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 
ef, which is equal to Ck, or to bB, 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 
hort conductor and a compound battery, after the first dis- 
charg >, is nearly the same as with a single battery. The exact 
quantity, according to the theory of Ohm, in a unit of length of 
n 
m+R 
sents the number of elements; A, the electromotive force of one 
_ element ; 7, 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 7, 
as is the case with a very short metallic conductor, it may be 
the conductor is given by the formula In this, » repre- 
gee RAe on Be : 
neglected, and then the expression becomes mar Pst and since 
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 electti- 
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. 
