KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 49 



sinh (a:±j-) = ±j cosh x- 

 cosh ( x ± j - J = ± j sii 

 tanh ( x ± j- 

 coth ( # ± j - J = tanh x 



' sinh # 

 coth x 



numeric. (52) 



We thus obtain 



Sj, — j - = coth 



and 



t / ;r 2 tanh 1.5 \ 



= coth" 1 1.810,296 

 = 0.621,818 hyp 



8 B = 0.621,818 +j^ hyp. 



hyps (53) 



This difficulty with seemingly impossible antitangents or anticotangents 

 is not encountered in the A. C. case. 



We inscribe this value of 8 B opposite B on the line AD. The angle 

 subtended by the whole line at A will then be 



0i + 3 B = 8 A = 2.621,818 +j^ hyps. 



The sen ding-end resistance of the grounded composite line is then at 

 A lf by (12), (37), (38), and (47), 



RgA = -l tanh S A ohms (54) 



= 1,000 tanh ( 2.621,818 + j't) 



= 1,000 coth 2.621,618 = 1,010.64 ohms, 



and the sending-end conductance, as in (48), 



GgA = yi coth S A 



= y x coth ( 2.621,818 + j^\ 



= 0.001 tanh 2.621,818 = 9.894,966 X 10"* mho. 



The architrave resistance, as in (49), is 

 vol. xlv. — 4 



