Part 4

On this page are some sketches of a half-orange and a half-apple. Can you tell the positions in which they were held? Notice the foreshortened circle in Sketch 2. The sections of the orange are changed in appearance very much as the petals of the daisy are foreshortened, in the middle sketch on page 22.

Read again the lesson on page 48. Then decide which sketch of the half-orange is most pleasing. Which picture of the half-apple do you like best?

Draw a half-lemon in a position showing a foreshortened circle of pleasing proportions.

The Foreshortened Square.

Circular shapes are not the only ones that are foreshortened when they are seen under certain conditions. Figure 1 on this page is a picture of a square hat-box, showing the top and two sides. Not one of the three shapes is seen as it would actually measure. The top looks like a long narrow diamond. It is not so different from the shape of a narrow ellipse as you might at first suppose. If you changed the straight lines into curved lines, rounding off the four corners or angles of the diamond, you would have an ellipse. You could also place a box like this turned cornerwise, so that its top would look like a straight line. Where would the top be to look like that?

The two sides of the box are also foreshortened in this position; they appear shorter from front to back than they really are. You can see that the two farther vertical edges or corners appear shorter than the nearer one, just as trees in the distance appear smaller than trees of equal size near you. The lines on the top and bottom of the box appear to slant upward, instead of keeping their actual direction, which is horizontal.

Figure 2 shows the same box with the cover off. The inside was lined with colored paper and the dark value of the diamond-shaped mass adds interest to the picture.

Place cornerwise, on a table in front of you, a large box with a square top. See if the three faces in sight are foreshortened. Notice if the edges appear changed, in direction and in length. Make a sketch in outline, showing just how the box appears to you.

Measuring a Foreshortened Surface.

A good way to prove to yourself that the appearance of a surface or shape differs from its reality, is to test it in some way.

The girl in the picture is measuring the appearance of a book. She has put two books on the desk, with their backs facing her. Under the cover of the top book she has placed a string long enough to allow her to hold both ends of it in one hand, in such a way as to hide the two ends of the cover. She knows that in reality the ends of the cover do not slant; they are perfectly horizontal. But she finds that to hide the ends of the cover she must bring the lines made by the string toward each other. This proves that the ends of the book in this position must be represented by slanting lines. When the strings hide the ends of the cover, she finds that they meet directly opposite the eye. Holding the string tight, and keeping their meeting point exactly opposite the eye, she slips a horizontal pencil between the two lines, starting near the place where they meet, and moving down until the pencil hides the further edge of the cover. The appearance of the cover is shown in the space bounded by the horizontal pencil, the nearer edge of the cover, and the two slanting parts of the string seen between them.

Arrange a large book on the desk in front of you. With a string, make the test that has been explained. Draw in values what you see.

The Study of Perspective.

=What a Picture may Show Us.= The pencil sketch on the next page would be quite difficult for you to draw, but it is not too difficult for you to understand and enjoy. It is one that will help you to use your eyes intelligently, in trying to find out of doors some of the things that are shown you in pictures. One of the best things that pictures can do for us is to help us to see in our own surroundings things that are interesting and beautiful.

=Perspective.= The lessons in this chapter have helped you to see how surfaces and shapes change in appearance, as they are seen under different conditions. You have also found that certain edges and outlines appear to change their direction, when seen in different positions. There is a name given to the study of these things, which you will often hear used. It is perspective. Perspective is only another name for the study of appearances, as differing from facts. You will hear some one say, for instance, that a certain sketch or picture is good in perspective; you will understand that the picture shows, in some interesting way, the effect of distance and position, or how certain appearances differ from actual facts.

=Perspective of the Railroad.= One of the best places in which to study perspective is on a bridge over a railroad track. You have noticed, no doubt, how the rails seem to come together as they stretch into the distance, and how the telegraph poles seem to grow shorter and shorter, until they disappear altogether. You know that the rails are just as far apart a mile away from you as they are at your feet, but a sketch drawn so would not be correct in perspective, because it would not show how the track looked.

=Perspective Affecting Apparent Size.= The sketch on page 58 will interest you. Have you watched an engine grow from a mere speck in the distance to its full size as it rushes past you, and then grow smaller and smaller again as it hurries away, and finally disappears in the far-off horizon?

=Perspective of a Street.= Do you see anything on page 64 that makes you think of the railroad? If you stand in the middle of the street and look down its length you will notice that the lines of the sidewalk seem to run together, that the trees and houses decrease in height as they are seen farther away, and that people in the distance appear smaller than people near you. When you can see these effects for yourself, you will begin to understand what the study of perspective means.

