Try similar experiments with the triangle, the pentagon, and the hexagon and observe that these exercises all show that lines and surfaces under certain conditions appear less than their true dimensions, and that this diminution takes place as soon as the surfaces are turned away from the glass slate.
When the square rests against the slate, with the centers of the square and slate coinciding, and the slate held so that half is above and half below the horizon line, all four corners of the square will be at equal distances from the eye so that a line from the eye to the center of, the slate and of the square is at right angles to the surface of the slate, the latter represents in these experiments what in scientific perspective is called the picture plane. Thus a sur face or plane appears its true relative dimensiOns only when it is at right angles to the direction in which it is seen.
It is for this reason that it is always necessary to arrange the surface on which a is made, at right angles to the eye, otherwise the surface and drawing upon it become foreshortened; that is, they appear less than their true dimensions.
It is easy to see from the drawing of the foreshortened square in Fig. 4, that of the two equal and parallel lines a L and c d the nearer appears the longer, although neither of the lines are fore shortened 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 appear ance upon the slate.
Place the tablet on the table and trace its appearance.
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 cilWczys appears an ellipse whose long occis 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 V 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 i feet from the front, so that its nearest edge appears hori zontal; that is, so that it is at right angles to the direction in which jt is seen. By tracing the appearance the following rules are illus trated: 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 parallel.
Exercise 4. The Square. Place the square tablet as in Exercise 3, and it will be seen that two of the edges are not fore shortened 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 con tinued as far as the slate will allow, the fact that they all converge will be readily seen; the drawing illustrates the following rule : Rule 7. Whed one line of a right angle vanishes toward the right, the otheV line vanishes toward the left.