Drawing For Beginners/Chapter 11
CHAPTER XI
Measuring and Perspective
THERE is no general way of doing things," says a great writer on art. "No recipe can be given for doing as much as the drawing of a bunch of grapes."
If there are no known recipes for drawing things successfully, there are, nevertheless, several methods by which the young artist is helped out of difficulties and started on the right path.
The application of a few rules of perspective, the use of plumb and parallel lines, the measurement and comparison of one part of a drawing with another part—all these things contribute toward the training of the eye and the quickening of the brain.
Provided that you honestly desire advice, there is nothing to be ascertained but the direction in which that advice should be followed.
In short, what do you wish to know? What is the special difficulty that perplexes your mind? Does your drawing look out of proportion? Is it too bulky for its height, too short, too thin, or too tall?
Then we will measure one part against another part.
Perhaps it seems to you that the object or objects in your drawing are falling forward or inclining backward.
Then we will apply a plumb-line.
If you have embarked on an ambitious subject as the drawing of a house, or a street, and you cannot 'make it look right'—"It won't go back," or (equally possible) "It won't come forward"—then we must delve into the mysteries of perspective and apply common sense and plain argument.
Perspective is sometimes called the grammar of art because it assists us to draw correctly, as the grammar of a language helps us to speak and write correctly.
In the first place let us consider proportions.
If you are sitting at your work, lean back in your chair and face the object that you are drawing, and hold a pencil or ruler
up at arm's length and level with your eyes. Close one eye and measure from one end of the ruler, or pencil, to the thumb, then swing the hand—still at arm's length—and compare the measurement with another portion of the same object.
Look at your drawing.
Compare the same proportions in your drawing. The proportions must agree.
Let us presume that you are drawing a simple subject such as a small basket and you are in doubt as to whether the depth of your drawing of the basket is too great for its width. Hold your pencil at arm's length and mark the depth with your thumb. Swivel your wrist, keeping your thumb in the same position on the pencil, and place it in mid-air on the outside edge of the basket, measuring the width and counting: "once," then shifting, "twice," again shifting, "thrice" (probably not quite three times).
Drop your arm and look at your drawing.
Measure the depth of the basket itself with your finger and thumb on your pencil and place the measurement against the width.
In that manner you can prove for yourself whether the proportions of your drawing are right or wrong.
The reason why we close one eye and extend the arm is this. By closing one eye we concentrate our vision. We see one object, minus all its distracting surroundings. When the elbow is straight the arm is extended at its greatest length. Without taking this precaution we might cheat ourselves and unconsciously alter the position of the hand, and confuse measurements.
By straightening the elbow we keep the hand at the same distance for all measurements.
Do not make a fetish of measuring. Use it merely as a check, as a corrective. Draw first, measure afterward. The obnoxious habit of measuring first, and ticking off the measurement on the paper, is a trick unworthy of an artist. Moreover, it is a trap. The more we measure the less we prove. It is quite possible to measure until we stupefy ourselves.
If you are in doubt—measure.
Ask yourself, "Have I made the nose too short?" Take a measurement of the nose and compare it with the length of the face. "Have I drawn the house too tall in comparison with the poplar-tree, or the fence too high for the barn?" Measure the house against the tree, or the height of the fence against the height of the barn.
Possibly the proportions of the house, tree, fence, or barn are fairly satisfactory, but you are not quite satisfied with the lines that run parallel with your eyes, the top of the roof, the top of the wall.
Then put up your pencil or ruler, holding it at one end and
parallel with your eye, and at arm's length. Close one eye. Raise or lower it until the roof or wall is almost but not quite covered. The pencil or ruler has a smooth unbroken edge, and every divergence from the straight line will be apparent. Parallel lines of roof, wall, box, or house can thus be easily corrected. But what of the upright lines—the lintel of the door, the frame of a window, the sides of a wall? How shall we prove whether we have drawn these correctly?
Take a piece of thick silk or cotton, preferably of a dark tint, and weighted with a lump of lead (or some similar heavy substance), and you have one of man's oldest tools, the plumb-line.
Hold this at arm's length and between the finger and thumb before the object of your drawing.
