Towler, John. The Silver Sunbeam. Joseph H. Ladd, New York: 1864. Electronic edition prepared from facsimile edition of Morgan and Morgan, Inc., Hastings-on-Hudson, New York. Second printing, Feb. 1974. ISBN 871000-005-9

Chapter XLI.
STEREOSCOPICITY.

THE property of seeing objects in relief has occupied the attention of philosophers from the earliest periods; and various reasons have been given for its existence. I have no hesitation in pronouncing them all false, excepting the one which I have published myself. The fact exists: we see objects in relief-what is the meaning of this expression:? Simply this: we can see at long and short distances at the same time. But the eye is a veritable lens, a corrected lens, and is subject to the ordinary laws of optics; the conjugate foci of objects at different distances are not on the same plane but at different distances; the retina, therefore, is not a surface, it is a substance having depth, and in this depth are found those conjugate foci of the different objects, producing thus in the sensitive and transparent substance a miniature solid picture. This is the simplest means to meet the end in view; and the Almighty makes use of the simplest means, and these means I think I have understood and analyzed. To see long and short distances at the same time, that is, to see objects in relief, requires the possession of a retina of the depth of about 1/100 of an inch in sensitiveness-now this is all that is required--the action of the ciliary nerve, the motion of the ciliary muscle, the layer-like structure of the crystalline lens, the action of the various straight and oblique muscles of the eye, the effect of the will, of the optic arteries, and numerous other contrivances, all these are not required in the production of this happy effect.

Euclid, it appears, though I know not where, attributes this phenomenon to the simultaneous impression of two dissimilar images of the same object in either eye of the observer.

Arago writes that when we see an entire object, the phenomenon is attributable to the rapidity of the action of the eye passing in quick succession from one part to another.

Pouillet's theory is this: he says that the crystalline lens consists of ellipsoidal layers superposed one over the other, endowed with the property of acting, that is, of refracting light independently of each other, or simultaneously.

Some authors maintain that the crystalline lens is moved by the ciliary muscle from or toward the retina with great rapidity during the action of the perception of relief.

Some maintain that the cornea is made to change its form by the instrumentality of some muscular action and thus to accommodate itself to different distances, or to compensate for the change.

Others again entertain the hypothesis that the eye-ball is either elongated or compressed by some muscular action, just as the distance is shorter or longer.

As I said, all these hypotheses seem to be false, because the minutest investigations have not yet discovered that the eye is elongated or compressed, that the crystalline lens is advanced or drawn back, that the crystalline lens is endowed with independent optical layers, that the ciliary muscle acts as described, that the cornea is in any way changed during the act of any perception. On the contrary, it is known to be a positive fact, that a single eye has a correct perception of relief-that many animals, such as ducks, fish, etc., have their eyes located in such a position as not to allow the simultaneous action of either eye on all occasions; it is supposed, however, they see as perfectly as human beings. It is a well-known fact that we can see near and distant objects, as for instance, the moon, a cloud, a church steeple, and the branches of a tree close by, without any change of the eye, and without any effort. It has been furthermore ascertained by microscopical examinations that the retina has thickness, transparency through this thickness, and is constituted of a conical or stick-like collocation of nervous material from before backward, which we have a right to suppose sensitive to the impressions of light throughout. With such a constitution of nerves the problem of long and short distance, or the problem of seeing in relief, is solved.

The problem of seeing pictures in relief, depends primarily upon the property which the eye possesses of seeing objects in relief; for if the eye were not endowed with this power, pictures as well as objects would be seen, as it were, projected flat on the ground glass of the camera. This depends secondarily on the combined action of two eyes; for a single eye can by no contrivance see any picture optically in relief.

It appears that Leonardo da Vinci has touched upon the subject of binocular vision in one of his manuscripts. This distinguished painter and scholar was born in 1452. There is nothing positive in anything he has left us about the power and rationale of seeing pictures in relief.

