Page:Scientific Memoirs, Vol. 2 (1841).djvu/419

Rh to a ring composed of any number of heterogeneous parts, if each part be of itself homogeneous and of the same thickness. I may here take as an example of this extension a ring composed of two heterogeneous parts. Let this ring be imagined as before open at one of its places of excitation and stretched out to form the right line $$\mathrm{ABC}$$ (fig. 2), so that $$\mathrm{AB}$$ and $$\mathrm{BC}$$ indicate the two heterogeneous parts of the ring. The perpendiculars $\mathrm{AF}$, $\mathrm{BG}$, will represent by their lengths the electrical forces present at the extremities of the part $\mathrm{AB}$; on the other hand, $$\mathrm{BH}$$ and $\mathrm{CI}$, those present at the extremities of the part $\mathrm{BC}$; accordingly $$\mathrm{AF} + \mathrm{CI}$$ or $$\mathrm{FK}$$ will represent the tension at the opened place of excitation, and $$\mathrm{GH}$$ the tension occurring at $$\mathrm{B}$$ at the point of contact. Now if we only bear in mind the permanent state of the circuit, the straight lines $$\mathrm{FG}$$ and $$\mathrm{HI}$$ will, from the reasons above mentioned, indicate by their position the mode of separation of the electricity in the ring; but whether the line $$\mathrm{AC}$$ will keep its place, or must be advanced further up or down, remains uncertain, and can only be found out in each distinct case by other separate considerations. If, for instance, the point $$\mathrm{O}$$ of the circuit is touched abductively, and thus deprived of all electricity, $$\mathrm{ON}$$ would disappear; and therefore the line $$\mathrm{LM}$$ drawn through $$\mathrm{N}$$ parallel with $$\mathrm{AC}$$ would in this case give the position of $$\mathrm{AC}$$ required. It is hence evident, how sometimes this, sometimes another, position of the line $$\mathrm{AC}$$ in the figure $\mathrm{FGHI}$, representing the separation of the electricity, may be the one suited to the circumstances; and herein we recognise the source of the variability of galvanic phænomena already mentioned.

It is, however, essentially requisite, in order to be able to judge thoroughly of the present case, to attend to a circumstance the mention of which has hitherto been purposely avoided, that the various considerations might be separated as distinctly as possible. The distances $$\mathrm{FK}$$ and $$\mathrm{GH}$$ are indeed given by the tensions existing at the two places of excitation, but the figure $$\mathrm{FGHI}$$ is not yet wholly determined by this alone. For instance, the points $$\mathrm{G}$$ and $$\mathrm{H}$$ might move down towards $$\mathrm{G}'$$ and $\mathrm{H}'$, so that $$\mathrm{G}'\mathrm{H}'$$ would equal $\mathrm{GH}$, giving rise to the figure $\mathrm{FG}'\mathrm{H}'\mathrm{I}$, which would indicate quite a different mode of separation of the electricity, although the individual tensions in it still retain their former magnitude.