The stereoscope

by David Brewster

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 0° 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 a long stripe of darkness over the surface on which it rests. Hence it is impossible to mistake a convexity 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 displayed 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 intensity 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 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 consequence 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, calcedony, 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 illusion 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 different growths of the shell, cut in different directions by the artificial surface, like the annual growth of wood in a 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 without 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.

Fig. 51.

A very remarkable illusion, affecting the apparent position of the drawings of geometrical solids, was first observed by the late Professor Neckar, of Geneva, who communicated it to me personally in 1832.[73] “The rhomboid AX,” ([Fig. 51],) he says, “is drawn so that the solid 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 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 considered 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 indistinctly, 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 this 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 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 consequently 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 attention 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 convexity 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.