to Electricity and Magnetism. 505 



72. Let us next return to the experiment with a battery 

 of a single element (G8.), and instead of increasing the in- 

 tensity of the apparatus, as in the last example, let the length 

 of the conductor be increased ; then the intensity of the 

 shock at the beginning of the current, as we have seen (14.), 

 will be diminished, while that of the one at the ending will be 

 increased. That the shock should be lessened at the begin- 

 ning, by increasing the length of the conductor, is not sur- 

 prising, since, as we might suppose, the increased resistance 

 to conduction would diminish therapidity of the development 

 of the current. But the secondary current, which is pro- 

 duced in the conductor of the primary current itself, as we have 

 seen (19), is the principal cause which lessens the intensity 

 of the shock, and the effect of this, as will be shown hereafter, 

 may also be inferred from the principles we have adopted. 



73. The explanation of the increased shock at the moment 

 of breaking the circuit with the long conductor, rests on 

 the assumption before mentioned (69.), that the velocity of the 

 diminution of a current is nearly the same in the case of a 

 long conductor as in that of a short one. But, to understand 

 the application of this principle more minutely, we must refer 

 to the change which takes place in the quantity of the current 

 in the conductor by varying its length; and this will be given 

 by another application of the formula before stated (71.). 

 This, in the case of a single battery, in which n equals unity, 

 becomes 



A 

 r + R' 



and since this, as will be recollected, represents the quantity 

 of current electricity in a unit of length ; of the conductor, we 

 readily infer from it that, by increasing the length of the con- 

 ductor, or the value of R, the quantity of current in a unit of 

 the length is lessened. And if the resistance of a unit of the 

 length of the conductor were very great in comparison with 

 that of ;• (the resistance of one element of the battery), then 

 the formula would become 



A 



R' 

 or tlie quantity in a single unit of the conductor woidd be in- 

 versely as its entire length, and hence the amount of current 

 electricity in the whole conductor would be a constant quan- 

 tity, whatever miglit be its length. This, however, can never 

 be the case in any of our expeiimcnts, since in no instance is 

 the resistance of R very great in reference to r, and therefoi-e 

 according to the formula (73.), the wliole quantity of current 



