If the light, therefore, suffers either a total or a partial refraction, or if it suffers no refraction at all, the extraordinary reflection must be made from faces of variable curvature. 265. The most unaccountable circumstance, however, accompanying the extraordinary reflection, is the difference of effect produced upon the surfaces m and n by removing the polish. The surface m retains its power of reflecting the primary extraordinary image, notwithstanding the roughness which is thus superinduced, while the surface n loses the power of reflecting the secondary image, and acquires the faculty of transmitting the whole of the colored pencil which composes it. The force, therefore, which reflects the primary extraordinary image, would appear to be different from that which reflects the secondary extraordinary image, the latter being wholly dependent on the smoothness of the surface. 266. Hitherto we have avoided all consideration of the cause which separates the extraordinary pencils into their component colors, nor can we pretend to afford even a plausible conjecture respecting their origin. It is quite obvious that the separation into colors is produced before the pencil suffers extraordinary reflection, and, as the transmitted colors are not complementary to those which are reflected, it is equally manifest that the phenomenon has no connexion with the colors of thin plates. If the spectra were produced by the ordinary dispersive force of the body, then the dispersion ought to be least in gum arabic, greater in wax, and still greater in realgar and the metals, whereas in all these cases the quantity of color appears to be the same. The extraordinary spectra have no resemblance whatever to those which are the effect of inflexion; and, even if we could suppose that the light was inflected by the grooves, the cause would be inadequate to explain the continuance of the color, when the plane of incidence coincides with the direction of the grooves, and when there are manifestly no angles to bend the passing light. 267. But, whatever be the cause of the phenomena of mother-of-pearl, the facts themselves are peculiarly instructive, and naturally lead us to the following conclusions: (1). Besides the ordinary forces which reflect and refract light, there reside without the surface of mother of pearl, and of all bodies to which its superficial configuration can be imparted, new forces which reflect light, and separate it into its component colors. (2). The lines which bound the space of reflecting actively in all surfaces which possess this configuration, are straight, and are not parallel to the grooved structure of the surface. Hence a surface which appears, even to the unassisted eye, to be full of eminences and depressions, is capable of reflecting light with perfect accuracy. (3). Since a particular configuration of surface, independent of chemical composition and crystalline structure, is capable of producing the most brilliant colors, may not the colors of all natural bodies be owing to the arrangement of their superficial particles, and may not the changes which these colors undergo by the action of light, heat, and atmospherical causes, arise from a corresponding change in the superficial structure? Dr. Brewster has endeavoured to communicate to wax the faculty of producing color possessed by Labrador spar, the metallic oxides, and various other bodies; but, though he has not succeeded in this attempt, it by no means follows that the color is not produced by the configuration of the surface. The structure may in these cases be so minute, that fluid wax cannot be forced into the grooves or depressions; and we have an approach to this delicacy of conformation in some specimens of mother-of-pearl, where the grooves cannot be seen by the most powerful microscopes. (4). Since a particular structure of surface is always accompanied with a new repulsive force, residing nearer the body than the common repulsive force which produces ordinary reflection, may there not reside also, near the surface of all crystallised bodies, a new refractive force which produces double refraction? And is not this supposition countenanced by the fact that the extraordinary pencil formed by Iceland spar suffers the ordinary as well as the extraordinary refraction? 268. We may conclude this head with a few remarks on the crimson and green light, which always accompanies the primary colored image. This mass of light is never produced by the wax, and as it appears, even when the rays are incident upon the mother-of-pearl from a fluid of the same refractive power, it is evidently unconnected with the forms of surface. These masses of color appear to have the same origin as the colors of thin plates described by Newton. Even when the angle of incidence is the same, the crimson light appears at one thickness of the mother-of-pearl, and the green at a less thickness; and the transmitted light consists of colors complementary to those of the reflected light. We are, therefore, in this case, presented with phenomena almost exactly the same as those of thin plates, though produced by plates of motherof-pearl of considerable thickness. 