The plumb-line will prove whether the door or window is perfectly upright (or perpendicular). Pull your drawing-block, or drawing-board, forward and let the plumb-line hang before the doubtful line of your sketch. The plumb-line always finds the true perpendicular.
When, however, you are drawing complicated subjects such as a large box, pieces of furniture, a portion of a room, house, or a street, you are faced with greater difficulties.
"How are things in a drawing made to go back?" is a question that requires a little more elucidation.
Probably as a small child you began to appreciate that as objects retire or recede, so must they become apparently smaller—a first rule of perspective.
Did you not sometimes play at the game of hiding from your sight a house or a tree by putting your finger, or even a single hair, close to your eye?
You must have noticed that the boat becomes smaller and smaller as it nears the horizon; that a man climbing a distant hill or mountain is reduced eventually to a mere speck; that a huge aeroplane looks no larger than a tiny fly among the clouds?
Therefore you have fully convinced yourself that objects must become smaller as they recede.
In other words, as objects retire, or are further from the eye, they occupy less space upon the field of vision.
The objects in the nearest part of your picture—that is 
You know that when you stand on the seashore and look seaward the extent of your vision is bounded by the meeting of the sea and sky, which boundary is called the horizon. The horizon is the line that follows the line of your eyes, the boundary line. The word is derived form the Greek horos, a limit or boundary.
When you stand on the beach and look at the sea your level position is low, and your horizon is low, because it is on a level with your eyes.
But climb the cliffs and turn seaward; the horizon is the level of your eyes.
Ascend to the very top of the cliffs. Now you are high indeed. Look again toward the horizon; it has extended; again it is the height of your eyes.
The line of the horizon is not always visible because of intervening objects, but as the horizon is the height of the artist's eye its position must be clearly understood, and indicated—for a time at least—in your drawings.
It is possible that you are still unconvinced. Perhaps you live in a city where roofs and houses block a distant horizon from view. Then we may apply another illustration and explain matters differently.
Suppose you descend to the street in a lift and look up at the buildings. What do you see? Every window, every cornice and roof, coming down to the level of your eye.
Now take the lift to the top story of your tall building. What do you then see? Everything is reversed. The eaves of each lower building, the roofs and cornices, rising to meet the level of your eye.
And the level of your eye is the height of your horizon.
"Is the thing below the level of my eye, or is it above the level of my eye?" is the inevitable question. You sit in a chair and look at the cornice, the beading, the top line of the picture frames, the mirror over the fireplace—
are they not above the eye-level and do they not come down to the level of the eye?
Cast your eye downward, still sitting on the same chair. What do you see? The outer edge of the carpet, the rug,
the wainscot, fender, the rail before the fireplace—all rise to the level of your eye.
You stand on a railway bridge and look at the long level stretch of the lines and you note that the rails—wide as they are below your feet—seem to narrow down to a point in the far distance on the horizon. That point is called (what else could it be called?) the Vanishing Point. And perspective says: All retiring lines have vanishing points.
Have you not observed the long straight street and its rows of lamp-posts or electric-light standards and noted that they diminish in size as they recede, though you know for a fact that they are all uniform in size?
As the lamps lessen in height, so does the pavement narrow, and the houses on each side of the street diminish. For all lines that lie parallel disappear to the same point on the horizon—the vanishing point.
The lines of the long esplanade by the sea, of the long buildings, of the long passage or tunnel, all recede, and if continued in our imagination meet at the level of the eye, which is the horizon. For the vanishing point is that point on the surface of the picture where retiring lines if continued would meet.
A large picture in a frame is perhaps the easiest example of parallel lines diminishing.
You are well aware that the sides of the picture are parallel. They are equal. Measure with an inch measure if you have any doubts on that point.
Now hang the picture on a wall; stand aside and at one end, several paces away, and make a quick sketch of it in its frame. Does not the near end of the frame appear larger than the far end? In other words, the picture-frame appears smaller as it recedes.
Measure the farthest end against the nearest by holding the pencil at arm's length. Continue the diminishing lines until they meet. Again we get the vanishing point resting on the (imaginary) line of the horizon at the height of our eye.
