (7); the resulting expressions are as follows: 



..00 



Hoz = COS I po(u)e-''o'Ji{ru)du s ^ 0, (21) 



Jo 



Tlu = COS I {pi{u)e-'^ + qx{u)e-'^')Ji{ni)du - b ^ z ^ 0, (22) 



TI2, = COS I pi{u)e'">'Ji{rii)du z ^ — b. (23) 



Jo 



From boundary conditions (8), (10), (12), and (14) and the values of 

 the :)(;-components as now determined, IIix being given by equation 

 (17), IIoi and 1121 being given in terms of it by equations (11) and 

 (15), the following equations are obtained: 



71^(^1 + gi) = Jo^po, 

 aijo^pi - Si) = - aoyo^po + m(to^ - 7i^)(/i - gi), 

 yiKpie-"^^ + qie"^^) = y2'^p2e-"^\ (24) 



aiji^ipie'"^^ — qie"^^) = aiy^pte'""^ 



+ u{l^ - 7i^)(/)e-"'* + gie"»*), 



the arguments of the functions being omitted as before. 

 From (24), px and gi are obtained as 



(70^ — 7i^)(ai72^ + "27]^) (/i + g\) 

 ^ - (71'' - 72'^)(«o7i^ - «i7o^)(/ig~°'^ + gig°'^)e-"t^ 



(q!o7i^ + Q:i7o^)(ai72^ + 0:271^) ' 



+ (ctoTi^ — Qii7o^)(Q:iT2^ — 0:271^) g"^*"' 



(70^ - 7i^)(ai722 - "271^) (/i + gi)^-^*"! 

 ^ + (71" - 72^)(a:o7i^ + ct\l^){j\e-"^^ + gig"''')g~"i^ _ 



(q:o7i^ + Q:i7o^)(q:iT2^ + "271'^) 



+ (ao7i^ ~ ai7o^)(Q;i72^ — a27i^)g~^''"i 



The tangential components of the electric force at 2 = are by (6) , 



(17), and (22): 



(25) 



Ex— — cy 



I (/i(w) + giiu))Joiru)du 

 Jo 



/^oo 



+ ^£:cos [- u(Mu) + gi{ii)) 



^^ Jo (26) 



d 



cos I 



Jo 



+ oci(pi(u) — qi(u))2Ji(ru)du, 



