KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 123 





ttj.20 



<- IdL •> £ <• Ia > 2. * La 



r-f---Aa. K----la > Z<r (-■■\a.----y.- ice-?--*- 2<r x-----A« <• Aof- .-»#■ 



«/w- 



tTTtTYTTV'' 



-W\*\A- 



c-ijstk 



"o'-'i'7jH:& 



V Y t T T^T T t ' ' 



-vdww- 



--w* 



Fiq.Zi 



Fi s ZZ 



F^- 



23 



L- 



•X*"- y----- la.'- 



: xe-x. ./» -X-- .-/>'■■ 



ivvvAAVyyVyvvvwvvvvw 



^ .,0. i ^ _ 



1? w ^|y 



• 0l».tS3Z 



:'1r1rlrv-tvi/it1/ t ' 



*- - c« x (a '•- * 



•X- X«'--- -* ,!*;; *- Jtf' X A*' > 



i f v •• 



V -r + r t ■ ' 



Figures 20, 21, 22, 23. — Reduction of a uniform actual line with loads 

 in series to an equivalent unloaded actual line. 



tank Aa' = tanh Aa 



= \AanhAatanh (Aa + o), (91) 



if o- < r and — = tanh S ; or 



coth Aa' = VcothAacoth (Aa + 7 ), 



a 



if o- > r and — = coth S'. 



To 



Also sinh /a' = sinh /a|/ 1 + ^ coth /a + ( - • J ; 



cosh /a' = cosh la -\ sinh la • 



r 



(92) 



(93) 

 4 (93a) 



4 This formula (93a) was first published by Dr. Campbell. See Bibliog- 

 raphy. 



