CHAPTER II.
ON THE REFRACTION OF LIGHT.
Refraction is the turning or bending of the rays of light out of their natural course.
Light, when proceeding from a luminous body—without being reflected from any opake substance or inflected by passing near one—is invariably found to proceed in straight lines without the least deviation. But if it happens to pass obliquely from one medium to another, it always leaves the direction it had before and assumes a new one. This change of direction, or bending of the rays of light, is what is called Refraction—a term which probably had its origin from the broken appearance which a staff or a long pole exhibits, when a portion of it is immersed in water—the word, derived from the Latin frango, literally signifying breaking or bending.
When light is thus refracted, or has taken a new direction, it then proceeds invariably in a straight line till it meets with a different medium,[7] when it is again turned out of its course. It must be observed, however, that though we may by this means cause the rays of light to make any number of angles in their course, it is impossible for us to make them describe a curve, except in one single case, namely, where they pass through a medium, the density of which either uniformly increases or diminishes. This is the case with the light of the celestial bodies, which passes downwards through our atmosphere, and likewise with that which is reflected upwards through it by terrestrial objects. In both these cases it describes a curve of the hyperbolic kind; but at all other times, it proceeds in straight lines, or in what may be taken for straight lines without any sensible error.
There are two circumstances essential to refraction. 1. That the rays of light shall pass out of one medium into another of a different density, or of a greater or less degree of resistance. 2. That they pass in an oblique direction. The denser the refracting medium, or that into which the ray enters, the greater will be its refracting power; and of two refracting mediums of the same density, that which is of an oily or inflammable nature will have a greater refracting power than the other. The nature of refraction may be more particularly explained and illustrated by the following figure and description.
Let ADHI fig. 2, be a body of water, AD its surface, C a point in which a ray of light BC enters from the air into the water. This ray, by the greater density of the water, instead of passing straight forward in its first direction to K, will be bent at the point C, and pass along in the direction CE, which is called the refracted ray. Let the line FG be drawn perpendicular to the surface of the water in C, then it is evident that the ray BC, in passing out of air, a rare medium, into a dense medium, as water, is refracted into a ray CE which is nearer to the perpendicular CG than the incident ray BC, and on the contrary, the ray EC passing out of a denser medium into a rarer will be refracted into CB, which is farther from the perpendicular.
figure 2.
The same thing may be otherwise illustrated as follows:—suppose a hole made in one of the sides of the vessel as at a, and a lighted candle placed within two or three feet of it, when empty, so that its flame may be at L, a ray of light proceeding from it will pass through the hole a in a straight line LBCK till it reach the bottom of the vessel at K, where it will form a small circle of light. Having put a mark at the point K, pour water into the vessel till it rise to the height AD, and the round spot that was formerly at K, will appear at E; that is, the ray which went straight forward, when the vessel was empty, to K, has been bent at the point C, where it falls into the the water, into the line CE. In this experiment it is necessary that the front of the vessel should be of glass, in order that the course of the ray may be seen; and if a little soap be mixed with the water so as to give it a little mistiness, the ray CE will be distinctly perceived. If, in place of fresh water we pour in salt water, it will be found that the ray BC is more bent at C. In like manner alcohol will refract the ray BC more than salt water, and oil more than alcohol, and a piece of solid glass, of the shape of the water, would refract the light still more than the oil.
The angle of refraction depends on the obliquity of the rays falling on the refracting surface being always such, that the sine of the incident angle is to the sine of the refracted angle, in a given proportion. The incident angle is the angle made by a ray of light and a line drawn perpendicular to the refracting surface, at the point where the light enters the surface. The refracted angle is the angle made by the ray in the refracting medium with the same perpendicular produced. The sine of the angle is a line which serves to measure the angle, being drawn from a point in one leg perpendicular to the other. The following figure (fig. 3.) will tend to illustrate these definitions.
figure 3.
