III. MODELS. 29 



The above work demonstrates the necessity for a reform in geometry, and 

 furnishes the necessary basis for establishing a new system adapted to satisfy 

 the requirements of an exact science. To the above are added 7 " Paragram " 

 Tablets, representing in natural organic connexion a synopsis of the principal 

 elements to be observed in every graphical representation. 



126. Model of the ruled cubic surface called the Cylindroid, 



Dr. Robert S. Ball, LL.D., F.R.S. 



This surface was discussed by Pliickcr in connexion with the theory of 

 the linear-complex. The kinematical and physical significance of the sur- 

 face will be found in the " Theory of Screws." The equation of the surface 

 is z (x* + y 2 ) '2mxy = O. 



127. Models (6) illustrating the relative bases of Descriptive 

 Geometry and the Organic Geometry of Form. 



Prof. Franz Tilser, Prague. 



128. Drawings. A collection, executed by the Students of 

 the Bohemian Polytechnic Institute, illustrative of the instruction 

 received in the subject of Organic Geometry of Form. 



Prof. Franz Tilser, Prague. 



129. Two specimens of Stereometrical Wire Models, 



with letters on cork. 



Prof. J. Joseph Oppel, Frankfort-on- Maine. 



130. Two specimens of Trigonometrical Wire Models, 

 with letters. Prof. J. Joseph Oppcl, Frankfort-on- Maine. 



131. Two specimens of Stereometrical Models of 

 Wood 9 with letters. 



Prof. J. Joseph Oppel, Frankfort-on- Maine. 



The auxiliary lines, diagonals, &c. are distinguished by wires of different 

 colours or thicknesses. They are in many cases movable, so that the perfect 

 figure can be constructed before the eyes of the pupil. 



Auxiliary planes are also distinguished by their colour. The angular 

 points are provided with metal pins, to which letters on cork plates can be 

 attached, so as to be turned upright towards the observer. 



These models have proved highly serviceable for instruction during the 

 past 20 years. 



132. Large Model of an Ellipsoid, of white cardboard, 

 on a turned stand. Prof. Dr. A. Brill, Munich. 



133. Cardboard Models of Surfaces of the second 

 order, on frames. Made up of circular sections. The sections 

 are attached to each other. Prof. Dr. A. Brill, Munich. 



This collection of models consists of : 



1. An Ellipsoid having 20 circular sections ; 



2. An Ellipsoid having 30 circular sections ; 



3. A Hyperboloid of one sheet ; 



4. A Hyperboloid of two sheets ; 



5. An Elliptic Paraboloid ; 



6. A Cone in two sheets ; and 



7. A Hyperbolic Paraboloid. 



