The sphere of action thus fixed by us, has, although it is infinitely small, precisely the same circumference as that introduced by Laplace, and called finite, where he lets the higher powers of the distance vanish compared with the lower, the reason of which may be found already in what has been stated above. The supposition of a finite distance of action in our sense would correspond to the case where Laplace still retains higher powers of distance together with the lower.
9. The bodies on which we observe electric phænomena are in most cases surrounded by the atmosphere; it is therefore requisite, in order to investigate profoundly the entire process, not to disregard the changes which may be produced by the adjacent air. According to the experiments left us by Coulomb on the diffusion of electricity in the surrounding atmosphere, the loss in force thus occasioned is (during a very short constant time), at least when the intensities are not very considerable, on the one hand proportional to the energy of the electricity, and on the other is dependent on a coefficient varying according to the cotemporaneous nature of the air, but otherwise invariable for the same air. The knowledge of this enables us to bring the influence of the atmosphere on galvanic phænomena into calculation wherever it might be requisite. It must however not be overlooked here, that Coulomb's experiments were made on electricity which had entered into equilibrium and was no longer in the process of excitation, with respect to which both observation and calculation have convinced us that it is confined to the surface of bodies, or merely penetrates to a very slight depth into their interior; for from thence may be drawn the conclusion, of some importance with respect to our subject, that all the electricity present in those experiments may have been directly concerned in the transference to the atmosphere. If we now connect with this observation the law just announced, according to which two elements, situated at any finite distance from each other, no longer exert any direct action on each other, we are justified in concluding, that where the electricity is uniformly diffused throughout the entire mass of a finite body, or at least so that proportionately but a small quantity resides in the vicinity of the surface, which case does not in general occur when it has entered into motion, the loss which is occasioned by the circumambient air can be but extremely small in comparison to that which takes place when the
