III. MODELS. 31 



152. Maximum of Attraction of the Earth's Surface. 



Ludwig Lohde, Berlin. 



153. A Geometric Body, executed in plaster of Paris, called 

 "Fodoid;" a transcendental curved surface, which is deter- 

 mined by the variable parallel co-ordinates p, <, and *, whose 

 equation represents the elliptic function 



The construction in plaster of Paris embraces the limits 

 *== + 1 to K= 1 and p=0 to $=*. 



154. The same Podoid, executed on a smaller scale, embracing 

 the limits K= -f 1 to *= 1, <p =0 to <p =2w. 



Prof. Dr. Edward Heis, Munster, Westphalia. 



155. Right 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. Ruled Surface of the fourth degree. 



Prof. Borchardt) Berlin. 



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

 equation 



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

 of the surface as shown on the model, whilst beyond each pair of right lines 

 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 z=0, and the two ellipses corresponding to z = + a ' 

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



158. Rectangular Parallelepiped, intersected by a skew 

 surface. Prof. Borchardt, Berlin. 



159. Right Circular Cylinder, with spiral surface inter- 

 secting it. Prof' Borchardt, Berlin. 



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

 known from the drawings, which he has furnished to Prof. Sckellbach's 

 ' Darstellende Optik." 



