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ON THE STEREOSCOPE.

INTRODUCTION.

When the artist represents living objects, or groups of them, and delineates buildings or landscapes, or when he copies from statues or models, he produces apparent solidity, and difference of distance from the eye, by light and shade, by the diminished size of known objects as regulated by the principles of geometrical perspective, and by those variations in distinctness and colour which constitute what has been called aerial perspective. But when all these appliances have been used in the most skilful manner, and art has exhausted its powers, we seldom, if ever, mistake the plane picture for the solid which it represents. The two eyes scan its surface, and by their distance-giving power indicate to the observer that every point of the picture is nearly at the same distance from his eye. But if the observer closes one eye, and thus deprives himself of the power of determining differences of distance by the convergency of the optical axes, the relief of the picture is increased. When the pictures are truthful photographs, in which the variations of light and shade are perfectly represented, a very considerable degree of relief and solidity is thus obtained; and when we have practised for a while this species of monocular vision, the drawing, whether it be of a statue, a living figure, or a building, will appear to rise in its different parts from the canvas, though only to a limited extent.

In these observations we refer chiefly to ordinary drawings held in the hand, or to portraits and landscapes hung in rooms and galleries, where the proximity of the observer, and lights from various directions, reveal the surface of the paper or the canvas; for in panoramic and dioramic representations, where the light, concealed from the observer, is introduced in an oblique direction, and where the distance of the picture is such that the convergency of the optic axes loses much of its distance-giving power, the illusion is very perfect, especially when aided by correct geometrical and aerial perspective. But when the panorama is illuminated by light from various directions, and the slightest motion imparted to the canvas, its surface becomes distinctly visible, and the illusion instantly disappears.

If we close one eye while looking at photographic pictures in the stereoscope, the perception of relief is still considerable, and approximates to the binocular representation; but when the pictures are mere diagrams consisting of white lines upon a black ground, or black lines upon a white ground, the relief is instantly lost by the shutting of the eye, and it is only with such binocular pictures that we see the true power of the stereoscope.

As an amusing and useful instrument the stereoscope derives much of its value from photography. The most skilful artist would have been incapable of delineating two equal representations of a figure or a landscape as seen by two eyes, or as viewed from two different points of sight; but the binocular camera, when rightly constructed, enables us to produce and to multiply photographically the pictures which we require, with all the perfection of that interesting art. With this instrument, indeed, even before the invention of the Daguerreotype and the Talbotype, we might have exhibited temporarily upon ground-glass, or suspended in the air, the most perfect stereoscopic creations, by placing a Stereoscope behind the two dissimilar pictures formed by the camera.

HISTORY OF THE STEREOSCOPE.

This palpable truth was known and published by ancient mathematicians. Euclid knew it more than two thousand years ago, as may be seen in the 26th, 27th, and 28th theorems of his Treatise on Optics. In these theorems he shews that the part of a sphere seen by both eyes, and having its diameter equal to, or greater or less than the distance between the eyes, is equal to, and greater or less than a hemisphere; and having previously shewn in the 23d and 24th theorems how to find the part of any sphere that is seen by one eye at different distances, it follows, from constructing his figure, that each eye sees different portions of the sphere, and that it is seen by both eyes by the union of these two dissimilar pictures.

In illustrating the views of Galen on the dissimilarity of the three pictures which are requisite in binocular vision, he employs a much more distinct diagram than that which is given by the Greek physician. "Let A," he says, "be the pupil of the right eye, B that of the left, and DC the body to be seen. When we look at the object with both eyes we see DC, while with the left eye we see EF, and with the right eye GH. But if it is seen with one eye, it will be seen otherwise, for when the left eye B is shut, the body CD, on the left side, will be seen in HG; but when the right eye is shut, the body CD will be seen in FE, whereas, when both eyes are opened at the same time, it will be seen in CD." These results are then explained by copying the passage from Galen, in which he supposes the observer to repeat these experiments when he is looking at a solid column.

In looking at this diagram, we recognise at once not only the principle, but the construction of the stereoscope. The double stereoscopic picture or slide is represented by HE; the right-hand picture, or the one seen by the right eye, by HF; the left-hand picture, or the one seen by the left eye, by GE; and the picture of the solid column in full relief by DC, as produced midway between the other two dissimilar pictures, HF and GE, by their union, precisely as in the stereoscope.

