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Previous solutions of the idealized saltwater intrusion problem known as the Henry problem are discussed, and possible reasons for the observed discrepancies between them are given. High-accuracy finite difference techniques are used to solve the nondimensionalized equations governing the problem, and a fine grid is used so that the solutions obtained contain only very small truncation errors. Such errors are investigated by means of grid refinement. Comparison of past results with the present solutions indicate, first, the presence of significant inaccuracy in certain earlier results and, second, the effects of numerical dispersion in other previous solutions calculated using relatively few grid points.