been the first to exhibit practically, by com- coalesce. Were it not for the binocular coinci bining the pictures of objects as seen with dence of two images of different magnitude, obeach eye, by means of an apparatus, consist- jects would appear single only, when the optic ing of two plane mirrors placed at an angle only, when the converging visual lines form axes converge immediately forward, for it is. of 90°, in which the eyes of the observer equal angles with the visual base, (the line see, by reflection, the superimposed images joining the centres of the two eyes,) that the of the two plane representations of the two pictures can be of equal magnitude, but object. when they form different angles, the distance from the object to each eye is different, and consequently the picture projected in each eye Transactions, 1838, pp. 385, 386. a different magnitude." Philosophical

has

Such is the principle upon which the operation of the stereoscope depends, and such its practical application. We come now to consider the theory of the process by which two plane figures apparently coalesce, and Having laid down these principles, as exhibit, in virtue of this apparent coales- proved by direct experiment, but which, as. cence, the perfect representation of the ob- we shall afterwards demonstrate both from ject in relief from which the figures were theory and experiment, are the results of intaken. In attempting to give such a theory, correct observation, Mr. Wheatstone goes Mr. Wheatstone proceeds to consider the on "to examine why two dissimilar pictures "Binocular vision of objects of different projected on the two retine give rise to the magnitudes," to which he devotes a section perception of an object in relief :" of his Paper:

"We will now inquire," he says, "what ef fect results from presenting similar images, differing only in magnitude, to analogous parts of the retina. For this purpose two squares or circles, differing obviously, but not extravagantly in size, may be drawn on two separate pieces of paper, and placed on the stereoscope, so that the reflected image of each shall be equally distant from the eye by which it is regarded. It will then be seen, that notwithstanding this difference, they coalesce, and occasion a single resultant perception."-Philosophical Transactions, 1838, p. 355.

Mr. Wheatstone then proceeds to describe an experiment for ascertaining the difference between the lengths of two lines which the eye, by some magic power hitherto unknown, can force into coalescence, or, to use his own words, for ascertaining "the limit of the difference of size within which the single appearance subsists." He does this by employing two images of equal magnitude, and making one of them visually less than the other, "by causing it to recede from the eye, while the other remains at a constant distance." "By this experiment," he adds, "the single appearance of two images of different size is demonstrated." Mr. Wheatstone then proceeds to give a sort of rule or law, for ascertaining the ratio between two lines which the eyes can force into coincidence or coalescence, so as to "occasion a single resultant perception:"

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

"That there is a degree of indistinctness in those parts of the field of view to which the eyes are not immediately directed, and which increases with the distance from that point, cannot be doubted, and it is also true, that the bled. In ordinary vision, it may be said, this objects thus obscurely seen, are frequently douindistinctness and duplicity is 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 all the pictures successively seen, while the distinctly; but is formed from a comparison of eyes were changing from one point of the 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 intensely If the pictures be too unequal in magnitude, fixed on one point of a binocular image in the the binocular coincidences does not take place. stereoscope. But on performing the experiIt appears that if the inequality of the pictures ment carefully it will be found, provided the picbe greater than the difference which exists be- ture do not extend too far beyond the centres of distween the projections of the same object, when tinct vision, that the image is still seen single, and seen in the most oblique position of the eyes, in relief, when in this condition. Were the (ie., both turned to the extreme right or ex- theory of corresponding points true, the aptreme left,) ordinarily employed, they do not pearance should be that of the superposition of

the two drawings, to which, however, it has not in optics, and the moment we allow them the slightest similitude." Philosophical Trans to be tampered with to obtain an explana actions, pp. 391, 392. tion of physical puzzles, we convert science into legerdemain, and philosophers into conjurors.

