the shadows of the knives are terminated, and distinguished from the first luminous fringes, by the lines eis and rip, till the meeting and crossing of the fringes,; and then those lines cross the fringes in the form of dark lines terminating the first luminous fringes on the inside, and distinguishing them from another light, which begins to appear at i, and illuminates all the triangular space ip D Es, comprehended by these dark lines and the right line DE. Of these hyperbolas one asymptote is the line D E, and the other asymptotes are parallel to the lines CA and CB. The sun shining into his darkened room, through the small hole mentioned above, he placed at the hole a prism to refract the light, and to form on the opposite wall the colored image of the sun; and he found that the shadows of all bodies held in the colored light, between the prism and the wall, were bordered with fringes of the color of that light in which they were held; and, comparing the fringes made in the several colored lights, he found that those made in the red light were the largest, those made in the violet were the least, and those made in the green were of a middle bigness. For the fringes with which the shadow of a man's hair were bordered, being measured across the shadow, at six inches from the hair, the distance between the middle and most luminous part of the first or innermost fringe on one side of the shadow, and that of the like fringe on the other side of the shadow, was in the full red light of an inch, and in the full violet The like distance between the middle and most luminous 1 parts of the second fringes, on either side of the shadow, was in the full red light, and the violet of an inch; and these distances of the fringes held the same proportion at all distances from the hair without any sensible variation. 27 57. From these observations it was evident, that the rays which made the fringes in the red light, passed by the hair at a greater distance than those which made the like fringes in the violet; so that the hair, in causing these fringes, acted alike upon the red light or least refrangible rays at a greater distance, and upon the violet or most refrangible rays at a less distance; and thereby occasioned fringes of different sizes, without any change in the color of any sort of light. It may therefore be concluded, that when the hair in the first observation was held in the white beam of the sun's light, and cast a shadow which was bordered with three fringes of colored light, those colors arose not from any new modifications impressed upon the rays of light by the hair, but only from the various inflections whereby the several sorts of rays were separated from one another, which before separation, by the mixture of all their colors, composed the white beam of the sun's light; but, when separated, composed lights of the several colors which they are originally disposed to exhibit. 58. The first person who pursued any experiinents similar to those of Newton on inflected .ight, was M. Maraldi; whose observations chiefly respect the inflection of light towards other bodies, whereby their shadows are partially illuminated; and many of the circumstances which he noticed relating to it are well worthy of attention. He exposed in the light of the sun a cylinder of wood three feet long and six lines and a half in diameter; when its shadow, being received upon a paper held close to it, was every where equally black and well defined, and continued to be so to the distance of twentythree inches from it. At a greater distance the shadow appeared to be of two different densities; for the two extremities of the shadow, in the direction of the length of the cylinder, were terminated by two dark strokes, a little more than a line in breadth. Within these dark lines there was a faint light, equally dispersed through the shadow, which formed a uniform penumbra, much lighter than the dark strokes at the extremity, or than the shadow received near the cylinder. As the cylinder was removed to a greater distance from the paper, the two black lines continued to be nearly of the same breadth, and the same degree of obscurity; but the penumbra in the middle grew lighter, and its breadth diminished, so that the two dark lines at the extremity of the shadow approached one another, till, at the distance of sixty inches, they coincided, and the penumbra in the middle entirely vanished. At a still greater distance a faint penumbra was visible; but it was ill defined, and grew broader as the cylinder was removed farther off, but was sensible at a very great distance. A narrow and faint penumbra was also seen on the outside of the dark shadow; and on the outside of this there was a tract more strongly illuminated than the rest of the paper. The breadth of the external penumbra increased with the distance of the shadow from the cylinder, and the breadth of the tract of light on the outside of it was also enlarged; but its splendor diminished with the distance. 