tion of a method to produce this extraordinary appearance is by a plane mirror and a concave one combined. Kircher also speaks of the possibility of exhibiting these pendulous images, and supposes that they are reflected from the dense air; and the most perfect and pleasing deception depending upon the images in the air is one of which this writer gives a particular account in his Ars Magna Lucis et Umbræ, p. 783. In this case the image is placed at the bottom of a hollow polished cylinder, by which means it appears like a real solid substance, suspended within the mouth of the vessel. In this manner, he says, he once exhibited a scene, when the images were so perfect that the spectators could not be persuaded, but by attempting to handle them, that they were not real substances. Among other amusing things that were either invented or improved by Kircher was the method of throwing the appearance of letters, and other forms of things, into a darkened room from without by means of a lens and a plane mirror. The figures or letters were written upon the face of the mirror, and inverted; and the focus of the lens was contrived to fall upon the screen or wall that received their images. In this manner, he says that with the light of the sun he could throw a plain and distinct image 500 feet. It was Kepler who first discovered the true reason of the apparent places of objects seen by reflecting mirrors, as it depends upon the angle which the rays of light, issuing from the extreme part of an object, make with one another after such reflections. In plane mirrors these rays are reflected with the same degree of inclination to one another that they had before their incidence; but he shows that this inclination is changed in convex and concave mirrors. Dr. Hooke was the first to observe, if not to describe, the beautiful colours that appear in thin plates of Muscovy glass. These, he says, are very beautiful to the naked eye, but much more so when they are viewed with a microscope. With this instrument he could perceive that these colours were ranged in rings surrounding the white specks or flaws in the above thin substance, that the order of the colours was the same as in the rainbow, and that they were often repeated ten times. But the colours, he says, were disposed as in the outer bow, and not the inner. He also observed that if there was a place where the colours were very broad, and conspicuous to the naked eye, they might be made, by pressing the place with the finger, to change places, and move from one part to another. Lastly, he observes, if great care be used, this substance may be split into plates of or of an inch in diameter, each of which will appear through a microscope to be uniformly adorned with some one vivid colour, and these plates will be found upon examination to be of the same thickness throughout. (For Sir D. Brewster's account of this phenomenon, see PRISMATIC SPECTRUM.) We may now detail the very interesting series of experiments performed by M. Bouguer, as, next to those of Sir Isaac Newton, his labours seem to have been the most successful. The object of his curious and elaborate experiments was to measure the degrees of light, whether emitted, reflected, or refracted, by different bodies. They were originally occasioned by an article of M. Mairan's in the memoirs of the French academy for 1721, in which the proportion of the light of the sun at the two solstices was supposed to be known; and his laudable attempt to verify what had been before taken for granted suggested a variety of new experiments, and opened to him and to the world a new field of optical knowledge. His first production upon this subject was a treatise entitled Essai d'Optique, which was received with general approbation. Afterwards giving more attention to this subject, he projected a much larger work, for which many more experiments were necessary: but he was prevented by a variety of interruptions from executing his design so soon as he had proposed; and he had hardly completed it at the time of his death, in 1758. În order to compare different degrees of light, he always contrived to place the bodies from which it proceeded, or other bodies illuminated by them, in such a manner as he could view them both distinctly at the same time; and he either varied the distances of these bodies or modified their light in some other way, till he could perceive no difference between them. Then, considering their different distances, or the other circumstances by which their light was affected, he calculated the proportions which they would have borne to each other at the same distance. To ascertain the quantity of light lost by reflection, he placed the mirror or reflecting surface, represented at B, fig. 1, Plate I. OPTICS, on which the experiment was to be made, exactly upright; and having taken two tablets of precisely the same colour, or of an equal degree of whiteness, he placed them exactly parallel to one another at E and D, and threw light upon them by means of a lamp or candle, P, placed in a right line between them. He then placed himself so that with his eye at A he could see the tablet E, and the image of the tablet D, reflected from the mirror B, at the same time: making them touch one another. He then moved the candle along the line ED, so as to throw more or less light upon either of them, till he could perceive no difference in the strength of the light that came to his eye from them. After this he had nothing more to do than to measure the distances EP and DP; for the squares of those distances expressed the degree in which the reflection of the mirror diminished the quantity of light. It is evident that, if the mirror reflected all the rays it received, the candle P must have been placed at C, at an equal distance from each of the tablets, in order to make them appear equally illu... minated; but, because much of the light is lost by reflection, they can only be made to appear equally bright by placing the candle nearer the tablet D, which is seen by reflection only. To find how much light is lost by oblique reflection, he took two equally polished plates, D and E, fig. 