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will be seen as at A, fig. 8, with its shadow on the right hand S of the cavity. As the candle C remains where it was, the observer instantly concludes that what was formerly a cavity must now be a spherical elevation or segment of a sphere, as nothing but a raised body could have its shadow on the right hand S. If a second candle is now placed on the right hand side of A, so that it is between two candles, and is equally illuminated by both, the elevation will again sink into a cavity, as in fig. 9.

294. If the object A, in place of being a cavity, is actually the raised segment of a solid sphere, the same phenomena will be observed, the inverting eye-piece converting it into a cavity. These two experiments may be made most successfully with a seal, and an impression taken from it.

295. It cannot therefore be doubted that the optical illusion of the conversion of a cameo into an intaglio, and of an intaglio into a cameo, by an inverting eye-piece, is the result of an operation of our own minds, whereby we judge of the forms of bodies by the knowledge we have acquired of light and shadow. The greater our knowledge is of this subject, the more readily does the illusion seize upon us; while, if we are but imperfectly acquainted with the effects of light and shadow, the more difficult is it to be deceived. If the hollow is not polished, but ground, and the surface round and of uniform color and smoothness, almost every person, whether young or old, will be subject to the illusion; but, if the object is the raised impression of a seal upon wax, we have often found that, when viewed with the eye-piece, it still seemed raised to the three youngest of six persons, while the three eldest were subject to the deception. By such trifling and often unappreciable circumstances is our judgment affected, that the same person at one moment sees the convexity raised, and at another time depressed, though viewed as nearly as possible under the same circumstances. This remarkable effect no doubt arises from the introduction of some casual reflected lights which the slightest change of position will produce.

296. Having thus seen how our judgment concerning elevations and depressions is affected by our degree of knowledge of the effects of light and shade, and by unappreciable causes, we shall proceed to consider how our judgment is again deceived by the introduction of new substances.

297. Let the depression A, illuminated by one candle as in fig. 7, be converted into an elevation as in fig. 8, by the application of an inverting eye-piece; then if another candle C', fig. 9, is introduced so as to illuminate the depression A in the same manner, and with nearly the same intensity as C does, the elevation will fall down into a depression. The cause of this is obvious: the application of the inverting eye-piece produces no effect whatever, for both the sides of the cavity are symmetrically illuminated. In moving round the second candle C' from its position C', so as to stand beside C, it is curious to observe the progress of the deception by which the depression is again changed into an elevation. 298. If, when the depression A, fig. 10, is converted into an elevation, we introduce a small

unpolished opaque body M, and place it either beside the hollow or in it, so that the body M, and its shadow m, may be distinctly seen by the microscope, we shall have the appearance shown in fig. 11, the elevation having sunk into a depression. This correction of the depression arises from the introduction of a new illusion, namely, that which arises from the shadow m; for it is evident that, as the body M appears to project its shadow in the direction M m, the luminous body must be supposed to be on the same side D; and the evidence that this is the case is more powerful than our knowledge that the candle is actually at C, because it co-exists along with our perception of the depression A, whereas our knowledge of the situation of the candle is an act of recollection.

299. This correction of the delusion may be effected in another manner, which is perhaps more complete. If, in place of the unpolished body, we use a pin with a highly polished head, as shown at M, fig. 12, and then apply the inverting eye-piece, we shall have the effect shown in fig. 13, the cavity A appearing depressed. The images of the candle C, being seen by reflection in the polished head of the pin M, is seen by the application of the eye-piece at s, on the right hand side of M in fig. 13, so that we immediately conceive, in opposition to our previous knowledge, that the candle must be at D; and hence the elevation falls into a depression the moment the pin head is pushed up into the field of view. The shadow M m has also its influence in the present case.

300. The next case in which this illusion is dispelled is when the sense of touch corrects the deduction formed through the medium of sight. Let the cavity A be raised into an elevation by the inverting eye-piece, as in fig. 8. Then if the cavity is sufficiently deep, and if we place the point of our finger in the cavity, the evidence which this gives us of its being a depression is superior to the evidence of its being a cavity arising from the inversion of the shadow; the apparent elevation will of course sink into a depression; but the moment the finger is withdrawn it will again rise into an elevation. If the cavity is a long groove, the part not touched by the finger will appear elevated, while the part touched by it will appear depressed.

301. Having thus considered some of the principal phenomena arising from the inversion of the object, we shall now proceed to explain some analogous facts which are owing to the semi-transparency of the body. If M N, fig. 14, is a plate of mother-of-pearl, and A a cavity ground or turned in it; then if this cavity is illuminated by a candle C, or by a window at C, in place of their being a shadow at the side s, as there would have been had the body been opaque, there is a quantity of refracted light seen along the whole side s next the candle. The consequence of this is that the cavity appears as an elevation when seen only by the naked eye, as it is only an elevated surface that could have the side s illuminated. The fact which we have now stated is a very important one, in so far as it may affect the labors of the sculptor. In some kinds of marble the transparency is so great that

the depressions and elevations in the human face cannot be represented by it with any degree of accuracy; and consequently transparent marble ought never to be used for works of any import

ance.

