KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 105 



The voltage at the nth leak is 



cosh (2 n - 1)0 cosh (2 n - 1) 



€n = €o c^sh* = f " cosh (2m -1)0 V0ltS ' (14) 



rtj 



Consequently, the voltages at successive junctions, e , e\, «2» • • • e 

 are respectively proportional to cosh 0, cosh 2 8, cosh 4 #, . . . 

 cosh 2 n# ; that is, to the cosine of the hyperbolic angle of the junc- 

 tion, measured from the far free end. 



Similarly, the voltages at successive leaks, ei, 62, . • . en are 

 respectively proportional to cosh#, cosh 3d, . . . cosh (2 n — 1)0; 

 that is, to the hyperbolic angle of the leak, measured from the far free 

 end. 



As we ascend along the line by steps of 6 from the far free end, the 

 voltages increase as follows: 



Angular Distance -, r ,. , r , 



from far free end. Point. Y oU l e ? Y? 1 ," 6 ' 



Hyps. 



Symbol. Volta. 



End e e 



a Tii cosh (9 



v Leak 1 ex e — r^ 



cosh0 



2 Junction 1 e\ e cosh 2 6 



Q t i o cosh 3 



6 v Leak 2 «2 e r~?r 



cosho 



4 Junction 2 e<2, e cosh 4 



m t\a t i cosh (2n — 1)0 



(2 n — 1) Leak n e n e — r~z — — 



cosh p 



2 nd Junction n e n e cosh 2 nO 



Current Strength. Far End Free. 

 The current strength at the sending end is : 



7 - = r o co'thX 2 a = r o coth t 2m0 am P ereS ' (15) 



where e m is the voltage impressed on the mth junction. 

 The current strength at the nth junction is : 



T sinh2n0 



7 " = Zw sinh2^ ampereS * (16) 



