30 SEC. 2. GEOMETRY. 



117. Intersecting Cylinder and Plane. By pulling the 

 brass ball the head brasses rotate together, and the cylinder de- 

 forms into, first, a hyperboloid, and then a cone, while the plane 

 deforms into, first, a paraboloid, and then again into a plane with 

 radiating lines. 



118. Fair of Intersecting Cylinders on circular bases. 

 By Dulling the brass ball the head brasses rotate together, and 

 the cylinders deform, first, into hyperboloids, and then into cones. 



119. Pair of Intersecting Cylinders on irregular bases. 

 By pulling the brass ball the head brasses rotate together, and 

 the cylinders deform, becoming at last cones. 



120. Groin. 



Model showing the deformation of a common groin, both ob- 

 liquely, and by splaying the vaults. The model shows not only the 

 intersection, but the plans of the intersection and of the generating 

 lines. 



121. Helix or Screw-thread. 



Model showing the transformation of the right line genera- 

 tors of a right cylinder into screw threads of various pitch or 

 obliquity. 



The pitch of a screw is the distance between two successive 

 turns, measured in a direction parallel to the axis. When this 

 distance is small, the screw is said to have a fine pitch ; when 

 great, a coarse or high pitch. 



COLLECTION OF MODELS CONTRIBUTED BY THE LONDON 

 MATHEMATICAL SOCIETY. 



123. Pliicker's Models (14) of certain quartic surfaces, 

 representing the equatorial form of complex surfaces. 



London Mathematical Society. 



At the meeting of the British Association at Nottingham, in 1866, Prof. 

 Pliicker read a paper on " Complexes of the Second Order." On this occasion 

 he showed a series of models constructed by Epkens, of Bonn, of which the 

 above are copies made for Dr. Hirst, and presented to the London Mathe- 

 matical Society. 



The following is Prof. Cayley's description of the models, extracted from 

 Nos. 37 and 38 of the Mathematical Society's Proceedings, vol. iii., pp. 281- 

 285, supplemented by a description of models A, B, C, D, E, F, drawn up 

 by Prof. Henrici. 



The Society possesses a series of 14 wooden models of surfaces, constructed 

 under the direction of the late Prof. Pliicker, in illustration of the theory 

 developed in his posthumous work " Neue Geometric des Raumes gegrvindet 

 " auf die Betrachtung der geraden Linie als Kaum-elemente," Leipzig, 1869. 



