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Angles of incidence.

Inclination of the peculiarly instructive, and naturally lead us to

faces m or 1. the following conclusions :86 41

(1). Besides the ordinary forces which reflect 20 8

and refract light, there reside without the sur70

15 9

face of mother of pearl, and of all bodies to 13 48

which its superficial configuration can be im60

12 19

parted, new forces which reflect light, and se12

1 20

parate it into its component colors,

(2). The lines which bound the space of reBut since the refraction cannot be completed flecting actively in all surfaces which possess this when the ray reaches the surfaces mor n, having configuration, are straight, and are not parallel passed through only half the space of refracting to the grooved structure of the surface. Hence activity, let us suppose the value of m correspond- a surface which appears, even to the unassisted ing to the partial refraction to be 1:300, and we

eye, to be full of eminences and depressions, is shall have the following values of 2 :

capable of reflecting light with perfect accuracy. Angles of Inclination of the

(3). Since a particular configuration of surincidence.

faces, m, n.

face, independent of chemical composition and 86° 41' 13° 34'

crystalline structure, is capable of producing the 70

9 16

most brilliant colors, may not the colors of all 65

1 19

natural bodies be owing to the arrangement of their 60

7 14

superficial particles, and may not the changes 12

0 20

which these colors undergo by the action of light,

heat, and atmospherical causes, arise from a corIf the light, therefore, suffers either a total or a responding change in the superficial structure ? partial refraction, or if it suffers no refraction at Dr. Brewster has endeavoured to communicate all, the extraordinary reflection must be made to wax the faculty of producing color possessed from faces of variable curvature.

by Labrador spar, the metallic oxides, and 265. The most unaccountable circumstance, various other bodies; but, though he has not suchowever, accompanying the extraordinary re ceeded in this attempt, it by no means follows flection, is the difference of effect produced upon that the color is not produced by the configurathe surfaces m and n by removing the polish. tion of the surface. The structure may in these The sarface m retains its power of reflecting the cases be so minute, that fluid wax cannot be primary extraordinary image, notwithstanding forced into the grooves or depressions; and we the roughness which is thus superinduced, while have an approach to this delicacy of conformathe surface n loses the power of reflecting the tion in some specimens of mother-of-pearl, where secondary image, and acquires the faculty of the grooves cannot be seen by the most powerful transmitting the whole of the colored pencil microscopes. which composes it. The force, therefore, which (4). Since a particular structure of surface is reflects the primary extraordinary image, would always accompanied with a new repulsive force, appear to be different from that which reflects residing nearer the body than the common rethe secondary extraordinary image, the latter pulsive force which produces ordinary reflecbeing wholly dependent on the smoothness tion, may there not reside also, near the surface of the surface.

of all crystallised bodies, a new refractive force 266. Hitherto we have avoided all considera- which produces double refraction ? And is not tion of the cause which separates the extraor- this supposition countenanced by the fact that dinary pencils into their component colors, nor the extraordinary pencil formed by Iceland spar can we pretend to afford even a plausible con- suffers the ordinary as well as the extraurdinary jecture respecting their origin. It is quite ob- refraction ? vious that the separation into colors is produced 268. We may conclude this head with a few before the pencil suffers extraordinary reflection, remarks on the crimson and green light, which and, as the transmitted colors are not complemen- always accompanies the primary colored image. tary to those which are reflected, it is equally This mass of light is never produced by the wax, manifest that the phenomenon has no connexion and as it appears

, even when the rays are inciwith the colors of thin plates. If the spectra dent upon the mother-of-pearl from a fluid of the were produced by the ordinary dispersive force same refractive power, it is evidently unconof the body, then the dispersion ought to be least nected with the forms of surface. These masses in gum arabic, greater in wax, and still greater of color appear to liave the same origin as the in realgar and the metals, whereas in all these colors of thin plates described by Newton. cases the quantity of color appears to be the Even when the angle of incidence is the same,

The extraordinary spectra have no re- the crimson light appears at one thickness of the semblance whatever to those which are the effect mother-of-pearl, and the green at a less thickof inflexion ; and, even if we could suppose that ness; and the transmitted light consists of colors the light was inflected by the grooves, the cause complementary to those of the reflected light. would be inadequate to explain the continuance We are, theresore, in this case, presented with of the color, when the plane of incidence coin- phenomena almost exactly the same as those of cides with the direction of the grooves, and when thin plates, though produced by plates of motherthere are manifestiy no angles to bend the pass- of-pearl of considerabie thickness. ing light.

