Imágenes de páginas
PDF
EPUB

610

Apparent Magnitude of Objects.

much of its field any object occupies. When ships are in chase, it is common by such an instrument, which will detect a change of visual angle, or apparent size, to view the fleeing or pursuing ship; and if the apparent size be observed to increase, the conclusion follows that the ships are nearing each other; if, on the contrary, the size diminishes, the chased ship is escaping.

840. By computation according to this rule, whenever the real size of a distant object is known, the distance is ascertainable, and, vice versa, when the distance is known the size is determinable; for it is evident that if a body, as a ship, known to be 100 feet tall, occupy or subtend in the field of vision the 360th part of a whole circle, or one degree, the whole circle must be in circumference 360 times 100 feet, or 36,000; and the diameter of any circle being, or more nearly of its circumference, while in the case supposed the distance of the ship is the half-diameter, we learn that distance Again, if we know the distance of a ship or other object to be a mile, and if we then find the visual angle subtended by the object to be the 1000th part of a circle, we know its true size to be the 1000th part of a circle, of which the half-diameter or radius is one mile. It is by applying this rule in a manner to be afterwards explained, that the size of the heavenly bodies is determined.

22

Few persons are aware of how rapidly the apparent magnitude of an object diminishes on its being removed farther from the eye. A removal of 100 feet renders the image formed on the retina by any object 100 times smaller than when the distance is one foot. Now, in the unaided human eye, the power of seeing minute objects has a limit, namely, when the object subtends in the field of view an angle of space of less than half a minute. There are many kinds of minute animals thus hidden from common unaided vision, owing to their small size, but which the microscope clearly shows, and proves them by their activities, to see one another as larger animals do. It has been common to believe that mere distance prevents the eyes from seeing minute things somewhat as a fog or other such obstacle does, and not because of the small size of the images then formed on the retina.

841. We now perceive that if the rays of light coming to the eye through a plate of glass set in a picture-frame, from objects seen beyond it, could leave marks in the glass at the points where they pass, and marks capable of giving out the same kind of light as the objects give, there would be formed upon the glass such a representation or picture of the objects viewed through it, that when held

Aim of Pictorial Illustration.

611

before the eye, it would produce on the retina an image or images the same in almost all respects as the objects themselves. From the different points of the glass, light would shoot to the eye of the same kinds and in the very same directions as that originally coming from the objects. Now the art of painting seeks so to dispose lights, shades, and colours on some plane surface, as to produce the sort of representation of objects here contemplated, while the picture-frame stands in lieu of the window-frame, or border of any opening through which the true scene is supposed to be viewed. It is admirable how perfectly this art now accomplishes its ends; and although there are still differences between the effect upon the eye of a picture and of the realities-which differences we shall consider presently, and how they may be combated so as to render the illusion almost perfect—it is not one of them, as might be supposed from the small extent of the canvas, or plane of the picture, that the images made on the retina are smaller than when produced by the objects themselves. Few people, before studying this subject, are aware that in good pictures, the different figures are in size made such that, at the distance from the eye at which the picture is meant to be viewed, they produce on the retina, the very same size of image as would be produced by the realities seen under the aspect represented in the picture. To become sensible of this, a person may look through a window-pane, having the eye fixed, at the distance of a foot from it, and may trace with a sharp point or pencil upon the glass (previously coated with gum) the outline of the scene beyond, perhaps a street or garden, and he will find that the outline of a man seen there at the distance of thirty paces, may be made perfectly to coincide with the person, so that, if opaque, it would just hide the person, will be scarcely half an inch tall, while the figure of a man a few hundred paces off will be so small that the eyes, nose, and other features could not be distinguished, even if they could be drawn.

842. It is remarkable that, although no fact in nature is more familiarly known to all, than that the apparent size of bodies is constantly changing to a person moving about among them, as explained in the preceding paragraphs, few have stated to themselves that philosophical truth. They soon learn, even as children, to make the necessary allowances, and move about safely among the things around them, judging correctly enough of sizes and positions of things. Then, as a person who reads the description of an elephant, does not deem the animal larger or smaller because of the size of

612

Apparent Size of Objects.

the types used in the printing, or of the accompanying engraved representation; and as a man, in a picture-gallery, viewing miniatures and larger portraits, does not conceive of the originals according to the size of the representations; and as a man viewing a correctly-executed picture of a Grecian temple, never dreams, unless his attention be specially directed to the fact, that, upon the canvas, the distant pillars of the rows are drawn much shorter than the near ones, the mind in all such cases merely using the signs to help it to conceive of the things according to previous knowledge, or to other principles of judging; so in any common case of examining by the eyes, the mind takes small account of the apparent size of objects, but passes instantly from the types to the realities, already in general more or less known. Few persons, for instance, reflect on the fact, that when two friends shake hands, each appears to the mere eye of the other much taller than when either has gone some paces away; or that one chair of a set, at the end of a room, appears to a person sitting at the other, only half as large as a chair in the middle of the room. But such facts may be immediately proved by looking through a tube or a ring at the same object when placed at different distances from the eye. Of a chair standing near, only a small part will be visible through the tube, while of a distant chair the whole and others around may be seen. At a few miles' distance a fleet of a hundred ships, or a mountain, may be seen through a finger-ring as the picture-frame. There are occasions, however, where previous knowledge and common collateral helps to the recognition of objects being wanting, the observer's attention is strongly aroused to the fact of the diminutive appearance produced by their distance; for instance, when a man, after a long sea-voyage, first approaches a land, of which the features are new to him, as when a European first arrives on an Indian coast, he can scarcely believe that the little specks which he sees scattered along the shore are spacious dwellings, or that what seem to him only luxuriant herbs or bushes, are magnificent palm-trees.