2, and caused them to be enlightened by the candle P; and while one of them, D, was seen at A, by reflection from B, placed in a position oblique to the eye, the other, E, was so placed as to appear contiguous to it; and removing the plate E, till the light which it reflected was no stronger than that which came from the image D, seen by reflection at B, he estimated the quantity of light that was lost by this oblique reflection by the squares of the distances of the two objects from the candle. It need scarcely be added that in these experiments all foreign light was excluded, that his eye was shaded, and that every other precaution was excluding all the light that was reflected from any observed in order to make his conclusions unques-thing else; and he found that the distance of the tionable. In order to ascertain the quantity of light lost by reflection with the greatest exactness, M. Bouguer introduced two beams of light into a darkened room, by the apertures P and Q, fig. 3, which he had so contrived that he could place them higher or lower, and enlarge or contract them at pleasure; and the reflecting surface (as that of a fluid contained in a vessel) was placed horizontally at O, whence the light coming through the hole P was reflected to R, upon the screen GH, where it was compared with another beam of light that fell upon S, through the hole Q, which he made so much less than P as that the spaces S and R were equally illuminated: and, by the proportion that the apertures P and Q bore to each other, he calculated what quantity of light was lost by the reflection at O. It was necessary, he observes, that the two beams of light PO and QS (which he usually made seven or eight feet long) should be exactly parallel, that they might come from two points of the sky equally elevated above the horizon, and having precisely the same intensity of light. It was also necessary that the hole Q should be a little higher than P, in order that the two images should be at the same height and near one another. It is no less necessary, he says, that the screen GH be exactly vertical, in order that the direct and reflected beams may fall upon it with the same inclination, since otherwise, though the two lights were perfectly equal, they would not illuminate the screen equally. This disposition, he says, serves to answer another important condition in these experiments; for the direct ray QS must be of the same length with the sum of the incident and reflected rays PO and OR, in order that the quantity of light introduced into the room may be sensibly proportional to the sizes of the apertures. We may now give the result of the experiments which he made to measure the quantity of light lost by reflection under a great variety of circumstances; but it may be better to introduce them by a reference to some which were made previous to them on the diminution of light by reflection, and the transmission of it to considerable distances through the air, by M. Buffon. Receiving the light of the sun in a dark place, and comparing it with the light of the sun reflected by a mirror, he found that at small distances, as four or five feet, about one half was lost by reflection, as he judged by throwing two reflected beams upon the same place, and comparing them with a beam of direct light; for then the intensity of them both seemed to be the same. Having received the light at greater distances, as at 100, 200, and 300 feet, he could hardly perceive that it lost any of its intensity by being transmitted through such a space of air. book from the candle, including the distance from the book to the looking-glass (which was only half a foot), was in all fifteen feet. He repeated the experiment several times, and always with nearly the same result; and therefore concluded that the quantity of direct light is to that of reflected as 576 to 225; so that the light of five candles reflected from a plane mirror is about equal to that of two candles. From these experiments it appeared that more light was lost by reflection of the candles than of the sun, which M. Buffon thought was owing to this circumstance, that the light issuing from the candle diverges, and therefore falls more obliquely upon the mirror than the light of the sun, the rays of which are nearly parallel. These experiments and observations of M. Buffon are curious; though it will be seen that they fall far short of those of M. Bouguer, both in extent and accuracy. We may now proceed to examine those which he made to ascertain the difference in the quantity of light reflected by glass and polished metal. Using a smooth piece of glass, one line in thickness, he found that when it was placed at an angle of 15° with the incident rays it reflected 628 parts of 1000 which fell upon it; at the same time that a metallic mirror, which he tried under the same circumstances, reflected only 561 of them. At a less angle of incidence much more light was reflected; so that at an angle of 3° the glass reflected 700 parts, and the metal something less, as in the former case. Trying the reflection of bodies that were not polished he found that a piece of white plaster, placed at an angle of 75° with the incident rays, reflected part of the light that is received from a candle nine inches from it. White paper, in the same circumstances, reflected in the same proportion; but, at the distance of three inches, they both reflected 150 parts of 1000 that were incident. Proceeding to make further observations on the subject of reflected light, he premises the two following theorems, which he demonstrates geometrically: 1. When the luminous body is at an infinite distance, and its light is received by a globe, the surface of which has a perfect polish, and absorbs no light, it reflects the light equally in all directions, provided it be received at a considerable distance. He only excepts the place where the shadow of the globe falls; but this, he says, is no more than a single point with respect to the immensity of the spherical surface which receives its light. 