THE STEREOSCOPE ITS HISTORY, THEORY, AND CONSTRUCTION WITH ITS APPLICATION TO THE FINE AND USEFUL ARTS AND TO EDUCATION. SIR DAVID BREWSTER, K.H., D.C.L., F.R.S., M.R.I.A., VICE-PRESIDENT OP THK ROYAL SOCIETY OF EDINBURGH, ONE OP THE BIGHT ASSOCIATES OF THE IMPERIAL INSTITUTE OP FRANCE, OFFICER OF THE LEGION OF HONOUR, CHEVALIER OF THE PRUSSIAN ORDER OP MERIT, HONORARY OR CORRESPONDING MEMBER OP THE ACADEMIES OF PETERSBURGH, VIENNA, BERLIN, COPENHAGEN, STOCKHOLM, BRUSSELS, GOTTINGEN, MODBNA, AND OP THE NATIONAL INSTITUTE OP '. '"WASHINGTON, Biq. WITIT FIFTY WtJOD LONDON: JOHN MURRAY, ALBEMARLE STREET. 1856. [The Right of Translation is reserved.'] EDINBURGH : T. CONSTABLE, TEISTFR TO HER MAJESTY. CONTENTS PACK INTRODUCTION, . . 1 CHAP. I. HISTORY OF THE STEREOSCOPE, . . 5 II. ON MONOCULAR VISION, OR VISION WITH ONE EYE 38 III. ON BINOCULAR VISION, OR VISION WITH Two EYES 47 IV. DESCRIPTION OP THE OCULAR, REFLECTING, AND LENTICULAR STEREOSCOPES, . . 53 V.-ON THE THEORY OF STEREOSCOPIC VISION, . 76 VI. ON THE UNION OF SIMILAR PICTURES IN BINOCULAR VISION, . . . .90 VII. DESCRIPTION OF DIFFERENT STEREOSCOPES, . 107 VIII. METHOD OF TAKING PICTURES FOR THE STEREOSCOPE . .131 IX. ON THE ADAPTATION OP THE PICTURES TO THE STEREOSCOPE. THEIR SIZE, POSITION, AND ILLUMINATION, . . . .159 X. APPLICATION OP THE STEREOSCOPE TO PAINT- ING, 166 XI. APPLICATION OF THE STEREOSCOPE TO SCULP- TURE, ARCHITECTURE, AND ENGINEERING, . 183 XII. APPLICATION OF THE STEREOSCOPE TO NA- . TURAL HISTORY, 189 216000 CONTENTS. PAGE CHAP. XIII. APPLICATION OF THE STEREOSCOPE TO EDU- CATIONAL PURPOSES, . . . .193 XIV. APPLICATION OF THE STEREOSCOPE TO PUR- POSES OF AMUSEMENT, . . . .204 XV. ON THE PRODUCTION OF STEREOSCOPIC PICTURES FROM A SINGLE PICTURE, . 200 XVI. ON CERTAIN FALLACIES OF SIGHT IN THE VISION OF SOLID BODIES 200 XVII. ON CERTAIN DIFFICULTIES EXPERIENCED IN THE USE OF THE STEREOSCOPE, . . 231 ON THE STEREOSCOPE, INTRODUCTION. THE Stereoscope, a word derived from orgggoc, solid, and V, to see, is an optical instrument, of modern inven- tion, 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 instru- ment, 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 Stereo- scope, 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 2 INTRODUCTION. copies from statues or models, he produces apparent soli- dity, 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 draw- ings 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 repre- sentations, where the light, concealed from the observer, is introduced in an oblique direction, and where the dis- tance of the picture is such that the convergency of the INTRODUCTION. 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 pano- rama is illuminated by light from various directions, and the slightest motion imparted to the canvas, its surface becomes distinctly visible, and the illusion instantly dis- appears. 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 piano, avail no- thing in the evolution of their relievo, or third dimen- sion. 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 appa- ratus 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 represen- tation ; 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 4 INTRODUCTION. 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 ah*, the most perfect stereoscopic crea- tions, by placing a Stereoscope behind the two dissimilar pictures formed by the camera. CHAPTER I. HISTORY OP THE STEEEOSCOPE. 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 6 THEOREMS OF EUCLID. CHAP. I. 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 phy- sician 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 demonstra- 1 Edit, of Pena, pp. 17, 18, Paris, 1577 ; or Opera, by Gregory, pp. 619, 620. Oxon. 1703. CHAP. I. EXPERIMENTS OF GALEN. 7 tions 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." 1 In such distinct and unambiguous terms, intelligible to the meanest capacity, does this illustrious writer announce the fundamental law of binocular vision the grand prin- ciple 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 1 De Usu Partium Carports Humani, edh. Lugduni, 1550, p. 593. 8 EXPERIMENTS OF BAPTISTA PORTA. CHAP. I. 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 theo- rems, and while he admits the correctness of the observa- tions of Galen, he endeavours to explain them upon other principles. 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 FIG. 1. 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 CHAP. I- EXPERIMENTS OF BAPTISTA PORTA. 9 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. 1 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. In the treatise on painting which he left behind him in MS., 2 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," 3 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 1 Joan. Baptistse Portee Neap., De Refractions Opticet parte, lib. v. p. 132, and lib. vi. pp. 143-5. Neap. 1593. 2 Trattata delta Pictura, Scultura, ed Architettura. Milan, 1584. 3 Dr. Smith's Compleat System o/Optickt, voL ii., Remarks, pp. 41 and 244. 10 LEONAEDO DA VINCI. CHAP. I. 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 FIG. 2. 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 ob- serves 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 CHAP. I. FRANCIS AGUILONIUS. 1 1 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, 1 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 quce ra crigsa (ta stereo) nuncu- pantur,) 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 demon- stration 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," 2 and is as follows : " When one object is seen with two eyes, the angles at 1 Opticorum Libri Sex Philosophis juxta ac Malhematicis utiles. Folio. Ant- verpiae, 1613. 2 In FIG. 1, AHF is the optical pyramid seen by the eye A, and BGB the optical pyramid seen by the eye B. 12 FRANCIS AGUILONIUS. CHAP. I. 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 evi- dent ; 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 termi- nated, (namely, HAF, GBE, 1 ) 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 repre- sentation 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 dis- tinctly 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 1 These angles are equal in this diagram and in the vision of a sphere, but they are inequal in other bodies. CHAP. I. FRANCIS AGUILONIUS. 13 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. What- ever 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." 1 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 impos- sible, that in binocular and stereoscopic vision a long line 1 Aguilonius, Opticorum, lib. ii. book xxxviii. pp. 140, 141. 14 FRANCIS AGUILONIUS. CHAP. I. 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 Agui- lonius supposes, they give to the tender and pulpy retina, the recipient of ocular pictures, the strange power of con- tracting or expanding itself in order to equalize inequal lines and inequal surfaces ! 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. D B FIG. 3. 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 CHAP. I. FRANCIS AGUILONIUS. 15 the section of the sphere as seen by both eyes. 1 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. 2 After demonstrating his theorems on the vision of spheres with one and both eyes, 3 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." 4 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, 5 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 i It is obvious that a complete hemisphere is not seen with both eyes. - Aguilonius, Opticorum, lib. iv. pp. 306, 307. 3 In the last of these theorems Aguilonius describes and explains, we believe for the first time, the conversion of relief in the vision of convex and concave surfaces. See Prop. xciv. p. 312. < Id., Id., p. 313. 5 Opera, torn. ii. p. 394. Lugduni, 1658. 16 FRANCIS AGTJILONIUS. CHAP. I. eye, and the right side of it with the right eye, two pictures sufficiently dissimilar. Andrew Tacquet, 1 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 awn surface, especially if it be roundish" 2 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 repre- sented in the figure." 3 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 distinguish- ing 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 1 Opera Mathematica Optica, tribus libris exposita, p. 136. 2 Opticfo, vol. ii., Remarks, pp. 41 and 245. s id., V oL i. p. 48, Fig. 106. CHAP. I. FRANCIS AGUILONIFS. 17 a near object not thicker than the said distance, and this a stream of water from which the moon was reflected, the two moons being placed nearly at the distance of the two eyes, or "2^ inches, and the two reflected moons at the same dis- tance. 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 pro- jected over one-third of the disc. The branch of the tree 20 MR. ELLIOT. CHAP. I. 