610 Mr. J. R. Carson on 



the interaxial separation between wires by c. The co- 

 ordinates of any point in the system with respect to the 

 axis of one wire are denoted by r l5 U and the co-ordinates of 

 the same point with respect "to the axis of the second or 

 return wire by r 2 , 2 , as shown in the sketch herewith. 



Before proceeding with the analysis of the specific problem,, 

 a very brief discussion of the fundamental field equations 

 will be given, in order to indicate the significance of certain 

 important simplifying assumptions employed in the sub- 

 sequent analysis and the restrictions thus imposed on the 

 generality of the solution. It may be remarked that these 

 simplifying assumptions are quite generally applicable to 

 problems in wave propagation where the surfaces of the 

 conductors are generated by lines parallel to the axis of 

 propagation. The discussion starts with Maxwell's equations 

 in a continuous medium : 



curl E = — flip H, ""| 



curl H = (4w\ + Ktp)E, 

 div. E = 0, 

 div. H = 0. ) 



• 



a-) 



In these equations E and H denote the electric and magnetic 

 forces, while \, /jl, and K are the conductivity, permeability, 

 and specific inductive capacity of the medium. It is assumed 

 throughout the following that elm. c.g.s. units are employed. 

 The axis of propagation will be taken as the axis of Z, and it 

 will be assumed that the electric and magnetic forces vary as 

 ex))(ipt — yz) ; consequently the frequency is p\2ir, y is the 

 propagation factor, and the operators d/dt and 'd/'dz are 

 replaceable by ip and — <y respectively. All six vector com- 

 ponents (Exyz, Hxyz) satisfy the wave equation 



@»/3* , +aW)* =5 -(™ , +7 , )fc • • (II.) 



where 



m 2 = - (±TT\fiip- {pjv) 2 ) and v = 1/^KjT. 



