312 ELEMENTARY LESSONS ON [CHAP. vi. 



be (reckoning 13 ohms to the mile of wire) at least 

 1300 ohms. Through this resistance a single such cell 

 would give a current of less than one milliweber-per- 

 second, for here E = I, R = 1300, r 2, and there- 

 fore 

 C = T. E = - = - -- 1 - of a weber- per -second, a 



R + r 1300 + 2 1302 



current far too weak to work a telegraph instrument. 



With fifty such cells in series we should have E 50, 

 r loo, and then 

 C = s 5 - = X 5 of a weber-per-second, or 



I3OO + IOO 1400 20 



over 35 milliwebers -per- second. In telegraph work, 

 where the instruments require a current of 5 to 10 milli- 

 webers-per-second to work them, it is usual to reckon an 

 additional Daniell's cell for every 5 miles of line, each 

 instrument in the circuit being counted as having as 

 great a resistance as I o miles of wire. 



If, however, the resistance of the external circuit be 

 small, such arrangements must be made as will keep the 

 total internal resistance of the battery small. Suppose, 

 for example, we wish merely to heat a small piece of 

 platinum wire to redness, and have stout copper wires 

 to connect it with the battery. Here the external 

 resistance may possibly not be' as much as one ohm. 

 In that case a single cell would give a current of J of a 

 weber-per-second (or 333 milliwebers) through the wire, 

 for here E = i, R i, and r = 2. But ten cells 

 would only give half as much again, or 476 milliwebers- 

 per- second, and fifty cells only 495 milliwebers -per- 

 second, and with an infinite number of such cells in 

 series the current could not possibly be more than 500 

 milliwebers -per- second, because every cell though it 

 adds i to E, adds 2 to R. It is clear then that where 

 the external resistance is small the practical advantage 

 of adding cells in series soon reaches a limit. 



But suppose in this second case, where the external 

 resistance of the circuit is small, we reduce also the 



i 