269. IV. Having seen, in the course of the preceding experiments, so many deviations from the ordinary laws of optics, Dr. Brewster sus pected that mother-of-pearl might exhibit similar anomalies in the polarisation of light. This conjecture was immediately confirmed by the discovery of a remarkable property, which forms the connecting link between the phenomena of polarisation, as effected by crystallised and uncrystallised bodies. 270. In all doubly refracting crystals, the opposite polarisation of the two images is invariably related to some axis or fixed line in the primitive form; while in uncrystallised bodies the polarisation is related to the planes of reflection and refraction, the reflected pencil being always polarised in an opposite manner to the refracting pencil. Thus, if A B, fig. 6, be a plate of glass, and Rra ray incident upon it, at the polarising angle, the reflected ray r S will be polarised in the same manner as one of the pencils formed by calcareous spar, and a small portion of the transmitted ray r T will also be polarised, but in a manner opposite to r S like the other pencil in calcareous spar: or, if the ray Rr is transmitted through a bundle of glass plates, the whole of the pencil r T will be polarised in that manner. 271. If we now suppose A B a single plate of mother-of-pearl about one-fortieth of an inch thick, and the angle of incidence Rr C about 60°, the reflected ray r S will be polarised as in every other transparent body; but the transmitted ray r T will be wholly polarised, and in the same manner as the reflected ray r S, while in every other transparent body that has been examined the ray r T possesses an opposite kind of polarisation. If we now turn the plate A B round its centre r, so as to preserve its inclinanation to the incident ray Rr, no change whatever takes place, the transmitted ray still retain ing its former polarity. 272. The angle of incidence Rr C, at which the transmitted light r T is wholly polarised, varies in the inverse ratio of the thickness of the plate A B, and the whole pencil is polarised at any angle greater than that angle. The relation between the angle of polarisation and the thickness of the plate remains to be determined; though he suspects it will be found that the tangents of the angles of incidence, at which the whole of the pencil is polarised, are inversely as the thickness of the plates. 273. The phenomena above described, Dr. Brewster has observed, in every piece of motherof-pearl that he has tried; and as they are not affected when the incident pencil is refracted from balsam of Tolu, or any other cement, into the mother-of-pearl, they are obviously unconnected with its superficial configuration. Ivory does not produce the same effect upon light. 274. From these results, the following conclusions are clearly deducible: (1). That mother-of-pearl polarises light in a manner different from all crystallised bodies, the polarisation having no reference to any fixed line in the plate. (2). That mother-of-pearl polarises light in a manner different from all uncrystallised bodies, the transmitted pencil being wholly polarised by a single plate, and in the same manner with the reflected pencil. (3). That if mother-of-pearl polarises light in virtue of its laminated structure, the lamina themselves must have the property of polarising light in a manner opposite to all other bodies. 275. Mr. J. F. W. Herschel, in repeating the above experiments of Dr. Brewster, observed some new phenomena exhibited by that singular body in its action on transmitted light, depending on the internal arrangement of its molecules, and at the same time connected with a peculiarity in its superficial appearance under the microscope, which seems to have eluded his notice. When a plate of mother-of-pearl, cut parallel to the natural surface of the shell, is reduced by grinding to a thickness between 4th and 5th of an inch, and highly polished on both sides (in which circumstances it is very transparent); if a distant candle be viewed through it, besides the pair of colored images described by Dr. Brewster, which have the same origin with those seen by reflection, there may be observed two large very brilliant and highly colored nebulous masses, one on each side of the candle, and equidistant from it, which may readily be distinguished from the preceding, by the following characters. 