Page:Scientific Memoirs, Vol. 2 (1841).djvu/515

mically changeable portion, which are in connexion with the other chemically unchangeable parts of the circuit, undergoing a gradual change during the decomposition till they arrive at their permanent state, giving rise at those places to an altered tension. If, for instance, we call $\zeta$ the value of $z$, which belongs to all places of the extent in question, before chemical change has begun in it, and designate the coefficient of the tension occurring at the extremities of this extent, supposing that it is the same at both ends, by $\phi ''$, and moreover express by $\mu$ and $\nu$ the latent electroscopic forces of those places of the chemically unalterable part of the circuit which are situated adjacent to the chemically changeable extent, the tensions existing at these places can be determined individually. They are, namely, previous to the commencement of chemical change, the following:

${\begin{aligned}&\phi ''[\mu -(n+(m-n)\zeta )],{\mbox{ and}}\\&\phi ''[(n+(m-n)\zeta )-\nu ];\end{aligned}}$

and after the permanent state in the decomposition has been attained, if we, as above, let $z'$ and $z''$ be those values of $z$ which belong in this state to those places, they are the following:

${\begin{aligned}&\phi ''[\mu -(n+(m-n)z')],{\mbox{ and}}\\&\phi ''[(n+(m-n)z'')-\nu ],\end{aligned}}$

their sum is therefore in one case

$\phi ''(\mu -\nu ),$

and in the other

$\phi ''(\mu -\nu )+\phi ''(m-n)(z''-z');$

consequently the increase of tension at those places is

$\phi ''(m-n)(z''-z').$

If we add this change of the tension to that above found, we obtain for the entire difference of the tension, produced by the decomposition until the commencement of the permanent state,

$(\phi ''-\phi ')(m-n)(z''-z'),$

which, if we substitute $\Phi$ for $\phi ''-\phi '$, changes into

$\Phi (n-m)(z''-z').$

If now we represent by $S$ the magnitude of the current, and by $A$ the sum of the tensions in the circuit, before any chemical change has commenced, by $S'$ the magnitude of the current, after the permanent state has been attained; lastly, by $L$ the