288 



THE ELECTRIC TELEGRAPH. 



so that, if we take away the shunt, the resistance r 2 becomes 

 infinite ; and giving this value to it in the above equation, 

 which may be written also 



R' =- R + - !J _ 



the whole circuit resistance becomes, 

 R' = R + r r 



The circuits and resistances of three or more parallel circuits 

 are calculated in the same way. 



It happens sometimes that several lines leave the same 

 station, and the question has been raised under what con- 

 ditions a single battery suffices to work them all at the same 

 time. 



Let the resistances of three lines, for instance, be r lt r 2 , 

 and 7*3, (Fig. 135), and the inten- 

 sities in them i l9 i 2 > aD ^ 4> respec- 

 tively, when the current of a battery, 

 w h se electro-motive force is E and 

 resistance R, passes parallel through 

 "* them. We must now find the 

 values of these intensities, and com- 

 pare them with those which would 

 Fig. 135. b e obtained if only one of the lines 



were inserted at a time. 

 By KirchofFs second law, 



IR + *>, = , 

 I R + t, r 2 = E, 



I B + t , r a 



E 



whence the intensities in the three lines are, 



E- IR 



E - IR 



to === 



and 



E IR 