269. IV. Having seen, in the course of the 267. But, whatever be the cause of the pheno- preceding experiments, so many deviations from mena of mother-of-pearl, the facts themselves are the ordinary laws of optics, Dr. Brewster sus


pected that mother-of-pearl might exhibit similar (3). That if mother-of-pearl polarises light anomalies in the polarisation of light. This in virtue of its laminated structure, the laminæ conjecture was immediately confirmed by the themselves must have the property of polarising discovery of a remarkable property, which forms light in a manner opposite to all other bodies. the connecting link between the phenomena of 275. Mr. J. F. W. Herschel, in repeating the polarisation, as effected by crystallised and un above experiments of Dr. Brewster, observed crystallised bodies.

some new phenomena exhibited by that singular 270. In all doubly refracting crystals, the op- body in its action on transmitted light, dependposite polarisation of the two images is invari- ing on the internal arrangement of its molecules, ably related to some axis or fixed line in the and at the same time connected with a peculiarity primitive form; while in uncrystallised bodies in its superficial appearance under the microthe polarisation is related to the planes of re- scope, which seems to have eluded his notice. fection and refraction, the reflected pencil being When a plate of mother-of-pearl, cut parallel to always polarised in an opposite manner to the the natural surface of the shell, is reduced by refracting pencil. Thus, if A B, fig. 6, be a plate grinding to a thickness between Ath and footh of of glass, and Rra ray incident upon it, at the an inch, and highly polished on both sides polarising angle, the reflected ray rs will be po- (in which circumstances it is very transparent); larised in the same manner as one of the pencils if a distant candle be viewed through it, besides formed by calcareous spar, and a small portion the pair of colored images described by Dr. of the transmitted ray r T will also be polarised, Brewster, which have the same origin with those but in a manner opposite to r S like the other seen by reflection, there may be observed two pencil in calcareous spar: or, if the ray Rr is large very brilliant and highly colored nebulous transmitted through a bundle of glass plates, the masses, one on each side of the candle, and whole of the pencil r T will be polarised in that equidistant from it, which may readily be distinmanner.

guished from the preceding, by the following cha271. If we now suppose A B a single plate of racters. mother-of-pearl about one-fortieth of an inch 276. The first pair of colored images, origithick, and the angle of incidence RrC about nating in the transferable superficial structure of 60°, the reflected ray rS will be polarised as in the pearl, are always similar in position and every other transparent body; but the trans- color, and complementary in brightness to those mitted ray r T will be wholly polarised, and in seen by extraordinary reflection.

In consethe same manner as the reflected ray rs, while quence, nothing can be more capriciously irrein every other transparent body that has been gular than their situation, brightness, and disexamined the ray r T possesses an opposite kind tance from the centre. On passing various parts of polarisation. If we now turn the plate A B of the plate, with a parallel motion between the round its centre r, so as to preserve its inclina- pupil of the eye and the candle, they will be seen nation to the incident ray Rr, no change what- to shift their direction, expand, contract, or disever takes place, the transmitted ray still retain appear altogether, with every change in the point ing its former polarity.

examined. This is not the case with the pair of 272. The angle of incidence R r C, at which nebulous masses now under consideration, which the transmitted light r T is wholly polarised, va- undergo little or no variation in any of these ries in the inverse ratio of the thickness of the particulars, through whatever portion of the plate A B, and the whole pencil is polarised at plate they are viewed. The axis of nebulous any angle greater than that angle. The relation dispersion then (or line joining the two nebulæ) between the angle of polarisation and the thick- is parallel to itself, or nearly so, throughout the ness of the plate remains to be determined; whole extent of the mother-of-pearl, and the though he suspects it will be found that the tan- energy of the cause producing it nearly or pergents of the angles of incidence, at which the fectly uniform. whole of the pencil is polarised, are inversely as 277. These nebulous masses are usually about the thickness of the plates.