Mr. Wheatstone proceeds to give two experiments, which he says are equally decisive against this theory, the first first of which Such was the state of our stereoscopic only is subject to rigorous examination. knowledge in 1838, after the publication of He draws "two lines about two inches Mr. Wheatstone's interesting and important long, and inclined towards each other, on a paper on the physiology of vision. In the sheet of paper, and having caused them to same year, at the meeting of the British coincide by converging the optic axes to a Association at Newcastle, and before the point nearer than the paper, he looks in-publication, or perhaps even the printing, tently on the upper end of the resultant of Mr. Wheatstone's Memoir, Sir David line, without allowing the eyes to wander Brewster communicated to the mathematical from it for a moment. The entire line will and physical section a paper "on the law appear single, and in its proper relief, &c. of visible direction," in which he established The eyes sometimes become fa- this great law of vision, which, though it tigued, which causes the line to become had been maintained by preceding writers, double at those parts, to which the optic had been more recently proved by the ilaxes are not fixed, but in such case all ap- lustrious D'Alembert to be incompatible pearance of relief vanishes. The same ex-with observation, and the admitted anatomy periment may be tried with more complex of the human eye. At the same meeting figures, but the pictures should not extend Mr. Wheatstone exhibited his stereoscopic too far beyond the centres of the retina." Now these are not the correct results of the experiment, for no sooner does the eye see the real phenomenon the duplicity of the image at all points but one-than Mr. Wheatstone ascribes it to ocular fatigue, and to too great an extension of the pictures. As the two lines are equal, in the present experiment, the difficulty of obtain ing an apparent combination of the lines is greatly diminished; but Mr. Wheatstone has previously maintained, that when the two fines are unequal they are not only single, but mathematically coalescent.

apparatus, which gave rise to an animated discussion between Dr. Whewell and Sir David Brewster, in which the learned Master of Trinity, adopting Mr. Wheatstone's views, already explained, maintained that the eye, or rather 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 we would have suggested, in order to have given the retina only half the trouble, that it contracted the long line as much as it expanded the short one, and thus caused In the different passages which we have now them to combine with a less exertion of quoted from Mr. Wheatstone's paper, and muscular power! Sir David Brewster, on in the remaining pages of it, he is obviously the other hand, maintained that the retina halting between truth and error, between had no such power, that so extreme an hytheories which he partly believes, and ill pothesis was not required, and that the law observed facts which he cannot reconcile of visible direction afforded the most perfect with them. Had he placed his reliance on explanation of all the stereoscopic phenothe law of visible direction, which in a pre-mena. Subsequent to this discussion, Mr. vious part of his paper he acknowledges to Wheatstone accepted of Sir David Brewshave been established in opposition to ter's demonstration of the law of visible D'Alembert by Sir David Brewster, and direction as satisfactory, and thus refers to it "with which," he says, "the laws of visible in his paper on the Stereoscope, in the Phil. direction for binocular vision ought to con- Transactions, to which we have so often retain nothing inconsistent," he would have ferred:seen the impossibility of the two eyes uniting two lines of unequal length; and had "The law of visible direction for monocular be believed in the law of distinct vision, vision has been variously stated by different opwhich has been established by the same tical writers. Some have maintained, with Drs. author, he would have seen the impossi- Reid and Porterfield, that every external point is bility of the two eyes obtaining single seen in the direction of a line passing from its vision of any more than one point of an picture on the retina through the centre of the object at a time. These laws of vision are that the visible direction of an object coincides eye; while others have supposed, with Dr. Smith, as rigorously true as any other physical laws with the visual ray, or the principal ray of the -as completely demonstrated as the law of pencil which flows from it to the eye. D'Alemgravity in astronomy, or the law of sines bert, furnished with imperfect data respecting the