The same may be said also of Giovanni Battista Della Porta and of Francis Aguillon, who both seem to have had some knowledge of binocular perception.

The first definite and positive acquaintance with this peculiar property is of modern date and is mentioned in 1832 in the third edition of Mayo's Outlines of Human Physiology. Wheatstone's reflecting stereoscope appeared in 1838; it appears from the evidence of Newmann, of Regent street, London, that Wheatstone was acquainted with a refracting prism that would produce the same effect. Brewster's refracting stereoscope appeared in 1850. Since its discovery by Brewster and its manufacture originally by the celebrated opticians, Soleil and Dubosc in Paris, stereoscopicity has occupied the attention of philosophers and amused the public as much as photography itself, which has been the means, in its turn, of rendering the stereoscopes so popular. Without photography the stereoscope would be, like the kaleidoscope, a mere philosophical toy.

The way in which photography has extended the influence of stereography is attributable to the facility it gives of obtaining consentaneously two dissimilar pictures of the same object in the exact conditions as they would be depicted by either eye of the spectator; for it is a well-known fact now that these pictures are endowed with differences depending upon the parallax of the object on the base line between the two eyes; the greater the parallactic angle, the greater the angular displacement of either picture an reference to the other.

For example, let a spectator stand before a pane of glass looking upon a church for instance. At the distance of distinct vision from the glass fix a metallic plate containing two small apertures, separated by a distance equal to that between the two eyes. Let the observer now, by means of a style dipped in thick printer's ink, trace the outline of the church on the glass as seen through the aperture of the right eye; in like manner, let him do the same through the aperture of the left eye. He will find that, instead of one church, two sketches will appear on the glass side by side, endowed with the following property as characteristically distinct from two engravings of the same object from the same plate. With a pair of compasses measure the distance between two corresponding points on the church which are nearest to the observer; measure also the distance between two corresponding points that are the most distant from the observer, it will be found that the latter measurement will exceed in length that of the former; and that this result will always be obtained; that is, the greater the distance of certain parts of the objects comprehended in a picture from the point of observation, the greater the difference of distance between two corresponding points in the foreground and two in the distant background. It will be found, moreover, that the distance between two corresponding points which are very remote from the eyes, or properly speaking at an infinite distance, is equal exactly to the distance between the eyes of the observer.

The parallactic angle is that angle which is comprehended between the axes of the eyes converging to a given point; and the distances between any two corresponding points is equal to twice the versed sine of the parallactic angle; but the versed sine of an angle is complementary to the sine, and the sine varies as the angle; thus, therefore, as the sine decreases, the versed sine increases; and in like manner the distances between corresponding points from anterior to remoter positions in the background will gradually increase. Such are the properties inherent in the two pictures of the same object as depicted on the retina of either eye, or on the ground glass of a binocular camera. Two photographs or pictures taken as thus described, side by side, are the mere interception of rays on a flat surface as they proceed from the object. It is natural therefore to suppose that these pictures, when beheld by the eyes, ought to give an impression of the reality in relief. By a minute investigation of the subject it is ascertained that conditions arise for the effectuation of this result, which at the first sight are not anticipated. One condition is to obtain the same convergence of the axes of the eyes as existed when the pictures were taken. To obtain this convergence is an effort for the eyes; and on this account there are but few persons who possess such perfect command of their eyes as to secure the right convergence for given pictures. It is far from being absolutely necessary that the convergence should be exactly the same as existed originally when the photographs were taken; there are, however, certain limits on either side, that is, it maybe a little either greater or less than that of the parallactic angle.

The object of this convergence is a very essential point in binocular perception producing relief; and the rationale of this perception of relief is not lucid on other Grounds than that which admits of the production of a virtual solid image in space, either at a distance beyond the pictures or in front of them. Such solid images are formed in space by the intersection of the rays that proceed from the corresponding points in either picture; for these rays, when they pass the optic centers of the eyes, form different parallactic angles, according as the distances apart are different, and thus intersect at variable distances corresponding with the points in the real object from which the pictures were taken.