In this figure BC is the incident ray, CE the refracted ray, DG the perpendicular, AD the sine of the angle of incidence ACD, and HR the sine of the angle of refraction GCE. Now, it is a proposition in optics that,—the sine AD of the angle of incidence BCD is either accurately or very nearly in a given proportion to the sine HR of the angle of refraction GCE. This ratio of the sines is as four to three, when the refraction is made out of air into water, that is AD is to HR as four to three. When the refraction is out of air into glass, the proportion is about as thirty-one to twenty, or nearly as three to two. If the refraction be out of air into diamond it is as five to two, that is AD : HR :: 5 : 2. The denser the medium is, the less is the angle and sine of refraction. If a ray of light MC, were to pass from air into water, or from empty space into air, in the direction MC perpendicular to the plane NO which separates the two mediums, it would suffer no refraction, because one of the essentials to that effect is wanting, namely, the obliquity of the incidence.
It may be also proper to remark, that a ray of light cannot pass out of a denser medium into a rarer, if the angle of incidence exceed a certain limit. Thus a ray of light will not pass out of glass into air, if the angle of incidence exceed 40° 11´; or out of glass into water, if the angle of incidence exceed 59° 20´. In such cases refraction will be changed into reflection.
The following common experiments, which are easily performed, will illustrate the doctrine of refraction. Put a shilling or any other small object which is easily distinguished, into a bason or any other similar vessel, and then retire to such a distance as that the edge of the vessel shall just hide it from your sight. If then you cause another person to fill the vessel with water, you will then find that the shilling is rendered perfectly visible, although you have not in the slightest degree changed your position. The reason of this is, that the rays of light, by which it is rendered visible, are bent out of their course. Thus, suppose the shilling to have been placed in the bottom of the bason at E, (fig. 2.) the ray of light BC which passes obliquely from the air into water at C, instead of continuing its course to K, takes the direction CE, and consequently an object at E would be rendered visible by rays proceeding in that direction, when they would not have touched it had they proceeded in their direct course.
The same principle is illustrated by the following experiment. Place a bason or square box on a table, and a candle at a small distance from it; lay a small rod or stick across the sides of the bason, and mark the place where the extremity of the shadow falls, by placing a shilling or other object at the point; then let water be poured into the bason, and the shadow will then fall much nearer to the side next the candle than before. This experiment may likewise be performed by simply observing the change produced on the shadow of the side of the bason itself. Again, put a long stick obliquely into deep water, and the stick will seem to be broken at the point where it appears at the surface of the water—the part which is immersed in the water appearing to be bent upwards. Hence every one must have observed that, in rowing a boat, the ends of the oars appear bent or broken every time they are immersed in the water, and their appearance at such times is a representation of the course of the refracted rays. Again, fill a pretty deep jar with water, and you will observe the bottom of the jar considerably elevated, so that it appears much shallower than it did before the water was poured in, in the proportion of nearly a third of its depth, which is owing to the same cause as that which makes the end of a stick immersed in water appear more elevated than it would do if there were no refraction. Another experiment may be just mentioned. Put a sixpence in a wine-glass, and pour upon it a little water. When viewed in a certain position, two sixpences will appear in the glass—one image of the sixpence from below, which comes directly to the eye, and another which appears considerably raised above the other, in consequence of the rays of light rising through the water, and being refracted. In this experiment the wine-glass should not be more than half filled with water.
The refraction of light explains the causes of many curious and interesting phenomena both in the heavens and on the earth. When we stand on the banks of a river, and look obliquely through the waters to its bottom, we are apt to think it is much shallower than it really is. If it be eight feet deep in reality, it will appear from the bank to be only six feet; if it be five feet and a half deep, it will appear only about four feet. This is owing to the effects of refraction, by which the bottom of the river is apparently raised by the refraction of the light passing through the water into air, so as to make the bottom appear higher than it really is, as in the experiment with the jar of water. This is a circumstance of some importance to be known and attended to in order to personal safety. For many school-boys and other young persons have lost their lives by attempting to ford a river, the bottom of which appeared to be within their reach, when they viewed it from its banks: and even adult travellers on horseback have sometimes fallen victims to this optical deception; and this is not the only case in which a knowledge of the laws of nature may be useful in guarding us against dangers and fatal accidents.
