Page:Scientific Memoirs, Vol. 2 (1841).djvu/418

electrical, state of the part. The line $\mathrm {AB}$ (Plate XXIV., fig. 1) may accordingly represent the ring extended in a straight line, and the lines $\mathrm {AF}$ and $\mathrm {BG}$ perpendicular to $\mathrm {AB}$ may indicate by their lengths the force of the positive electricities situated at the extremities $\mathrm {A}$ and $\mathrm {B}$. If now the straight line $\mathrm {FG}$ be drawn from $\mathrm {F}$ to $\mathrm {G}$, also $\mathrm {FH}$ parallel to $\mathrm {AB}$, the position of $\mathrm {FG}$ will give the mode of separation of the electricity, and the quantities $\mathrm {BG} {\frac {\quad }{}}\mathrm {AF}$ or $\mathrm {GH}$ the tension occurring at the extremities of the ring; and the force of the electricity at any other place $\mathrm {C}$, may easily be expressed by the length of $\mathrm {CD}$ drawn through $\mathrm {C}$ perpendicularly to $\mathrm {AB}$. But, from the nature of the galvanic excitation, merely the quantity of the tension or the length of the line $\mathrm {GH}$, therefore the difference of the lines $\mathrm {AF}$ and $\mathrm {BG}$, is determined, but not at all the absolute magnitudes of the lines $\mathrm {AF}$ and $\mathrm {BG}$; consequently the mode of separation may be represented quite as well by any other line parallel to the former, e.g. by $\mathrm {IK}$, for which the tension still constantly retains the same value expressed by $\mathrm {KN}$, because the ordinates situated at present below $\mathrm {AB}$ assume a relation opposed to their former one. Which of the infinitely numerous lines parallel to $\mathrm {FG}$ would express the actual state of the ring cannot be stated in general, but must in each case be separately determined from the circumstances which occur. Moreover, it is easily conceived that, as the position of the line sought is given, it would be completely determined for one single part of the ring by the determination of any one of its points, or, in other words, by the knowledge of the electric force. If, for instance, the ring lost all its electricity by abduction at the place $\mathrm {C}$, the line $\mathrm {LM}$ drawn through $\mathrm {C}$ parallel to $\mathrm {FG}$ would in this case express with perfect certainty the electrical state of the ring. This variability in the separation of the electricity is the source of the changeableness of the phænomenon peculiar to the galvanic circuit. I may further add, that it is evidently quite indifferent whether the position of the line $\mathrm {FG}$ with respect to that of $\mathrm {AB}$ be fixed; or whether the position of the line $\mathrm {FG}$ remain constantly the same, and the position of $\mathrm {AB}$ with respect to it be altered. The latter course is by far the more simple where the separation of the electricity assumes a more complex form.

The conclusions just arrived at, which hold for a ring homogeneous throughout its whole extent, may easily be ex-