the crown of the arch, which is semi-circular, and cut through a wall 5 feet thick and 16 feet high, showing a length of wall of 5 feet on each side of the postern. Scale 30, or 3 feet to 1 inch.

8. Of a box 3 feet long, 2 feet wide, and 1.6 deep, made of inch board, with a circular hole 6 inches in diameter on each side and end. Scale

9. A table 3 feet wide, 44 feet long, 3 feet high, the top is 2 inches thick. The legs 2 inches square, are fixed at 2 inches from the outside of the table. A circular hole 14 foot in diameter, is in the centre of the top of the table.

10. A truncated cone, base 3 inches in diameter, height 4 inches, diameter of upper end 2 inches.

11. A piece of timber 4 feet long, 2 feet wide, and 3 inches thick, a hole in the shape of a frustrum of a cone is bored through its thickness, in the centre of its length and breadth. The upper diameter of the hole is 1 foot, the lower diameter 6 inches. Scale

12. A hexagonal right prism 9 feet long, each edge of the base measuring 2 feet, and having one of its faces resting on the ground. Scale.

13. A box 6 feet long, 4 feet wide, and 3 feet high, lid 6 inches thick, opened at an angle of 40°. The sides of the box 2 inches thick.

Scale

14. A one roomed cottage, of which half the roof has been removed. Exterior dimensions, length 16 feet, breadth 14 feet, height of walls 12 feet, of roof 5 feet, wall 1 foot thick. In the short side, a door 3 feet wide and 8 feet high, is ascended with 2 steps, each 1 foot broad and 4 feet long; in the long side are two semicircular windows, each 5 feet 6 high to the springing of the arch, and 3 ft. 6 inches wide, whose sills are at 2 feet 6 inches from the ground. Scale 4 ft. to 1 inch.

15. Of an octagonal prism of 1 inch side, 5 inches high, standing on one of its ends.

16. Of a hexagonal right prism of 1 inch side and 5 inches high, standing on one of its ends, and surmounted by a hexagonal pyramid 3 inches high, and whose edge coincides with the edges of the prism.

17. Of a flight of 3 steps, each 10 feet long, 1.6 wide, and 9 inches rise. Scale.

18. Of a small case of instruments with a lid open at an angle of 48°.

19. Of a double cross standing on a pedestal, choosing your own dimensions

20. Of a block of wood 4 inches long, 2.5 inches broad, and 2 inches high, having one of its upper corners cut off in such a manner that the section made shows an equilateral triangle of 1 inch side.

PERSPECTIVE.

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The term "Perspective" is derived from the Latin "Perspicere," to see through its object is to represent on a plane the exact form or representation of objects as they would appear were they seen through some assumed transparent medium placed between them and the spectator.

In the Diagram 1, Pl. LI, I have endeavoured to give some idea of the meaning of the terms used by artists, &c. to indicate the position and names of the several points, lines, planes, &c. used in perspective.

Let A represent the ground, or horizontal plane.

The ground, or horizontal plane, is the horizontal surface upon which the object and spectator are supposed to stand.

Let B represent the picture plane.

The picture plane, or perspective plane, is any supposed transparent medium interposing between the spectator and the object, the lower part of which, G L, meeting the ground plane, to which it is perpendicular, is termed the ground line. N.B.-These two planes are assumed to be of indefinite extent.

Let C represent the original object. An object is given at first in plan, which determines its position, length and breadth, according to actual dimensions, but not its height.

Let E represent the eye of the spectator, placed vertically at a given height above its position, on the ground plane S, termed the station.

The line E-PS, always perpendicular to the picture plane, is termed the line of sight, axis of vision, or line of direction; it proceeds from the eye of the spectator to the picture plane, at which extremity it is termed point of sight the point of sight, PS, or perspective centre, is therefore the further extremity of the line of sight.

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H H, the horizon, or horizontal line, is a line drawn on the picture plane, parallel to the ground line, and of indefinite extent, perpendicular to the line of sight.

Diagram 2 gives the actual plan of the object to be put in perspective. VSV, the angle of vision, or visual angle, is that space which the spectator can embrace with his eye without turning his head to the right or left. It forms a sector of 60°, so that the line of sight, L S, becomes in plan a perpendicular, bisecting an equilateral triangle, whose base lies on the horizon, and whose apex coincides with the eye of the spectator, S.

P D, points of distance, are points placed right and left of the point of sight, equal to its distance from the eye. LC, line of contact, is a line drawn in the prolongation of one of the sides of the object to the picture plane. Its

use is to determine in the elevation the height of the object and of its several parts. N.B.-When parallel lines or planes of different altitudes are receding from each other, it is often convenient to project several lines of contact.

V R, visual rays, form a pyramid, or cone of rays proceeding from every visible point or angle of the plan, and converging towards the eye of the spectator till it crosses the picture plane, on which it forms. P, the picture, or representation of the object as seen in Diagram 3, which represents the elevation of the picture plane, whose base, or ground line, G L, is supposed to be removed from its original position, H H, Diagram 2, and reduced to the horizon. The vertical projectors of the two diagrams coinciding with each other.

Vanishing lines, V L, are lines proceeding from the eye of the spectator to the horizon, parallel to the sides of the object. Their extremities, or points, where they meet the horizontal, are termed vanishing points. V P.

N.B.-All lines, or planes which are parallel to each other in the plan, tend or converge towards the same vanishing point in the elevation.

We have already observed that the axis of vision is always represented by a line perpendicular to the picture plane, and proceeding from the eye of the spectator. It follows, therefore, that not only its length is equal to the distance of the eye to the picture plane, but that likewise its height above the station determines that of the horizon above the ground line, to which it is parallel in the picture plane.

It is perhaps unnecessary to observe that the height of the horizon varies in every case with that of the eye of the spectator. Whatever may be the position of the latter, whether he is lying on the ground, or standing up; whether he is placed on the top of a ladder, a tower, or a mountain,

the apparent height of the horizon always equals that of the eye above the ground line.

When the sides of an object form any angle with the picture plane we use the method of "Oblique Perspective." When the sides of an object are perpendicular or parallel to the picture plane, we employ that of "Parallel Perspective."

The method of putting an object in parallel perspective is simple. We have already said that vanishing lines are lines drawn from the eye of the spectator to the horizon parallel to the sides of the object. It is evident that this applies only to oblique perspective, for were we to attempt by this method to put in perspective a line parallel to the picture plane, we would find it impossible. We must, therefore, adopt some other means. The most convenient is to suppose the object to be enclosed in a square, each of whose diagonals forming an angle of 45° with the picture plane, and whose sides being perpendicular to the same, will converge towards the point of sight, which in this method becomes the sole vanishing point.

The following diagrams will, I trust, prove sufficiently explicit.

Required the perspective of a square in three positions, A, B and C.

In the first position A, the point of sight, P S, is opposite the square, and contiguous to the ground line, G L.

In the second position B, the square is still contiguous to GL, but to the left of P S.

In the third position C, the square is at a given distance from G L, and to the right of P. S. (Fig. 3.)