276. The first pair of colored images, originating in the transferable superficial structure of the pearl, are always similar in position and color, and complementary in brightness to those seen by extraordinary reflection. In consequence, nothing can be more capriciously irregular than their situation, brightness, and distance from the centre. On passing various parts of the plate, with a parallel motion between the pupil of the eye and the candle, they will be seen to shift their direction, expand, contract, or disappear altogether, with every change in the point examined. This is not the case with the pair of nebulous masses now under consideration, which undergo little or no variation in any of these particulars, through whatever portion of the plate they are viewed. The axis of nebulous dispersion then (or line joining the two nebula) is parallel to itself, or nearly so, throughout the whole extent of the mother-of-pearl, and the energy of the cause producing it nearly or perfectly uniform. 277. These nebulous masses are usually about twice the distance of the colored images, described by Dr. Brewster from the centre; and, except the plate be very thin, are much larger and more conspicuous, and particularly distinguished from them by the equable gradation and softening of their colors, which are those of the prismatic spectrum, the red being outermost. Their angle of deviation, or distance from the central image, increases on inclining the plate in the plane passing through them; while their brightness rapidly diminishes, the former being a minimum, and the latter a maximum, at a perpendicular incidence. This angle, as well as the shape and color of the nebulæ, is the same, or nearly so, in all the specimens Mr. Herschel has examined; nor does any marked variation in these particulars arise by a variation in the thickness of the plate, or by cutting it at any moderate angle with the natural surface; only, in the latter case, the maximum of their inten 278. The extraordinary images seen by refiection, and their complementary pair by transmission, are completely obliterated by surrounding the mother-of-pearl with oil, or varnishing its surfaces. This, however, is so far from impairing the nebulous masses, that it heightens them a little, by perfecting the polish; and, should any doubt arise as to the identity of either pair, it may thus be immediately removed. From all these circumstances, compared with what Dr. Brewster has demonstrated respecting the former pair of images, we might reasonably conclude that the latter are entirely unconnected with any peculiarity in the superficial structure, and Mr. Herschel scarcely expected the application of the microscope to afford farther information, or lead to any result worth notice. On examining, however, many specimens of mother-of-pearl with a powerful double microscope, he found that this extraordinary body, in addition to the irregular grooved superficial structure, as described by Dr. Brewster, possesses another of great regularity and delicacy; but, like the former, resisting every attempt to impair it by polishing the surface. It may be seen to most advantage on a thin polished specimen, in which the first set of undulations vary a good deal in direction and coarseness. When we view such a plate successively with a series of increasing magnifiers, under a double microscope, a power of 123 will barely show, and one of 229 completely verify, the appearance of a minute system of rounded undulations, consisting as it were of fibres occasionally branching from each other, but never continued for any length. They are uniformly diffused over the whole surface, and, in their general direction, disposed in straight and exactly parallel lines, running from one end to the other. In consequence, they cross the first set of grooves at all angles, giving the whole surface much the appearance of a piece of twilled silk, or the larger waves of the sea intersected with minuter riplings. 279. The interval between these undulated appearances is nearly the same in all the specimens Mr. H. has examined. To ascertain it, twentyfive were counted in the space of an inch, in an image projected on a plane ten inches from the eye, while the diameter of a small wire, projected on the same plane with the same power, measured seven inches. The diameter of this wire taken by the sphærometer being 0.0227 inches gives 0-000129, orth of an inch for their mutual distance. To see them distinctly, a careful management of the illumination from below is necessary, and candle light must be used. 280. To demonstrate the connexion of these undulations (which, whether real or apparent, we shall for brevity call the second set of grooves, denoting those observed by Dr. Brewster by the first set) with the nebulous masses above described, Mr. Herschel chose å plate in which the first set varied from the extreme of coarseness to that of delicacy, and were particularly irregular in their direction and curvature. In this he carefully marked, by small ink circles, numbered 1, 2, 3, 4, 5, 6, 7, which were hen subjected to microscopic examination. At No. 1 and 2 the two sets of grooves coincided in direction. At No. 3 they made an angle rather more than 45° by the eye. At No. 4 no grooves of the first set could be seen, but a power of 229 showed some obscure and very irregular traces of coarse elevations and depressions. With this power, however, the second set were seen precisely as in every other part of the surface, and in the same uniform direction. 