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 land- scape, certainly a very imperfect one, was seen in relief, composed of three distances. Owing, no doubt, to the difficulty of procuring good bin- ocular 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 disco- very 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 sub- ject 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 IvC'onardo da Vinci was not aware " that the object (c in CHAP. I. MR. WHEATSTONE. 21 Fig. 2) presented a different appearance to each eye." " He failed" lie adds, " to observe this, and no subsequent writer, to my knowledge, has supplied the omission. The projection of tivo obviously dissimilar pictures on the tivo retinae, 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 dis- similarity 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 ob- viously 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. 22 MR. WHEATSTONE. CHAP. I. He was thus led to construct an apparatus, to be after- wards 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 pub- lication of his invention, but not in the general conception of a stereoscope. After describing his apparatus, Mr. "YVheatstone 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 remltant 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., CHAP. I. MR. WHEATSTONE. 23 both turned to the extreme right or the extreme left) ordi- narily 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 retinae 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 ong, 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 conver- gence 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 24 MR. WHEATSTONE. CHAP. I. 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 care- fully, 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." a 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. Wheat- stone 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 1 Phil. Trans., 1838, pp. 391, 392. CHAP. I. ME. WHEATSTONE. 25 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 over- ruling 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 pre- ceding 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 mil 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 whioji 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 retinae." 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 26 MR. WHEATSTONE. CHAP. I. from the eye being fatigued. In the combination of more complex figures, such as two similar rectilineal figures con- tained 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 acknow- ledges I have established, and " with which," he says, " the laws of visible direction for binocular vision ought to con- tain nothing inconsistent," he would have seen the impos- sibility 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 CHAP. I. MR. WHEATSTONE. 27 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 meet- ing 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 dif- ferent 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 appa- rent whole from which they were taken as seen by each 28 RECENT KESEAECHES. CHAP. I. eye. These views were made public iu 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 Edin- burgh, in January 1843, a paper On the law of visible position in single and binocular vision, and on the repre- sentation 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. Wheat- stone 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 uni- versal use. They were constructed in St. Andrews and Dundee, of various materials, such as wood, tinplate, brass, CHAP. I. STEREOSCOPIC PORTRAITURE. 29 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 bin- ocular 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 stereo- scope 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 gene- rally circulated and greatly admired. This successful appli- cation 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 exhi- bited in 1849 to the British Association,) to construct the lenticular stereoscope, and photographers to execute binocu- lar 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 30 LENTICULAE STEKEOSCOPE. CHAP. I. the instrument to the Abbe 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^ the Abbe 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, acti- vity, and affability will extend the reputation of the distinguished artists of the Rue de 1'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, pro- cured 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." ' December 28, 1550. CHAP. I. LENTICULAR STEEEOSCOPE. 31 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 col- lection of philosophical instruments which M. Duboscq con- tributed 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, how- ever, became so great, that opticians of all kinds devoted themselves to the manufacture of the instrument, and pho- tographers, 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 stereo- scope. 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 for- gotten, 1 Mr. Wheatstone printed, in the Philosophical Transactions for 1852, a paper on Vision, in which he says 1 " Le fait est," says the Abb6 Moigno, " que le sterdoxcope par r/flexion ttait pretquc complelcment oublie, lor-que Sir David Brewster construisit son s-t(5reoscope par refraction que nous aliens dScrire." Cosmos, vol. i. p. 4, 1852. 32 LENTICULAR STEREOSCOPE. CHAP. I. 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." 1 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 refract- ing stereoscope for viewing Daguerreotypes of small dimen- sions, 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." 2 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 ab- solutely 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. 1 PMl. Trans., 1852, p. 6. - Ibid., pp. 9, 10. CHAP. I. LENTICULAR STEREOSCOPE. 33 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 Abbe* 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 1 5th August 1 854, 1 with the following illogical commentary by the editor. " Nous avons eu tort mille fois d'accorder a notre illustre ami, Sir David Brewster, 1'invention du ste're'oscope par reTrac- tion. M. Wheatstone, en effet, a mis entre nos mains une lettre datde, le croirait on, du 27 Septembre 1838, dans lequel nous avons lu ces mots dents par 1'illustre savant Ecossais : 1 1 have also stated that you promised to order for me your stereoscope, both with reflectors and PRISMS. J'ai aussi dit (a Lord Rosse 2 ) que vous aviez promis de commander pour moi votre ste're'oscope, celui avec rdflecteurs et celui avec prismes.' Le ste're'oscope par refraction est done, aussi bien que le ste're'oscope par reflexion, le ste're'oscope de M. Wheat- stone, qui 1'avait invent^ en 1838, et le faisaik construire a cette dpoque pour Sir David Brewster lui-me'me. Ce que Sir David Brewster a imagined, et c'est une ide'e tres inge'- nieuse, dont M. Wheatstone ne lui disputat jamais la gloire, c'est de former les deux prismes du ste're'oscope par refraction avec les deux moitie's d'une meme lentille." That the reader may form a correct idea of the conduct of Mr. Wheatstone in making this claim indirectly, and in 1 Vol. v. livre viii. p. 241. 2 Mr. Andrew Ross, the celebrated optician ! 34 LENTICULAR STEREOSCOPE. CHAP. I. 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 stereo- scope, 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 Abbs' Moigno to make, and which, though made a year and a half ago, he has not enabled the Abbe" 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 achro- matic prisms, and in 1848, when I described my single prism stereoscope, I stated what I now find is not cor- rect, that / believed Mr. Wheatstone had used two achro- matic prisms. The following letter from Mr. Andrew Ross will prove the main fact that he never constructed CHAP. I. LENTICULAR STEREOSCOPE. 35 for me, or for Mr. Wheatstone, any refracting stereo- scope : " 2, FEATHERS-TONE BUILDINGS, 28th September 1854. "DEAR SIR, In reply to yours of the llth 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. 1 also recollect that I did not proceed to manufacture them in consequence of the great bulk of an achromatized prism, with reference to their power of deviating a ray of light, and at that period glass sufficiently free from striae could not readily be obtained, and was consequently very high- priced. I remain, &c. &c. " ANDREW Ross. " To Sir David Brewster." Upon the receipt of this letter I transmitted a copy of it to the Abbs' 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 Abbe 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, 1 in which I mention my belief, now i The Abbg gave an abstract of this paper in the French journal La Presse, December 28, 1850. 36 LENTICULAK STEEEOSCOPE. CHAP. I. 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 Abbs' also must bear the responsibility of a glaring misin- terpretation of my letter of 1838. In that letter I say that Mr. Wheatstone promised to order certain things from Mr, Ross, and the Abb^ 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. Boss. 