On Gauss's proof of the normal law of errors

Extract

Gauss gave a well-known proof that under certain conditions the postulate that the arithmetic mean of a number of measures is the most probable estimate of the true value, given the observations, implies the normal law of error. I found recently that in an important practical case the mean is the most probable value, although the normal law does not hold. I suggested an explanation of the apparent discrepancy, but it does not seem to be the true one in the case under consideration.