Page:Scientific Memoirs, Vol. 2 (1841).djvu/435

change, by each variation originating either in the magnitude of a tension or in the reduced length of a part, which latter is itself again determined, both by the actual length of the part, as well as by its conductibility and by its section. This variety of change may be limited, by supposing only one of the enumerated elements to be variable, and all the remainder constant. We thus arrive at distinct forms of the general equation corresponding to each particular instance of the general capability of change of a circuit. To render the meaning of this phrase evident by an example, I will suppose that in the circuit only the actual length of a single part is subjected to a continual change; but that all the other values denoting the magnitude of the current remain constantly the same, and, consequently, also in its equation. If we designate by $x$ this variable length, and the conductibility corresponding to the same part by $\chi$, its section by $\omega$, and the sum of the reduced lengths of all the others by $\Lambda$, so that $L=\Lambda +{\frac {x}{\chi \cdot \omega }}$ , then the general expression for the current changes into the following:

$S={\frac {A}{\Lambda +{\frac {x}{\chi \cdot \omega }}}}$;

or if we multiply both the numerator and denominator by $\chi \omega$, and substitute $a$ for $\chi \omega A$, and $b$ for $\chi \omega \Lambda$ into the following:

$S={\frac {a}{b+x}}$,

where $a$ and $b$ represent two constant magnitudes, and $x$ the variable length of a portion of the circuit fully determined with respect to its substance and its section. This form of the general equation, in which all the invariable elements have been reduced to the smallest number of constants, is that which I had practically deduced from experiments to which the theory here developed owes its origin^[1]. The law which it expresses relative to the length of conductors, differs essentially from that which Davy formerly, and Becquerel more recently, were led to by experiments; it also differs very considerably from that advanced by Barlow, as well as from that which I had previously drawn from other experiments, although the two latter come much nearer to the truth. The first, in fact,

1. See Schweigger's Jahrbuch, 1826. Part 2.