THE STEREOSCOPE
ITS HISTORY, THEORY, AND CONSTRUCTION

WITH ITS APPLICATION TO THE FINE AND USEFUL ARTS
AND TO EDUCATION.

BY
SIR DAVID BREWSTER,
K.H., D.C.L., F.R.S., M.R.I.A.,

VICE-PRESIDENT OF THE ROYAL SOCIETY OF EDINBURGH, ONE OF THE EIGHT
ASSOCIATES OF THE IMPERIAL INSTITUTE OF FRANCE, OFFICER OF THE
LEGION OF HONOUR, CHEVALIER OF THE PRUSSIAN ORDER OF MERIT,
HONORARY OR CORRESPONDING MEMBER OF THE ACADEMIES
OF PETERSBURGH, VIENNA, BERLIN, COPENHAGEN,
STOCKHOLM, BRUSSELS, GÖTTINGEN, MODENA,
AND OF THE NATIONAL INSTITUTE OF
WASHINGTON, ETC.

WITH FIFTY WOOD ENGRAVINGS.

LONDON:
JOHN MURRAY, ALBEMARLE STREET.
1856.

[The Right of Translation is reserved.]

EDINBURGH:
T. CONSTABLE, PRINTER TO HER MAJESTY.

CONTENTS

ON THE STEREOSCOPE.

INTRODUCTION.

The Stereoscope, a word derived from στέρεος, solid, and σκόπειν, to see, is an optical instrument, of modern invention, for representing, in apparent relief and solidity, all natural objects and all groups or combinations of objects, by uniting into one image two plane representations of these objects or groups as seen by each eye separately. In its most general form the Stereoscope is a binocular instrument, that is, is applied to both eyes; but in two of its forms it is monocular, or applied only to one eye, though the use of the other eye, without any instrumental aid, is necessary in the combination of the two plane pictures, or of one plane picture and its reflected image. The Stereoscope, therefore, cannot, like the telescope and microscope, be used by persons who have lost the use of one eye, and its remarkable effects cannot be properly appreciated by those whose eyes are not equally good.

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.

The effects of stereoscopic representation are of a very different kind, and are produced by a very different cause. The singular relief which it imparts is independent of light and shade, and of geometrical as well as of aerial perspective. These important accessories, so necessary in the visual perception of the drawings in plano, avail nothing in the evolution of their relievo, or third dimension. They add, doubtless, to the beauty of the binocular pictures; but the stereoscopic creation is due solely to the superposition of the two plane pictures by the optical apparatus employed, and to the distinct and instantaneous perception of distance by the convergency of the optic axes upon the similar points of the two pictures which the stereoscope has united.

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.

CHAPTER I.
HISTORY OF THE STEREOSCOPE.

When we look with both eyes open at a sphere, or any other solid object, we see it by uniting into one two pictures, one as seen by the right, and the other as seen by the left eye. If we hold up a thin book perpendicularly, and midway between both eyes, we see distinctly the back of it and both sides with the eyes open. When we shut the right eye we see with the left eye the back of the book and the left side of it, and when we shut the left eye we see with the right eye the back of it and the right side. The picture of the book, therefore, which we see with both eyes, consists of two dissimilar pictures united, namely, a picture of the back and the left side of the book as seen by the left eye, and a picture of the back and right side of the book as seen by the right eye.

In this experiment with the book, and in all cases where the object is near the eye, we not only see different pictures of the same object, but we see different things with each eye. Those who wear spectacles see only the left-hand spectacle-glass with the left eye, on the left side of the face, while with the right eye they see only the right-hand spectacle-glass on the right side of the face, both glasses of the spectacles being seen united midway between the eyes, or above the nose, when both eyes are open. It is, therefore, a fact well known to every person of common sagacity that the pictures of bodies seen by both eyes are formed by the union of two dissimilar pictures formed by each.

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.[1] 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.

More than fifteen hundred years ago, the celebrated physician Galen treated the subject of binocular vision more fully than Euclid. In the twelfth chapter of the tenth book of his work, On the use of the different parts of the Human Body, he has described with great minuteness the various phenomena which are seen when we look at bodies with both eyes, and alternately with the right and the left. He shews, by diagrams, that dissimilar pictures of a body are seen in each of these three modes of viewing it; and, after finishing his demonstration, he adds,—

“But if any person does not understand these demonstrations by means of lines, he will finally give his assent to them when he has made the following experiment:—Standing near a column, and shutting each of the eyes in succession;—when the right eye is shut, some of those parts of the column which were previously seen by the right eye on the right side of the column, will not now be seen by the left eye; and when the left eye is shut, some of those parts which were formerly seen by the left eye on the left side of the column, will not now be seen by the right eye. But when we, at the same time, open both eyes, both these will be seen, for a greater part is concealed when we look with either of the two eyes, than when we look with both at the same time.”[2]

In such distinct and unambiguous terms, intelligible to the meanest capacity, does this illustrious writer announce the fundamental law of binocular vision—the grand principle of the Stereoscope, namely, that the picture of the solid column which we see with both eyes is composed of two dissimilar pictures, as seen by each eye separately. As the vision of the solid column, therefore, was obtained by the union of these dissimilar pictures, an instrument only was wanted to take such pictures, and another to combine them. The Binocular Photographic Camera was the one instrument, and the Stereoscope the other.

The subject of binocular vision was studied by various optical writers who have flourished since the time of Galen. Baptista Porta, one of the most eminent of them, repeats, in his work On Refraction, the propositions of Euclid on the vision of a sphere with one and both eyes, and he cites from Galen the very passage which we have given above on the dissimilarity of the three pictures seen by each eye and by both. Believing that we see only with one eye at a time, he denies the accuracy of Euclid’s theorems, and while he admits the correctness of the observations of Galen, he endeavours to explain them upon other principles.

Fig. 1.

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.[3]

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.

Fig. 2.

In the treatise on painting which he left behind him in MS.,[4] Leonardo da Vinci has made a distinct reference to the dissimilarity of the pictures seen by each eye as the reason why “a painting, though conducted with the greatest art, and finished to the last perfection, both with regard to its contours, its lights, its shadows, and its colours, can never shew a relievo equal to that of the natural objects, unless these be viewed at a distance and with a single eye,”[5] which he thus demonstrates. “If an object c be viewed by a single eye at a, all objects in the space behind it—included, as it were, in a shadow ecf, cast by a candle at a—are invisible to an eye at a; but when the other eye at b is opened, part of these objects become visible to it; those only being hid from both eyes that are included, as it were, in the double shadow cd, cast by two lights at a and b and terminated in d; the angular space edg, beyond d, being always visible to both eyes. And the hidden space cd is so much the shorter as the object c is smaller and nearer to the eyes. Thus he observes that the object c, seen with both eyes, becomes, as it were, transparent, according to the usual definition of a transparent thing, namely, that which hides nothing beyond it. But this cannot happen when an object, whose breadth is bigger than that of the pupil, is viewed by a single eye. The truth of this observation is, therefore, evident, because a painted figure intercepts all the space behind its apparent place, so as to preclude the eyes from the sight of every part of the imaginary ground behind it. Hence,” continues Dr. Smith, “we have one help to distinguish the place of a near object more accurately with both eyes than with one, inasmuch as we see it more detached from other objects beyond it, and more of its own surface, especially if it be roundish.”

We have quoted this passage, not from its proving that Leonardo da Vinci was acquainted with the fact that each eye, a, b, sees dissimilar pictures of the sphere c, but because it has been referred to by Mr. Wheatstone as the only remark on the subject of binocular vision which he could find “after looking over the works of many authors who might be expected to have made them.” We think it quite clear, however, that the Italian artist knew as well as his commentator Dr. Smith, that each eye, a and b, sees dissimilar parts of the sphere c. It was not his purpose to treat of the binocular pictures of c, but his figure proves their dissimilarity.

The subject of binocular vision was successfully studied by Francis Aguillon or Aguilonius,[6] 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, (de genere illorum quæ τὰ στέρεα [ta sterea] nuncupantur,) 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,”[7] and is as follows:—

“When one object is seen with two eyes, the angles at the vertices of the optical pyramids (namely, haf, gbe, [Fig. 1]) 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, (namely, haf, gbe,[8]) 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 (minime sibi congruunt) the representation of the object must appear confused and disturbed (confusa ac perturbata) to the primary sense.”

“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, (sibi mutuo exacte congruunt,) 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 (the common sense) 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.”[9]

Such is Aguilonius’s theory of binocular vision, and of the union of the two dissimilar pictures in each eye by which a solid body is seen. It is obviously more correct than that of Dr. Whewell and Mr. Wheatstone. Aguilonius affirms it to be contrary to reason that two dissimilar pictures can be united into a clear and distinct picture, as they are actually found to be, and he is therefore driven to call in the aid of what does not exist, a common sense, which rectifies the picture. Dr. Whewell and Mr. Wheatstone have cut the Gordian knot by maintaining what is impossible, that in binocular and stereoscopic vision a long line is made to coincide with a short one, and a large surface with a small one; and in place of conceiving this to be done by a common sense overruling optical laws, as Aguilonius supposes, they give to the tender and pulpy retina, the recipient of ocular pictures, the strange power of contracting or expanding itself in order to equalize inequal lines and inequal surfaces!

Fig. 3.

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.[10] 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.[11]

After demonstrating his theorems on the vision of spheres with one and both eyes,[12] 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.”[13]

Optical writers who lived after the time of Aguilonius seem to have considered the subject of binocular vision as exhausted in his admirable work. Gassendi,[14] though he treats the subject very slightly, and without any figures, tells us that we see the left side of the nose with the left eye, and the right side of it with the right eye,—two pictures sufficiently dissimilar. Andrew Tacquet,[15] though he quotes Aguilonius and Gassendi on the subject of seeing distances with both eyes, says nothing on the binocular vision of solids; and Smith, Harris, and Porterfield, only touch upon the subject incidentally. In commenting on the passage which we have already quoted from Leonardo da Vinci, Dr. Smith says, “Hence we have one help to distinguish the place of a near object more accurately with both eyes than with one, inasmuch as we see it more detached from other objects beyond it, and more of its own surface, especially if it be roundish.”[16] If any farther evidence were required that Dr. Smith was acquainted with the dissimilarity of the images of a solid seen by each eye, it will be found in his experiment with a “long ruler placed between the eyebrows, and extended directly forward with its flat sides, respecting the right hand and the left.” “By directing the eyes to a remote object,” he adds, “the right side of the ruler seen by the right eye will appear on the left hand, and the left side on the right hand, as represented in the figure.”[17]

In his Treatise on Optics, published in 1775, Mr. Harris, when speaking of the visible or apparent figures of objects, observes, that “we have other helps for distinguishing prominences of small parts besides those by which we distinguish distances in general, as their degrees of light and shade, and the prospect we have round them.” And by the parallax, on account of the distance betwixt our eyes, we can distinguish besides the front part of the two sides of a near object not thicker than the said distance, and this gives a visible relievo to such objects, which helps greatly to raise or detach them from the plane in which they lie. Thus the nose on a face is the more remarkably raised by our seeing both sides of it at once.“[18] That is, the relievo is produced by the combination of the two dissimilar pictures given by each eye.

Without referring to a figure given by Dr. Porterfield, in which he actually gives drawings of an object as seen by each eye in binocular vision,[19] the one exhibiting the object as seen endwise by the right eye, and the other the same object as seen laterally by the left eye, we may appeal to the experience of every optical, or even of every ordinary observer, in support of the fact, that the dissimilarity of the pictures in each eye, by which we see solid objects, is known to those who have never read it in Galen, Porta, or Aguilonius. Who has not observed the fact mentioned by Gassendi and Harris, that their left eye sees only the left side of their nose, and their right eye the right side, two pictures sufficiently dissimilar? Who has not noticed, as well as Dr. Smith, that when they look at any thin, flat body, such as a thin book, they see both sides of it—the left eye only the left side of it, and the right eye only the right side, while the back, or the part nearest the face, is seen by each eye, and both the sides and the back by both the eyes? What student of perspective is there—master or pupil, male or female—who does not know, as certainly as he knows his alphabet, that the picture of a chair or table, or anything else, drawn from one point of sight, or as seen by one eye placed in that point, is necessarily dissimilar to another drawing of the same object taken from another point of sight, or as seen by the other eye placed in a point 2½ inches distant from the first? If such a person is to be found, we might then admit that the dissimilarity of the pictures in each eye was not known to every student of perspective.[20]

Such was the state of our knowledge of binocular vision when two individuals, Mr. Wheatstone, and Mr. Elliot, now Teacher of Mathematics in Edinburgh, were directing their attention to the subject. Mr. Wheatstone communicated an important paper on the Physiology of Vision to the British Association at Newcastle in August 1838, and exhibited an instrument called a Stereoscope, by which he united the two dissimilar pictures of solid bodies, the τὰ στέρεα, (ta sterea of Aguilonius,) and thus reproduced, as it were, the bodies themselves. Mr. Wheatstone’s paper on the subject, which had been previously read at the Royal Society on the 21st of June, was printed in their Transactions for 1838.[21]

Mr. Elliot was led to the study of binocular vision in consequence of having written an Essay, so early as 1823, for the Class of Logic in the University of Edinburgh, “On the means by which we obtain our knowledge of distances by the Eye.” Ever since that date he was familiar with the idea, that the relief of solid bodies seen by the eye was produced by the union of the dissimilar pictures of them in each eye, but he never imagined that this idea was his own, believing that it was known to every student of vision. Previous to or during the year 1834, he had resolved to construct an instrument for uniting two dissimilar pictures, or of constructing a stereoscope; but he delayed doing this till the year 1839, when he was requested to prepare an original communication for the Polytechnic Society, which had been recently established in Liverpool. He was thus induced to construct the instrument which he had projected, and he exhibited it to his friends, Mr. Richard Adie, optician, and Mr. George Hamilton, lecturer on chemistry in Liverpool, who bear testimony to its existence at that date. This simple stereoscope, without lenses or mirrors, consisted of a wooden box 18 inches long, 7 broad, and 4½ deep, and at the bottom of it, or rather its farther end, was placed a slide containing two dissimilar pictures of a landscape as seen by each eye. Photography did not then exist, to enable Mr. Elliot to procure two views of the same scene, as seen by each eye, but he drew the transparency of a landscape with three distances. The first and most remote was the moon and the sky, and a stream of water from which the moon was reflected, the two moons being placed nearly at the distance of the two eyes, or 2½ inches, and the two reflected moons at the same distance. The second distance was marked by an old cross about a hundred feet off; and the third distance by the withered branch of a tree, thirty feet from the observer. In the right-hand picture, one arm of the cross just touched the disc of the moon, while, in the left-hand one, it projected over one-third of the disc. The branch of the tree touched the outline of a distant hill in the one picture, but was “a full moon’s-breadth” from it on the other. When these dissimilar pictures were united by the eyes, a landscape, certainly a very imperfect one, was seen in relief, composed of three distances.

Owing, no doubt, to the difficulty of procuring good binocular pictures, Mr. Elliot did not see that his contrivance would be very popular, and therefore carried it no farther. He had never heard of Mr. Wheatstone’s stereoscope till he saw his paper on Vision reprinted in the Philosophical Magazine for March 1852, and having perused it, he was convinced not only that Mr. Wheatstone’s theory of the instrument was incorrect, but that his claim to the discovery of the dissimilarity of the images in each eye had no foundation. He was, therefore, led to communicate to the same journal the fact of his having himself, thirteen years before, constructed and used a stereoscope, which was still in his possession. In making this claim, Mr. Elliot had no intention of depriving Mr. Wheatstone of the credit which was justly due to him; and as the claim has been publicly made, we have described the nature of it as a part of scientific history.

In Mr. Wheatstone’s ingenious paper of 1838, the subject of binocular vision is treated at considerable length. He gives an account of the opinions of previous writers, referring repeatedly to the works of Aguilonius, Gassendi, and Baptista Porta, in the last of which the views of Galen are given and explained. In citing the passage which we have already quoted from Leonardo da Vinci, and inserting the figure which illustrates it, he maintains that Leonardo da Vinci was not aware “that the object (c in [Fig. 2]) presented a different appearance to each eye.” “He failed,” he adds, “to observe this, and no subsequent writer, to my knowledge, has supplied the omission. The projection of two obviously dissimilar pictures on the two retinæ, when a single object is viewed, while the optic axes converge, must therefore be regarded as a new fact in the theory of vision.” Now, although Leonardo da Vinci does not state in so many words that he was aware of the dissimilarity of the two pictures, the fact is obvious in his own figure, and he was not led by his subject to state the fact at all. But even if the fact had not stared him in the face he must have known it from the Optics of Euclid and the writings of Galen, with which he could not fail to have been well acquainted. That the dissimilarity of the two pictures is not a new fact we have already placed beyond a doubt. The fact is expressed in words, and delineated in drawings, by Aguilonius and Baptista Porta. It was obviously known to Dr. Smith, Mr. Harris, Dr. Porterfield, and Mr. Elliot, before it was known to Mr. Wheatstone, and we cannot understand how he failed to observe it in works which he has so often quoted, and in which he professes to have searched for it.

This remarkable property of binocular vision being thus clearly established by preceding writers, and admitted by himself, as the cause of the vision of solidity or distance, Mr. Wheatstone, as Mr. Elliot had done before him, thought of an instrument for uniting the two dissimilar pictures optically, so as to produce the same result that is obtained by the convergence of the optical axes. Mr. Elliot thought of doing this by the eyes alone; but Mr. Wheatstone adopted a much better method of doing it by reflexion. He was thus led to construct an apparatus, to be afterwards described, consisting of two plane mirrors, placed at an angle of 90°, to which he gave the name of stereoscope, anticipating Mr. Elliot both in the construction and publication of his invention, but not in the general conception of a stereoscope.

After describing his apparatus, Mr. Wheatstone proceeds to consider (in a section entitled, “Binocular vision of objects of different magnitudes”) “what effects will result from presenting similar images, differing only in magnitude, to analogous parts of the retina.” “For this purpose,” he says, “two squares or circles, differing obviously but not extravagantly in size, may be drawn on two separate pieces of paper, and placed in the stereoscope, so that the reflected image of each shall be equally distant from the eye by which it is regarded. It will then be seen that notwithstanding this difference they coalesce and occasion a single resultant perception.” The fact of coalescence being supposed to be perfect, the author next seeks to determine the difference between the length of two lines which the eye can force into coalescence, or “the limits within which the single appearance subsists.” He, therefore, unites two images of equal magnitude, by making one of them visually less from distance, and he states that, “by this experiment, the single appearance of two images of different size is demonstrated.” Not satisfied with these erroneous assertions, he proceeds to give a sort of rule or law for ascertaining the relative size of the two unequal pictures which the eyes can force into coincidence. The inequality, he concludes, must not exceed the difference “between the projections of the same object when seen in the most oblique position of the eyes (i.e., both turned to the extreme right or the extreme left) ordinarily employed.” Now, this rule, taken in the sense in which it is meant, is simply a truism. It merely states that the difference of the pictures which the eyes can make to coalesce is equal to the difference of the pictures which the eyes do make to coalesce in their most oblique position; but though a truism it is not a truth, first, because no real coincidence ever can take place, and, secondly, because no apparent coincidence is effected when the difference of the picture is greater than what is above stated.

From these principles, which will afterwards be shewn to be erroneous, Mr. Wheatstone proceeds “to examine why two dissimilar pictures projected on the two retinæ give rise to the perception of an object in relief.” “I will not attempt,” he says, “at present to give the complete solution of this question, which is far from being so easy as at first glance it may appear to be, and is, indeed, one of great complexity. I shall, in this case, merely consider the most obvious explanations which might be offered, and shew their insufficiency to explain the whole of the phenomena.

“It may be supposed that we see only one point of a field of view distinctly at the same instant, the one, namely, to which the optic axes are directed, while all other points are seen so indistinctly that the mind does not recognise them to be either single or double, and that the figure is appreciated by successively directing the point of convergence of the optic axes successively to a sufficient number of its points to enable us to judge accurately of its form.

“That there is a degree of indistinctness in those parts of the field of view to which the eyes are not immediately directed, and which increases with the distance from that point, cannot be doubted; and it is also true that the objects there obscurely seen are frequently doubled. In ordinary vision, it may be said, this indistinctness and duplicity are not attended to, because the eyes shifting continually from point to point, every part of the object is successively rendered distinct, and the perception of the object is not the consequence of a single glance, during which a small part of it only is seen distinctly, but is formed from a comparison of all the pictures successively seen, while the eyes were changing from one point of an object to another.

“All this is in some degree true, but were it entirely so no appearance of relief should present itself when the eyes remain intently fixed on one point of a binocular image in the stereoscope. But in performing the experiment carefully, it will be found, provided the picture do not extend far beyond the centres of distinct vision, that the image is still seen single, and in relief, when in this condition.”[22]

In this passage the author makes a distinction between ordinary binocular vision, and binocular vision through the stereoscope, whereas in reality there is none. The theory of both is exactly the same. The muscles of the two eyes unite the two dissimilar pictures, and exhibit the solid, in ordinary vision; whereas in stereoscopic vision the images are united by reflexion or refraction, the eyes in both cases obtaining the vision of different distances by rapid and successive convergences of the optical axes. Mr. Wheatstone notices the degree of indistinctness in the parts of the picture to which the eyes are not immediately directed; but he does not notice the “confusion and incongruity” which Aguilonius says ought to exist, in consequence of some parts of the resulting relievo being seen of one size by the left eye alone,—other parts of a different size by the right eye alone, and other parts by both eyes. This confusion, however, Aguilonius, as we have seen, found not to exist, and he ascribes it to the influence of a common sense overruling the operation of physical laws. Erroneous as this explanation is, it is still better than that of Mr. Wheatstone, which we shall now proceed to explain.

In order to disprove the theory referred to in the preceding extract, Mr. Wheatstone describes two experiments, which he says are equally decisive against it, the first of them only being subject to rigorous examination. With this view he draws “two lines about two inches long, and inclined towards each other, on a sheet of paper, and having caused them to coincide by converging the optic axes to a point nearer than the paper, he looks intently on the upper end of the resultant line without allowing the eyes to wander from it for a moment. The entire line will appear single, and in its proper relief, &c.... The eyes,” he continues, “sometimes become fatigued, which causes the line to become double at those parts to which the optic axes are not fixed, but in such case all appearance of relief vanishes. The same experiment may be tried with small complex figures, but the pictures should not extend too far beyond the centre of the retinæ.”

Now these experiments, if rightly made and interpreted, are not decisive against the theory. It is not true that the entire line appears single when the axes are converged upon the upper end of the resultant line, and it is not true that the disappearance of the relief when it does disappear arises from the eye being fatigued. In the combination of more complex figures, such as two similar rectilineal figures contained by lines of unequal length, neither the inequalities nor the entire figure will appear single when the axes are converged upon any one point of it.

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.

In consequence of this discussion, I was led to repeat my experiments, and to inquire whether or not the eyes in stereoscopic vision did actually unite the two lines of different lengths, or of different apparent magnitudes. I found that they did not, and that no such union was required to convert by the stereoscope two plane pictures into the apparent whole from which they were taken as seen by each eye. These views were made public in the lectures on the Philosophy of the Senses, which I occasionally delivered in the College of St. Salvator and St. Leonard, St. Andrews, and the different stereoscopes which I had invented were also exhibited and explained.

In examining Dr. Berkeley’s celebrated Theory of Vision, I saw the vast importance of establishing the law of visible direction, and of proving by the aid of binocular phenomena, and in opposition to the opinion of the most distinguished metaphysicians, that we actually see a third dimension in space, I therefore submitted to the Royal Society of Edinburgh, in January 1843, a paper On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina. More than twelve years have now elapsed since this paper was read, and neither Mr. Wheatstone nor Dr. Whewell have made any attempt to defend the views which it refutes.

In continuing my researches, I communicated to the Royal Society of Edinburgh, in April 1844, a paper On the knowledge of distance as given by binocular vision, in which I described several interesting phenomena produced by the union of similar pictures, such as those which form the patterns of carpets and paper-hangings. In carrying on these inquiries I found the reflecting stereoscope of little service, and ill fitted, not only for popular use, but for the application of the instrument to various useful purposes. I was thus led to the construction of several new stereoscopes, but particularly to the Lenticular Stereoscope, now in universal use. They were constructed in St. Andrews and Dundee, of various materials, such as wood, tin-plate, brass, and of all sizes, from that now generally adopted, to a microscopic variety which could be carried in the pocket. New geometrical drawings were executed for them, and binocular pictures taken by the sun were lithographed by Mr. Schenck of Edinburgh. Stereoscopes of the lenticular form were made by Mr. Loudon, optician, in Dundee, and sent to several of the nobility in London, and in other places, and an account of these stereoscopes, and of a binocular camera for taking portraits, and copying statues, was communicated to the Royal Scottish Society of Arts, and published in their Transactions.

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.

After endeavouring in vain to induce opticians, both in London and Birmingham, (where the instrument was exhibited in 1849 to the British Association,) to construct the lenticular stereoscope, and photographers to execute binocular pictures for it, I took with me to Paris, in 1850, a very fine instrument, made by Mr. Loudon in Dundee, with the binocular drawings and portraits already mentioned. I shewed the instrument to the Abbé Moigno, the distinguished author of L’Optique Moderne, to M. Soleil and his son-in-law, M. Duboscq, the eminent Parisian opticians, and to some members of the Institute of France. These gentlemen saw at once the value of the instrument, not merely as one of amusement, but as an important auxiliary in the arts of portraiture and sculpture. M. Duboscq immediately began to make the lenticular stereoscope for sale, and executed a series of the most beautiful binocular Daguerreotypes of living individuals, statues, bouquets of flowers, and objects of natural history, which thousands of individuals flocked to examine and admire. In an interesting article in La Presse,[23] the Abbé Moigno gave the following account of the introduction of the instrument into Paris:—

“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 (Scotch) 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.”

While the lenticular stereoscope was thus exciting much interest in Paris, not a single instrument had been made in London, and it was not till a year after its introduction into France that it was exhibited in England. In the fine collection of philosophical instruments which M. Duboscq contributed to the Great Exhibition of 1851, and for which he was honoured with a Council medal, he placed a lenticular stereoscope, with a beautiful set of binocular Daguerreotypes. This instrument attracted the particular attention of the Queen, and before the closing of the Crystal Palace, M. Duboscq executed a beautiful stereoscope, which I presented to Her Majesty in his name. In consequence of this public exhibition of the instrument, M. Duboscq received several orders from England, and a large number of stereoscopes were thus introduced into this country. The demand, however, became so great, that opticians of all kinds devoted themselves to the manufacture of the instrument, and photographers, both in Daguerreotype and Talbotype, found it a most lucrative branch of their profession, to take binocular portraits of views to be thrown into relief by the stereoscope. Its application to sculpture, which I had pointed out, was first made in France, and an artist in Paris actually copied a statue from the relievo produced by the stereoscope.

Three years after I had published a description of the lenticular stereoscope, and after it had been in general use in France and England, and the reflecting stereoscope forgotten,[24] Mr. Wheatstone printed, in the Philosophical Transactions for 1852, a paper on Vision, in which he says that he had previously used “an apparatus in which prisms were employed to deflect the rays of light proceeding from the pictures, so as to make them appear to occupy the same place;” and he adds, “I have called it the refracting stereoscope.”[25] Now, whatever Mr. Wheatstone may have done with prisms, and at whatever time he may have done it, I was the first person who published a description of stereoscopes both with refracting and reflecting prisms; and during the three years that elapsed after he had read my paper, he made no claim to the suggestion of prisms till after the great success of the lenticular stereoscope. The reason why he then made the claim, and the only reason why we do not make him a present of the suggestion, will appear from the following history:—

In the paper above referred to, Mr. Wheatstone says,—“I recommend, as a convenient arrangement of the refracting stereoscope for viewing Daguerreotypes of small dimensions, the instrument represented, ([Fig. 4],) shortened in its length from 8 inches to 5, and lenses 5 inches focal distance, placed before and close to the prisms.”[26] Although this refracting apparatus, which is simply a deterioration of the lenticular stereoscope, is recommended by Mr. Wheatstone, nobody either makes it or uses it. The semi-lenses or quarter-lenses of the lenticular stereoscope include a virtual and absolutely perfect prism, and, what is of far more consequence, each lens is a variable lenticular prism, so that, when the eye-tubes are placed at different distances, the lenses have different powers of displacing the pictures. They can thus unite pictures placed at different distances, which cannot be done by any combination of whole lenses and prisms.

In the autumn of 1854, after all the facts about the stereoscope were before the public, and Mr. Wheatstone in full possession of all the merit of having anticipated Mr. Elliot in the publication of his stereoscopic apparatus, and of his explanation of the theory of stereoscopic relief, such as it was, he thought it proper to revive the controversy by transmitting to the Abbé Moigno, for publication in Cosmos, an extract of a letter of mine dated 27th September 1838. This extract was published in the Cosmos of the 15th August 1854,[27] with the following illogical commentary by the editor.

“Nous avons eu tort mille fois d’accorder à notre illustre ami, Sir David Brewster, l’invention du stéréoscope par réfraction. M. Wheatstone, en effet, a mis entre nos mains une lettre datée, le croirait on, du 27 Septembre 1838, dans lequel nous avons lû ces mots écrits 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 (à Lord Rosse[28]) que vous aviez promis de commander pour moi votre stéréoscope, celui avec réflecteurs et celui avec prismes.’ Le stéréoscope par réfraction est donc, aussi bien que le stéréoscope par réflexion, le stéréoscope de M. Wheatstone, qui l’avait inventé en 1838, et le faisait construire à cette époque pour Sir David Brewster lui-même. Ce que Sir David Brewster a imaginée, et c’est une idée très ingénieuse, dont M. Wheatstone ne lui disputât jamais la gloire, c’est de former les deux prismes du stéréoscope par réfraction avec les deux moitiés d’une même lentille.”

That the reader may form a correct idea of the conduct of Mr. Wheatstone in making this claim indirectly, and in a foreign journal, whose editor he has willingly misled, I must remind him that I first saw the reflecting stereoscope at the meeting of the British Association at Newcastle, in the middle of August 1838. It is proved by my letter that he and I then conversed on the subject of prisms, which at that time he had never thought of. I suggested prisms for displacing the pictures, and Mr. Wheatstone’s natural reply was, that they must be achromatic prisms. This fact, if denied, may be proved by various circumstances. His paper of 1838 contains no reference to prisms. If he had suggested the use of prisms in August 1838, he would have inserted his suggestion in that paper, which was then unpublished; and if he had only once tried a prism stereoscope, he never would have used another. On my return to Scotland, I ordered from Mr. Andrew Ross one of the reflecting stereoscopes, and one made with achromatic prisms; but my words do not imply that Mr. Wheatstone was the first person who suggested prisms, and still less that he ever made or used a stereoscope with prisms. But however this may be, it is a most extraordinary statement, which he allows the Abbé Moigno to make, and which, though made a year and a half ago, he has not enabled the Abbé to correct, that a stereoscope with prisms was made for me (or for any other person) by Mr. Ross. I never saw such an instrument, or heard of its being constructed: I supposed that after our conversation Mr. Wheatstone might have tried achromatic prisms, and in 1848, when I described my single prism stereoscope, I stated what I now find is not correct, that I believed Mr. Wheatstone had used two achromatic prisms. The following letter from Mr. Andrew Ross will prove the main fact that he never constructed for me, or for Mr. Wheatstone, any refracting stereoscope:—

”2, Featherstone Buildings,
28th September 1854.

“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 striæ 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 Abbé 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.

In reference to the comments of the Abbé Moigno, it is necessary to state, that when he wrote them he had in his possession my printed description of the single-prism, and other stereoscopes,[29] in which I mention my belief, now proved to be erroneous, that Mr. Wheatstone had used achromatic prisms, so that he had, on my express authority, the information which surprised him in my letter. The Abbé also must bear the responsibility of a glaring misinterpretation of my letter of 1838. In that letter I say that Mr. Wheatstone promised to order certain things from Mr. Ross, and the Abbé declares, contrary to the express terms of the letter, as well as to fact, that these things were actually constructed for me. The letter, on the contrary, does not even state that Mr. Wheatstone complied with my request, and it does not even appear from it that the reflecting stereoscope was made for me by Mr. Ross.

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[30] 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.

CHAPTER II.
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.

Every visible object radiates, or throws out in all directions, particles or rays of light, by means of which we see them either directly by the images formed in the eye, or indirectly by looking at images of them formed by their passing through a small hole, or through a lens placed in a dark room or camera, at the end of which is a piece of paper or ground-glass to receive the image.

In order to understand this let h be a very small pin-hole in a shutter or camera, mn, and let ryb be any object of different colours, the upper part, r, being red, the middle, y, yellow, and the lower part, b, blue. If a sheet of white paper, br, is placed behind the hole h, at the same distance as the object rb is before it, an image, br, will be formed of the same ray and the same colours as the object rb. As the particles or rays of light move in straight lines, a red ray from the middle part of r will pass through the hole h and illuminate the point r with red light. In like manner, rays from the middle points of y and b will pass through h and illuminate with yellow and blue light the points y and b. Every other point of the coloured spaces, r, y, and b, will, in the same manner, paint itself, as it were, on the paper, and produce a coloured image, byr, exactly the same in form and colour as the object ryb. If the hole h is sufficiently small no ray from any one point of the object will interfere with or mix with any other ray that falls upon the paper. If the paper is held at half the distance, at b′y′ for example, a coloured image, b′y′r′, of half the size, will be formed, and if we hold it at twice the distance, at b″r″ for example, a coloured image, b″y″r″, of twice the size, will be painted on the paper.

Fig. 4.

As the hole h is supposed to be so small as to receive only one ray from every point of the object, the images of the object, viz., br, b′r′, b″r″, will be very faint. By widening the hole h, so as to admit more rays from each luminous point of rb, the images would become brighter, but they would become at the same time indistinct, as the rays from one point of the object would mix with those from adjacent points, and at the boundaries of the colours r, y, and b, the one colour would obliterate the other. In order, therefore, to obtain sufficiently bright images of visible objects we must use lenses, which have the property of forming distinct images behind them, at a point called their focus. If we widen the hole h, and place in it a lens whose focus is at y, for an object at the same distance, hy, it will form a bright and distinct image, br, of the same size as the object rb. If we remove the lens, and place another in h, whose focus is at y′, for a distance hy, an image, b′r′, half of the size of rb, will be formed at that point; and if we substitute for this lens another, whose focus is at y″, a distinct image, b″r″, twice the size of the object, will be formed, the size of the image being always to that of the object as their respective distances from the hole or lens at h.

With the aid of these results, which any person may confirm by making the experiments, we shall easily understand how we see external objects by means of the images formed in the eye. The human eye, a section and a front view of which is shewn in [Fig. 5, a], is almost a sphere. Its outer membrane, abcde, or mno, [Fig. 5, b], consists of a tough substance, and is called the sclerotic coat, which forms the white of the eye, a, seen in the front view. The front part of the eyeball, cxd, which resembles a small watch-glass, is perfectly transparent, and is called the cornea. Behind it is the iris, cabe, or c in the front view, which is a circular disc, with a hole, ab, in its centre, called the pupil, or black of the eye. It is, as it were, the window of the eye, through which all the light from visible objects must pass. The iris has different colours in different persons, black, blue, or grey; and the pupil, ab, or h, has the power of contracting or enlarging its size according as the light which enters it is more or less bright. In sunlight it is very small, and in twilight its size is considerable. Behind the iris, and close to it, is a doubly convex lens, df, or ll in [Fig. 5, b], called the crystalline lens. It is more convex or round on the inner side, and it is suspended by the ciliary processes at lc, lc′, by which it is supposed to be moved towards and from h, in order to accommodate the eye to different distances, or obtain distinct vision at these distances. At the back of the eye is a thin pulpy transparent membrane, rr o rr, or vvv, called the retina, which, like the ground-glass of a camera obscura, receives the images of visible objects. This membrane is an expansion of the optic nerve o, or a in [Fig. 5, a], which passes to the brain, and, by a process of which we are ignorant, gives us vision of the objects whose images are formed on its expanded surface. The globular form of the eye is maintained by two fluids which fill it,—the aqueous humour, which lies between the crystalline lens and the cornea, and the vitreous humour, zz, which fills the back of the eye.

Fig. 5, A.

Fig. 5, B.

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.

If the eye mn consisted only of a hollow ball with a small aperture h, an inverted image, ab, of any external object ab would be formed on the retina ror, exactly as in [Fig. 4]. A ray of light from a passing through h would strike the retina at a, and one from b would strike the retina at b. If the hole h is very small the inverted image ab would be very distinct, but very obscure. If the hole were the size of the pupil the image would be sufficiently luminous, but very indistinct. To remedy this the crystalline lens is placed behind the pupil, and gives distinctness to the image ab formed in its focus. The image, however, still remains inverted, a ray from the upper part a of the object necessarily falling on the lower part a of the retina, and a ray from the lower part b of the object upon the upper part b of the retina. Now, it has been proved by accurate experiments that in whatever direction a ray aha falls upon the retina, it gives us the vision of the point a from which it proceeds, or causes us to see that point, in a direction perpendicular to the retina at a, the point on which it falls. It has also been proved that the human eye is nearly spherical, and that a line drawn perpendicular to the retina from any point a of the image ab will very nearly pass through the corresponding point a of the object ab,[31] so that the point a is, in virtue of this law, which is called the Law of visible direction, seen in nearly its true direction.

When we look at any object, ab, for example, we see only one point of it distinctly. In [Fig. 5] the point d only is seen distinctly, and every point from d to a, and from d to b, less distinctly. The point of distinct vision on the retina is at d, corresponding with the point d of the object which is seen distinctly. This point d is the centre of the retina at the extremity of the line aha, called the optical axis of the eye, passing through the centre of the lens lh, and the centre of the pupil. The point of distinct vision d corresponds with a small hole in the retina called the Foramen centrale, or central hole, from its being in the centre of the membrane. When we wish to see the points a and b, or any other point of the object, we turn the eye upon them, so that their image may fall upon the central point d. This is done so easily and quickly that every point of an object is seen distinctly in an instant, and we obtain the most perfect knowledge of its form, colour, and direction. The law of distinct vision may be thus expressed. Vision is most distinct when it is performed by the central point of the retina, and the distinctness decreases with the distance from the central point. It is a curious fact, however, that the most distinct point d is the least sensitive to light, and that the sensitiveness increases with the distance from that point. This is proved by the remarkable fact, that when an astronomer cannot see a very minute star by looking at it directly along the optical axis dd, he can see it by looking away from it, and bringing its image upon a more sensitive part of the retina.

But though we see with one eye the direction in which any object or point of an object is situated, we do not see its position, or the distance from the eye at which it is placed. If a small luminous point or flame is put into a dark room by another person, we cannot with one eye form anything like a correct estimate of its distance. Even in good light we cannot with one eye snuff a candle, or pour wine into a small glass at arm’s length. In monocular vision, we learn from experience to estimate all distances, but particularly great ones, by various means, which are called the criteria of distance; but it is only with both eyes that we can estimate with anything like accuracy the distance of objects not far from us.

The criteria of distance, by which we are enabled with one eye to form an approximate estimate of the distance of objects are five in number.

1. The interposition of numerous objects between the eye and the object whose distance we are appreciating. A distance at sea appears much shorter than the same distance on land, marked with houses, trees, and other objects; and for the same reason, the sun and moon appear more distant when rising or setting on the horizon of a flat country, than when in the zenith, or at great altitudes.

2. The variation in the apparent magnitude of known objects, such as man, animals, trees, doors and windows of houses. If one of two men, placed at different distances from us, appears only half the size of the other, we cannot be far wrong in believing that the smallest in appearance is at twice the distance of the other. It is possible that the one may be a dwarf, and the other of gigantic stature, in which case our judgment would be erroneous, but even in this case other criteria might enable us to correct it.

3. The degree of vivacity in the colours and tints of objects.

4. The degree of distinctness in the outline and minute parts of objects.

5. To these criteria we may add the sensation of muscular action, or rather effort, by which we close the pupil in accommodating the eye to near distances, and produce the accommodation.

With all these means of estimating distances, it is only by binocular vision, in which we converge the optical axes upon the object, that we have the power of seeing distance within a limited range.

But this is the only point in which Monocular is inferior to Binocular vision. In the following respects it is superior to it.

1. When we look at oil paintings, the varnish on their surface reflects to each eye the light which falls upon it from certain parts of the room. By closing one eye we shut out the quantity of reflected light which enters it. Pictures should always be viewed by the eye farthest from windows or lights in the apartment, as light diminishes the sensibility of the eye to the red rays.

2. When we view a picture with both eyes, we discover, from the convergency of the optic axes, that the picture is on a plane surface, every part of which is nearly equidistant from us. But when we shut one eye, we do not make this discovery; and therefore the effect with which the artist gives relief to the painting exercises its whole effect in deceiving us, and hence, in monocular vision, the relievo of the painting is much more complete.

This influence over our judgment is beautifully shewn in viewing, with one eye, photographs either of persons, or landscapes, or solid objects. After a little practice, the illusion is very perfect, and is aided by the correct geometrical perspective and chiaroscuro of the Daguerreotype or Talbotype. To this effect we may give the name of Monocular Relief, which, as we shall see, is necessarily inferior to Binocular Relief, when produced by the stereoscope.

3. As it very frequently happens that one eye has not exactly the same focal length as the other, and that, when it has, the vision by one eye is less perfect than that by the other, the picture formed by uniting a perfect with a less perfect picture, or with one of a different size, must be more imperfect than the single picture formed by one eye.

CHAPTER III.
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 ¹/₁₃th part greater than when they are seen with one eye.[32] 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.[33]

Fig. 6.

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, ([see p. 14],) 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.

Fig. 7.

Let us first suppose that we look with both eyes, r and l, [Fig. 7], upon a luminous point, d, which we see single, though there is a picture of it on the retina of each eye. In looking at the point d we turn or converge the optical axes dhd, d′h′ d, of each eye to the point d, an image of which is formed at d in the right eye r, and at d′ in the left eye l. In virtue of the law of visible direction the point d is seen in the direction dd with the eye r, and in the direction d′d with the eye l, these lines being perpendicular to the retina at the points d, d′. The one image of the point d is therefore seen lying upon the other, and consequently seen single. Considering d, then, as a single point of a visible object ab, the two eyes will see the points a and b single by the same process of turning or converging upon them their optical axes, and so quickly does the point of convergence pass backward and forward over the whole object, that it appears single, though in reality only one point of it can be seen single at the same instant. The whole picture of the line ab, as seen with one eye, seems to coincide with the whole picture of it as seen with the other, and to appear single. The same is true of a surface or area, and also of a solid body or a landscape. Only one point of each is seen single; but we do not observe that other points are double or indistinct, because the images of them are upon parts of the retina which do not give distinct vision, owing to their distance from the foramen or point which gives distinct vision. Hence we see the reason why distinct vision is obtained only on one point of the retina. Were it otherwise we should see every other point double when we look fixedly upon one part of an object. If in place of two eyes we had a hundred, capable of converging their optical axes to one point, we should, in virtue of the law of visible direction, see only one object.

The most important advantage which we derive from the use of two eyes is to enable us to see distance, or a third dimension in space. That we have this power has been denied by Dr. Berkeley, and many distinguished philosophers, who maintain that our perception of distance is acquired by experience, by means of the criteria already mentioned. This is undoubtedly true for great distances, but we shall presently see, from the effects of the stereoscope, that the successive convergency of the optic axes upon two points of an object at different distances, exhibits to us the difference of distance when we have no other possible means of perceiving it. If, for example, we suppose g, d, [Fig. 7], to be separate points, or parts of an object, whose distances are go, do, then if we converge the optical axes hg, h′ g upon g, and next turn them upon D, the points will appear to be situated at g and d at the distance gd from each other, and at the distances OG, OD from the observer, although there is nothing whatever in the appearance of the points, or in the lights and shades of the object, to indicate distance. That this vision of distance is not the result of experience is obvious from the fact that distance is seen as perfectly by children as by adults; and it has been proved by naturalists that animals newly born appreciate distances with the greatest correctness. We shall afterwards see that so infallible is our vision of near distances, that a body whose real distance we can ascertain by placing both our hands upon it, will appear at the greater or less distance at which it is placed by the convergency of the optical axes.

We are now prepared to understand generally, how, in binocular vision, we see the difference between a picture and a statue, and between a real landscape and its representation. When we look at a picture of which every part is nearly at the same distance from the eyes, the point of convergence of the optical axes is nearly at the same distance from the eyes; but when we look at its original, whether it be a living man, a statue, or a landscape, the optical axes are converged in rapid succession upon the nose, the eyes, and the ears, or upon objects in the foreground, the middle and the remote distances in the landscape, and the relative distances of all these points from the eye are instantly perceived. The binocular relief thus seen is greatly superior to the monocular relief already described.

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.

CHAPTER IV.
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.

The Ocular Stereoscope.

We have already stated that objects are seen in perfect relief when we unite two dissimilar photographic pictures of them, either by converging the optic axes upon a point so far in front of the pictures or so far beyond them, that two of the four images are combined. In both these cases each picture is seen double, and when the two innermost of the four, thus produced, unite, the original object is seen in relief. The simplest of these methods is to converge the optical axes to a point nearer to us than the pictures, and this may be best done by holding up a finger between the eyes and the pictures, and placing it at such a distance that, when we see it single, the two innermost of the four pictures are united. If the finger is held up near the dissimilar pictures, they will be slightly doubled, the two images of each overlapping one other; but by bringing the finger nearer the eye, and seeing it singly and distinctly, the overlapping images will separate more and more till they unite. We have, therefore, made our eyes a stereoscope, and we may, with great propriety, call it the Ocular Stereoscope. If we wish to magnify the picture in relief, we have only to use convex spectacles, which will produce the requisite magnifying power; or what is still better, to magnify the united pictures with a powerful reading-glass. The two single images are hid by advancing the reading-glass, and the other two pictures are kept united with a less strain upon the eyes.

As very few people can use their eyes in this manner, some instrumental auxiliary became necessary, and it appears to us strange that the simplest method of doing this did not occur to Mr. Elliot and Mr. Wheatstone, who first thought of giving us the help of an instrument. By enabling the left eye to place an image of the left-hand picture upon the right-hand picture, as seen by the naked eye, we should have obtained a simple instrument, which might be called the Monocular Stereoscope, and which we shall have occasion to describe. The same contrivance applied also to the right eye, would make the instrument Binocular. Another simple contrivance for assisting the eyes would have been to furnish them with a minute opera-glass, or a small astronomical telescope about an inch long, which, when held in the hand or placed in a pyramidal box, would unite the dissimilar pictures with the greatest facility and perfection. This form of the stereoscope will be afterwards described under the name of the Opera-Glass Stereoscope.

Fig. 8.

Description of the Ocular Stereoscope.

A stereoscope upon the principle already described, in which the eyes alone are the agent, was contrived, in 1834, by Mr. Elliot, as we have already had occasion to state. He placed the binocular pictures, described in [Chapter I]., at one end of a box, and without the aid either of lenses or mirrors, he obtained a landscape in perfect relief. I have examined this stereoscope, and have given, in [Fig. 8], an accurate though reduced drawing of the binocular pictures executed and used by Mr. Elliot. I have also united the two original pictures by the convergency of the optic axes beyond them, and have thus seen the landscape in true relief. To delineate these binocular pictures upon stereoscopic principles was a bold undertaking, and establishes, beyond all controversy, Mr. Elliot’s claim to the invention of the ocular stereoscope.

If we unite the two pictures in [Fig. 8], by converging the optic axes to a point nearer the eye than the pictures, we shall see distinctly the stereoscopic relief, the moon being in the remote distance, the cross in the middle distance, and the stump of a tree in the foreground.

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.

Fig. 9.

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.

Description of the Reflecting Stereoscope.

This form of the stereoscope, which we owe to Mr. Wheatstone, is shewn in [Fig. 10], and is described by him in the following terms:—“aa′ are two plane mirrors, (whether of glass or metal is not stated,) about four inches square, inserted in frames, and so adjusted that their backs form an angle of 90° with each other; these mirrors are fixed by their common edge against an upright b, or, which was less easy to represent in the drawing against the middle of a vertical board, cut away in such a manner as to allow the eyes to be placed before the two mirrors. c, c′ are two sliding boards, to which are attached the upright boards d, d′, which may thus be removed to different distances from the mirrors. In most of the experiments hereafter to be detailed it is necessary that each upright board shall be at the same distance from the mirror which is opposite to it. To facilitate this double adjustment, I employ a right and a left-handed wooden screw, r, l; the two ends of this compound screw pass through the nuts e, e′, which are fixed to the lower parts of the upright boards d, d, so that by turning the screw pin p one way the two boards will approach, and by turning them the other they will recede from each other, one always preserving the same distance as the other from the middle line f; e, e′ are pannels to which the pictures are fixed in such manner that their corresponding horizontal lines shall be on the same level; these pannels are capable of sliding backwards or forwards in grooves on the upright boards d, d′. The apparatus having been described, it now remains to explain the manner of using it. The observer must place his eyes as near as possible to the mirrors, the right eye before the right-hand mirror, and the left eye before the left-hand mirror, and he must move the sliding pannels e, e′ to or from him till the two reflected images coincide at the intersection of the optic axes, and form an image of the same apparent magnitude as each of the component pictures. The picture will, indeed, coincide when the sliding pannels are in a variety of different positions, and, consequently, when viewed under different inclinations of the optic axes, but there is only one position in which the binocular image will be immediately seen single, of its proper magnitude, and without fatigue to the eyes, because in this position only the ordinary relations between the magnitude of the pictures on the retina, the inclination of the optic axes, and the adaptation of the eye to distinct vision at different distances, are preserved. In all the experiments detailed in the present memoir I shall suppose these relations to remain undisturbed, and the optic axes to converge about six or eight inches before the eyes.

Fig. 10.

“If the pictures are all drawn to be seen with the same inclination of the optic axes the apparatus may be simplified by omitting the screw rl, and fixing the upright boards d, d′ at the proper distance. The sliding pannels may also be dispensed with, and the drawings themselves be made to slide in the grooves.”

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.”

“Careful attention,” he adds, “would enable an artist to draw and paint the two component pictures, so as to present to the mind of the observer, in the resultant perception, perfect identity with the object represented. Flowers, crystals, busts, vases, instruments of various kinds, &c., might thus be represented, so as not to be distinguished by sight from the real objects themselves.”

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:—

1. It is a clumsy and unmanageable apparatus, rather than an instrument for general use. The one constructed for me was 16½ inches long, 6 inches broad, and 8½ inches high.

2. The loss of light occasioned by reflection from the mirrors is very great. In all optical instruments where images are to be formed, and light is valuable, mirrors and specula have been discontinued. Reflecting microscopes have ceased to be used, but large telescopes, such as those of Sir W. and Sir John Herschel, Lord Rosse, and Mr. Lassel, were necessarily made on the reflecting principle, from the impossibility of obtaining plates of glass of sufficient size.

3. In using glass mirrors, of which the reflecting stereoscope is always made, we not only lose much more than half the light by the reflections from the glass and the metallic surface, and the absorbing power of the glass, but the images produced by reflection are made indistinct by the oblique incidence of the rays, which separates the image produced by the glass surface from the more brilliant image produced by the metallic surface.

4. In all reflections, as Sir Isaac Newton states, the errors are greater than in refraction. With glass mirrors in the stereoscope, we have four refractions in each mirror, and the light transmitted through twice the thickness of the glass, which lead to two sources of error.

5. Owing to the exposure of the eye and every part of the apparatus to light, the eye itself is unfitted for distinct vision, and the binocular pictures become indistinct, especially if they are Daguerreotypes,[34] by reflecting the light incident from every part of the room upon their glass or metallic surface.

6. The reflecting stereoscope is inapplicable to the beautiful binocular slides which are now being taken for the lenticular stereoscope in every part of the world, and even if we cut in two those on paper and silver-plate, they would give, in the reflecting instrument, converse pictures, the right-hand part of the picture being placed on the left-hand side, and vice versa.

7. With transparent binocular slides cut in two, we could obtain pictures by reflection that are not converse; but in using them, we would require to have two lights, one opposite each of the pictures, which can seldom be obtained in daylight, and which it is inconvenient to have at night.

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.

Description of the Lenticular Stereoscope.

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.

Fig. 11.

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:—

If we look at a with one eye through the centre of a convex glass, with which we can see it distinctly at the distance of 6 inches, which is called its focal distance, it will be seen in its place at a. If we now move the lens from right to left, the image of a will move towards b; and when it is seen through the right-hand edge of the lens, the image of a will have reached the position c, half-way between a and b. If we repeat this experiment with the portrait b, and move the lens from left to right, the image of b will move towards a; and when it is seen through the left-hand edge of the lens, the image of b will have reached the position c. Now, it is obviously by the right-hand half of the lens that we have transferred the image of a to c, and by the left-hand half that we have transferred the image of b to c. If we cut the lens in two, and place the halves—one in front of each picture at the distance of 2½ inches—in the same position in which they were when a was transferred to c and b to c, they will stand as in [Fig. 12], and we shall see the portraits a and b united into one at c, and standing out in beautiful relief,—a result which will be explained in a subsequent chapter.

Fig. 12.

The same effect will be produced by quarter lenses, such as those shewn in [Fig. 13]. These lenses are cut into a round or square form, and placed in tubes, as represented at r, l, in [Fig. 14], which is a drawing of the Lenticular Stereoscope.

Fig. 13.

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.

Fig. 14.

If we now put the slide ab, [Fig. 11], into the horizontal opening at s, turning up the sneck above s to prevent it from falling out, and place ourselves behind r, l, we shall see, by looking through r with the right eye and l with the left eye, the two images a, b united in one, and in the same relief as the living person whom they represent. No portrait ever painted, and no statue ever carved, approximate in the slightest degree to the living reality now before us. If we shut the right eye r we see with the left eye l merely the portrait a, but it has now sunk into a flat picture, with only monocular relief. By closing the left eye we shall see merely the portrait b, having, like the other, only monocular relief, but a relief greater than the best-painted pictures can possibly have, when seen even with one eye. When we open both eyes, the two portraits instantly start into all the roundness and solidity of life.

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.

Fig. 15.

One of the earliest forms which I adopted was that which is shewn in [Fig. 15], as made by M. Duboscq in Paris, and which may be called stereoscopic spectacles. The two-eye lenses l, r are held by the handle h, so that we can, by moving them to or from the binocular pictures, obtain distinct vision and unite them in one. The effect, however, is not so good as that which is produced when the pictures are placed in a box.

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

Fig. 16.

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.

Now, since, in the stereoscope, when looked into with two eyes, we see the picture in relief with the same accuracy as, in ordinary binocular vision, we see the same object in relief by uniting on the retina two pictures exactly the same as the binocular ones, the mere statement of this fact has been regarded as the theory of the stereoscope. We shall see, however, that it is not, and that it remains to be explained, more minutely than we have done in Chapter III., both how we see objects in relief in ordinary binocular vision, and how we see them in the same relief by uniting ocularly, or in the stereoscope, two dissimilar images of them.

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

Fig. 17.

In [Fig. 17] is shewn a semi-lens mn, with its section m′n′. If we look at any object successively through the portions aa′a″ in the semi-lens mn, corresponding to aa′a″ in the section m′n′, which is the same as in a quarter-lens, the object will be magnified equally in all of them, but it will be more displaced, or more refracted, towards n, by looking through a′ or a′ than through a or a, and most of all by looking through a″ or a″, the refraction being greatest at a″ or a″, less at a′ or a′, and still less at a or a. By means of a semi-lens, or a quarter of a lens of the size of mn, we can, with an aperture of the size of a, obtain three different degrees of displacement or refraction, without any change of the magnifying power.

If we use a thicker lens, as shewn at m′n′nm, keeping the curvature of the surface the same, we increase the refracting angle at its margin n′n, we can produce any degree of displacement we require, either for the purposes of experiment, or for the duplication of large binocular pictures.

When two half or quarter lenses are used as a stereoscope, the displacement of the two pictures is produced in the manner shewn in [Fig. 18], where ll is the lens for the left eye e, and l′l′ that for the right eye e′, placed so that the middle points, no, n′o′, of each are 2½ inches distant, like the two eyes. The two binocular pictures which are to be united are shewn at ab, ab, and placed at nearly the same distance. The pictures being fixed in the focus of the lenses, the pencils ano, a′n′o′, bno, b′n′o′, will be refracted at the points n, o, n′, o′, and at their points of incidence on the second surface, so as to enter the eyes, e, e′, in parallel directions, though not shewn in the Figure. The points a, a, of one of the pictures, will therefore be seen distinctly in the direction of the refracted ray—that is, the pencils an, ao, issuing from a′, will be seen as if they came from a′, and the pencils bn, bo, as if they came from b′, so that ab will be transferred by refraction to a′b′. In like manner, the picture ab will be transferred by refraction to a′b′, and thus united with a′b′.

Fig. 18.

The pictures ab, ab thus united are merely circles, and will therefore be seen as a single circle at a′b′. But if we suppose ab to be the base of the frustum of a cone, and cd its summit, as seen by the left eye, and the circles ab, cd to represent the base and summit of the same solid as seen by the right eye, then it is obvious that when the pictures of cd and cd are similarly displaced or refracted by the lenses ll l′l′, so that cc′ is equal to aa′ and dd′ to bb′, the circles will not be united, but will overlap one another as at c′d′, c′d′, in consequence of being carried beyond their place of union. The eyes, however, will instantly unite them into one by converging their axes to a remoter point, and the united circles will rise from the paper, or from the base a′b′, and place the single circle at the point of convergence, as the summit of the frustum of a hollow cone whose base is a′b′. If cd, cd had been farther from one another than ab, ab, as in Figs. [20] and [21], they would still have overlapped though not carried up to their place of union. The eyes, however, will instantly unite them by converging their axes to a nearer point, and the united circles will rise from the paper, or from the base ab, and form the summit of the frustum of a raised cone whose base is a′b′.

In the preceding illustration we have supposed the solid to consist only of a base and a summit, or of parts at two different distances from the eye; but what is true of two distances is true of any number, and the instant that the two pictures are combined by the lenses they will exhibit in relief the body which they represent. If the pictures are refracted too little, or if they are refracted too much, so as not to be united, their tendency to unite is so great, that they are soon brought together by the increased or diminished convergency of the optic axes, and the stereoscopic effect is produced. Whenever two pictures are seen, no relief is visible; when only one picture is distinctly seen, the relief must be complete.

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.

CHAPTER V.
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.

Fig. 19.

In order to understand how the two pictures, when placed the one above the other, rise into relief, we must first explain the manner in which a solid object itself is, in ordinary vision, seen in relief, and we shall then shew how this process takes place in the two forms of the ocular stereoscope, and in the lenticular stereoscope. For this purpose, let abcd, [Fig. 19], be a section of the frustum of a cone, that is, a cone with its top cut off by a plane cedg, and having aebg for its base. In order that the figure may not be complicated, it will be sufficient to consider how we see, with two eyes, l and r, the cone as projected upon a plane passing through its summit cedg. The points l, r being the points of sight, draw the lines ra, rb, which will cut the plane on which the projection is to be made in the points a, b, so that ab will represent the line ab, and a circle, whose diameter is ab, will represent the base of the cone, as seen by the right eye r. In like manner, by drawing la, lb, we shall find that a′b′ will represent the line ab, and a circle, whose diameter is a′b′, the base aebg, as seen by the left eye. The summit, cedg, of the frustum being in the plane of projection, will be represented by the circle cedg. The representation of the frustum abcd, therefore, upon a plane surface, as seen by the left eye l, consists of two circles, whose diameters are ab, cd; and, as seen by the right eye, of other two circles, whose diameters are ab, cd, which, in [Fig. 20], are represented by ab, cd, and ab, cd. These plane figures being also the representation of the solid on the retina of the two eyes, how comes it that we see the solid and not the plane pictures? When we look at the point b, [Fig. 19], with both eyes, we converge upon it the optic axes lb, rb, and we therefore see the point single, and at the distances lb, rb from each eye. When we look at the point d, we withdraw the optic axes from b, and converge them upon d. We therefore see the point d single, and at the distances ld, rd from each eye; and in like manner the eyes run over the whole solid, seeing every point single and distinct upon which they converge their axes, and at the distance of the point of convergence from the observer. During this rapid survey of the object, the whole of it is seen distinctly as a solid, although every point of it is seen double and indistinct, excepting the point upon which the axes are for the instant converged.

Fig. 20.

From these observations it is obvious, that when we look with both eyes at any solid or body in relief, we see more of the right side of it by the right eye, and more of the left side of it by the left eye. The right side of the frustum abcd, [Fig. 19], is represented by the line db, as seen by the right eye, and by the shorter line db′, as seen by the left eye. In like manner, the left side ac is represented by ca′, as seen by the left eye, and by the shorter line ca′, as seen by the right eye.

When the body is hollow, like a wine glass, we see more of the right side with the left eye, and more of the left side with the right eye.

If we now separate, as in [Fig. 20], the two projections shewn together on [Fig. 19], we shall see that the two summits, cd, cd, of the frustum are farther from one another than the more distant bases, ab, ab, and it is true generally that in the two pictures of any solid in relief, the similar parts that are near the observer are more distant in the two pictures than the remoter parts, when the plane of perspective is beyond the object. In the binocular picture of the human face the distance between the two noses is greater than the distance between the two right or left eyes, and the distance between the two right or left eyes greater than the distance between the two remoter ears.

We are now in a condition to explain the process by which, with the eyes alone, we can see a solid in relief by uniting the right and left eye pictures of it,—or the theory ocular stereoscope. In order to obtain the proper relief we must place the right eye picture on the left side, and the left eye picture on the right side, as shewn in [Fig.21], by the pictures abcd, abcd, of the frustum of a cone, as obtained from [Fig. 19].

Fig. 21.

In order to unite these two dissimilar projections, we must converge the optical axes to a point nearer the observer, or look at some point about m. Both pictures will immediately be doubled. An image of the figure ab will advance towards p, and an image of ab will likewise advance towards p; and the instant these images are united, the frustum of a cone, which they represent, will appear in relief at mn, the place where the optic axes meet or cross each other. At first the solid figure will appear in the middle, between the two pictures from which it is formed and of the same size, but after some practice it will appear smaller and nearer the eye. Its smallness is an optical illusion, as it has the same angle of apparent magnitude as the plane figures, namely, mnl = abl; but its position at mn is a reality, for if we look at the point of our finger held beyond m the solid figure will be seen nearer the eye. The difficulty which we experience in seeing it of the size and in the position shewn in [Fig. 21], arises from its being seen along with its two plane representations, as we shall prove experimentally when we treat in a future chapter of the union of similar figures by the eye.

The two images being thus superimposed, or united, we shall now see that the combined images are seen in relief in the very same way that in ordinary vision we saw the real solid, abcd,[ Fig. 19], in relief, by the union of the two pictures of it on the retina. From the points a, b, c, d, a, b, c, d, draw lines to l and r, the centres of visible direction of each eye, and it will be seen that the circles ab, ab, representing the base of the cone, can be united by converging the optical axes to points in the line mn, and that the circles cd, cd, which are more distant, can be united only by converging the optic axes to points in the line op. The points a, a, for example, united by converging the axes to m, are seen at that point single; the points b, b at n single, the points c, c at o single, the points d, d at p single, the centres s, s of the base at m single, and the centres s′, s′ of the summit plane at n single. Hence the eyes l and r see the combined pictures at mn in relief, exactly in the same manner as they saw in relief the original solid mn in [Fig. 19].

In order to find the height mn of the conical frustum thus seen, let d = distance op; d = ss, the distance of the two points united at m; d′ = s′s′, the distance of the two points united at n; and c = lr = 2½ inches, the distance of the eyes. Then we have—

As the summit plane op rises above the base mn by the successive convergency of the optic axes to different points in the line onp, it may be asked how it happens that the conical frustum still appears a solid, and the plane op where it is, when the optic axes are converged to points in the line mmn, so as to see the base distinctly? The reason of this is that the rays emanate from op exactly in the same manner, and form exactly the same image of it, on the two retinas as if it were the summit cd, [Fig. 19], of the real solid when seen with both eyes. The only effect of the advance of the point of convergence from n to m is to throw the image of n a little to the right side of the optic axis of the left eye, and a little to the left of the optic axis of the right eye. The summit plane op will therefore retain its place, and will be seen slightly doubled and indistinct till the point of convergence again returns to it.

It has been already stated that the two dissimilar pictures may be united by converging the optical axes to a point beyond them. In order to do this, the distance ss′ of the pictures, [Fig. 21], must be greatly less than the distance of the eyes l, r, in order that the optic axes, in passing through similar points of the two plane pictures, may meet at a moderate distance beyond them. In order to explain how the relief is produced in this case, let ab, cd, ab, cd, [Fig. 22], be the dissimilar pictures of the frustum of a cone whose summit is cd, as seen by the right eye, and cd as seen by the left eye. From l and r, as before, draw lines through all the leading points of the pictures, and we shall have the points a, a united at m, the points b, b at n, the points c, c at o, and the points d, d at p, the points s, s at m, and the points s′, s′ at n, forming the cone mnop, with its base mn towards the observer, and its summit op more remote. If the cone had been formed of lines drawn from the outline of the summit to the outline of the base, it would now appear hollow, the inside of it being seen in place of the outside as before. If the pictures ab, ab are made to change places the combined picture would be in relief, while in the case shewn in [Fig. 21] it would have been hollow. Hence the right-eye view of any solid must be placed on the left hand, and the left-eye view of it on the right hand, when we wish to obtain it in relief by converging the optic axes to a point between the pictures and the eye, and vice versa when we wish to obtain it in relief by converging the optic axes to a point beyond the pictures. In every case when we wish the combined pictures to represent a hollow, or the converse of relief, their places must be exchanged.

Fig. 22.

In order to find the height mn, or rather the depth of the cone in [Fig. 22], let d, d, c, c, represent the same quantities as before, and we shall have

When d, c, d, d′ have the same values as before, we shall have MN = 18·7 feet!

When c = d, mp will be infinite.

We have already explained how the two binocular pictures are combined or laid upon one another in the lenticular stereoscope. Let us now see how the relief is obtained. The two plane pictures abcd, abcd, in [Fig. 18], are, as we have already explained, combined or simply laid upon one another by the lenses ll, l′l′, and in this state are shewn by the middle circles at aabb, ccdd. The images of the bases ab, ab of the cone are accurately united in the double base ab, ab, but the summits of the conical frustum remain separate, as seen at c′d′, c′d′. It is now the business of the eyes to unite these, or rather to make them appear as united. We have already seen how they are brought into relief when the summits are refracted so as to pass one another, as in [Fig. 18]. Let us therefore take the case shewn in [Fig. 20], where the summits cd, cd are more distant than the bases ab, ab. The union of these figures is instantly effected, as shewn in [Fig. 23], by converging the optic axes to points m and n successively, and thus uniting c and c and d and d, and making these points of the summit plane appear at m and n, the points of convergence of the axes lm, rm, and ln, rn. In like manner, every pair of points in the summit plane, and in the sides am, bn of the frustum, are converged to points corresponding to their distance from the base ab of the original solid frustum, from which the plane pictures abcd, abcd, were taken. We shall, therefore, see in relief the frustum of a cone whose section is amnb.

Fig. 23.

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

1. When a drawing of any object or series of objects is executed on a plane surface from one point of sight, according to the principles of geometrical perspective, every point of its surface that is visible from the point of sight will be represented on the plane.

2. If another drawing of the same object or series of objects is similarly executed on the same plane from a second point of sight, sufficiently distant from the first to make the two drawings separate without overlapping, every point of its surface visible from this second point of sight will also be represented on the plane, so that we shall have two different drawings of the object placed, at a short distance from each other, on the same plane.

Fig. 24.

3. Calling these different points of the object 1, 2, 3, 4, &c., it will be seen from [Fig. 24], in which l, r are the two points of sight, that the distances 1, 1, on the plane mn, of any pair of points in the two pictures representing the point 1 of the object, will be to the distance of any other pair 2, 2, representing the point 2, as the distances 1′p, 2′ p of the points of the object from the plane mn, multiplied inversely by the distances of these points from the points of sight l, r, or the middle point o between them.

4. If the sculptor, therefore, or the architect, or the mechanist, or the surveyor, possesses two such pictures, either as drawn by a skilful artist or taken photographically, he can, by measuring the distances of every pair of points, obtain the relief or prominence of the original point, or its distance from the plane mn or ab; and without the use of the stereoscope, the sculptor may model the object from its plane picture, and the distances of every point from a given plane. In like manner, the other artists may determine distances in buildings, in machinery, and in the field.

5. If the distance of the points of sight is equal to the distance of the eyes l, r, the two plane pictures may be united and raised into relief by the stereoscope, and thus give the sculptor and other artists an accurate model, from which they will derive additional aid in the execution of their work.

6. In stereoscopic vision, therefore, when we join the points 1, 1 by converging the optic axes to 1′ in the line pq, and the points 2, 2 by converging them to 2′ in the same line, we place these points at the distances o1, oO2, and see the relief, or the various differences of distance which the sculptor and others obtained by the method which we have described.

7. Hence we infer, that if the stereoscopic vision of relief had never been thought of, the principles of the instrument are involved in the geometrical relief which is embodied in the two pictures of an object taken from two points of sight, and in the prominence of every part of it obtained geometrically.

CHAPTER VI.
ON THE UNION OF SIMILAR PICTURES
IN BINOCULAR VISION.

In uniting by the convergency of the optic axes two dissimilar pictures, as shewn in [Fig. 18], the solid cone mn ought to appear at mn much nearer the observer than the pictures which compose it. I found, however, that it never took its right position in absolute space, the base mn of the solid seeming to rest on the same plane with its constituent pictures ab, ab, whether it was seen by converging the axes as in [Fig. 18] or in [Fig. 22]. Upon inquiring into the reason of this I found that the disturbing cause was simply the simultaneous perception of other objects in the same field of view whose distance was known to the observer.

In order to avoid all such influences I made experiments on large surfaces covered with similar plane figures, such as flowers or geometrical patterns upon paper-hangings and carpets. These figures being always at equal distances from each other, and almost perfectly equal and similar, the coalescence of any pair of them, effected by directing the optic axes to a point between the paper-hanging and the eye, is accompanied by the instantaneous coalescence of them all. If we, therefore, look at a papered wall without pictures, or doors, or windows, or even at a considerable portion of a wall, at the distance of three feet, and unite two of the figures,—two flowers, for example, at the distance of twelve inches from each other horizontally, the whole wall or visible portion of it will appear covered with flowers as before, but as each flower is now composed of two flowers united at the point of convergence of the optic axes, the whole papered wall with all its flowers will be seen suspended in the air at the distance of six inches from the observer! At first the observer does not decide upon the distance of the suspended wall from himself. It generally advances slowly to its new position, and when it has taken its place it has a very singular character. The surface of it seems slightly curved. It has a silvery transparent aspect. It is more beautiful than the real paper, which is no longer seen, and it moves with the slightest motion of the head. If the observer, who is now three feet from the wall, retires from it, the suspended wall of flowers will follow him, moving farther and farther from the real wall, and also, but very slightly, farther and farther from the observer. When he stands still, he may stretch out his hand and place it on the other side of the suspended wall, and even hold a candle on the other side of it to satisfy himself that the ghost of the wall stands between the candle and himself.

In looking attentively at this strange picture some of the flowers have the aspect of real flowers. In some the stalk retires from the plane of the picture. In others it rises from it. One leaf will come farther out than another. One coloured portion, red, for example, will be more prominent than the blue, and the flower will thus appear thicker and more solid, like a real flower compressed, and deviating considerably from the plane representation of it as seen by one eye. All this arises from slight and accidental differences of distance in similar or corresponding parts of the united figures. If the distance, for example, between two corresponding leaves is greater than the distance between other two corresponding leaves, then the two first when united will appear nearer the eye than the other two, and hence the appearance of a flower in low relief, is given to the combination.

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 little practice will enable the observer to realize and to maintain the singular binocular vision which replaces the real picture.[35] The occasional retention of the picture after one eye is closed, and even after both have been closed and quickly reopened, shews the influence of time over the evanescence as well as over the creation of this class of phenomena. On some occasions, a singular effect is produced. When the flowers or figures on the paper are distant six inches, we may either unite two six inches distant, or two twelve inches distant, and so on. In the latter case, when the eyes have been accustomed to survey the suspended picture, I have found that, after shutting or opening them, I neither saw the picture formed by the two flowers twelve inches distant, nor the papered wall itself, but a picture formed by uniting all the flowers six inches distant! The binocular centre (the point to which the optic axes converged, and consequently the locality of the picture) had shifted its place, and instead of advancing to the real wall and seeing it, it advanced exactly as much as to unite the nearest flowers, just as in a ratchet wheel, when the detent stops one tooth at a time; or, to speak more correctly, the binocular centre advanced in order to relieve the eyes from their strain, and when the eyes were opened, it had just reached that point which corresponded with the union of the flowers six inches distant.

Fig. 25.

We have already seen, as shewn in [Fig. 22], that when we fix the binocular centre, that is, converge the optic axes on a point beyond the dissimilar pictures, so as to unite them, they rise into relief as perfectly as when the binocular centre, as shewn in [Fig. 18], is fixed between the pictures used and the eye. In like manner we may unite similar pictures, but, owing to the opacity of the wall and the floor, we cannot accomplish this with paper-hangings and carpets. The experiment, however, may be made with great effect by looking through transparent patterns cut out of paper or metal, such as those in zinc which are used for larders and other purposes. Particular kinds of trellis-work, and windows with small squares or rhombs of glass, may also be used, and, what is still better, a screen might be prepared, by cutting out the small figures from one or more pieces of paper-hangings. The readiest means, however, of making the experiment, is to use the cane bottom of a chair, which often exhibits a succession of octagons with small luminous spaces between them. To do this, place the back of the chair upon a table, the height of the eye either when sitting or standing, so that the cane bottom with its luminous pattern may have a vertical position, as shewn in [Fig. 25], where mn is the real bottom of the chair with its openings, which generally vary from half an inch to three-fourths. Supposing the distance to be half an inch, and the eyes, l, r, of the observer 12 inches distant from mn, let lad, lbe be lines drawn through the centres of two of the open spaces a, b, and rbd, rce lines drawn through the centres of b and c, and meeting lad, lbe at d and e, d being the binocular centre to which the optic axes converge when we look at it through a and b, and c the binocular centre when we look at it through b and c. Now, the right eye, r, sees the opening b at d, and the left eye sees the opening a at d, so that the image at d of the opening consists of the similar images of a and b united, and so on with all the rest; so that the observer at l, r no longer sees the real pattern mn, but an image of it suspended at mn, three inches behind mn. If the observer now approaches mn, the image mn will approach to him, and if he recedes, mn will recede also, being 1½ inches behind mn when the observer is six inches before it, and twelve inches behind mn when the observer is forty-eight inches before it, the image mn moving from mn with a velocity one-fourth of that with which the observer recedes.

The observer resuming the position in the figure where his eyes, l, r, are twelve inches distant from mn, let us consider the important results of this experiment. If he now grasps the cane bottom at mn, his thumbs pressing upon mn, and his fingers trying to grasp mn, he will then feel what he does not see, and see what he does not feel! The real pattern is absolutely invisible at mn, where he feels it, and it stands fixed at mn. The fingers may be passed through and through between the real and the false image, and beyond it,—now seen on this side of it, now in the middle of it, and now on the other side of it. If we next place the palms of each hand upon mn, the real bottom of the chair, feeling it all over, the result will be the same. No knowledge derived from touch—no measurement of real distance—no actual demonstration from previous or subsequent vision, that there is a real solid body at mn, and nothing at all at mn, will remove or shake the infallible conviction of the sense of sight that the cane bottom is at mn, and that dl or dr is its real distance from the observer. If the binocular centre be now drawn back to mn, the image seen at mn will disappear, and the real object be seen and felt at mn. If the binocular centre be brought further back to f, that is, if the optic axes are converged to a point nearer the observer than the object, as illustrated by [Fig. 18], the cane bottom mn will again disappear, and will be seen at uv, as previously explained.

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 2½ inches, as appears from [Fig. 22].

In making these experiments, the observer cannot fail to be struck with the remarkable fact, that though the openings mn, mn, uv, have all the same apparent or angular magnitude, that is, subtend the same angle at the eye, viz., dlc, dre, yet those at mn appear larger, and those at uv smaller, than those at mn. If we cause the image mn to recede and approach to us, the figures in mn will invariably increase as they recede, and those in uv diminish as they approach the eye, and their visual magnitudes, as we may call them, will depend on the respective distances at which the observer, whether right or wrong in his estimate, conceives them to be placed,—a result which is finely illustrated by the different size of the moon when seen in the horizon and in the meridian. The fact now stated is a general one, which the preceding experiments demonstrate; and though our estimate of magnitude thus formed is erroneous, yet it is one which neither reason nor experience is able to correct.

It is a curious circumstance, that, previous to the publication of these experiments, no examples have been recorded of false estimates of the distance of near objects in consequence of the accidental binocular union of similar images. In a room where the paper-hangings have a small pattern, a short-sighted person might very readily turn his eyes on the wall when their axes converged to some point between him and the wall, which would unite one pair of the similar images, and in this case he would see the wall nearer him than the real wall, and moving with the motion of his head. In like manner a long-sighted person, with his optical axes converged to a point beyond the wall, might see an image of the wall more distant, and moving with the motion of his head; or a person who has taken too much wine, which often fixes the optical axes in opposition to the will, might, according to the nature of his sight, witness either of the illusions above mentioned.

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.”[36]

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.[37]

Before quitting the subject of the binocular union of similar pictures, I must give some account of a series of curious phenomena which I observed by uniting the images of lines meeting at an angular point when the eye is placed at different heights above the plane of the paper, and at different distances from the angular point.

Fig. 26.

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.

Fig. 27.

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

GC = GO, Cos. A = 1 and A = 0.

When the eye at any position, e″ for example, sees the points a and b united at d″, it sees also the whole lines ac, bc forming the image d″c. The binocular centre must, therefore, run rapidly along the line d″c; that is, the inclination of the optic axes must gradually diminish till the binocular centre reaches c, when all strain is removed. The vision of the image d″c, however, is carried on so rapidly that the binocular centre returns to d″ without the eye being sensible of the removal and resumption of the strain which is required in maintaining a view of the united image d″c. If we now suppose ab to diminish, the binocular centre will advance towards g, and the length and inclination of the united images dc, d′c, &c., will diminish also, and vice versa. If the distance rl ([Fig. 26]) between the eyes diminishes, the binocular centre will retire towards e, and the length and inclination of the images will increase. Hence persons with eyes more or less distant will see the united images in different places and of different sizes, though the quantities a and AB be invariable.

While the eyes at e″ are running along the lines ac, bc, let us suppose them to rest upon the points ab equidistant from c. Join ab, and from the point g, where ab intersects gc, draw the line ge″, and find the point d″ from the formula

Hence the two points a, b will be united at d″, and when the angle e″gc is such that the line joining d and c is perpendicular to gc, the line joining d″c will also be perpendicular to gc, the loci of the points d″d″, &c., will be in that perpendicular, and the image dc, seen by successive movements of the binocular centre from d″ to c, will be a straight line.

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, Δ″, (not seen in the Figure) beyond g, we shall have

and if we join the point Δ″ thus found and c, the line Δ′c will be the united image of ac and bc, the binocular centre ranging from Δ″ to c, in order to see it as one line. In like manner, we may find the position and length of the image Δ‴c, Δ′c, and Δc, corresponding to the position of the eyes at e‴e and e. Hence all the united images of ac, bc, viz., cΔ‴, cΔ″, &c., will lie below the plane of abc, and extend beyond a vertical line ng continued; and they will grow larger and larger, and approximate in direction to cg as the eyes descend from e‴ to m. When the eyes are near to m, and a little above the plane of abc, the line, when not carefully observed, will have the appearance of coinciding with cg, but stretching a great way beyond g. This extreme case represents the celebrated experiment with the compasses, described by Dr. Smith, and referred to by Professor Wheatstone. He took a pair of compasses, which may be represented by acb, ab being their points, ac, bc their legs, and c their joint; and having placed his eyes about e, above their plane, he made the following experiment:—“Having opened the points of a pair of compasses somewhat wider than the interval of your eyes, with your arm extended, hold the head or joint in the ball of your hand, with the points outwards, and equidistant from your eyes, and somewhat higher than the joint. Then fixing your eyes upon any remote object lying in the plane that bisects the interval of the points, you will first perceive two pair of compasses, (each by being doubled with their inner legs crossing each other, not unlike the old shape of the letter W). But by compressing the legs with your hand the two inner points will come nearer to each other; and when they unite (having stopped the compression) the two inner legs will also entirely coincide and bisect the angle under the outward ones, and will appear more vivid, thicker, and larger, than they do, so as to reach from your hand to the remotest object in view even in the horizon itself, if the points be exactly coincident.”[38] Owing to his imperfect apprehension of the nature of this phenomenon, Dr. Smith has omitted to notice that the united legs of the compasses lie below the plane of abc, and that they never can extend further than the binocular centre at which their points a and b are united.

There is another variation of these experiments which possesses some interest, in consequence of its extreme case having been made the basis of a new theory of visible direction, by the late Dr. Wells.[39] Let us suppose the eyes of the observer to advance from e to n, and to descend along the opposite quadrant on the left hand of ng, but not drawn in [Fig. 27], then the united image of ac, bc will gradually descend towards cg, and become larger and larger. When the eyes are a very little above the plane of abc, and so far to the left hand of ab that ca points nearly to the left eye and cb to the right eye, then we have the circumstances under which Dr. Wells made the following experiment:—“If we hold two thin rules in such a manner that their sharp edges (ac, bc in [Fig. 27]) shall be in the optic axes, one in each, or rather a little below them, the two edges will be seen united in the common axis, (gc in [Fig. 27];) and this apparent edge will seem of the same length with that of either of the real edges, when seen alone by the eye in the axis of which it is placed.” This experiment, it will be seen, is the same with that of Dr. Smith, with this difference only, that the points of the compasses are directed towards the eyes. Like Dr. Smith, Dr. Wells has omitted to notice that the united image rises above gh, and he commits the opposite error of Dr. Smith, in making the length of the united image too short.

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.

CHAPTER VII.
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—

1. The Tubular Reflecting Stereoscope.

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.

In Mr. Wheatstone’s stereoscope he employs two mirrors, each four inches square—that is, he employs thirty-two square inches of reflecting surface, and is therefore under the necessity of employing glass mirrors, and making a clumsy, unmanageable, and unscientific instrument, with all the imperfections which we have pointed out in a preceding chapter. It is not easy to understand why mirrors of such a size should have been adopted. The reason of their being made of common looking-glass is, that metallic or prismatic reflectors of such a size would have been extremely expensive.

Fig. 28.

It is obvious, however, from the slightest consideration, that reflectors of such a size are wholly unnecessary, and that one square inch of reflecting surface, in place of thirty-two, is quite sufficient for uniting the binocular pictures. We can, therefore, at a price as low as that of the 4-inch glass reflectors, use mirrors of speculum metal, steel, or even silver, or rectangular glass prisms, in which the images are obtained by total reflexion. In this way the stereoscope becomes a real optical instrument, in which the reflexion is made from surfaces single and perfectly flat, as in the second reflexion of the Newtonian telescope and the microscope of Amici, in which pieces of looking-glass were never used. By thus diminishing the reflectors, we obtain a portable tubular instrument occupying nearly as little room as the lenticular stereoscope, as will be seen from [Fig. 28], where ABCD is a tube whose diameter is equal to the largest size of one of the binocular pictures which we propose to use, the left-eye picture being placed at CD, and the right-eye one at AB. If they are transparent, they will be illuminated through paper or ground-glass, and if opaque, through openings in the tube. The image of AB, reflected to the left eye L from the small mirror mn, and that of CD to the right eye R from the mirror op, will be united exactly as in Mr. Wheatstone’s instrument already described. The distance of the two ends, n, p, of the mirrors should be a little greater than the smallest distance between the two eyes. If we wish to magnify the picture, we may use two lenses, or substitute for the reflectors a totally reflecting glass prism, in which one or two of its surfaces are made convex.[40]

2. The Single Reflecting Stereoscope.

This very simple instrument, which, however, answers only for symmetrical figures, such as those shewn at A and B, which must be either two right-eye or two left-eye pictures, is shewn in [Fig. 29]. A single reflector, MN, which may be either a piece of glass, or a piece of mirror-glass, or a small metallic speculum, or a rectangular prism, is placed at MN. If we look into it with the left eye L, we see, by reflexion from its surface at C, a reverted image, or a right-eye picture of the left-eye picture B, which, when seen in the direction LCA, and combined with the figure A, seen directly with the right eye R, produces a raised cone; but if we turn the reflector L round, so that the right eye may look into it, and combine a reverted image of A, with the figure B seen directly with the left eye L, we shall see a hollow cone. As BC + CL is greater than RA, the reflected image will be slightly less in size than the image seen directly, but the difference is not such as to produce any perceptible effect upon the appearance of the hollow or the raised cone. By bringing the picture viewed by reflexion a little nearer the reflector MN, the two pictures may be made to have the same apparent magnitude.

Fig. 29.

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.

Fig. 30.

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.

3. The Double Reflecting Stereoscope.