Let us procure a cardboard-box, and placing it on a table, three-quarter view, and about the height of the eye, take up our pencils and proceed to sketch it. In all probability you will say, "I can't tell whether the lines are running up or down."
Can you see the top of the box? If you sit about the same height as myself, you will say, "Yes, I can see a little bit of the top."
If we see even a small portion of the top, the eye is above the top, and if the eye is above the box, what must the lines do but rise to the level of the eye?
The top of the box is nearest to the level of the eye, and
the lower part of the box is farther away (the depth of the box is between). Therefore the top lines of the box rise a little, but the bottom lines rise a great deal.
If we have two lines which go gently on, one at a slight angle and one at a stiff angle, what must be the final result? They will meet at the height of your eye, or at your horizon.
The higher you sit on your chair, the more you can see of the top of the box. The lower you sit, the less you can see.
Place the same box on the floor, sit on a chair, and make a drawing of it.
Then place the box at a height—say on the top of a cupboard about 6 ½ feet high—and draw it again.
In the first drawing, up come the lines to meet the level of your eye. In the second sketch, down come the lines to the same level. In other words, your horizon in the first drawing is higher than your object, in the second drawing it is lower than your object.
Some things have more than one vanishing point—for instance, this same cardboard-box. A box is an angular object. It has two sides which run parallel, and two ends which also run parallel one with another.
Place the box so that two sides can be observed, and sketch it lightly and without measuring. Roughly sketch its position, and decide whether the eye is above or below the top of the box, i.e, whether the horizon is low or high. Then draw the line of the horizon right across the paper, because both vanishing points must be on the same level—at the same horizon.
Young artists find it difficult to accept this fact. They are exceedingly prone to provide a different horizon for each difficult angle.
The horizon at sea runs straight across the line of vision; as you know, it runs level with the eyes. Then why try to reach several horizons in the same picture?
In other words, it is not reasonable to assume two horizons in drawing one object. If more of one side of the box is seen than the other, then the side of which we have the broader view will have its vanishing point farther away. The side of the box presenting a more acute angle will have its vanishing point nearer.
The vanishing points will be near or far apart according to the angles.
The farther the vanishing points are apart, the farther we are from the object; and the nearer we are to the object, the nearer we are to the object, the nearer together are the vanishing points.
We may now feel justified in drawing something a little more ambitious and a little more interesting than a box. If we select something the shape of which bears a general resemblance to that of a box and place it in the same position, 
When you are sketching houses, boxes, or other objects, that demand clear perspective, do not begin by drawing a mere plan of the lines. Remember you are trying to be an artist.
Sketch your house first, then puzzle out your perspective. Check the drawing by the perspective, never the perspective by the drawing. You will find, as time goes on, that you will rightly register the perspective with more and more ease.
Rules for perspective might be cited without end, but a few diagrams well studied will obviate many questions.
Receding lines that are not parallel to the earth, says a perspective rule, do not meet on the horizon, but either above or below.
The sloping lid of a box, the sloping flap of a cellar, and the sloping roof of a house do not lie parallel with the earth. This rule is clearly demonstrated in the diagrams shown on pp. 130 and 131.
The student often meets in examination papers the statement: "The drawing of a direct front view, or a full side view, will disqualify a candidate."
"Why is this?" students invariably ask.
Think for a minute.
A box, a table, a wall, that faces your vision exactly has lines that lie parallel, and never meet. They cannot meet because they do not recede from you.
A full front view, or a full side view, has no vanishing point right or left. 
Then we have this rule:
Parallel lines that do not recede never have the appearance of meeting anywhere.
Look at the diagram of a village street.
The nature of the ground prevents the building of a long straight street, and the houses are dotted about. Although they present a diminishing effect (they are receding from the vision), yet they diminish to the horizon at four different points. Observe this well; it will demonstrate that:
If there are ten retiring lines and all parallel, there will be only one vanishing point for all; but if among the ten there are not two parallel lines, there will be no vanishing points.
perspective comes to our aid when we are perplexed with curves of arches, bridges, and doorways—beautiful objects that tempt the pencil and deceive the eye.
