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The paper discusses a practical procedure which compensates for the effect of taking running means, and a numerical example is worked out. The procedure simply requires the evaluation of further running means and should prove readily applicable in many cases where the need arises. In this procedure, which has already gained importance in more general form in other fields (as the method of successive substitutions), a criterion of convergence has been given ; and it is a major aim of the paper to illustrate, using running means as an instance, that the utility of the method of successive substitutions is wider than is indicated by this criterion.

Correcting for Running Means by Successive Substitutions