This article investigates the claim of Gauss, made in Theoria Motus,that deviations from the normal distribution is of no importance in practice relative to whether the method of generalized least squares yields the most probable value under the density criterion. The main result of the article is that given an independence assumption the method of generalized least squares yields the most probable value under the density criterion if and only if the observational errors are median zero normally distributed. As a consequence, the method of generalized least squares carries within itself a normal distribution assumption, in this sense. The corresponding claim under Pearson’s distance criterion is also studied, yielding a similar conclusion.