2. The quantity of light reflected in one certain direction will always be exactly the same, whether it be reflected by a very great number of small polished hemispheres, by a less number of larger hemispheres, or by a single hemisphere, provided they occupy the same base, or cover the same groundplan. He afterwards made the same experiments with candles, in the following manner: he placed himself The use he proposes to make of these theorems is opposite to a looking-glass, with a book in his hand, to assist him in distinguishing whether the light rein a room perfectly dark; and having one candle flected from bodies be owing to the extinction of it lighted in the next room, at the distance of about within them, or whether the roughness or eminences forty feet, he had it brought nearer to him by degrees, which cover them have not the same effect with the till he was just able to distinguish the letters of the small polished hemispheres above mentioned. book, which was then twenty-four feet from the He begins with observing, that, of the light recandle. He then received the light of the candle, re-flected from Mercury, one-fourth at least is lost, and flected by the looking-glass, upon his book, carefully that probably no substances reflect more than this; the rays were received at an angle of 1140 of inci- | agree with his observations, he drew up the followdence, that is, measured from the surface of the re-ing table of the quantity of light reflected from flecting body, and not from the perpendicular, which the surface of water, at different angles with the he says is what we are to understand whenever he inentions the angle of incidence. The most striking observations which he made with respect to this subject are those which relate to the very great difference in the quantity of light reflected at different angles of incidence. In general, he says, reflection is stronger at small angles of incidence, and weaker at large ones. The difference is excessive when the rays strike the surface of transparent substances with different degrees of obliquity; but it is almost as great in some opaque substances, and it was always more or less so in every thing that he tried. He found the greatest inequality in black marble, which with an angle of 3° 35′ of incidence, though not perfectly polished, reflected almost as well as quicksilver. Of 1000 rays which it received, it returned 600; but, when the angle of incidence was 14°, it reflected only 156; when it was 30°, it reflected fifty-one; and, when it was 80°, it returned only twenty-three. Similar experiments made with metallic mirrors always gave the differences much less considerable. The greatest was hardly ever an eighth or a ninth part of it, but they were always in the same way. The great difference between the quantity of light reflected from the surface of water at different angles of incidence is truly surprising; but our author observes that this difference was greater when the smallest inclinations were compared with those which were near to a right angle. He sometimes suspected that at very small angles of incidence the reflection from water was even greater than from quicksilver. All things considered, he thought it was not quite so great, though it was very difficult to determine the precise difference between them. In very small angles, he says, water reflects nearly three-fourths of the direct light. "There is no person," he observes, "but has sometimes felt the force of this strong reflection from water, when he has been walking in still weather on the brink of a lake opposite to the sun. In this case, the reflected light is, or sometimes a greater pro- | portion of the light that comes directly from the sun, which is an addition to the direct rays of the sun that cannot fail to be very sensible. The direct light of the sun diminishes gradually as it approaches the horizon, while the reflected light at the same time grows stronger: so that there is a certain elevation of the sun in which the united force of the direct reflected light will be the greatest possible, and this he says is twelve or thirteen degrees." The nature of reflection, as it results from natural causes, is in no case more beautifully illustrated than in the effects of the sun's rays in the Alpine regions. With the thermometer below the freezing point, the traveller will frequently find his skin scorched and his eyes so affected by the glare of the reflected sunbeams as to be incapable of enjoying the most majestic scenery. It may be proper to add that a similar effect is produced on the visual organs by passing over the highly reflecting surface of a plain of sand. In order to procure a common standard by which to measure the proportion of light reflected from various fluid subsances, Mr. Bouguer selected water as the most commodious; and partly by observation and partly by calculation, which he always found to surface. Angles of incidence, Rays reflected of 1000. Angles of incidence. Rays reflected of 1000. ૐ 721 17 178 692 20 145 669 25 97 639 30 65 614 112257025 Pouring a quantity of water into a vessel containing quicksilver, it is evident that there will be two images of any object seen by reflection from them, one at the surface of the water and the other at that of the quicksilver. In the largest angles of incidence, the image at the surface of the water will disappear, which will happen when it is about a sixtieth or an eightieth part less luminous than the image at the surface of the quicksilver. Depressing the eye, the image on the water will grow stronger, and that on the quicksilver weaker in proportion; till at last the latter will be incomparably weaker than the former, and at an angle of about ten degrees they will be equally luminous. According to the table, of the incident rays are reflected from the water at this angle of ten degrees. At the surface of the mercury they were reduced to 500; and of these, part being reflected back upon it from the under surface of the water, only 333 remained to make the image from the mercury. Continuing his observations on the diminution of light occasioned by the reflection of opaque bodies obliquely situated, he compared it with the appearances of similar substances which