First sketch the arch or window, marking the direction of the base, the thickness of the wall; then, if you are in doubt about the rightful position of the curve, and the highest point of the arch, enclose the base lines in a square, drop a line from each corner, and at the intersection (or meeting-place) draw an upright line; that should find the centre of the arch.
In other words, enclose curves shapes in rectangular shapes.
Although a single arch, or even a couple of arches, might be sketched fairly correctly without such aid, a cluster of arches presents a more complicated problem, and we should feel justified in using this method of checking perspective.
Circles, we know, are exceedingly difficult to draw correctly. An artist, of course, should draw circles without resorting to mechanical means, but a beginner, on occasion, may wish to check his drawing of a circle by enclosing it in a square.
In Fig. 57 we have an upright circle in a square, also a circle enclosed in a square and in perspective—i.e, receding from the spectator.
Strictly speaking, many perspective problems belong to geometry and not to art, and provided that we understand a few simple rules, we need not worry ourselves with intricate problems.
But there is one deduction to which we must pay attention.
Every receding line or surface must necessarily be foreshortened.
What is foreshortening?
A coin seen upright and straight in front is a perfect circle; a coin seen lying down is a coin diminished and a coin foreshortened. In the first example the circle is complete. In the second example the surface of the coin is receding and the coin appears to be thicker in the part nearest the spectator. It does not appear to be a perfect circle.
Every object or thing that advances toward the spectator is foreshortened. For instance, some one points a finger directly at the artist. What does the artist see? He sees the tip of the finger, the tip of the thumb, the width of bent fingers, knuckles, palm, and arm, but the planes or surfaces that recede—such as the shaft of the finger itself, the fore-
arm, and the upper arm—all these are seen in a foreshortened state.
Put up your own hand and clench your fingers, but with the thumb erect. Now lower the upper part of the thumb, inclining it away from your vision. Your thumb is now foreshortened, the upper part is receding.
The human figure, being a rounded object, must always present some parts foreshortened.
In the head, the width of the shoulder, the width of the hips, the smooth rounded limbs, the curves of foot and hand—nowhere do we find an absolutely flat surface.
If you wish to find the human figure depicted without any foreshortening, you must refer to the drawings and carvings of the ancient Egyptians. In Fig. 58 we have a copy from a carving produced about the year 1490 B.C. (For the laws of perspective were all but unknown until the fifteenth century.) And what do you find?
The head in profile, the shoulders squarely and flatly presented (front view), the legs apparently tacked on to a flat surface instead of a rounded body, for they do not recede one behind the other, but present knee against knee-joint, ankle against ankle, and foot against foot. And to add to the peculiarities of early Egyptian art, the front view of the eye is inserted along the profile view of the forehead, nose, mouth, and chin.
Does this not bring home that unless you absorb a few laws of perspective, proportions, and foreshortening, you will find yourself heavily handicapped?
You can provide yourself with a good deal of amusement and useful instruction by searching for perspective, not only in your own paintings and drawings, but in the work of other people.
Study pictures in books and magazines, and photographs in the daily papers, and you will find endless examples of perspective.
By tracing parallel lines and finding vanishing points of planes and surfaces, much that bewildered you in the past will become clear and reasonable.
Planes, horizontal planes and perpendicular planes, are terms constantly used with regard to perspective.
A horizontal plane is a plane parallel with the earth; a perpendicular plane is one perpendicular to the earth. The top of a table and the ceiling of a room are horizontal planes; the walls of the room are perpendicular planes.
It might, very reasonably, be concluded that in using the words "tracing parallel lines" I intend to convey that lines should be drawn across the pictures. But that certainly was not my intention. There is no necessity to commit the crime of scribbling with pencil or ink on the printed pages. A thread of white or black silk or cotton laid upon the surface will serve your purpose.
To explain more clearly. Lay a thread of cotton on one of the perspective diagrams, hold one end on the vanishing point, and from that angle swivel the thread on to the various parallel lines. Remove the thread to each vanishing point.