refractive densities of the humours of the eye,* College of St. Salvator and St. Leonard, St. calculated that the apparent magnitudes of ob- Andrews, and the different stereoscopes which jects would differ widely on the two suppositions, he invented were also exhibited and exand concluded that the visible point of an object was not seen in either of these directions, but plained. Mr. Wheatstone's inventions were sensibly in the direction of a line joining the at the same time fully communicated to the point itself and its image on the retina; but he class, and his stereoscopic apparatus was acknowledged that he could assign no reason for even lent to the students to take to their this law. Sir David Brewster, provided with own lodgings, that they might fully appremore accurate data, has shewn that these three ciate the value of his labours. lines so nearly coincide with each other, that at In examining Dr. Berkeley's celebrated an inclination of 300, a line perpendicular to the theory of vision, the undoubted foundation point of impression on the retina, passes through of our sceptical philosophy, to which two the common centre, and does not deviate from the real line of visible direction more than half a lectures were generally devoted, Sir David degree, a quantity too small to interfere with the Brewster saw the vast importance of estabpurposes of vision. We may therefore assume, lishing, upon an impregnable basis, the law in all our future reasonings, the truth of the fol- of visible direction, and of proving by the lowing definition given by this eminent philoso- aid of binocular phenomena, and in opposipher,-As the interior of the eyeball is as nearly tion to the opinion of the most distinguished as possible a perfect sphere, lines perpendicular to the surface of the retina must all pass through metaphysicians, that we actually see a third dimension in one single point, namely, the centre of its spherispace. He, therefore, submitcal surface. This one point may be called the ted to the Royal Society of Edinburgh, on centre of visible direction, because every point the 23d January and the 6th February, of a visible object will be seen in the direction 1843, a paper "On the law of visible posi of a line drawn from the centre to the visible tion in single and binocular vision, and on point.' "It is obvious that the result of any attempt Union of dissimilar Plane Pictures on the the representation of solid figures by the to explain the simple appearance of objects to both eyes, or, in other words, the law of visible Nearly ten years have elapsed direction for binocular vision, ought to contain since this paper was published, and no reply nothing inconsistent with the law of visible di- has, as far as we know, been made to it by rection for monocular vision."-Phil. Trans. Mr. Wheatstone or any of his friends. 1838, pp. 387-8.

Retina."

In continuing his researches, Sir D. Brewster submitted to the Royal Society of Notwithstanding this acceptance of the Edinburgh, on the 15th of April 1844, a law of visible direction, and the correctness of the conclusion at which he has here paper "On the knowledge of distance given arrived, every succeeding page of Mr. by binocular vision," and on the 6th of May Wheatstone's paper, in which he explains sion of relief by inverted vision," or, to use of the same year, another "On the converthe phenomena of the stereoscope, not only a word recently introduced by Mr. Wheatstands in direct opposition to this law, but as we shall shew in the sequel, in direct op- During these inquiries, Sir David Brewster stone, on Pseudoscopic vision with one eye. position to the most obvious and irrefragable invented, and had constructed in St. Anexperiments.

drews and Dundee several new stereoscopes, In consequence of the discussion at Newbut particularly the Lenticular stereoscope, castle, and the high authority upon which the law of visible direction was impugned, all materials, of wood, of tin, of brass, and now in universal use. They were made of Sir David Brewster re-examined the subject, of bristol board, and of all sizes, from that repeated his calculations, and especially set himself to determine by rigorous experi- now generally adopted to a miscroscopic variety which could be carried in the ments, whether or not the human eye had the power of causing two lines of different for them, and binocular pictures taken by pocket. New drawings were executed lengths or of different apparent magnitudes the sun, were lithographed for the instrument to coalesce into one. He found that the by Mr. Schenck of Edinburgh. eye had no such power, and that no such power was required to convert the two plane Dundee, with various binocular diagrams, scopes made by Mr. Loudon, optician, pictures for the stereoscope into the apparent lithographed at his expense, were sent to solids from which they were taken, as seen by each eye. These views were made public other places in England, and an account of several of the nobility in London, and to in the lectures on the Philosophy of the these stereoscopes, and their application to Senses, which he occasionally delivered in the portraiture and sculpture, and of a binocular camera for taking portraits and copying statues, was submitted to the Royal Scottish

*And also, he might have added, respecting the relative positions of the different parts of the eye.

