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figures viewed in a direction perpendicular to the plane in which they are drawn, but a series of very curious results have been recently published by Sir David Brewster, on the union of the images of lines meeting at an angular point, when the eye is placed at different heights above the plane of the paper, and at different distances from the angular point. In these experiments, two lines, or two binocular or plane pictures, forming an angle with each other, can be united by the eye or by the stereoscope, so as to exhibit a single object inclined at any angle we choose, on the ground on which they appear, from 90° to 180°, their apparent magnitude diminishing as they advance towards the end of their quadrantal motion. This remarkable effect, which cannot be well explained without diagrams, admits of being made a very popular exhibition.*
It would be unprofitable to devote any more of our space to this branch of the subject. Those who have occupied themselves with the study of binocular vision, have necessarily observed many phenomena which, though highly interesting, it would be too tedious to describe. Sir David Brewster has indicated in the following passage several of these phenomena, which others may have also seen, and which, no doubt, will be brought forward by subsequent observers as new discoveries:-"In the course," says he, "of the investigation which I have now brought to a close, I have had occasion to observe several interesting phenomena which it would be out of place to describe at present. They relate partly to the effects produced by uniting unequal and dissimilar pictures which have a tendency to represent incompatible solids-to the union of dissimilar pictures where the parts of the solid lie wholly or principally in a plane perpendicular to a line joining the eyes and the object, and to the plane of the optic axes; 1-to the union of pictures, one of which is more or less turned round in its own plane ;-to the phenomena exhibited by uniting the images of two similar real solids, the one elevated and the other depressed; to the union of dissimilar plane figures which should at the same time give a solid in relief, and in the converse of relief; and to the union of portions of dissimilar figures, those which are wanting in the one figure existing in the other. Among the singular effects produced under these various conditions, nothing is more remarkable than the tend
*Edinburgh Transactions, vol. xv. pp. 667-671.
Such as the magnified teeth of a saw or a thin section of a hexagonal prism, whose axis is parallel to a line joining the eyes and the object.
In order to produce simultaneously this double effect, the lines of the pyramid, for example, which are to give the converse of relief, should be fainter than the other lines, or in different and feebler colours.
Conversion of Relief-Cameos and Intaglios.
ency or desire, as it were, of the eyes to unite and fix the two pictures hovering before them, and convert them into some figure of three dimensions, (sometimes in relief, sometimes in the converse, sometimes in both at the same time); and the suddenness with which the images start into union, give birth to a solid figure, on which the optic axes are converged, and release the eyes from that unnatural condition in which they had previously been placed."
We come now to another branch of the subject of binocular vision, which possesses a very high degree of interest, namely, what has been improperly called the converse or conversion of relief, an effect which is shewn in the conversion of cameos into intaglios, and of intaglios into cameos, by inverted vision either with one or two eyes. This subject has been hitherto treated as one of monocular vision, but the influence of two eyes over the phenomena has been recently studied by Sir David Brewster in his paper "On the Conversion of Relief by Inverted Vision." It had hitherto been believed, that the first notice of the remarkable fact of the conversion of an intaglio or hollow seal, into a cameo or a raised one, was published in the Philosophical Transactions by Dr. Philip Gmelin of Wurtemberg in 1744; but we have found a very interesting account of the principal phenomena in Aguilonius's Opticorum Sex Libri already referred to. After proving that convex and concave surfaces appear plane when seen at a considerable distance, he then goes on to shew that the same surfaces when seen at a moderate distance frequently appear converse, that is the concave convex, and the convex 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 circumstance of the mind being imposed upon, by not knowing in what direction the light which illuminates the body reaches it. He states, that a concavity differs from a convexity only in this respect, 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 remarks also, that in pictures imitating nature, a similar mistake is committed as to the form of surfaces. He supposes that a circle is drawn upon a table and shaded on one side, so as 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 which it contains. But if we view it at a short distance, and suppose the light to come from the same side as the part not in shadow, the plane circle will appear to be convex, and if we suppose the light to come from the same side as the shaded part, the circle will appear to be a concavity.
In these experiments of Aguilonius the mind alone acts, and deceives us. There is no physical change in the conditions of the
light or of the eye of the observer, such as we shall have presently to consider. Sir David Brewster, who had not seen the observations of Aguilonius which are now here published for the first time in English, and which have been noticed by no writer on the subject either foreign or domestic, made a number of experiments on the influence of the mind in thus deceiving itself, not upon artificially shaded planes as Aguilonius did, but upon real concavities and convexities, and obtained some singular results. "If we take," says he, "one of the intaglio moulds (about three or four inches long) used for making the bas-relief of that able artist Mr. Henning, and direct the eye to it steadily without noticing surrounding objects, we may coax ourselves into the belief that the intaglio is actually a bas-relief. It is difficult at first to produce the deception, but a little practice never fails to accomplish it. We have succeeded in carrying this deception so far, as to be able by the eye alone to raise a complete hollow mask of the human face (the size of life) into a projecting head. In order to do this we must exclude the vision of other objects, and also the margin or thickness of the cast. This experiment cannot fail to produce a very great degree of surprise to those who succeed in it; and it will, no doubt, be regarded by the sculptor, who can use it, as a great auxiliary in his art."
