On Electro-Dynamic 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 acurrent 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 
battery, in which m equals unity, becomes r+R? 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 i 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 
A 
become R oF 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 
ina 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) 
nt n, h 
ever, as shown by the galvanometer, should be ce tnenty 
ay 
te 