281. At No. 5 the first set, as they approached this point, grew smaller and smaller, requiring powers of 26, 34, 43, 123, in succession to perceive them. With this latter power the second set just became visible; while with 229, both sets were seen crossing each other at right angles, with the most perfect regularity and distinctness, the former being about twice the breadth of the latter. At No. 6 the direction of the first set varied a good deal, crossing the second from 45° to 60. At No. 7 they crossed at a small angle. 282. Mr. H. now detached the mother-ofpearl, and by passing a small sun-beam successively through each of the marked spots, and noticing the relative situations of the two pairs of colored images, it appeared that At No. 1 and 2 the axes of dispersion in the first and second pair of colored images were coincident. At No. 3 they made an angle of 45° with each other. At No. 4 there were no colored images of the first pair whatever, while those of the second pair had precisely the same appearance and direction as in the other parts of the plate. At No. 5 the axes of dispersion formed a right angle, the images of the first pair being very vivid, and separated by an unusually large interval. At No. 6 the angles of dispersion formed an angle of 60°. At No. 7 they were 17° inclined to each other. 283. In general, in different specimens, he could always predict, à priori, the situation of the nebulous masses of the second pair, by observing with the microscope the direction of the second set of grooves to which they are invariably at right angles; and the connexion between the two phenomena is thus clearly demonstrated. Yet this connexion is not, as in the case of the reflected colors, that of cause and effect. nebulous masses, as we have seen, subsist when the grooves, if any, are obliterated by immersion in a fluid of equal refractive density. It is, therefore, in the internal structure of the pearl The that we must look for the common cause of both occurrences. When we examine a thin plate of this substance by polarised light, the phenomena of a crystal with two axes of double refraction are observed; the isochromatic lines being perfectly regular, and similarly disposed in all parts of the surface, and the colors, though not vivid and somewhat hazy, yet following in their proper order, and extending sometimes to six, seven, or eight, repetitions of the same color from either pole. If now, we notice the situation of the axes of double refraction, with respect to what has above been called the axis of nebulous dispersion, we shall find that the latter is in all cases at right angles to the plane in which the former lie, or to the optic meridian of the crystal. 284. The nebulous masses then, in all probability, originate in a regular laminated structure, perpendicular to the natural surface of the shell, and uniformly pervading all the coats of which it consists. The lamina, to agree with the above facts, must run parallel to each other, and in lines nearly straight along the whole surface, and the alternate ones at least must be regular crystals, having their optic meridians parallel to their own plane, and their optic axis (by which is meant the axis of symmetry in their spheroid of double refraction) perpendicular to the natural surface. The intermediate laminæ, if composed of the same substance, must have their axes inclined to those of the former at some determinate angle. The grooved appearance above described may possibly arise from an actual difference in the resistance of these two sets of lamina to the action of the polishing particles, and therefore consist in a real difference of level; but this Mr. Herschel much doubts, from the simple fact, that he has never been able to transfer their impression to other transparent bodies, such as melted rosin, shell-lac, balsam of Tolu, &c., though in all cases the first set of grooves, however fine, has been transferred with the utmost fidelity, and the 7700th part of an inch, though a very minute quantity to our senses, appears to him enormously too wide to oppose the free introduction of a fluid under such circumstances. It is more probable that the appearance is a mere optical illusion, though a most complete one, arising from the difference, of action of the contiguous surfaces on the light transmitted from below. 