3i6 POPULAR SCIENCE MONTHLY. 



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 gener- 

 osity 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 pro- 

 fessor 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 pro- 

 portionally 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. Prob- 

 ably 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 difEerence 

 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 repre- 

 sented 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 universit)^ 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- 