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 2 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 pic cures for the instru- ment, 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 mu- seums of ancient and modern life in the sacred precincts 1 No. 54, Cheapside, and 313, Oxford Street. The prize of twenty guineas which they offered for the best short popular treatise on the Stereoscope, has been ad- judged to Mr. Lonie, Teacher of Mathematics in the Madras Institution, St. Andrews. The second prize was given to the Rev. R. Graham, Abernyte, Perthshire. CHAP. I. LENTICULAR STEREOSCOPE. 37 of the domestic circle and among those scenes of the picturesque and the sublime which are so affectionately asso- ciated with the recollection of our early days, and amid which, even at the close of life, we renew, with loftier sen- timents and nobler aspirations, the youth of our being, which, in the worlds of the future, is to be the commence- ment of a longer and a happier existence. 38 MONOCULAR VISION. CHAP. TL 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 direc- tions, 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 KB 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 CHAP. II. MONOCULAR VISION. 39 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 FIG. 4. Y and B will pass through H and illuminate with yellow and Ulue 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. 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 40 MONOCULAR VISION. CHAP. II. the hole H, so as to admit more rays from each luminous point of EB, 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 E,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 dis- tance, HY, it will form a bright and distinct image, br, of the same size as the object EB. If we remove the lens, and place another in H, whose focus is at y, for a distance HY, an image, 6V, half of the size of EB, 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 under- stand 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, ABODE, 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 CHAP. II. MONOCULAR VISION. 41 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. FIG. 5, A. The iris has different colours in different persons, black, blue, or grey ; and the pupil, a b, 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 twi- light its size is considerable. Behind the iris, and close to it, is a doubly convex lens, df, or LL in Fig. 5, B, called FIG. 5, B. 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 dis- 42 MONOCULAR VISION. CHAP. II. tances, or obtain distinct vision at these distances. At the back of the eye is a thin pulpy transparent membrane, rr o rr, or v vv, 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. 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 deter- mine 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, a 6, 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 crystal- line lens is placed behind the pupil, and gives distinctness to the image a b 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, CHAP. II. MONOCULAR VISION. 43 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 AH a 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, 1 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 AH a, called the optical axis of the eye, passing through the centre of the lens L^, and the centre of the pupil. The point of distinct vision d corre- sponds with a small hole in the retina called tfye 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. l Edinburgh Transactions, vol. xv. p. 349, 1843 ; or Philosophical Magazine, voL xxv. pp. 356, 439, May and June 1844. 44 CRITERIA OF DISTANCE. CHAP. II. 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 dis- tance from the central point. It is a curious fact, how- ever, that the most distinct point d is the least sensitive to light, and that the sensitiveness increases with the dis- tance 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 di>, 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 CHAP. II. CRITERIA OF DISTANCE. 45 for the same reason, the sun and moon appear more dis- tant 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 appear- ance 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. 46 CRITERIA OF DISTANCE. CHAP. II. 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 de- ceiving 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 geome- trical 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 stereo- scope. 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. CHAP. III. BINOCULAR VISION. 47 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 dif- ferent 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 -f-gtla. part greater than when they are seen with one eye. 1 The cause 1 Smith's Opticks, vol. ii., Remarks, p. 107. Harris makes the difference ^th or iSth; Optics, p. 117. 48 BINOCULAR VISION. CHAP. III. 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. 1 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,) FIG. 6. 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 1 This variation of the pupil is mentioned by Bacon. CHAP. III. BINOCULAR VISION. 49 philosophers, how we see objects single with two eyes. Bap- tista 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. Let us first suppose that we look with both eyes, E and L, Fig. 7, upon a luminous point, D, which we see single, FIG. 7. 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 CHD, cfn'D, of each eye to the point D, an image of which is formed at d in the right eye R, and at d 1 in the left eye L. In virtue of the law of visible direction the point D is seen in the direction dn with the eye R, and in the direction d'v with the eye L, these lines being perpen- dicular to the retina at the points d, d'. The one image of the point D is therefore seen lying upon the other, and con- sequently seen single. Considering t 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 converg- D 50 BINOCULAR VISION. CHAP. HI. ing 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 tine for great distances, but we shall presently see, from the effects of the stereo- scope, 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 CHAP. in. BINOCULAR VISION. 51 possible means of perceiving it. If, for example, we sup- pose 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 what- ever 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 dis- tance 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 repre- sentation. 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 dis- tance 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 fore- ground, the middle and the remote distances in the land- scape, and the relative distances of all these points from the eye are instantly perceived. The binocular relief thus 52 BINOCULAR VISION. CHAP. IIL 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. CHAP. IV. THE OCULAR STEREOSCOPE. 53 CHAPTER IV. DESCRIPTION OF THE OCULAR, THE REFLECTING, AND THE LENTICULAR STEREOSCOPES. ALTHOUGH it is by the combination of two plane pic- tures 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 axts, no relief would be produced. This is equally true when we unite two dissimilar photo- graphic 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 them- selves successively upon, and uniting, the similar points in each picture that correspond to different distances from the observer. 54 THE OCULAR STEREOSCOPE. CHAP. IV. 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 combina- tion 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 there- fore 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 CHAP. IV. THE OCULAR STEREOSCOPE. 55 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 ringer 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 pic- tures are united. If the finger is held up near the dis- similar 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 stereo- scope, 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 mag- nify 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 en- abling 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 56 THE OCULAR STEREOSCOPE. CHAP. IV. 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. 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 FIG. 8. accurate though reduced drawing of the binocular pictures executed and used by Mr. Elliot. I have also united the CHAP. IV. THE OCULAR STEEEOSCOPE. 57 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 stereo- scopic 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 dis- tance, 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, FIG. 9. by looking at a point beyond them we shall also observe the stereoscopic relief. In this position Mr. Elliot saw the relief without any effort, and even without being conscious that he was not viewing the pictures under ordinary vision. This tendency of the optic axes to a distant convergency is so rare that I have met with it only in one person. As the relief produced by the union of such imperfect 58 REFLECTING STEREOSCOPE. CHAP. IV. 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. 1 0, and is described by him in the following terms : " A A' 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 CHAP. IV. REFLECTING STEREOSCOPE. 