Part 17

A musical string gives a very feeble sound when vibrating alone, on account of the small quantity of air set in motion; but when attached to a sounding-board, as in the harp and piano-forte, it communicates its undulations to that surface, and from thence to every part of the instrument; so that the whole system vibrates isochronously, and by exposing an extensive undulating surface, which transmits its undulations to a great mass of air, the sound is much reinforced. The intensity is greatest when the vibrations of the string or sounding body are perpendicular to the sounding-board, and least when they are in the same plane with it. The sounding-board of the piano-forte is better disposed than that of any other stringed instrument, because the hammers strike the strings so as to make them vibrate at right angles to it. In the guitar, on the contrary, they are struck obliquely, which renders the tone feeble, unless when the sides, which also act as a sounding-board, are deep. It is evident that the sounding-board and the whole instrument are agitated at once by all the superposed vibrations excited by the simultaneous or consecutive notes that are sounded, each having its perfect effect independently of the rest. A sounding-board not only reciprocates the different degrees of pitch, but all the nameless qualities of tone. This has been beautifully illustrated by Professor Wheatstone in a series of experiments on the transmission through solid conductors of musical performances, from the harp, piano, violin, clarinet, &c. He found that all the varieties of pitch, quality, and intensity are perfectly transmitted with their relative gradations, and may be communicated, through conducting wires or rods of very considerable length, to a properly disposed sounding-board in a distant apartment. The sounds of an entire orchestra may be transmitted and reciprocated by connecting one end of a metallic rod with a sounding-board near the orchestra, so placed as to resound to all the instruments, and the other end with the sounding-board of a harp, piano, or guitar, in a remote apartment. Professor Wheatstone observes, “The effect of this experiment is very pleasing; the sounds, indeed, have so little intensity as scarcely to be heard at a distance from the reciprocating instrument; but, on placing the ear close to it, a diminutive band is heard in which all the instruments preserve their distinctive qualities, and the pianos and fortes, the crescendos and diminuendos, their relative contrasts. Compared with an ordinary band heard at a distance through the air, the effect is as a landscape seen in miniature beauty through a concave lens, compared with the same scene viewed by ordinary vision through a murky atmosphere.”

Every one is aware of the reinforcement of sound by the resonance of cavities. When singing or speaking near the aperture of a wide-mouthed vessel, the intensity of some one note in unison with the air in the cavity is often augmented to a great degree. Any vessel will resound if a body vibrating the natural note of the cavity be placed opposite to its orifice, and be large enough to cover it, or at least to set a large portion of the adjacent air in motion. For the sound will be alternately reflected by the bottom of the cavity and the undulating body at its mouth. The first impulse of the undulating substance will be reflected by the bottom of the cavity, and then by the undulating body, in time to combine with the second new impulse. This reinforced sound will also be twice reflected in time to conspire with the third new impulse; and, as the same process will be repeated on every new impulse, each will combine with all its echoes to reinforce the sound prodigiously. Professor Wheatstone, to whose ingenuity we are indebted for so much new and valuable information on the theory of sound, has given some very striking instances of resonance. If one of the branches of a vibrating tuning-fork be brought near the embouchure of a flute, the lateral apertures of which are stopped so as to render it capable of producing the same sound as the fork, the feeble and scarcely audible sound of the fork will be augmented by the rich resonance of the column of air within the flute, and the tone will be full and clear. The sound will be found greatly to decrease by closing or opening another aperture; for the alteration in the length of the column of air renders it no longer fit perfectly to reciprocate the sound of the fork. This experiment may be made on a concert flute with a C tuning-fork. But Professor Wheatstone observes, that in this case it is generally necessary to finger the flute for B, because, when blown into with the mouth, the under-lip partly covers the embouchure, which renders the sound about a semitone flatter than it would be were the embouchure entirely uncovered. He has also shown, by the following experiment, that any one among several simultaneous sounds may be rendered separately audible. If two bottles be selected, and tuned by filling them with such a quantity of water as will render them unisonant with two tuning-forks which differ in pitch, on bringing both of the vibrating tuning-forks to the mouth of each bottle alternately, in each case that sound only will be heard which is reciprocated by the unisonant bottle.

