Page:Scientific Memoirs, Vol. 2 (1841).djvu/440

follows that the one combination is most active in those cases where the other ceases to be so, and vice versâ. If therefore we are in possession of a certain number of simple circuits intended to act upon the portion whose reduced length is $\Lambda$, much depends on the way in which they are placed, in order to produce the greatest effect of current; whether all be side by side, or all in succession, or whether part be placed by the side of each other, and part in series. It may be mathematically shown that it is most advantageous to form them into a voltaic combination, of so many equal parts, that the square of this number be equal to the quotient ${\frac {\Lambda }{L}}$. When ${\frac {\Lambda }{L}}$ is equal to, or smaller than $\Lambda$, they had best be arranged by the side of each other, and in succession when ${\frac {\Lambda }{L}}$ is equal to, or larger than the square of the number of all the elements. We see in this determination the reason why in most cases a simple circuit, or at least a voltaic combination of only a few simple circuits, is sufficient to produce the greatest effect. If we bear in mind, that since the quantity of the current is the same at all places of the circuit, its intensity at the various places must be in inverse proportion to the magnitude of the section there situated, and if we grant that the magnetic and chemical effects, as well as the phænomena of light and heat in the circuit, are direct indications of the electrical current, and that their energy is determined by that of the current itself, then a detailed analysis of the current, here indicated merely in outline, will lead to the perfect explanation of the numerous and partially enigmatical anomalies observed in the galvanic circuit, in as far as we are justified in considering the physical nature of the circuit as invariable^[1]. Those great differences which are frequently met with in the statements of various observers, and which are not consequences of the dimensions of their different apparatus, have undoubtedly their origin in the double capability of change of the hydro-circuits, and will therefore cease when this circumstance is taken into consideration on a repetition of the experiments.

The remarkable variability in the circle of action of one and the same multiplier in various circuits, and of different multipliers in the same circuit, is completely explained by the

1. See Schweigger's Jahrbuch, 1826, Part 2, where I have given a somewhat more detailed explanation of the separate points.