It is likewise owing to this refractive power in water, that a skilful marksman who wishes to shoot fish under water, is obliged to take aim considerably below the fish as it appears, because it seems much nearer the top of the water than it really is. An acquaintance with this property of light is particularly useful to divers, for, in any of their movements or operations, should they aim directly at the object, they would arrive at a point considerably beyond it; whereas, by having some idea of the depth of the water, and the angle which a line drawn from the eye to the object makes with its surface, the point at the bottom of the water, between the eye and the object at which the aim is to be taken, may be easily determined. For the same reason, a person below water does not see objects distinctly. For, as the aqueous humour of the eye has the same refractive power as water, the rays of light from any object under water will undergo no refraction in passing through the cornea, and aqueous humour, and will therefore meet in a point far behind the retina. But if any person accustomed to go below water should use a pair of spectacles, consisting of two convex lenses, the radius of whose surface is three tenths of an inch—which is nearly the radius of the convexity of the cornea—he will see objects as distinctly below water as above it.
It is owing to refraction, that we cannot judge so accurately of magnitudes and distances in water as in air. A fish looks considerably larger in water than when taken out of it. An object plunged vertically into water always appears contracted, and the more so as its upper extremity approaches nearer the surface of the water. Every thing remaining in the same situation, if we take the object gradually out of the water, and it be of a slender form, we shall see it become larger and larger, by a rapid developement, as it were, of all its parts. The distortion of objects, seen through a crooked pane of glass in a window, likewise arises from its unequal refraction of the rays that pass through it. It has been calculated that in looking through the common glass of a window, objects appear about the one thirtieth of an inch out of their real place, by means of the refraction.
Refraction likewise produces an effect upon the heavenly bodies, so that their apparent positions are generally different from their real. By the refractive power of the atmosphere, the sun is seen before he comes to the horizon in the morning, and after he sinks beneath it in the evening; and hence this luminary is never seen in the place in which it really is, except when it passes the zenith at noon, to places within the torrid zone. The sun is visible, when actually thirty-two minutes of a degree below the horizon, and when the opake rotundity of the earth is interposed between our eye and that orb, just on the same principle as, in the experiment with the shilling and basin of water, the shilling was seen when the edge of the basin interposed between it and the sight. The refractive power of the atmosphere has been found to be much greater, in certain cases, than what has been now stated. In the year 1595 a company of Dutch sailors having been wrecked on the shores of Nova Zembla, and having been obliged to remain in that desolate region during a night of more than three months—beheld the sun make his appearance in the horizon about sixteen days before the time in which he should have risen according to calculation, and when his body was actually more than four degrees below the horizon; which circumstance has been attributed to the great refractive power of the atmosphere in those intensely cold regions. This refraction of the atmosphere, which renders the apparent rising and setting of the sun both earlier and later than the real, produces at least one important beneficial effect. It procures for us the benefit of a much longer day, at all seasons of the year, than we should enjoy, did not this property of the atmosphere produce this effect. It is owing to the same cause that the disks of the sun and moon appear elliptical or oval, when seen in the horizon, their horizontal diameters appearing longer than their vertical—which is caused by the greater refraction of the rays coming from the lower limb, which is immersed in the densest part of the atmosphere.
The illumination of the heavens which precedes the rising of the sun, and continues sometime after he is set—or, what is commonly called the morning and evening twilight—is likewise produced by the atmospherical refraction—which circumstance forms a very pleasing and beneficial arrangement in the system of nature. It not only prolongs to us the influence of the solar light, and adds nearly two hours to the length of our day, but prevents us from being transported all at once from the darkness of midnight to the splendour of noon-day, and from the effulgence of day to the gloom and horrors of the night—which would bewilder the traveller and navigator in their journeys by sea or land, and strike the living world with terror and amazement.