302. Illusions arising from the same cause may be observed even when the surface of the object is perfectly plain and smooth. If M N, fig. 15, is the surface of a mahogany table, M N nm a section of it, and a be a section of a knot in the wood, then it often happens, from the transparency of the thin edge at a, next the candle, that that side is illuminated while the opposite side at c is dark, the eye being placed in the plane of the section a bc. The consequence of this is that the spot a bc appears to be a hollow in the table.

303. Hence arises the appearance in certain plates of agate, which has obtained for it the name of hammered agate. The surface on which these cavities appears is a section of small spherical aggregations of siliceous matter like abc in fig. 15, which present exactly the same phenomenon, arising from the same cause as the knots in mahogany and other woods.

304. The very same phenomenon is, as we have already stated, often seen in mother-of-pearl. Indeed it is so common in this substance that it is almost impossible to find a mother-of-pearl counter which seems to have its surface flat, although they are perfectly so when examined by the touch. Owing to the refraction of the light by the different growths of the shell lying in different planes, the flattest surface seems to be unequal and undulating.

vex.

305. Dr. Brewster states that one of the finest deceptions which he ever met with, arising from the disposition of light and shadow, presented itself on viewing through a telescope the surface of a growing field of corn, illuminated by the sun when near the horizon. This field, on Sir Walter Scott's estate at Abbotsford, was about two miles distant, and was divided into furrows, which were directed to the eye of the observer, as shown in fig. 16, where A B, CD, EF, represent the furrows. These furrows are of course depressed, and the growing corn rises gradually from two adjacent ones towards the middle mn, op, so that the surfaces Am C, Co E, were conThe drills of corn on the highest summits mn, op, caught the rays of the setting sun, which shone upon them very obliquely in the direction Ss, and illuminated their summits laterally, while the furrows AB, CD, EF, were in shadow. The consequence of this disposition of the light and shade was, that the whole field seemed to be trenched, and the corn to be growing in the trenches as well as upon the elevated beds between them. The half furrow AB nm, being shaded on its edge A B, and illuminated on its edge mn, became the elevated part of the trenched ground, while the other half m n CDappeared the sunk part, in consequence of the side mn being illuminated, and its other side CD in shade. At a certain period of the day this deception did not take place, and it was dispelled the moment the sun had set. The telescope had no effect whatever in producing it, as it showed objects erect.

306. An illusion of an analogous nature Dr. Brewster once observed when looking at the abbey church of Paisley, where the clustered columns of a Gothic pillar all sunk into hollow flutings. The cause of this deception was not discovered, but it must have arisen from some mistaken notion respecting the direction in which the object was illuminated.

307. The last species of illusion of this nature, and perhaps the most remarkable of all of them, may be produced by a continued effort of the mind to deceive itself. If we take one of the intaglio moulds used for making bas-reliefs, and direct the eye steadily to it without noticing surrounding objects, we may entice 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. Dr. Brewster states that he has succeeded in car rying this deception so far as to be able, by the eye alone, to raise a complete hollow mask of the human face 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.

308. The phenomena arising from atmospheric refraction may be best understood by an examination of the apparent alteration in the colors of the heavens

309. If the light of the setting-sun, by passing through a long tract of air, be divested of a portion of its rays, the remainder, which is transmitted, will illuminate the western clouds with an orange color, and as the sun sets more and more, a great number are reflected, while the clouds grow more deeply red, till at length the entire disappearance of the sun leaves them of a leaden hue.

310. When a direct spectrum is thrown on colors darker than itself, it mixes with them; as the yellow spectrum of the setting-sun, thrown on the green grass, becomes a greener yellow. But, when a direct spectrum is thrown on colors brighter than itself, it becomes instantly changed into the reverse spectrum, which mixes with those brighter colors. So the yellow spectrum of the setting sun thrown on the luminous sky becomes blue, and changes with the color or brightness of the clouds on which it appears. But the reverse spectrum mixes with every kind of color on which it is thrown, whether brighter than itself or not: thus, the reverse spectrum obtained by viewing a piece of yellow silk, when thrown on white paper, was a lucid blue-green; when thrown on black Turkey leather became a deep violet: and the spectrum of blue silk, thrown on white paper, was a light yellow; on black silk was an obscure orange; and the blue spectrum obtained from orange-colored silk, thrown on yellow, became a green.

