ON ELECTRO-DYNAMIC INDUCTION. 25 



n A 

 rn + R' 



In this, n represents 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 veiy short me- 

 tallic conductor, it may be neglected, and then the expression becomes 



nA A 

 — or -; 

 rn r 



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 electricity 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 ex- 

 ample, 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 dimi- 

 nished, 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 con- 

 duction would diminish the rapidity of the development of the current. But 

 the secondary current, which is produced in the conductor of the primary cur- 

 rent itself, as we have seen, (19,) is the principal cause which lessens the in- 

 tensity 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 applica- 

 tion of this principle more minutely, we must refer to the changes which take 

 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' 



VIII. — G 