A Beautiful Baptismal Font.

In the fine old city of Parma, in northern Italy, is a beautiful cathedral, built hundreds of years ago. Near the cathedral is a building much smaller in size called a baptistery, a place where baptisms are made in connection with church services. This baptistery is built of red and gray marble, and is one of the finest in Italy. It contains but one room, and in the middle of its floor, under the beautiful dome, is a very large font, carved from one piece of yellowish red marble. In one corner of the room is a smaller font--the one shown you on this page. It is standing on a lion whose paws are set upon the head of a ram, and it is richly carved in foliage and in strange animal forms. To it are still brought for baptism all the children born in Parma.

MEASURING AND PLANNING

IF WE CARE TO CONTINUE THE SEARCH, WE MAY FIND AN ARC EXTENDED TO A SEMICIRCLE, A SPIRAL, OR EVEN TO A COMPLETE RING, ALMOST AS TRUE AS IF STRUCK WITH A COMPASS, AND WITH THE TELLTALE DROOPING OR BROKEN GRASS-BLADE STILL AT WORK WITH EVERY STIR OF THE BREEZE.

"FAIRY RINGS" THE CHILDREN USED TO CALL THEM.

I HAVE PICTURED BOTH THE RING AND THE FAIRY.

WILLIAM HAMILTON GIBSON IN SHARP EYES.

Some Tools With Which to Measure and Plan.

By the time you have come to this chapter in your book, you will have drawn a great many pictures of objects. In doing this you have depended on your eyes and hand alone. You have not used a ruler to measure with, nor any tool that would tell you the exact length of a line or the exact size of any shape.

But sometimes it is necessary that a line or shape should be of exact length or size. On this page are shown some very simple tools which you can make yourself, and which you will find useful in carrying out the lessons in this chapter on Measuring and Planning. Figure I is a "circle maker." It can be used in place of a compass. To make it, take a strip of cardboard seven inches long and one inch wide. Bisect its short edges and rule a line connecting these points. Upon this line, mark off, by measuring with a ruler, inch, half-inch, and quarter-inch spaces. Through these points draw lines, and pierce holes with a pin where they cross the center line. A pin placed through the first hole will act as a pivot. Push a sharp pencil through one of the other holes, just far enough to allow the lead to make a mark. The pin marks the center, and the pencil swings around it, as shown in the sketch at the top of page 68. The line drawn by the pencil is the circumference of the circle. The distance between the center and the circumference is the radius of a circle. We speak of one radius and of two or more _radii_ of a circle.

Figure II is a little tool that will help you to draw square corners. Mark with a ruler upon an end and one side of the back of an envelope, the spaces for inches, and their divisions into halves and quarters. "Square corner" is another name for right angle. You will often wish to use this measure, called a test square, in squaring corners, and in drawing lines at right angles to each other. A No. 9 envelope will be a good size to use, as the long edge will serve as a ruler. You can make the drawings in this chapter with a ruler and compass, or you can use these simple tools, made by yourself.

Dividing a Circular Space.

There are many ways in which a circular shape may be divided and decorated. Sketch B shows two circles drawn around the same center, with different radii. Such circles are called concentric. Sketch C shows the circle divided into fourths. To do this, place the angle of your test square at the center of the circle and rule two radii. Repeat to secure four right angles at the center of the circle.

Sketches D, F, and G show circles divided into sixths, by setting off the radius six times on the circumference, and drawing diameters connecting these points.

Sketch E shows a circle divided into thirds. Set off the radius six times on the circumference; draw a radius from every other point.

Draw concentric circles, and divide them into halves, fourths, thirds, and sixths.

Some Divisions of Square Spaces.

A square is said to be on its diameters when one of its diameters is vertical and the other horizontal; it is said to be on its diagonals when the diagonals are in this position. Sketch A shows the larger square on its diameters and the small inner square on its diagonals.

To draw a square on its diameters, place your test square to locate the lower left corner of the square, and draw the two sides at right angles, extending the lines to the desired length. Use your test square in drawing all other corners of your square. For the diameters, bisect each side and connect the points of bisection. For a design plan like Sketch A, bisect the semi-diameters and connect these points. Diameters of a square bisect opposite sides; diagonals bisect opposite angles.

In Sketch B, each side is quadrisected, or divided into fourths, and the opposite points connected. This division of a square may be used for a decorative plan in a number of ways, one of which is shown in the sketch.

To draw a square in the position of Sketch C, use your test square, and draw the diagonals first, dividing them into inch spaces. Connect the ends of the diagonals to get a square. In the plan for the border design in Sketch C, connect the outer points on the diagonals to form the space for a border decoration.

Draw two squares, one on its diameters, and one on its diagonals. Show by divisions made in each, some plan for a design.

How an Oblong Space May be Divided.

You can draw an oblong with your test square in the same way that you drew a square, measuring the sides to get the length you wish. In Sketch A the semi-diameters are bisected and the points connected, forming a diamond-shaped space, something like a square on its diagonals. In making the unit used in the upper half of this space, the lines of the triangle are changed very slightly, but this change makes an interesting decoration. In Sketch B the sides are quadrisected, and the space is divided by connecting some of the opposite points, making an oblong on its diameters for the middle space. In the upper half of this space a simple shape, very like a square, is used. It can be reversed, as can the triangular shape in Sketch A, to fill the lower half of the space.

Sketch C shows a plan for dividing the oblong into many small squares. In each of these, or in every other one, a simple unit could be placed, to make an "all-over" pattern.

Draw an oblong, and by dividing its sides, make a plan for a decorative design. Show how a decoration can be made by slightly changing the lines of an enclosing shape.

The Equilateral Triangle.

With the help of your circle maker or compass you can easily draw an equilateral triangle.

Rule a horizontal line of any desired length, for the base of your triangle--that side upon which the triangle seems to rest. Place the pivot of your circle maker at one end of the line, and take a radius equal to its length. Draw above this line part of the circumference of a circle, called an arc. Then take as a center the other end of the horizontal line, and with the same radius, draw an intersecting arc. Rule lines from the intersecting arcs to each end of the line. You have drawn an equilateral triangle.

Sketches A and B show you how an equilateral triangle may be divided. Sketch C shows how one line may divide the triangle into two shapes, whose outlines may be slightly changed or modified, to make a decoration.

For a surface covering like Sketch D, construct one equilateral triangle and carry the base line across the paper. Rule a line parallel to this, passing through the apex of the triangle. Set off upon these lines lengths equal to one side of your triangle. Draw lines connecting these points, as shown in the sketch. Repeat this process for a surface covering.

A Case for Newspaper Clippings.

When you know how to measure accurately and can plan good proportions, you can make many simple articles, both useful and beautiful.

To make the case for newspaper clippings shown on this page, cut an oblong of stiff manila paper, 8-1/2 x 9-1/2 inches. Use your test square in measuring all corners, to get right angles. Then cut an oblong 9-1/2 x 10-1/2 inches of "cover" paper, of some good color. Fit the manila oblong within this, in such a way as to leave an inch margin of colored paper all around it. Fold over this margin, pasting it down neatly. Cut an oblong 8-1/4 x 9-1/4 inches, of tinted paper of lighter weight. Lay this oblong as an inside lining to the cover, pasting to leave a narrow margin of the dark cover paper around the lining. Place the cover on your desk, with the long edges from left to right. Fold the nearer edge to meet the farther edge. Crease well. Bisect the crease, and place a point 3/8 of an inch up from the crease. Measure three inches from each end, and place points at these distances, 3/8 of an inch up from the crease. Within the folded cover, place six or eight No. 9 envelopes, the bottom edges of the envelopes touching the crease. Fit the envelopes within the cover, to leave an equal margin around the front and ends of the case. Holding the envelopes firmly within the cover, make holes with an eyelet punch at the points placed for them. Tie the envelopes in the case with raffia, tape, or cord.

How to Draw Letters.

=Before the Days of Printing.= There was once a time when all the books in the world were lettered by hand. This hand printing was done by men called monks, who lived in monasteries, away from the noise and bustle of the world, and who often devoted their whole lives to the lettering of religious books. They did this lettering on sheepskin or parchment instead of on paper, and they spared no pains in making these manuscripts as beautiful as possible. Color was often used for initials and for capital letters, and sometimes artistically designed borders were placed around the lettering, making each page in these manuscript books as beautiful as a picture. The great amount of time that was necessary to make one of these books made them very expensive, and only people of great wealth could own them.

=Type and the Printing Press.= When type and the printing press were invented, the printer at first tried to make his pages look like the manuscript pages of the monks. For this reason, the earlier printing was artistic, although the letters were not as clear and perfect as type letters are now. The first books printed from type were also expensive, but little by little the process was made cheap, until at last type letters lost much of their beauty. Lately, however, printers have realized that single letters are like design units in an all-over pattern. The size of the letters, their shapes and thickness, the spaces between them, and the spaces between the lines are all of great importance.

