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These mathematical researches are of the most difficult order, and can therefore obtain general acquiescence but gradually; it is thus a fortunate chance that in an important part of the propagation or transmission of electricity in consequence of its peculiar nature, those difficulties almost entirely disappear.

To place this portion before the public is the object of the present Memoir, and therefore so many only of the complex cases have been admitted as seemed requisite to render the transition apparent.

The nature and form commonly given to galvanic apparatus favor the propagation of the electricity only in one dimension; and the velocity of its diffusion combined with the constancy with which a source of galvanic electricity acts, is the cause of the assumption by the galvanic phenomena, for the most part, of a character which does not vary with time. These two conditions, to which galvanic phenomena are most frequently subjected, viz., change of the electric state in a single dimension, and its independency of time, are however