Draw the vertical line which is the short axis of both ellipses. Bisect the short axis of the outer ellipse, and draw the long axis of this ellipse. Bisect the short axis of the inner ellipse, and draw its long axis. It will be seen that the long axes are parallel but do not coincide, and that both are in front of the point which rep resents the center of the circles.
Each diameter of the larger circle is divided into four equal parts. The four equal &paces on the diameter which forms the short axis appear unequal, according to Rule 9. The. diameter which is parallel to the long axes of the ellipses. has four equal spaces upon it. and they appear equal. This diameter is behind the long axes, but generally a very short distance; and in practice. if the distance 1 2 between the ellipses measured on the long axis is one-fourth of the entire long axis, then the distance between the ellipses measured on the short axis must be a perspective fourth of the entire short axis. This illustrates the following rule: Rule 23. Foreshortened concentric circles appear ellipses whose short axes coincide. The distance between the ellipses on the short axis is perspectively the same proportion of the entire short axis, as the distance between the ellipses measured on the long axis, is aeornetrically the same proportion of the entire long axis.
Exercise 13. Frames. In the frames are found regular con centric polygons with parallel sides, the angles of the inner poly gons being in straight lines connecting the angles of the outer polygon with its center. In polygons having an even number of sides, the lines containing the angles of the polygons form diagon als of the figure, as in the square.
In polygons having an odd number of sides, the lines con taining the angles of the polygon are perpendicular to the sides opposite the angles, as in the triangle.
Draw upon large triangular and square tablets the lines shown in Fig. 22. Place the tablets horizontally On the table, or support them vertically, and trace upon the slate the appearance of the edges and all the lines drawn upon them. The tracings illustrate the following rule: Rule 24. In representing the regular frames, the angles of the inner figure must be in straight lines passing from the angles of the outer figure to the center. These lines are alti tud-es or diagonals of the polygons.
20. After making the tracings described in the foregoing exercises, draw (not trace) freehand on the slate the various tab lets, arranged to illustrate each one of the exercises. This is really drawing from objects, and where the rods are used to connect the tablets the figures are equivalent to geometric solids. After the proportions of the surfaces are correctly indicated, lines connect ing the corresponding corners of the tablets should be drawn to complete the representation of solid figures. The lines indicating the rods and those lines which in a solid form would naturally be invisible, may be erased. By the use of the three rods of different lengths, three figures of similar character but different proportions may be obtained. These should each be drawn, but each in a dif ferent position.
The following directions, which are based on general prin ciples, apply to all drawing whether from objects or from the flat, for worli in pencil or in any other medium; drawing from another drawing, a photograph or a print, whether at the same size or larger, is called working from the flat.
21. General Directions for Drawing Objects. First observe carefully the whole mass of the object, its general proportions and the direction of lines as well as the width of the angles. Then sketch the outlines rapidly with very light lines, and take care that all corrections are made, not by erasing but by lightly drawing new lines as in Fig. 23. By working in this manner much time is saved and the drawing gains in freedom. Where the drawing is kept down to only one line which is corrected by erasure, the line becomes hard and wiry, and there is a tendency to be satisfied with something inaccurate rather than erase a line which has taken much time to produce. There is always a difficulty at first in draw ing lines light enough, and it is well for the beginner to make the first trial lines with a rather hard pencil. Practice until the habit of sketching lines lightly is fixed. The ideal is to be aide to set down exact proportions at the first touch. This, however, is attained by com paratively few artists, and only after long study, but the student will soon find himself able to ob tain correct proportions with only a few corrections.