The following figure will illustrate the position now stated, and the manner in which the refraction of the atmosphere produces these effects. Let A a C, fig. 4, represent one half of our globe, and the dark space between that curve and B r D, the atmosphere. A person standing on the earth’s surface at a would see the sun rise at b, when that luminary was in reality only at c—more than half a degree below the horizon. When the rays of the sun, after having proceeded in a straight line through empty space, strike the upper part of the atmosphere at the point d, they are bent out of their right-lined course, by the refraction of the atmosphere, into the direction d a, so that the body of the sun, though actually intercepted by the curve of the earth’s convexity consisting of a dense mass of land or water, is actually beheld by the spectator at a. The refractive power of the atmosphere gradually diminishes from the horizon to the zenith, and increases from the zenith to the horizon, in proportion to the density of its different strata, being densest at its lower extremity next the earth, and more rare towards its higher regions. If a person at a had the sun, e, in his zenith, he would see him where he really is; for his rays coming perpendicularly through the atmosphere, would be equally attracted in all directions, and would therefore suffer no inflection. But, about two in the afternoon, he would see the sun at i, though, in reality, he was at k, thirty-three seconds lower than his apparent situation. At about four in the afternoon he would see him at m, when he is at n, one minute and thirty-eight seconds from his apparent situation. But at six o’clock, when we shall suppose he sets, he will be seen at o, though he is at that time at p, more than thirty-two minutes below the horizon. These phenomena arise from the different refractive powers of the atmosphere at different elevations, and from the obliquity with which the rays of light fall upon it; for we see every object along that line in which the rays from it are directed by the last medium through which they passed.
figure 4.
The same phenomena happen in relation to the moon, the planets, the comets, the stars, and every other celestial body, all of which appear more elevated, especially when near the horizon, than their true places. The variable and increasing refraction from the zenith to the horizon, is a source of considerable trouble and difficulty in making astronomical observations, and in nautical calculations. For, in order to determine the real altitudes of the heavenly bodies, the exact degree of refraction, at the observed elevation, must be taken into account. To the same cause we are to ascribe a phenomenon that has sometimes occurred—namely, that the moon has been seen rising totally eclipsed, while the sun was still visible in the opposite quarter of the horizon. At the middle of a total eclipse of the moon, the sun and moon are in opposition, or 180 degrees asunder; and, therefore, were no atmosphere surrounding the earth, these luminaries, in such a position, could never be seen above the horizon at the same time. But, by the refraction of the atmosphere near the horizon, the bodies of the sun and moon are raised more than 32 minutes above their true places, which is equal, and sometimes more than equal to the apparent diameters of these bodies.
Extraordinary cases of refraction in relation to terrestrial objects.
In consequence of the accidental condensation of certain strata of the atmosphere, some very singular effects have been produced in the apparent elevation of terrestrial objects to a position much beyond that in which they usually appear. The following instance is worthy of notice. It is taken from the Philosophical Transactions of London for 1798, and was communicated by W. Latham, Esq., F.R.S., who observed the phenomenon from Hastings, on the south coast of England:—‘On July 26, 1797, about five o’clock in the afternoon, as I was sitting in my dining-room in this place, which is situated upon the Parade, close to the sea-shore, nearly fronting the south, my attention was excited by a number of people running down to the sea-side. Upon inquiring the reason, I was informed, that the coast of France was plainly to be distinguished by the naked eye. I immediately went down to the shore, and was surprised to find that, even without the assistance of a telescope, I could very plainly see the cliffs on the opposite coast, which, at the nearest part, are between forty and fifty miles distant, and are not to be discerned from that low situation by the aid of the best glasses. They appeared to be only a few miles off, and seemed to extend for some leagues along the coast. I pursued my walk along the shore eastward, close to the water’s edge, conversing with the sailors and fishermen upon the subject. They at first would not be persuaded of the reality of the appearance; but they soon became so thoroughly convinced by the cliffs gradually appearing more elevated, and approaching nearer, as it were, that they pointed out and named to me the different places they had been accustomed to visit, such as the Bay, the Old Head, or Man, the Windmill, &c. at Boulogne, St. Vallery, and other places on the coast of Picardy, which they afterwards confirmed, when they viewed them through their telescopes. Their observations were, that the places appeared as near as if they were sailing, at a small distance, into the harbours. The day on which this phenomenon was seen was extremely hot; it was high water at Hastings about two o’clock, P.M., and not a breath of wind was stirring the whole day.’ From the summit of an adjacent hill, a most beautiful scene is said to have presented itself. At one glance the spectators could see Dungeness, Dover Cliffs, and the French coast, all along from Calais to St. Vallery, and, as some affirmed, as far to the westward as Dieppe, which could not be much less than eighty or ninety miles. By the telescope, the French fishing-boats were plainly seen at anchor, and the different colours of the land on the heights, with the buildings, were perfectly discernible.
