the echo becomes multiple instead of single. Buildings, rocks, clumps of trees, even clouds can produce such reflection, as in the case of thunder.

The following quotation fairly sums up the best known of these phenomena.1 "In ancient and modern works a number of multiple echoes are mentioned, the surprising effects of which may be questioned, but which are all easily explained by successive reflection.

"Such an echo is said to have existed at the tomb of Metella, the wife of Crispus, which repeated a whole verse of the Eneid as many as eight times. Addison speaks of an echo which repeated the noise of a pistol-shot fifty-six times, like that of Simonetta in Italy. The echo of Verdun, formed by two large towers about fifty-two metres apart, repeats the same word twelve or thirteen times. The great Pyramid of Egypt contains subterranean chambers connected by long passages, in which words are repeated ten times. Barthius speaks of an echo situated near Coblenz, on the borders of the Rhine, which repeats the same syllable seventeen times, with a very peculiar effect, the person speaking being scarcely heard, while the repetitions produced by the echo are very distinct sounds. Among echoes in England may be noted one in Woodstock Park, which repeats seventeen syllables by day, and twenty by night; while in the Whispering Gallery of St. Paul's, the slightest sound is answered from one side of the dome to the other."

Reflection from Gases. -Reflection may also take place from layers of gases possessing different densities, a fact which has been studied by Tyndall. Sound from a high-pitched reed being conducted through a tube towards a sensitive flame serving as an indicator, was cut off by the interposition of a coal-gas burner of the ordinary "bat's-wing" kind; and by holding the latter at a suitable angle, the sound could be reflected from the flame, through another tube, in sufficient quantity to excite a second sensitive burner.

On account of the great difference of density reflection is nearly total at the boundary between air and solid or liquid matter. Hence sound in air is not easily communicated to water, and sounds whose origin is under water are heard with difficulty in air.

Sound Shadows.-When waves of sound impinge upon an obstacle, a portion of the motion being thrown back as an echo, there is formed under cover of the obstacle a sort

Guillemin's Forces of Nature, p. 140.

of sound-shadow. To produce this in anything like optical perfection, the dimensions of the intervening body must be considerable. The standard is the wave-length of the vibration, and it requires almost as extreme conditions to produce rays in the case of sound, as in optics to avoid producing them. Still, sound-shadows thrown by hills or buildings, are often tolerably complete.'

Refraction of Sound by the Atmosphere is produced (1) by temperature, or (2) by wind.

1. The deviation of sonorous rays from a rectilinear course, due to heterogeneity of the atmosphere, has practical interest. The change of pressure at different levels does not give rise to refraction, since the velocity of sound is independent of density; but, as Reynolds has pointed out, the case is different with variations of temperature as usually met with. These are determined chiefly by the rarefaction or condensation which a portion of air must undergo in its passage from one level to another. Thus acoustical refraction dependent on temperature has almost the same explanation as that of the optical phenomenon of mirage. In the normal state of the air a ray starting horizontally, turns gradually upwards, and at a sufficient distance passes over the head of an observer on the same level as the source. The sound is heard, if at all, by diffraction. The observer may be said to be situated in a sound-shadow, though no obstacle may intervene.

The refraction is increased when the sun shines, and diminishes during rainfall.

2. It has long been known that sounds are generally better heard to leeward than to windward of the source, but Professor Stokes first showed that increasing velocity of wind must interfere with the rectilinear propagation of sound-rays. When the wind increases overhead, a horizontal ray travelling to windward is gradually bent upwards; rays travelling with the wind, on the other hand, are bent downwards, so that an observer to leeward hears by means of a ray which starts with a slight upward inclination, and which has the advantage of being out of the way of obstructions for the greater part of the course.2

The results of Reynolds's experiments were

1. When there is no wind, sound proceeding over a rough surface is more intense above than below.

2. If the wind-velocity be greater above, sound is lifted to windward, and not destroyed.

3. Under the same conditions it is brought down to leeward, and its range is extended at the surface of the ground. Atmospheric refraction has been much studied with reference to fog signals at sea. Tyndall has moreover shown that sound may be intercepted by alternate layers of gases of different density. It is probable that both causes are concerned in the capricious behaviour of these warnings. Lord Rayleigh, moreover, points out that there is a difference in behaviour between long and short sounds. This agrees with Tyndall's observation that in some states of the weather a howitzer firing a 3 lb. charge commanded a larger range than the whistles, trumpets, or siren, while on other days the inferiority of the gun to the siren was demonstrated in the clearest manner.

Influence of Fog.-It has generally been believed, on the authority of Derham, that the influence of fog was prejudicial to the dispersion of sound. Tyndall proved that this opinion is erroneous, and that its passage is favoured by the homogeneous condition of the atmosphere which accompanies fog. When the air is saturated with moisture, the fall of temperature with elevation is much less rapid than in dry air, on account of the condensation of vapour which accompanies expansion. From a calculation of Thomson's1 it appears that in warm fog the effect of evaporation and condensation would be to diminish the fall of temperature by one-half. The acoustical refraction due to temperature would thus be lessened, and in other respects the condition of the air would be favourable to the propagation of sound, provided no obstacle were offered by the suspended particles themselves.

Manchester Memoirs, 1861-2.

CHAPTER III.

INTENSITY, CONSONANCE, INTERFERENCE.

Intensity of Sound. -The waves of rarefaction and condensation issuing from a sonorous body in a homogeneous medium, like the "rays" of light proceeding from a candle, must not be regarded as moving merely in a linear direction. It is true that both in the case of sound, and in that of light, the communication between the producer and the recipient takes a linear form; but the real constitution of the unconfined sound-wave is spherical. There being nothing to impede the oscillation of the ultimate particles, each impulse spreads in an enlarging and concentric shell, the quantity of matter set in motion augmenting as the square of the distance from the source. The intensity, or loudness, must therefore diminish in the same ratio. This is termed the law of Inverse Squares, and is true also for light. The small space through which each particle vibrates backward and forward is termed the amplitude of its undulation, and the intensity of sound is proportional to the square of this amplitude.

If the sonorous wave be confined in a tube, of course its progressive extinction by transference of motion to rapidly increasing masses of matter does not take place, and it may be conveyed for long distances with only very slight enfeeblement. On this principle are constructed the ordinary speaking-tubes. M. Biot, in the experiments by which he determined the velocity of sound in solid bodies, proved the fact that sound transmitted by the air in the waterpipes of Paris was not sensibly enfeebled at the distance of nearly a kilometre. Two persons speaking in whispers could easily hold a conversation through these pipes. "There is

only one way not to be heard," says M. Biot; "not to speak at all."1

There is, however, an important difference between the propagation of sound in a uniform tube and in an open

space. In the former case, the layers of air corresponding to successive wave-lengths are of equal mass, and their move

Quoted in Guillemin's Forces of Nature. Regnault found the report of a pistol in a pipe of 110m. to be audible at a distance equivalent to 10,000 metres.