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

same, the volume of a mass of air is inversely as the pressure it supports," shows that this is true of all gases within certain limits. Hence the velocity, on high mountains, or even at the bottom of mines, does not vary if the temperature is constant. With an increase of temperature sound travels faster, with a decrease, slower. The rate of transmission is increased about two feet for each degree Centigrade, or 1·14 feet for each degree Fahrenheit. At the temperature of 60 degrees Fahrenheit we may reckon the velocity of sound at about 1,120 feet per second, or 12 miles per minute.

By this means the distance of a sonorous body may be roughly measured, the velocity being about a mile in 4ķ seconds at medium temperatures.

The depth of the well in Carisbrook Castle has thus been determined, by dropping in a stone, and watching for the sound in the water, allowing of course a correction for the time of fall. The clock of the Houses of Parliament strikes the first blow of the hour within a second of Greenwich time; but five or six seconds have to be allowed for transmission of the sound to even moderately distant stations.

Velocity in Liquids.-The velocity with which sound is propagated in liquids was admirably demonstrated by the classical experiments of Colladon and Sturm, made in the Lake of Geneva. The observers were stationed in two boats on opposite sides of the lake. The sound was emitted from a bell struck by a hammer under the water, and received by a long speaking-tube with a vibrating plate covering its larger orifice, which was sunk vertically in the lake at the other station, the ear of the listener being applied to its smaller end. At the moment of striking the bell some powder was lighted by a match fixed to the hammer, and the determination was made by counting with a chronometer the time elapsing between the flash and the sound. The stations were determined to be 13,487 metres apart; the interval was 9 seconds; thus giving 1,435 metres for the velocity per second in water at 8° Centigrade. It appears, from subsequent experiments, that temperature causes considerable variation in the rate of transmission even in fluids, though far less than in gases; the velocity in the Seine at 15° Centigrade

having been 1,437 metres, in sea-water at 20° – 1,453, and at 23° - 1,460.

Velocity in Solid Bodies. It is owing to the high elasticity of solid bodies such as glass and steel, that the velocity of sound-transmission in them is so great, in spite of their increased density.

The simplest mode of demonstrating this velocity is by means of the Sonometer for longitudinal vibrations of wires already named.

If two wires be stretched side by side in this apparatus, of equal length and thickness, but of different material, the notes, which have been already stated to be independent of tension, will be found to differ considerably. For instance, if they be of steel and brass, the former will be the sharper, owing to the greater velocity in the more elastic metal. With iron and brass the ratio is that of 11: 17, representing an approximate velocity of 11,000 feet per second in the latter, and of 17,000 in the former.

Other methods of determination are given further on. Some of the principal determinations may here be summarized.

1. The most rapid of all forms of matter.

2. In free solids V Young's modulus of elasticity.

3. The changes from heat very small.

4. Solids not isotropic.

Computational determination follows from V = VE which applies to

matter generally.

D'

Wave Motion.-It must, however, be clearly understood that the velocity thus spoken of does not imply the translation of material particles from one terminus to the other. There is nothing resembling the flight of a rifle bullet between a source of sound and the observer's ear. The process is essentially one of wave motion; a condition in which, though each individual particle passes through a very small distance from its original position of rest, it propagates the imparted impulse to its neighbours, and each neighbouring particle to those successively in contact with it.

It is therefore necessary here to advert briefly to wave motion generally, and to the theory of undulation as applied to sound.

"The theory of the transmission of sound through the air," says Professor Airy,' "as well as through other bodies, is especially founded upon the conception of the transmission of waves, in which the nature of the motion is such that the movement of every particle is limited, while the law of relative movement of neighbouring particles is transmitted to an unlimited distance, either without change, or with change

1 Airy on Sound and Atmospheric Vibrations.

following a definite law. In sound we have states of condensation and states of rarefaction, travelling on continually without limit in one direction; while the motion of every individual particle is extremely small, and is alternately backwards and forwards. This is the conception of a wave as depending on the motion of particles in the same line as that in which the wave travels. But there are other kinds of movement of particles, which are equally included under the conception of wave. The motion of the particles may be entirely transverse to the horizontal line; here it is not states of condensation and rarefaction that travel continually in the same direction, but states of elevation and depression that so travel. This is the kind of wave which is recognised as applying to Polarized Light. But in all these there is one general character; that a state of displacement travels on continually in one direction without limit; while the motion of each particle is, or may be, small and of oscillatory character. This is the general conception of a wave. The idea appears to have been first entertained by Newton, and was certainly first developed by him, for the purpose of explaining, what till then was totally obscure, the transmission of sound through air; it is worked out in the third book of the Principia, and among the many wonderful novelties of that wonderful work, it is not the least interesting or the least important. The mere conception of the motion of particles in the way pointed out is a very small part of Newton's work; the really important step is to show that the condensations and rarefactions produced by these motions will, by virtue of the known properties of air, produce such mechanical pressures upon every separate particle, that the different changes of motion which those pressures will produce on each individual particle, will be such that the assumed laws of movement will necessarily be maintained.”

To reconcile his theoretical inference for the velocity of sound with observed measurements, he suggested the idea that the dimensions of air-particles produced a sensible effect. It has been subsequently discovered that the apparent discrepancy depends on changes of temperature developed by the ultimate rarefactions and condensations of which the sound wave consists.

Newton originally computed the velocity at 0° Centigrade to be 916 feet per second. He took into account only the change of elasticity resulting from a change of density,

Lee's Acoustics, Light, and Heat.