Test any of the perspective examples in this way by merely laying the thread on the paper, holding the right thumb on the thread at the vanishing point. An old reel with a small quantity of cotton is, perhaps, easiest to handle, then the thread does not slip out of the left hand.
Use black thread if the drawing is lightly sketched on white paper, and white thread if the picture is in a dark tone.
Let me presume that you wish to analyse the perspective of the accompanying photograph of a picture-gallery, which is a very simple example.
Lay the thread first against the lowest line of the left wall, and find the inclination of the floor; then lay it on the top line near the ceiling. You will easily discover the point where these two lines meet. Hold the thread on that place and test the right-hand side of the picture by laying the thread first against the base and then against the summit of the pillars.
By careful adjustment you will soon fix the actual position of the vanishing point, which lies, does it not, between the two dark frames on the facing (far) wall and the light frames of the two adjoining pictures.
All the pictures on the left-hand wall lie parallel with the wall and diminish as they recede. All the pillars on the right side diminish both in height and bulk. Is not the nearer pillar a great deal larger in girth than the next, and the second pillar larger than the third?
Although the pictures are grouped at different heights from the ground, yet they all diminish to the same vanishing 
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The pictures on the far wall exactly face the spectator, therefore they do not diminish.
You were told to lay the thread first on the floor, then on the ceiling. This is always the wisest plan. If you find the boundary lines correctly, then all within those lines falls into place.
When you are drawing from Nature always check the outside lines. If sketching the whole of the house, find the top line of the roof, and the base of the walls; then the rest of the roof, the windows, doorways, lintel, and porch will all fall into place and save you an enormous amount of needless bother. If the outside lines are correct, then it stands to reason that everything within those lines will agree.
It matters not whether it is only a box or a house, a barn or a chair, a boat or a book—always, always check the extreme limit.
By the very simple aid of a thread you can discover many things. You can trace the low horizon of pictures that represent the low-lying ground. You will also discover that the low horizon gives ample space for the sky, and that clouds also conform to the laws of perspective and disappear as they recede.
Pictures of interiors of houses are extremely interesting. There you note that the walls, floor, and ceiling (or rafters of the roof) diminish to the same vanishing point (because they lie parallel one to another), but that the chairs and tables, unless they are arranged parallel with the walls, have each a separate vanishing point, though each vanishing point must, of necessity, meet on the same horizon. (See Fig. 53)
By making a friend of perspective and interesting ourselves in its various little problems, looking not only for the perspective in our own drawings, but for the perspective in others, we shall soon acquire a useful amount of knowledge. Shadows and reflections both bow to the law of perspective. Reflections in water, we are told, are geometrical but not pictorial. Objects are repeated in water geometrically.
All reflections of lines parallel with the surface of the water vanish on the horizon at the same point.
For example, we sketch two upright posts supporting a beam of wood.
The beam diminishes as it inclines toward the horizon; carry on these diminishing lines till they meet on the horizon.
The lines in the beam of wood reflected in the water are parallel with those in the actual beam above; these too must incline to the same vanishing point.
If a bridge is sketched with the curve of its arch reflected in the water, the reflection must incline toward the same horizon and the same vanishing point.
It is quite possible that you are a keen observer, and that your quick eye has already noticed these facts. Nevertheless there is no harm in impressing them upon you. Water is exceedingly deceptive. The rippling play of the winds on the surface and the break of the waves are apt to lead the eye astray. Which point was realized by many of the Old Masters, who safeguarded themselves by omitting reflections and painting sky and water with the same colour and the same brush.
Now for a final observation; perhaps you have not noticed that the reflection of the sun and the moon, the stars and the clouds, are the same distance below the horizon as the originals are above.
It is by no means uncommon to find a young student neglecting shapes and proportions of shadows; and here perspective holds out a helping hand.
The extent of the shadow is ruled by the position of the source of light.
When the sun is high in the heavens the shadows are comparatively short. When the sun is sinking the rays elongate. That is a matter of pure observation. Even a baby will 
By comparing diagrams of sun and shade you can make your own deductions.
The sun is so far removed from the earth's surface that its rays are parallel. But the rays from lamp or candle radiate on all sides and cannot be considered parallel.