59. He repeated these experiments with three other cylinders of different dimensions; and from them all he inferred, that every opaque cylindrical body, exposed to the light of the sun, makes a shadow which is black and dark to the distance of thirty-eight to forty-five diameters of the cylinder which forms it; and that, at a greater distance, the middle part begins to be illuminated in the manner described above. Other rays were deflected from the body, and formed a strong light on the outside of the shadow, and which might at the same time contribute to dilute the outer shadow, though he supposed that penumbra to be occasioned principally by that part of the paper not being enlightened, except by a part of the sun's disk only, according to the known principles of optics. The same experiments he made with globes of several diameters; but he found that, whereas the shadows of the cylinders did not disappear but at the distance of forty-one of their diameters, those of the globes were not visible beyond fifteen of their diameters; which he thought was owing to the light being inflected on every side of a globe, and consequently in such a quantity as to disperse the shadows sooner than in the case of the cylinders. In all these cases the penumbra occasioned by the inflected light began to be visible at a less distance from the body in the stronger light of the sun than in a weaker, on account of the greater quantity of rays inflected in those circumstances. 60. M. Maraldi, being sensible that the above mentioned phenomena of the shadows were caused by inflected light, was induced to give more particular attention to this remarkable property, and to repeat the experiments of Grimaldi and Sir Isaac Newton in a darkened room. In doing this, he observed that, besides the enlarged shadow of a hair, a fine needle, &c, the bright gleam of light that bordered it, and the three colored rings next to this enlightened part, when the shadow was at a considerable distance from the hair, the dark central shadow was divided in the middle by a mixture of light; and hat it was not of the same density, except when it was very near the hair. This new appearance is exactly similar to what he had observed with respect to the shadows in the open day-light above-mentioned. 61. Having placed a bristle in the rays of the sun, admitted into a dark chamber by a small hole, at the distance of nine feet from the hole it made a shadow, which, being received at five or six feet from the object, he observed to consist of several streaks of light and shade. The middle part was a faint penumbra, bordered by a darker shadow, and after that by a narrower penumbra; next to which was a light streak broader than the dark part, and next to the streak of light, the red, violet, and blue colors were seen as in the shadow of the hair. He also placed in the same rays, several needles of different sizes; but the appearances were so exceedingly various and singular, that he does not recite them. He exposed in the rays of the sun, admitted by a small hole into a dark chamber, a plate two inches long, and a little more than half a line broad. This plate being fixed perpendicularly to the rays, at the distance of nine feet from the hole, a faint light was seen uniformly dispersed over the shadow, when it was received perpendicularly to it, and very near. The shadow of the same plate, being received at the distance of two feet and a half, was divided into four very narrow black streaks, separated by small lighter intervals equal to them. The boundaries of this shadow on each side had a penumbra, which was terminated by a very strong light, next to which were the colored streaks of red, violet, and blue, as before. 62. The shadow of the same plate, at four feet and a half distance from it, was divided into two black streaks only, the two outermost having disappeared; but these two black streaks which remained were broader than before, and separated by a lighter shade, twice as broad as one of the former black streaks, when the shadow was taken at two feet and one-third. This penumbra in the middle had a tinge of red. After the two black streaks there appeared a pretty strong penumbra, terminated by the two streaks of light, which were now broad and splendid, after which followed the colored streaks. A second plate, two inches long and a line broad, being placed like the former fourteen feet from the hole by which the rays of the sun were admitted, its shadow, being received perpendi cularly very near the plate, was illuminated by a faint light, equally dispersed, as in the preceding plate. But being received at thirteen feet from the plate, six small black streaks began to be visible. At seventeen feet from the plate, the black streaks were broader, more distinct, and more separated from the streaks that were less dark. At forty-two feet from the plate, only two black streaks were seen in the middle of the penumbra. This middle penumbra between the two black streaks was tinged with red. Next to the black streaks there always appeared the streaks of light which were broad, and the colored streaks next to them. Receiving the shadow of the same plate at the distance of seventy-two feet, the appearances were the same as in the former situation, except that the two black streaks were broader, and the interval between them, occupied by the penumbra, was