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BELL SYSTEM TECHNICAL JOURNAL 



of the wave motion. The second state of motion occurs, therefore, 

 throrghout continuous ranges or bands of frequencies. 



No other state of motion is possible. With given initial amplitude 

 and pha^e any possible wave motion is completely defined by its 

 attenuation and phase change. All possible combinations of these 

 two elements have been included in the two states, since the excluded 

 conditions on each assumption have been included as a consequence 

 of the other assumption. Thus, the exclusion of no attenuation in 

 the first assumption was found necessarily to accompany the phase 

 change of the second assumption; currents in phase or opposed, 

 which were excluded from the second assumption, were found to be 

 necessary features accompanying the first assumption. There remains 

 only to consider the critical frequencies separating the two states of 

 motion. At these frequencies there can be no attenuation and lag 

 angles of multiples of ^tt, including zero, only. At symmetrical 

 points the iterative impedance of the line must be a pure reactance 

 to satisfy the first state of motion, and a pure resistance to satisfy 

 the second state of motion. The only iterative impedances which 

 satisfy these conditions are zero and infinity. 



Some details relating to the pass and stop bands and the criti- 

 cal frequencies are brought together in the following table, where 

 ■" stop ( ± )" refers to stop bands, the current being in phase or op- 

 posed in successive sections, and where 7 and k refer to the line obtained 

 by uniformly distributing I/Z2 with respect to Zi. 



TABLE I. 



For Ladder Artificial Line, Fig. 4 



