There are two ways of treating data which are distributed in this manner: (i) One may actually go over to the logarithms y = log x and proceed as though y were normal or nearly so; in this case m is calculated as the mean of y and ois the standard deviation of y and the usual formulas ?m = o,\Vn, uJa = o/V2n would apply. (2) Or one may fit the transform by moments on the original data, in which case the values of m and a may be somewhat different and their standard deviations will be determined by other formulas. We propose to discuss briefly some matters, connected with the logarithmic transform, which we believe have had insufficient emphasis. To make the discussion less abstract we shall give numerical illustrations obtained from the distribution of the percentage net debt (state and municipal) of the forty-eight states relative to the wealth of the state as estimated a decade

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.,