This singular phenomenon was doubtless occasioned by an extraordinary refraction produced either by an unusual expansion, or condensation of the lower strata of the atmosphere, arising from circumstances connected with the extreme heat of the season. The objects seem to have been apparently raised far above their natural positions; for, from the beach at Hastings, a straight line drawn across towards the French coast, would have been intercepted by the curve of the waters. They seem also to have been magnified by the refraction, and brought apparently four or five times nearer the eye than in the ordinary state of the atmosphere.
The following are likewise instances of unusual refraction:—When Captain Colby was ranging over the coast of Caithness, with the telescope of his great Theodolite, on the 21st of June, 1819, at eight o’clock, P.M. from Corryhabbie Hill, near Mortlich, in Banffshire, he observed a brig over the land of Caithness, sailing to the westward in the Pentland Frith, between the Dunnet and Duncansby heads. Having satisfied himself as to the fact, he requested his assistants, Lieutenants Robe and Dawson, to look through the telescope, which they immediately did, and observed the brig likewise. It was very distinctly visible for several minutes, while the party continued to look at it, and to satisfy themselves as to its position. The brig could not have been less than from ninety to one hundred miles distant; and, as the station on Corryhabbie is not above 850 yards above the sea, the phenomenon is interesting. The thermometer was at 44°. The night and day preceding the sight of the brig had been continually rainy and misty, and it was not till 7 o’clock of the evening of the 21st that the clouds cleared off the hill.[8]
Captain Scoresby relates a singular phenomenon of this kind, which occurred while he was traversing the Polar seas. His ship had been separated by the ice from that of his father for a considerable time, and he was looking out for her every day, with great anxiety. At length, one evening, to his utter astonishment, he saw her suspended in the air, in an inverted position, traced on the horizon in the clearest colours, and with the most distinct and perfect representation. He sailed in the direction in which he saw this visionary phenomenon, and actually found his father’s vessel by its indication. He was divided from him by immense masses of icebergs, and at such a distance, that it was quite impossible to have seen the ship in her actual situation, or to have seen her at all, if her spectrum had not been thus raised several degrees above the horizon into the sky by this extraordinary refraction. She was reckoned to be seventeen miles beyond the visible horizon, and thirty miles distant.
Mrs. Somerville states, that a friend of her’s, while standing on the plains of Hindostan, saw the whole upper chain of the Himalaya mountains start into view, from a sudden change in the density of the air, occasioned by a heavy shower, after a long course of dry and hot weather. In looking at distant objects through a telescope, over the top of a ridge of hills, about two miles distant, I have several times observed, that some of the more distant objects which are sometimes hid by the interposition of a ridge of hills, are, at other times, distinctly visible above them. I have sometimes observed, that objects near the middle of the field of view of a telescope, which was in a fixed position, have suddenly appeared to descend to the lower part, or ascend to the upper part of the field, while the telescope remained unaltered. I have likewise seen, with a powerful telescope, the Bell Rock Lighthouse, at the distance of about twenty miles, to appear as if contracted to less than two-thirds of its usual apparent height, while every part of it was quite distinct and well-defined, and in the course of an hour or less, it appeared to shoot up to its usual apparent elevation—all which phenomena are evidently produced by the same cause to which we have been adverting.