twice the distance of the colored images, de273. The phenomena above described, Dr. scribed by Dr. Brewster from the centre; and, Brewster has observed, in every piece of mother- except the plate be very thin, are much larger of-pearl that he has tried; and as they are not and more conspicuous, and particularly distinaffected when the incident pencil is refracted guished from them by the equable gradation and from balsam of Tolu, or any other cement, into softening of their colors, which are those of the the mother-of-pearl, they are obviously uncon- prismatic spectrum, the red being outermost. nected with its superficial configuration. Ivory Their angle of deviation, or distance from the does not produce the same effect upon light. central image, increases on inclining the plate in

274. From these results, the following con- the plane passing through them; while their clusions are clearly deducible :

brightness rapidly diminishes, the former being (1). That mother-of-pearl polarises light in a a minimum, and the latter a maximum, at a permanner different from all crystallised bodies, pendicular incidence. This angle, as well as the the polarisation having no reference to any fixed shape and color of the nebulæ, is the same, or line in the plate.

nearly so, in all the specimens Mr. Herschel has (2). That mother-of-pearl polarises light in a examined; nor does any marked variation in manner different from all uncrystallised bodies, these particulars arise by a variation in the the transmitted pencil being wholly polarised by thickness of the plate, or by cutting it at any a single plate, and in the same manner with the moderate angle with the natural surface; only, reflected pencil.

in the latter case, the maximum of their inten

sity, and minimum of distance, takes place at undulations (which, whether real or apparent, such an angle of incidence that the ordinary ray we shall for brevity call the second set of traverses the substance in a direction perpendi- grooves, denoting those observed by Dr. Brewcular to the natural surface of the shell, which is ster by the first set) with the nebulous masses also the direction of its greatest transparency. above described, Mr. Herschel chose à plate in The minimum angle of deviation in the nebu- which the first set varied from the extreme of lous images appears to be

coarseness to that of delicacy, and were particuFor the extreme red about

10° 29' larly irregular in their direction and curvature. For the mean rays

6 59

In this he carefully marked, by small ink circles, For the extreme violet.

4 16

numbered 1, 2, 3, 4, 5, 6, 7, which were •hen

subjected to microscopic examination. 278. The extraordinary images seen by re Åt No. 1 and 2 the two sets of grooves cofiection, and their complementary pair by trans- incided in direction. mission, are completely obliterated by surround At No. 3 they made an angle rather more than ing the mother-of-pearl with oil, or varnishing its 45° by the eye. surfaces. This, however, is so far from impairing At No. 4 no grooves of the first set could be the nebulous masses, that it heightens them a seen, but a power of 229 showed some obscure little, by perfecting the polish; and, should any and very irregular traces of coarse elevations doubt arise as to the identity of either pair, it and depressions. With this power, however, may thus be immediately removed. From all the second set were seen precisely as in every these circumstances, compared with what Dr. other part of the surface, and in the same uniBrewster has demonstrated respecting the former form direction. pair of images, we might reasonably conclude 281. At No. 5 the first set, as they approached ihat the latter are entirely unconnected with any this point, grew smaller and smaller, requiring peculiarity in the superficial structure, and Mr. powers of 26, 34, 43, 123, in succession to perHerschel scarcely expected the application of the ceive them. With this latter power the second microscope to afford farther information, or lead set just became visible; while with 229, both to any result worth notice. On examining, how- sets were seen crossing each other at right ever, many specimens of mother-of-pearl with a angles, with the most perfect regularity and dispowerful double microscope, he found that this tinctness, the former being about twice the extraordinary body, in addition to the irregular breadth of the latter. grooved superficial structure, as described by At No. 6 the direction of the first set varied Dr. Brewster, possesses another of great regu a good deal, crossing the second from 450 to 60. larity and delicacy; but, like the former, resist At No. 7 they crossed at a small angle. ing every attempt to impair it by polishing the 282. Mr. H. now detached the mother-ofsurface. It may be seen to inost advantage on a pearl, and by passing a small sun-beam succesthin polished specimen, in which the first set of sively through each of the marked spots, and undulations vary a good deal in direction and noticing the relative situations of the two pairs coarseness. When we view such a plate succes- of colored images, it appeared that sively with a series of increasing magnifiers, At No. 1 and 2 the axes of dispersion in the under a double microscope, a power of 123 first and second pair of colored images were cowill barely show, and one of 229 completely incident. verify, the appearance of a minute system of At No. 3 they made an angle of 45° with rounded undulations, consisting as it were of each other. fibres occasionally branching from each other, At No. 4 there were no colored images of the but never continued for any length. They are first pair whatever, while those of the second uniformly diffused over the whole surface, and, pair had precisely the same appearance and diin their general direction, disposed in straight and rection as in the other parts of the plate. exactly parallel lines, running from one end to At No. 5 the axes of dispersion formed a the other. In consequence, they cross the first right angle, the images the first pair being set of grooves at all angles, giving the whole very vivid, and separated by an unusually large surface much the appearance of a piece of twilled interval. silk, or ihe larger waves of the sea intersected At No. 6 the angles of dispersion formed an with minuter riplings.

