THE great differences which exist between the drawings from nature made by' artists in a free-hand way, and those obtained by following the rules of scientific perspective cause the perplexing questions which are discussed in Chap. VII. These questions must be considered by the teacher, for even the youngest pupils who discover that parallel retreating lines appear to vanish will wish to know why vertical lines do not appear to vanish, and if so why they are not so represented. In the same way other points will be brought before the teacher, and all teachers should thus understand the subject, at least so as to be able to apply the few rules given in Chap. VII.
Teachers should not, however, discuss the different theories of Chap. VII with young pupils, and all through the grammar school these questions should, as far as possible, be avoided. It will not be difficult to do this, for when- pupils draw from single objects or groups causing small visual angles, the principal difference between what the eye sees and the drawing that the artist makes, is that the artist does not represent the convergence of vertical lines.
Teachers will obtain the best results by beginning the study of free-hand drawing by the use of the slate, which in a short time will make pupils practically familiar with the perspective principles which are valuable to the artist. When pupils have used the slate some time, they may be led to discover and state the principles which govern the appearance of the type forms, and when they can draw correctly, applying the rules to test drawings of single objects and groups causing small visual angles, they may begin to draw interiors and subjects causing large visual angles. But even in this work it is only necessary that drawings be made in accord with the few rules given, and teachers should not expect pupils to generally consider theories upon which experienced instructors and artists are often in doubt ; the rules of Chap. VII are all that the pupil requires.
No one ever drew from nature correctly simply from study of theory, and time spent upon theory, whether the free-hand or the scientific, is wasted if some practical ability to draw from nature is not possessed. Pupils who cannot draw approximately correct representations of single simple objects should spend their time in drawing rather than in study of theory ; but those who begin drawing by the use of the slate may quickly understand the most important rules of this chapter, for the slate enables pupils to understand what would otherwise require many months of serious study. Generally the best results will be obtained by giving theory lessons to pupils who have used the slate and can draw fairly well, but teachers may use their judgment upon this point.
Chap. VII shows that the artist makes scientific perspective drawings only when obliged to do so, as such drawings are generally very different from the appearances which objects present to the eye ; and teachers must decide that young pupils should not study scientific perspective, nor any pupils who wish to draw free-hand, until they are able to draw from simple objects correctly and understand model drawing.
Scientific perspective has caused much harm to art, for false representations of prism forms are generally accepted as correct, and the art student who discovers that the subject gives drawings very different from what he sees often wholly neglects perspective, to the great detriment of his work.
Scientific perspective is absolutely necessary to the artist, who often finds that it gives the most satisfactory representation of a geometric subject. It is also valuable to the architect and the illustrator, and the teacher should understand its principles. But whenever it is taught, the fact that its drawings differ from what the eye sees, and are distortions unless seen from the station-point, should be carefully explained.
For most of an artist's work knowledge of model drawing is not only all that he requires, but better than knowledge of scientific perspective. The principles of model drawing are few and simple, and even the young pupil, if he will follow the directions given, will find the free-hand perspective interesting and easy to understand ; for there are no planes, lines, and points to be imagined, and no difficult processes to be understood and carried out. There is no confusion resulting from many technical names and operations. The subject may be presented so that it can be readily understood, and should be studied, as it will be of value to all.
The following lessons are to be given in the public schools as indicated in the "Outline of Lessons for Grammar Grades." They are not to be given to pupils who are unable to draw the forms by eye alone with some degree of correctness.
Lesson I. -- Foreshortened Planes and Lines.
Cut from paper a circle and a square 4" in diameter, having projecting pieces as at A and B. Place the circle upon the back of the slate and trace its real shape. Then swing the circle back and trace its foreshortened appearance.
Draw the real shape and the foreshortened appearance of the square in the same way, holding the slate vertical, and so that half the square is above and half below the level of the eye.
The cards are to be held against the slate by means of the projecting pieces, and they should be revolved so that they are seen edgewise and at different angles.
A square card may be cut so as to revolve from an angle instead of a side.
Similar experiments may be made with other figures, and the entire lesson devoted to observation of the facts which illustrate the following rule :
Any plane or line which is not at right angles to a line from its centre to the eye, is foreshortened, and does not appear its true dimensions.
NOTE 1.--A surface is at right angles to the direction in which it is seen when its opposite corners are equally distant from the eye. A line is at right angles to the direction in which it is seen when its ends are equally distant from the eye.
NOTE 2. -- If any pupils are unable to trace the appearance of the square while holding the slate on the level of the eye, they may observe the appearance, and then place the slate in the usual position and draw from memory. This drawing may then be tested by placing the square at the back of the slate, and holding both in their original positions.
Lesson II. -- Parallel and Equal Lines not Foreshortened, and Vertical Lines.
Draw the square B upon the slate, as explained in Lesson I. Its vertical edges appear unequal, and illustrate Rule 2.
Rule 2. The nearer of two parallel and equal lines which are not foreshortened appears the longer.
Place the drawing in the book to illustrate the rule. Drawings may be traced from the slate to thin paper, and then transferred to the book by tracing or any other means.
Unless directions to the contrary are given, all tracings made during these lessons are to be transferred to the drawing-book to illustrate the rules printed therein.
Trace the vertical lines of a cube or prism placed on the desk and near the eye, to illustrate the following rule. (This tracing may be omitted in the book.)
Rule 3. Vertical lines appear to converge when they are above or below the level of the eye, but their convergence is not represented, and vertical edges are always represented by vertical lines.
Lesson III. -- The Horizontal Circle.
