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is zero. This results from what was said a few pages back about the most probable measure in a Scheme being its M. In a Scheme of Errors the M is equal to 0, therefore the most Probable Error in such a Scheme is O .also. It is astonishing that mathematicians, who are the most precise and perspicacious of men, have not long since revolted against this cumbrous, slip-shod, and misleading phrase. They really mean what I should call the Mid-Error, but their phrase is too firmly established for me to uproot it. I shall however always write the word Probable when used in this sense, in the form of "Prob. " ; thus "Prob. Error," as a continual protest against its illegitimate use, and as some slight safeguard against its misinterpretation. Moreover the term Probable Error is absurd when applied to the subjects now in hand, such as Stature, Eye-colour, Artistic Faculty, or Disease. I shall therefore usually speak of Prob. Deviation.

Though the value of our Q is the same as that. of the Prob. Deviation, Q is not a convertible term with Prob. Deviation. We shall often have to speak of the' one without immediate reference to the other, just as we speak of the diameter of the circle without reference to any of its properties, such as, if lines are drawn from its ends to any point in the circumference, they will meet at a right angle. The Q of a Scheme is as definite a phrase as the Diameter of a Circle, but we cannot replace Q in that phrase by the words Prob. Deviation, and speak of the Prob. Deviation of a Scheme, without doing some violence to language. We