268 Prof. A. Steinhauser on the Theory 



reflexion, provided we neglect the possible conduction of sound 

 through solid bodies. 



Whether that operation puts us in a position to form a 

 judgment concerning the direction in which the source of 

 sound is situated, will be seen from what follows. 



Let A A / in figure 9 be the line of sight, /i and/ 2 the effec- 

 tive surfaces of the pinnae for rays of sound turned by re- 

 flexion at the surface W from the direction S into the direction 

 s, a the angle which the rays of sound make with the line of 

 sight before reflexion, and u r the angle they make after re- 

 flexion. Then it is readily seen that, since neither of the sur- 

 faces of the pinnae can be directly reached by the rays S, the 

 hearer will receive an impression identical with that which he 

 would receive if the source of sound were situated in front to 

 the left in the direction of the reflected rays s. .Now it fol- 

 lows from figure 9 that 



(j} = a +ry and a = (£ + 7, 

 and that 



«. = <£ — 7? and 7=a — <£. 



Substituting for 7 its value in the equation u r = cj)—y, we 

 have 



or 



a r =2(f> — ot. 



That which is heard, therefore, indirectly in the direction u 

 makes the same impression as that heard directly in the direc- 

 tion a r ; in which case u r , whose value is dependent on (£, may 

 ivithout any change of the direction of the rays of sound S, 

 assume an indefinite number of different values, since the po- 

 sition of the reflecting surface may as well be any other than 

 it is, or there may be many reflecting surfaces. 



And since, for all remaining directions of rays of sound, the 

 effect upon the ear may be radically different according to the 

 nature of the surrounding reflecting surfaces, no conclusion can 

 be drawn from this effect as to the direction in which the source 

 of sound is situated : indeed it raises very illusory suggestions; 

 for ice suppose the source of sound to be in a particular direction 

 in front in the region of direct binaural hearing, whereas it is 

 situated behind in the region of indirect hearing. 



These illusions of the source of sound being apparently 

 situated behind instead of before, do not appear always, nor 

 even very frequently, and may seem quite different in different 

 cases, as is proved both by the sensations which at almost every 

 moment impress themselves upon the attentive observer and 



