by all but its author, till a more fortunate inventor reproduces it under a new form, and with more valuable and extensive properties.

Even for centuries, the Microscope of Roger Bacon, and of Drebbel, served but to astonish the young and amuse the curious; and without greatly detracting from the merits of Leuwenhoek, and other naturalists who used it, we may safely assert, that till it became achromatic by the labours of Lister, Ross, and others, it was not fitted for those noble researches in natural history and physiology, in which it has performed so important a part. The refracting Telescope, too, whose inventor we cannot confidently name, was a small and useless toy, till Galileo turned it to the heavens; and though in the hands of Huygens and Hevelius, it added new satellites to our system, and displayed new forms and structures in the primary planets, yet it was only, when made achromatic, through the labours of Hall, Dollond, Frauenhofer, and others, that it became an essential instrument for the advancement of astronomy. The Reflecting Telescope presents to us the same peculiarity. We do not know its inventor. Even in Sir Isaac Newton's hands, and as constructed and applied by himself, it effected no discoveries in the heavens. Sir William Herschel gave it magnifying and penetrating power, and opened its eye upon those glorious worlds, which in the dark bosom of space might have been for ever concealed. Even then, however, the sidereal universe presented new subjects of research. Matter, as if reduced to its elements, whitened in nebulous forms the more distant regions of space, and the genius of Lord Rosse was evoked to construct gigantic instruments, to resolve into suns and systems the pale atoms of light which clustered on the receding frontier of creation.

Like these valuable inventions, the Stereoscope has had its infancy and its manhood. At first a simple experiment exhibited by a rude and imperfect apparatus, it was soon forgotten; and it was not till the discovery of its true theory and its valuable applications, and till the invention of new combinations by which these applications were to be effected, that it was brought into public notice, and made one of the most popular and interesting instruments which science has presented to the arts. We propose, therefore, to devote this article to an account of the history, construction, and application of the Stereoscope, and of those principles and phenomena of binocular vision, or vision with two eyes, on which it depends, and with which it is connected.

The term Stereoscope, from σTepeos a solid, and σкоπew to see, is the name of an apparatus employed by Mr. Wheatstone, "for representing solid figures," by combining in one image two plane representations of the object as seen by each eye separately,

Leonardo da Vinci on Binocular Vision.

167

a combination which can be easily effected by the two eyes alone, without the aid of any apparatus, merely by directing them to a point nearer than the two plane representations of the solid. The fundamental facts in binocular vision, on which this remarkable illusion depends, may be thus expressed :

When we view, with both eyes, or with each eye successively, any solid object, that is, any object in relief, or in the converse of relief, any cameo or intaglio, for example, each eye sees the object differently, or, what is the same thing, dissimilar pictures of the object are painted on the two retina.

This important fact has been long ago published by optical writers, and is well known to optical observers, though Mr. Wheatstone has claimed it "as a new fact in the theory of vision." The first writer who has distinctly referred to it, is the clebrated Leonardo da Vinci, in his " Treatise on Painting." The following account of his observations is given by Dr. Robert Smith:-*

"Leonardo da Vinci," says Dr. Smith, "has made a curious observation, not improper to be mentioned in this place :† That 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. Which he thus demonstrates :-If an object, C, be viewed by a single eye at A, all objects in the space behind it, included, as it were, in a shadow, ECF, cast by a candle at A, are invisible to the eye at A; but when the other eye at B is opened, part of these objects become visible to it; those only being hid from both eyes that are included, as it were, in the double shadow C D, cast by two lights at A and B, and terminated in D; the angular space, ED G, beyond D being always visible to both eyes. And the hidden space, C D, is so much the shorter, as the object, C, is smaller and nearer to the eyes. Thus, he observes, that the object, C, seen with both eyes, becomes, as it were, transparent, according to the usual definition of a transparent thing; namely, that which hides nothing beyond it. But this cannot happen, when an object, whose breadth is bigger than that of the pupil, is viewed by a single eye. The truth of this observation is, therefore, evident; because a painted figure intercepts all the space behind its apparent place; so as to preclude the eyes from the sight of every part of the imaginary ground behind it."

* Compleat System of Opticks, vol. ii. Remarks, p. 41, 2 244. As Dr. Smith does not give this passage under inverted commas, it might have been presumed that it was an abstract of Leonardo da Vinci's Observations. Mr. Wheatstone gives the passage in inverted commas, and calls Dr. Smith's paragraph a quotation from Leonardo's Trattato della Pittura, and he refers to a separate work, viz., " A Treatise of Painting," p. 178, London, 1721, as if it were a different work from Leonardo's. We mention this, as we were misled by the mistake to search for it as a separate treatise. Since this note was written we have looked into the Trattato, &c. Roma, 1817, p. 245-6, and find that the passage referred to is not a quotation. + Treatise of Painting, p. 178. London, 1721.