broader also, and tinged with a deeper red. 63. In the same rays of the sun he placed different plates, larger than the former, one of them a line and a half, another two lines, another three lines broad, &c., but receiving their shadows upon paper, he could not perceive in them those streaks of faint light which he had observed in the shadows of the small plates, though he received these shadows at the distance of fifty-six feet. Nothing was seen but a weak light, equally diffused as in the shadows of the two smallest plates, received very near them. The streaks of light in the shadows of needles of a middling size, our author ascribed to the rays of light which are inflected at different distances from the bodies; and he imagined that their crossing one another was sufficient to account for the variations observable in them at different distances. The extraordinary size of the shadows of these small substances M. Maraldi thought to be occasioned by the shadow from the enlightened part of the sky, added to that which was made by the light of the sun, and also to a vortex occasioned by the circulation of the inflected light behind the object. 64. M. Maraldi, having made the preceding experiments upon single long substances, had the curiosity to place two of them so as to cross one another in a beam of the sun's light. The shadows of two hairs placed in this manner, and received at some distance from them, appeared to be painted reciprocally one upon another, so that the obscure part of one of them was visible upon the obscure part of the other. The streaks of light also crossed one another, and the colored streaks did the same. Having placed a needle and a hair crossing one another, their shadows, at the same distance, exhibited the same appearances as the shadows of the two hairs, though the shadow of the needle was the stronger. He also placed in the rays of the sun a bristle and a plate of iron a line thick, so that they crossed one another obliquely; and when their shadows were received at the same distance, the light and dark streaks of the shadow of the bristle were visible so far as the shadow of the plate on the side of the acute angle, but not on the side of the obtuse angle, whether the bristle or the plate were placed next to the ray. The plate made a shadow sufficiently dark, livided into six black streaks; and these were again divided by as many light ones equal to them; and yet all the streaks belonging to the shadow of the bristle were visible upon it. 65. M. Maraldi exposed several small globes in the light of the sun in his dark chamber, and compared their shadows with those of the long substances, as he had done in the day-light, and the appearances were still similar. There was much more light in the shadows of the globes than in those of the cylinders, not only when they were both of an equal diameter, but when that of the globe was larger than that of the cylinder, and the shadows of both the bodies were received at the same distance. He could perceive no difference of light in the shadows of the plates which were a little more than one line broad, though they were received at the distance of seventy-two feet; but he could easily see a difference of shades in those of the globes, taken at the same distance, though they were two lines and a quarter in diameter. To explain the colors at the edges of these shadows, he contrived to throw some of the shadows upon others; and the following observations, though they did not enable him to accomplish what he intended, are worth reciting:-Having thrown several of the similar colors upon one another, and thereby produced a tinge more lively than before, he threw the gleam of light, which always intervened between the colors and the darker part of the shadow, upon different parts of other shadows; and observed that, when it fell upon the exterior penumbra made by another needle, it produced a beautiful sky-blue color, almost like that which was produced by two blue colors thrown together. When the same gleam of light fell upon the deeper shadow, in the middle, it produced a red color. He placed two plates of iron, each three or four lines broad, very near one another, but with a very small interval between them; and having placed them in the rays of the sun, and received their shadows at fifteen or twenty feet from them, he saw no light between them but a continued shadow, in the middle of which were some streaks of a lively purple, parallel to one another, and separated by other black streaks; but between them there were other streaks, both of a very faint green, and also of a pale yellow. 66. If a solid opaque body, such as a hair, a slender wire, &c., be placed in the stream of light within the room, the size of the shadow of that body will be found different from what it ought to be if the rays of light were not bent in passing by it. This bending of the rays of light by passing, not through, but near the surface of a body, is called the inflection of light. 