59 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 FIG. 10. is opposite to it. To facilitate this double adjustment, I employ a right and a left-handed wooden screw, r, I ; 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// E, E' are pan- nels 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 ex- plain the manner of using it. The observer must place his eyes as near as possible to the mirrors, the right eye 60 REFLECTING STEREOSCOPE. CHAP. IV. 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. " If the pictures are all drawn to be seen with the same inclination of the optic axes the apparatus may be simpli- fied by omitting the screw r I, 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 instru- ment 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. 1 0, 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 CHAP. IV. REFLECTING STEREOSCOPE. 61 that the effect was wholly or in part due to these circum- stances, 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 pro- jections, 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 obvi- ously 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 representa- tions 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. Weclgewood 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 day-light, till they disappeared, or permanent outlines of them might have been taken and coloured after nature. Mr. Fox Talbot's beautiful process of producing perma- 62 DEFECTS OF THE REFLECTING STEREOSCOPE. CHAP. IV. nent 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 16J inches long, 6 inches broad, and 81 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 suffi- cient size. 3. In using glass mirrors, of which the reflecting stereo- scope is always made, we not only lose much more than half the light by the reflections from the glass and the me- tallic 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 CHAP. IV. DEFECTS OF THE REFLECTING STEREOSCOPE. 63 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, espe- cially if they are Daguerreotypes, 1 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 beau- tiful 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 convert ; but in using them, we would require to have two lights, one oppo- site 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 stereo- scope never came into use, even after photography was capable of supplying binocular pictures. As a set-off against these disadvantages, it has been i Mr. Wheatstone himself says, " that it is somewhat difficult to render the two Daguerreotypes equally visible." Phil. Trans., 1852, p. 6. 64 LENTICULAR STEREOSCOPE. CHAP. IV. 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 in- tended to produce accurate results, possessed the defects which I have described, and was ill fitted for general use, both from its size and its price, it occurred to me that the union of the dissimilar pictures could be better effected by means of lenses, and that a considerable magnifying power would be thus obtained, without any addition to the instrument. If we suppose A, B, Fig. 11, to be two portraits, A a por- trait of a gentleman, as seen by the left eye of a person FIG. 11. 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 CHAP. IV. LENTICULAR STEREOSCOPE. doing this by lenses may be explained, to persons not ac- quainted with optics, in the following manner : If we look at A with one eye through the centre of a con- vex 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 ri^-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 21 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. 1 2, and we shall see the FIG. 12. portraits A and B united into one at c, and standing out in beautiful relief, a result which will be explained in a sub- sequent chapter. 66 LENTICULAR STEREOSCOPE. CHAP. IV. The same effect will be produced by quarter lenses, such as those shewn in Fig. 1 3. These lenses are cut into a round PIG. 13. or square form, and placed in tubes, as represented at R, L in Fig. 14, which is a drawing of the Lenticular Stereoscope. This instrument consists of a pyramidal box, Fig. 14, blackened inside, and having a lid, c D, 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. 1 3, 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 sim- plest 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 parallelo- gram. 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- CHAP. IV. LENTICULAR STEREOSCOPE. 67 sighted or short-sighted persons, or for coloured glasses and other purposes. If we now put the slide AB, Fig. 11, into the horizontal opening at s, turning up the sneck above s to prevent it FIG. 14. 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, approxi- mate 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 68 LENTICULAR STEREOSCOPE. CHAP. IV. 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 por- traits 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 stereo- scope against the sky or the artificial light, for which pur- pose 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 c D. The lenticular stereoscope may be constructed of various materials and in different forms. I had them made origi- ginally of card-board, tin-plate, wood, and brass j but wood CHAP. IV. LENTICULAR STEREOSCOPE. 69 is certainly tlie best material when cheapness is not an object. 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 FIG. 15. 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 dis- tance from the lenses. 70 LENTICULAR STEREOSCOPE. CHAP. IV. Another form, analogous to this, but without the means of moving the pictures, is shewn in Fig. 1 6, as made by M. Duboscq. The adjustment is effected by moving the FIG. 16. 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-stereo- scope, 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 pyra- midal, 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 CHAP. IV. LENTICULAR STEREOSCOPE. 71 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 reflec- tions, and the sensibility of the eyes diminished. The exclusion of alt 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 accu- 72 LENTICULAK STEEEOSCOPE. CHAP. IV. racy 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. In Fig. 17 is shewn a semi-lens MN, with its section FIG. 17. 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, CHAP. IV. LENTICULAR STEREOSCOPE. 73 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'rcm, keeping the curvature of the surface the same, we increase the re- fracting angle at its margin N' n, we can produce any degree of displacement we require, either for the purposes of experi- ment, 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, n o, n'o', of each are 2-J inches distant, like the two eyes. The two binocular pictures which are to be united are shewn at a b, 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, "Brio, 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 b n, bo, as if they came from V, so that a b will be transferred by refraction to a'b'. In like manner, the picture A B will be transferred by refraction to A'B', and thus united with a' b f . 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 a b 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 74 LENTICULAR STEREOSCOPE. CHAP. IV. 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 cd is equal to a A! and DD' to BB', the circles will not be united, but will overlap one another as at CHAP. IV. LENTICULAR STEREOSCOPE. 75 c'D', cfd'j 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' 3', and place the single circle at the point of con- vergence, 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 refrac- tion at the second surface of the lenses, nor the parallelism of the rays when they enter the eye, facts well known in elementary optics. 76 THEORY OF THE STEREOSCOPE. CHAP. V. 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 com- bined or laid upon one another in the last of these instru- ments, we shall now proceed to consider the theory of stereoscopic vision. 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 A BCD, Fig. 1 9, be a section of the frustum of a cone, that is, a cone with its top cut off by a plane cevg, 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 cei>g. 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, 6, so that a b will represent the line AB, and a circle, whose diameter is a b, will represent the base of the cone, as seen by the right CHAP. V. THEORY OF THE STEEEOSCOPE. 77 eye E. In like manner, by drawing LA, LB, we shall find that A' B' will represent the line A B, and a circle, whose FIG. 19. diameter is A'B', the base AEBG, as seen by the left eye. The summit, cevg, of the frustum being in the plane of projection, will be represented by the circle cevg. The representation of the frustum A BCD, therefore, upon a plane 78 THEORY OF THE STEREOSCOPE. CHAP. V. surface, as seen by the left eye L, consists of two circles, whose diameters are A B, CD ; and, as seen by the right eye, of other two circles, whose diameters are a 6, CD, which, in Fig. 20, are represented by AB, CD, and ab, cd. These FIG. 9u. 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 1 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, tbe 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. 