520

Line of the Horizon.

that direction, marks upon the picture or its plane extended, the true vanishing point of such lines.

851. It will now be understood why, in a long arched tunnel, or a cathedral, with many longitudinal lines on its floor, walls, roof, &c., all such lines, seen by an eye looking along from one end, appear

Lone

Fig. 206.

to converge to a point at the other, like the radii of a spider's web; and why, similarly, in the representation of the interior of an ordinary room (fig. 206), here sketched as viewed from one end, ali the lines of the corners, tops and bottoms of windows, floor, stripes on a carpet, edges of tables, &c., being in

reality parallel to one another, tend to the same vanishing point at v. The appearance of the lines in the floor of this room may recal that of the furrows in a ploughed field as seen from one end, when they appear like the ribs of a fan spread out towards the spectator.

852. By far the most important vanishing point in common scenes is the middle of the line of the horizon, and in a picture properly placed it is at the exact height of the eye of the spectator. It is marked s in figs. 205 and 207, and v in fig. 206. Because in houses, the roofs, foundations, floors, windows, tables, and other furniture, &c., are nearly all horizontal, the vanishing points of their principal lines and surfaces must be somewhere in the horizon, and for most of them near the middle of the picture. In holding up a pictureframe, through which to view a scene suitable for a picture, it is found most generally befitting to cause the line of the horizon to cross the frame at about one-third from the bottom of it: this fact becomes the reason of the rule in painting, so to place the horizontal line of the picture. In beginning a picture, this line is usually the first line drawn on the canvas, as marking the place of the vanishing points of all level lines and surfaces. And the eye of the spectator is supposed to be placed before the middle of it, and generally about as far from the picture as the picture itself is long,

Determination of the Point of Sight.

621 such being the extent of view which the eye at one time most conveniently commands.

Understanding now that the apparent or perspective direction of all lines in a scene is towards their vanishing points, and the rule having been given for determining these points in a drawing, it is now to be inquired how much of a line drawn to any vanishing point belongs to the known magnitude of the object which it touches; in other words, how much an object is in perspective fore shortened in consequence of its distance and obliquity of position in regard to the eye.

853. If we suppose A S P (fig. 207) to represent a plate of glass standing edgeways, on which a picture might be painted, and that towards the point, S, in it an eye is looking horizontally from the point, D; evidently then, a line from P continued in the direction of B and beyond, until vanishing from sight, would have as its perspective image or representation on the glass the line from P to S; S being then the point of sight in the picture, and the pictorial vanishing point of the line,

D

Fig. 207.

P B, however far extended. Now, to divide the representative line, PS, so as to correspond with any given portions of the original line, P B, &c., it would be necessary only to draw other lines from the place of the eye, D, to the line, P B, in the situations desired, and these lines would cut the perspective line, S P, in the proportions required. For instance, the portion of true line, ab, would be represented by that portion of the image line, S P, included between the two lines, a D, and b D, and so of any other portions.

854. There are figures drawn on mathematical scales by which such problems as the above can be at once approximatively solved; and it would be possible by trigonometrical calculation to solve them exactly in all cases; but the most generally convenient mode in practice is to sketch on the intended drawing (as that of which the boundaries are given in the adjoining figure, 208) the kind of measure required, by setting off from the point of sight, S, a distance on the horizontal line, as at D, equal to the distance of the eye from the picture, and then by oblique lines drawn from D to the base line, PR, to cut the perpendicular line, P S, in the situations desired.

622

Perspective of Squares.

This is done in the last figure, which differs from the present chiefly in having the point of distance, D, marked before its point of sight, instead cf here, laterally. And the line, PS, being always cut by the oblique line from D in proportion to the length of base-line concerned between P and the extremity of the oblique line, a horizontal line drawn through any point in the line from D, cuts in due proportions the other lines which have their vanishing points in the horizontal line, at S, for instance, a S, P S, &c. Thus, to draw in perspective, on the surface above represented and prepared, a chessboard or board of squares, it is necessary to set off half the breadth of the board on the base-line to the right and left of P, viz., at b

and a, and then to draw to the point of sight, as a vanishing point, the lines, a s and 6 s, part of which lines will therefore represent the sides of the board, and then to draw the diagonal, D b, which for the reasons above stated will cut the lines, P S and a s, in proportion to the length of base-line to the right of their extremities; aefb, therefore, is a square seen in perspective, and any number of smaller included squares are made by drawing lines from the vanishing points to equal divisions on the base, and making cross horizontal lines where the diagonal cuts these.

