188 Prof. A. Steinhauser on the Theory 



Now the fraction 4— ~ is in all cases less than the fraction 



ft— L ii + mit 



■r — r-\ hence also tan a and the angle a become less than they 



would be if both ears heard equally well. Consequently the 

 direction in which the source of sound appears to be moves 

 towards the right, or towards that side on which the ear of 

 better hearing is situated. In the case of a complete deafness 



of one earm= go ; hence tan a. = — ? . tan /3 = tan /3, and a = 



~r *2 

 —(3, where the negative angle is to be reckoned on the right 

 of the line of sight. 



2. Let two consonant tones be produced by organ-pipes (in 

 the apparatus to be described below, which I call a homo- 

 phone, and which is for the ears the analogue of the stereo- 

 scope for the eyes), but in such a manner that one tone, 

 having the intensity i ly shall affect the left ear only, and the 

 other tone having the intensity i 2 shall affect only the right 

 ear; then, at least when the eyes are closed, the two impressions 

 unite in a single impression which appears to be produced 

 by a source of sound in the direction a as determined by 

 equation (2) :— { { 



tan a= r . tan p. 



This apparatus is shown in plan in figure 4 ; where abc re- 

 presents a wooden tube of square cross section, closed at a and 

 c, and provided at b with a mouthpiece through which a con- 

 tinuous blast of air from a bellows may be introduced. Near 

 the ends a and c, two flute organ-pipes, p 1 and p 2 , are inserted 

 into two holes in the tube. The pitch of these pipes is alike ; 

 but the relative intensities of their tones can be brought to any 

 desired proportion by means of the valves m and n, which re- 

 gulate the current of air. The cardboard funnels T x and T 2 

 respectively lead the tones to the ears Ox and 2 of the observer 

 whose head is represented at K. 



3. Suppose two persons, A and B, for whom the values of 

 /3 differ, to make an estimation of the direction of a sound 

 under precisely similar conditions, and that in both cases, 

 therefore, the sound-rays and the line of sight include the angle 

 a ; agreeably with that which has preceded, the measurements 

 for reckoning the sound-rays which respectively enter the left 

 and right ears for the two observers will be 



A. m 1 =/sin(a + /3 1 ) 

 and ni =/sin(/3 1 — a); 



B. ?7^ 2 =/sin(a + /3 2 ) 

 and n 2 =f sin (fi 2 — a) . 