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 CHAP. V. THEOEY OP THE STEREOSCOPE. 79 of it by the left eye. The right side of the frustum A BCD, Fig. 1 9, is represented by the line D 6, as seen by the right eye, and by the shorter line D B', 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 c a', 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, abed, of the frustum of a cone, as obtained from Fig. 19. In order to unite these two dissimilar projections, we must converge the optical axes to a point nearer the ob- 80 THEORY OF THE STEREOSCOPE. CHAP. V. server, or look at some point about M. Both pictures will immediately be doubled. An image of the figure a b will advance towards p, and an image of AB will likewise FIG. 21. advance towards p ; and the instant t l nese images are united, the frustum of a cone, which they represent, will appear in CHAP. V. THEORY OF THE STEREOSCOPE. 81 relief at MJS T , 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, mn~L = ABL ; but its position at M isr 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, A BCD, Fig. 19, in relief, by the union of the two pictures of it on the retina. From the points A, B, c, D, a, 6, c, - The distance of the left ear e, in the right-eye picture, from the nose n, will be ne = yt'n -|- N'E' E'e. In order to simplify the diagram we have made the original, or left-eye picture, a front view, in which the nose is in the middle of the face, and the line joining the ears parallel to the plane of the picture. When the position of the nose and the ears has been thus approximately obtained, the artist may, in like manner, determine the place of the pupils of the two eyes, the point of the chin, the summit of the eyebrows, the prominence of the lips, and the junction of the nose with the teeth, by assuming, under the guidance of the original picture, the distance of these different parts from the plane of projec- tion. In the same way other leading points in the figure and drapery may be found, and if these points are deter- CHAP. XV. FROM A SINGLE PICTURE. 215 mined with tolerable accuracy the artist will be able to draw the features in their new place with such correctness as to give a good result in the stereoscope. In drawing the right-eye picture the artist will, of course, employ as the groundwork of it a faint photo- graphic impression of the original, or left-eye picture, and he may, perhaps, derive some advantage from placing the original, when before the camera, at such an inclination to the axis of the lens as will produce the same diminution in the horizontal distance between any two points in the head, at a mean distance between JST and N', as projected upon the plane AB. The line N'E"', for example, which in the left-eye photograph is a representation of the cheek NE", is reduced, in the right-eye photograph, to nef, and, therefore, if the photograph on .AB, as seen by the right eye, were placed so obliquely to the axis of the lens that N'e was reduced to nd, the copy obtained in the camera would have an approximate resemblance to the right-eye picture required, and might be a better groundwork for the right-eye picture than an accurate copy of the photograph on AB, taken when it is perpendicular to the axis, of the lens. In preparing the right-eye picture, the artist, in place of using paint, might use very dilute solutions of aceto-nitrate of silver, beginning with the faintest tint, and darkening these with light till he obtained the desired effect, and, when necessary, diminishing the shades with solutions of the hypo-sulphite of soda. When the picture is finished, and found satisfactory, after examining its relief in the stereoscope, a negative picture of it should be obtained in the camera, and positive copies taken, to form, with the ori- ginal photographs, the pair of binocular portraits required. 216 FALLACIES IN VISION. CHAP. XVI. CHAPTER XVI. ON CERTAIN FALLACIES OF SIGHT IN THE VISION OF SOLID BODIES. IN a preceding chapter I have explained a remarkable fallacy of sight which takes place in the stereoscope when we interchange the binocular pictures, that is, when we place the right-eye picture on the left side, and the left-eye picture on the right side. The objects in the foreground of the picture are thus thrown into the background, and, vice versa, the same effect, as we have seen, takes place when we unite the binocular pictures, in their usual position, by the ocular stereoscope, that is, by converging the optic axes to a point between the eye and the pictures. In both these cases the objects are only the plane representations of solid bodies, and the change which is produced by their union is not in their form but in their position. In certain cases, however, when the object is of some magnitude in the picture, the form is also changed in consequence of the inverse position of its parts. That is, the drawings of objects that are naturally convex will appear concave, and those which are naturally concave will appear convex. In these phenomena there is no mental illusion in their production. The two similar points in each picture, if they are nearer to one another than other two similar CHAP. XVI. FALLACIES IN VISION. 217 points, must, in conformity with the laws of vision, appear nearer the eye when combined in the common stereoscope. When this change of place and form does not appear, as in the case of the human figure, previously explained, it is by a mental illusion that the law of vision is controlled. The phenomena which we are about to describe are, in several respects, different from those to which we have re- ferred. They are seen in monocular as well as in binocular vision, and they are produced in all cases under a mental illusion, arising either from causes over which we have no control, or voluntarily created and maintained by the observer. The first notice of this class of optical illusion was given by Aguilonius in his work on optics, to which w^e have already had occasion to refer. 1 After proving that convex and concave surfaces appear plane when seen at a considerable distance, he shews that the same surfaces, when seen at a moderate distance, frequently appear what he calls converse, that is, the concave convex, and the con- vex concave. This conversion of forms, he says, is often seen in the globes or balls which are fixed on the walls of fortifications, and he ascribes the phenomena to ,the circum- stance of the mind being imposed upon from not knowing in what direction the light falls upon the body. He states that a concavity differs from a convexity only in this re- spect, that if the shadow is on the same side as that from which the light comes it is a concavity, and if it is on the opposite side, it is a convexity. Aguilonius observes also, that in pictures imitating nature, a similar mistake is com- mitted as to the form of surfaces. He supposes that a circle is drawn upon a table and shaded on one side so as 1 See Chap i. p. 15. 218 FALLACIES IN VISION. CHAP. XVI. to represent a convex or a concave surface. When this shaded circle is seen at a great distance, it appears a plane surface, notwithstanding the shadow on one side of it ; but when we view it at a short distance, and suppose the light to come from the same side of it as the part not in shadow, the plane circle will appear to be a convexity, and if we suppose the light to come from the same side as the shaded part, the circle will appear to be a concavity. More than half a century after the time of Aguilonius, a member of the Eoyal Society of London, at one of the meetings of that body, when looking at a guinea through a compound microscope which inverted the object, was sur- prised to see the head upon the coin depressed, while other members were not subject to this illusion. Dr. Philip Gmelin l of Wurtemberg, having learned from a friend, that when a common seal is viewed through a compound microscope, the depressed part of the seal appeared elevated, and the elevated part depressed, obtained the same result, and found, as Aguilonius did, that the effect was owing to the inversion of the shadow by the microscope. One person often saw the phenomena and another did not, and no effect was produced when a raised object was so placed between two windows as to be illuminated on all sides. In 1780 Mr. Rittenhouse, an American writer, repeated these experiments with an inverting eye-tube, consisting of two lenses placed at a distance greater than the sum of their focal lengths, and he found that when a reflected light was thrown on a cavity, in a direction opposite to that of the light which came from his window, the cavity was i Phil. Trans. 