Such are some of the striking effects produced by the refraction of light. It enables us to see objects in a direction where they are not; it raises, apparently, the bottoms of lakes and rivers: it magnifies objects when their light passes through dense mediums: it makes the sun appear above the horizon, when he is actually below it, and thus increases the length of our day: it produces the Aurora and the evening twilight, which forms, in many instances, the most delightful part of a summer day: it prevents us from being involved in total darkness, the moment after the sun has descended beneath the horizon: it modifies the appearances of the celestial bodies, and the directions in which they are beheld: it tinges the sun, moon, and stars, as well as the clouds, with a ruddy hue, when near the horizon: it elevates the appearance of terrestrial objects, and, in certain extraordinary cases, brings them nearer to our view, and enables us to behold them when beyond the line of our visible horizon. In combination with the power of reflection, it creates visionary landscapes, and a variety of grotesque and extraordinary appearances, which delight and astonish, and sometimes appal the beholders. In short,—as we shall afterwards see more particularly—the refraction of light through glasses of different figures, forms the principle on which telescopes and microscopes are constructed, by which both the remote and the minute wonders of creation have been disclosed to view. So that had there been no bodies capable of refracting the rays of light, we should have remained for ever ignorant of many sublime and august objects in the remote regions of the universe, and of the admirable mechanism and the countless variety of minute objects which lie beyond the range of the unassisted eye in our lower creation, all of which are calculated to direct our views, and to enlarge our conceptions of the Almighty Creator.
In the operation of the law of refraction in these and numerous other instances, we have a specimen of the diversified and beneficent effects which the Almighty can produce by the agency of a single principle in nature. By the influence of the simple law of gravitation, the planets are retained in their orbits, the moon directed in her course around the earth, and the whole of the bodies connected with the sun preserved in one harmonious system. By the same law the mountains of our globe rest on a solid basis, the rivers flow through the plains toward the seas, the ocean is confined to its prescribed boundaries, and the inhabitants of the earth are retained to its surface and prevented from flying upwards through the voids of space. In like manner the law by which light is refracted produces a variety of beneficial effects essential to the present constitution of our world and the comfort of its inhabitants. When a ray of light enters obliquely into the atmosphere, instead of passing directly through, it bends a little downwards, so that the greater portion of the rays which thus enter the atmospheric mass, descend by inflection to the earth. We then enjoy the benefit of that light which would otherwise have been totally lost. We perceive the light of day an hour before the solar orb makes its appearance, and a portion of its light is still retained when it has descended nearly eighteen degrees below our horizon. We thus enjoy, throughout the year, seven hundred and thirty hours of light which would have been lost, had it not been refracted down upon us from the upper regions of the atmosphere. To the inhabitants of the polar regions this effect is still more interesting and beneficial. Were it not for their twilight, they would be involved, for a much longer period than they now are, in perpetual darkness; but by the powerful refraction of light which takes place in the frigid zones, the day sooner makes its appearance towards spring, and their long winter nights are, in certain cases, shortened by a period of thirty days. Under the poles, where the darkness of night would continue six months without intermission, if there were no refraction, total darkness does not prevail during the one half of this period. When the sun sets, at the North pole about the 23rd of September, the inhabitants (if any) enjoy a perpetual aurora, till he has descended 18 degrees below the horizon. In his course through the ecliptic the sun is two months before he can reach this point, during which time there is a perpetual twilight. In two months more he arrives again at the same point, namely 18 degrees below the horizon, when a new twilight commences, which is continually increasing in brilliancy, for other two months, at the end of which the body of this luminary is seen rising in all its glory. So that, in this region, the light of day is enjoyed, in a greater or less degree, for ten months without interruption, by the effects of atmospheric refraction; and, during the two months when the influence of the solar light is entirely withdrawn, the moon is shining above the horizon for two half months without intermission; and thus it happens, that no more than two separate fortnights are passed in absolute darkness; and this darkness is alleviated by the light of the stars and the frequent coruscations of the Aurora Borealis. Hence, it appears, that there are no portions of our globe that enjoy, throughout the year, so large a portion of the solar light, as these northern regions, which is chiefly owing to the refraction of the atmosphere.
