The eye of the observer is 4.5 inches from the picture plane, opposite the point of the triangle which rests on the horizontal plane, and 2.5 inches above the horizontal plane. (Fig. 36.)

26. A right pyramid has an equilateral triangle of 2.2 inches side for its base, and is 3.8 inches high; it is laid on one of its faces: show its projection (1). Show likewise the plan and elevation of the same pyramid lying on one of its faces, with one side of its base forming an angle of-70° with the vertical plane (2). Draw the perspective of the same pyramid; horizon 2 inches, distance from the station to the nearest point of the object which coincides with the picture plane, 6 inches (3). Scale. (Fig. 36, 2.) 27. An octohedron formed by two square pyramids joined at their bases, each pyramid is 3 inches high and 1 inch edge, and is laid on one of its faces: its axis forms an angle of 30° with the picture plane; station to object 12 inches, to picture plane 9 inches, horizon 4 inches. (Fig. 37.)

28. One of the diagonals of a cube of 2 inches edge passes through the eye and is perpendicular to the picture plane: draw its perspective, other conditions optional. (Fig. 38.)

It is hoped that after having solved the preceding problems, the pupil will no longer require either explanation or demonstration, but will be enabled to solve any further questions.

When not otherwise given, the conditions are optional. Required the perspective of a cube which has one of its faces horizontal, and the diameter of that face perpendicular to the picture plane: assume two positions of the eye, one above and the other below the upper surface of the cube.

The perspective of a regular tetrahedron 3 inch edge, having one of its faces parallel to the picture plane.

A block of stone 6 feet long, 4 feet wide, and 3 feet thick is placed on one end, and another of the same size is laid flat on the top of it: draw its perspective; station to object 9 feet, to picture plane 6 feet, horizon 6 feet, angle 40°. Scale.

A table 4 feet long, 2.5 feet wide, and 2.5 feet high; the top is 2 inches thick, the legs 2 inches square and fixed at 1.5 inch from the outside of the table; a circular hole 1.5 foot in diameter is in the centre of the top of the table; the eye is 6.5 feet above the horizontal plane and 6 feet from the picture plane, which is 1 foot distant from the nearest part of the table, and at an angle of 40° with its longest side. Scale.

The perspective of a cross, of which the upright is 5 feet high, cross piece 3 feet long and 1 foot below the top, each piece being eight inches square; the eye of the observer is 10 feet distant, 3 feet above the top, and in a direction making an angle of 45° with the front of the Scale

cross.

A box 6 feet long, 4 feet wide, 4 feet high, lid 1 foot thick opened at an angle of 45°; horizon 5 feet, object to picture 6 feet, to station 10 feet; its longest side forms an angle of 30° with the picture plane: show details, thickness, &c.

A regular parallelopipedon stands on a horizontal plane with its longest side inclined to the picture plane at an angle of 20°.

Length of the solid 12 feet, breadth 10 feet, height 7 feet, height of eye 12 feet; line of sight directed to a point 2.5 feet to the right of the prolongation of the nearest perpendicular edge, station to object 20 feet. Scale.

The perspective of a block of masonry is required.

It is 20 feet high, with a frontage of 17 feet and depth of 13 feet, and is perforated longitudinally and transversely by semicircular arches springing at the same height, viz., 10.5, and intersecting each other, the piers are 4.25 square; angle 20° with picture plane; line of sight 5 feet to the right of the nearest angle, horizon 6 feet, station to object 25 feet, to picture plane 20 feet.

The perspective of a rectangular block of masonry 24 feet long, 20 feet high, and 16 feet broad, pierced by an arch springing at a height of 10 feet, and of a semicircular form, with a span of 12 feet; the station is opposite a point on one side of its centre. Scale

The perspective of a right pyramid 3 inches high on a square base of 1.5 inch, one of whose sides forms an angle of 20 degrees with the picture plane, and whose nearest angle is 1 inch beyond it; the eye is directed to a point to the left of the pyramid: other conditions optional.

A rectangular prism 2 inches high, having for its base a triangle whose sides equal 2, 2.5 and 1.7 respectively, one of whose sides forms an angle of 30° with the picture plane, the nearest angle at 1 inch from it; the observer's eye is 6 inches from the picture plane, opposite the nearest angle of the base and 2 inches above the horizontal plane on which it stands.

One of the diagonals of a cube of 2 inches edge passes through the eye, and is perpendicular to the picture plane : draw its perspective.

The sides of a triangle equal 2.5, 2.5 and 2.75 inches respectively, the longest side is to stand vertical at a distance of .25 inch from the picture plane, the eye of the observer is to be 1.75 inch above the horizontal plane, the point of sight directed at about 3 inches on either side of the triangle, whose plane is to have an inclination of 30° to the picture plane: other conditions optional.

A cottage, of which half the roof has been removed, consists of one room, the external dimensions of which are, length 15 feet, breadth 12 feet, height 10 feet 5 inches; in one of the longest sides, which forms an angle of 30° with the picture plane, are two windows with semicircular heads, each 5.5 feet high to the springing of the arches, and 3.5 feet wide; 2.5 inches from the ground: in one of the shortest sides is a doorway 3 feet wide and 7.5 feet high, reached by two steps each 3 feet long, 1 foot wide, and 6 inches thick; ridge of roof 18 feet above the ground; the walls are 1 foot thick; the walls containing the windows and door are to be the nearest to the picture plane, which is 6 feet distant from it: station to object 20 feet, horizon 5 feet. Scale 1.

The perspective of an equilateral triangular board, 3 inches side, one side resting on a horizontal plane and forming an angle of 40° with the picture plane, which it does not touch. The face of the board is inclined to the horizon at an angle of 55°; height of observer's eye 1.5 inch, point of sight 1 inch to the left of the object.

The perspective of an isosceles triangle whose base equals 2.9 inches and sides 2.1 inches. The triangle stands on a horizontal plane with one of its angular points in the picture plane; its longest side is inclined to the horizon at an angle of 20°, its plane inclined to the hori zontal plane at an angle of 50°, and the trace of its plane inclined to the picture plane at an angle of 20°.

The eye of the observer is 4.5 inches from the picture. plane, opposite the point of the triangle which rests on the horizontal plane, and 2.7 inches above the horizontal plane.

THE END.

G. NORMAN, PRINTER, MAIDEN LANE, COVENT GARDEN.