Lines in Telephonic Transmission. 321 



and (19) is quite general and has been applied to a variety 

 of cases of interest, such as artificial lines with mutual 

 induction between loads, S. P. Thompson's compensated cable, 

 and periodic lines of two or more different intervals, but 

 these constructions lie outside the scope of this paper. 



III. 



To give a precise and comprehensive idea of the per- 

 formance of the loaded line, formulae (18) and (19) must be 

 reduced to diagrams giving the attenuation coefficient (A), 

 velocity (V), and line impedance (K). The diagrams can 

 best be constructed for the correction factors a, 77, «:, defined 

 by the equations : — 



A---« 



R + R' / {] 



/f -T-,; • • • • (20) 



2 V L+L' 



Y = V ,_L =, ..... (21) 



K = K/s y L + L ', I (22) 



where R, L, C, R', I/, are the line resistance, inductance, 

 and capacity, and the load resistance and inductance, all 

 per unit of length. We can reduce the number of inde- 

 pendent variables from 7 to 4 by introducing in place of 

 R, L, C, R', I/, d, p, the new variables &>, 8, p, X defined by 



co=pxl ^(L + L'JCJ, (23) 



fi R + R' /~C~ 



R' 

 P=H' • • • (25) 



*=F- :• • • ^ 



For a discussion of practical applications we may assume 

 that there is no leakage, no line inductance, and that S is 

 small. While leakage, on a heavily loaded line, seriously 

 increases the attenuation, the effect of small leakage will be 

 given with sufficient accuracy by the correction (7) for uni- 

 form lines. The practical effect of distributing a small 

 portion of the total inductance along the line must be to make 

 the line act a trifle more like a uniform line. Its general 

 effect as shown by Godfrey's results will be discussed later. 