Some eyes have a very great facility of converging their axes; in which case the rays from corresponding points intersect in front of the pictures and very nearly, if not exactly, at a distance half-way between the pictures and the eyes; in this case, (as may be seen on referring to this subject discussed at large, page 73, etc., Vol. XIV. of Humphrey's Journal) the effect of relief is inverted, the most distant points being projected forward, whilst the anterior points are seen in the extreme background. This is the natural consequence of the intersection of lines at angles that depend upon the peculiar distance apart of the corresponding points in the pictures.

Where eyes do not possess this great degree or facility of convergence, the intersections will, with the same degree of geometrical consequence, take place beyond the pictures and at variable distances beyond. The solid picture in this case will not be inverted; but it will vary in magnitude according as the intersections occur nearer to the pictures of farther from them. Persons, therefore, endowed with this less degree of convergence, have the pleasure of beholding a, magnified solid picture, of which the magnitude is sometimes very great; whereas, those whose optical axes can easily converge, see a solid image uniformly of half the size of the pictures, but which is on this account very sharp and pleasing.

All eyes can be tutored with very little difficulty to receive this impression of relief from two photographs possessing the conditions required.

In order that the solid picture in the latter case shall be direct, that is, not pseudoscopic, the pictures must be inverted, the left being pasted upon the right side; and the right on the left side. TWO photographs, so mounted, I have denominated a Strabonic Stereograph, to distinguish it from the ordinary stereograph.

Another condition, in order to see pictures in relief, by the binocular perception, is the cosentaneous independent action of either eye. From this circumstance either eye beholds the two images; but the two interior ones intersect, are therefore superimposed and form thus only one image, which is the solid image; the two outside images are flat, and do not attract the attention to any great extent, by reason of the superior brilliancy of the middle picture. The rationale of this delightful phenomenon, as hitherto given in all our text-books on the subject, is so far erroneous, from the fact that it is asserted that each eye sees its corresponding picture as the object was seen when the pictures were taken. If this were true, we ought to see only the solid image, and not the two outside flat pictures.

All the instruments, called stereoscopes, are mere optical contrivances whereby in the first place the requisite convergence is obtained with facility; secondly, they magnify the image in relief; and thirdly, they shut off the two outside flat pictures. They are not essential at all to the perception of relief furthermore than as accessories, The philosophy of stereoscopicity is very simple, it is founded solely on the production of intersections of rays from corresponding points of two pictures, the distance of which points must be endowed with the requisite differences; from these intersections or superimpositions a virtual solid image is formed which is then regarded as a real object, which produces the perception of relief in either eye, because the conjugate picture in the retina is also solid.

It is evident, then, that a single eye can never see a flat picture in. relief, because the requisite intersections can not take place; but we are by no means allowed to argue from this that a single eye can not appreciate relief or distance in real objects, or that relief is the result of binocular perception. This is an absurdity into which many investigators of nature have fallen; they have not comprehended the true origin of this perception, which depends upon the sensitiveness of the retinal film through a certain thickness, and not alone on a surface.

Eyes may be tutored to see two photographs in relief by the following expedients, and without the aid of stereoscopes.

All persons accustomed to close reading or writing, or to the use of magnifying spectacles are more inclined to see strabonically than otherwise. They can, in plain language, easily squint inwardly and see the end of the nose.

Strabonic Stereograph.

In the first place, therefore, prepare a number of strabonic stereographs of architectural structures, as follows: "Take the ordinary stereographs of the views in question and throw them into a pail of water until the photographs easily separate from the in mounts. Remove the photographs, and passing over the backs with a sponge dipped in starch paste, transpose them upon the original mounts or upon new ones; that is, fix the right-hand photograph on the left side, and vice versa. The student next has to learn to see double. This is effected by holding up the thumb before the eyes, so as to see two thumbs; when he is expert at this, let him next hold up in front of his eyes, at the regular reading distance, both his thumbs, and try if he can see four thumbs. As soon as this is effected, then, by bringing the thumbs closer together, so that their distance apart is about two inches and a half; the two middle ones can be made to overlap each other, whereby three thumbs will appear. The difficulty is now overcome; for the eyes, when well-practised in this strabonic exploit, are prepared for regarding a stereograph which is mounted as above described, when, with a little patience, three photographs will appear, of which the middle one will be very distinct, finely defined, and in full and natural relief, exhibiting all the solidity of reality.

