of Binaura I Audition . 193 



hears only with intensity - instead of intensity i ly and the right 



i " x 

 ear with intensity — instead of intensity i 2 . The direction in 

 x 



which the source of sound is estimated to be situated is, in 



accordance with our preceding paragraphs, given by the 



equation 



tana= r? 



h ■ h 



which cancels into 



+ - 



X X 



tan a= — — r tan 3. 



^l + ^2 



But since this equation gives the same angle which was found 

 when both ears possessed normal hearing powers, it follows 

 that the power of perception of the direction of a sound is not 

 vitiated by an equal hardness of hearing of both ears. This is 

 indeed reasonable on other grounds, since the distance of the 

 source of sound on which the intensities of the two sensations 

 is dependent, but of which the ratio between those intensities 

 is independent, exercises no influence on the perception of the 

 direction. 



The second case may obviously be referred to cases already 

 treated in detail, if we make the supposition that we may take 

 the "effective surfaces" of magnitudes proportional to the 

 respective powers of the two ears. 



Best hearing ivith one ear must obviously occur when 

 m=/sin (a + /3) becomes a maximum, which, since (3 remains 

 constant for a single individual, will occur when sin (* + /3) = 1 , 

 or when (« + /3) = 90°, or, finally, when a = 90°-/3. This 

 agrees with figure 3, if the direction of the rays of sound be 

 made perpendicular to the surface of the pinna f ly in which 

 case m—f 1 =f. 



Finally, let us consider that the greatest number of rays of 

 sound which can be received by both ears is measured, accord- 

 ing to what has been established early in § 4, by the expres- 

 sion 2/ sin /3, in which case the source of sound is situated in 

 the line of sight ; further, that the greatest number of rays of 

 sound which can be received by one ear is measured by/, in 

 which case the ear in question is turned towards the source of 

 sound. Hence it follows that, assuming the specified positions 

 of best hearing, the hearer will hear better with one ear than 

 with both ears, if in his case 



/>2/sin/3. 



