26 CONTRIBUTIONS TO ELECTRICITY AND MAGNETISM. 



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 in- 

 creasing the length of the conductor, 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 r, (the resistance 

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



A 

 ~R' 



or the quantity in a single unit of the conductor would be inversely as its en- 

 tire 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 

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

 formula, (73,) the whole quantity of current electricity in a long 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 diminu- 

 tion 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 times less ; and 

 these inferences I have found in accordance with the results of experiments, 

 (75.) If, however, instead of placing the helix on one spire of the long con- 

 ductor, it be submitted at once to the influence of all the twenty spires, then 

 the intensity of the shock should be twenty times greater, since twenty times 

 the quantity of current electricity collapses, if we may be allowed the expres- 

 sion, in the same time, and exerts at once all its influence on the helix. If, in 

 addition to this, we add the consideration that the whole quantity of current 

 electricity in a long conductor is greater than that in a short one, (73,) we shall 



