THE method of moments has been much used to fit frequency functions whether in the Pearson or the Gram-Charlier or the Edgeworth system. In the monograph in which R. A. Fisher laid the foundation for so much of the modern development of mathematical statistics and, in particular, for his theory of the estimation of values of unknown parameters of frequency distributions of known type, he indicated that type of frequency function which could be fitted with perfect efficiency, as he termed it, by the use of the first four moments.' It is an important matter in statistical theory to follow up this suggestion of Fisher's even though one may not often fit the type of function proposed. The frequency function in question, viz.,