1744. CHAP. XVI. FALLACIES IN VISION. raised into an elevation by looking through a tube without any lens. In this experiment the shadow was inverted, just as if he had looked through his inverting eye-tube. In studying this subject I observed a number of singular phenomena, which I have described in my Letters on Natural Magic, 1 but as they were not seen by binocular vision I shall mention only some of the more important facts. If we take one of the intaglio moulds used by the late Mr. Henning for his bas-reliefs, and direct the eye to it steadily, without noticing surrounding objects, we may distinctly see it as a bas-relief. After a little practice I have succeeded in raising a complete hollow mask of the human face, the size of life, into a projecting head. This result is very surprising to those who succeed in the experi- ment, and it will no doubt be regarded by the sculptor who can use it as an auxiliary in his art. Till within the last few years, no phenomenon of this kind, either as seen with one or with two eyes, had been noticed by the casual observer. Philosophers alone had been subject to the illusion, or had subjected others to its influence. The following case, however, whiclj occurred to Lady Georgiana Wolff, possesses much interest, as it could not possibly have been produced by any voluntary effort. " Lady Georgiana," says Dr. Joseph Wolff in his Journal, " observed a curious optical deception in the sand, about the middle of the day, when the sun was strong : all the foot-prints, and other marks that are indented in the sand, had the appearance of being raised out of it. At these times there was such a glare, that it was unpleasant for the 1 Letter v. pp. 98-107. See also the Edinburgh Journal of Science, Jan. 1826, vol. iv. p. 99. 220 FALLACIES IN VISION. CHAP. XVI. eye." 1 Having no doubt of the correctness of this obser- vation, I have often endeavoured, though in vain, to wit- ness so remarkable a phenomenon. In walking, however, in the month of March last, with a friend on the beach at St. Andrews, the phenomenon presented itself, at the same instant, to myself and to a lady who was unacquainted with this class of illusions. The impressions of the feet of men and of horses were distinctly raised out of the sand. In a short time they resumed their hollow form, but at differ- ent places the phenomenon again presented itself, sometimes to myself, sometimes to the lady, and sometimes to both of us simultaneously. The sun was near the horizon on our left hand, and the white surf of the sea was on our right, strongly reflecting the solar rays. It is very probable that the illusion arose from our considering the light as coming from the white surf, in which case the shadows in the hollow foot-prints were such as could only be produced by foot-prints raised from the sand, as if they were in relief. It is possible that, when the phenomenon was observed by Lady Georgiana Wolff, there may have been some source of direct or reflected light opposite to the sun, or some un- usual brightness of the clouds, if there were any in that quarter, which gave rise to the illusion. When these illusions, whether monocular or binocular, are produced by an inversion of the shadow, either real or supposed, they are instantly dissipated by holding a pin in the field of view, so as to indicate by its shadow the real place of the illuminating body. The figure will appear raised or depressed, according to the knowledge which we obtain of the source of light, by introducing or withdrawing i Journal, 1839, p. 169. CHAP. XVI. FALLACIES IN VISION. 221 the pin. When the inversion is produced by the eye-piece of a telescope, or a compound microscope, in which the field of view is necessarily small, we cannot see the illuminating body and the convex or concave object (the cameo or intaglio) at the same time ; but if we use a small inverting telescope, 1-1- or 2 inches long, such as that shewn at MN, Fig. 36, we obtain a large field of view, and may see at the same time the object and a candle placed beside it. In this case the illusion will take place according as the candle is seen beside the object or withdrawn. If the object is a white tea-cup, or bowl, however large, and if it is illuminated from behind the observer, the re- flected image of the window will be in the concave bottom of the tea-cup, and it will not rise into a convexity if the illumination from surrounding objects is uniform ; but if the observer moves a little to one side, so that the reflected image of the window passes from the centre of the cup, then the cup will rise into a convexity, when seen through the inverting telescope, in consequence of the position of the luminous image, which could occupy its place only upon a convex surface. If the concave body were cut out of a piece of chalk, or pure unpolished marble, it would appear neither convex nor concave, but flat. Very singular illusions take place, both with one and two eyes, when the object, whether concave or convex, is a hollow or an elevation in or upon a limited or extended surface that is, whether the surface occupies the whole visible field, or only a part of it. If we view, through the inverting telescope or eye-piece, a dimple or a hemispherical cavity in a broad piece of wood laid horizontally on the table, and illuminated by quaquaversus light, like that of the sky, it 222 FALLACIES IN VISION. CHAP. XVI. will instantly rise into an elevation, the end of the telescope or eye-piece resting on the surface of the wood. The change of form is, therefore, not produced by the inversion of the shadow, but by another cause. The surface in which the cavity is made is obviously inverted as well as the cavity, that is, it now looks downward in place of upward ; but it does not appear so to the observer leaning upon the table, and resting the end of his eye-piece upon the wooden surface in which the cavity is made. The surface seems to him to remain where it was, and still to look upwards, in place of looking downwards. If the observer strikes the wooden surface with the end of the eye-piece, this conviction is strengthened, and he believes that it is the lower edge of the field of view, or object-glass, that strikes the apparent wooden surface or rests upon it, whereas the wooden surface has been inverted, and optically separated from the lower edge of the object-glass. In order to make this plainer, place a pen upon a sheet of paper with the quill end nearest you, and view it through the inverting telescope : The quill end will appear farthest from you, and the paper will not appear inverted. In like manner, the letters on a printed page are inverted, the top of each letter being nearest the observer, while the paper seems to retain its usual place. Now in both these cases the paper is inverted as well as the quill and the letters, and in reality the image of the quill and of the pen, and of the lower end of the letters, is nearest the observer. Let us next place a tea-cup on its side upon the table, with its concavity towards the observer, and view it through the inverting telescope. It will rise into a convexity, the nearer margin of the cup appearing farther off than the bottom. CHAP. XVI. FALLACIES IN VISION. 223 If we place a short pen within the cup, measuring as it were its depth, and having its quill end nearest the ob- server, the pen will be inverted, in correspondence with the conversion of the cup into a convexity, the quill end appear- ing more remote, like the margin of the cup which it touches, and the feather end next the eye like the summit of the convex cup on which it rests. In these experiments, the conversion of the concavity into a convexity depends on two separate illusions, one of which springs from the other. The first illusion is the erroneous conviction that the surface of the table is looking upwards as usual, whereas it is really inverted ; and the second illusion, which arises from the first, is, that the nearest point of the object appears farthest from the eye, whereas it is nearest to it. All these observations are equally appli- cable to the vision of convexities, and hence it follows, that the conversion of relief, caused by the use of an inverting eye-piece, is not produced directly by the inversion, but by an illusion arising from the inversion, in virtue of which we believe that the remotest side of the convexity is nearer our eye than the side next us. In order to demonstrate the correctness of this explana- tion, let the hemispherical cavity be made in a stripe of wood, narrower than the field of the inverting telescope with which it is viewed. It will then appear really inverted, and free from both the illusions which formerly took place. The thickness of the stripe of wood is now distinctly seen, and the inversion of the surface, which now looks downward, immediately recognised. The edge of the cavity now ap- pears nearest the eye, as it really is, and the concavity, though inverted, still appears a concavity. The same effect is pro- 224 FALLACIES IN VISION. CHAP. XVI. duced when a convexity is placed on a narrow stripe of wood. Some curious phenomena take place when we view, at different degrees of obliquity, a hemispherical cavity raised into a convexity. At every degree of obliquity from to 90, that is, from a vertical to a horizontal view of it, the elliptical margin of the convexity will always be visible, which is impossible in a real convexity, and the elevated apex will gradually sink till the elliptical margin becomes a straight line, and the imaginary convexity completely levelled. The struggle between truth and error is here so singular, that while one part of the object has become con- cave, the other part retains its convexity ! In like manner, when a convexity is seen as a concavity, the concavity loses its true shape as it is viewed more and more obliquely, till its remote elliptical margin is en- croached upon, or eclipsed, by the apex of the convexity ; and towards an inclination of 90 the concavity disap- pears altogether, under circumstances analogous to those already described. If in place of using an inverting telescope we invert the concavity, by looking at its inverted image in the focus of a convex lens, it will sometimes appear a convexity and sometimes not. In this form of the experiment the image of the concavity, and consequently its apparent depth, is greatly diminished, and therefore any trivial cause, such as a preconception of the mind, or an approximation to a shadow, or a touch of the concavity by the point of the finger, will either produce a conversion of form or dis- sipate the illusion when it is produced. In the preceding Chapter we have supposed the con* CHAP. XVI. FALLACIES OF VISION. 