The extension of the use of the relaxation method from two to three dimensions has for a long time been desirable; the use of a three-dimensional network has been thought to be impractical because it has been supposed that it must require the superposition of a set of plane nets each drawn on a separate sheet. An alternative method was proposed by Tranter (1) in which he attempted to replace one threedimensional problem by a set of two-dimensional problems; his method is satisfactory, but in an extremely limited capacity in that it only solves Laplace's (or Poisson's) equation inside a volume which is bounded by a cylinder (of any crosssection) with plane ends normal to the generators. In this paper we show that provided the work is properly set out, then there is no particular difficulty in the use of a three-dimensional network; as illustrative examples solutions have been found for the steady temperature-distribution problem used by Tranter in describing his method (for comparison); and also for the electric potential-distribution inside a quadrant electrometer.