KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 57 



Find the T-leak admittance by following formula (88) or (90). This 

 may be regarded as formula (17) modified by the application of n—l 

 ratios of cosines in (88), or of n—l ratios of sines in (90) ; that is, one 

 such ratio for each junction. The opposite-end line-branch impedance 

 will then be the sending-end impedance minus the leak impedance. 

 The process must be repeated after freeing the line at the distant end 

 and developing line-angles towards A. 



One complete equivalent circuit, say the n, of a composite line of 

 n sections calls then for the determination n—l line-angles first in one 

 direction and then in the other. The formulas are well adapted to 

 logarithmic computation. If, however, only the receiving-end impe- 

 dance of the composite line is required, then we need only develop the 

 line angles in one direction over the line so as to apply one of the 

 architrave formulas, and neglect the pillars of the l~l. 



Loaded Composite Lines. 

 Definitions. 



Loads in a line may be either regular or casual. Regular loads are 

 such as are applied at regular intervals, in order to improve the cur- 

 rent delivery on telephone lines. Casual loads are of an irregular or 

 incidental character, such as might occur at section-junctions or at 

 the ends of a composite line. In the former case they would be inter- 

 mediate casual loads, and in the latter case, terminal casual loads. 

 Only casual loads will be here discussed ; because it is easy, with the 

 aid of formulas already known, to substitute an equivalent smooth 

 unloaded line for any uniformly loaded line. 



Loads may also be divided into two classes ; namely, (1) those 

 applied in series with the line, or impedance loads, such as coils of 

 impedance or resistance, and (2) those applied in derivation to the line, 

 or leak loads. 



Intermediate Impedance Loads. 



The case of an intermediate impedance load, of 100 ohms, inserted 

 at the junction BC in the composite line last considered, is presented 

 in Figure 9. The system differs from that of Figure 8 only in the 

 addition of this load. 



Equivalent !~l. First Method. 



To compute the equivalent n, A"F"GG (Figure 9), hyperbolically, 

 ground the line at one end, say as at Fi, and develop the line-angles 

 towards A x . The only change in this process affected by the load is at 

 the junction CB. The sending-end impedance at C is 



