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ACOUSTICS 49 the report of a gun was heard before the word “Fire.” where U0 is the velocity at 0° C., and a is the coefficient of More recently Jaques (Phil. Mag. 1879, vii. p. 219) has expansion '00365. How if the temperature is higher investigated the transmission of the report from a cannon overhead than at the surface, the velocity overhead is in different directions, finding that it rose to a maximum greater. If a wave front is in a given position, as a 1, of 1267 ft7sec. at 70 to 90 feet in the rear, and then fell (Fig. 4), at a given instant, the upper part moving faster off. If, too, the sound be confined in pipes so that the 1234 12 3 4 intensity cannot diminish rapidly the normal velocity is exceeded. Thus Regnault in his classical experiments (Phil. Mag. 1868, xxxv. p. 161) found that the velocity of a 6 the report of a pistol carried through a pipe diminished Fig. 4. with the intensity, and his results have been confirmed by Violle and Yautier (Phil. Mag. 1888, xxvi. p. 77). Possibly gains on the lower, and the front tends to swing round as the prolonged boom into which the report of a gun changes shown by the successive positions in a 2, 3, and 4 ; that is, at a distance is due to some kind of break-down and the sound tends to come down to the surface. This is well lengthening out of the original disturbance when the front illustrated by the remarkable horizontal carriage of sound on a still clear frosty morning, when the surface layers of of the pressure wave becomes impossibly steep. Some light has been thrown on the curious “ whispering air are decidedly colder than those above. At sunset, too, gallery ” case of reflection of sound by observations made after a warm day, if the air is still, the cooling of the earth by radiation cools the lower layers, and sound carries Re fie crIO n ^ Lord Rayleigh in the circular gallery at the excellently over a level surface. But usually the lower ‘ base of the dome of St. Paul’s Cathedral. An old explanation of the effect consisted in ascribing it to the layers are warmer than the upper layers, and the velocity concentration of the sound rays after single reflection from below is greater than the velocity above. Consequently a the surface to a focus conjugate to the source, or to the wave front such as h 1 tends to turn upwards, as shown in crowding in a caustic (O. A. § 38). But Lord Rayleigh finds the successive positions b 2, 3, and 4. Sound is then not that “ the abnormal loudness with which a whisper is heard so well heard along the level, but may still reach an is not confined to the position diametrically opposite to that elevated observer. On a hot summer’s day the temperaoccupied by the whisperer, and therefore, it would appear, ture of the surface layers may be much higher than that does not depend materially upon the symmetry of the dome. of the higher layers, and the effect on the horizontal The whisper seems to creep round the gallery horizontally, carriage of sound may be very marked. It is well known that sound travels far better with the not necessarily along the shorter arc, but rather along that arc towards which the whisperer faces. This is a conse- wind than against it. Stokes showed that this effect is quence of the very unequal audibility of a whisper in front one of refraction, due to variation of velocity of efract,oa and behind the speaker, a phenomenon which may'easily the air from the surface upwards (B. A. Rep. ^ 1857, p. 22). It is, of course, a matter of be observed in the open air ” (Sound, ii. § 287). Let Fig. 3 represent a horizontal section of the dome through common observation that the wind increases in velocity the source P. Let OPA he the radius through from the surface upwards. An excellent illustration of ®P. Let PQ represent a ray of sound making this increase was pointed out by Osier in the shape of old d with the tangent at A. Let OH = OP cos d clouds; their upper portions always appear dragged for* be the perpendicular on PQ. Then the re- ward and they lean over, as it were, in the direction in flected ray QR and the ray reflected at R, and so on, will all touch the circle drawn with OH which the wind is going. The same kind of thing happens as radius. A ray making less than d with with sound-wave fronts when travelling with tlie wind. ^ the tangent will with its reflections touch a The velocity of any part of a wave front relative to the larger circle. Hence all rays between ± 9 will ground will be the normal velocity of sound + the Fig. 3. be confined in the space between the outer dome and a circle of radius OP cos 6, and the velocity of the wind at that point. Since the velocity weakening of intensity will be chiefly due to vertical spreading. increases as we go upwards, the front tends to swing Rayleigh points out that this clinging of the sound to round and travel downwards, as shown in the successive the surface of a concave wall does not depend on the positions a 1, 2, 3, and 4, in Fig. 4, when we must suppose exactness of the spherical form. He suggests that the the wind to be blowing from left to right. But if the propagation of earthquake disturbances is probably affected wind is against the sound the velocity of a point of the by the curvature of the surface of the globe, which may act wave front is the normal velocity - the wind velocity at the point, and so decreases as we rise. Then the front like a whispering gallery. In some cases of echo, when the original sound is a tends to swing round and travel upwards as shown in the compound musical note, the octave of the fundamental successive positions 6 1, 2, 3, and 4, in Fig. 4, where the tone is reflected much more strongly than that tone itself. wind is travelling from right to left. In the first case the This is explained by Rayleigh (Sound, ii. § 296) as a waves are more likely to reach and be perceived by an consequence of the irregularities of the reflecting surface. observer level with the source, while in the second case The irregularities send back a scattered reflection of the they may go over his head and not be heard at all. Many of the well-known phenomena of optical diffracdifferent incident trains, and this scattered reflection tion may be imitated with sound-waves, especially if the becomes more copious the shorter the wave length. Hence the octave, though comparatively feeble in the waves be short. Lord Rayleigh has given various exincident train, may predominate in the scattered reflection amples, and accounts of experiments and theory will be found in his Sound, vol. ii. constituting the echo. A simple mode of forming Lissajous figures, to find the Osborne Reynolds (Proc. R. S. xxii. 1874, p. 531) first pointed out that refraction would result from a varia- ratio of the frequencies of two forks, consists in attaching Tempera- tion in the temperature of the air at different two small plane mirrors, one on the prong of ture ' heights. The velocity of sound in air is inde- one fork, the other on a prong of another ^dpiuh refraction. penqen^ 0f the pressure, but varies with the fork. The two forks are arranged so that one vibrates in a vertical, the other in a horizontal temperature, its value at t° C. being (O. A. § 18)— plane, and they are so placed that a converging beam U = u0(l+f), of light, received in one mirror, is reflected to the S. I.—7