KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. Ill 



points by $' hyps. Formulas (6) to (18) will then apply, except that 

 where the strength of the received current to ground enters into con- 

 sideration, as in (56) and (62), the surge-resistance r must be replaced 

 by a new surge-resistance: 



*"' = ~^r, ohms - (51) 



sinn <p' 



Thus, the sending-end resistance at junction n becomes, by (6) : 



R f<T = r coth (L 2 a + </>') = r coth (2 n8 + <f>') ohms. (52)- 



The resistance at the nth leak, excluding the same, is, by (7) : 



p , , cosh [(2 n- 1 ) 6 + <f>'] 



R' n ,f* = r ' . \) ' J ohms. (53) 



sinn [(2 71 — 2)6 + <f>] 



The resistance at the nth leak, including the same, is, by (8) : 

 n , , cosh [(2 rc- 1)0 + </>'] 



The ratio of resistance at and excluding the (n + l)th leak to that at 

 and including the nth leak is, by (10) : 



R'n+l.g* COsh[(2tt+ 1)0 + (/>'] 



R' g<Tin ~ cosh[(2n- 1)6+ <I>'Y k °^ ) 



The receiving-end resistance is, by (26) : 



R l<7 = To'" cosh (2 m6 + </>') = r '" cosh (Z 2 a + <£') 



= r sinh 2 m6 + a- cosh 2 md ohms. (56) 



The voltage at junction n is, by (13) : 



cosh (2 n6 + </>') cosh (2 n6 + <£') 

 ^ = <"cosh(2m* + *') = '° cosh*' V ° ltS - (57) 



At the distant end, or junction 0, it is : 



e m cosh <f>' e m cosh <£' 



eo ° " cosh (2 md + </>') ~ cosh (L 2 a + </,') VOltS - {M) 



At the nth leak, it is, by (14) 



cosh [(2 n - 1)6 + <£'] 



cosh [(2 m — 1) 6 + <£'] cosh 6 cosh <f>' 



cosh[(2n - 1)61 + *'] e cosh[(2n- 1)8 + $'] 