Upon this interesting paragraph Mr. Wheatstone makes the following observations:

"Had Leonardo da Vinci taken, instead of a sphere, a less simple figure for the purpose of his illustration, a cube, for instance, he would not only have observed, that the object obscured from each eye a different part of the more distant field of view, but the fact would also, perhaps, have forced itself upon his attention, that the object presented a different appearance to each eye. He failed to do this, and no subsequent writer, within my knowledge, has supplied the omission; the projection of two obviously dissimilar pictures on the two retina, when a single object is viewed while the optic axes converge, must, therefore, be regarded as a new fact in the theory of vision."-Pp. 372, 373.

Now, it is quite true, that Leonardo da Vinci does not state that the two spheres do not present a different appearance to each eye; but his figure demonstrates ocularly, that each eye sees different pictures, because each eye sees parts of the sphere which are not seen by the other, two pictures so dissimilar, that if combined, they would represent the sphere in relief. In commenting upon the passage, Dr. Smith observes, that we distinguish the place of a near object "more accurately with both eyes than with one, in as much as we see it more detached from other objects beyond it, and more of its own surface, especially if it be roundish." Here Dr. Smith does not speak merely of a sphere, but of any solid object whatever, and as he distinctly states that the two eyes exhibit parts of the object which are not seen by one eye, the pictures on each eye must be dissimilar. And in proof that Dr. Smith considers the demonstration of Leonardo da Vinci already quoted, as referring, not only" to the object obscured from each eye," but to the pictures of the sphere in each eye, he draws the conclusion, “that an object does not appear larger to both eyes than to one, unless by reason of some particular circumstances, as in the observation of Leonardo da Vinci."*

Subsequent writers, too, were well acquainted with the existence of dissimilar pictures in binocular vision. Mr. Harris remarks in his Treatise on Optics,t that "by an inspection of the figures, it is manifest enough, that a larger segment of a round object can be seen with both eyes open, than with one eye alone;" and in Dr. Smith's curious experiment with a pair of compasses,+ and in Dr. Wells' experiment with two rulers, § referred to by Mr. Wheatstone, the pictures seen by each eye were totally dissimilar.

Dr. Smith, indeed, who first made the experiment with the ruler, gives a drawing of it by each eye, and not only shews in

* Opticks, vol. ii., Remarks, p. 109, 708.

+ Page 113, 64.

Optics, vol. vi. p. 388, 977, 978.

§ Wells' Essay on Single Vision with Two Eyes, p. 44.

Each Eye sees Dissimilar Pictures of Solids.

*

169 the drawing that the right eye sees the right side only, and the left eye the left side, but he distinctly states that the right side of the ruler is seen by the right eye, and the left side by the left eye. But to remove all doubt, if there could be any doubt, of the truth of our position, we have only to refer to Dr. Porterfield's Treatise on the Eye, where he actually gives drawings of an object as seen by each eye, the one exhibiting the object as viewed "endwise" by the right eye, (to use a word of Dr. Berkeley's,) and the other the same object as viewed laterally by the left eye. These views of the object as seen by the eye, not as drawn in Dr. Porterfield's diagram, are actually binocular pictures, suited to the stereoscope, if a line protended from the eye, which the instrument will display as stretching out into space.†

In support of these observations, we may refer to the experience of every optical, or even of every ordinary observer. What artist does not shut one eye when he paints or models? Who has not observed the fact, that their left eye sees only the left side of their nose, and their right eye only the right side, two pictures altogether dissimilar? Who has not noticed, that when they look at any thin, flat body, edgewise, such as a thin book, they see both sides of it, the left eye only the left side, and the right eye only the right side, while the edge or back nearest the face is seen by both eyes. What student of perspective, male or female, who has

* Vol. I., Book III., chap. III., axiom 2, pp. 412, 413, plate v., fig. 37. Edinburgh, 1759.

