The capacity of two parallel planes can be calculated at once if we neglect the distribution of the lines of force near the edges of the plates, and assume that the only field is the uniform field between the plates. Let V1 and V2 be the potentials of the plates, and let a charge Q be given to one of them. If S is the surface of each plate, and d their distance, then the electric force E in the space between them is E = (V1-V2)/d. But if [sigma] is the surface density, E = 4[pi][sigma], and [sigma] = Q/S. Hence we have (V1 - V2) d = 4[pi]Q/S or C = Q/(V1 - V2) = S/4[pi]d (13). In this calculation we neglect altogether the fact that electric force distributed on curved lines exists outside the interspace between the plates, and these lines in fact extend from the back of one plate to that of the other. G.R. Kirchhoff (_Gesammelte Abhandl._ p. 112) has given a full expression for the capacity C of two circular plates of thickness t and radius r placed at any distance d apart in air from which the edge effect can be calculated. Kirchhoff's expression is as follows:-- [pi]r² r / 16[pi]r(d+t) d + t\ C = ------ + ------ ( d log_[epsilon] ------------ + t log_[epsilon] ----- ) (14). 4[pi]d 4[pi]d \ [epsilon]d² t / In the above formula [epsilon] is the base of the Napierian logarithms. The first term on the right-hand side of the equation is the expression for the capacity, neglecting the curved edge distribution of electric force, and the other terms take into account, not only the uniform field between the plates, but also the non-uniform field round the edges and beyond the plates. Guard plates. In practice we can avoid the difficulty due to irregular distribution of electric force at the edges of the plate by the use of a guard plate as first suggested by Lord Kelvin.[8] If a large plate has a circular hole cut in it, and this is nearly filled up by a circular plate lying in the same plane, and if we place another large plate parallel to the first, then the electric field between this second plate and the small circular plate is nearly uniform; and if S is the area of the small plate and d its distance from the opposed plate, its capacity may be calculated by the simple formula C = S/4[pi]d. The outer larger plate in which the hole is cut is called the "guard plate," and must be kept at the same potential as the smaller inner or "trap-door plate." The same arrangement can be supplied to a pair of coaxial cylinders. By placing metal plates on either side of a larger sheet of dielectric or insulator we can construct a condenser of relatively large capacity. The instrument known as a Leyden jar (q.v.) consists of a glass bottle coated within and without for three parts of the way up with tinfoil. Systems of condensers.