Surface of the thread of the square screw; generation, s by planes and conical cylinders; tangent planes; curve of contact of a circumscribed cone.
The curve of contact of a circumscribed cylinder is a helix whose step is half that of the surface. Determination of the osculating paraboloid. At any point whatever of the surface, the absolute lengths of the radii of curvature are equal.
Representation and shading of the screw with a square thread, and of its nut.
Observations on the general ruled helicoidal surface, and on the surface of intrados of the winding staircase.
Lesson 35. Different Helicoidal Surfaces.
Saint-Giles screw, worm-shaped screw and helicoidal surfaces to any generatrix. Every tangent to the meridian generatrix describes a screw surface with triangular thread, which is circumscribed about the surface, along a helix, and may be used to resolve the problems of tangent planes, circumscribed cylinders, &c.
Helicoid of the open screw, its generation, tangent planes.
Lessons 36–37. Topographical Surfaces.
Approximate representation of a surface by the figured horizontal projections of a series of equidistant horizontal s. This method of representation is especially adapted to topographical surfaces, that is to say, surfaces which a vertical line can only meet in one point.
Lines of greatest slope. Trace of a line of equal slope between two given points.