Page:Scientific Memoirs, Vol. 2 (1841).djvu/429

 Rh demonstrate by a short statement of their consequences; at the same time I consider it necessary to observe, that both equations refer to all possible galvanic circuits whose state is permanent, consequently they comprise the voltaic combination as a particular case, so that the theory of the pile needs no separate comment. In order to be distinct, I shall constantly, instead of employing the equation $$u =\frac y - O + c$$, only take the third figure, and therefore will merely remark here, once for all, that all the consequences drawn from it hold generally.

In the next place, the circumstance that the separation of the electricity, diffusing itself over the galvanic circuit, maintains at the different places a permanent and unchangeable gradation, although the force of the electricity is variable at one and the same place, deserves a closer inspection. This is the reason of that magic mutability of the phænomena which admits of our predetermining at pleasure the action of a given place of the galvanic circuit on the electrometer, and enables us to produce it instantly. To explain this peculiarity I will return to figure 3. Since the figure of separation $$F G H I K L$$, is always wholly determined from the nature of any circuit; but its position with respect to the circuit $$A D$$, as was seen, is fixed by no inherent cause, but can assume any change produced by a movement common to all its points in the direction of the ordinates, the electrical condition of each point of the circuit expressed by the mutual position of the two lines, may be varied constantly, and at will, by external influences. When, for example, $$A D$$ is at any time the position representing the actual state of the circuit, so that, therefore, the ordinate $$S Y''$$ expresses by its length the force of the electricity at the place of the circuit to which that ordinate belongs, then the electrical force corresponding to the point $$A$$, at the same time will be represented by the line $$A F$$. If now the point $$A$$ be touched abductively, and thus be entirely deprived of all its force, the line $$A D$$ will be brought into the position $$F M$$, and the force previously existing in the point $$S$$ will be expressed by the length $$X Y$$; this force, therefore, has suddenly undergone a change, corresponding to the length $$S X''$$. The same change would have occurred if the circuit had been touched abductively at the point