174 BELL SYSTEM TECHNICAL JOURNAL 



z= - b: 



Ti'ni, = 72'n2., (12) 



dx dz dx dz ' 



Ti'^ni^ = 72'n2.. (15) 



From boundary conditions (9), (11), (13), and (15), the x-components 

 of the Hertzian vectors can be determined separately and then used 

 in finding the 2-components. 



For the 3c-components the arbitrary functions /(X) and g{\) can be 

 determined from the boundary conditions if in (7) n = 0. These 

 components are therefore taken as follows: 



Hox" = fo(u)e-''o'Jo(ru)du 2^0, (16) 



Jo 



Hix = (/i(M)e"i^ + gi{u)e-''^')Joiru)dii - b ^ z ^ 0, (17) 



Jo 



nsx = f2(.u)e''^-'Jo(ru)du z ^ ~ b. (18) 



Jo 



The arbitrary functions /(m) and g(u) are then determined by the 

 following equations, obtained from (9), (11), (13), and (15): 



7i^«i(/i - gi) = Ayo^ue-"°'' - 7o^«o/o, 



7i'«o(/i + gi) = Ayohie-"oh + 7o2ao/o, (19) 



7i2(/ie-«»* + gie«'*) = 72y2e-«=^ 



where for convenience the argument u of the arbitrary functions has 

 been omitted. 



The solutions of (19) for/i and gi are 



_ 2Au(a^ + a2) ,,^ 

 /i A ' 



_ lAujai - «2) ,,„_;,,„, 



SI ^ » 



where 



A = o») 4- ai)(ai + a2) + ("o - ai)(ai - a2)e-^^''K 



