202 Lord Rayleigh on the Propagation of Electric 

 giving 



F,Q,B=^+"4(£, £ O), . . . (12) 



v( a ;M)=^)(^ -j o). . . . (is) 



And liere again it makes no difference to these forms at what 

 points (V x , r 2 ) the dielectric is replaced by conductors. 



For the moment these simple examples may suffice to illus- 

 trate the manner in which the propagation along z takes 

 place, and to show that <p is determined by conditions com- 

 pletely independent of p and its associated m. In further 

 discussions it will save much circumlocution to suppose that 

 p and m are zero and thus to drop the exponential factor. 

 The problem is then strictly reduced to two dimensions and 

 relates to charges and steady currents upon cylindrical con- 

 ductors, the currents being still entirely superficial. When 

 <f) is once determined for any case of this kind, the exponential 

 factor may be restored at pleasure with an arbitrary value 

 assigned to p and the corresponding value, viz. p/Y, to m. 



The usual expressions for electric and magnetic energies 

 will then apply, everything being reckoned per unit length 

 parallel to z. It suffices for practical purposes to limit 

 ourselves to the case of a single outgoing and a single 

 return conductor. We may then write 



Electric energy = a ^ C iar £ e j (14) 



bJ 2 x capacity' v ' 



Magnetic energy =|x self-induction x (current) 2 ; . (15) 



and the value of the self-induction in the latter case is the 

 reciprocal of that of the capacity in the former. 



Thus, for a dielectric bounded by coaxal conductors at 

 r=9-j and r = r 2 , we have <£ = logr, and 



self-induction = (capacity) -1 = 2 log— . . . . (16) 



r x 



Among the cases for which the solution can be completely 

 effected may be mentioned that of a dielectric bounded by 

 confocal elliptical cylinders. 



More important in practice is the case of parallel circular 

 wires. In Lecher's arrangement, which has been employed 

 by numerous experimenters, the wires are of equal diameter; 

 and it is usually supposed to be necessary to maintain them 

 at a distance apart which is very great in comparison 

 with that diameter. The general theory above given shows 