843. For the same reason that a distant body to the naked eye, appears diminutive, namely, the smallness of the visual angle subtended by it, so does a distant motion to the eye appear slow. A railway train dashing past a spectator at rest may startle, nay, appal him by its speed; but if viewed, at the same time, by another from the side of a distant hill, it seems to be gliding gently along. A ship driven before a tempest seems to a sailor on board almost to fly through the white foam which surrounds her; but if then seen by a

Foreshortening of Objects.

613

spectator on shore, she is scarcely perceived to change her place. A balloon high in the air, borne along on the wings of the wind, at the rate of seventy or eighty miles an hour, may still for a considerable time leave a spectator on earth doubtful whether it be in motion at all, or in what direction it moves. The moon in her orbit wheels round the earth at the rate of hundreds of miles an hour, yet, owing to her distance from it, her motion is not visible to the naked eye of the inhabitants of the earth, except by comparing her positions at considerable intervals of time. In respect to bodies still more distant than the moon, the truth at present under consideration is still more striking.

Having now explained how the apparent transverse measure or breadth of bodies and of space, in other words, the visual angle subtended by them, is affected by their distance from the eye, we proceed to show how it is affected also by their position.

Because light moves in straight lines, no part of an opaque body can be seen, between which and the eye there is not straight open space. A globe before the eye, however turned, preserves the same appearance in the field of view, and its outline traced upon a plate of glass held across between it and the eye, is, like its direct shadow upon a wall, always a circle; but an egg, which if held in one position produces a circular outline or image, when held in another, produces an image which is oval. A wheel when viewed sideways appears a perfect circle, when viewed edgeways it appears a broad straight band or line, and in any intermediate position it appears oval. The apparent form of a body, then, may give only partial information as to its shape, to be taken with the experience of seeing it in other aspects. If a man had never seen an egg but endways he could not have known that it was not a sphere.

844. If any long straight object, as a wooden beam, be placed witb one of its ends directly to the eye, that end only can be seen, and according to the case, may appear a square or circle of the diameter of the beam; if it then be placed with its side directly to the eye, its whole length will be seen; and if placed in any intermediate position, it will appear more or less shortened; in all cases, its outline on the retina being similar to that of its shadow on a wall behind the person, A man has advanced on the point of a spear turned directly to his eye without seeing it, or on the end of a bar of iron carried on the shoulder of a porter in the street. A common telescope held with its end to the eye appears a perfect circle, if then inclined a little, it seems to jut out on one side, and as the inclination is increased, it

514

Rules of Foreshortening;

juts out more and more, until it displays its whole length. A great ship of war, of which the stern is towards a near spectator, might appear to him a round wooden building with ordinary windows; but as it turns, or as the spectator moves to one side, it gradually reveals the long batteries of cannon. A straight row of a thousand similar objects, as of trees, pillars, or soldiers in rank, may appear to a person at the extremity, as only one object of the kind, the nearest individual completely hiding all the others; but if viewed from the side and at a certain distance, the individuals may be counted. The appearances now treated of, exemplify what is called foreshortening, and are to be noted wherever surfaces or lines are not placed so as directly to face the spectator.

845. One of the commonest cases of foreshortening is when the eye looks more or less obliquely along an extended plane surface, on the ground, for instance, or on the face of the sea, by estimating aright the foreshortening of which, judgment is formed of the distance or situation of the objects placed thercon. And it will be readily perceived that in all such cases the more distant portions of the surface, are progressively more foreshortened than the nearer. Thus, a man standing at a (fig. 204), on a plain, as a b, with his eye at c, if looking

Fig. 204.

down before him, looks on a portion of the surface, a d, almost directly, or with little foreshortening, and an extent, as a d, equal to the height of the eye, will sub

tend in his eye an angle of 45°, or half a right angle, viz., the angle, a cd, which is half of the whole angular space subtended from his feet to the horizon, however distant; the next equal portion of the plane, viz., d f, will subtend a much smaller angle, viz., d c ƒ, the next, viz., ƒ c g, an angle smaller still, and so on, as he carries his view more and more forward, the surface becoming more and more oblique to his visual ray, until at last the light rather skims along the level than rises. This explains why a person having a side view of a row of separate objects, as of men in line, trees, or pillars, can look through or between the nearest of them, but towards the extremity sees them as if standing in close contact, or as if forming a continued surface. The same remark explains why distinct masses of cloud, scattered uniformly over the sky, with wide

« AnteriorContinuar »