ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 559 



where r is the high frequency radius of the tube. Thus i?o is the d.-c. 

 resistance of the tube if the curvature is neglected. Then we have 

 approximately 



R 



Ro 



u sinh u + sin u t 

 2 cosh u — cos u Ir ' 



(87) 



if the tube is fairly thin. The curvature correction is positive if the 



Fig. 3 — The transfer impedance from one surface of a cylindrical shell to the other. 

 The curve represents its ratio to the d-c. resistance. 



return path is external, and negative if it is internal. The graph of 

 the first term is shown in Fig. 5. 



An interesting observation can be made at once from the formulae 

 (83) for the self-resistances of a tubular conductor. If the frequency 

 is kept fixed and the thickness of the conductor is increased from 0, 

 its resistance (with either return) passes through a sequence of maxima 

 and minima.^^ The first minimum occurs when w = tf, i.e., when 



2* The general fluctuating character of this function was noted by Mrs. S. P. 

 Mead [12]. 



