208 PIERCE. 



easier to supply the required mutual inductance than it is to leave it 

 out, so that by using the mutual inductance between sections we can 

 increase the frequency range for a specified constancy of time retarda- 

 tion to three times the range without the mutual inductance, and this 

 can be done with a better space factor and with a significant diminu- 

 tion of cost. 



13. Constancy of Surge Impedance also Somewhat Improved 

 by Introducing Mutual Inductance = .ILo between Series Sec- 

 tions of a Low Resistance Line. — Equation (7) is the general ex- 

 pression for surge impedance of the line of Figure 1. When the series 

 impedances are inductances and the shunt impedances are capacities, 

 as in Figure 3, Zi and 22 take on the values given in (9) and (10). 

 These substituted into (7) give 



L -ui Hr , / m' 



■ — - — c^ + i j .7^ VlcA 1 



IR, 



R 



Ro ViCsco 



(30) 



Equation (30)^ is the general expression for surge impedance of a line 

 of the type shown in Figure 3. In this equation L = ii+ 2M, and 



Ro= Vl/cI. 



It is seen that, if the resistance of the line is low, the imaginary 

 term in (30) is small, and the real term tends to approach independ- 

 ence of CO as 4M approaches L. Making M = .lLi= L/l2, as is 

 required in order to make T less dependent on frequency, has the 

 effect of cutting the real term containing co- by about | and hence the 

 introduction of ilf = . IZi reduces the dependence of surge impedance 

 on frequency for low resistance lines. 



1 The corresponding equation (142) p. 317 of El. Osc. and Waves has in the 

 first printing of the book an error, that has been corrected in the Second Im- 

 pression of 1921. 



