it as too difficult for the prima. This is a mistake. On the contrary, there are minds which, though highly gifted, and of a philosophical turn, yet lack the sort of subordinate attention that is necessary in order, for instance, to carry out a long trigonometrical calculation, and which find themselves much more at ease in analytical geometry. The fact that analytical geometry prepares the way through the differential and integral calculus to the last and highest aims of mathematics, and hence to their most difficult portion, should only form one reason more for beginning the study of it in the gymnasium. And, not to pass by unanswered an objection which might be raised, I would remark that, owing to the flourishing state of mathematical instruction in our universities for a long time past, the present masters of mathematics in the higher classes of our gymnasia are, almost without exception, qualified to teach analytical geometry, and would even be glad were they authorized to teach that branch. Many of the highest living authorities in this department share in the views which I have here expressed. Then, too, in several gymnasia of non-Prussian Germany, analytical geometry is already taught.
I will not now dwell on the fact that the freshmen in our medical classes, who, in the course of their studies, and later, in the practice of their art, have to depend largely on a right use of their senses, bring from the gymnasium only a very defective training in this respect. I omit the consideration of this, because we have not to do here with the medical student as such, but only in so far as he typifies the student in general; and I take him as a type because my observations on the work of the gymnasium are based principally on the results seen in him. Here the question arises, whether the gymnasium attains its end better in the case of students belonging to the other faculties. To a certain extent it does. With those who later devote themselves to the intellectual sciences, natural disposition and home-surroundings will oftentimes be more favorable to humanistic studies than with those who are impelled by hereditary realism toward medicine and the investigation of Nature. Besides, students of theology and jurisprudence are more favorably situated for retaining their humanistic culture than are students of medicine, who from their first semester have to do with a world of things which have no connection, save through their terminology, with classical studies. Hence the average degree of humanistic culture among medical students is a very good test for determining how far the gymnasium is in a condition to oppose the encroachments of realism.
But even when we take into account all the youths who receive a gymnasium education, however diverse their tendencies as regards branches of study, we do not find in them so quick an interest in classical studies as would justify us in seriously expecting from it a reaction in the idealistic sense. Not reckoning philologists, who of course are not within the scope of our remarks just now, there are but few stu-
- Highest class in the gymnasium.