=A Simple Alphabet.= On the next page is a simple alphabet, planned on squared paper. You can print in this style, any title or words you may wish on a program or book-cover. Plan your printing on a separate piece of paper, marking the height of the space you intend to fill with the letters. Quadrisect this height and draw through these points horizontal lines. Lay off on the lower horizontal, distances equal to the quadrisection. From these points erect vertical lines, using your test square. Mark in a sketchy way the width of each letter in the word you are planning, making the thickness of each letter the width of a square, and leaving the same distance (the width of a square) between each letter. Be careful to keep uniform thickness in slanting lines and curves, as in K and C. Avoid angles in your curves. If you have more than one word in your line, leave three squares for the space between the words, and if more than one line of printing is used, guard against too much space between the lines. The width of two squares would be a safe distance in a style like this.

=Transferring the Letters.= When your plan is complete, rub soft lead pencil evenly over the back of the paper, and place the plan exactly where you wish the lettering to go, on your book-cover or program, with the lead painting next to the cover. Then mark over the letters with a sharp point, and a faint tracing will appear on the under surface. You can then finish your lettering in ink or color, as you prefer.

All lettering must be done with much care, with exactness, and with the greatest neatness.

DESIGN

Colors in Full Intensity and their Neutral Values.

=Light and Dark Colors.= When you painted an autumn scene like the one on page 2, you found that it could be done with three colors--yellow, red, and blue. Blue made the sky and water; blue and yellow the grass and the foliage of the smaller tree; blue and red the distance; yellow, red, and blue the tree trunks and the autumn colors of the large tree. Look again at the sketch. Do you see that the two trees are darker than the grass, that the water and the sky are of nearly the same value, and that the tree-trunks are the darkest colors in the picture? In the winter scene on page 8, and in the spring picture of the yellow bush, both dark and light colors have been used. The colored flower studies all show dark and light colors. Both light and dark colors are needed to express truth and beauty, just as in music we need both high and low tones for perfect melody.

=An Orderly Arrangement of Colors.= In Chart A these colors are arranged in an orderly way. Yellow (Y) is the lightest color and is placed directly opposite violet (V), the darkest color in the circle. Yellow-orange (YO) and yellow-green (YG) come next to yellow on either side. Then orange (O) and green (G) follow, and next to them are red-orange (RO) and blue-green (BG). Next in the circle are red (R) and blue (B), and after them red-violet (RV) and blue-violet (BV). The colors in the chart are the strongest that your three colors can make. Colors of this strength are said to be in full intensity.

=Expressing Colors in Neutral Values.= On page 4 are "finder" pictures taken from the autumn scene on page 2. These are done in gray washes that correspond to the colors in the autumn sketch. The trees are shown in grays that make them just as dark as the trees in the colored picture. When we make gray washes just as light and as dark as colors that we wish to represent, we say that we express those colors in neutral values.

=The Neutral Value Scale.= In Chart D the scales are arranged to show the grays or neutral values that correspond to the different colors in their full intensity. In this chart yellow is as light as the gray wash called High Light (HL). Yellow-orange and yellow-green are of the same value as Light (L). Orange and green are of the same value as Low Light (LL). Red-orange and blue-green are of the same value as Middle (M). Red and blue equal the neutral value High Dark (HD). Red-violet and blue-violet are equal to Dark (D), and violet, the darkest color, is expressed by Low Dark (LD). Low Dark is almost black.

The Neutral Value Scale.

A scale of neutral values, larger in size than that on page 78, is printed on this page. White and black are added. They do not correspond to any color, but they help us to see the many steps that may be taken between them. Only seven of these steps from black to white are shown in our scale. Of course there are other grays, not represented in the scale, just as there are tones of music not expressed in the musical scale or octave. The musical scale and this value scale are used to help locate all other notes and all other degrees of light and dark. You could make, for instance, other grays between High Light and White. But it is useful to know that certain grays have definite names, and definite places in the scale.

With the aid of this larger scale, we can more easily compare the values of the colors of a landscape, a flower, or a still-life group with the same values in gray. Turn to pages 8 and 9. On page 8 the winter landscape is in color, and you see the same scene on page 9 in neutral values. In it the sky and part of the snow are of the same value, and they match the gray marked High Light in the scale. The distant hill is Low Light; the dark band of trees on the horizon is High Dark, and the tree in the foreground is Dark. In this way you can find in the scale the neutral values used in a picture.

Name the values of the hyacinth, on page 53. What values were used in the moonlight picture on page 10? Make a little scale showing these values and giving their names.