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 dependence 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 pronunciation, 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 English, in whose eyes an infraction of its rules appears to be, as it were, a sacrilege. The more closely this blemish in our educational practice 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, accompanied by 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 algebra, particularly in its application to geometry; indetermined equations; 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.
