ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 547 



Comparing this with equation (44), we have the following relation 

 between the external inductance and the capacity 



CLe = etx. (46) 



Propagation Constants of Coaxial Pairs 



Since the relation between electromotive intensity and current is 

 linear, we are justified in writing the intensities at the adjacent 

 surfaces of the pair in the form 



E.{h') = Z,'I, E.{a") = ZJ'I, (47) 



where Zh and Za." depend only upon the material of the conductors 

 and the geometry of the system. These quantities will be called sur- 

 face impedances of the inner and outer conductors, respectively. 

 Inserting (47) in (39) we obtain 



A = Z^'I, 



^ L-coM - —^1 / log^' + A = - ZJ'I, 



(48) 



by means of which A and V may be expressed in terms of Z},' and Za". 

 If we solve the first of these for A and substitute the value thus derived 

 in the second we get, by virtue of (45), 



^' log ^,- = Za" + Z," + io:Le, (49) 



27r(g + icoe) ^ h' 

 or, by (43) 



r2 = YZ, (50) 



where for brevity we have written 



Z = Za" + Z,' + ic^Le. (51) 



Direct Conversion of the Circularly Symmetric Field Equa- 

 tions INTO Transmission Line Equations 



As the practical applications of Maxwell's theory become more 

 numerous, it becomes increasingly important to formulate its exact 

 connection with transmission line theory. With this purpose in mind, 

 let us attempt to throw (2) into the form of the transmission line 

 equations. 



The obvious plan of attack is to introduce into (2) the transverse 

 voltage V and the longitudinal current /, in place of the intensities 

 E and //. The total current is introduced by substituting (7/2 7rp) for 

 H^, and the total voltage by integrating the set of equations (2) in 

 the transverse direction. The first equation gives us nothing of 



