Page:Scientific Memoirs, Vol. 2 (1841).djvu/444

at its extremities must still always remain $\alpha$, and consequently be

${\frac {\alpha }{\Lambda }}={\frac {\alpha }{\lambda }}+{\frac {\alpha }{\lambda '}}+{\frac {\alpha }{\lambda ''}}$,

or

${\frac {1}{\Lambda }}={\frac {1}{\lambda }}+{\frac {1}{\lambda '}}+{\frac {1}{\lambda ''}}$,

which equation serves to determine the value of $\Lambda$. But if this value is known, and we call $A$ the sum of all the tensions in the circuit, and $L$ the reduced length of the non-divided portion of the circuit, we obtain, as is known, for the magnitude of the current in the last-mentioned circuit

${\frac {A}{L+\Lambda }}$,

which is equal to the sum of the currents occurring in the separate branches. Now since it has already been proved that the currents in the separate branches are in inverse proportion to one another as the reduced lengths of these branches, we obtain for the magnitude of the current in the branch whose reduced length is $\lambda$,

${\frac {A}{L+\Lambda }}\centerdot {\frac {\Lambda }{\lambda }}$;

in the branch whose reduced length is $\lambda '$,

${\frac {A}{L+\Lambda }}\centerdot {\frac {\Lambda }{\lambda '}}$;

and in the branch whose reduced length is $\lambda ''$,

${\frac {A}{L+\Lambda }}\centerdot {\frac {\Lambda }{\lambda ''}}$.

This remote, and hitherto but slightly noticed peculiarity of the galvanic circuit, I have also found to be perfectly confirmed by experiment^[1].

I herewith conclude the consideration of such galvanic circuits which have already attained the permanent state, and which neither suffer modifications by the influence of the surrounding atmosphere, nor by a gradual change in their chemical composition. But from this point the simplicity of the subject decreases more and more, so that the previous elementary treatment soon entirely disappears. With respect to those

1. Schweigger's Jahrbuch, 1827.