Through a given point, to pass a perpendicular to a given plane, and to construct the projections of the point of meeting of the right line and of the plane. Through a given point, to pass a right line perpendicular to a given right line, and to construct the projections of the point of meeting of the two right lines. A plane being given, to find the angles which it forms with the planes of projection. Two planes being given, to construct the angle which they form between them. Two right lines which cut each other being given, to construct the angle which they form between them. To construct the angle formed by a right line and by a plane given in position in space. _Problems relating to tangent planes._ To draw a plane tangent to a cylindrical surface or to a conical surface, 1º through a point taken on the surface; 2º through a point taken out of the surface; 3º parallel to a given right line. Through a point taken on a surface of revolution, whose meridian is known, to pass a plane tangent to that surface. _Problems relating to the intersection of surfaces._ To construct the section made, on the surface of a right and vertical cylinder, by a plane perpendicular to one of the planes of projection.--To draw the tangent to the curve of intersection.--To make the development of the cylindrical surface, and to refer to it the curve of intersection, and also the tangent. To construct the intersection of a right cone by a plane perpendicular to one of the planes of projection. Development and tangent. To construct the right section of an oblique cylinder.--To draw the tangent to the curve of intersection. To make the development of the cylindrical surface, and to refer to it the curve which served as its base, and also its tangents. To construct the intersection of a surface of revolution by a plane, and the tangents to the curve of intersection.--To resolve this question, when the generating line is a right line which does not meet the axis. To construct the intersection of two cylindrical surfaces, and the tangents to that curve. To construct the intersection of two oblique cones, and the tangents to that curve. To construct the intersection of two surfaces of revolution whose axes meet. VII. OTHER REQUIREMENTS. The preceding six heads complete the outline of the elementary course of mathematical instruction which it was the object of this article to present; but a few more lines may well be given to a mere enumeration of the other requirements for admission to the school. MECHANICS comes next. The programme is arranged under these heads: Simple motion and compound motion; Inertia; Forces applied to a free material point; Work of forces applied to a movable point; Forces applied to a solid body; Machines.