ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 567 



O^n the other hand, if there is to be no reflection this must equal 

 fj.Je by equation (24). Hence 



-coth ah = J-- (105) 



If ah is small, coth ah equals approximately I /ah, and • 



A=^^icm. (106) 



Under these conditions, the generalized flux of energy across the 

 inner surface of the disk is, in accordance with the text under "The 

 Complex Poynting Vector," page 555, and equation (14), 



Jb' 



E,H^*p dpd<p =-^ J^ log ^ P. (107) 



Thus, the impedance of this disk is a pure resistance equal to the 

 characteristic impedance of the coaxial pair. 



Cylindrical Waves and the Problem of Cylindrical Shields ^^ 

 It is well known that when two transmission lines are side by side, 

 to a greater or lesser extent they interfere with each other. This 

 interference is usually analyzed into "electromagnetic crosstalk" and 

 ' ' electrostatic crosstalk. ' ' 



Thus, electric currents in a pair of parallel wires produce a magnetic 

 field with lines of force perpendicular to the wires. These lines cut 

 the other pair of wires and induce in them electromotive forces, thereby 

 producing what is usually called the "electromagnetic crosstalk"; 

 this crosstalk is seen to be proportional to the current flowing in the 

 first pair. The "electrostatic crosstalk," on the other hand, is caused 

 by electric charges induced on the wires of the second system; these 

 charges are proportional to the potential difference existing between 

 the wires of the "disturbing" transmission line. 



The distinction between two types of crosstalk is valid, although 

 the terminology is somewhat unfortunate; the word "electromagnetic" 

 is used in too narrow a sense and the word "electrostatic" is a con- 

 tradiction in terms since electric currents and charges in a transmission 

 line are variable. The terms "impedance crosstalk" and "admittance 

 crosstalk" would be preferable because the former is due to a dis- 

 tributed mutual series impedance between two lines and the latter is 

 produced by a distributed mutual shunt admittance. 



^^ Since this paper was written, a related paper has been published by Louis V. 

 King [18]. However, the physical picture here developed appears to be new. 

 The earliest writer who treated the problem of electromagnetic shielding is H. 

 Pleijel [21]. 



