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Having no doubt of the correctness of this observation, I have often endeavoured, though in vain, to witness so remarkable a phenomenon. In walking, however, in the month of March last, with a friend on the beach at St. Andrews, the phenomenon presented itself, at the same instant, to myself and to a lady who was unacquainted with this class of illusions. The impressions of the feet of men and of horses were distinctly raised out of the sand. In a short time they resumed their hollow form, but at different places the phenomenon again presented itself, sometimes to myself, sometimes to the lady, and sometimes to both of us simultaneously. The sun was near the horizon on our left hand, and the white surf of the sea was on our right, strongly reflecting the solar rays. It is very probable that the illusion arose from our considering the light as coming from the white surf, in which case the shadows in the hollow foot-prints were such as could only be produced by foot-prints raised from the sand, as if they were in relief. It is possible that, when the phenomenon was observed by Lady Georgiana Wolff, there may have been some source of direct or reflected light opposite to the sun, or some unusual brightness of the clouds, if there were any in that quarter, which gave rise to the illusion.

When these illusions, whether monocular or binocular, are produced by an inversion of the shadow, either real or supposed, they are instantly dissipated by holding a pin in the field of view, so as to indicate by its shadow the real place of the illuminating body. The figure will appear raised or depressed, according to the knowledge which we obtain of the source of light, by introducing or withdrawing

1 Journal, 1839, p. 189.

the pin. When the inversion is produced by the eye-piece of a telescope, or a compound microscope, in which the field of view is necessarily small, we cannot see the illuminating body and the convex or concave object (the cameo or intaglio) at the same time; but if we use a small inverting telescope, 1 or 2 inches long, such as that shewn at MN, Fig. 36, we obtain a large field of view, and may see at the same time the object and a candle placed beside it. In this case the illusion will take place according as the candle is seen beside the object or withdrawn.

If the object is a white tea-cup, or bowl, however large, and if it is illuminated from behind the observer, the reflected image of the window will be in the concave bottom of the tea-cup, and it will not rise into a convexity if the illumination from surrounding objects is uniform; but if the observer moves a little to one side, so that the reflected image of the window passes from the centre of the cup, then the cup will rise into a convexity, when seen through the inverting telescope, in consequence of the position of the luminous image, which could occupy its place only upon a convex surface. If the concave body were cut out of a piece of chalk, or pure unpolished marble, it would appear neither convex nor concave, but flat.

Very singular illusions take place, both with one and two eyes, when the object, whether concave or convex, is a hollow or an elevation in or upon a limited or extended surfacethat is, whether the surface occupies the whole visible field, or only a part of it. If we view, through the inverting telescope or eye-piece, a dimple or a hemispherical cavity in a broad piece of wood laid horizontally on the table, and illuminated by quaquaversus light, like that of the sky, it

will instantly rise into an elevation, the end of the telescope or eye-piece resting on the surface of the wood. The change of form is, therefore, not produced by the inversion of the shadow, but by another cause. The surface in which the cavity is made is obviously inverted as well as the cavity, that is, it now looks downward in place of upward; but it does not appear so to the observer leaning upon the table, and resting the end of his eye-piece upon the wooden surface in which the cavity is made. The surface seems to him to remain where it was, and still to look upwards, in place of looking downwards. If the observer strikes the wooden surface with the end of the eye-piece, this conviction is strengthened, and he believes that it is the lower edge of the field of view, or object-glass, that strikes the apparent wooden surface or rests upon it, whereas the wooden surface has been inverted, and optically separated from the lower edge of the object-glass.

In like

In order to make this plainer, place a pen upon a sheet of paper with the quill end nearest you, and view it through the inverting telescope: The quill end will appear farthest from you, and the paper will not appear inverted. manner, the letters on a printed page are inverted, the top of each letter being nearest the observer, while the paper seems to retain its usual place. Now in both these cases the paper is inverted as well as the quill and the letters, and in reality the image of the quill and of the pen, and of the lower end of the letters, is nearest the observer. Let us next place a tea-cup on its side upon the table, with its concavity towards the observer, and view it through the inverting telescope. It will rise into a convexity, the nearer margin of the cup appearing farther off than the bottom.

;

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

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