Since the above paragraph was written we have found a complete confirmation of the opinion which it contains in Aguilonii Opticorum Sex Libri, Antwerpiæ, 1613, folio. In the fourth book of this elaborate work Aguilonius treats at great length of the Fallacies of Vision, De Fallaciis Aspectus, and discusses the subject of Binocular Vision with great distinctness. After shewing, what Euclid did before him, how to find the part of a sphere, whether convex or concave, that is seen by one eye, he gives a separate diagram, (lib. iv. prop. lxxxv. p. 307,) in which he proves that each eye, in binocular vision, sees different pictures of it, the portion of the sphere that is seen by the left eye being invisible to the right eye, and vice versa, there being one portion of it between these two that is seen by both eyes. He then lays down a rule for ascertaining in all solids whatever, which part of the body is seen by one eye, and which part by the other. This rule may be thus expressed: If a line or ray, as he calls it, drawn to the one eye reaches it, that part will be seen; but if it does not reach it, that is, if it is stopped by any prominence on the body, it will not be seen. To the mass of rays that reaches each eye, and gives the vision of it to that eye, he gives the name of the optical pyramid, which is different for each eye. The following is the passage in which he shews that in all bodies whatever the same rule holds, and that the pictures of such bodies in each eye are dissimilar. Non sphæræ modo, sed etiam cylindro et cono, ac ceteris corporibus universis convenit, eam quæ spectatur portionem radiis tangentibus comprehendi. Cum enim tangentes lineæ extremæ sint illarum omnium quæ ab uno eodemque signo (in quo oculus positus esse intelligatur) ad propositum corpus duci possunt; perspicue sequitur, eam corporis partem quæ ridetur, tangentibus undique radiis contineri. In hac enim parte nullum punctum reperire est a quo recta linea ad oculum duci non possit, per quam proinde aspectabilis forma recta efferatur. Page 313. In an earlier part of his work, namely in book ii.,*

* Aguilonii Opticorum Sex Libri. Lib. II. prop. 38, A.B.

drawn the picture of a chair or a table from one point of sight, or as seen by one eye, does not know for certain that the picture of the chair or table drawn from another point of sight, or as seen by the other eye, must be dissimilar to the first?

"We have other helps," says Mr. Harris, " for distinguishing the prominences of small parts, besides those by which we distinguish distances in general, in their degrees of light and shade, and the prospect we have round them. And by the parallax on account of the distance between our eyes, we can distinguish besides the front part the two sides of a near object not thicker than the said distance, and this gives a visible relievo to such objects, which helps greatly to raise or detach them from the plane on which they lie. Thus the nose on a face is the more remarkably raised by our seeing each side of it at once."--Treatise on Optics, p. 171, § 205.

That is, the relievo is produced by the combination of the two dissimilar pictures given by the two eyes, which is clearly the principle of the stereoscope,-a principle which Mr. Wheatstone has the merit of having been the first to exhibit practically, by combining

where he is treating of the vision of solids of all forms, de genere illorum quæ ru Tigra (ta sterea) Græce nuncupantur, he has great difficulty in explaining, and fails in doing it, why the two dissimilar pictures, arising from the same parts of the solid being at different distances from each eye, do not, when united, give a confused and imperfect view of it. Cum res una duobus spectatur oculis, anguli qui ad rertices sunt pyramidum opticarum, non semper equales inter se existunt: nam præter directum obtutum, quo pyramides æquales esse oportet, in quamcunque partem limi oculi concertantur, imparibus semper angulis formas rerum admittunt, quorum is major est quæ ad propinquiorem oculum terminatur ; is vero minor, qui oculum spectat remotiorem. Quod sane manifestum per se esse arbitror: id cero admiratione dignum puto, quo pacto fiat ut quæ limis oculis cernuntur non omnia confusa ac velut informia videantur, etsi per axes opticos in res ipsas defixos intuitus fiant. Nam majoribus spectata angulis majora, minora minoribus apparent. Si ergo res una eademque altero quidem oculo major, altero vero minor propter angulorum in quos pyramides terminantur inequalitatem conspiciatur, illa profecto se ipsa major et minor, eodem tempore, et eodem intuente videbitur, atque ita cum singulorum oculorum phantasiæ minime sibi congruant, confusa quædam ac perturbata rei imago sensui principi exhibebitur. Aguilonius does not venture to assert that though the solids are seen clearly and distinctly, (clare et perspicue cernuntur,) the major and the minor line exactly coincide, (sibi mutuo et exacte congruunt,) but he talks of a common sense exerting its power to correct the imperfect union, and prevent the dissimilarity of the two pictures from passing into the primary sense: Non tamen eadem diversitas in primarium sensum transit si modo per axes intuitus fit.

But, to go still farther back in the history of optics, the celebrated Physician Galen, who lived seventeen hundred years ago, has given such a distinct account of the phenomena of binocular vision, in the 13th chapter of the 10th_book of his work, De usu portionis corporis humani, that it is certain that he was clearly acquainted with the dissimilarity of the pictures in each eye. We are almost ashamed to adduce any evidence to prove that every author who has written on the binocular vision of solids, and every optical observer who has looked at them, were well acquainted with the fact which Mr. Wheatstone claims "as a new one in the theory of vision" discovered by himself, namely, that there is a "projection of two obviously dissimilar pictures on the two retina when a single object is viewed while the optic axes conterge," and consequently that the vision of objects in relief is produced by the union of these two dissimilar pictures.

* Edit. Lugduni, 1550. Tom. ii. pp. 591-594.