534 THE POPULAR SCIENCE MONTHLY. 



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 be- 

 ginning the study of it in the gymnasium. And, not to pass by unan- 

 swered 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 de- 

 partment 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 ex- 

 tent it does. With those who later devote themselves to the intellect- 

 ual sciences, natural disposition and home-surroundings will oftentimes 

 be more favorable to humanistic studies than with those who are im- 

 pelled by hereditary realism toward medicine and the investigation of 

 Nature. Besides, students of theology and jurisprudence are more fa- 

 vorably 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 clas- 

 sical studies as would justify us in seriously expecting from it a reac- 

 tion 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- 



1 Highest class in the gymnasium. 



