By the aid of Taylor expansion, the formulae of the numerical solutions of the equations of heat conduction and of wave motion are easily calculated. On heat conduction, the errors of these formulae are of the order of τ3 for each dimension, if τ be a sufficiently small time. On onedimensional wave motion, no error is perceived except for the initial time, the errors for which are of the order of τ3. On two- and three-dimensional wave motions, the errors are of the order of τ_??_ excepting for the initial time, the errors for which are of the order of τ_??_.