Galen, therefore, and the Neapolitan philosopher, who has employed a more distinct diagram, certainly knew and adopted the fundamental principle of the stereoscope; and nothing more was required, for producing pictures in full relief, than a simple instrument for uniting HF and GE, the right and left hand dissimilar pictures of the column.

The subject of binocular vision was successfully studied by Francis Aguillon or Aguilonius, a learned Jesuit, who published his Optics in 1613. In the first book of his work, where he is treating of the vision of solids of all forms, he has some difficulty in explaining, and fails to do it, why the two dissimilar pictures of a solid, seen by each eye, do not, when united, give a confused and imperfect view of it. This discussion is appended to the demonstration of the theorem, "that when an object is seen with two eyes, two optical pyramids are formed whose common base is the object itself, and whose vertices are in the eyes," and is as follows:--

In FIG. 1, AHF is the optical pyramid seen by the eye A, and BGE the optical pyramid seen by the eye B.

"When one object is seen with two eyes, the angles at the vertices of the optical pyramids are not always equal, for beside the direct view in which the pyramids ought to be equal, into whatever direction both eyes are turned, they receive pictures of the object under inequal angles, the greatest of which is that which is terminated at the nearer eye, and the lesser that which regards the remoter eye. This, I think, is perfectly evident; but I consider it as worthy of admiration, how it happens that bodies seen by both eyes are not all confused and shapeless, though we view them by the optical axes fixed on the bodies themselves. For greater bodies, seen under greater angles, appear lesser bodies under lesser angles. If, therefore, one and the same body which is in reality greater with one eye, is seen less on account of the inequality of the angles in which the pyramids are terminated, the body itself must assuredly be seen greater or less at the same time, and to the same person that views it; and, therefore, since the images in each eye are dissimilar the representation of the object must appear confused and disturbed to the primary sense."

These angles are equal in this diagram and in the vision of a sphere, but they are inequal in other bodies.

"This view of the subject," he continues, "is certainly consistent with reason, but, what is truly wonderful is, that it is not correct, for bodies are seen clearly and distinctly with both eyes when the optic axes are converged upon them. The reason of this, I think, is, that the bodies do not appear to be single, because the apparent images, which are formed from each of them in separate eyes, exactly coalesce, but because the common sense imparts its aid equally to each eye, exerting its own power equally in the same manner as the eyes are converged by means of their optical axes. Whatever body, therefore, each eye sees with the eyes conjoined, the common sense makes a single notion, not composed of the two which belong to each eye, but belonging and accommodated to the imaginative faculty to which it assigns it. Though, therefore, the angles of the optical pyramids which proceed from the same object to the two eyes, viewing it obliquely, are inequal, and though the object appears greater to one eye and less to the other, yet the same difference does not pass into the primary sense if the vision is made only by the axes, as we have said, but if the axes are converged on this side or on the other side of the body, the image of the same body will be seen double, as we shall shew in Book iv., on the fallacies of vision, and the one image will appear greater and the other less on account of the inequality of the angles under which they are seen."

In his fourth and very interesting book, on the fallacies of distance, magnitude, position, and figure, Aguilonius resumes the subject of the vision of solid bodies. He repeats the theorems of Euclid and Gassendi on the vision of the sphere, shewing how much of it is seen by each eye, and by both, whatever be the size of the sphere, and the distance of the observer. At the end of the theorems, in which he demonstrates that when the diameter of the sphere is equal to the distance between the eyes we see exactly a hemisphere, he gives the annexed drawing of the mode in which the sphere is seen by each eye, and by both. In this diagram E is the right eye and D the left, CHFI the section of that part of the sphere BC which is seen by the right eye E, BHGA the section of the part which is seen by the left eye D, and BLC the half of the great circle which is the section of the sphere as seen by both eyes. These three pictures of the solids are all dissimilar. The right eye E does not see the part BLCIF of the sphere; the left eye does not see the part BLCGA, while the part seen with both eyes is the hemisphere BLCGF, the dissimilar segments BFG, CGF being united in its vision.

After demonstrating his theorems on the vision of spheres with one and both eyes, Aguilonius informs us, before he proceeds to the vision of cylinders, that it is agreed upon that it is not merely true with the sphere, but also with the cylinder, the cone, and all bodies whatever, that the part which is seen is comprehended by tangent rays, such as EB, EC for the right eye, in Fig. 3. "For," says he, "since these tangent lines are the outermost of all those which can be drawn to the proposed body from the same point, namely, that in which the eye is understood to be placed, it clearly follows that the part of the body which is seen must be contained by the rays touching it on all sides. For in this part no point can be found from which a right line cannot be drawn to the eye, by which the correct visible form is brought out."