Stereo

Society of Arts, in 1849, and published in, and for which he received a council medal, their Transactions.* he placed one of Sir David Brewster's Len. After endeavouring, though in vain, to ticular Stereoscopes with a fine series of induce some London opticians and photo- Binocular Daguerreotypes. The Stereoscope graphers to construct his stereoscope and attracted the particular notice of the Queen, execute binocular pictures for it, Sir David and M. Soleil executed a beautiful instruBrewster carried to Paris in the spring of ment which was presented to Her Majesty 1850, a very fine instrument, executed by in his name by Sir David Brewster. In Mr. Loudon, optician in Dundee, and a consequence of this public exhibition of it, binocular photographic portrait of Dr. M. Soleil received several orders from EngAdamson of St. Andrews, by himself. He land, and a large number of the Lenticular showed this instrument to M. l'Abbé Stereoscopes were thus introduced into this Moigue, t the distinguished author of L'Op- country. The demand, however, became so tique Moderne, and to M. Soleil, and his great that English workmen, and particuson-in-law, M. Duboscq Soleil, the eminent larly Mr. Pearce, 36, Bedford Bury, Covent Parisian opticians, and to some members of Garden, devoted themselves to their manuthe Institute of France. These gentlemen facture, and sold in a few months many hunsaw at once the value of the instrument, dreds if not thousands of the instrument. not merely as one of amusement, but as an The Photographers, both Daguerreotypists important auxiliary in the arts of portraiture and Talbotypists now take Binocular porand sculpture. M. Duboscq Soleil imme- traits, to be thrown into relief by the Stereodiately began to make the new stereoscope scope, as an important branch of their profor sale, and executed a series of the most fession, and we have no doubt that the time beautiful binocular daguerreotypes of living is near at hand when no other portraits will individuals, statues, boquets of flowers, and be taken. The Sculptors too are beginning objects of Natural History, which thousands to see the application of the Stereoscope to of individuals flocked to examine with the their art, and we have recently learned from new instrument. After giving a brief notice Paris, that an artist in that city has modelled of the labours of Mr. Wheatstone, and of a statue from the relievo produced in the Sir David Brewster's lenticular stereoscope, Stereoscope. and binocular camera, for taking the pictures with mathematical accuracy, the Abbé Moigno in the article placed in our list of papers on the Stereoscope, gives the following account of the introduction of the instrument into Paris:—

Such is a brief history of the introduction of the Lenticular Stereoscope into Paris and London, and of its application to portraiture and sculpture. The Stereoscopic apparatus of Mr. Wheatstone had been before the public for upwards of twelve years, without exciting any general notice, and without any "In his last visit to Paris, Sir David Brewster useful application being made of it; and yet intrusted the models of his Stereoscope to M. when Sir David Brewster's instrument beJules Duboscq, son-in-law and successor of M. Soleil, and whose intelligence, activity, and affa- came an article of general sale in London, bility will extend the reputation of the distin- his Lenticular Stereoscope was sold as an guished artists of the Rue de l'Odéon, 35. M. invention of Mr. Wheatstone's, and with his Jules Duboscq has set himself to work with in- name actually attached to it. An article apdefatigable ardour; without requiring to have peared in the "Illustrated News" of January recourse to the Binocular Camera, he has with 26th, 1852, in which the Lenticular Stereothe ordinary Daguerreotype Apparatus procured scope, as made by M. Soleil, is represented a great number of dissimilar pictures of statues, in a drawing under the name of the Refractbas-reliefs, and portraits of celebrated individuals, &c. &c. His Stereoscopes are constructed ing Stereoscope, as if to conceal both the with more elegance and even with more perfec- nature of the instrument and the name of tion than the original English instruments, and its inventor, and we have no hesitation in while he is showing their wonderful effects to characterizing the whole article as one of natural philosophers and amateurs who have the most extraordinary perversions of scienflocked to him in crowds, there is a spontaneous and unanimous cry of admiration."-La Presse, Dec. 28, 1850.

2

In the beautiful collection of philosophical instruments which M. Duboscq Soleil contributed to the Great Exhibition of 1851,

See The Transactions of the Royal Society of Edin. Vol. XV. Part III. pp. 349-368, and the Phil. Magazine for May and June 1844, Vol. XXIV., pp. 356 and 439.

tific history with which we are acquainted. The theory of the instrument is not ascribed to the person to whom we owe it. It is called a modification of an instrument to which it has no resemblance whatever, and its peculiar property of magnifying by means of semi-lenses, or quarter-lenses, the plane pictures to which it is directed, at the same time that it unites them to produce the solid, or rather the figure in three dimensions, a

property which enables us to make Micro- as correspond with the distances, Ee, Nn, and

scopic Stereoscopes,* is never one mentioned.

