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As the relief produced by the union of such imperfect pictures was sufficient only to shew the correctness of the principle, the friends to whom Mr. Elliot shewed the instrument thought it of little interest, and he therefore neither prosecuted the subject, nor published any account of his contrivance.

Mr. Wheatstone suggested a similar contrivance, without either mirrors or lenses. In order to unite the pictures by converging the optic axes to a point between them and the eye, he proposed to place them in a box to hide the lateral image and assist in making them unite with the naked eyes. In order to produce the union by looking at a point beyond the picture, he suggested the use of "a pair of tubes capable of being inclined to each other at various angles," the pictures being placed on a stand in front of the tubes. These contrivances, however, though auxiliary to the use of the naked eyes, were superseded by the Reflecting Stereoscope, which we shall now describe.

The figures to which Mr. Wheatstone applied this instrument were pairs of outline representations of objects of three dimensions, such as a cube, a cone, the frustum of a square pyramid, which is shewn on one side of E, E? in Fig. 10, and in other figures; and he employed them, as he observes, "for the purpose of illustration, for had either shading or colouring been introduced it might be supposed that the effect was wholly or in part due to these circumstances, whereas, by leaving them out of consideration, no room is left to doubt that the entire effect of relief is owing to the simultaneous perception of the two monocular projections, one on each retina."

This expectation has never been realized, for it is obviously beyond the reach of the highest art to draw two copies of a flower or a bust with such accuracy of outline or colour as to produce "perfect identity," or anything approaching to it, "with the object represented."

Photography alone can furnish us with such representations of natural and artificial objects; and it is singular that neither Mr. Elliot nor Mr. Wheatstone should have availed themselves of the well-known photographic process of Mr. Wedgewood and Sir Humphry Davy, which, as Mr. Wedgewood remarks, wanted only "a method of preventing the unshaded parts of the delineation from being coloured by exposure to the day, to render the process as useful as it is elegant." When the two dissimilar photographs were taken they could have been used in the stereoscope in candle-light, or in faint daylight, till they disappeared, or permanent outlines of them might have been taken and coloured after nature.

Mr. Fox Talbot's beautiful process of producing permanent photographs was communicated to the Royal Society in January 1839, but no attempt was made till some years later to make it available for the stereoscope.

In a chapter on binocular pictures, and the method of executing them in order to reproduce, with perfect accuracy, the objects which they represent, we shall recur to this branch of the subject.

Upon obtaining one of these reflecting stereoscopes as made by the celebrated optician, Mr. Andrew Ross, I found it to be very ill adapted for the purpose of uniting dissimilar pictures, and to be imperfect in various respects. Its imperfections may be thus enumerated:--

Owing to these and other causes, the reflecting stereoscope never came into use, even after photography was capable of supplying binocular pictures.

As a set-off against these disadvantages, it has been averred that in the reflecting stereoscope we can use larger pictures, but this, as we shall shew in a future chapter, is altogether an erroneous assertion.

Having found that the reflecting stereoscope, when intended to produce accurate results, possessed the defects which I have described, and was ill fitted for general use, both from its size and its price, it occurred to me that the union of the dissimilar pictures could be better effected by means of lenses, and that a considerable magnifying power would be thus obtained, without any addition to the instrument.

If we suppose A, B, Fig. 11, to be two portraits,--A a portrait of a gentleman, as seen by the left eye of a person viewing him at the proper distance and in the best position, and B his portrait as seen by the right eye, the purpose of the stereoscope is to place these two pictures, or rather their images, one above the other. The method of doing this by lenses may be explained, to persons not acquainted with optics, in the following manner:--

This instrument consists of a pyramidal box, Fig. 14, blackened inside, and having a lid, CD, for the admission of light when required. The top of the box consists of two parts, in one of which is the right-eye tube, R, containing the lens G, Fig. 13, and in the other the left-eye tube, L, containing the lens H. The two parts which hold the lenses, and which form the top of the box, are often made to slide in grooves, so as to suit different persons whose eyes, placed at R, L, are more or less distant. This adjustment may be made by various pieces of mechanism. The simplest of these is a jointed parallelogram, moved by a screw forming its longer diagonal, and working in nuts fixed on the top of the box, so as to separate the semi-lenses, which follow the movements of the obtuse angles of the parallelogram. The tubes R, L move up and down, in order to suit eyes of different focal lengths, but they are prevented from turning round by a brass pin, which runs in a groove cut through the movable tube. Immediately below the eye-tubes R, L, there should be a groove, G, for the introduction of convex or concave lenses, when required for very long-sighted or short-sighted persons, or for coloured glasses and other purposes.

