Page:Scientific Memoirs, Vol. 2 (1841).djvu/511

${\frac {\phi mn}{i(m\beta -n\alpha )}}=\psi ={\frac {\chi \phi mn}{\chi '(m\beta -n\alpha )}}$,

passes into

$0=\chi \omega {\frac {du}{dx}}+\psi \omega [\alpha z+\beta (1-z)]-\chi \omega (n-m){\frac {dz}{dx}}$.

(♁)

This equation undergoes no change, as indeed is required by the nature of the subject, when $m$, $\alpha$, $z$, and $n$, $\beta$, $1-z$ are respectively interchanged, and, at the same time, the sign of $\phi$ is changed, as according to the remark made in the preceding paragraph, must take place, since by this transformation the direction of the decomposition is transferred from one constituent to the other.

36. In order to be able to deduce from this equation the mode of the diffusion of the two constituents in the fluid, i.e. the value of $z$, we ought to know the power of conduction $\chi$, and the electroscopic force $u$ at each point of the portion in the act of decomposition, the values, however, of which, are themselves dependent on that diffusion. Experience, as yet, leaves us in uncertainty respecting the change of conductibility, which occurs when two fluids are mixed in various proportions with one another, and likewise with respect to the law of tensions, which is followed by different mixtures of the same constituents in various proportion; for, if we do not err, no experiments have been instituted relatively to the latter law, and the law of the change produced in the conducting power of a fluid, by the mixture of another, is not yet decidedly established by the experiments of Gay Lussac and Davy. For this reason we have been inclined to supply this want of experience by hypothesis. We have, it is true, constantly endeavoured to conceive the nature of the action in question, in its connexion with those with whose properties we are better acquainted; but, nevertheless, we wish the determinations given to be regarded as nothing more than fictions, which are only to remain until we become by experiment in possession of the true law.

With regard to what relates to the change in the power of conduction of a body, by mixture with another, we have been guided by the following considerations. We suppose two adjacent parts of a circuit of the same section $\omega$, whose lengths are $v$ and $w$, and whose powers of conduction are $a$ and $b$; then, when $\mathrm {A}$ is the sum of the tensions in the circuit, and $\mathrm {L}$ the reduced length of the remaining portion of the circuit, the mag-