67. Let X, fig. 3, be the hole (about the fiftieth part of an inch) of the light's passage into a darkened room, and let X A, X B, be lines drawn from each external opposite edge on one side of the solar disc, to each external opposite edge on the contrary side of the hole, crossing one another: X C D will represent the beam of light after its passage through the hole, at ail distances therefrom, considerably larger than the penumbral cone E A B. 68. At seven feet from the hole the breadth of the beam was 8 parts of an inch. If the light had not been beut, that breadth could not have exceeded . Hence it must be concluded that the light, being attracted by the sides of the hole, is inflected, and of course caused to proceed more divergingly than otherwise it would have done. 69. With a hole one-tenth of an inch wide, or wider, the centre of the beam was composed of the dense direct light of the sun unchanged in its passage; but farther therefrom, towards the borders of the beam, this light began to increase in density, and gradually decayed more and more in the approaches nearer and nearer to the borders, becoming at last considerably diluted and evanescent, and rendering the edge of the beam ill-defined and indistinct. 70. With a smaller hole than the last the central dense light entirely disappeared, and, with a hole yet smaller than this, the external edges of the beam became more condensed and better defined; and the whole beam of light became, as before described, of more uniform density in all its parts. With a hole smaller than any of the foregoing, about th part of an inch wide, various colors began to appear in the beam, the central parts of which became now, in their turn, more diluted than the rest, the external parts denser than these, and bordered with tinges of yellow and red light on the very edge or margin of the beam. 71. All these appearances are to be ascribed to the same attractions of the edges of the holes, and of the different parts of the edges. These, when the hole is large, affect only the parts of the light passing nearest to them; when the hole is reduced they attract and dilate the whole of the passing light; when the hole is yet more considerably diminished, they act, not only each part upon the light passing nearest to each, but each part also upon the light passing nearest to each opposite part of the edge, condensing by diminishing the attraction and diffusion of the light on the edges of the beam, and rendering the whole more equably and uniformly divergent, and these at last, when the hole is in its most reduced state, of about th part of an inch wide, by their various actions produce colors in the passing light. 72. In the beam of solar light passing through the small hole th part of an inch wide, the shadows of very slender bodies, such as pins, needles, straw, hairs, &c., were observed to be considerably broader, as they ought to be in this divergent light, than the bodies themselves; but, as each of these bodies exercises upon the light passing by it the same attractions by which the light is bent in passing through the hole, the author of these experiments concluded that a part of the light would be in every case bent, in passing by, towards the body into the shadow, and illuminate it and diminish its breadth. 73. Across a beam of solar light, admitted into a dark chamber through a small hole in a thin piece of lead, nearly 3th of an inch wide, a hair of a man's head was interposed, and the beam being received on a screen or sheet of white paper, with an obliquity convenient for the purpose, the following appearances were noted: 74. At the termination of the shadow, whose intensity or darkness was not considerable, the following orders and distinctions of colors appeared. First and nearest to the dark or blue parts of the shadow might be seen a diluted blue, changing into a breadth of white light, followed by breadths of yellow and red. To these succeeded an interval of diluted shade, then breadths of diluted violet, blue, diluted green, yellow, red; then green, diluted yellow, red; diluted green, red; white, diluted red, and finally, white light. These are the more general orders of the colors. Of these orders the three first were sufficiently obvious and distinct; the last evanescent and requiring accommodation of circumstances to produce, and attention to perceive them. 75. When the distance of observation from the hair was very small, and before the first bright streak of light began to appear, the shadow of the hair was distinct and well-defined, and of intense blackness. At a greater distance this shadow appeared to be divided by a parallel line of light throughout its whole length, into two parts, and resembled a double shadow, or the shadows of two hairs, but was by no means of the same degree of blackness as was the single shadow observed close to the hair. At still greater distances it increased in breadth and diminished in blackness, whilst the transverse dimensions of the dividing line of light increased at the same time, until, at a considerable distance from the hair, this intermediate band or line of light began to put on the appearance of colors on its edges, and to assume, on both sides externally, casts of yellowish and reddish light. By further increase of distance this apparent shadow, these dark intervals became more diluted, and of nearly the same color throughout, the line of light more and more diffused, and was at last extinguished by the extreme diffusion and ultimate invisibility of the light that produced it. 76. Whilst at all these different distances these changes proceed in the shadow, and in the light nearest to the body, in the other adjoining parts of the light passing next in order of distance by the hair considerable changes are also produced. 