a mere judgment of merit. Since the estimate is confessedly only approximate, the student receives the benefit of every uncertainty. If any mistake has to be made, let him be encouraged by a false estimate that includes full credit rather than discouraged by one that does injustice. The numerical estimate of average success expressed as a percentage thus tends to become continually higher unless the generosity of the examiner is periodically and frequently checked by having his attention called to the absurdity of recording the majority of his students as distinguished. Dr. Ruffner says: "A temporizing professor who loves popularity, and desires, like the old man in the fable, to please everybody, is sure to be guilty of this fault, and, like many a politician, to sacrifice permanent good for temporary favor." If the passing mark is high, for example, 75 per cent., all marks will be proportionally high. What this limiting mark should be depends upon the idea underlying it. If the grade assigned means that the student is credited with knowing half, or three fourths, or nine tenths of what an ideally perfect student would know of the subject of study, the corresponding grade should obviously be 50, 75 or 90 per cent. Probably this is the most usual theoretic interpretation. But in practise the fundamental question is, in a large proportion of cases, not whether the student's attainments can be expressed accurately by a percentage, but merely whether in the teacher's judgment he ought to be passed or not. If so, his marks will be above the arbitrary limit, whatever may be the numerical value of this. If not, it makes little difference whether the grade assigned to the failure is 10, 30 or 50 per cent. In an institution where the teaching is good and where the discipline is firm and consistent, it is not often that more than one fourth of all students fail to pass in their studies. Theoretically, therefore, 25 per cent, would be better than 75 per cent, for the passing mark. This would mean no lowering of standard, but only a more rational system of marking than that which is most common. If results be represented graphically, the curve showing variation in grades attained would have its maximum corresponding to 50 per cent. This is an arithmetical mean between perfection and total failure, and should therefore be the numerical representation of the average grade. The curve would thus be substantially the symmetrical 'probability curve,' which is divided into two equal parts by the maximum ordinate, as shown in the accompanying diagram.
This study of the distribution of students' grades is worth more than passing notice, because it affords the best means of showing the tendency in relation to distinctions generally. Many years ago in a western university by comparison of the grades of 287 students in physics, it was found that the average grade attained was about 85 per cent. In the institution with which the present writer is con-
