We feared that cobwebbed in those entanglements of line there lurked our old enemies, Euclid and Geometry. My own distrust has never been wholly dispelled ; for which reason, out of sympathy for a new generation of art students, I have tried to set down the matter in plain words and to divest it of some problematical exercises dear only to the mathematical mind. These, in truth, sometimes lead to a negative result—the " which is impossible " of Euclid—or they have but little bearing on our art. Johnson has said : " Long calculations or complex diagrams affright the timorous and inexperienced from a second view, but if we have skill sufficient to analyse them into simple, principles, it will be discovered that our fear was groundless. Her laws are not difficult to understand if they are taken one at a time, together with an explanation of the reasoning on which they are based. This is the method which I have followed in Part I.

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When practising it we are not concerned with their apparent changes of colour or tone, though those also help us to recognise the distance separating us, or that of one object from another.

Visual rays. Tracing on glass. Height of objects at varying distances traced on glass. On the other hand, the rays from the object close to the glass have only just started on their journey and so are still wide apart.

Width of objects traced. We shall be satisfied that their apparent length, as traced on the glass Fig. We have seen that the height and width of objects as they appear to us is determined by the converging rays from their extremities to our eye ; that objects really equal in size appear shorter and narrower when further away.

Depths of objects on a level surface traced. Notice, however, that the eye is above the pins i. Since the pins were placed at equal distances apart, their spacing, as shown on the glass, would also fix the depths of the ground surface between them Fig.

Theory of tracing applied to measurements on a canvas. In a perspective drawing our canvas is supposed to be a glass, and on it we trace only those objects that we can see through it without moving our heads.

But painters should be practical ; so set up a canvas and prove to yourself that objects of equal size when far off appear narrower, shorter, and less deep than the near ones, and that the spaces between them undergo a corresponding reduction. To do this, follow the instructions in Figs. Posts marked on edge and carried across to required position. Be yourself the Painter. See that your canvas is vertical and so placed that the posts are just visible at one edge.

With one eye shut and head still, mark off the heights of the posts where they seem to touch the canvas. Behave as in the last exercise ; tick off the position of each nail on the edge of the canvas. These nails might represent the cracks between floor-boards, and our drawing shows that each board would appear one above the other Fig. Theory of tracing to explain why parallel receding lines appear to meet. It can be explained by tracing in this way—Fig. The tracing on the glass would look like this Fig.

The dots on the glass showing where the rays pass through it. In Fig. As we have secured the width of a piece of the track at its near and far end, we can join the ends on each side to make the rails. The tracing on the glass Fig. The spot on the glass where the receding lines appear to end or meet is at the same level as your eye Fig.

The trace of a level receding surface seen from below. The reverse happens when our eye is lower than the object Fig. Let us again draw our piece of railroad as in Fig. Above it we can draw the ceiling if we still follow out Fig. Our drawing Fig. On the other hand, if we see their under side the lines must be made to run down the canvas as they recede.

Perched on a masthead we could, by moving round, examine the far distance where the sky and sea seem to meet, until piece by piece the whole circumference had come under our scrutiny Fig.

On land we rarely get anything but an interrupted view of a portion of the horizon. When standing or sitting on flat land the surface between us and the distant horizon is so foreshortened that mere hedges and bushes may hide miles of country and blot out the horizon. From a hill-top we look down upon the flat land, and the former narrow strip between us and the horizon looks deeper ; also from this height we see more distant land.

Example of a low horizon. This explains that the curvature of the earth between us and the horizon is a real consideration for the landscape and sea painter, and it provides a reason for our seeing more distance from a height than from a slight rise. The horizon on our picture. We draw this level line of the horizon straight across our picture. It is a matter of artistic taste and judgment whether we place it low, high, or in the centre of our canvas. It is essential, however, to understand that the position of the horizon line in relation to all the objects in our picture affords evidence of how high up we ourselves were when painting the scene.

For instance, if we stand while we paint a whole length figure on level ground the horizon line would be cut by the head of our portrait Fig.

But if we sit to paint him then the horizon line will pass through his waist Fig. It would be an absurd proceeding to begin a painting of an imaginary scene without first fixing the place where you suppose yourself to be painting it from. The relative position of the horizon line and the principal figures or other objects must be decided on at the onset; after that the locality and size of all additional objects will be governed by the horizon.

When you are painting an actual scene, you will draw the horizon line, whether it is visible or not in Nature, on your picture as soon as you have decided on the size of the principal objects. The horizon in Nature will be at the exact height of your eye, i. II, III ; so if standing in a room our horizon would be roughly 5 ft. Drawn by George Cole, Example of a high horizon. If our model is standing on a throne and we sit to paint on a low stool, our horizon is about the level of his feet.

Out of doors a slight rise on otherwise level ground would present a similar effect see Illus. In a room we can find the horizon by measuring the height of our eye from the ground and chalk-marking that height on the wall facing us.

Out of doors on hilly ground a stick with the height of our eye marked on it can be stuck in the ground just in front of us ; where that mark cuts the view will be the horizon.

In this way the horizon, though a low one, is actually three-quarters of the way up the canvas. If you were to look down the barrel of a gun, holding it quite level Fig.

It is the spot that a level line running directly away from us tends to. Van Eyck. Photo Mansel. The horizon as shown by the distant view passes behind the heads of the figures. The painter must also have been sitting, because if he had been standing his horizon would have been above their heads see Chap. The lines of the pavements, capitals, and plinth of the columns all tend towards one spot on the horizon at its centre. To obtain the depth of each tile, see end of Chap.

The drawing of their pattern is explained in Chap. In a composed picture we can place the P. If you see on a picture the representation of what was in Nature a level receding line, drawn as a vertical line, then you will know that the far end of it points to the P. From this picture we know that the painter stood at his work, and looked straight down the line marked X.

If you sat astride a very long straight level wall looking down it, then the far end of the wall would seem to end at the P. This being so, we will in future call the station point Painter. Side view of Fig. Example of receding lines meeting at the P. All level receding lines that are in Nature at right angles to the front of our face i. IV as will be explained in Chap. But there are level lines in Nature placed at other angles than this, and they tend to other spots on the horizon Illus.

Each level line or set of parallel lines has its own V. Besides these level lines there are others on inclined planes that run to vanishing points above or below the horizon, according to their position. Some of these level receding lines will be at such an angle that the points they run to will be further to the left or right than the width of ground we propose to paint, and consequently will be outside the extremities of our picture as V.

As for some of the inclined planes, the lines of these will sometimes tend to points far above or below that portion of the ground or sky we wish to include in our picture. In practice we may draw the scene on a small scale in the middle of a large sheet of paper so as to have room for these outside V.

Then we can square up see Note 1 in Appendix the little picture and enlarge it on the selected canvas. Another way is to use the floor as an extension of your canvas. Sign up to read more!


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