285. The regularity of structure here supposed is not at all incompatible with the irregular and arbitrary disposition of the grooves described by Dr. Brewster. These are the intersections of the plain artificial surface with the thin coats deposited in succession by the living animal, which, though laid symmetrically on each other, like the lamina of mica, have yet a slight degree of irregular curvature, and a small and varying inclination to the polished face. Their form and breadth is regulated by this curvature and inclination, like the level lines traced by a receding tide on a slightly inclined sea-beach, or those on the surface of a wooden board, where its concentric layers rise in succession at different angles to the surface. Indeed, the face of an ordinary deal plank, cut at some distance from the centre of the tree, however coarse the simile may appear, when smoothed by planing and afterwards subjected to the friction of rough particles, as in a floor, is a lively and faithful representation of the surface of a polished plate of mother-of-pearl, in which the edges of the lamina reduced to the utmost tenuity, by the effect of their inclination to the general surface, are torn up in their direction of least resistance, by the action of the polishing particles. This is rendered perfectly evident by the microscopic examination of the surface in different stages of its progress, from the rough grinding to the most perfect polish, when the grooves, from an irregular, jagged, and deeply indented outline, will be seen to assume a greater and greater neatness of termination, till their curvature acquires that graceful and flowing character which ultimately distinguishes them. 286. The remarkable phenomena to which we now propose to direct the attention of our readers, while they possess all the interest which belongs to them as physical facts, have attached to them another kind of interest not less deserving of attention. To those who are in the practice of exercising a presumptuous confidence in their own judgments, and who trust in the indications of their senses as infallible guides, we would recommend the particular study of this class of deceptions. They will here find their judgments deluded, where every thing is favorable to the discovery of the truth; and even when they are aware of the source of the deception they will find themselves again brought under its dominion, and again released from it, by the operation of the most trivial circumstances which they are not able to discover, and the influence of which, if they do discover them, they are not able to appreciate. If all this takes place in matters of simple observation, where the senses of sight and of touch are allowed their undisturbed exercise, how much more liable must they be to error where their passions, their prejudices, or their feelings, concur in promoting the delusion, or even in any remote degree prepare the mind for its reception! 287. The class of deceptions to which we allude were, so far as we know, first noticed at one of the early meetings of the Royal Society of London, when a compound microscope, on a new construction, was exhibited. When the members were looking through it at a guinea, some of them saw the head upon the coin depressed, while others considered it to be raised, as it was in reality. 288. This deception was studied by Dr. Philip Frederick Gmelin, of Wirtemberg, who communicated the following observations upon it to the Royal Society in 1774 289.Being informed by a friend,' says he, that if a common seal was applied to the focus of a compound microscope, or optical tube, which has two or three convex or plano-convex lenses, that part which is cut the deepest in it would appear very convex, and so on the contrary; and that sometimes, but very seldom, it would appear in the same state as to the naked eye. I was desirous to make the observation myself, and found it constantly to happen as my friend told me. I thought the experiment worthy of being farther prosecuted; and accordingly on the 16th of April, the morning not being very clear, but in a pretty light chamber, I viewed a watch hanging against a plain wall through the optical tube; the whole of it appeared concave, and fixed into the wall. I also observed some flies that were running about the wall, and they appeared in like manner. I also viewed a small globe of a thermometer filled with red spirit, and this also seemed hollow, and fixed within the frame. I found the same to happen with the round parts of garments of all colors, and with the brazen protuberances of a small cabinet; all which appeared concave, and deeply sunk into the cloth and wood. I also viewed a small stag's head cut in wood, and hanging horizontally on the wall; this also appeared concave, and fixed into the wall. 290. After this I observed a ball of Fahrenheit's thermometer, full of quicksilver: but it did not change its natural convexity, nor did the empty glass ball of the inverted thermometer hanging against the wall, though the lower ball of the same, filled with red spirit, and that also of Fahrenheit's filled with spirit, lost their convexity. Hence I presently concluded that white or shining uncolored bodies appear under the focus of this tube in the same manner as they appear to the naked eye; at the same time I must fairly acknowledge that an assisting friend has sometimes made observations directly opposite to mine in the same circumstances; nay, in a darker day, I myself have found