of Electric Oscillations along Parallel Wires. GO 7 



(1) Two wires of slightly different diameters, the wires 



being (a) opposite, as in the usual experimental 

 arrangement, or (6) similar. 



(2) Three wires in an isosceles triangle, the base wires 

 being opposite. 



(3) Four wires in rectangular arrangement, any grouping. 



(4) 2n wires in regular polygon, consecutive wires being 



opposite. 



(5) n wires in regular polygon, all the wires being similar. 



§ 4. Statement of Results for Single-wire case. 

 We shall use the following quantities in addition to those 

 already defined : — 



>=v=?< <;> 



where V is the velocity of radiation, \ the wave-length in 

 free space. 



h=(l-i)\/^, ...... (2) 



H, p being the permeability and resistivity of the wire. 



^W=0-(^) 3 V . .(3) 



c 2 is the function of the quantities \, k which will appear in 

 the final equations. 



Take now the case of the single isolated wire as worked 

 out by Sommerfeld. We have three vectors to deal with, 

 viz., lengthwise electric force, radial electric force, and mag- 

 netic force in circles concentric with the wire. The values 

 of these which satisfy the differential equations, inside and 

 outside the wire, are : — 



Inside. Outside. 



Lengthwise electric force... dJ 'k 2 r) DK (c»*J f 



Radial electric force d . j- Ji(k 2 r) D — K } (cr) 



K 2 C 



Magnetic force d . — 2 J/M D *A K,(cr) 



p pc / 



■* 

 r is the distance from the axis of the wire. The J's and 



K"s are the cylinder functions; d, Dare constants. The mag- 

 nitude m has been neglected in comparison with k 2 (v. Thomson 

 or Sommerfeld, loc. cit.). Expressing that the tangential com- 

 ponents are continuous we have, if a is the radius of the wire, 



d^ Kjca) k^ K } (ca) 



D J (yt 2 a) ~ k 2 cJ x {k 2 a) • • • • W 



> (4) 