Cc; that is, the nose will rise higher than the eyes, because the optic axes must unite Having thus given a brief history of the at a greater height above the plane, in order introduction of the Stereoscope, and of the to bring the points N, n, together. The general principles of Binocular Vision, which whole of this process is distinctly representit is intended to illustrate, we shall now ed in figs. 16 and 17 of Sir David Brewsproceed to explain its theory and describe ter's paper on the Law of Visible Direction, its construction as an instrument applicable and in conformity with that law. In this, as to the advancement of the fine arts. When in all the phenomena of binocular vision, we look at a statue with one eye, suppose we must consider all images as formed by the left, and project it upon a plane surface, points of the objects which they represent, or draw it as seen by that eye, we shall have and we must recollect, not merely that only the left eye represented by a point which one point of any object can be seen diswe may call E, the tip of the nose by a tinctly and singly at the same instant, but point N, and the chin by a point C. If we that in the union of dissimilar pictures, only do the same with the right eye, without two similar points at a certain distance can moving the head, we shall have another pic be thus united, a new convergence of the ture in which e is the left eye of the statue, optic axes being necessary to unite any other on the nose, and c the chin. If we now place pair of similar points. these two pictures side by side opposite the In the case of geometrical diagrams or eyes to which they belong, we shall see in plane pictures consisting of lines, each inthe picture obtained by the left eye more of clined line of the picture seen by one eye, the right side of the statue, and in the pic being less or greater than the corresponding ture obtained by the right eye more of the inclined line in the picture seen by the other, left side of the statue. The two pictures the lines never coalesce, and never can by of the statue thus taken are therefore dis- any process be made to coalesce as mainsimilar. The distance Ee between the two tained by Wheatstone and Whewell. When left eyes of the picture will be less than the the nearest end of one line coincides with distance Nn between the two noses, because the corresponding termination of the other, the eyes are nearer the plane of projection the remotest ends of the lines are seen than the noses, and the distance Cc between separate and indistinct; and when the rethe two chins will be intermediate between motest ends coincide in a single point, the Ee and Nn, that is Nn Ee and Ce Ee. nearest ends are seen separate and indistinct. When we look at the statue with both eyes, To get over a difficulty, by supposing it pos the dissimilar pictures of it are united on sible that a short line could be made to cothe retina and seen as one. When we look incide at each end with a long one, would be at the left eye E of the statue, we see it dis- a hypothesis of the same order, as if the tinctly and singly by converging the optic astronomer were to surmount a difficulty axes to the point E. In like manner when about the tides, by supposing that the moon we see N distinctly and singly, we converge acted upon our seas according to the law of the optic axes to N; but when we have done the squares, and the sun according to the this the point E is seen double and not so distinct as before. When we look at the statue we see only one point of it single and distinct at the same instant, but the two eyes, with the rapidity of lightning, run over every part of it, uniting the two images of that point in succession, and thus producing a general and apparent coalescence of the two images. In the very same manner, when we unite the two dissimilar pictures placed beside each other, either by the eyes The various distances between all the similar alone or by the Stereoscope, when the pic points in the two plane pictures, such as the tures are interchanged we can unite only two distance of the two right ears, the two right points at once, namely, Ee, or Nn, or Cc, eyes, and the two noses which may be called and these points are seen raised above the 10, 11, 12, (10 being the shortest distance of plane, and placed at such distances from it the most prominent points,) correspond with the distances of the same points of the solid, from the eye represented by 20, 22, 24, &c., or any other numbers which measure the dis

By means of the Microscopic Stereoscope, Binocular Daguerreotypes for lockets and rings may be used in the instrument and magnified.

law of the cubes of the distances. The laws of vision, in virtue of which, and the process by which, we see a solid, a body of three dimensions in space, are precisely the same as those by which we see it by the successive and rapid union of similar points of the two pictures, by a change in the convergency of the optical axis. The law or rule, according to which this vision of the solid is effected may be thus expressed :