Hold the circular tablet horizontally and at the level of the eye. Then draw its appearance upon the slate.
Place the tablet horizontally upon a block or upon
books at the back of the desk, and trace its appearance upon the slate. The slate should rest upon the desk and be held at the proper angle by the left hand.
Place the tablet upon the desk, and trace its appearance.
The distance between the eye and the object and between the eye and the slate should be the same for both tracings.
The tracings illustrate the following rules :
Rule 4. The horizontal circle appears a horizontal straight line when it is at the 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 5. The farther above or below the level of the eye a horizontal circle is placed, the wider it appears. The short axis of the ellipse representing a horizontal circle changes its length as the circle is raised or lowered. The long axis is always represented of the same length, whatever the level of the circle.
NOTE.-- The level of the circle remaining the same, its apparent width changes with the distance of the eye from the circle.
Lesson IV. -- Parallel Lines.
Place a 2 1/2" square tablet at the middle of the back of the desk so that its edges are parallel to those of the desk, and trace its appearance upon the slate. Transfer the tracing from the slate to the book, by the use of tracing paper or any other means, to illustrate the following rules, which may be verified by repeated experiments with any sets of parallel edges:
Rule 6. Parallel retreating edges appear to vanish, that is, converge toward a point.
NOTE. -- Retreating edges are those which have one end nearer the eye than the other. Upon solids the farther end of any edge is a point of an invisible surface of the object.
Rule 7. Parallel edges which are parallel to the slate, that is, at right angles to the direction in which they are seen, do not appear to converge, and any parallel edges whose ends are at equal distances from the eye appear actually parallel.
Lesson V. -- Parallel Retreating Horizontal Lines.
Place a large book horizontally at the middle of the back of the desk, with its edges parallel to those of the desk and its bound edge towards the pupil. Place a string under the upper cover of the book, and close against the binding. Hold the left end of the string in the right hand, so that it appears to cover the left retreating edge of the book. At the same time, hold the right end of the string with the left hand, so that it appears to cover the right edge of the book. When both edges are covered, look at the point where the two parts of the string cross, and see that it is on the level of the eye. This illustrates the rule:
Rule 8. Parallel retreating horizontal edges appear to vanish at the level of the eye.
Trace upon the slate the lines of two walls as seen when looking
into a corner of the schoolroom. Trace the lines -- at the ceiling and those at the top and bottom of the blackboard. This tracing and that of the square and book below the eye illustrate the following rule :
Rule 9. Horizontal retreating lines above the eye appear to descend or vanish downward, and horizontal retreating lines below the eye appear to ascend or vanish upward. The vanishing point of any set of parallel retreating horizontal lines is at the level of the eye.
Lesson VI-- The Square.
Place a square tablet at the middle of the back of the desk, with its edges parallel to those of the desk. Two of the edges are not foreshortened, and are represented by parallel horizontal lines. The other edges vanish at a point over the tablet, and on the level of 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 the edges appear horizontal, and when the lines of the tracing are continued as far as the slate will allow, the fact that they converge will be readily seen, and the drawing illustrates the following rule :
Rule 10. 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 11 . 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.
Now turn the square so that its edges are at equal angles with the edges of the desk, and trace its edges and its diagonals. The two lower lines of the drawing ab and be make
equal angles with the edge of the slate, and , also the two upper lines cd and da, but the
angles of the upper lines are not the same as those of the lower lines. One diagonal of the
square is represented by a vertical line, and the other by a horizontal line. This drawing illustrates the following rules :
Rule 12. When the two lines of a horizontal right angle extend to right and left at equal angles with the picture plane, they are represented by lines which make equal angles with a horizontal line.
Rule 13. When the sides of a horizontal square are at equal angles with the picture plane, the nearer ones appear of equal length, and at equal angles with a horizontal line, and the same is true of the farther sides. One diagonal of the square appears a horizontal line, and the other appears a vertical line.
Conversely : When one diagonal of a horizontal square appears vertical, the other appears horizontal, and the nearer and farther sides appear at respectively equal angles with a horizontal line.
Lesson VII. -- The Appearance of Equal Spaces on Any Line.
Cut from paper a square of three inches, and draw its diagonals. Place this square horizontally at the middle of the back of the desk, with its edges parallel to those of the desk, and then trace its appearance and its diagonals upon the slate.
NOTE. -- The diagonals of a square bisect each other and give the centre of the square.
Compare the distance from the nearer end (1) of either diagonal to the centre of the square (2) with that from the centre of the square to the farther end of the diagonal (3), for an illustration of the following rule :
Rule 14. Equal distances on any retreating line appear unequal, the nearer of any two appearing the longer.
Transfer the tracing from the slate to the book.
Lesson VIII. -- The Triangle.
Draw upon an equilateral triangular tablet a line from an angle to the centre of the opposite side. (This line is called an altitude.)
Connect the triangular tablet with the square tablet, and place them on the desk 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 t4), and also the following rule :
Rule 15. The upper angle of a vertical isosceles or equilateral triangle, whose base is horizontal, appears in a vertical line erected at the perspective centre of the base.
Lesson IX. -- 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. This illustrates the following rule :
Rule 16. When one face only of a prism is visible, it appears its real shape.
Place the cube represented by tablets 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 :
Rule 17. When two or more faces of a cube are seen, none of them can appear their real shapes.
Place the cubical form on the desk, with the tablets vertical, and one of them seen edgewise, D, and discover that the other tablet does not appear a straight line. This illustrates the following rule :
Rule 18. Only one end of a prism can appear a straight line at any one time.