SOME PROBLEMS IN THE THEORY OF ERRORS OF DIRECT OBSERVATTONS AS VIEWED FROM THE THEORY OF MATHEMATICAL STATISTICS.

Probably every one of us, while studying the method of least squares, feels the lack of rigorousness in its reasoning, and is not quite satisfied with its theory.The author proposes that theory of errors(i.e. the method of least squares)should be treated as a branch of applied mathematics, and be studied in the light of probability theory and mathematical statistics. In the present time, the theory of errors has not enough connection with probability theory and mathematical statistics as it should.In this paper, the author tries to analyse some problems in direct observations of equal weights from the view-point of mathematical statistics, he examined the derivation of the law of normal distribution (Gaussian law), the definition of "true value" and "true error", introduces to the reader the ideas of population, sampling and samples, convergence, in probability, applies the ideas of consistent and unbiased estimation in estimating the population mean and population variance, and thus obtains a better derivation of Bessel's formula, points out the incorrectness of equating the true error of the mean and the mean square error of the mean.Finally, the author explains the idea of large and small samples, and the application of "Students distribution" in finding the confidence interval of the arith-matical mean.