Page:Scientific Memoirs, Vol. 2 (1841).djvu/436

 424 is nothing more than a formula of interpolation, which is valid only for a relatively very short variable part of the entire circuit, and, nevertheless, is still applicable in very different possible modes of conduction, which is already evident, from its merely admitting the variable portion of the circuit, and leaving out of consideration all the other part; but all partake in common of this evil, that they have admitted a foreign source of variability, produced by the chemical change of the fluid portion of the circuit, of which I shall speak more fully hereafter. I have already treated, in other places, more at length of the relations of the various forms of the law to one another.

From the numerous separate peculiarities of the galvanic circuit resulting from the general equation I will here merely mention a few. It is immediately evident that a change in the arrangement of the parts has no influence on the magnitude of the current if the sum of the tensions be not affected by it. Nor is the magnitude of the current altered, when the sum of the tensions, and the entire reduced length of the circuit, change in the same proportion; consequently a circuit, the sum of whose tensions is very small in comparison to that of another circuit, may still produce a current, which, in energy, may be equal to that in the other circuit, when merely that which it loses in force of tensions is replaced by a shortening of its reduced length. In this circumstance is the source of the peculiar difference between thermo- and hydro-circuits. In the former only metals occur as parts of the circuit; in the latter, besides the metals, aqueous fluids, whose power of conduction, in comparison to that of the metals, is exceedingly small; on which account the reduced lengths of the fluid surpass, beyond all proportion, those of the metallic parts, with in all respects equal dimensions, and even remain considerably greater when diminished by shortening their actual lengths, and increasing their sections, so long, at least, as this diminution is not carried too far. And thence it is that the reduced length of the thermo-circuit is, in general, far smaller than that of the hydro-circuit, whence we may infer a tension smaller in the same proportion in the former, although the magnitude of the current,