196 



PIERCE. 



cent a mutual inductance M, which may be set equal to zero in case 

 results without M are required. The mutual inductance between 

 non-adjacent elements is supposed to be negligible in all cases. 



The line is supposed to terminate at both ends in a series half- 

 element of complex impedance Zi/2 so constructed as to have also 

 mutual inductance M with its neighboring series section. 



?t 



in-, 



MM 



« z, — 5. 



< — ^— ^ 



6' 



Figure 1. General type of artificial line containing mutual inductance 

 between adjacent series elements. 



The line is shown connected to an input terminal apparatus of 

 complex e.m.f. e and complex impedance 20 and connected to an out- 

 put apparatus of complex impedance Zf. 



The artificial line here shown may be regarded as consisting of n-1 

 loops and two terminal series half elements, or it may be considered 

 to consist of n sections, known as T-sections, each of the character 

 shown in Figure 2. 



Figure 2. A T-section. 



It may be noted that the treatment of other general types of lines 

 (for example, lines of 7r-sections) are deducible from the treatment of 

 the line of Figure 1 by postulating certain changes in the terminal 

 conditions. 