Several attempts have been made to imitate the articulation of the letters of the alphabet. About the year 1779, MM. Kratzenstein of St. Petersburg, and Kempelen of Vienna, constructed instruments which articulated many letters, words, and even sentences. Mr. Willis of Cambridge has adapted cylindrical tubes to a reed, whose length can be varied at pleasure by sliding joints. Upon drawing out a tube while a column of air from the bellows of an organ is passing through it, the vowels are pronounced in the order, _i_, _e_, _a_, _o_, _u_. On extending the tube, they are repeated after a certain interval, in the inverted order, _u_, _o_, _a_, _e_, _i_. After another interval they are again obtained in the direct order, and so on. When the pitch of the reed is very high, it is impossible to sound some of the vowels, which is in perfect correspondence with the human voice, female singers being unable to pronounce _u_ and _o_ in their high notes. From the singular discoveries of M. Savart on the nature of the human voice, and the investigations of Mr. Willis on the mechanism of the larynx, it may be presumed that ultimately the utterance or pronunciation of modern languages will be conveyed, not only to the eye, but also to the ear of posterity. Had the ancients possessed the means of transmitting such definite sounds, the civilised world would still have responded in sympathetic notes at the distance of many ages.

SECTION XVIII.

Refraction—Astronomical Refraction and its Laws—Formation of Tables of Refraction—Terrestrial Refraction—Its Quantity—Instances of extraordinary Refraction—Reflection—Instances of extraordinary Reflection—Loss of Light by the Absorbing Power of the Atmosphere—Apparent Magnitude of Sun and Moon in the Horizon.

NOT only everything we hear but all we see is through the medium of the atmosphere. Without some knowledge of its action upon light, it would be impossible to ascertain the position of the heavenly bodies, or even to determine the exact place of very distant objects upon the surface of the earth; for, in consequence of the refractive power of the air, no distant object is seen in its true position.

All the celestial bodies appear to be more elevated than they really are; because the rays of light, instead of moving through the atmosphere in straight lines, are continually inflected towards the earth. Light passing obliquely out of a rare into a denser medium, as from vacuum into air, or from air into water, is bent or refracted from its course towards a perpendicular to that point of the denser surface where the light enters it (N. 189). In the same medium, the sine of the angle contained between the incident ray and the perpendicular is in a constant ratio to the sine of the angle contained by the refracted ray and the same perpendicular; but this ratio varies with the refracting medium. The denser the medium, the more the ray is bent. The barometer shows that the density of the atmosphere decreases as the height above the earth increases. Direct experiments prove that the refractive power of the air increases with its density. It follows therefore that, if the temperature be uniform, the refractive power of the air is greatest at the earth’s surface, and diminishes upwards.

A ray of light from a celestial object falling obliquely on this variable atmosphere, instead of being refracted at once from its course, is gradually more and more bent during its passage through it so as to move in a vertical curved line, in the same manner as if the atmosphere consisted of an infinite number of strata of different densities. The object is seen in the direction of a tangent to that part of the curve which meets the eye; consequently the apparent altitude (N. 190) of the heavenly bodies is always greater than their true altitude. Owing to this circumstance, the stars are seen above the horizon after they are set, and the day is lengthened from a part of the sun being visible, though he really is behind the rotundity of the earth. It would be easy to determine the direction of a ray of light through the atmosphere if the law of the density were known; but, as this law is perpetually varying with the temperature, the case is very complicated. When rays pass perpendicularly from one medium into another, they are not bent; and experience shows, that in the same surface, though the sines of the angles of incidence and refraction retain the same ratio, the refraction increases with the obliquity of incidence (N. 189). Hence it appears that the refraction is greatest at the horizon, and at the zenith there is none. But it is proved that, at all heights above ten degrees, refraction varies nearly as the tangent of the angular distance of the object from the zenith, and wholly depends upon the heights of the barometer and thermometer. For the quantity of refraction at the same distance from the zenith varies nearly as the height of the barometer, the temperature being constant; and the effect of the variation of temperature is to diminish the quantity of refraction by about its 480th part for every degree in the rise of Fahrenheit’s thermometer. Not much reliance can be placed on celestial observations, within less than ten or twelve degrees of the horizon, on account of irregular variations in the density of the air near the surface of the earth, which are sometimes the cause of very singular phenomena. The humidity of the air produces no sensible effect on its refractive power; and it has been proved that the amount of refraction is the same whatever be the velocity of the incident light, that is whether the light comes from a star in that part of the heavens towards which the earth is going, or from one in that part of the sky whence it is receding.