reflected the light perpendicularly. Using pieces of silver made very white, he found that when one of them was placed at an angle of 75° with respect to the light it reflected only 140 parts out of 1000. He then varied the angle, and also used white plaster and fine Dutch paper, and drew up the following table of the proportion of the light reflected from each of those substances at certain angles. Supposing the asperities of opaque bodies to consist of very small planes, it appears from these observations that there are fewer of them in those bodies which reflect the light at small angles of incidence than at greater; and our author says that the case was nearly the same with respect to all the opaque bodies that he tried. None of them had their roughness equivalent to small hemispheres, which would have dispersed the light equally in all directions; and from the data in the preceding table he deduces mathematically the number of the little planes that compose those surfaces, and that are inclined to the general surface at the angles above mentioned, supposing that the whole surface contains 1000 of them that are parallel to itself, so as to reflect the light perpendicularly, when the luminous body is situated at right angles with respect to it. His conclusions reduced to a table corresponding to the preceding are as follows : Inclinations of the small surfaces with respect to the large one. small planes of each particular inclination, from considering the quantity of light reflected by each, allowing those that have a greater inclination to the common surface to take up proportionably less space than those which are parallel to it. And, comparing the quantity of light that would be reflected by small planes thus disposed with the quantity of light that was actually reflected by the three substances above mentioned, he found that plaster, notwithstanding its extreme whiteness, absorbs much light; for that. of 1000 rays that fall upon it, of which 166 or 167 ought to be reflected at an angle of 77°, only 67 are in fact returned; so that 100 out of 167 were extinguished, that is, about three-fifths. Having considered the surfaces of bodies as consisting of planes only, he thus explains himself :— "Each small surface, separately taken, is extremely irregular, and some of them are really concave and others convex ; but, in reducing them to a middle state, they are to be considered as planes." Nevertheless he considers them as planes only with respect to the reception of the rays; for as they are almost all curves, and as, besides this, many of those whose situation is different from others contribute to the same effect, the rays always issue from an actual or imaginary focus, and after reflection always diverge from each other. If it be asked, What becomes of those rays that are reflected from one asperity to other? he shows that very few of the rays can be in those circumstances, since they must fall upon planes which have more than 45° of obliquity to the surface, of which there are very few in natural bodies. These rays must also fall at the bottom of those planes, and must meet with other planes similarly situated to receive them; and, considering the great irregularity of the surfaces of opaque bodies, it may be concluded that very few of the rays are thus reflected upon the body itself, and that the little that is so reflected is probably lost to the spectators, being extinguished in the body. The attempts of the Abbé Nollet to fire inflammable substances by the power of the solar rays collected in the foci of burning mirrors have a near relation to the present subject. Considering the great power of burning mirrors and lenses, it will appear surprising that this celebrated experimental philosopher should not be able to fire any liquid substance. But, though he made the trial with all the care imaginable, he was not able to do it either with spirit of wine, olive oil, oil of turpentine, or ether; and, though he could fire sulphur, yet he could not succeed with Spanish-wax, resin, black pitch, or suet. He both threw the focus of these mirrors upon the substances themselves and also upon the fumes that rose from them; but all the These variations in the number of little planes, or surfaces, he expresses in the form of a curve, and afterwards shows, geometrically, what would be the effect if the bodies were enlightened in one direction and viewed in another, upon which subject he has several curious theorems and problems: as, the position of the eye being given, to find the angle at which the luminous body must be placed, in order to its reflecting the most light; or, the situation of the luminous body being given, to find a proper situation for the eye, in order to see it the most enlightened, &c. But it would carry us too far into geometry to follow him through all these disqui-effect was that the liquor boiled, and was dispersed sitions. Since the planets, as this accurate observer takes notice, are more luminous at their edges than at their centres, he concludes, from the above-mentioned principles, that the bodies which form them are constituted in a manner different from ours, particularly that their opaque surfaces consist of small planes, more of which are inclined to the general surface than they are in terrestrial substances; and that there are in them an infinity of points, which have exactly the same splendour. Our philosopher and geometrician next proceeds to ascertain the quantity of surface occupied by the in vapour or very small drops, but would not take fire. When linen rags and other solid substances were moistened with any of these inflammable liquids they would not take fire till the liquid was dispersed in vapour, so that rags thus prepared were longer in burning than those that were dry. M. Baumé, who assisted M. Nollet in some of these experiments, observed further that the same substances which were easily fired by the flame of burning bodies could not be set on fire by the contact of the hottest bodies that did not actually flame. Neither ether nor spirit of wine could be fired with a hot coal or hot iron unless they were of a white heat. |