Ill MODELS. 23 



This is (for a certain position of the lower semicircle) a skew surface with 

 a director plane, the plane being vertical. The director curves are: one of 

 them a circle divided equidistantly, the other a semicircle divided so as to 

 keep the strings parallel to the director plane. 



109. Intersection of Two Cones 'having double contact 

 with one another, that is to say, having a pair of tangent planes 

 in common. 



The consequence of their having double contact is that their curve of inter- 

 section breaks up into two plane ellipses. 



The vertices of the cones slide along a rule which turns on a universal 

 joint. See also model No. 38. 



110. Common Groin. Intersection of two cylinders having 

 a pair of common tangents. The model may be set square or 

 oblique. 



111. Intersection of Two Cylinders, one piercing the 

 other so as to give two separate loops of intersection. 



112. Intersection of Two Cylinders, having a common 

 tangent, so as to give a curve having a double point at the point 

 of contact. 



113. Intersection of Two Cylinders, neither completely 

 piercing the other, so as to give only one loop of intersection. 



114. Intersection of Two Cones, having double contact, 

 along a pair of plane ellipses. 



115. Groin. Oblique intersection of two splayed vaults of the 

 same spring. 



116. A Pair of Intersecting Planes, which, by pulling the 

 brass ball so as to give simultaneous rotation to the two upper 

 rods, deform into paraboloids first, and then into planes described 

 by radiating strings. 



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. A Pair of Intersecting Cylinders on circular bases. 

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

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



119. A Fair 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 



