ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 545 

 to p, we have 



E =J- 



In 





/log^ + ^, (39) 



g + ^coe 

 where ^ is a constant to be determined from the boundary conditions.^^ 



The Potential Difference Between Two Coaxial Cylinders 



Equation (36) relates the transverse electromotive intensity to the 

 total current flowing in the inner conductor. In practice, however, 

 we are interested in the difference of potential between the conductors, 

 that is, in the transverse electromotive force rather than the electro- 

 motive intensity. This potential difference V is obtained at once 

 from equation (37) by integration: 



V = f E,dp = ^ ,^! . , f 



d, r/log«^ 



p 2x(g + icoe) 



(40) 



This transverse E.M.F. produces a transverse electric current which 

 is partly a conduction current — if the dielectric is not quite perfect — • 

 and partly a displacement (or "capacity") current. 



Now, the total transverse current per centimeter length of line is 



Ip = 2irp{g + iuie)Ep. 



Then, by equation (37), we have 



Ip = TL (41) 



Therefore, equation (40) becomes 



logy 



27r(g + ijcoe) 



The ratio of a current to the electromotive force that produces it 

 is called admittance. Hence, the distributed radial admittance per 



1' The following system of notation will be adhered to throughout the remainder 

 of the paper: The inner radius of any cylindrical conductor is denoted by a, and its 

 outer radius by b. When several coaxial conductors are used, they are differen- 

 tiated by superscripts; a' , a" , a*^*, • • • referring to their inner radii, for example, 

 and b' , b", i<^', • ■ • to their outer radii. This convention also applies to conduc- 

 tivities, permeabilities, and other physical constants of the conductors in question. 



For convenience, we have written the ratio of p to the outer radius of the inner 

 conductor in place of p; this change affects only the arbitrary constant A which will 

 eventually be assigned the value required by the boundary conditions. When 

 written in this form, the first term of E^ vanishes on the surface of the inner con- 

 ductor which is a convenience in determining the value of A. 



