64 PROCEEDINGS OF THE AMERICAN ACADEMY. 



out the load, the receiving-end resistance of the line, or the architrave 

 of its equivalent l~l, is, by Figure 8, 44,247 ohms. If the load is added 

 at the A end of the line, the receiving-end resistance becomes 48,619.7 

 ohms ; but if added at the F end, it is only 46,192. When the same 

 coil is inserted as an intermediate load, its influence on the receiving- 

 end resistance is not so great. In A. C. composite lines, the opportuni- 

 ties for such variations are more marked. In all cases, however, the 

 application of a terminal impedance o- to a line (single or composite), 

 increases the receiving-end or architrave impedance of that line in the 



ratio — ^ — ; where B g is the sending-end-impedance of the line at 



JXg 



the loaded end before the load is applied. This is true whether the 

 loaded end is made the sending or receiving end of the circuit. For 

 single lines, B g has the same value at either end, and therefore the 

 ratio of increase in receiving-end impedance is the same at whichever 

 end of a single line the load o- is applied ; whereas, for composite lines, 

 we have seen that B g is different, in general, at the two ends. 



Intermediate Leak Loads. 



Equivalent U. First Method. 



Suppose a leak load to be applied at a junction between sections 

 such as at DE (Figure 12). We proceed to compute the equivalent n 

 of the loaded composite line by grounding one end, as at Fi. We 

 develop the line-angles towards Ai. On arriving at E we have 

 B zE = z s tanh 6 3 = 1,155.292 ohms. Hence G gB = l/B tB = 

 8.655,82 X 10" 4 mho. To this sending-end admittance we add the 

 admittance y of the leak ; so that the sending-end admittance at J), 

 including the leak, is 



G 9 d = y + GgE mhos (113) 



= 13.655,82 X 10T* mho. 



Consequently the sending-end resistance at D, including the leak, is 



B gD =l/G gD ohms, (114) 



= 732.289 ohms. 

 The line-angle at D is then 



S i , = tanh- 1 f^\ hyps (115) 



= 0.383,964 hyp. 

 The remaining line-angles are found in the regular way. 



