It is easy to see from the drawing of the foreshortened square in Fig. 4, that of the two equal and parallel lines a b and c d the nearer appears the longer, although neither of the lines are foreshortened as the respective ends of each are equally distant from the eye. This illustrates the following rule :

Rule 2. Of two equal and parallel lines, the nearer appears the longer.

Exercise 2. The Horizontal Circle. Hold the circular tablet horizontally and at the level of the eye. Observe that it appears a straight line.

Place the tablet horizontally on a pile of books about half way between the level of the eye and the level of the table. Trace the appearance upon the slate.

Place the tablet on the table and trace its appearance.

Fig. 6. Horizontal Circles.

Fig. 6. Horizontal Circles.

While making both tracings the distance between the eye and the object, and the eye and the slate should be the same.

Hold the tablet at different heights above the level of the eye and observe that the ellipse widens as the height above the eye increases. These exercises illustrate the following; rules:

Rule 3. A horizontal circle appears a horizontal straight line when it is at a level of the eye. When below or above this level the horizontal circle always appears an ellipse whose long axis is a horizontal line.

Rule 4. As the distance above or below the level of the eye increases the ellipse appears to widen. The short axis of any ellipse which represents a horizontal circle changes its length as the circle is raised or lowered. The long axis is always repre-sented by practically the same length at whatever level the circle is seen.

Place the tablet on the table almost directly below the eye and trace its appearance.

Move it back to the farther edge of the table and trace it. It will be seen that where the level of the circle remains the same, its apparent width changes with the distance from the eye to the circle.

Exercise 3. Parallel Lines. Place the square tablet on the table 1 1/2 feet from the front, so that its nearest edge appears horizontal; that is, so that it is at right angles to the direction in which it is seen. By tracing the appearance the following rules are illustrated:

Rule 5. Parallel retreating edges appear to vanish, that is, to converge toward a point.

Rule 6. Parallel edges which are parallel to the slate, that is, at right angles to the direction at which they are seen, do not appear to converge. and any parallel edges whose ends are equally distant from the eye appear actually paralleI.

Exercise 4. The Square. Place the square tablet as in Exercise 3, and it will be seen that two of the edges are not foreshortened but are represented by parallel horizontal lines. The others vanish at a point over the tablet on a level with the eye.

Now place the tablet so that its edges are not parallel to those of the desk and trace its appearance on the slate. None of its edges appear horizontal, and when the lines of the tracing are continued as far as the slate will allow, the fact that they all converge will be readily seen; the drawing illustrates the following rule :

Parallel Lines.

Parallel Lines.

Rule 7. When one line of a right angle vanishes toward the right, the other line vanishes toward the left.

The drawing also shows that the edges appear of unequal length and make unequal angles with a horizontal line and illustrates the following rule :

Rule 8. When two sides of a square retreat at unequal angles, the one which is more nearly parallel to the picture plane (the slate) appears the longer and more nearly horizontal.

Exercise 5. The Appearance of Equal Spaces on Any Line. Cut from paper a square of three inches and draw its diagonals.

Place this square horizontally in the middle of the back of the table, with its edges parallel to those of the table, and then trace its appearance and its diagonals upon the slate. (Fig. 8.) Note.-The diagonals of a square bisect each other and give the center of the square.

Compare the distance from the nearer end, 1, of either diagonal to the center of the square, 2, with that from the center of the square to the farther end of the diagonal, 3, for an illustration of the following rule:

Rule 9. Equal distances on any retreating line appear unequal, the nearer of any two appearing the longer.

Exercise 6. The Triangle. Draw upon an equilateral triangular tablet a line from an angle to the center of the opposite side. (This line is called an altitude.)

Connect the triangular tablet with the square tablet, and place them on the table so that the base of the triangle is foreshortened, and its altitude is vertical. Trace the triangle and its altitude upon the slate. The tracing illustrates the fact that the nearer half of a receding line appears longer than the farther half (see Rule 9), and also the following rule:

Rule 10. The upper angle of a vertical isosceles or equilateral triangle, whose base is horizontal, appears in a vertical line erected at the perspective center of the base.

Fig. 8. Equal Space on any Line.

Fig. 8. Equal Space on any Line.

Fig. 9. The Triangle.

Fig. 9. The Triangle.

Exercise 7. The Prism. Connect two square tablets by a rod to represent a cube, and hold the object so that one tablet only is visible, and discover that it must appear its real shape, A, Fig. 10. This illustrates the following rule:

Rule 11. When one face only of a prism is visible, it appears its real shape.

Place the cube represented by tablets (Fig. 10) in the middle of the back of the desk, and trace its appearance. First, when two faces only of the solid would be visible (B); and, second, when three faces would be seen (C). These tracings illustrate the following rule: