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 oftwodissimilar 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 seedifferent picturesof the same object, but we seedifferent thingswith 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, bothglasses 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 thatthe 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 thanfifteen hundredyears ago, the celebrated physician Galen treated the subject of binocular vision more fully than Euclid. In thetwelfthchapter 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 therighteye is shut, some of those parts of the column which were previously seen by therighteye on therightside of the column, will not now be seen by thelefteye; and when thelefteye is shut, some of those parts which were formerly seen by thelefteye on theleftside of the column, will not now be seen by therighteye. 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, thatthe 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 workOn 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 aboveon 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. “Leta,” he says, “be the pupil of the right eye,bthat of the left, anddcthe body to be seen. When we look at the object with both eyes we seedc, while with the left eye we seeef, and with the right eyegh. But if it is seen with one eye, it will be seen otherwise, for when the left eyebis shut, the bodycd, on the left side, will be seen inhg; but when the right eye is shut, the bodycdwill be seen infe, whereas, when both eyes are opened at the same time, it will be seen incd.” These resultsare 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 byhe; the right-hand picture, or the one seen by the right eye, byhf; the left-hand picture, or the one seen by the left eye, byge; and the picture of the solid column in full relief bydc, as produced midway between the other two dissimilar pictures,hfandge, 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 unitinghfandge, 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 arelievoequal 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 objectcbe viewed by a single eye ata, all objects in the space behindit—included, as it were, in a shadowecf, cast by a candle ata—are invisible to an eye ata; but when the other eye atbis 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 shadowcd, cast by two lights ataandband terminated ind; the angular spaceedg, beyondd, being always visible to both eyes. And the hidden spacecdis so much the shorter as the objectcis smaller and nearer to the eyes. Thus he observes that the objectc, 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 accuratelywith both eyes than with one, inasmuch as we see it more detached fromother objects beyond it,and more of its own surface, especially if it be roundish.”

We have quoted this passage, not from itsprovingthat Leonardo da Vinci was acquainted with the fact that each eye,a,b, sees dissimilar pictures of the spherec, 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,aandb, sees dissimilar parts of the spherec. It was not his purpose to treat of the binocular pictures ofc, 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 quæτὰ 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, acommon sense, which rectifies the picture. Dr. Whewell and Mr. Wheatstone have cut the Gordian knot by maintaining what is impossible, that in binocular and stereoscopicvision 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 diagrameis the right eye anddthe left,chfithe section of that part of the spherebcwhich is seen by the right eyee,bhgathe section of the part which is seen by the left eyed, andblcthehalf 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 eyeedoes not see the partblcifof the sphere; the left eye does not see the partblcga, while the part seen with both eyes is the hemisphereblcgf, the dissimilar segmentsbfg,cgfbeing 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 aseb,ecfor the right eye, inFig. 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, “theright side of the ruler seen by the right eyewill appear on the left hand, andthe 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 distinguishingprominences of small partsbesides those by which we distinguish distances in general, as their degrees of light and shade, andthe 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 sidesof 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, oranything else, drawn fromone point of sight, or as seen by one eye placed in that point, isnecessarily dissimilarto 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, theτὰ στέρεα, (ta stereaof 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 eyewas 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. Thefirstand 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. Theseconddistance was marked by an old cross about a hundred feet off; and thethirddistance 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 treetouched 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 thePhilosophical Magazinefor 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 (cinFig. 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 isnot a new factwe 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 bettermethod 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 ofstereoscope, 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 obviouslybut 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 simplya truism. It merely states that the difference of the pictures which the eyescanmake to coalesce is equal to the difference of the pictures which the eyes do make to coalesce in their most oblique position; but thougha truismit is nota 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 examinewhytwo dissimilar pictures projected on the two retinægiverise to the perceptionof 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 supposedthat 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 isa degree of indistinctnessin those parts of the field of view to which the eyes are not immediately directed, and whichincreases with the distance from that point, cannot be doubted; and it is also true that the objects there obscurely seen arefrequently doubled. Inordinaryvision, 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 whicha 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 isin some degreetrue, but were it entirely sono 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 betweenordinary 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 noticesthe degree of indistinctnessin 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 acommon senseoverruling 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 saysare 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. Theentire 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 notdecisive againstthe 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 reliefwhen 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 visiondid actuallyunite 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 theapparent whole from which they were taken as seen by each eye. These views were made public in the lectures on thePhilosophy 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 paperOn 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 paperOn the knowledge of distance as given by binocular vision, in which I described several interesting phenomena produced by the union ofsimilarpictures, 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 theLenticular Stereoscope, now in universal use. They were constructed in St. Andrews and Dundee, of various materials, such aswood, 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 shewedthe instrument to the Abbé Moigno, the distinguished author ofL’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 inLa 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 therelievoproduced 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 thePhilosophical Transactionsfor 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 therefractingstereoscope.”[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 withrefractingand 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 therefractingstereoscope 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 adeteriorationof the lenticular stereoscope, is recommended by Mr. Wheatstone, nobody either makes it or uses it. The semi-lenses or quarter-lenses of the lenticular stereoscopeinclude 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 theCosmosof 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 andPRISMS. 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 ofAugust 1838. It is proved by my letter that he and I then conversed on the subject ofprisms, 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 beachromatic 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 hadonly oncetried 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, thatI believedMr. Wheatstone had usedtwoachromatic prisms. The following letter from Mr. Andrew Ross will prove the main fact thathe never constructed for me, or for Mr. Wheatstone, any refracting stereoscope:—

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