Many persons experience a difficulty in seeing the portraits single when they first look into a stereoscope, in consequence of their eyes having less power than common over their optic axes, or from their being more or less distant than two and a half inches, the average distance. The two images thus produced frequently disappear in a few minutes, though sometimes it requires a little patience and some practice to see the single image. We have known persons who have lost the power of uniting the images, in consequence of having discontinued the use of the instrument for some months; but they have always acquired it again after a little practice.

If the portraits or other pictures are upon opaque paper or silver-plate, the stereoscope, which is usually held in the left hand, must be inclined so as to allow the light of the sky, or any other light, to illuminate every part of the pictures. If the pictures are on transparent paper or glass, we must shut the lid CD, and hold up the stereoscope against the sky or the artificial light, for which purpose the bottom of the instrument is made of glass finely ground on the outside, or has two openings, the size of each of the binocular pictures, covered with fine paper.

In using the stereoscope the observer should always be seated, and it is very convenient to have the instrument mounted like a telescope, upon a stand, with a weight and pulley for regulating the motion of the lid CD.

The lenticular stereoscope may be constructed of various materials and in different forms. I had them made originally of card-board, tin-plate, wood, and brass; but wood is certainly the best material when cheapness is not an object.

The same objection applies to a form otherwise more convenient, which consists in fixing a cylindrical or square rod of wood or metal to C, the middle point between L and R. The binocular slide having a hole in the middle between the two pictures is moved along this rod to its proper distance from the lenses.

Another form, analogous to this, but without the means of moving the pictures, is shewn in Fig. 16, as made by M. Duboscq. The adjustment is effected by moving the eye-pieces in their respective tubes, and by means of a screw-nut, shewn above the eye-pieces, they can be adapted to eyes placed at different distances from one another. The advantage of this form, if it is an advantage, consists in allowing us to use larger pictures than can be admitted into the box-stereoscope of the usual size. A box-stereoscope, however, of the same size, would have the same property and other advantages not possessed by the open instrument.

Another form of the lenticular stereoscope, under the name of the cosmorama stereoscope, has been adopted by Mr. Knight. The box is rectangular instead of pyramidal, and the adjustment to distinct vision is made by pulling out or pushing in a part of the box, instead of the common and better method of moving each lens separately. The illumination of the pictures is made in the same manner as in the French instrument, called the cosmorama, for exhibiting dissolving views. The lenses are large in surface, which, without any reason, is supposed to facilitate the view of the binocular pictures, and the instrument is supported in a horizontal position upon a stand. There is no contrivance for adjusting the distance of the lenses to the distance between the eyes, and owing to the quantity of light which gets into the interior of the box, the stereoscopic picture is injured by false reflections, and the sensibility of the eyes diminished. The exclusion of all light from the eyes, and of every other light from the picture but that which illuminates it, is essentially necessary to the perfection of stereoscopic vision.

When by means of any of these instruments we have succeeded in forming a single image of the two pictures, we have only, as I have already explained, placed the one picture above the other, in so far as the stereoscope is concerned. It is by the subsequent action of the two eyes that we obtain the desired relief. Were we to unite the two pictures when transparent, and take a copy of the combination by the best possible camera, the result would be a blurred picture, in which none of the points or lines of the one would be united with the points or lines of the other; but were we to look at the combination with both eyes the blurred picture would start into relief, the eyes uniting in succession the separate points and lines of which it is composed.

Before proceeding, however, to this subject, we must explain the manner in which half and quarter lenses unite the two dissimilar pictures.

In the preceding diagram we have not shewn the refraction at the second surface of the lenses, nor the parallelism of the rays when they enter the eye,--facts well known in elementary optics.

