Page:Scientific Memoirs, Vol. 2 (1841).djvu/442

 430 the extreme action of the same multiplier may serve not merely to determine the tensions in various circuits, but it also indicates that the extreme action may be also augmented to the same degree as the sum of the tensions is increased, which may be effected by forming a voltaic combination with several simple circuits. If we represent the actual length of a coil of the multiplier by $$l$$, its couductibility by $$\chi$$, and its section by $$\omega$$, so that $$\lambda = \frac$$, the expression for the extreme action of the multiplier is converted into from which it will be seen that the extreme action of two multipliers of different metals, constructed of wire of the same thickness, are in the same ratio to each other as the conductibilities of these metals, and that the extreme actions of two multipliers formed of wire of the same metal, are in the same proportion to each other as the sections of the wires. All these various peculiarities of the multiplier I have shown to be founded on experience, partly on experiments performed by other persons, and partly on those by myself. The most recent experiments made on this subject on thermo-circuits, have, in a different, and, in a certain sense, opposite manner, already afforded the conclusion deduced above from an equation of the reduced lengths, that the sum of the tensions in a thermo-circuit is far weaker than in the ordinary hydro-circuits; and a preliminary comparison has convinced me, that, with respect to the heating effects, if they are to be predicted with certainty, a voltaic combination of some hundred well-chosen simple thermo-circuits is requisite, and for chemical effects of some energy a far greater apparatus. Experiments, which place this prediction beyond doubt, will afford a new and not unimportant confirmation to the theory here propounded.

The previous considerations are also sufficient to indicate the process which is carried on when the galvanic circuit is divided at any place into two or more branches. For this purpose I call attention to the circumstance, that at the time we found the equation $$S = \frac$$, we also obtained the rule that the magnitude of the current in any homogeneous part of the galvanic