ON THE PROPAGATION OF SOUND. 293 



spherical pulse arrives at the surface of a plane solid obstacle, it is reflected 

 precisely in the same manner as we have already seen that a wave of water 

 is reflected, and assumes the form of a pulse proceeding from a centre at an 

 equal distance on the opposite side of the surface. This reflection, when it 

 returns back perpendicularly, constitutes what is commonly called an 

 echo ; but in order that the echo may be heard distinctly, it is necessary 

 that the reflecting object be at a distance moderately great, otherwise the 

 returning sound will be confused with the original one ; and it must either 

 have a smooth surface, or consist of a number of surfaces arranged in a 

 suitable form ; thus there is an echo not only from a distant wall or rock, 

 but frequently from the trees in a wood, and sometimes, as it is said, even 

 from a cloud. 



If a sound or a wave be reflected from a curved surface, the new direction 

 which it will assume may be determined, either from the condition that the 

 velocity with which the impulse is transmitted must remain unaltered, or 

 from the law of reflection, which requires that the direction of the reflected 

 pulse or wave be such as to form an angle with the surface, equal to that 

 which the incident pulse before formed with it. Thus if a sound or wave 

 proceed from one focus of an ellipsis, and be reflected at its circumference, 

 it will be directed from every part of the circumference towards the other 

 focus, since the distance which every portion of the pulse has to pass over 

 in the same time, in following this path, is the same, the sum of the lines 

 drawn from the foci to any part of the curve being the same ; and it may 

 also be demonstrated that these lines form always equal angles with the 

 curve on each side. The truth of this proposition may be easily shown by 

 means of the apparatus already described for exhibiting the motions of the 

 waves of water ; we may also confirm it by a simple experiment on a dish 

 of tea : the curvature of a circle differs so little from that of an ellipsis of 

 small eccentricity, that if we let a drop fall into the cup near its centre, the 

 little wave which is excited will be made to converge to a point at an equal 

 distance on the other side of the centre. (Plate XXV. Fig. 340, 341.) 



If an ellipsis be prolonged without limit, it will become a parabola : hence 

 a parabola is the proper form of the section of a tube calculated for collect- 

 ing a sound which proceeds from a great distance into a single point, or 

 for carrying a sound nearly in parallel directions to a very distant place. 

 It appears, therefore, that a parabolic conoid is the best form for a hearing 

 trumpet, and for a speaking trumpet ; but for both purposes the parabola 

 ought to be much elongated, and to consist of a portion of the conoid re- 

 mote from the vertex ; for it is requisite, in order to avoid confusion, that 

 the sound should enter the ear in directions confined within certain limits : 

 the voice proceeds also from the mouth without any very considerable di- 

 vergence, so that the parts of the curve behind the focus would in both cases 

 be wholly useless. A trumpet of such a shape does not very materially 

 differ from a part of a cone ; and conical instruments are found to answer 

 sufficiently well for practice ; it appears, however, unnecessary to suppose, 

 as Mr. Lambert has done, that they differ essentially in principle from 

 parabolic trumpets.* It is not yet perfectly decided whether or no a speak- 

 * On Acoustic Instruments, Hist, et Mem. de Berlin, 1763, p. 87. 



