[Footnote 31: As this definition in its simple form is apt to give rise to misunderstandings, elucidations are usually added to it. It is clear that we cannot lift a quantity of electricity to _K_, without changing the distribution on _K_ and the potential on _K_. Hence, the charges on _K_ must be conceived as fixed, and so small a quantity raised that no appreciable change is produced by it. Taking the work thus expended as many times as the small quantity in question is contained in the unit of quantity, we shall obtain the potential. The potential of a body _K_ may be briefly and precisely defined as follows: If we expend the element of work _dW_ to raise the element of positive quantity _dQ_ from the earth to the conductor, the potential of a conductor _K_ will be given by _V = dW/dQ_.] [Footnote 32: In this article the solidus or slant stroke is used for the usual fractional sign of division. Where plus or minus signs occur in the numerator or denominator, brackets or a vinculum is used.--_Tr._] [Footnote 33: A sort of agreement exists between the notions of thermal and electrical capacity, but the difference between the two ideas also should be carefully borne in mind. The thermal capacity of a body depends solely upon that body itself. The electrical capacity of a body _K_ is influenced by all bodies in its vicinity, inasmuch as the charge of these bodies is able to alter the potential of _K_. To give, therefore, an unequivocal significance to the notion of the capacity (_C_) of a body _K_, _C_ is defined as the relation _Q_/_V_ for the body _K_ in a certain given position of all neighboring bodies, and during connexion of all neighboring conductors with the earth. In practice the situation is much simpler. The capacity, for example, of a jar, the inner coating of which is almost enveloped by its outer coating, communicating with the ground, is not sensibly affected by charged or uncharged adjacent conductors.] [Footnote 34: These formulæ easily follow from Newton's theorem that a homogeneous spherical shell, whose elements obey the law of the inverse squares, exerts no force whatever on points within it but acts on points without as if the whole mass were concentrated at its centre. The formulæ next adduced also flow from this proposition.]