If we place a short pen within the cup, measuring as it were its depth, and having its quill end nearest the observer, the pen will be inverted, in correspondence with the conversion of the cup into a convexity, the quill end appearing more remote, like the margin of the cup which it touches, and the feather end next the eye like the summit of the convex cup on which it rests.

In these experiments, the conversion of the concavity into a convexity depends on two separate illusions, one of which springs from the other. The first illusion is the erroneous conviction that the surface of the table is looking upwards as usual, whereas it is really inverted; and the second illusion, which arises from the first, is, that the nearest point of the object appears farthest from the eye, whereas it is nearest to it. All these observations are equally applicable to the vision of convexities, and hence it follows, that the conversion of relief, caused by the use of an inverting eye-piece, is not produced directly by the inversion, but by an illusion arising from the inversion, in virtue of which we believe that the remotest side of the convexity is nearer our eye than the side next us.

In order to demonstrate the correctness of this explanation, let the hemispherical cavity be made in a stripe of wood, narrower than the field of the inverting telescope with which it is viewed. It will then appear really inverted, and free from both the illusions which formerly took place. The thickness of the stripe of wood is now distinctly seen, and the inversion of the surface, which now looks downward, immediately recognised. The edge of the cavity now appears nearest the eye, as it really is, and the concavity, though inverted, still appears a concavity. The same effect is pro

duced when a convexity is placed on a narrow stripe of wood.

Some curious phenomena take place when we view, at different degrees of obliquity, a hemispherical cavity raised into a convexity. At every degree of obliquity from 0° to 90°, that is, from a vertical to a horizontal view of it, the elliptical margin of the convexity will always be visible, which is impossible in a real convexity, and the elevated apex will gradually sink till the elliptical margin becomes a straight line, and the imaginary convexity completely levelled. The struggle between truth and error is here so singular, that while one part of the object has become concave, the other part retains its convexity!

In like manner, when a convexity is seen as a concavity, the concavity loses its true shape as it is viewed more and more obliquely, till its remote elliptical margin is encroached upon, or eclipsed, by the apex of the convexity; and towards an inclination of 90° the concavity disappears altogether, under circumstances analogous to those already described.

If in place of using an inverting telescope we invert the concavity, by looking at its inverted image in the focus of a convex lens, it will sometimes appear a convexity and sometimes not. In this form of the experiment the image of the concavity, and consequently its apparent depth, is greatly diminished, and therefore any trivial cause, such as a preconception of the mind, or an approximation to a shadow, or a touch of the concavity by the point of the finger, will either produce a conversion of form or dissipate the illusion when it is produced.

In the preceding Chapter we have supposed the con

vexity to be high and the concavity deep and circular, and we have supposed them also to be shadowless, or illuminated by a quaquaversus light, such as that of the sky in the open fields. This was done in order to get rid of all secondary causes which might interfere with and modify the normal cause, when the concavities are shallow, and the convexities low and have distinct shadows, or when the concavity, as in seals, has the shape of an animal or any body which we are accustomed to see in relief.

Let us now suppose that a strong shadow is thrown upon the concavity. In this case the normal experiment is much more perfect and satisfactory. The illusion is complete and invariable when the concavity is in or upon an extended surface, and it as invariably disappears, or rather is not produced, when it is in a narrow stripe.

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

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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 dif ferent growths of the shell, cut in different directions by the artificial surface, like the annual growth of wood in a