III. MODELS. 29 



107. Skew Helixoid. 



This surface is described by a right line, which always passes through the 

 axis of a cylinder, and makes a constant angle with that axis. It also passes 

 through a helix or screw thread traced on the cylinder. The model only 

 shows the surface, not the cylinder. The section by a horizontal plane is the 

 spiral of Archimedes. It is the surface of what is known as the screw with 

 a triangular thread. 



This is not the commonest form of the skew helixoid ; that is best seen on 

 the underside of a screw staircase, or on the driving face of a common screw- 

 propeller. In these, two generating lines are at right angles to the axis. 



The surface may also be considered as generated by a line which makes a 

 constant angle with a given fixed line, and moves up that line, and at the 

 same time turns round it, at uniform rates. 



108. Skew Surface with its tangent paraboloid, capable of 

 transformation into another skew surface while the paraboloid 

 deforms into a plane. 



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

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

 them a circle divided equidistautly, 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. 114. 



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. 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. 