It is obvious that a complete hemisphere is not seen with both eyes.

Id., p. 313.

Id., vol. i. p. 48, Fig. 196.

In the different passages which we have quoted from Mr. Wheatstone's paper, and in the other parts of it which relate to binocular vision, he is obviously halting between truth and error, between theories which he partly believes, and ill-observed facts which he cannot reconcile with them. According to him, certain truths "may be supposed" to be true, and other truths may be "in some degree true," but "not entirely so;" and thus, as he confesses, the problem of binocular and stereoscopic vision "is indeed one of great complexity," of which "he will not attempt at present to give the complete solution." If he had placed a proper reliance on the law of visible direction which he acknowledges I have established, and "with which," he says, "the laws of visible direction for binocular vision ought to contain nothing inconsistent," he would have seen the impossibility of the two eyes uniting two lines of inequal length; and had he believed in the law of distinct vision he would have seen the impossibility of the two eyes obtaining single vision of any more than one point of an object at a time. These laws of vision are as rigorously true as any other physical laws,--as completely demonstrated as the law of gravity in Astronomy, or the law of the Sines in Optics; and the moment we allow them to be tampered with to obtain an explanation of physical puzzles, we convert science into legerdemain, and philosophers into conjurors.

Such was the state of our stereoscopic knowledge in 1838, after the publication of Mr. Wheatstone's interesting and important paper. Previous to this I communicated to the British Association at Newcastle, in August 1838, a paper, in which I established the law of visible direction already mentioned, which, though it had been maintained by preceding writers, had been proved by the illustrious D'Alembert to be incompatible with observation, and the admitted anatomy of the human eye. At the same meeting Mr. Wheatstone exhibited his stereoscopic apparatus, which gave rise to an animated discussion on the theory of the instrument. Dr. Whewell maintained that the retina, in uniting, or causing to coalesce into a single resultant impression two lines of different lengths, had the power either of contracting the longest, or lengthening the shortest, or what might have been suggested in order to give the retina only half the trouble, that it contracted the long line as much as it expanded the short one, and thus caused them to combine with a less exertion of muscular power! In opposition to these views, I maintained that the retina, a soft pulpy membrane which the smallest force tears in pieces, had no such power,--that a hypothesis so gratuitous was not required, and that the law of visible direction afforded the most perfect explanation of all the stereoscopic phenomena.

It had never been proposed to apply the reflecting stereoscope to portraiture or sculpture, or, indeed, to any useful purpose; but it was very obvious, after the discovery of the Daguerreotype and Talbotype, that binocular drawings could be taken with such accuracy as to exhibit in the stereoscope excellent representations in relief, both of living persons, buildings, landscape scenery, and every variety of sculpture. In order to shew its application to the most interesting of these purposes, Dr. Adamson of St. Andrews, at my request, executed two binocular portraits of himself, which were generally circulated and greatly admired. This successful application of the principle to portraiture was communicated to the public, and recommended as an art of great domestic interest.

December 28, 1550.

"In his last visit to Paris, Sir David Brewster intrusted the models of his stereoscope to M. Jules Duboscq, son-in-law and successor of M. Soleil, and whose intelligence, activity, and affability will extend the reputation of the distinguished artists of the Rue de l'Odeon, 35. M. Jules Duboscq has set himself to work with indefatigable ardour. Without requiring to have recourse to the binocular camera, he has, with the ordinary Daguerreotype apparatus, procured a great number of dissimilar pictures of statues, bas-reliefs, and portraits of celebrated individuals, &c. His stereoscopes are constructed with more elegance, and even with more perfection, than the original English instruments, and while he is shewing their wonderful effects to natural philosophers and amateurs who have flocked to him in crowds, there is a spontaneous and unanimous cry of admiration."

