394 BELL SYSTEM TECHNICAL JOURNAL 



chapter, a short and quite personal derivation of Maxwell's equations (1-15, 

 p. 69), Dr. Schelkunoflf without taking breath adds immediately: "Since we 

 are concerned primarily with fields varying harmonically with time, we 

 replace the instantaneous field intensities and current densities by the corre- 

 sponding complex variables and write Maxwell's equations as follows: 



J Ends = -jf ic^nHn dS - f J MndS, 

 j Hnds ^ ff (? + io^e)E„ dS -hff Jn dS: 



(1-16) 



Thus the sacrosanct Maxwell equations are swept away with movie-like 

 swiftness, and instead we have the steady-state equations of a medium char- 

 acterized by a distributed series impedance iw/x and a distributed shunt ad- 

 mittance g-\-iw€ (p. 81). 



The analogy with a transmission line whose series inductance is ju, shunt 

 conductance g and shunt capacitance e, all taken per unit length, is inescap- 

 able (p. 243). In particular the above primary constants simply beg to be 

 transformed into the familiar secondary constants of transmission line 

 theory ; here the intrinsic propagation constant a and the intrinsic impedance 

 ■q are defined by 



(T = \^iwiJ.{g + /coe), n = A/ ^^. (9-1) 



y g + icoe 



(p. 81) {(T is in neper/meter, rj in ohms; the book is written in MKS — p. 60). 

 For free space we shall have g — 0, and the following numerical values of the 

 fundamental constants (p. 82): 



impedance of free space 770 ~ 1207r ohms, (9-4) 



characteristic velocity vo ~ 3.10^ meters/second. 



Surprising as it may appear to transmission engineers and sound engineers, 

 who daily handle their respective characteristic impedances Zo or pc, there 

 still are very competent physicists who balk at the idea of free space having a 

 characteristic impedance of about 377 ohms. Yet, in the words of Professor 

 Ronold W. P. King:^ "The existence of such a characteristic resistance for 

 electromagnetic effects is just as mysterious, but not more so, than the exist- 

 ence of the finite velocity I'o-" Dr. Schelkunoff explains very well how this 

 constant could have been overlooked by the builders of the classical theory: 

 "The physicist concentrates his attention on one particular wave: a wave of 

 force or a wave of velocity or a wave of displacement. His original differen- 

 tial equations may be of the first order and may involve both force and 



' Mimeographed "Notes on Antennas" for the course of Electronics and Cathode Ray 

 Tubes (Eng. 270), Harvard University. 



