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 sections. 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. Intersection of a plane and a surface, of two surfaces, of a straight line and a surface. Tangent planes, cones, and cylinders circumscribed about topographical surfaces. Use of a topographical surface to replace a table of double-entry when the function of two variables, which it represents, is continuous. It is often possible, by a suitable anamorphosis, to make an advantageous transformation in the curves of level. LESSON 38. _Revision._ Review of the different methods of geometrical drawing. Advantages and disadvantages of each. Comparison of the different kinds of surfaces, _résumé_ of their general properties. Object, method, and spirit of descriptive geometry. _SECOND YEAR._ STEREOTOMY.--WOOD-WORK. LESSONS 1-4. _Generalities._ Notions on the mode of action of forces in carpentry. Resistance of a piece of wood to a longitudinal effort and to a transversal effort. Distinction between resistance to flexure and resistance to rupture. Beams. Advantages of the triangular system, St. Andrew’s cross. LESSONS 5-8. _Roofs._ Ordinary composition of roofs. Distribution of pressures in the different parts of a girded roof. Design of the different parts of roofs, &c., &c. LESSONS 9-10. _Staircases._ MASONRY. LESSONS 11-12. _Generalities._ Notions on the settlement of vaulted roofs. Principal forms of vaults, _en berceau_, &c., &c. Distribution of the pressures, &c. Division of the intrados. Nature of the surfaces at the joints, &c., &c. LESSONS 13-15. _Berceaux and descentes._ LESSONS 16-22. _Skew Arches._ Study of the general problem of skew arches. First solution. Straight arches _en échelon_. Second solution: Orthogonal _appareil_. True and principal properties of the orthogonal trajectories of the parallel sections of an elliptical or circular cylinder. Right conoid, having for directrices the axis of the circular cylinder and an orthogonal trajectory. The intersection of this conoid by a cylinder about the same axis is an orthogonal trajectory for a series of parallel sections.