This remarkable phenomenon was observed by the same author in four other cases where the mind and the unassisted eye of the observer were alone employed. In the mineral called Hammered Agate, the name is derived from the dimples or apparently concave round spots which cover it, as if they had been produced by the blows of a hammer. The concavity of these spots arises from the edge opposite to the light being always the most luminous, and as this can take place only in concavities, these spots have the appearance of being hollow. The same thing takes place on whatever side we place the light. The same fact is frequently exhibited by the round sections of knots in highly polished tables of mahogany and other woods. When the eye is placed so that the line joining it and the knot forms a great angle with the surface of the table, the side next the light is dark, while the side opposite to it is light, and consequently the section of the knot appears to be hollow. The same thing is finely seen in motherof-pearl. Owing to this property of transparent bodies, it is obvious that in alabaster and partially transparent marble busts, a depression and elevation cannot be truly represented, an observation which merits the attention of the sculptor. Other two illusions of an analogous character are described in the same paper. In one of these, the clustered columns of a Gothic pillar sunk
*Edinburgh Journal of Science, Jan. 1826, vol. iv. p. 108. † Ibid. P. 106. In the passage here referred to there is a mistake respecting the side of the knot, which the intelligent reader will easily correct.
Inversion of Form-Single and Binocular Cameoscopes. 199
into hollow fluting, and in another, a field of wheat viewed through an erecting telescope, when illuminated by the setting sun, exhibited the strange appearance of having been trenched, and of the wheat growing in the trenches as well as upon the elevated beds between them, an effect which would have perplexed the painter had such a conversion of form formed part of his picture. Another example of this class of illusions is by Dr. Joseph Wolff in his Journal.* "Lady Georgiana," says he, "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 eye."
Dr. Gmelin of Wurtemberg, describes these illusions as seen under a different condition. He had learned from a friend, "that if a common seal was applied to the focus of a compound microscope or optical tube, which has two or three convex or planoconvex lenses, that part which is cut the deepest in it would appear very convex, and so on the contrary; and that sometimes, but very seldom, it would appear in the same state as to the naked eye." Dr. Gmelin found these results to be true, and he extended them considerably. He found, however, that friends who assisted him saw often the very converse of what he saw, and that on a darker day he could not see what he had seen the day before. He concluded, however, that all these fallacies were owing to shadow, and "that when the raised object was so placed between the windows that it must be illuminated on all sides, it did not change its convexity. Mr. Rittenhouse, in 1780, explained these illusions by the inversion of the shadow by means of the inverting eye-tube. He used an eye-piece with two lenses placed at a distance greater than the sum of their focal lengths, and "by throwing a reflected light on the cavities observed, in a direction opposite to that of the light which came from his window, he was able to see them raised into elevations by looking through a tube without any lens. This, however, was still seeing them by inverted vision, for he inverted the shadows, though his tube did not invert the objects themselves.
Our limits will not permit us to describe the various interesting changes, apparently very capricious, which take place by introducing into the field of view, a pin whose shadow shews a new direction of the illuminating body, or by combining the sensations of touch with those of vision.† We shall confine ourselves
* Journal, 1839, p. 189.
An account of these experiments will be found in Sir David Brewster's Letters on Natural Magic, and the theory of the conversion of relief, in his Memoir on that subject, referred to in the list at the head of this article.
to a notice of the Single and the Binocular Cameoscope, for converting cameos into intaglios, and generally for altering, optically, the forms and inverting the distances of bodies. The Single cameoscope consists of two lenses, achromatic if possible, of short focus, placed like the optical tube of Gmelin, at nearly the sum of their focal distances. If the lenses are equal they will have no magnifying power, and if magnifying power is desired, one of the lenses must have a shorter focus than the other. With this instrument convex bodies appear concave, and concave convex, near objects are placed at a distance, and many other illusions are produced which are very interesting. The Binocular Cameoscope consists of two of these little inverting teleoscopes placed together exactly like a double opera glass, so that whatever is seen by the one is seen by the other. With this instrument we combine the effects produced by the inversion of the solid with the stereoscopic effect arising from the binocular pictures which are combined by the instrument. We observe in the newspapers that an instrument to which Mr. Wheatstone gives the name of Pseudoscope is advertised for sale, and we see in the article already referred to in the Illustrated News, that it shews the same effects as those which are shewn in the cameoscope. We have now before us one of these pseudoscopes, but we have seen no other account of it but the notice of its effects. It is a most capricious and unsatisfactory instrument, which often fails to shew what it ought to shew. It seems to us to differ in nothing from the cameoscope excepting that the inversion of the objects and their double pictures are produced by two reflecting prisms in place of lenses, the inversion of the prisms being an inversion only in a direction parallel to the line joining the eyes of the observer, whereas in the binocular cameoscope the inversion is in every direction. The inversion of the picture by means of prisms is precisely the same as that which is used in the total reflection stereoscope already referred to. It is not easy to get two prisms properly ground to throw the two images exactly together. In the instrument which we recently got from a skilful London optician, not only was one of the prisms made of glass filled with striæ, but owing to the incorrect position of the rectangular faces of the two prisms, the one image could not be brought to lie upon the other. An instrument with lenses is therefore much more appropriate and correct.
In our list of papers at the head of this article we have referred to one on the chromatic stereoscope. When we look at the coloured boundary lines of a map through the opposite edges of a reading glass 2 inches in diameter or more, the lines rise in relief from the paper. Sir David Brewster was thus led to construct chromatic stereoscopes in which relief was obtained by difference of