225 vexity to be high and the concavity deep and circular, and we have supposed them also to be shadowless, or illumi- nated by a quaquaversus light, such as that of the sky in the open fields. This was done in order to get rid of all secondary causes which might interfere with and modify the normal cause, when the concavities are shal- low, and the convexities low and have distinct shadows, or when the concavity, as in seals, has the shape of an animal or any body which we are accustomed to see in relief. Let us now suppose that a strong shadow is thrown upon the concavity. In this case the normal experiment is much more perfect and satisfactory. The illusion is complete and invariable when the concavity is in or upon an extended surface, and it as invariably disap- pears, or rather is not produced, when it is in a narrow stripe. In the secondary forms of the experiment, the inversion of the shadow becomes the principal cause of the illusion ; but in order that the result may be invariable, or nearly so, the concavities must be shallow and the ' convexities but slightly raised. At great obliquities, however, this cause of the conversion of form ceases to produce the illusion, and in varying the inclination from to 90 the cessation takes place sooner with deep than with shallow cavities. The reason of this is that the shadow of a concavity is very different at great obliquities from the shadow of a convexity. The shadow never can emerge out of a cavity so as to darken the surface in which the cavity is made, whereas the shadow of a convexity soon extends beyond the outline of its base, and finally throws 226 FALLACIES OF VISION. CHAP. XVI. a long stripe of darkness over the surface on which it rests. Hence it is impossible to mistake a con- vexity for a concavity when its shadow extends beyond its base. When the concavity upon a seal is a horse, or any other animal, it will often rise into a convexity when seen through a single lens, which does not invert it ; but the illusion disappears at great obliquities. In this case, the illusion is favoured or produced by two causes ; the first is, that the form of the horse or other animal in relief is the one which the mind is most disposed to seize, and the second is, that we use only one eye, with which we cannot measure depths as well as with two. The illusion, however, still takes place when we employ a lens three or more inches wide, so as to permit the use of both eyes, but it is less certain, as the binocular vision enables us in some degree to keep in check the other causes of illusion. The influence of these secondary causes is strikingly dis- played in the following experiment. In the armorial bearings upon a seal, the shield is often more deeply cut than the surrounding parts. With binocular vision, the shallow parts rise into relief sooner than the shield, and continue so while the shield remains depressed ; but if we shut one eye the shield then rises into relief like the rest. In these experiments with a single lens a slight variation in the position of the seal, or a slight change in the inten- sity or direction of the illumination, or particular reflexions from the interior of the stone, if it is transparent, will favour or oppose the illusion. In viewing the shield at the deepest portion with a single lens, a slight rotation of the seal round the wrist, backwards and forwards, will CHAP. XVI. FALLACIES OF VISION. 227 remove the illusion, in consequence of the eye perceiving that the change in the perspective is different from what it ought to be. In my Letters on Natural Magic, I have described several cases of the conversion of form in which inverted vision is not employed. Hollows in mother-of-pearl and other semi-transparent bodies often rise into relief, in con- sequence of a quantity of light, occasioned by refraction, appearing on the side next the light, where there should have been a shadow in the case of a depression. Similar illusions take place in certain pieces of polished wood, cal- cedony, mother-of-pearl, and other shells, where the surface is perfectly plane. This arises from there being at that place a knot, or growth, or nodule, differing in transparency from the surrounding mass. The thin edge of the knot, &c., opposite the candle, is illuminated by refracted light, so that it takes the appearance of a concavity. From the same cause arises the appearance of dimples in certain plates of calcedony, which have received the name of hammered calcedony, or agate, from their having the look of being dimpled with a hammer. The surface on which these cavities are seen contains sections of small spherical formations of siliceous matter, which exhibit the same illu- sion as the cavities in wood. Mother-of-pearl presents similar phenomena, and so common are they in this substance that it is difficult to find a mother-of-pearl button or counter which seems to have its surface flat, although it is perfectly so when examined by the touch. Owing to the different refractions of the incident light by the dif- ferent growths of the shell, cut in different directions by the artificial surface, like the annual growth of wood in a 228 FALLACIES OP VISION. CHAP. XVI. dressed plank, the surface of the mineral has necessarily an inequal and undulating appearance. In viewing good photographic or well-painted miniature portraits in an erect and inverted position, and with or with- out a lens, considerable changes take place in the apparent relief. Under ordinary vision there is a certain amount of relief depending upon the excellence of the picture. If we invert the picture, by turning it upside down, the relief is perceptibly increased. If we view it when erect, with a lens of about an inch in focal length, the relief is still greater ; but if we view it when inverted with the same lens the relief is very considerably diminished. A very remarkable illusion, affecting the apparent posi- tion of the drawings of geometrical solids, was first ob- served by the late Professor Neckar, of Geneva, who com- municated it to me personally in 1832. 1 " The rhom- boid AX," (Fig. 51,) he says, " is drawn so that the solid FIG. 51. angle A should be seen nearest to the spectator, and the solid angle x the farthest from him, and that the face ACBD should be the foremost, while the face XDC is behind. But 1 See Edinburgh Philosophical Journal, November 1832, vol. i. p. 334. CHAP. XVI. FALLACIES OF VISION. 229 in looking repeatedly at the same figure, you will perceive that at times the apparent position of the rhomboid is so changed that the solid angle x will appear the nearest, and the solid angle A the farthest, and that the face ACDB will recede behind the face XDC, which will come forward, which effect gives to the whole solid a quite contrary- apparent inclination." Professor Neckar observed this change " as well with one as with both eyes," and he con- sidered it as owing " to an involuntary change in the adjustment of the eye for obtaining distinct vision. And that whenever the point of distinct vision on the retina was directed to the angle A for instance, this angle, seen more distinctly than the other, was naturally supposed to be nearer and foremost, while the other angles, seen indis- tinctly, were supposed to be farther away and behind. The reverse took place when the point of distinct vision was brought to bear upon the angle x. What I have said of the solid angles (A and x) is equally true of the edges, those edges upon which the axis of the eye, or the central hole of the retina, are directed, will always appear forward ; so that now it seems to me certain that thia little, at first so puzzling, phenomenon depends upon the law of distinct vision." In consequence of completely misunderstanding Mr. Neckar's explanation of this