Page:Scientific Memoirs, Vol. 2 (1841).djvu/437

in the thermo-circuit, cedes in nothing to that in the hydro-circuit. The great difference between a thermo- and hydro-circuit, both of which produce a current of the same energy, is evident when the same change is made on both, as will be shown in the following consideration. Let the reduced length of a thermo-circuit be $L$, and the sum of its tensions $A$, the reduced length of an hydro-circuit $mL$, and the sum of its tensions $mA$, then the magnitude of the current in the former is expressed by ${\frac {A}{L}}$, in the latter by ${\frac {mA}{mL}}$, and is consequently the same in both circuits. But this equality of the current no longer exists if the same new part $\lambda$ of the reduced length be introduced into both, for then the magnitude of the current is in the first

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

in the second

${\frac {mA}{mL+\lambda }}.$

If we connect with this determination an evaluation, even if merely superficial, of the quantities $m$, $L$, and $\lambda$, we shall readily be convinced that in cases where the simple hydro-circuit can still produce in the part $\lambda$ actions of heat or chemical decomposition, the simple thermo-circuit may not possess the hundredth, and in some cases not the thousandth part of the requisite force, whence the absence of similar effects in it is easily to be understood. We are also able to understand why a diminution of the reduced lengths of the thermo-circuit (by increasing, for instance, the section of the metals constituting it) cannot give rise to the production of those effects, although the magnitude of its current may be increased by this means to a higher degree than in the hydro-circuit producing such effects. This difference in the conductibility of metallic bodies and aqueous fluids, is the cause of a peculiarity noticed with respect to hydro-circuits, which it is here, perhaps, the proper place to mention. Under the usual circumstances, the reduced length of the fluid portion is so large, in comparison to that of the metallic portion, that the latter may be overlooked, and the former alone taken instead of the reduced length of the entire circuit; but then the magnitude of the current in circuits which have the same tension is in the inverse ratio to the reduced length of the fluid