Page:Scientific Memoirs, Vol. 2 (1841).djvu/428

 416 which leaves the absolute magnitude of the lines $$\lambda, \lambda', \lambda$$ uncertain, so that the magnitudes $$\lambda, \lambda', \lambda$$ shall not be merely proportional to the said quotients, but shall be likewise equal to them, and henceforth vary this limitation in accordance with the meaning of the expression "reduced lengths," the first of the two preceding equations becomes which gives the following generally: The magnitude of the current in any homogeneous portion of the circuit is equal to the quotient of the difference between the electrical forces present at the extremities of this portion divided by its reduced length. This expression for the forces of the current will be continued to be employed subsequently. The second of the former equations passes, by the adopted change, into which is generally true, and already reveals the equality of the force of the current at all parts of the circuit; in words it may be thus expressed: The force of the current in a galvanic circuit is directly as the sum of all the tensions, and inversely as the entire reduced length of the circuit, bearing in mind that at present by reduced length is understood the sum of all the quotients obtained by dividing the actual lengths corresponding to the homogeneous parts by the product of the corresponding conductibilities and sections.

From the equation determining the force of the current in a galvanic circuit in conjunction with the one previously found, by which the electric force at each place of the circuit is given, may be deduced with ease and certainty all the phænomena belonging to the galvanic circuit. The former I had already some time ago derived from manifoldly varied experiments with an apparatus which allows of an accuracy and certainty of measurement not suspected in this department; the latter expresses all the observations pertaining to it, which already exist in great number, with the greatest fidelity, which also continues where the equation leads to results no longer comprised in the circle of previously published experiments. Both proceed uninterruptedly hand in hand with nature, as I now hope to