Page:Scientific Memoirs, Vol. 2 (1841).djvu/506

In both cases a positive value of the expression shows that the pressure takes place in an opposite direction to that of the abscissæ; a negative value, on the contrary, indicates that the pressure is exerted in the direction of the abscissæ. To deduce from these individual tendencies of the constituents the force with which both endeavour to separate from each other, we must remember that this force is given by the twofold difference between the quantities of motion which each constituent would of itself assume, were it associated to the other by no coherence, and those quantities of motion which each constituent must assume were it strongly combined to the other. We thus readily find for the decomposing force of the circuit the following expression:

$4i.z(1-z).{\frac {m\beta -n\alpha }{\alpha z+\beta (1-z)}}.\mathrm {S}$,

from which we learn that the decomposing force of the circuit is proportional to the electric current, and also to a coefficient dependent on the chemical nature of each place of the circuit.

If this expression has a positive value, it indicates that the separation of the constituent $\mathrm {A}$ takes place in a contrary direction to that of the abscissæ, that of the constituent $\mathrm {B}$ in the direction of the abscissæ; but if this expression has a negative value, it denotes a separation in the reverse direction. It is besides evident, at first sight, that the decomposing force of the circuit is constantly determined by the absolute value of the expression.

If $\alpha =\beta$, the decomposing force of the circuit changes into

$4i.z(1-z)(m-n).\mathrm {S}$.

If $mz+n(1-z)=0$, i.e. if the latent electroscopic forces, existing in the united constituents, are equal and opposed; or, what is the same, if the body, situated in the disc $\mathrm {M}$, is perfectly neutral, in which case $m$ and $n$ have constantly opposite values, we obtain, for the decomposing force of the circuit, the following expression:

$4i.{\frac {mn}{m-n}}.\mathrm {S}$.

The form of the general expression found for the decomposing force of the circuit shows that this force disappears; first, when $\mathrm {S} =0$, i.e. when no electric current exists; secondly,