angle of 60° 279. The interval between these undulated ap At No. 7 they were 17° inclined to each pearances is nearly the same in all the specimens other. Mr. H, has examined. To ascertain it, twenty 283. In general, in different specimens, he five were counted in the space of an inch, in an could always predict, à priori, the situation of image projected on a plane ten inches from the the nebulous masses of the second pair, by obeye, while the diameter of a small wire, pro- serving with the microscope the direction of the jected on the same plane with the same power, second set of grooves to which they are invariameasured seven inches. The diameter of this bly at right angles; and the connexion between wire taken by the sphærometer being 0·0227 the two phenomena is thus clearly demonstrated. inches gives 0.000129, or oth of an inch for Yet this connexion is not, as in the case of the their mutual distance. To see them distinctly, reflected colors, that of cause and effect. The a careful management of the illumination from nebulous masses, as we have seen, subsist when below is necessary, and candle light must be the grooves, if any, are obliterated by immersion used.

in a fluid of equal refractive density. It is, 280. Tu Jemonstrate the connexion of these therefore, in the internal structure of the pearl

that we must look for the common cause of both may appear, when snioothed by planing and afoccurrences. When we examine a thin plate of terwards subjected to the friction of rough parthis substance by polarised light, the phenomena ticles, as in a floor, is a lively and faithful repreof a crystal with two axes of double refraction sentation of the surface of a polished plate of are observed ; the isochromatic lines being per- mother-of-pearl, in which the edges of ine laminæ fectly regular, and similarly disposed in all parts reduced to the utmost tenuity, by the effect of of the surface, and the colors, though not vivid their inclination to the general surface, are torn and somewhat hazy, yet following in their proper up in their direction of least resistance, by the order, and extending sometimes to six, seven, action of the polishing particles. This is renor eight, repetitions of the same color from dered perfectly evident by the microscopic exaeither pole. If now, we notice the situation mination of the surface in different stages of its of the axes of double refraction, with respect progress, from the rough grinding to the most to what has above been called the axis of perfect polish, when the grooves, from an irregunebulous dispersion, we shall find that the lar, jagged, and deeply indented outline, will be latter is in all cases at right angles to the plane in seen to assume a greater and greater neatness of which the former lie, or to the optic meridian of termination, till their curvature acquires that the crystal.

