Page:Scientific Memoirs, Vol. 2 (1841).djvu/433

perty of galvanic circuits, representing, as it were, their entire nature, had already been noticed long ago in various bad conducting bodies, and its origin sought for in their peculiar constitution^[1]; I have, however, enumerated in a letter to the editor of the Annalen der Physik^[2], the conditions under which this property of the galvanic circuit may be observed, even in the best conductors, the metals; and the necessary precautions, founded on experience, by which the success of the experiment is assured, described in it, are in perfect accordance with the present considerations.

The expression ${\frac {A}{L}}\centerdot {\frac {(\lambda )}{(l)}}$, denoting the dip of any portion of the circuit, vanishes when $L$ is indefinitely great, while $A$ and ${\frac {(\lambda )}{(l)}}$ retain finite values. Consequently, if $L$ assumes an indefinitely great value, while $A$ remains finite, the dip of the straight lines representing the separation of the electricity, in all such parts of the circuit, whose reduced length has a finite ratio to the actual length, vanishes, or what comes to the same thing, the electricity is of equal force at all places of each such part. Now, since $L$ represents the sum of the reduced lengths of all the parts of the circuit, and these reduced lengths evidently can only assume positive values, $L$ becomes indefinite as soon as one of the reduced lengths assumes an infinite value. Further, since the reduced length of any part represents the quotient obtained by dividing the actual length by the product of the conductibility and the section of the same part, it becomes infinite when the conductibility of this part vanishes, i. e. when this part is a non-conductor of electricity. When, therefore, a part of the circuit is a non-conductor, the electricity expands uniformly over each of the other parts, and its change from one part to the other is equal to the whole tension there situated. This separation of the electricity, relative to the open circuit, is far more simple than that in the closed circuit, which has hitherto formed the object of our consideration, as is geometrically represented by the lines $FG$, $HI$, $KL$, (fig. 3) taking a position parallel to $AD$. It distinctly demonstrates that the difference between the electrical forces, occurring at any two

1. Gilbert's Annalen, vol. viii. pp. 205, 207, and 456. Vol. x. p. 11.
2. Jahrgang, 1826. Part v. p. 117.