The refraction of light by the atmosphere, combined with its power of reflecting it, is likewise the cause of that universal light and splendour which appears on all the objects around us. Were the earth disrobed of its atmosphere, and exposed naked to the solar beams—in this case, we might see the sun without having day, strictly so called. His rising would not be preceded by any twilight as it now is. The most intense darkness would cover us till the very moment of his rising; he would then suddenly break out from under the horizon with the same splendour he would exhibit at the highest part of his course, and would not change his brightness till the very moment of his setting, when in an instant all would be black as the darkest night. At noon day we should see the sun like an intensely brilliant globe shining in a sky as black as ebony, like a clear fire in the night seen in the midst of an extensive field, and his rays would show us the adjacent objects immediately around us; but the rays which fall on the objects remote from us would be for ever lost in the expanse of the heavens. Instead of the beautiful azure of the sky, and the colours which distinguish the face of nature by day, we should see nothing but an abyss of darkness, and the stars shining from a vault as dark as chaos. Thus there would be no day, such as we now enjoy, without the atmosphere: since it is by the refraction and reflections connected with this aerial fluid that light is so modified and directed, as to produce all that beauty, splendour and harmony, which appear on the concave of the sky, and on the objects which diversify our terrestrial abode.
The effect of refraction, in respect to terrestrial objects, is likewise of a beneficial nature. The quantity of this refraction is estimated by Dr. Maskelyne at one-tenth of the distance of the object observed, expressed in degrees of a great circle. Hence, if the distance be 10,000 fathoms, its tenth part 1000 fathoms, is the sixtieth part of a degree, or one minute, which is the refraction in altitude. Le Gendre estimates it at one fourteenth; De Lambre at one eleventh; and others at a twelfth of the distance; but it must be supposed to vary at different times and places according to the varying state of the atmosphere. This refraction, as it makes objects appear to be raised higher than they really are, enlarges the extent of our landscapes, and enables us to perceive distant objects which would otherwise have been invisible. It is particularly useful to the navigator at sea. It is one important object of the mariner when traversing his course, to look out for capes and headlands, rocks and islands, so as to descry them as soon as they are within the reach of his eye. Now, by means of refraction, the tops of hills and the elevated parts of coasts, are apparently raised into the air, so that they may be discovered several leagues further off on the sea than they would be, did no such refractive power exist. This circumstance is therefore a considerable benefit to the science of navigation, in enabling the mariner to steer his course aright, and to give him the most early warning of the track he ought to take, or of the dangers to which he may be exposed.
In short, the effects produced by the refraction and reflection of light on the scenery connected with our globe, teach us that these principles, in the hand of the Almighty, might be so modified and directed, as to produce the most picturesque, the most glorious and wonderful phenomena, such as mortal eyes have never yet seen, and of which human imagination can form no conception; and in other worlds, more resplendent and magnificent than ours, such scenes may be fully realized, in combination with the operation of physical principles and agents, with which we are at present unacquainted. From what we already know of the effects of the reflection and the refraction of light, it is not beyond the bounds of probability to suppose, that in certain regions of the universe, light may be reflected and refracted through different mediums, in such a manner, as to present to the view of their inhabitants the prominent scenes connected with distant systems and worlds, and to an extent, as shall infinitely surpass the effects produced by our most powerful telescopes.