The two outside pictures are indistinct, and the eyes will soon learn to neglect them; or they may be entirely removed from the field of view by the use of a frustum of a pyramid formed of cardboard, whose height is equal to half the distance of distinct vision, that is, half the reading distance; the side of its upper base one inch and a quarter, and that of the lower three inches. By placing the lower base next the eyes and looking through it, the stereoscopic picture will appear alone and distinct.

The second method is founded on a reverse principle, that is, by excluding the rays of light from the middle of the field of view, comprehending a space of one inch and a quarter square. This is effected by placing a piece of cardboard of this width in the middle, half-way between the eyes and the photographs, of which the latter are fixed at the regular reading distance; or the same object can be effected as follows: Take a slip of wood about two feet long, two inches wide and one inch thick; take secondly, a piece of cardboard of the size of a stereograph, and bisect the two parallel sides and the two parallel ends, and join the points of bisection. Where these lines meet we have the center the cardboard. From this point right and left on the larger line, mark off a space one inch and a quarter in length, and at either extremity thus marked off draw a circle half an inch in diameter. Lay the slip of wood on its flat surface on a table, and tack the piece of cardboard to one end of the slip at right angles to the table, with an equal portion of cardboard projecting at either end. Previously, however the wide surface of the slip must be divided longitudinally into two halves, by running a saw from end to end so as to form a groove about a quarter of an inch deep; and at a distance from the cardboard, at the end, equal to the reading distance, another groove is sawed at right angles to the former and of the same depth; in the latter groove an ordinary, stereograph is placed, and along the longitudinal groove a piece of cardboard at right angles to it. Now let the observer look through the two apertures at the stereograph; it is evident that the right eye can see only the right photograph, whilst the left eye is restricted in like manner to the left. By concentrating the individual attention of each eye to its respective picture, by pressing the external parts of the ball of either eye with the fingers, or by compressing the eyes as in frowning, the two pictures may be caused to overlap each other, when a new picture will appear possessed of the full stereoscopic effect, apparently of a larger size than the originals. The magnitude in this case will vary with the angle of convergence; if this should happen to be the same as that formed by the axes of the eyes or the lenses when the pictures were taken, the solid picture will be of the same size as the apparent size of the object from which the photographs were taken; at all other degrees of convergence the magnitude will vary.

Now the solid picture, produced by either process, can be magnified ad libitum by means of eye-lenses or spectacles; and when these eye-glasses are fixed in proper receptacles, they are then denominated refracting stereoscopes; but it will be seen that they are far from being indispensable; they are, in fact, mere accessories.

The differences of distance between the corresponding points on two photographs taken stereographically, being functions of the parallactic angle, can be easily calculated, and consequently artificial stereographs can be delineated geometrically. The results drawn from such calculations furnish means for detecting the inherent properties of stereoscopicity or their total absence in any given photographs or designs. In this way it was conclusively determined that the drawings of Chimenti were not stereoscopic. Pages of print can be set stereoscopically, so that one line alternately stands above the other, or in any way whatever. The following is a typographic stereograph. It is formed by setting the alternate lines at different distances from one another; that is, the distance from T to T in the first lines is greater by about one sixteenth of an inch than the distance from H to H in the second lines; and all the rest are set accordingly. Viewed by the stereoscope the odd lines will be seen standing far back behind the even lines; an increase of difference will throw the odd lines still further back into the background. An irregularity of difference produces an irregularity in the relief: