A developable surface is the envelop of the position of a movable plane; it is composed of two sheets which meet. It may be considered as generated by a straight line, which moves so as to remain always a tangent to a fixed curve. Theory of shade and shadow, of the penumbra, of the brilliant point, of curves of equal intensity, of bright and dark edges. Atmospheric light: direction of the principal atmospheric ray. Notions on the degradation of tints; construction of curves of equal tint. Influence of light reflected by neighboring bodies. Received convention in geometrical drawing on the direction of the luminous ray, &c. Perspective of shadows. LESSONS 14-15. _Construction of Lines of Shadows and of Perspective of Surfaces._ Use of circumscribed cones and cylinders, and of the normal parallel to a given straight line. General method of construction of lines of shadow and of perspective of surfaces by plane sections and auxiliary cylindrical or conical surfaces. Construction of lines of shadow and perspective of a surface of revolution. The curve of contact of a cone circumscribed about a surface of the second degree is a plane curve. Its plane is parallel to the diametral plane, conjugate to the diameter passing through the summit of the cone. The curve of contact of a cylinder circumscribed about a surface of the second degree is a plane curve, and situated in the diametral plane conjugate to the diameter parallel to the axis of the cylinder. The plane parallel sections of a surface of the second degree are similar curves. The locus of their centers is the diameter conjugate to that one of the secant planes which passes through the center of the surface. General study of surfaces with reference to the geometrical constructions to which their use gives rise. LESSON 16. _Complementary Notions on Developable Surfaces._ Development of a developable surface; construction of transformed curves and their tangents. Developable surface; an envelop of the osculating planes of a curve. The osculating plane of a curve at a given point may be constructed by considering it as the edge of regression of a developable surface; this construction presents some uncertainty in practice. Notions on the helix and the developable helicoid. Approximate development of a segment of an undevelopable surface. LESSONS 17-18. _Hyperbolic Paraboloid._ Double mode of generation of the paraboloid by straight lines; plane-directers; tangent planes, vertex, axis, principal planes; representation of this surface. Construction of the tangent plane parallel to a given plane. Construction of plane sections and of curves of contact, of cones, and circumscribed cylinders. Scalene paraboloid. Isosceles paraboloid. Identity of the paraboloid with one of the five surfaces of the second degree studied in analytical geometry.