of Binaural Audition. 265 



mated is defined by the equation 



tan a' =^^/ tan ft 



% i + l 2 



or, replacing the fraction by its value just found, 

 tana' = tan <j). 



And hence it must follow that &! = cj>, since the second possible 

 value of ex! , namely 180° + (£, is inapplicable to the problem, 

 as is readily seen. 



The effect which, in binaural hearing, a completely reflecting 

 vertical wall exercises upon the perception of direction consists 

 in this — that the observer of the source of sound seeks it always 

 in the direction of the reflecting wall, independently of the direc- 

 tion in which it may be actually situated. 



For example, let the source of sound be estimated to be 

 situated in the line of sight, then must « / = and also <£ = 0. 

 This shows that the source of sound will always be estimated 

 and sought for in the line of sight if the completely reflecting 

 wall runs parallel to this direction. 



Again, let the source of sound be estimated to lie on the 

 other side of the line of sight to that in which it is really 

 situated, and in a direction making an angle with the line of 

 sight equal to that which it really incloses ; then obviously 

 a! = — a and also (p = — «. 



Finally, let the wall W so reflect the sound that no illusion 

 thereby affects the perception of the direction; then a' = « and 

 <£ = a, which result coincides with that already found for this 

 case. 



Now imagine in figure 7 an additional second reflecting 

 wall W, vertically placed, and making with the line of sight 

 the angle $' ', and let us investigate whether this cannot be so 

 placed that the power of perceiving the direction will not be 

 injuriously affected by a single reflexion of the sound at each 

 wall. We should find, after a rather troublesome process of 

 development, that the required condition will only be fulfilled 

 if 



tan (<£ + (//) = tan 2a, 



which, in consequence of the existing circumstances, can again 

 only be true if <p — <p f = ci. In that case both walls are paral- 

 lel to the direction of the source of sound, and hardly any re- 

 flexion takes place at their surfaces. 



Therefore the perception of the direction will be unaffected by 

 two vertical reflecting walls only when these run parallel to the 

 direction of the rays of sound. 



The results developed in the preceding paragraph concern- 



