38 SEC. 2. GEOMETRY. 



The construction in plaster of Paris embraces the limits 

 K= -f 1 to K= 1 and <p0 to <=7r. 



Prof. Dr. Edward Heis, Munster, Westphalia. 



154. The same Fodoid 9 executed on a smaller scale, embracing 

 the limits K= + ! to K= l, 0>=0 to <p=2v. 



Prof. Dr. Edward ffeis, Miinster, Westphalia. 



155. Hight double circular Cone, of white wood. 



Prof. Borchardt, Berlin. 



On the one sheet of the double cone 'are shown, by sections, the circle, 

 the ellipse, and the hyperbola ; on the other, the circle, the parabola, and 

 the corresponding hyperbola. The model takes to pieces at the sections. 



156. Elliptic Cone, of white and brown wood. 



Prof. Borchardt, Berlin. 



On the oblique cone are shown the two circular sections, and the elliptic, 

 hyperbolic, and parabolic sections. At the sections of the ellipse and parabola 

 the model takes to pieces ; the other sections are shown by the lines defined 

 by the dark and light wood. 



157. Huled Surface of the fourth degree. 



Prof. Borcha.rdt, Berlin. 



This model represents a surface of the fourth order determined by the 

 equation 



3* 2 8g =1 



(2-0)2 ( + o) 2 



The surface has two double right lines, between which lies a finite sheet 

 of the surface as shown on the model, whilst beyond each double right line 

 there extends a. second and third infinite sheet of the surface. Every hori- 

 zontal section of the surface is an ellipse. Of these are shown the circular 



section corresponding to zQ, and the two ellipses corresponding to z = a 

 The model can be taken to pieces at each of these sections. 



158. Bectangular Parallelepiped, intersected by a skew 

 surface. Prof. Borchardf, Berlin. 



159. Bight Circular Cylinder, with spiral surface inter- 

 secting it. Prof Borchardf, Berlin. 



These five models, Nos. 155-159, were executed by the late Ferd. Engel, 

 known from the drawings, which he has furnished to Pro/. Schellbach's 

 " Darstellende Optik." 



160. String Model, representing a hyperboloid of one sheet. 

 On it are shown the principal ellipse, the asymptotic cone, and a 

 tangential surface, in threads of different colours. 



Dr. Wiccke, Casscl. 



This model represents by means of strings (kept tight by springs) of 

 different colours the hyperboloid of one sheet and its principal auxiliary- 

 surfaces. The two sides of the surface are shown by the green and red strings 

 respectively ; the principal ellipse is given by the points at which the strings 

 pass through the network stretched on the frame ; the asymptotic cone is 

 shown by yellow, and a tangent plane by white strings. 



