Page:Scientific Memoirs, Vol. 2 (1841).djvu/451

Rh on uncertain ground, as there is no touchstone for its hypotheses, and in fact it would be far better to wait a more fit time; but when it goes to work with the proper authority, it enriches, at least in an indirect manner, the field it occupies with new natural phænomena, as universal experience shows. I have thought it necessary to premise these general remarks, as they not only serve to throw more light on what follows, but also because they explain the reason why the galvanic phænomena have not long since been mathematically treated with greater success, although, as we shall subsequently find, the requisite course has been already earlier pursued in another, apparently less prepared, branch of Physics.

After these reflections we will now proceed to the establishment of the fundamental laws themselves.

3. When two electrical elements, $$E$$ and $$E'$$, of equal magnitude, of like form and similarly placed with respect to each other, but unequally powerful, are situated at the proper distance from each other, they exhibit a mutual tendency to attain electric equilibrium, which is apparent in both constantly and uninterruptedly approaching nearer to the mean of their electric state, until they have actually attained it. That is to say, both elements reciprocally change their electric state so long as a difference continues to exist between their electroscopic forces; but this change ceases as soon as they have both attained the same electroscopic force. Consequently this change of the electric difference of the elements is so dependent that the one disappears at the same time with the other. We now suppose that the change, effected in an extremely short instant of time in both elements, is proportional to the difference of their cotemporaneous electroscopic force and the magnitude of the instant of time; and without yet attending to any material distinctions of the electricity, it is always to be understood that the forces designated by + and — are to be treated exactly as opposite magnitudes. That the change is effected accurately according to the difference of the forces, is a mathematical supposition, the most natural because it is the most simple; all the rest is given by experiment. The motion of electricity is effected in most bodies so rapidly that we are seldom able to determine its changes at the various places, and on that account we are not in a condition to discover by observation the law according to which they act. The galvanic phænomena, in which such Rh