4 BELL SYSTEM TECHNICAL JOURNAL 



wise unrestricted. This generalized artificial line possesses the well- 

 known sectional artificial line structure but it need not be an imita- 

 tion of, or a substitute for, any known, real, transmission line con- 

 necting together distant points. The general artificial line is shown 

 by Fig. 1 where N, N,. . . . are the identical unrestricted networks 

 which may contain resistance, self-inductance, mutual inductance, 

 and capacity. 



In discussing this type of structure as a wave-filter, the point of 

 view of an artificial line is adopted for the reason that it is advan- 

 tageous to regard the distribution of alternating currents as being 

 dependent upon both propagation and terminal conditions, which 

 are to be separately considered. In this way the attenuation, or 



Fig. 1 — Generalized Artificial Line as Considered in the Present Paper, where 

 N, N, . . . are Identical Arbitrary Electrical Networks 



falling off, of the current from section to section may be most directly 

 studied. Terminal effects are not to be ignored, but are allowed 

 for, after the desired attenuation effects have been secured, possibly 

 by an increase in the number of sections to be employed. 



The fundamental property of this generalized artificial line, which 

 includes uniform lines as a special case, is the mode in which the 

 wave motion changes from one section to the next, and may be stated 

 as follows: 



Wave Propagation Theorem 



Upon an infinite artificial line a steady forced sinusoidal disturbance 

 falls off exponentially j ram one section to the next, while the phase changes 

 by a constant amount. Reversing the direction of propagation does 

 not alter either the attenuation or phase change. When complex quan- 

 tities are employed the exponential includes the phase change."^ This 

 theorem is proved, without mathematical equations, by observing 



^ This theorem is not new, but it is ordinarily derived by means of differential or 

 difference equations whereas it may be derived from the most elementary general 

 considerations, thus avoiding all necessity of using differential or difference equa- 

 tions, as illustrated in my paper "On Loaded Lines in Telephonic Transmission" 

 {Phil. Mag., vol. 5, pp. 313-331, 1903). In that discission, as well as in this present 

 one, it is tacitly assumed that the line is either an actual line with resistance, or the 

 limit of such a line as the resistance vanishes, so that the amplitude of the wave 

 never increases towards the far end of an infinite line. 