Bodies, whether luminous or not, are only visible by the rays which proceed from them. As the rays must pass through strata of different densities in coming to us, it follows that, with the exception of stars in the zenith, no object either in or beyond our atmosphere is seen in its true place. But the deviation is so small in ordinary cases that it causes no inconvenience, though in astronomical and trigonometrical observations due allowance must be made for the effects of refraction. Dr. Bradley’s tables of refraction were formed by observing the zenith distances of the sun at his greatest declinations, and the zenith distances of the pole-star above and below the pole. The sum of these four quantities is equal to 180°, diminished by the sum of the four refractions, whence the sum of the four refractions was obtained; and, from the law of the variation of refraction determined by theory, he assigned the quantity due to each altitude (N. 191). The mean horizontal refraction is about 35ʹ 6ʺ, and at the height of forty-five degrees it is 58ʺ·36. The effect of refraction upon the same star above and below the pole was noticed by Alhazen, a Saracen astronomer of Spain, in the ninth century; but its existence was known to Ptolemy in the second, though he was ignorant of its quantity.

The refraction of a terrestrial object is estimated differently from that of a celestial body. It is measured by the angle contained between the tangent to the curvilineal path of the ray where it meets the eye, and the straight line joining the eye and the object (N. 192). Near the earth’s surface the path of the ray may be supposed to be circular; and the angle at the centre of the earth corresponding to this path is called the horizontal angle. The quantity of terrestrial refraction is obtained by measuring contemporaneously the elevation of the top of a mountain above a point in the plain at its base, and the depression of that point below the top of the mountain. The distance between these two stations is the chord of the horizontal angle; and it is easy to prove that double the refraction is equal to the horizontal angle, increased by the difference between the apparent elevation and the apparent depression. Whence it appears that, in the mean state of the atmosphere, the refraction is about the fourteenth part of the horizontal angle.

Some very singular appearances occur from the accidental expansion or condensation of the strata of the atmosphere contiguous to the surface of the earth, by which distant objects, instead of being elevated, are depressed. Sometimes, being at once both elevated and depressed, they appear double, one of the images being direct, and the other inverted. In consequence of the upper edges of the sun and moon being less refracted than the lower, they often appear to be oval when near the horizon. The looming also or elevation of coasts, mountains, and ships, when viewed across the sea, arises from unusual refraction. A friend of the author’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 very long course of dry and hot weather. Single and double images of objects at sea, arising from sudden changes of temperature which are not so soon communicated to the water on account of its density as to the air, occur more rarely and are of shorter duration than similar appearances on land. In 1818 Captain Scoresby, whose observations on the phenomena of the polar seas are so valuable, recognised his father’s ship by its inverted image in the air, although the vessel itself was below the horizon. He afterwards found that she was seventeen miles beyond the horizon, and thirty miles distant. Two images are sometimes seen suspended in the air over a ship, one direct and the other inverted, with their topmasts or their hulls meeting, according as the inverted image is above or below the direct image (N. 193). Dr. Wollaston has proved that these appearances are owing to the refraction of the rays through media of different densities, by the very simple experiment of looking along a red-hot poker at a distant object. Two images are seen, one direct and another inverted, in consequence of the change induced by the heat in the density of the adjacent air. He produced the same effect by a saline or saccharine solution with water and spirit of wine floating upon it (N. 194).

Many of the phenomena that have been ascribed to extraordinary refraction seem to be occasioned by a partial or total reflection of the rays of light at the surfaces of strata of different densities (N. 189). It is well known that, when light falls obliquely upon the external surface of a transparent medium, as on a plate of glass or a stratum of air, one portion is reflected and the other transmitted. But, when light falls very obliquely upon the internal surface, the whole is reflected, and not a ray is transmitted. In all cases the angles made by the incident and reflected rays with a perpendicular to the surface being equal, as the brightness of the reflected image depends on the quantity of light, those arising from total reflection must be by far the most vivid. The delusive appearance of water, so well known to African travellers and to the Arab of the desert as the Lake of the Gazelles, is ascribed to the reflection which takes place between strata of air of different densities, owing to radiation of heat from the arid sandy plains. The mirage described by Captain Mundy in his Journal of a Tour in India probably arises from this cause. “A deep precipitous valley below us, at the bottom of which I had seen one or two miserable villages in the morning, bore in the evening a complete resemblance to a beautiful lake; the vapour which played the part of water ascending nearly half way up the sides of the vale, and on its bright surface trees and rocks being distinctly reflected. I had not been long contemplating this phenomenon, before a sudden storm came on and dropped a curtain of clouds over the scene.”

