ON THE PROPAGATION OF SOUND. , 37o 



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 ecjual angles with the curve on 

 each side. The truth of this proposition may be easily shown by means of the ap- 

 paratus 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 curva- 

 ture 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 soond 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 car in directions confined within certain limits: 

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

 ence, 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 

 apart 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 speaking trumpet 

 has any immediate effect in strengthening the voice, independently of the 

 reflection of sound. (Plate XXV. Fig. 342.) 



An umbrella, held in a proper position over the head, may serve to collect 