311. Of the natural phenomena produced occasionally by the separation of the primary colors the rainbow is one of the most beautiful. This meteor, which in poetical language is called the iris, never makes its appearance except when the spectator is situated between the sun and a shower of rain; and that this conclusion is just any one may satisfy himself by the following experiment:-Fill a hollow glass globe with water, and susvend it in the sun, in such a

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manner that it may be raised or lowered at pleasure; at a certain height above the eye of the spectator, who looks at it with his back to the sun, the globe will appear to be red; let it then be slowly lowered, and it will appear to be orange, and afterwards, in succession, as it descends, it will appear yellow, green, blue, indigo, and violet. Hence the same drop of rain, which must be considered as a little globe, supplies all the seven colors to the eye. There are sometimes two rainbows seen at the same time, one within the other, and, what may seem remarkable, the order of the colors of the exterior bow is the reverse of that of the interior one. When two bows are seen, the exterior one is comparatively faint, and it is, therefore, sometimes called the false or secondary bow; while the greater distinctness of the interior one has obtained for it the appellation of the primary bow. The rainbow was one of those phenomena which astonished and perplexed the ancients; and, after many absurd and unsuceessful conjectures, their best philosophers, Pliny and Plutarch, relinquished the enquiry as one which was above the reach of human investigation. In the year 1611 Antonio de Dominis made a considerable advance, however, towards the theory of the rainbow, by suspending a glass globe in the sun's light, when he found that, while he stood with his back to the sun, the colors of the rainbow were reflected to his eye in succession by the globe, as it was moved higher or lower. He was, however, unable to account for the production of the different colors, as the experiments with the prism had not yet been made, and it was reserved for Newton to perfect the discovery. 312. To trace the progress of a ray of light through a drop of rain in each of these bows, will explain the cause of their differing in brightness. In the true or primary bow, the rays of light arrive at the spectator's eye, after two refractions and one reflection.

313. Thus, let A, in plate V. fig. 1, be a drop of rain, and S a ray from the sun falling on the upper part of the drop. It will suffer a refraction, and, instead of going forward in a right line, it will be bent to n; at n part of it will emerge, but the remainder will be reflected to g; at g it will be again refracted on passing into the air towards the eye at h; being thus twice refracted and once reflected, the ray is separated into its primitive colors; the red part, which is least thrown out of its course, makes an angle, at its emergence, with the incident solar ray of 40° 2′, as Sf h; and the violet, being the most easily thrown out of its course, makes with the solar light an angle of 40° 17′. The different colors, therefore, at the distance of the spectator, are considerably separated, and affect the eye in succession with the seven colors; but the succession is so quick, and so many drops fall through the same circuit in the same time, that the mind loses the idea of succession, and the bow seems permanent as long as the shower continues in a proper direction for the eye.

314. The exterior or secondary bow is formed by two reflections and two refractions. Let B represent one of the drops of rain forming this bow; a ray, T, from the sun, falling upon it at

r, is refracted, and falls upon the back of the drop at s; from the transparency of the drop a portion of it passes through towards w, but the remainder of it is reflected towards t; here again, for the same reason as before, part of it emerges from the drop, in the direction x, but the portion still left is reflected to u, where it is refracted towards the spectator, with the red rays uppermost. The great quantity of light lost at each reflection is the cause of the indistinctness of this bow, and therefore we cannot be surprised that we rarely, if ever, see bows formed by a still greater number of reflections within the drops; for, though they may exist, they are too faint to be seen. The secondary bow cannot be seen when the elevation of the sun is above 54° 7′, and it is broader than the interior bow, because the rays are more dispersed before they reach the eye.

315. The marine or sea bow is a phenomenon sometimes observed in a much agitated sea; when the wind, sweeping part of the tops of the waves, carries them aloft, so that the sun's rays falling upon them, are refracted, &c., as in a common shower, and paint the colors of the bow.

316. Rohault mentions colored bows on the grass, formed by the refraction of the sun's rays in the morning dew. Dr. Langwith, indeed, once saw a bow lying on the ground, the colors of which were almost as lively as those of the common rainbow. It was extended several hundred yards, and was not round, but oblong, being as he conceived the portion of an hyperbola. The colors took up less space, and were much more lively in those parts of the bow which were near him than in those which were at a distance.

317. We may now notice a peculiar perspective appearance of aerial light and shade. It occurred on the evening of August 19th, 1826; and was observed from the undercliff at the back of the Isle of Wight, just above Puckaster Cove. The sky was clear; the sun had just set to those who were standing where the appearance was observed; when several enormous rays of light and shade were remarked towards the east, north-east, and south-east, all radiating in straight lines from a spot rather south of east, and just upon the horizon. They were ten or twelve in number, did not join at the place whence they appeared to originate, but seemed to emerge from an obscure portion of surface of a convex form, 8° or 9° in horizontal extent, and about the third of that in height. The rays extended from 30° to 40° on the right and left from the centre, but were of less extent as they became more vertical. They diminished gradually in intensity at the extremities, until they could be traced no farther. The appearance slowly faded away, some of the rays disappearing before others, but was observed upon the whole for about half an hour.

318. At first the phenomenon seemed inexplicable, but after a little consideration was referred (and as it appeared from after observations correctly) to an effect of aerial perspective. The rays which seemed to originate from a common centre on the east were really only the intervals between long shadows caused by the

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