graceful and flowing character which ultimately 284. The nebulous masses then, in all proba- distinguishes them. bility, originate in a regular laminated structure, 286. The remarkable phenomena to which we perpendicular to the natural surface of the shell, now propose to direct the attention of our readand uniformly pervading all the coats of which ers, while they possess all the interest which beit consists. The laminæ, to agree with the above longs to them as physical facts, have attached to facts, must run parallel to each other, and in lines them another kind of interest not less deserving nearly straight along the whole surface, and the of attention. To those who are in the practice altervate ones at least must be regular crystals, of exercising a presumptuous confidence in their having their optic meridians parallel to their own own judgments, and who trust in the indications plane, and their optic axis (by which is meant of their senses as infallible guides, we would reihe axis of symmetry in their spheroid of double commend the particular study of this class of derefraction) perpendicular to the natural surface. ceptions. They will here find their judgments The intermediate laminæ, if composed of the deluded, where every thing is favorable to the same substance, must have their axes inclined to discovery of the truth; and even when they are those of the former at some determinate angle. aware of the source of the deception they will The grooved appearance above described may find themselves again brought under its dominion, possibly arise from an actual difference in the and again released from it, by the operation of resistance of these two sets of laminæ to the the most trivial circumstances which they are not action of the polishing particles, and therefore able to discover, and the influence of which, if consist in a real difference of level; but this Mr. they do discover them, they are not able to apHerschel much doubts, from the simple fact, that preciate. If all this takes place in matters of he has never been able to transfer their impres- simple observation, where the senses of sight and of sion to other transparent bodies, such as melted touch are allowed their undisturbed exercise, how rosin, shell-lac, balsam of Tolu, &c., though in much more liable must they be to error where all cases the first set of grooves, however fine, their passions, their prejudices, or their feelings, has been transferred with the utmost fidelity, and concur in promoting the delusion, or even in any the 7700th part of an inch, though a very minute remote degree prepare the mind for its reception ! quantity to our senses, appears to him enor 287. The class of deceptions to which we mously too wide to oppose the free introduction allude were, so far as we know, first noticed at of a fluid under such circumstances. It is more one of the early meetings of the Royal Society of probable that the appearance is a mere optical London, when a compound microscope, on a illusion, though a most complete one, arising new construction, was exhibited. When the from the difference of action of the contiguous members were looking through it at a guinea, surfaces on the light transmitted from below. some of them saw the head upon the coin de

285. The regularity of structure here sup- pressed, while others considered it to be raised, posed is not at all incompatible with the irregu- as it was in reality. lar and arbitrary disposition of the grooves de 288. This deception was studied by Dr. Philip scribed by Dr. Brewster. These are the inter- Frederick Gmelin, of Wirtemberg, who commusections of the plain artificial surface with the nicated the following observations upon it to the thin coats deposited in succession by the living Royal Society in 1774 :animal, which, though laid symmetrically on each 289. • Being informed by a friend,' says he, other, like the laminæ of mica, have yet a slight that if a common seal was applied to the focus of degree of irregular curvature, and a small and a compound microscope, or optical tube, which varying inclination to the polished face. Their has two or three convex or plano-convex lenses, form and breadth is regulated by this curvature that part which is cut the deepest in it would and inclination, like the level lines traced by a appear very convex, and so on the contrary; and receding tide on a slightly inclined sea-beach, or that sometimes, but very seldom, it would appear those on the surface of a wooden board, where in the same state as to the naked eye. I was its concentric layers rise in succession at different desirous to make the observation myself, and angles to the surface. Indeed, the face of an or found it constantly to happen as my friend told dinary deal plank, cut at some distanee from the me. I thought the experiment worthy of being centre of the tree, however coarse the simile fariner prosecuted ; and accordingly on the 16th

of April, the morning not being very clear, looked on it perpendicularly, near the window, but in a pretty light chamber, I viewed a watch it no longer appeared so depressed, and surhanging against a plain wall through the optical rounded with a shady ring; whence I began to tube; the whole of it appeared concave, and suspect that all those fallacies were owing to fixed into the wall. I also observed some flies shade, just as painters can elevate or depress a that were running about the wall, and they ap- figure by making the ground lighter or deeper. peared in like manner. I also viewed a small Thus when the raised object was so placed beglobe of a thermometer filled with red spirit, tween the windows that it must be illuminated on and this also seemed hollow, and fixed within the all sides, it did not change its convexity. But frame. I found the same to happen with the at last I discovered a method of making objects round parts of garments of all colors, and with appear always with their natural convexity. Ii the brazen protuberances of a small cabinet; all any object hung against a wall, or was contiguous which appeared concave, and deeply sunk into to it in any situation whatsoever, I viewed sidethe cloth and wood. I also viewed a small stag's ways, in such a manner as not to oppose the head cut in wood, and hanging horizontally on tube directly against it, but below the eminence the wall; this also appeared concave, and fixed near the plain at some distance. By those means into the wall.

