of Binaural Audition. 185 



man with organs in reserve. This ground is also not un- 

 assailable, since indeed it is nature which permits mankind to be 

 overtaken by disease which, on account of the close connexion 

 between the double organ, almost invariably attacks both or- 

 gans. So, usually, blindness attacks both eyes, deafness both 

 ears, excepting always the comparatively few cases in which 

 the imprudence of men, or accident, has destroyed one of the 

 two similar organs. 



Timidly. A certain faculty, perhaps, which man acquires 

 from the possession of two ears, and therefore by hearing with 

 two ears. We arrive at the conjecture that this may be the case 

 by bringing into comparison two analogous facts in acoustics 

 and optics : — that, in many cases at least, the place in which 

 the source of sound is situated may be tolerably correctly 

 judged of from the sensation of the sound ; and that man ac- 

 quires a special faculty by the possession of two eyes, which, 

 as is known, affords him a perception of distance. 



Now it will be shown in the sequel, that the power which 

 man acquires in certain cases by hearing with two ears, con- 

 sists in the faculty of discriminating the direction in which the 

 source of sound is situated. 



On the other hand, the distance of the source of sound can 

 only be estimated approximately from the relative intensity of 

 the sensation of sound, if the source of sound he knoivn ; for 

 then the distance at which the source of sound is situated can 

 be empirically determined from the difference between the 

 perceived intensity and the known absolute intensity, or that 

 which the source of sound would have in the immediate 

 neighbourhood. In this manner, the distance of an enemy is 

 inferred in warfare from the intensity of the cannonading, 

 or the distance of a carriage from the loudness of its rum- 

 bling. 



It has been shown that we may distinguish between direct, 

 indirect, and mixed binaural audition ; the next branch of our 

 subject is therefore the theory of direct binaural audition. 



1. The Theory of Direct Binaural Audition. 



1. Let A A' be the direction of vision, or line of sight ; ah 

 and ac (or/ x and/g) the effective surfaces of the two pinnae 

 for the (approximately) parallel rays of sound S, a the 

 angle which these rays make with the line of sight, and /3 

 the angle between the surfaces of the pinnae and the line of 

 sight. Then, if de is perpendicular to S, ad ( = m) measures 

 the number of sound-rays which reach the left ear, and ae the 

 number of sound-rays which reach the right ear. 