ON THE THEORY OF STEREOSCOPIC VISION.

Having, in the preceding chapter, described the ocular, the reflecting, and the lenticular stereoscopes, and explained the manner in which the two binocular pictures are combined or laid upon one another in the last of these instruments, we shall now proceed to consider the theory of stereoscopic vision.

The theory of the stereoscope may be expressed and illustrated in the following manner, without any reference to binocular vision:--

ON THE UNION OF SIMILAR PICTURES IN BINOCULAR VISION.

In continuing our survey of the suspended image another curious phenomenon often presents itself. A part of one, or even two pieces of paper, and generally the whole length of them from the roof to the floor, will retire behind the general plane of the image, as if there were a recess in the wall, or rise above it as if there were a projection, thus displaying on a large scale the imperfection in the workmanship which otherwise it would have been difficult to discover. This phenomenon, or defect in the work, arises from the paper-hanger having cut off too much of the margin of one or more of the adjacent stripes or pieces, or leaving too much of it, so that, in the first case, when the two halves of a flower are joined together, part of the middle of the flower is left out, and hence, when this defective flower is united binocularly with the one on the right hand of it, and the one on the left hand united with the defective one, the united or corresponding portion being at a less distance, will appear farther from the eye than those parts of the suspended image which are composed of complete flowers. The opposite effect will be produced when the two portions of the flowers are not brought together, but separated by a small space. All these phenomena may be seen, though not so conveniently, with a carpet from which the furniture has been removed. We have, therefore, an accurate method of discovering defects in the workmanship of paper-hangers, carpet-makers, painters, and all artists whose profession it is to combine a series of similar patterns or figures to form an uniformly ornamented surface. The smallest defect in the similarity or equality of the figures or lines which compose a pattern, and any difference in the distance of single figures is instantly detected, and what is very remarkable a small inequality of distance in a line perpendicular to the axis of vision, or in one dimension of space, is exhibited in a magnified form at a distance coincident with the axis of vision, and in an opposite dimension of space.

A sheet of Queen's heads may be advantageously used to accustom the eyes to the union of similar figures.

This method of uniting small similar figures is more easily attained than that of doing it by converging the axes to a point between the eye and the object. It puts a very little strain upon the eyes, as we cannot thus unite figures the distance of whose centre is equal to or exceeds 2 1/2 inches, as appears from Fig. 22.

Illusions of both these kinds, however, have recently occurred. A friend to whom I had occasion to shew the experiments, and who is short-sighted, mentioned to me that he had on two occasions been greatly perplexed by the vision of these suspended images. Having taken too much wine, he saw the wall of a papered room suspended near him in the air; and on another occasion, when kneeling, and resting his arms on a cane-bottomed chair, he had fixed his eyes on the carpet, which had accidentally united the two images of the open octagons, and thrown the image of the chair bottom beyond the plane on which he rested his arms.

After hearing my paper on this subject read at the Royal Society of Edinburgh, Professor Christison communicated to me the following interesting case, in which one of the phenomena above described was seen by himself:--"Some years ago," he observes, "when I resided in a house where several rooms are papered with rather formally recurring patterns, and one in particular with stars only, I used occasionally to be much plagued with the wall suddenly standing out upon me, and waving, as you describe, with the movements of the head. I was sensible that the cause was an error as to the point of union of the visual axes of the two eyes; but I remember it sometimes cost me a considerable effort to rectify the error; and I found that the best way was to increase still more the deviation in the first instance. As this accident occurred most frequently while I was recovering from a severe attack of fever, I thought my near-sighted eyes were threatened with some new mischief; and this opinion was justified in finding that, after removal to my present house, where, however, the papers have no very formal pattern, no such occurrence has ever taken place. The reason is now easily understood from your researches."

Other cases of an analogous kind have been communicated to me; and very recently M. Soret of Geneva, in looking through a trellis-work in metal stretched upon a frame, saw the phenomenon represented in Fig. 25, and has given the same explanation of it which I had published long before.