An occurrence which happened on the 18th of November, 1804, was probably produced by reflection. Dr. Buchan, while watching the rising sun from the cliff about a mile to the east of Brighton, at the instant the solar disc emerged from the surface of the ocean, saw the cliff on which he was standing, a windmill, his own figure and that of a friend, depicted immediately opposite to him on the sea. This appearance lasted about ten minutes, till the sun had risen nearly his own diameter above the surface of the waves. The whole then seemed to be elevated into the air, and successively vanished. The rays of the sun fell upon the cliff at an incidence of 73° from the perpendicular, and the sea was covered with a dense fog many yards in height, which gradually receded before the rising sun. When extraordinary refraction takes place laterally, the strata of variable density are perpendicular to the horizon, and, if combined with vertical refraction, the objects are magnified as when seen through a telescope. From this cause, on the 26th of July, 1798, the cliffs of France, fifty miles off, were seen as distinctly from Hastings as if they had been close at hand; and even Dieppe was said to have been visible in the afternoon.

The stratum of air in the horizon is so much thicker and more dense than the stratum in the vertical, that the sun’s light is diminished 1300 times in passing through it, which enables us to look at him when setting without being dazzled. The loss of light, and consequently of heat, by the absorbing power of the atmosphere, increases with the obliquity of incidence. Of ten thousand rays falling on its surface, 8123 arrive at a given point of the earth if they fall perpendicularly; 7024 arrive if the angle of direction be fifty degrees; 2831, if it be seven degrees; and only five rays will arrive through a horizontal stratum. Since so great a quantity of light is lost in passing through the atmosphere, many celestial objects are altogether invisible from the plain, which may be seen from elevated situations. Diminished splendour, and the false estimate we make of distance from the number of intervening objects, lead us to suppose the sun and moon to be much larger when in the horizon than at any other altitude, though their apparent diameters are then somewhat less. Instead of the sudden transitions of light and darkness, the reflective power of the air adorns nature with the rosy and golden hues of the Aurora and twilight. Even when the sun is eighteen degrees below the horizon, a sufficient portion of light remains to show that at the height of thirty miles it is still dense enough to reflect light. The atmosphere scatters the sun’s rays, and gives all the beautiful tints and cheerfulness of day. It transmits the blue light in greatest abundance; the higher we ascend, the sky assumes a deeper hue; but, in the expanse of space, the sun and stars must appear like brilliant specks in profound blackness.

SECTION XIX.

Constitution of Light according to Sir Isaac Newton—Absorption of Light—Colours of Bodies—Constitution of Light according to Sir David Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light—The Achromatic Telescope—Homogeneous Light—Accidental and Complementary Colours—M. Plateau’s Experiments and Theory of Accidental Colours.

IT is impossible thus to trace the path of a sunbeam through our atmosphere without feeling a desire to know its nature, by what power it traverses the immensity of space, and the various modifications it undergoes at the surfaces and in the interior of terrestrial substances.

Sir Isaac Newton proved the compound nature of white light, as emitted from the sun, by passing a sunbeam through a glass prism (N. 195), which, separating the rays by refraction, formed a spectrum or oblong image of the sun, consisting of seven colours, red, orange, yellow, green, blue, indigo, and violet—of which the red is the least refrangible, and the violet the most. But, when he reunited these seven rays by means of a lens, the compound beam became pure white as before. He insulated each coloured ray, and, finding that it was no longer capable of decomposition by refraction, concluded that white light consists of seven kinds of homogeneous light, and that to the same colour the same refrangibility ever belongs, and to the same refrangibility the same colour. Since the discovery of absorbent media, however, it appears that this is not the constitution of the solar spectrum.