"Nous avons eu tort mille fois d'accorder ? notre illustre ami, Sir David Brewster, l'invention du st?r?oscope par r?fraction. M. Wheatstone, en effet, a mis entre nos mains une lettre dat?e, le croirait on, du 27 Septembre 1838, dans lequel nous avons l? ces mots ?crits par l'illustre savant Ecossais: 'I have also stated that you promised to order for me your stereoscope, both with reflectors and PRISMS. J'ai aussi dit que vous aviez promis de commander pour moi votre st?r?oscope, celui avec r?flecteurs et celui avec prismes.' Le st?r?oscope par r?fraction est donc, aussi bien que le st?r?oscope par r?flexion, le st?r?oscope de M. Wheatstone, qui l'avait invent? en 1838, et le faisait construire ? cette ?poque pour Sir David Brewster lui-m?me. Ce que Sir David Brewster a imagin?e, et c'est une id?e tr?s ing?nieuse, dont M. Wheatstone ne lui disput?t jamais la gloire, c'est de former les deux prismes du st?r?oscope par r?fraction avec les deux moiti?s d'une m?me lentille."

Vol. v. livre viii. p. 241.

Mr. Andrew Ross, the celebrated optician!

"DEAR SIR,--In reply to yours of the 11th instant, I beg to state that I never supplied you with a stereoscope in which prisms were employed in place of plane mirrors. I have a perfect recollection of being called upon either by yourself or Professor Wheatstone, some fourteen years since, to make achromatized prisms for the above instrument. I also recollect that I did not proceed to manufacture them in consequence of the great bulk of an achromatized prism, with reference to their power of deviating a ray of light, and at that period glass sufficiently free from striae could not readily be obtained, and was consequently very high-priced.--I remain, &c. &c.

"ANDREW ROSS. "To Sir David Brewster."

Upon the receipt of this letter I transmitted a copy of it to the Abb? Moigno, to shew him how he had been misled into the statement, "that Mr. Wheatstone had caused a stereoscope with prisms to be constructed for me;" but neither he nor Mr. Wheatstone have felt it their duty to withdraw that erroneous statement.

Such is a brief history of the lenticular stereoscope, of its introduction into Paris and London, and of its application to portraiture and sculpture. It is now in general use over the whole world, and it has been estimated that upwards of half a million of these instruments have been sold. A Stereoscope Company has been established in London for the manufacture and sale of the lenticular stereoscope, and for the production of binocular pictures for educational and other purposes. Photographers are now employed in every part of the globe in taking binocular pictures for the instrument,--among the ruins of Pompeii and Herculaneum--on the glaciers and in the valleys of Switzerland--among the public monuments in the Old and the New World--amid the shipping of our commercial harbours--in the museums of ancient and modern life--in the sacred precincts of the domestic circle--and among those scenes of the picturesque and the sublime which are so affectionately associated with the recollection of our early days, and amid which, even at the close of life, we renew, with loftier sentiments and nobler aspirations, the youth of our being, which, in the worlds of the future, is to be the commencement of a longer and a happier existence.

No. 54, Cheapside, and 313, Oxford Street. The prize of twenty guineas which they offered for the best short popular treatise on the Stereoscope, has been adjudged to Mr. Lonie, Teacher of Mathematics in the Madras Institution, St. Andrews. The second prize was given to the Rev. R. Graham, Abernyte, Perthshire.

ON MONOCULAR VISION, OR VISION WITH ONE EYE.

In order to understand the theory and construction of the stereoscope we must be acquainted with the general structure of the eye, with the mode in which the images of visible objects are formed within it, and with the laws of vision by means of which we see those objects in the position which they occupy, that is, in the direction and at the distance at which they exist.

But though we are ignorant of the manner in which the mind takes cognizance through the brain of the images on the retina, and may probably never know it, we can determine experimentally the laws by which we obtain, through their images on the retina, a knowledge of the direction, the position, and the form of external objects.

ON BINOCULAR VISION, OR VISION WITH TWO EYES.

We have already seen, in the history of the stereoscope, that in the binocular vision of objects, each eye sees a different picture of the same object. In order to prove this, we require only to look attentively at our own hand held up before us, and observe how some parts of it disappear upon closing each eye. This experiment proves, at the same time, in opposition to the opinion of Baptista Porta, Tacquet, and others, that we always see two pictures of the same object combined in one. In confirmation of this fact, we have only to push aside one eye, and observe the image which belongs to it separate from the other, and again unite with it when the pressure is removed.

