68 PROCEEDINGS OF THE AMERICAN ACADEMY. 



To complete the T, the line is freed at A, as at A 4 (Figure 13), and 

 the line-angles are developed toward F. We then have for the sending- 

 end admittance at F, 



Gf F = y z tanh 8, mhos. (124) 



The sending-end conductance at F , including the leak admittance 



G/pb = y + 2/a tanh 8, mhos. (125) 



The apparent surge-admittance y Q at F is defined by the condition, 



G jro = y tanh S, mhos, (126) 



whence 



mhos. (127) 



mhos (128) 



mhos, (129) 

 and the line-branch impedance FO follows at once from (89). 



Equivalent T. Second Method. 



By the alternative method, the T-leak admittance, when the line is 

 freed at A, is 



, • i /, sinh 8 D sinh 8 P G^. , ,. „^ x 



g' = i/i sinh 0i • . , f • -T-r-/ • -— mhos (130) 



v J sinh8 c sinh8 fi G fP v ' 



— 41.066 X 10" 8 mho. 



Similarly, when the line is freed at F (Figure 13), and the correspond- 

 ing line-angles are set, 



,_ sinh S g sinh 8 C sinh 8 A , 



cosh 8, sinh 8 D sinh 8 B 



The line-branch impedances are determined in the regular way. 



Resume of Rules applying to Casual Loads in Composite Lines. 



In the accompanying Table the changes effected by loads in the 

 formulas for p" and g' are collected together as an aid to computation. 



