142 Contributions to Electricity and Magnetism. 



contrary directions, and both within the time of a single swing 

 of the needle, and, consequently, will neutralize each other. 

 The resulting deflecting force will, therefore, be represented by 

 e/", which is equal to Ck. or to 6B, in Fig. 18. 



The intensity of the shock at the breaking is represented as 

 being the same in the two figures, by the similarity of the rate 

 of descent of the part CD of the curve in each. 



71. We have said (69) that the quantity of current electricity 

 in a short conductor and a compound battery, after the first dis- 

 charge, is nearly the same as with a single battery. The exact 

 quantity, according to the theory of Ohm, in a unit of length of 



uA. 

 the conductor is given by the formula — -r^ In this, n repre- 

 sents the number of elements ; A, the electromotive force of one 

 element ; r, the resistance to conduction of one element ; and R, 

 the length of the conductor, or rather its resistance to conduction 

 in terms of r. Now, when R is very small, in reference to rn, 

 as is the case with a very short metallic conductor, it may be 



nA. A . 



neglected, and then the expression becomes — or — ; and smce 



this expresses the quantity of current electricity in a unit of the 

 length of the circuit, with either a single or a compound battery, 

 therefore, with a short conductor, the quantity of current electri- 

 city in the two cases is nearly the same. 



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

 single element, (68,) and instead of increasing the intensity of 

 the apparatus, as in the last example, let the length of the con- 

 ductor be increased ; then the intensity of the shock at the be- 

 ginning 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 beginning, by increasing the 

 length of the conductor, is not surprising, since, as we might 

 suppose, the increased resistance to conduction would diminish 

 the rapidity of the development of the current. But the secon- 

 dary current, which is produced 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. 



