52 PROCEEDINGS OF THE AMERICAN ACADEMY. 



It may be inferred from the preceding reasoning that for the case of 

 a composite line of two sections with different surge-impedances, the 

 receiving-end impedance of the line in the absence of receiving instru- 

 ments, which is the architrave of the line- n , has the same value from 

 each end of the line. The leak of the composite line-T has also one 

 and the same value, computed from either end. Both the (1 and the 

 T are, however, dissymmetrical. Each requires two separate computa- 

 tions and line-angle distributions, one from each end. 



Summary of Two- Section Formulas. 



If we expand formulas (40) and (49), we obtain for the architrave of 

 the composite line n 



p" = zi sinh Oi cosh 6 2 + z 2 cosh #i sinh 2 ohms (64) 



_ ~! + ~2 ginh ^ + qj + ~1 - ~2 g inh ( Qi _ Q^ ohmg 4 ( 65 ) 



= z x sinh 0i . . / ohms (line grounded at A) (66) 



sinh o c 



= z 2 sinh 8 D — r-^ ohms (line grounded at A) (67) 



cosn o c 



= z 2 sinh 6» ' . . ."* ohms (line grounded at D) (68) 



sinh b B 



CO^H Or 



= Zx sinh S A — ' ohms (line grounded at D). (69) 



Similarly, if we expand formulas (58) and (62), we obtain 



g = y l sinh #i cosh 6 2 + y 2 cosh 0i sinh 0» mhos (70) 



= y±±y± sinh (0! + 2 ) + '^-=^- 2 sinh (6 X - 2 ) mhos (71) 



= y\ sinh t . •" mhos (line freed at A) (72) 



= y 2 sinh 8 D — r-^ mhos (line freed at A) (73) 



= y 2 sinh 6 2 ". , A mhos (line freed at D) (74) 



= ?/i sinh 8 A — " . C mhos (line freed at D). (75) 



J cosh 8* v 



4 Formulas (64) and (6.5) were first published as receiving-end impedances 

 of a two-section composite line by Dr. G. di Pirro. See Bibliography. 



