When this

to represent a convex or a concave surface. shaded circle is seen at a great distance, it appears a plane surface, notwithstanding the shadow on one side of it; but when we view it at a short distance, and suppose the light to come from the same side of it as the part not in shadow, the plane circle will appear to be a convexity, and if we suppose the light to come from the same side as the shaded part, the circle will appear to be a concavity.

More than half a century after the time of Aguilonius, a member of the Royal Society of London, at one of the meetings of that body, when looking at a guinea through a compound microscope which inverted the object, was surprised to see the head upon the coin depressed, while other members were not subject to this illusion.

Dr. Philip Gmelin1 of Wurtemberg, having learned from a friend, that when a common seal is viewed through a compound microscope, the depressed part of the seal appeared elevated, and the elevated part depressed, obtained the same result, and found, as Aguilonius did, that the effect was owing to the inversion of the shadow by the microscope. One person often saw the phenomena and another did not, and no effect was produced when a raised object was so placed between two windows as to be illuminated on all sides.

In 1780 Mr. Rittenhouse, an American writer, repeated these experiments with an inverting eye-tube, consisting of two lenses placed at a distance greater than the sum of their focal lengths, and he found that when a reflected light was thrown on a cavity, in a direction opposite to that of the light which came from his window, the cavity was

1 Phil. Trans. 1744.

raised into an elevation by looking through a tube without any lens. In this experiment the shadow was inverted, just as if he had looked through his inverting eye-tube.

In studying this subject I observed a number of singular phenomena, which I have described in my Letters on Natural Magic,1 but as they were not seen by binocular vision I shall mention only some of the more important facts. If we take one of the intaglio moulds used by the late Mr. Henning for his bas-reliefs, and direct the eye to it steadily, without noticing surrounding objects, we may distinctly see it as a bas-relief. After a little practice I have succeeded in raising a complete hollow mask of the human face, the size of life, into a projecting head. This result is very surprising to those who succeed in the experiment, and it will no doubt be regarded by the sculptor who can use it as an auxiliary in his art.

Till within the last few years, no phenomenon of this kind, either as seen with one or with two eyes, had been noticed by the casual observer. Philosophers alone had been subject to the illusion, or had subjected others to its influence. The following case, however, which occurred to Lady Georgiana Wolff, possesses much interest, as it could not possibly have been produced by any voluntary effort. "Lady Georgiana," says Dr. Joseph Wolff in his Journal, "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

:

1 Letter v. pp. 98-107. See also the Edinburgh Journal of Science, Jan. 1826, vol. iv. p. 99.

"1

eye. 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 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. In like 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.