Page:Scientific Memoirs, Vol. 2 (1841).djvu/498

${\frac {1}{\Lambda }}={\frac {1}{\lambda }}+{\frac {1}{\lambda '}}+{\frac {1}{\lambda ''}}+$ &c.

From the preceding explanations we may conclude, that when $\mathrm {A}$ denotes the sum of all the tensions, and $\mathrm {L}$ the entire reduced length of the circuit without adjacent conductors, the magnitude of the current, while the adjacent conductors are in connexion with the circuit, will be expressed in the circuit itself by

${\frac {\mathrm {A} }{\mathrm {L} +\Lambda }}$;

in the joint conductor, whose reduced length is $\lambda$, by

${\frac {\mathrm {A} }{\mathrm {L} +\Lambda }}.{\frac {\Lambda }{\lambda }}$;

in the joint conductor, whose reduced length is $\lambda '$, by

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

in the joint conductor, whose reduced length is $\lambda ''$, by

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

and so on, where for $\Lambda$ its value obtained from the equation

${\frac {1}{\Lambda }}={\frac {1}{\lambda }}+{\frac {1}{\lambda '}}+{\frac {1}{\lambda ''}}+$ &c.

has to be placed.

29. That in the above the galvanic current is found to be of equal magnitude at all places of the circuit, arises from the value of ${\frac {du}{dx}}$, deduced from the equation

$u={\frac {\mathrm {A} }{\mathrm {L} }}y-\mathrm {O} +c$,

being constant. This circumstance no longer happens if we start from the equations given in §22 and 23. In all these cases ${\frac {du}{dx}}$ is dependent on $x$, which indicates that the magnitude of the current is different at different places of the circuit. We may hence draw the conclusion, that the electric current is only of equal intensity at all places of the circuit, when the circuit has already assumed a permanent state, and the atmosphere has no sensible action upon it. This property likewise appears best adapted to enable us to find out, by experiment, whether