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SUMMARYThe method presented in Part I of this paper' is extended to problems governed by a system of partial differential equations. The basic clarity and simplicity of the method is preserved.The domain of integration is covered by a net of orthogonal (not necessarily equidistant) straight lines. Choosing again highest derivatives with respect to each of the co-ordinates as unknowns, it is possible to reduce the problem to a system of integral equations along the lines of the adopted net.The subsequent procedure is basically the same as in Part I. The results prove to be of remarkable accuracy even for very coarse nets.