Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/415

324.] 324.] To construct a framework of linear conductors which shall have any given coefficients of conductivity forming a symmetrical system.

Let the space be divided into equal small cubes, of which let the figure represent one. Let the coordinates of the points $$0,\, L,\, M,\, N, $$ and their potentials be as follows: $ \begin{array}{lllll} \quad \quad & x & y & z\quad & Potential. \\ O & 0 & 0 & 0 & 0 \\ L & 0 & 1 &1 & 0+Y+Z, \\ M & 1 & 0 & 1 & 0+Z+X, \\ N & 1 & 1 & 0 & 0+X+Y. \end{array} $

Let these four points be connected by six conductors, of which the conductivities are respectively

The electromotive forces along these conductors will be and the currents Of these currents, those which convey electricity in the positive direction of $$x$$ are those along $$LM,\, LN,\, OM$$ and $$ON,$$ and the quantity conveyed is Similarly whence we find by comparison with the equations of conduction, Art. 298,