S46 Dr. Draper on the Use of a Secondary Wire as a 



to n certain extent Ohm's theory of the voltaic pile. It is a 

 condition, in tracing the action ot wires of different lengths, to 

 assume, that the electromotive power of the generating pair 

 is under all circumstances constant, and hence it may be con- 

 veniently represented by unity. But the electromotive power 

 of any pair plainly depends on two things, the quantity of 

 electricity that the pair can evolve and its absolute tension. 

 The theory of Ohm, as may be gathered from the memoir of 

 Prof. Jacobi on electromotive machines, and also from M. 

 Lenz's papers*, confounds those two important conditions. 



Now the results given in the foregoing table, proving that 

 wires conduct in the inverse ratio of their lengths, prove also 

 that the addition of increasing lengths of wire does not in 

 anywise alter the electromotive power; yet we have clearly 

 shown that this addition is inevitably attended with an increase 

 of tension. Here therefore is an apparent contradiction. 



But this contradiction is only apparent, and when properly 

 understood leads to a most remarkable result. 



It is true, that we are compelled to assume that the electro- 

 motive power of a pair is independent of the length of the 

 connecting wire; but this constancy of electromotive power 

 does not necessarily imply that the relations of quantity and 

 tension, which conjointly produce it, are not themselves vari- 

 able. In the case before us, we have direct proof that the 

 tension increases, and also that the quantity decreases, as the 

 connecting wire becomes longer, and the converse; yet the 

 electromotive power varying directly with them both, they 

 mustof necessity bear such a relation to each other, that their 

 product shall always be equal to unity. Hence we infer, 



That the law of Marriotte in relation to the ponderable 

 elastic fluids, holds also in the case of electricity developed by 

 voltaic action, the elastic force or tension of a given quantity 

 being inversely as the space it occupies f. 



[* See Taylor's Scientific Memoirs, vol. i. p. 311, 503, and vol. ii. p. 1. 

 Edit.] 



t The formula given by the German natural philosopher is, 



where F represents the intensity of the current, E the electromotive 

 power, and I -\- >. the sum of all the resistances of the electric circle. 

 Now if we decompose E into two factors, representing individually the 

 quantity and the tension, 



q . — 

 F = ^— — "- will be the general formula for the 



intensity or force of the current, independent of the length of the con- 

 ducting wire. 



