PNEUMATICS. 



3! 



fig. 32. 



though one of these reflections might 

 l^e insufficient to render the echo per- 

 ceptible, yet their combined effect cannot 

 fail to do" so. 



When accident or design has placed 

 surfaces in such a position, an echo will 

 therefore be the consequence, and it 

 may even happen that the same point C 

 will be the centre of several concentrical 

 circles of reflecting surfaces, in which 

 case there will be as many reverbera- 

 tions of the sound. 



If the sound be produced at one point, 

 and the auditor be placed at another, 

 the reflecting surfaces must be placed 

 in an ellipse, of which those two points 

 are the foci. This will be easily under- 

 stood by the aid of the known properties 

 of this curve. 



Let S (fig, 33.) be the place of the 

 sounding body, and A the place of the 

 audit or, "and with these points as foci, 

 let an ellipse B, C, D, &c, be described. 

 Let B, C, D, E, &c. be plane surfaces, 

 coinciding at the points B, C, D, E, &c. 

 \vith the curve, or, more strictly speak- 



ing, tangents, to the curve at these 

 points. By the established properties 

 of this curve, the sums of the distances 

 of each point in it from the foci A S are 

 the same ; that is, AB + BS = AC-t- 

 C S = A D + D S, &c. Also the angles 

 which each pair of these lines make 

 with the respective tangents are equal ; 

 that is, the angle A B a is equal to the 

 angle S B b, A C c = S C d, &c. Hence 

 it follows, that sounds proceeding from 

 S in the direction S B will be reflected 

 Jig. 33. 



from B in the direction B A ; also the 

 sound from S to C will be reflected from 

 C to A ; and in the same manner the 

 rays of sound proceeding from S and 

 striking on D, E, F, &c. will also be 

 reflected to A. And since the spaces 

 through which these several rays have 

 to move, viz. SB + BA, SC + CA, 

 S D + D A, &c. are equal, they will all 

 arrive at A at the same instant,' and will 

 consequently be sufficient to produce 

 sensation. The sound of S will, therefore, 

 be first heard directly along S A, and 

 afterwards by the reflections just de- 

 scribed. If it happen that there are a 

 sufficient number of reflecting surfaces 

 in several ellipses having the same points 

 S A as foci, there will be several repeti- 

 tions of the echo. 



CHAPTER VIII. 

 Works upon this Branch of Science. 



Gravesande's Mathematical Elements of Natural Philosophy, book II, part III. 

 Fursrusorfs Lectures on Select Subjects, Lc-ct. VI. 



These two works give a popular exhibition of the science; and describe fully the 

 experiments which illustiate it, and the machines to which it is applied. Rowning's 

 Natural Philosophy Drives an easy and somewhat more superficial account of it. 



The heads of the subject, but only as heads for lecturing from, are to be found more 

 learnedly given in Prof. Playfair and Dr. M. Young's Outlines of Natural Philosophy. 



History of the Fundamental Discovery 

 Galileo's Dialogues. The rise of fluids in tubes by suction is ascribed to nature's hoiror 



of a vacuum, but some of the experiments by which the weight of air is shewn are 



described. 

 Pascal Nouvelles Experiences touchant leVuide. This was first published before 



IfiiS, the date of the Torricellian Experiment, and Pascal adopts Galileo's notion. 



After 1643 he followed Torricelli, and caused the experiment of Fuy do Dome to be 



made on the fall of the mercury, as we mount in the atmosphere, and repeated it 



in a church at Paris. 



