SMOOTH LINES AND SIMULATING NETWORKS 29 



forms in Figs. 15c and 15d, though each containing a superfluous 

 element, are of interest because they have the same forms as though 

 obtained by connecting in parallel two networks of the forms already 

 depicted in Figs. 12c and 12b respectively. 



Modifications For Leaky Lines 



For lines whose leakance is not quite negligible a study of the 

 formulas and graphs of the line impedance indicates that the effects 

 of such leakance can be sufficiently taken into account by a mere slight 

 reproportioning of the network without the addition of any further 

 element, except that a small series inductance might be a slight im- 

 provement in those cases where the leakance increases rapidly with 

 the frequency. 



Appendix A 

 Equations of the Components of the Line Impedance 



This Appendix contains the equations for the rectangular compon- 

 ents and the equation for the angle of the relative impedance z and of 

 the impedance K, corresponding to most of the various forms of the 

 equations employed in this paper for expressing z and K. It thereby 

 includes the equations for all the graphs employed in representing 

 z and K. It contains also the equations for the network of curves of 

 2 and K in the complex plane for certain of the more important limit- 

 ing cases involving not more than one parameter. 



With regard to the notation it will be recalled that z=x-\-iy and 

 K = M-\-iN. The angles of z and K will be denoted by ag z and ag K, 

 respectively, "ag" being an abbreviation for "angle of". 



Equation (10) : z = \j 7i 



+ iF 



(b+i)F' 



j 6 + /^+V(l+6 2 ) (1 + F 2 ) , 

 2 (l+b 2 ) F 



x=\ 



\-bF 

 y = 



2(l+b 2 )Fx 



1-bF 



agz=-h tan 