77. The shadow that first appeared close to the hair is perfectly and truly a shadow, being produced by the interception of the passing light by the hair. 78. This shadow, however, quickly ceases to appear, the rays of light nearest to it on both sides of the hair being bent into it at considerable angles of inflection and dispersion, and crossing, illuminating, and extinguishing it. 79. The rays of light are not only bent, they are also distributed or divided into different rays of different colors, in angles of dispersion greater as the distances are less, and less as the distances are greater, in such a manner that of different colors at the same distance, the purples, blues, greens, yellows, and reds, are bent towards the body; the purples most, each of the others in due succession less, and the reds least, according to the order of their statement; and of colors of the same sorts, at different distances, the nearer more than the more remote, and the more remote less than the nearer. So various, however, are the bendings of different colors at different distances, that in certain distinct portions of light, and at different distances of observation, the more remote and the nearer rays of different colors contained within each of those portions or divisions of the light, become variously intermingled with each other, and, by their various intermixtures, form each of these divisions into party-colored fringes; whilst, the rays of different divisions never mixing with those of others, the intervals of the divisions are preserved, and become the dark intervals which separate the fringes. 80. The discoveries of M. A. Fresnel respecting the inflexion of light are in the highest degree important, and cannot fail to be regarded as affording a strong confirmation of the Huygenian theory of light. The following is a summary of the principal results: 81. (1.) M. Fresnel found that the fringes formed by inflexion may be examined by an eyeglass, without receiving them upon a white surface; and, by adapting a micrometer to the eyeglass, he was able to determine their breadths, even to the 100th or 200th part of a millimetre. 82. (2.) By following the external fringes to their origin by means of a lens with a short focus, he perceived the third fringe at the distance of less than the 100th of a millimetre from the edge of the inflecting body. 83. (3.) The inflexion of the passing light is influenced by the distance of the radiating or luminous point from the inflecting body, as appears from the following results : 84. Hence it follows that the ray suffers a less degree of inflexion in proportion to the distance from which it diverges. 85. (4.) When the inflexion of the same fringe is measured at different distances behind the inflecting body, the distance of the radiant point remaining the same, it is found to be different at different distances; and hence it follows that the successive positions of the same fringe are not in a straight line, but form a curve whose concavity is turned towards the inflecting body. The lines which join the different positions of the fringe of all the orders of colors are hyperbolas, having for their common foci the radiating point and the edge of the inflecting body. In some of M. Fresnel's experiments the sagitta of curvature was about one millimetre, or the twentyfifth part of an inch, which is nearly fifty times greater than the error of observation. 86. (5.) M. Fresnel measured the fringes produced by various bodies, and found, by accurate measurement, that they all produced the same inflexion, the back of a razor giving the same fringes as its sharp edge. 87. Results of a similar kind were obtained by Dr. Brewster in two sets of experiments, one of which was made in 1798, and the other in 1812 and 1813. He compared the fringes formed by gold leaf with those made by masses of gold; those formed by films which produced the colors of thin plates with those formed by masses of the same substance. He examined the effects of platinum, diamond, and cork, in inflecting the light; the effects of grooves in metallic surfaces, &c.; and of cylinders of glass immersed in fluids of the same refractive power: and from these he concluded that the Newtonian theory of inflexion could not be true; that the inflexion was not produced by any force inherent in the bodies themselves, but arose from a property of the light itself, which always shows itself when divergent light was stopped in its progress. 