my observations quite contrary to those I had made the day before. Hence, though the observations with the seal held constantly the same, I imagined there must be some particular circumstances hitherto undiscovered in which these objects appear thus perverted. I therefore endeavoured to discover some certain laws, according to which these perverted objects appeared when exposed to these foci, and some others according to which they constantly appeared as when they were exposed to the naked eye. After various experiments I partly obtained my end. 291. As often as I viewed any object rising upon a plane, of what color soever, provided it was neither white nor shining, with the eye and optical tube directly opposite to it, the elevated parts appeared depressed, and the depressed parts elevated, as it happened in the seal, as often as I held the tube perpendicularly, and brought it in such a manner that its whole surface almost covered the last glass of the tube; and in like manner it happened under the compound microscope. But as often as I viewed any of the other objects depending perpendicularly from a perpendicular plane in such a manner that the tube was supported in a horizontal situation directly opposite to it, the same always happened and the appearance was not altered when the object hung obliquely or even horizontally. I was mightily delighted with the observation of a tobacco-pipe, which had a porcelain bowl of a snowy whiteness, and a tube of horn almost black, and hung obliquely from a beam; the bowl preserved its natural convexity, and the tube was deeply sunk, and seemed to be almost immersed in the wall. I also observed that, when I placed the watch horizontally upon a horizontal plane, and then But looked on it perpendicularly, near the window, it no longer appeared so depressed, and surrounded with a shady ring; whence I began to suspect that all those fallacies were owing to shade, just as painters can elevate or depress a figure by making the ground lighter or deeper. Thus when the raised object was so placed between the windows that it must be illuminated on all sides, it did not change its convexity. at last I discovered a method of making objects appear always with their natural convexity. If any object hung against a wall, or was contiguous to it in any situation whatsoever, I viewed sideways, in such a manner as not to oppose the tube directly against it, but below the eminence near the plain at some distance. By those means the protuberance of the instrument and other objects always appeared to me of their true natural convexity. With regard to the seal I held it in such a manner that the whole circumference was perpendicular, or rather a little inclined. Then I applied the lower side of the tube exactly to the upper margin of the disc of the seal, so that the tube formed an obtuse angle with the seal; then, carefully preserving the same situation, I very gently raised the tube from the rim of the seal upon its face; and then I always saw the seal with its true natural face. But why all these things happen exactly after the same manner I do not pretend to determine; nor why white or uncolored transparent bodies, rising in any manner above any plain, afford an exception from that rule of vision, and do not appear depressed when viewed after the method above-mentioned.' 292. In the year 1780 this subject occupied the attention of David Rittenhouse, president of the American Philosophical Society, who gave a correct explanation of the illusion, by referring it to the inversion of the shadow by the eyetube. He employed in his observations an eyepiece, having two lenses placed at a distance greater than the sum of their focal distances; and by throwing a reflected light on the cavities observed, in a direction opposite to that of the light which came from his window, he was able to see them raised into elevations by looking through a tube without any lenses. Mr. Rittenhouse also observed that, by putting his finger into the cavity, the illusion ceased to take place. 293. Having thus given a brief detail of the experiments of Gmelin and Rittenhouse we shall proceed to explain more minutely the principles on which this illusion depends. It will afterwards be seen that inverting telescopes and microscopes are not necessary to the production of this iilusion; but it may be best seen by viewing with the eye-piece of an achromatic telescope the engraving upon a seal when illuminated either by a candle or the window of an apartment. This eye-piece inverts the objects to which it is applied like the compound microscope, and the excavations or depressions of the seal are immediately raised up into elevations like a cameo, or a bas-relief. The cause of this illusion will be understood from fig. 7, where A represents a spherical cavity illuminated by a candle C. The shadow of the cavity will of course be on the left side S, and, therefore, if we view it through an inverting eye-piece or microscope, the cavity |