ignorance of the hideous pedantry of a mediæval grammarian might involve the pain and humiliation of corporal punishment.
That all, or most, of this has been swept away is ground for unmixed satisfaction. But it does not absolutely follow that what is being substituted for it is beyond comment or improvement. There may be errors and pedantries developing in the new as in the older system. Nor are they difficult to point out.
The teaching of science has tended to give an impulse to the computative, to the disadvantage of the judicial and appreciative functions of students' minds. Indeed, the computative faculty, so highly developed at times in men not otherwise liberally educated, is not the widest in intellectual scope, nor the fittest preparation for some branches of life-work. Men in after-life are called upon to use their imaginative powers, to sift evidence, and to weigh symptoms, as well as to solve problems. They may adopt artistic or literary pursuits, they may choose the professions of law or of medicine. In all these, the attempt to reduce the subject-matter laid before them to the strict conditions of an equation or a ratio, so far from being a fruitful mental effort, may absolutely prove a hindrance. There is a common type of mind which fails to see a proof which is not of the character of demonstration, and which, in its absence, neglects to use the faculty of judgment and decision so necessary in the common affairs of business.
The computing school, and especially those who teach its physical branches, very correctly and consistently insist upon the solving of problems as a test of thorough knowledge. Mr. Day, whose work appears to be mainly performed "in the laboratory of King's College, under the direction of Professor Adams," in an excellent collection of questions upon electrical measurement, says, "It is now universally admitted that numerical exercises are necessary in the study of the experimental sciences, both as giving practice in the application of the various theories, and as affording tests of ability to comprehend as well as to apply that which has been learned."
It must be remembered, however, that, even among advanced and professed mathematicians, the faculty of solving problems is very unequally distributed—a fact which is openly recognized at the great mathematical University of Cambridge. The problems themselves are often open to comment, as partaking of the nature of enigmas, or riddles, rather than as fair tests of knowledge. Like riddles, moreover, they exercise a kind of fascination on their concocters, and are very liable to figure in papers of questions. The writer, for instance, has seen in a paper on physics a question which involved an indeterminate equation, and of which the solutions were infinite in number. Surely this should have been relegated to its kindred algebra. But an instance which has occurred within the present year is so exceptional as to deserve quotation. It was a pass, not an honors paper.