260 THE ELECTRIC TELEGRAPH. 



Dividing both numerator and denominator of the above 

 fraction, (IV., by the number of elements, n, we get 



E 



which becomes, if we set p = 0, 



affording us light upon another relation of the galvanic 

 current, viz., that when the resistance exterior to the battery 

 is so small that it may be neglected, the current of a number 

 of elements will do no more work than that of a single 

 pair. 



The first of these laws applies to a battery used for working 

 a long line of telegraph, whose resistance with the coils of 

 the apparatus is very great in comparison with that of the 

 elements, and where it is evident a large battery is necessary. 

 The second law applies to a local circuit, where the resist- 

 ance of the circuit is small and a few elements do as well as 

 a great number. 



Secondly, let n elements be so combined that all the copper 

 poles are connected together to form a common positive pole, 

 and all the zincs to form a common negative pole. In this 

 case we have still a single element, but of n times larger 

 surface. Theory and experiment prove alike that the 

 electro- motive force of the system is exactly that of a single 

 element, and, according to Ohm's law, the intensity is 

 expressed by 



I.-- 1- "* . . (YIL 



p+ np + r 



Here the external resistance p remains the same, but that 

 of the battery is reduced to . And now by setting, in turn, 



the resistances p and r as very small in comparison with each 

 other, we find mathematically what good the combination 

 can do us. 