88. (6.) The fringes in the interior of the shadow were first explained by Dr. Thomas Young. He showed, in the clearest manner, that they were formed by the interference of two portions of light coming from the opposite sides of the inflecting body. Having introduced the sun's light into a dark room, through two small holes very near each other, he received the admitted light upon a sheet of paper from each of the holes separately, and observed no particular effect. But when the light was admitted through both the holes at the same time, so as to interfere, a series of obscure and brilliant fringes was produced. 89. M. Fresnel obtained a similar effect by reflecting light from two metallic mirrors slightly inclined to each other, and whose surfaces were nearly in the same plane. The formation of these bands depends on the lengths of the paths of two interfering portions of light. When the paths are exactly of the same length, the two portions of light will form a very brilliant fringe, having an intensity greater than that of either portion. If the next brilliant fringe corresponds to a difference of paths equal to d, then other brilliant fringes will be formed when the differences of the paths are 2 d, 3 d, 4 d, &c. When the differences of the paths are d; d+d; 2 d + § d, or } d, d, d, the interfering portions neutralise or destroy one another, and consequently produce a black fringe. The quantity d has a different value for the rays of different colors, and varies as the length of the fits in Newton's theory. M. Fresnel has found d to beth of a millimetre for red light. 90. This beautiful theory of Dr. Young is embraced by M. Fresnel. Both these philosophers had ascribed the exterior fringes to the interference of the direct rays with rays reflected from the margin of the inflecting body. M. Fresnel, however, has since found that this explanation is insufficient; for the real place of the fringe is sometimes th of a millimetre different from what it should be upon this supposition; and at any rate, if the hypothesis were true, the extent and curvature of the margin of the inflecting body would have an influence upon the intensity of the fringes, which is contrary to experiment. He is therefore obliged to admit that the rays which pass at a sensible distance from the inflecting body are made to deviate from their primitive direction, and concur also in the production of the colored fringes. 91. It is by no means easy to explain to general readers the hypothesis by which M. Fresnel has accounted for the fringes upon the principle of interference; but we shall attempt to make it as intelligible as possible. 92. Let A M E, fig. 4, be a luminous wave or undulation, propagated from the radiant point C, and partly intercepted by the inflecting body AG. Then, if we suppose it divided into an infinity of small arcs Am, m'm, m M, Mn, nn', n'n", &c., M. Fresnel obtains the intensity of any point (P) of the wave A ME, when it has reached the position BP D, by supposing elementary waves to be propagated from every point m, m', M, n, n', &c., of its preceding position at AME. These elementary waves are propagated in all directions, and with intensities sensibly equal when they do not deviate much from the perpendicular. M. Fresnel does not take into account the waves which are most inclined, and which, according to his hypothesis, destroy one another; and in this way he determines the intensity of the light resulting from the reciprocal influence of all the rays which are slightly inclined to the perpendicular. By thus combining the principle of Huygens with Dr. Young's law of interference, he has obtained a formula which represents the observations with surprising accuracy. 93. (7) The phenomena of inflexion are considered by M. Fresnel to be inexplicable on the Newtonian theory of the emission of luminous particles; while almost all of them may be directly deduced from the Huygenian Theory of Undulations. 94. There are two very important and comparatively new branches of optical science to which we must now direct our readers' attention, namely, the double refraction and polarisation of light. 95. About the middle of the seventeenth century Dr. Erasmus Bartholinus, a physician at Copenhagen, and the author of several excellent works on geometry, procured, from some of the Danish merchants that frequented Iceland, a crystal stone like a rhombick or rhomboid prism, which, when broken into small pieces, kept the same figure. It was dug out of a very high mountain, not far from the Bay of Roerfiord, in 65° of lat. Its whole body was rather clear than bright, and of the color of limpid water; but that color, when it was immersed in water and dried again, became dull. With this substance, which from its locality was called Iceland crystal, Bartholinus made a number of experiments both chemical and optical; and, having discovered some of the singular effects which it produced upon light, he published an account of them at Copenhagen in 1669, under the title of Experimenta Crystalli Islandici Dis —diaclastici, quibus mira et insolita refractio detegitur. There does not appear to be a copy of this work in this country, but the want of it is well supplied by an account of sundry experiments made and communicated by Dr. Erasmus Bartholinus, addressed to Dr. Oldenburgh, and printed in the sixty-seventh number of the Philosophical Transactions. From this account we shall select those parts which relate to double |