ECHO 389 server at the same instant ; he will then per- ceive an echo of twice the intensity of that produced by either reflector separately. The curvature of an elliptical mirror is such that all the rays of sound, or to speak more properly the whole wave of sound, that starts from one focus will be reflected precisely to the other focus, so that the ear placed at this point per- ceives a sound as intense as that at the origin ; this principle is applied in the construction of whispering galleries, where, however, circular or other curved surfaces frequently replace the ellipse. If a sound originate near the focus of a parabolic mirror, the reflected portion of the wave will be confined to a cylindrical or coni- cal space in front of the mirror; a principle that finds application in the construction of speaking trumpets and tubes, ear trumpets, sounding boards for pulpits, &c. The louder portions of the rolling of artillery or of a clap of thunder are doubtless sometimes the effect of a concentration of several echoes reflected from objects properly placed with respect to the observer. On the other hand, a convex surface scatters the waves of sound and dimin- ishes the intensity of the echo ; a principle that finds frequent application in the construction of large halls, whose walls, ceilings, pillars, &c., are covered with protuberant convex ornaments. If the reflecting surfaces are ar- ranged in a promiscuous manner, there will be heard a confused mixture of echoes, each per- haps so faint that the direct sound greatly pre- ponderates; and in the case of many public halls it will be noticed that if empty the speaker's voice is unpleasantly reechoed, while if filled by an audience the echoes become much subdued and often inappreciable. So also a wave of sound passing through a mix- ture of heterogeneous bodies (such as a forest, currents of hot and cold air, a glass full of champagne, a stratum of rock full of faults and fissures, &c.) is quite completely broken up into smaller pulses moving in every possible direction. Thus fog bells and whistles, and indeed all other sounds, are heard further du- ring cloudy and foggy weather, and during the night, when the earth is shaded from the sun's heat; and balloonists testify that during the night they hear terrestrial sounds more dis- tinctly. A mixture of rapid currents, even if the liquid be homogeneous, has the same effect ; so that the attempts made in 1870 during the siege of Paris to send sound signals through the waters of the Seine were quite unsuccess- ful, the range of distinct hearing being far less than in the quiet waters of a lake. The nature of a pulse of sound is such that if two or more pulses meet under certain conditions they will interfere with each other so as to produce silence instead of sound at the point of their in- tersection. The echoes within rooms of regular symmetrical proportions do thus interfere with each other, and to a slight extent with the direct waves of sound, so that the loudness of the sounds perceived by the ear varies greatly with a change of position of a few feet. In order that reflected waves should thus pro- duce silence, they must have travelled over paths differing in length by some odd multiple (3, 5, 101, &c.) of a half of the wave length peculiar to the pitch of the sound in question. Because of the variety in the length of the waves that issue from the vocal organs, it follows that a point in an auditorium may be unfavor- able to the perception of certain notes in the speaker's voice or in the music of an orchestra, yet favorable to the perception of all others. In the study of the acoustic properties of public halls, Langhans (1810) and Orth (1871) have made valuable investigations. Some of their results are as follows : 1. The phenomena of interference are of minor importance as dis- turbing elements, while the principal evil to be avoided is the confusion and repetition of echoes. 2; It is less important to provide for the concentration of the sounds of the speak- er's voice than for the suppression of all echoes. 3. A difference of path between the direct and the reflected sounds of from 15 to 22 ft. does not disturb and may even assist the hearing ; a difference of from 185 to 215 ft. may be dis- regarded because of the comparative feebleness of the echo ; a difference of 30 ft. is to be avoided, as being the most annoying. 4. Low roofs, as in theatres, are advantageous ; high ceilings, as in Gothic churches, are of no de- cided advantage, and may help to produce un- desirable echoes. 5. If wood panelling or plaster is introduced to deaden the echo, it is most important to attend to the backing by which the panels are fastened to the walls. The pitch of an echo, like that of any sound, depends on the rapidity with which the in- dividual pulses encounter the tympanum. When these pulses follow each other at the rate of from 10 to 16 per second, the ear ceases to be able to separate one from another, and the whole are merged in an apparently con- tinuous humming noise or a musical note of low pitch ; the pitch increases directly as the rapidity of the pulsation. If the pulses occur at irregular intervals, and with unequal inten- sities, a noise or a sense of confusion is pro- duced. These principles find an application in the case of sound reflected from a series of plane reflecting surfaces, such as the palings of a fence, a row of square pillars, &c. ; in these cases the original sound does not appear to be echoed, but instead thereof we hear a musical note, generally of high pitch, lasting for a second or two only, and rapidly diminishing in intensity ; if the observer be in motion, the in- dividual echoes reach his ear more or less rapidly than if he be stationary, thus producing a corresponding change in the pitch. Lord Eayleigh has shown that a group of bodies whose dimensions are quite small in com- parison with the wave lengths of sound reflect the first harmonic or octave 16 times more powerfully than the fundamental tone ; and in general the reflecting or diverting power of