Let AC, BC, Fig. 26, be two lines meeting at C, the plane passing through them being the plane of the paper, and let them be viewed by the eyes successively placed at E?, E?, E?, and E, at different heights in a plane, GMN, perpendicular to the plane of the paper. Let R be the right eye, and L the left eye, and when at E?, let them be strained so as to unite the points A, B. The united image of these points will be seen at the binocular centre D?, and the united lines AC, BC, will have the position D?C. In like manner, when the eye descends to E?, E?, E, the united image D?C will rise and diminish, taking the positions D?C, D?C, DC, till it disappears on the line CM, when the eyes reach M. If the eye deviates from the vertical plane GMN, the united image will also deviate from it, and is always in a plane passing through the common axis of the two eyes and the line GM.

If at any altitude EM, the eye advances towards ACB in the line EG, the binocular centre D will also advance towards ACB in the line EG, and the image DC will rise, and become shorter as its extremity D moves along DG, and, after passing the perpendicular to GE, it will increase in length. If the eye, on the other hand, recedes from ACB in the line GE, the binocular centre D will also recede, and the image DC will descend to the plane CM, and increase in length.

The preceding diagram is, for the purpose of illustration, drawn in a sort of perspective, and therefore does not give the true positions and lengths of the united images. This defect, however, is remedied in Fig. 27, where E, E?, E?, E? is the middle point between the two eyes, the plane GMN being, as before, perpendicular to the plane passing through ACB. Now, as the distance of the eye from G is supposed to be the same, and as AB is invariable as well as the distance between the eyes, the distance of the binocular centres OO, D, D?, D?, D?, P from G, will also be invariable, and lie in a circle ODP, whose centre is G, and whose radius is GO, the point O being determined by the formula

Hence, in order to find the binocular centres D, D?, D?, D?, &c., at any altitude, E, E?, &c., we have only to join EG, E?G, &c., and the points of intersection D, D?, &c., will be the binocular centres, and the lines DC, D?C, &c., drawn to C, will be the real lengths and inclinations of the united images of the lines AC, BC.

When GO is greater than GC there is obviously some angle A, or E?GM, at which D?C is perpendicular to GC.

This takes place when

When O coincides with C, the images CD, CD?, &c., will have the same positions and magnitudes as the chords of the altitudes A of the eyes above the plane GC. In this case the raised or united images will just reach the perpendicular when the eye is in the plane GCM, for since

In the preceding observations we have supposed that the binocular centre D?, &c., is between the eye and the lines AC, BC; but the points A, C, and all the other points of these lines, may be united by fixing the binocular centre beyond AB. Let the eyes, for example, be at E?; then if we unite A, B when the eyes converge to a point, ??, beyond G, we shall have

If in this form of the experiment we fix the binocular centre beyond C, then the united images of AC, and BC descend below GC, and vary in their length, and in their inclination to GC, according to the height of the eye above the plane of ABC, and its distance from AB.

DESCRIPTION OF DIFFERENT STEREOSCOPES.

Although the lenticular stereoscope has every advantage that such an instrument can possess, whether it is wanted for experiments on binocular vision--for assisting the artist by the reproduction of objects in relief, or for the purposes of amusement and instruction, yet there are other forms of it which have particular properties, and which may be constructed without the aid of the optician, and of materials within the reach of the humblest inquirers. The first of these is--

In this form of the instrument, shewn in Fig. 28, the pictures are seen by reflexion from two specula or prisms placed at an angle of 90?, as in Mr. Wheatstone's instrument. In other respects the two instruments are essentially different.

If we substitute for the single reflector MN, two reflectors such as are shewn at M, N, Fig. 30, or a prism P, which gives two internal reflexions, we shall have a general stereoscope, which answers for landscapes and portraits.

The reflectors M, N or P may be fitted up in a conical tube, which has an elliptical section to accommodate two figures at its farther end, the major axis of the ellipse being parallel to the line joining the two eyes.

The double reflecting stereoscope, in both its forms, is a general instrument for portraits and landscapes, and thus possesses properties peculiar to itself.

The reflectors may be glass or metallic specula, or total reflexion prisms.

It is scarcely necessary to state that this stereoscope is applicable only to those diagrams and forms where the one image is the reflected picture of the other.

See Chap. i. pp. 33-36.

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