TWEXTY-SETENTU ANNUAL MEETING. 93 



tion of the Polytechnic of Zurich. Models of surfaces of the fourth order 

 were made by Kummer from 1860 to 1870. His pupil-disciple, Schwarz, con- 

 structed also a set of models, among which are minimal surfaces and the 

 central surface of the ellipsoid. On the occasion of a meeting of mathema- 

 ticians in Gottingen, a large exhibition of models was arranged, which had 

 a great success. Thus, A. Brill, F. Klein and W. Dyck started the construc- 

 tion of models in the mathematical seminary of the Polytechnic Institute of 

 Munich in a systematic manner. Since 1877 more than a hundred models 

 of all kinds have appeared there. They are not all intended purely for 

 mathematical teaching, but also for the use in lectures on perspective, 

 mechanics, and mathematical physics. As it is seen from this fact, higher 

 institutions of mathematical learning begin to put particular stress upon 

 the collection of models as means of illustration. The value of mathematical 

 models is almost inappreciable, because there are no other means that con- 

 tribute more to a refined intuition. Collections of mathematical models 

 will become, for the mathematical departments of the universities, poly- 

 technics, and colleges, what the museums of natural history are for the 

 biological departments. 



