Page:Scientific Memoirs, Vol. 2 (1841).djvu/453

 Rh in comparison with their relative distances, a function, to be determined separately for each given case from their dimensions and their mean distance, must be substituted for the product of the magnitudes of the two elements, and which we will designate where it is employed by $$F$$.

5. Hitherto we have taken no notice of the influence of the mutual distance of the elements between which an equalization of their electric state takes place, because as yet we have only considered such elements as always retained the same relative distance. But now the question arises, whether this exchange is directly effected only between adjacent elements, or if it extends to others more distant, and how on the one or the other supposition is its magnitude modified by the distance? Following the example of Laplace, it is customary in cases where molecular actions at the least distance come into play, to employ a particular mode of representation, according to which a direct mutual action between two elements separated by others, still occurs at finite distances, which action, however, decreases so rapidly, that even at any perceptible distance, be it ever so minute, it has to be considered as perfectly evanescent. Laplace was led to this hypothesis, because the supposition that the direct action only extended to the next element produced equations, the individual members of which were not of the same dimension relatively to the differentials of the variable quantities ,—a non-uniformity which is opposed to the spirit of the differential calculus. This apparent unavoidable