Page:Scientific Memoirs, Vol. 2 (1841).djvu/452

 440 changes occur in a constant form, are therefore of the highest importance for testing this assumption: for if the conclusions drawn from the supposition are thoroughly confirmed by those phænomena, it is admissible, and may then be applied without any further consideration to all analogous researches, at least within the same limits of force.

We have assumed, in accordance with the observations hitherto made, that when by any two exteriorly like constituted elements, whether they be of the same or of different matter, a mutual change in their electrical state is produced, the one loses just so much force as the other gains. Should it hereafter be shown by experiments that bodies exhibit a relation similar to that which in the theory of heat is termed the capacity of bodies, the law we have established will have to undergo a slight alteration, which we shall point out in the proper place.

4. When the two elements $$E$$ and $$E'$$ are not of equal magnitude, it is still allowed to regard them as sums of equal parts. Granting that an element $$E$$ consist of $$m$$ perfectly equal parts, and the other $$E'$$ of $$m'$$ exactly similar parts, then, if we imagine the elements $$E$$ and $$E'$$ exceedingly small in comparison with their mutual distance, so that the distances from each part of the one to each part of the other element are equal, the sum of the actions of all the $$m'$$ parts of the element $$E'$$ on a part of $$E$$ will be $$m'$$ times that which a single part exerts, and the sum of all the actions of the element $$E'$$ on all the $$m$$ parts of $$E$$ will be $$m m'$$ times that which a part of $$E'$$ exerts on a part of $$E$$. It is hence evident, that in order to ascertain the mutual actions of dissimilar elements on each other, they must be taken as proportional not merely to the difference of their electroscopic forces and their duration, but also to the product of their relative magnitudes. We shall in future term the sum of the electroscopic actions, referred to the magnitude of the elements—by which therefore we have to understand the force multiplied by the magnitude of the space over which it is diffused, in the case where the same force prevails at all places in this space—the quantity of electricity, without intending to determine anything thereby with respect to the material nature of electricity. The same observation is applicable to all figurative expressions introduced, without which, perhaps for good reasons, our language could not exist.

In cases where the elements cannot be regarded as evanescent