illusion, Mr. Wheatstone has pronounced it to be erroneous, but there can be no doubt of its correctness ; and there are various experiments by which the principle may be illustrated. By hiding with the finger one of the solid angles, or making it indistinct, by a piece of dimmed glass, or throwing a slight shadow over it, the other will appear foremost till the obscuring 230 FALLACIES OF VISION. CHAP. XVI. cause is removed. The experiment may be still more satisfactorily made by holding above the rhomboid a piece of finely-ground glass, the ground side being farthest from the eye, and bringing one edge of it gradually down till it touches the point A, the other edge being kept at a distance from the paper. In this way all the lines diverging from A will become dimmer as they recede from A, and con- sequently A will appear the most forward point. A similar result will be obtained by putting a black spot upon A, which will have the effect of drawing our atten- tion to A rather than to x. From these experiments and observations, it will be seen that the conversion of form, excepting in the normal case, depends upon various causes, which are influential only under particular conditions, such as the depth of the hollow or the height of the relief, the distance of the object, the sharpness of vision, the use of one or both eyes, the inversion of the shadow, the nature of the object, and the means used by the mind itself to produce the illusion. In the normal case, where the cavity or con- vexity is shadowless, and upon an extended surface, and where inverted vision is used, the conversion depends solely on the illusion, which it is impossible to resist, that the side of the cavity or elevation next the eye is actually farthest from it, an illusion not produced by inversion, but by a false judgment respecting the position of the surface in which the cavity is made, or upon which it rests. CHAP. XVII. DIFFICULTY IN USING THE STEREOSCOPE. 231 CHAPTER XVII. ON CERTAIN DIFFICULTIES EXPERIENCED IN THE USE OF THE STEREOSCOPE. THERE are many persons who experience great difficulty in uniting the two pictures in the stereoscope, and conse- quently in seeing the relief produced by their union. If the eyes are not equal in focal length, that is, in the dis- tance at which they see objects most distinctly ; or if, from some defect in structure, they are not equally good, they will still see the stereoscopic relief, though the picture will be less vivid and distinct than if the eyes were in every respect equal and good. There are many persons, however, whose eyes are equal and perfect, but who are not able to unite the pictures in the stereoscope. This is the more remarkable, as children of four or five years of age see the stereoscopic effect when the eye-tubes are accommodated to the distance between their eyes. The difficulty experienced in uniting the binocular pictures is sometimes only tem- porary. On first looking into the instrument, two pictures are seen in place of one ; but by a little perseverance, and by drawing the eyes away from the eye-tubes, and still looking through them, the object is seen single and in per- fect relief. After having ceased to use the instrument for 232 DIFFICULTY IN USING THE STEREOSCOPE. CHAP. XVH. some time, the difficulty of uniting the pictures recurs, but, generally speaking, it will gradually disappear. In those cases where it cannot be overcome by repeated trials, it must arise either from the distance between the lenses being greater or less than the distance between the CHAP. XVII. DIFFICULTY IN USING THE STEKEOSCOPK 233 eyes, or from some peculiarity in the power of converging the optical axes, which it is not easy to explain. If the distance between the pupils of the two eyes, E, E', Fig. 52, which has been already explained on Fig. 18, is less than the distance between the semi-lenses L, L', then, instead of looking through the middle portions no, n'o', of the lenses, the observer will look through portions between o and L, and o' and L', which have a greater power of re- fracting or displacing the pictures than the portions no, n'o', and therefore the pictures will be too muck displaced, and will have so far overpassed one another that the observer is not able to bring them back to their place of union, half- way between the two pictures in the slide. If, on the other hand, the distance between the pupils of the observer's eyes is greater than the distance between the semi-lenses L, L', then, instead of looking through the por- tions no, n'o' of the lenses, the observer will look through portions between n and L, and n' and L', which have a less power of refracting or displacing the pictures than the por- tions no, n'o', and therefore the pictures will be so little displaced as not to reach their place of union, and will stand at such a distance that the observer is not able to bring them up to their proper place, half-way between the two pictures in the slide. Now, in both these cases of over and under displacement, many persons have such a power over their optical axes, that by converging them to a point nearer than the picture, they would, in the first case, bring them back to their place of union, and by converging them to a point more remote than the picture, would, in the second case, bring them up to their place of union j but others are very defective in 234 DIFFICULTY IN USING THE STEREOSCOPE. CHAP. XVH. this power of convergence, some having a facility of converg- ing them beyond the pictures, and others between the pic- tures and the eye. This last, however, namely, that of near convergence, is by far the most common, especially among men ; but it is of no avail, and the exercise of it is injurious when the under refracted pictures have not come up to their place of union. The power of remote converg- ence, which is very rare, and which would assist in bringing back the over refracted pictures to their place of union, is of no avail, and the exercise of it is injurious when the pictures have been too much displaced, and made to pass beyond their place of union. When the stereoscope is perfectly adapted to the eyes of the observer, and the general union of the pictures effected, the remote parts of the picture, that is, the objects seen in the distance, may be under refracted, while those in the foreground are over refracted, so that while eyes which have the power of convergence beyond the picture, unite the more distant objects which are under refracted, they experience much difficulty in uniting those in the foreground which are over refracted. In like manner, eyes which have the power of near convergence will readily unite objects in the foreground which are over refracted, while they expe- rience much difficulty in uniting objects in the distance which are under refracted. If the requisite power over the optical axes is not acquired by experience and persever- ance, when the stereoscope is suited to the eyes of the observer, the only suggestion which we can make is to open the eyes wide, and expand the eyebrows, which we do in staring at an object, or in looking at a distant one, when we wish to converge the axes, as in Fig. 22, to a point CHAP. XVII. DIFFICULTY IN USING THE STEEEOSCOPE. 235 beyond the pictures, and to contract the eyes and the eye- brows, which we do in too much light, in looking at a near object, when we wish to converge the optic axes, as in Fig. 21, to a point between the pictures and the eye. When the binocular pictures are taken at too great an angle, so as to produce a startling amount of relief, the distance between similar points in each picture, both in the distance and in the foreground, is much greater than it ought to be, and hence the difficulty of uniting the pictures is greatly increased, so that persons who would have expe- rienced no difficulty in uniting them, had they been taken at the proper angle, will fail altogether in bringing them into stereoscopic relief. In these observations, it is understood that the observer obtains distinct vision of the pictures in the stereoscope, either by the adjustment of the moveable eye-tubes, if they are moveable, as they ought to be, or by the aid of convex or concave glasses for both eyes, either in the form of spectacles, or separate lenses placed immediately above, or immediately below the semi-lenses in the eye tubes. If the eyes have different focal lengths, which is not oinfrequently the case, lenses differing in convexity or concavity should be employed to equalize them. EDINBURGH: T. CONSTABLE, PRFNTBETO HER MAJESTY. , RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 - ALL BOOKS MAY BE RECALLED AFTER 7 DAYS __ 2-month loans may be renewed by calling Jj (415) 642-6753 _ 1-year loans may be recharged by bringing books to NRLF j~- Renewals and recharges may be made 4 days ^N prior to due date "I DUE AS STAMPED BELOW AU6 8 1991 SEP 1 6 ,993 ; _- x_-"'-u^'l-.'-N^ > > Rec. Moffitt l lUTQ DISC CIRC JUH 27*93 AUG 191994 iwii y MOV 1 4 19 CIRCULATION PEPT. AUG 7 1999 MAY 4 2003 ILEY U.C. BERKELEY LIBRARIES THE UNIVERSITY OF CALIFORNIA LIBRARY