It might have been supposed that an object seen by both eyes would be seen twice as brightly as with one, on the same principle as the light of two candles combined is twice as bright as the light of one. That this is not the case has been long known, and Dr. Jurin has proved by experiments, which we have carefully repeated and found correct, that the brightness of objects seen with two eyes is only ?/??th part greater than when they are seen with one eye. The cause of this is well known. When both eyes are used, the pupils of each contract so as to admit the proper quantity of light; but the moment we shut the right eye, the pupil of the left dilates to nearly twice its size, to compensate for the loss of light arising from the shutting of the other.

This variation of the pupil is mentioned by Bacon.

This beautiful provision to supply the proper quantity of light when we can use only one eye, answers a still more important purpose, which has escaped the notice of optical writers. In binocular vision, as we have just seen, certain parts of objects are seen with both eyes, and certain parts only with one; so that, if the parts seen with both eyes were twice as bright, or even much brighter than the parts seen with one, the object would appear spotted, from the different brightness of its parts. In Fig. 6, for example, the areas BFI and CGI, the former of which is seen only by the left eye, D, and the latter only by the right eye, E, and the corresponding areas on the other side of the sphere, would be only half as bright as the portion FIGH, seen with both eyes, and the sphere would have a singular appearance.

It has long been, and still is, a vexed question among philosophers, how we see objects single with two eyes. Baptista Porta, Tacquet, and others, got over the difficulty by denying the fact, and maintaining that we use only one eye, while other philosophers of distinguished eminence have adopted explanations still more groundless. The law of visible direction supplies us with the true explanation.

Since objects are seen in relief by the apparent union of two dissimilar plane pictures of them formed in each eye, it was a supposition hardly to be overlooked, that if we could delineate two plane pictures of a solid object, as seen dissimilarly with each eye, and unite their images by the convergency of the optical axes, we should see the solid of which they were the representation. The experiment was accordingly made by more than one person, and was found to succeed; but as few have the power, or rather the art, of thus converging their optical axes, it became necessary to contrive an instrument for doing this.

The first contrivances for this purpose were, as we have already stated, made by Mr. Elliot and Mr. Wheatstone. A description of these, and of others better fitted for the purpose, will be found in the following chapter.

DESCRIPTION OF THE OCULAR, THE REFLECTING, AND THE LENTICULAR STEREOSCOPES.

Although it is by the combination of two plane pictures of an object, as seen by each eye, that we see the object in relief, yet the relief is not obtained from the mere combination or superposition of the two dissimilar pictures. The superposition is effected by turning each eye upon the object, but the relief is given by the play of the optic axes in uniting, in rapid succession, similar points of the two pictures, and placing them, for the moment, at the distance from the observer of the point to which the axes converge. If the eyes were to unite the two images into one, and to retain their power of distinct vision, while they lost the power of changing the position of their optic axes, no relief would be produced.

This is equally true when we unite two dissimilar photographic pictures by fixing the optic axes on a point nearer to or farther from the eye. Though the pictures apparently coalesce, yet the relief is given by the subsequent play of the optic axes varying their angles, and converging themselves successively upon, and uniting, the similar points in each picture that correspond to different distances from the observer.

As very few persons have the power of thus uniting, by the eyes alone, the two dissimilar pictures of the object, the stereoscope has been contrived to enable them to combine the two pictures, but it is not the stereoscope, as has been imagined, that gives the relief. The instrument is merely a substitute for the muscular power which brings the two pictures together. The relief is produced, as formerly, solely by the subsequent play of the optic axes. If the relief were the effect of the apparent union of the pictures, we should see it by looking with one eye at the combined binocular pictures--an experiment which could be made by optical means; but we should look for it in vain. The combined pictures would be as flat as the combination of two similar pictures. These experiments require to be made with a thorough knowledge of the subject, for when the eyes are converged on one point of the combined picture, this point has the relief, or distance from the eye, corresponding to the angle of the optic axes, and therefore the adjacent points are, as it were, brought into a sort of indistinct relief along with it; but the optical reader will see at once that the true binocular relief cannot be given to any other parts of the picture, till the axes of the eyes are converged upon them. These views will be more readily comprehended when we have explained, in a subsequent chapter, the theory of stereoscopic vision.

If we place the two pictures as in Fig. 9, which is the position they had in Mr. Elliot's box, and unite them, by looking at a point beyond them we shall also observe the stereoscopic relief. In this position Mr. Elliot saw the relief without any effort, and even without being conscious that he was not viewing the pictures under ordinary vision. This tendency of the optic axes to a distant convergency is so rare that I have met with it only in one person.

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.

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