that although announced for performance in Paris, it has not hitherto been used.

A curious accidental source of sound appears to have been several times discovered. It possesses no practical importance, but affords an apt illustration of the theory of harmonics. If a piece of the ordinary vulcanite tubing, such as is used for conveying gas, and which is prevented from collapsing by a spiral wire coiled round its internal surface, be cut to a length of about 18 inches, and gently blown into, a soft musical note of feeble but reedy quality is produced. On pressing the force of wind, it rises successively to higher notes, which will be found on examination to follow roughly the order of the common chord to the foundation tone. It is obvious that the wire coiled inside the tube produces a series of equidistant obstacles, competent to throw the air into regular vibration; the rapidity of which vibration, and the consequent pitch of the note produced, vary with the speed at which the air is blown into the calibre of the tube.

The only remaining source of sound is the human voice but this is of so much importance that it will be considered separately in a later chapter.

CHAPTER II.

MODES OF PROPAGATION OF SOUND. VELOCITY. WAVE-MOTION. REFLECTION. REFRACTION.

The Propagation of Sound appears to take place to some extent through all bodies, but in very different amounts and with varying degrees of velocity. This factor has been found to vary directly as the square root of the bodies' elasticity, and inversely as the root of its density. The formula

therefore serves for all forms of matter. Solids, however, being liable to many kinds of strain, and fluids, whether liquids or gases, to only one, we may have different values of E, and different velocities of transmission for the same solid. In a perfectly free solid this value of E is identical with Young's modulus. The great majority of solids however transmit sound more rapidly in one direction than in others. In solids, moreover, the thermal correction, to be spoken of presently, is very small, as it is also in fluids, whereas in air it is large.

By the Earth.-There is distinct evidence of its transmission through the solid mass of the earth itself for long distances. Humboldt says, "At Caracas, in the plains of Calabozo, and on the borders of Rio Apure, one of the affluents of the Oronoko; that is to say, over an extent of 130,000 square kilometres, one hears a frightful report, without experiencing any shock, at the moment when a torrent of lava flows from the volcano St. Vincent, situated in the Antilles, at a distance of 1,200 kilometres. At the time of the great eruption of Cotopaxi in 1744, the subterranean reports were heard at Honda, on the borders of Magdalena; yet the distance between these two points is 810 kilometres

;

their difference of level is 5,500 metres, and they are separated by the colossal mountainous masses of Quito Pasto and Popayan, and by numberless ravines and valleys. The sound was evidently not transmitted by the air but by the earth, and at a great depth. At the time of the earthquake of New Granada in February, 1835, the same phenomena were reproduced in Popayan, at Bogota, at Santa Maria, and in the Caracas, where the noise continued for seven hours without shocks; also at Haiti in Jamaica, and on the borders of Nicaragua." i

No better illustration of the conveyance of sound by solid media can be found, than that which occurred in the recent colliery accident (1877). Coal is an excellent conductor of sound, being both light and elastic. It was possible from the very first of the noble attempts to rescue the five imprisoned miners, to communicate with them through a long barrier of intervening coal, by knocking on the external surface of the seam in which they were incarcerated. In the same way they were able, as it were, to telegraph back the fact of their existence to their rescuers.

Mons. Biot experimented on a cast-iron pipe 951 metres in length, and found that sound is propagated through this metal with a mean velocity of 3,250 metres a second, or more than 9 times that through air of the same temperature. The pipe used was of rather heterogeneous material, a fact which renders the quantitative determination somewhat doubtful.

An ingenious application of the principle of propagation through solids occurs in Wheatstone's Telephone, exhibited at the Polytechnic Institution many years ago. A band of performers, with violin, clarinet, piano, and other instruments, were placed in a basement room, through the ceiling of which rods of fir-wood were passed into a concert-room above. Each rod was attached by its lower extremity to one of the instruments, at its upper end it was connected with a consonator such as will be described later. When the instruments were played, not only the actual notes, but even the quality and character of each were distinctly audible to any number of listeners in the concert-room. It will be seen from the Table that fir-wood transmits sound at the enormous velocity of 5,994 metres per second, or more than eighteen times that of its transmission in air.

A clever toy has been lately sold by which the transmission of sound through solids may be simply demonstrated. It consists of two tin cylinders, each closed at one end, and

I Quoted in Guillemin's Forces of Nature.

joined together by means of a wire, or even an elastic string, of several yards length. A sentence gently spoken into one cylinder can be distinctly heard by applying the ear to the orifice of the other, when it is quite inaudible from distance through the air.

The Telephone of Graham Bell acts on a totally different principle, converting the vibrations of a metallic plate into magneto-electric currents in a coil of wire surrounding a small magnet. By an exactly similar apparatus at the other end of the conducting line, the undulatory currents thus produced are reconverted into musical tones.

The Microphone of Prof. Hughes really substitutes for a feeble sound, one much louder produced by varying resistance between opposed conductors. It is therefore essentially a relay.

Velocity in Air.-The velocity of sound in air has been the subject of many experiments since the time of Newton. Those of Goldingham, published in the Philosophical Transactions for 1823, of Arago in 1825, of Myrbach and Stampfer at Vienna, of Moll and Van Beek in Holland, and of Gregory, seem the most trustworthy. The observations have generally been those of the flash and the report of a distant cannon. The same observer notes both phenomena with the same watch, and if the distance of the gun be several miles, there is ample time to write down the observation of the flash, before preparing for observation of the sound.

It has, however, been pointed out by Airy' that there is a physiological circumstance, the effects of which have hitherto escaped notice, but which probably produces a sensible error; it is that two different senses, sight and hearing, are employed

On Sound and Atmospheric Vibrations, with the Mathematical Elements Music.

in noting the two phenomena, and we are not certain that impressions are received by them with equal speed. Indeed we believe that the perception of sound is slower by a measurable quantity, perhaps 02", than the perception of light, and this may affect the result with an error amounting to some hundreds of feet. It would be preferable if two observers noted, in the same manner, the time of the sound passing two isolated points. By using signals given reciprocally from two stations beyond both the observing points it will be easy to obtain a result for the time of passage of the sound, independent of the habits of each observer, independent of the different indications of their timekeepers, and independent of the velocity of the wind.

It is possible that a still closer determination might be made by adding to the Astronomer Royal's excellent method some form of electric chronograph, and perhaps the recording phonautograph described later on.

In Gases. The velocity of sound in gases is directly proportional to the square root of their elasticity, and inversely proportional to the square root of their respective densities. The most remarkable case is that of hydrogen, which being about sixteen times lighter than oxygen, conveys sound about four times as fast.

The velocity being a function of the elasticity and density of the medium conveying the sound, the variation of either factor will cause it to be more or less rapidly propagated. Air in a close vessel, unable to expand, when subjected to heat, transmits sound more rapidly than when cooler. Air, moreover, expanding freely with heat, becomes rarefied, and this diminution of density, with unaltered elasticity, has a similar effect.

At a freezing temperature, the velocity has been found to be 1090 feet in a second.

The density of hydrogen being much less than that of air, and the elasticity the same, the fact above stated is fully accounted for. The reverse is true of carbonic acid, a very heavy gas.

The relation of the two is best expressed by the simple mathematical formula above given.

V being the velocity, E the elasticity, and D the density. The law of Boyle and Marriotte, "that the temperature being the

E

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