On the composition of elementary errors

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Abstract
Analysis of statistical distributions. 1. Let m and σ denote the mean and the standard deviation of a statistical variable X, and let W(x) be the probability function of that variable as defined in the first paper 1 This journal, 1928, p. 13. We shall refer to that paper by the letter I. — The sense in which the words probability function and frequency function are used here must be carefully observed, If the probability that a certain variable lies between x and x+dx is f(x) dx, then f(x) is the frequency function of the variable. The probability function is, in cases where a finite frequency function ex-ists, equal to the integral of the latter, taken over the interval from -∞ to x — The notations of the present paper will, as a rule, correspond to those of I, the most important exception being the symbol n , which will here always denote the number of observations in a statistical series and not, as in I, the number of elementary components. View all notes , Art. 1. If we put (cf. I, formula (3)) F(x) is the probability function of the variable , with the mean value 0 and the standard deviation 1. Denoting by µ2, µ3, ... the moments of W(x) , taken about the mean (cf. I, Art. 7, where m is supposed to be zero), we put, following Charlier,

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