855. Much of the delight which the art of painting is calculated to afford is lost to the world, because persons in general are not taught how to look at a picture. Unless a spectator place himself where he can see the objects in true perspective, so that he may fancy himself looking at the realities through a window or opening, everything must appear to him false and distorted. The eye should be opposite to the point of sight of the picture, and therefore on a level with the line of the horizon, and it should be at the required distance from the picture, which is generally at least as great as the length of the picture. It needs not to be said that the fault of the

Estimate of Magnitude.

623

artist cannot be remedied by any position of the spectator. It is very common, for instance, to see miniature resemblances of architectural structures so foreshortened and tapered that the eye, to see them in true perspective, would require to be within an inch of the paper. These at the usual distance from the eye of ten or twelve inches are seen as hideous distortions. The specimens in the few preceding pages necessarily exemplify in a degree this error, because the point of distance had to be marked where there was but a small page. The figures, therefore, by any person studying the subject in detail, should be drawn on a scale so much larger as to allow the eye really to view them at the distance supposed.

856. A means of judging of the dimensions of bodies by the visual angle, and which depends neither on the absolute size of the image, nor on the foreshortening of the ground plane on which the body stands, is, to use known objects in view as measures for others near them which are unknown.

If a person of our acquaintance be standing at some distance from us near another person who is a stranger, we know how tall the stranger is by taking the acquaintance as a measure.

In pictorial representations of objects previously unknown, as to young people must at first be the Egyptian pyramids, the bodies of the whale, the elephant, or the camel, human beings may be represented around them to serve as measures for the less-known object. The Colossus of Rhodes seen from afar might to a stranger have appeared but an ordinary statue of a man, but the exact magnitude would have been known as soon as a ship of known dimensions were seen sailing into port between his gigantic limbs.

When an unpractised eye is first directed from a distance to a great ship, it will on many accounts dwell upon the object with wonder and admiration; but it may not judge truly of the enormous magnitude until it sees another vessel of known size near to it, or can perceive the sailors climbing on the rigging, and appearing there, by comparison, as little birds appear aniong the branches of a lofty tree.

By having a measure of this kind presented to us, the magnitude and elevation of great edifices are rendered more obvious. The magnificent pile of St. Paul's, in London, becomes still more striking to persons passing by when they discover visitors looking from the balconies near the summit-cross. These appear so minute among the surrounding huge masses that for a while a spectator is disposed to doubt whether they can be full-grown men.

624

Estimate of Dimensions.

Many persons cannot distinguish between the little pilot balloon (sometimes despatched before a great one to show the direction of the wind) and the great balloon itself, until under the last they perceive the aëronauts as little black objects in the basket.

Strangers visiting Switzerland, on first entering a great valley there, are often deceived as to its extent. Being familiar generally with more lowly hills and shorter valleys at home, which, however, from being near to the eyes, form bulky images, and having at first no other measure of comparison, they almost universally underrate the Alpine dimensions :-they will wonder, for instance, in the valley of Chamouni, that they should be travelling swiftly for hours without seeming to approach the end.

The author, in sailing past the Canary Islands, had a view of the far-famed Peak of Teneriffe. It had been in sight during the afternoon of the preceding day, at a distance of more than 100 miles, disappointing general expectation by appearing then only as an ordinary island rising out of the ocean; but next morning, when the ship had arrived within a shorter distance, and while another ship of the fleet, of seventy-four guns, holding her course six miles nearer to the land, served as a measure, it stood displayed as the most stupendous object which had ever been seen by most of those on board. The great ship in question appeared but as a speck rising from the sea, when compared with the huge prominence beyond it towering sublimely far above the clouds. Teneriffe alone of high mountains rises very directly out of the bosom of the ocean to an elevation of 13,000 feet, and, as an object of contemplation, therefore, is more impressive than even the still loftier summits of Chimborazo or the Himalayas, which rise from elevated plains, and in the midst of other heights only a little less elevated than them. selves.

It is because objects which are nearly on a level with us, as con trasted with such as either rise much above or fall much below, are usually surrounded by other known objects which serve as measures of comparison, that we judge so much more correctly of the size and distance of things near our level than of others.

A man walking like ourselves on the sea-shore or other level, may be recognized at a considerable distance; and probably it may not occur to us, that he appears much smaller on account of the distance; but if the same man be seen afterwards at an equal distance above us, collecting the sea-fowl's eggs on the face of a cliff, or if afterwards, when we have ourselves reached a height, we see