the protuberance of the instrument and other ob290. After this I observed a ball of Fahren- jects always appeared to me of their true natural heit's thermometer, full of quicksilver : but it convexity. With regard to the seal I held it in did not change its natural convexity, nor did the such a manner that the whole circumference was empty glass ball of the inverted thermometer perpendicular, or rather a little inclined. Then hanging against the wall, though the lower ball I applied the lower side of the tube exactly to of the same, filled with red spirit, and that also the upper margin of the disc of the seal, so that of Fahrenheit's filled with spirit, lost their con- the tube formed an obtuse angle with the seal;

vexity. Hence I presently concluded that white then, carefully preserving the same situation, I : or shining uncolored bodies appear under the very gently raised the tube from the rim of the

focus of this tube in the same manner as they seal upon its face ; and then I always saw the appear to the naked eye ; at the same time I must seal with its true natural face. But why all these fairly acknowledge that an assisting friend has things happen exactly after the same manner I sometimes made observations directly opposite do not pretend to determine; nor why white or to mine in the same circumstances; nay, in a uncolored transparent bodies, rising in any mandarker day, I myself have found my observations ner above any plain, afford an exception from quite contrary to those I had made the day be- that rule of vision, and do not appear depressed fore. Hence, though the observations with the when viewed after the method above-mentioned.' seal held constantly the same, I imagined there 292. In the year 1780 this subject occupied must be some particular circumstances hitherto the attention of David Rittenhouse, president of undiscovered in which these objects appear thus the American Philosophical Society, who gave a perverted. I therefore endeavoured to discover correct explanation of the illusion, by referring some certain laws, according to which these per- it to the inversion of the shadow by the eyeverted objects appeared when exposed to these tube. He employed in his observations an eyefoci, and some others according to which they piece, having two lenses placed at a distance constantly appeared as when they were exposed greater than the sum of their focal distances ; to the naked eye.

After various experiments I and by throwing a reflected light on the cavities partly obtained my end.

observed, in a direction opposite to that of the 291. . As often as I viewed any object rising light which came from his window, he was able upon a plane, of what color soever, provided it to see them raised into elevations by looking was neither white nor shining, with the eye and through a tube without any lenses. Mr. Rittenoptical tube directly opposite to it, the elevated house also observed that, by putting his fuger parts appeared depressed, and the depressed into the cavity, the illusion ceased to take place. parts elevated, as it happened in the seal, as often 293. Having thus given a brief detail of the as I held the tube perpendicularly, and brought experiments of Gmelin and Rittenhouse we shall it in such a manner that its whole surface almost proceed to explain more minutely the principles covered the last glass of the tube; and in like man on which this illusion depends. It will afterper it happened under the compound microscope. wards be seen that inverting telescopes and miBut as often as I viewed any of the other objects croscopes are not necessary to the production of depending perpendicularly from a perpendicular this iilusion; but it may be best seen by viewing plane in such a manner that the tube was sup with the eye-piece of an achromatic telescope ported in a horizontal situation directly opposite the engraving upon a seal when illuminated either to it, the same always happened and the appear- by a candle or the window of an apartment. ance was not altered when the object hung ob- This eye-piece inverts the objects to which it is liquely or even horizontally. I was mightily de- applied like the compound microscope, and the lighted with the observation of a tobacco-pipe, excavations or depressions of the seal are immewhich had a porcelain bowl of a snowy white- diately raised up into elevations like a cameo, or

and a tube of horn almost black, and hung a bas-relief. The cause of this illusion will be obliquely from a beam ; the bowl preserved its understood from fig. 7, where A represents a natural convexity, and the tube was deeply sunk, spherical cavity illuminated by a candle C. The and seemed to be almost immersed in the wall. shadow of the cavity will of course be on the I also observed that, when I placed the watch left side nd,

if view it through horizontally upon a horizontal plane, and then an inverting eye-piece or microscope, the cavity


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