. PROGRESS OF HIGHER SCIENCE-TEACHING, 677 



ignorance of the hideous pedantry of a mediaeval grammarian might 

 involve the pain and humiliation of corporal punishment. 



That all, or most, of this has been swept away is ground for un- 

 mixed 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 com- 

 putative, to the disadvantage of the judicial and appreciative func- 

 tions 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 busi- 

 ness. 



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 un- 

 equally 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, more- 

 over, 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 indeter- 

 minate 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 excep- 

 tional as to deserve quotation. It was a pass, not an honors paper. 



