For further information on the qualities of dielectrics the reader is referred to the following sources:--J. Hopkinson, "On the Residual Charge of the Leyden Jar," _Phil. Trans._, 1876, 166 [ii.], p. 489, where it is shown that tapping the glass of a Leyden jar permits the reappearance of the residual charge; "On the Residual Charge of the Leyden Jar," ib. 167 [ii.], p. 599, containing many valuable observations on the residual charge of Leyden jars; W.E. Ayrton and J. Perry, "A Preliminary Account of the Reduction of Observations on Strained Material, Leyden Jars and Voltameters," _Proc. Roy. Soc._, 1880, 30, p. 411, showing experiments on residual charge of condensers and a comparison between the behaviour of dielectrics and glass fibres under torsion. In connexion with this paper the reader may also be referred to one by L. Boltzmann, "Zur Theorie der elastischen Nachwirkung," _Wien. Acad. Sitz.-Ber._, 1874, 70. _Distribution of Electricity on Conductors._--We now proceed to consider in more detail the laws which govern the distribution of electricity at rest upon conductors. It has been shown above that the potential due to a charge of q units placed on a very small sphere, commonly called a point-charge, at any distance x is q/x. The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges q1, q2, q3, &c., distributed in any manner, is the sum of them separately, or q1/x1 + q2/x2 + q3/x3 + &c. = [Sigma](q/x) = V (17), where x1, x2, x3, &c., are the distances of the respective point charges from the point in question at which the total potential is required. The resultant electric force E at that point is then obtained by differentiating V, since E = -dV/dx, and E is in the direction in which V diminishes fastest. In any case, therefore, in which we can sum up the elementary potentials at any point we can calculate the resultant electric force at the same point.