272 Prof. A. Steinhauser on the Theory 



flexion alone. Then following the assumptions previously 

 made, on summing up the indirect and direct effects, we ob- 

 tain from equation (3)^ 



tana= ' 1 + pl ~^ tan/3; 

 H + P1 + P2 



and hence by calculation we can find the angle within the 

 region of direct binaural hearing in which the source of sound 

 is erroneously imagined to lie. 



The angle a becomes equal to the angle /3 when p x and p 2 

 become simultaneously zero, or indeed when p 2 = 0, which 

 may be stated as follows : — If a source of sound be situated in 

 the region of mixed binaural hearing, we seek it always in front 

 of us, and in the direction of a line drawn through the surface 

 of the pinna on which the direct rays do not fall, provided 

 either that the indirect rays are of null intensity, or that they 

 reach the other pinna only. 



Again, if the indirect effects were known as such, and were 

 separated from the direct effects, as occurs already in the theory 

 of indirect binaural audition, a means of making an exact 

 estimate of the direction of a source of sound would still be 

 wanting ; but still it is possible by experience to perceive that 

 the source of sound is situated in one of the two regions of mixed 

 hearing, from the circumstance that only one ear is reached by 

 direct rays, and the other is reached by none but indirect rays. 



It is situated, therefore, in the region of mixed hearing, 

 respectively on the left and right sides, when direct rays enter 

 only the left ear or only the right ear, and when none but in- 

 direct rays enter the left ear or the right ear respectively. 



Moreover, in the case of mixed binaural hearing, it is pos- 

 sible to determine the region only, but not the direction, in 

 which the source of sound is situated. 



Concluding Eemakks. 



11. In order to facilitate a survey of the more essential 

 results of the foregoing theory of binaural audition, they are 

 recapitulated and briefly set forth in the following paragraphs. 



The whole 360° of the region of binaural hearing divides 

 itself into three portions : — in front, the region of direct hear- 

 ing ; at the two sides, the regions of mixed hearing ; and at the 

 back, the region of indirect hearing. 



Under favourable circumstances, and without moving the 

 head, we are, in consequence of our binaural hearing, able to 

 decide from the sensations of sound in which region of hearing 

 the source of sound is situated. 



And exact knowledge of the direction in which the source 

 of sound is situated, and an estimate of any motion executed 



