Then introducing the notion of a law of facility Of error give precise meaning to the phrase most probable value, cannot do better than to adopt that law Of facility in accord ance with which the arithmetical mean is the most probable value. After deriving this law and showing that it leads to the principle of least squares, he says This principle, which in all applications of mathematics to natural philosophy ad mits of very frequent use, ought everywhere to hold good as an axiom by the same right as that by which the arithmetical mean between several Observed values Of the same quantity is adopted as the most probable value. (art.