Page:Scientific Memoirs, Vol. 2 (1841).djvu/490

situated between two points of excitation, we then very simply obtain

$S={\frac {A}{L}},$

where $L$ denotes the entire reduced length of the circuit, and $A$ the sum of all its tensions. By means of this equation we obtain the magnitude of the electric current of a galvanic circuit, composed of any number of prismatic parts, which has acquired its permanent state, which is not affected by the surrounding atmosphere, and the single sections of which possess in all their points one and the same electroscopic force; in this category are comprised the most frequently occurring cases, on which account we shall dissect this result in the most careful manner.

Since $A$ represents the sum of all the tensions in the circuit, and $L$ the sum of the reduced lengths of all the individual parts, there results, in the first place, from the equation found, the following general properties relative to the electric current of the galvanic circuit.

I. The electric current is decidedly of equal magnitude at all places of a galvanic circuit, and is independent of the value of the constant $c$, which, as we have seen, fixes the intensity of the electroscopic force at a determined place. In the open circuit the current ceases entirely, for in this case the reduced length $L$ acquires an infinitely great value.

II. The magnitude of the current, in a galvanic circuit, remains unchanged when the sum of all its tensions and its entire reduced length are varied, either not at all, or in the same proportion; but it increases, the reduced length remaining the same, in proportion as the sum of the tensions increases, and the sum of the tensions remaining the same, in proportion as the reduced length of the circuit diminishes. From this general law we will, moreover, particularly deduce the following.

1. A difference in the arrangement and distribution of the individual points of excitation, by a transposition of the parts of which the circuit consists, has no influence on the magnitude of the current when the sum of all the tensions remains the same. Thus, for instance, the current would remain unaltered in a circuit formed in the order copper, silver, lead, zinc, and a fluid, even when the silver and lead