Page:Scientific Memoirs, Vol. 2 (1841).djvu/432

and by $(\omega )$ the section of the same part, may also be written thus:

${\frac {A}{L}}\centerdot {\frac {(\lambda )}{(\chi )(\omega )}}$.

This expression leads to a more detailed knowledge of the separation of the electricity in a galvanic circuit. For since $A$ and $L$ designate values which remain identical for each part of the same circuit, it is evident that the dips in the separate homogeneous parts of a circuit are to one another inversely as the products of the conductibility, and the section of the part. If consequently a part of the circuit surpasses all others from the circumstance, that the product of its conductibility and its section is far smaller than in the others, it will be the most adapted to reveal, by the magnitude of its dip, the differences of the electric force at its various points. If its actual length is, at the same time, not inferior to those of the other parts, its reduced length will far surpass those of the other parts; and it is easily conceived that such a relation between the various parts can be brought about, that even its reduced length may remain far greater than the sum of the reduced lengths of all the other parts. But in this case the reduced length of this one part is nearly equal to the reduced lengths of the entire circuit, so that we may substitute, without committing any great error, ${\frac {(l)}{(\chi )(\omega )}}$ for $L$, if $(l)$ represent the actual length of the said part, $(\chi )$ its conductibility, and $(\omega )$ its section; but then the dip of this part changes nearly into

${\frac {A}{(l)}}$,

whence it follows that the difference of the electrical forces at the extremities of this part is nearly equal to the sum of all the tensions existing in the circuit. All the tensions seem, as it were, to tend towards this one part, causing the electrical separation to appear in it with otherwise unusual energy, when all the tensions, or, at least, the greater part in number and magnitude, are of the same kind. In this way the scarcely perceptible gradation in the separation of the electricity, in a closed circuit, may be rendered distinctly evident, which, otherwise, would not be the case without a condenser, on account of the weak intensity of galvanic forces. This remarkable pro-