ACOUSTICS. 



lie in the surface of the oblong spheroid, 

 generated by the revolution of this ellipse 

 round its major axis. See Coxic SEC- 

 TIONS. As there may be several sphe- 

 roids of different magnitudes, so there 

 may be several different echoes of the 

 same original sound. And as there may 

 happen to be agreaternumberofreflecting 

 points in the surface of an exterior sphe- 

 roid than in that of an interior, a second or 

 a third echo may be much more powerful 

 than the first, provided that the superior 

 number of reflecting points, that is, the 

 superior number of reflecting pulses pro- 

 pagated to the ear, be more than sufficient 

 to compensate for the decay of sound 

 which arises from its being propagated 

 through a greater space. This is finely 

 illustrated in the celebrated echoes at the 

 lake of Killarney, in Kerry, where the first 

 return of the sound is much inferior in 

 strength to those which immediately suc- 

 ceed it. From what has been laid down 

 it appears, that, for the most powerful 

 echo, the sounding body should be in one 

 focus of the ellipse, which is the section 

 of the echoing spheroid, and the hearer in 

 the other. However, an echo may be 

 heard in o.her situations, though not so 

 favourably ; as such a number of reflect- 

 ed pulses may arrive at the same time at 

 the ear, as may be sufficient to excite a 

 distinct perception. 1 hus a person often 

 hears the echo of his own voice ; but for 

 this purpose he should stand at least 63 

 or 64 feeL from the reflecting- obstacle, 

 according to what has been said before. 



if a beU, a, fig. 5, be struck, and the 

 undulations of the air strike the wal! c d 

 in a perpendicular direction, they will be 

 reflected back in the same line ; and if a 

 person be situated between a and r, as at 

 j; he would hear the sound of :he bell by 

 means of the undulations as they went to 

 the wall, and he would hear it again as 

 they came back, after the reflection, which 

 would be the echo of the sound. So a 

 person standing at x might, in speaking in 

 the direction of the wall c d, hear the echo 

 of his own voice. But in both cases the 

 distance c x must be 63 or 64 feet. If the 

 undulations strike against the wall oblique- 

 ly, they will be reflected off obliquely on 

 the other side ; if, for instance, a person 

 stand at m, and there be any obstacle be- 

 tween that place and the bell, so as to pre- 

 vent him hearing the direct sound, he may 

 nevertheless hear the echo from the wall 

 c d, provided the direct sound fall in that 

 sort of oblique direction, so as to force the 

 reflected undulations along the lime c m. 

 At the common rate of speaking, we do 



not pronounce above three syllables and a 

 half, that is, seven half syllables in a se- 

 cond ; therefore,that the echo may return 

 just as soon as three syllables are ex- 

 pressed, twice the distance of the speaker 

 from the reflecting object must be equal 

 to 1000 feet; for as sound describes 1142 

 feet in a second, 6-7ths of that space, thai 

 is, lOOu feet nearly ,will be described while 

 six half, or three whole, syllables are pro- 

 nounced ; that is, the speaker must stand 

 near 500 feet from the obstacle. And, in 

 general, the distance of the speaker from 

 the echoing surface, for any number of 

 syllables, must be equal to the seventh 

 part of the product of 1142feet multiplied 

 by that number. In churches we never 

 hear a distinct echo of the voice, but a 

 confused sound, when the speaker utters 

 his words too rapidly ; because the great- 

 est difference of distance between the di- 

 rect and reflected courses of such a num- 

 ber of pulses as would produce a distinct 

 sound is never in any church equal to 127 

 feet, the limit of echoes. But though the 

 first reflected pulses may produce no echo, 

 both on account of their being too few in 

 number, and too rapid in their return to 

 the ear, yet it is evident, that the reflect- 

 ing surface may be so formed, as that the 

 pulses wliich come to the ear, after two 

 reflections or more, may, after having de- 

 scribed 127 feet or more, arrive at the ear 

 in sufficient numbers, and also so nearly 

 at the same instant, as to produce an echo, 

 though the distance of the reflecting sur- 

 face from the ear be less than the limit of 

 echoes. This is confirmed by a singular 

 echo in a grotto on the banks of the little 

 brook called the Dinan, about two miles 

 from Castlecomber, in the county of Kil- 

 kenny. As you enter the cave, and con- 

 tinue speaking loud, no return of the voice 

 is perceived; but on your arriving at a 

 certain point, which is not above 14 or 15 

 feet from the reflecting surface, a very 

 distinct echo is heard. Now this echo 

 cannot arise from the. first course of pul- 

 ses that are reflected to the ear, because 

 the breadth of the cave is so small, that 

 they would return too quickly to produce 

 a distinct sensation from that of the origi- 

 nal sound: it therefore is produced by 

 those pulses, which, after having been re- 

 flected several times from one side, of the 

 grotto to the other, and having run over 

 a greater space than 127 feet, arrived at 

 the ear in considerable numbers, and not 

 more distant from each other in point of 

 time than the ninth part of a second. M, 

 De la Grange demonstrated, that all im- 

 pressions are reflected by an obstacle ter- 



