190 Prof. A. Steinhauser on the Theory 



For observer B : 

 m 2 =/sin (a + j3 2 ) =/sin 50°, 

 n 2 =/sin ((3 2 — a)=/sin 10° ; 

 consequently the ratio of the intensities is 



m 2 : n 2 = sin 50° : sinl0°=0'766 : 0'173 = 4'4 : 1. 



The source of sound will therefore be sought for by observer 

 A in a direction 20 degrees to the left of the line of sight when 

 the intensity of the sensation of sound in the left ear is more 

 than eight times as great as that of the sensation in the right 

 ear, but by the observer B when the intensity of the sensa- 

 tion in the left ear is not quite 4J times as great as that in the 

 right ear. 



I think, then, I may not inaccurately conclude that the per- 

 ception of the direction becomes the more certain as the differ- 

 ence between the intensities of the sensations of sound in the 

 left and right ears is the greater — -just as analogously the dis- 

 tance of a body may be the more surely estimated in binocular 

 vision the smaller that distance is, or as the directions of the 

 two optic axes differ more and more widely. 



The difference between the two intensities will, under similar 

 conditions, be greatest for that individual for whom the differ- 

 ence m—n has the greatest value. And since 



m— w=/sin(a + /3)— /sin (/3 — a) 



=/(sin cl cos /3 + cos a sin /3— sin /3 cos a + cos /3 sin a) 

 = 2/ sin a cos /3, 



this value becomes greater as cos/3 becomes greater, or as 

 angle /3 itself becomes less ; consequently the smaller the angle 

 included between the line of sight and the surfaces of the pinna?, 

 the more certain will be the perception of the direction of sounds. 



4. We are now prepared to pursue the investigation of the 

 direction of best hearing, i. e. of the direction in which a source 

 of sound at a given distance must be situated in order that it 

 may be heard or perceived best. 



Hearing is obviously better in proportion as the rays of 

 sound which reach the ears from the source of sound at the 

 given distance are more numerous, or as the dimensions m 

 and n of figure 3 are the greater. Hearing with the two ears 

 will therefore be best produced when the value of the sum 

 m + n is greatest. Now it was shown that 



m =/sin (a +J3) ==/(sin u cos /9 + cos a sin /3), 



n=f sin (/?—«) =/(sin /3 cos «— cos /3 sin a) ; 



