On the theory of errors and least squares

Abstract

Where we have no previous knowledge of the probable degree of precision of a set of observations, the correct procedure is to assume that the probability of a value of h in the range dh is proportional to dh/h. The result is applied to the theory of least squares. Where the number of observations is small, the probability of error is more widely distributed than is given by the usual formula. In the extreme case of 2 observations and 1 unknown, the probable error of the mean is equal to the standard deviation.