On Electro- Dynamit Induction. 143 



73. The explanation of the increased shock at the moment of 

 breaking the circuit with the long conductor, rests on the assump- 

 tion 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 



A 



battery, in which n equals unity, becomes p ; and since this, 



as will be recollected, represents the quantity of current electri- 

 city in a unit of length of the conductor, we readily infer from 

 it, that by increasing the length of the conductor, or the value 

 of R, the quantity of current in a unit of the length is lessen- 

 ed. And if the resistance of a unit of the length of the con- 

 ductor were very great in comparison with that of r, (the resist- 

 ance of one element of the battery,) then the formula would 



become ^ , or the quantity in a single unit of the conductor would 



be inversely as its entire length, and hence the amount of current 

 electricity in the whole conductor would be a constant quantity, 

 whatever might be its length. This, however, can never be the 

 case in any of our experiments, since in no instance is the resist- 

 ance of R very great in reference to r, and therefore, according 

 to the formula, (73,) the whole quantity of current electricity in 

 along conductor is always somewhat greater than in a short one. 

 74. Let us, however, in order to simplify the conditions of the 

 induction at the ending of a current, suppose that the quantity in 

 a unit of the conductor is inversely as its whole length, or, in 

 other words, that the quantity of current electricity is the same 

 in a long conductor as in a short one ; and let us also suppose, for 

 an example, that the length of the spiral conductor, Fig. 3, was 

 increased from one spire to twenty spires ; then, if the velocity 

 of the diminution of the section of the current is the same (69) 

 in the long conductor as in the short one, the shock which would 

 be received by submitting the helix to the action of one spire of 

 the long coil would be nearly of the same intensity as that from 

 one spire of the short conductor ; the quantity of induction, how- 

 ever, as shown by the galvanometer, should be nearly twenty 



