532 THE POPULAR SCIENCE MONTHLY. 



these evidences of defective scholarship were glossed over at the time 

 of the examination by some mechanical contrivance. How far these 

 young men were familiar with the personages, the thoughts, and the 

 forms of the ancient world, whether they had any sense of our depend- 

 ence on the ancients, and of our being their intellectual descendants 

 for that is the sum and substance of humanism I of course have 

 had no opportunity for determining. Nor did I get any systematic 

 information of their historical knowledge. However, their indifference 

 toward broad ideas and historic sequence makes it difficult for me to 

 believe that they are permeated with the spirit of antiquity, or that 

 they had received a sound historical training. 



To all this I must add another deplorable fact. For the most part 

 these young people wrote 'in ungrammatical and inelegant German. 

 Owing to the unsettled state of our orthography, our word-formation, 

 and our construction of sentences, instruction in the mother-tongue is 

 more difficult among ourselves than among people who have a settled 

 usage in language. But the young people, as a rule, did not even 

 suspect that any one could care about purity of language and pronun- 

 ciation, force of expression, brevity, or pointedness of style. One is 

 ashamed, as a German, of such barbarism as this, knowing what care 

 instruction in the mother-tongue receives from the French and Eng- 

 lish, in whose eyes an infraction of its rules appears to be, as it were, 

 a sacrilege. The more closely this blemish in our educational prac- 

 tice is connected with a deep-lying national defect, the more is it to be 

 wished that the gymnasia had been successful in removing it. This 

 neglect of the mother-tongue is, in the youth of the present day, ac- 

 companied b} r a lack of acquaintance with the German classics that is 

 oftentimes astounding. Time was when, in Germany, no one any 

 longer quoted from the first part of " Faust," because quotation had 

 been overdone. Is the time now coming when it can no longer be 

 quoted, because no one would understand the allusion ? 



With respect to instruction in mathematics, I know that but few 

 masters succeed in advancing all their pupils equally. Clearly there 

 are minds highly gifted in other respects, but to which mathematics is 

 a book with seven seals. I would only remark upon the mathematical 

 programme prescribed by tradition and convention for the highest class 

 in our gymnasia. In a semi-official plan of studies this programme is 

 given as follows : " Geometry of solids, with mensuration of surfaces and 

 volumes ; geometrical and stereometrical problems ; problems in alge- 

 bra, particularly in its application to geometry ; indetermined equa- 

 tions ; continued fractions ; the binomial theorem." Though under 

 "problems in algebra, particularly in its application to geometry," 

 analytical geometry might be included, that branch is omitted from 

 the gymnasial plan of studies by a ministerial decision of ancient date, 

 but still in full force, and the mathematical programme of the highest 

 realschulen surpasses in this respect that of the gymnasia. 



