412 Prof. S. P. Thompson on the Function of 



from back, front, above, or below. By altering the position 

 of the flaps, we alter the relative intensities of the two sounds 

 as received in the ears; and this can be done without the 

 blindfolded observer knowing how the flaps are set. If, for 

 example, the flaps are set to catch sounds from behind, the 

 observer will imagine that he is looking in the direction of the 

 sound when he is looking in precisely the reverse direction. 

 But when the simple tones of tuning-forks are used, the instru- 

 ment fails to gives satisfactory illusions, except for very shrill 

 tones, when the experiments are made out of doors. 



9. The following criticisms on the rival theories and on 

 some of the results of mathematical and experimental deduc- 

 tions therefrom will now be in place. 



(a) All the theories assume that we have a rotation-sense — 

 that is to say, that when we turn round to face a sound, Ave 

 are conscious how much (in angular measurement) we have 

 turned round. Lord Rayleigh, in his experiments, kept the 

 head still, and estimated the angular direction of the sound 

 without turning the head. In this case association with pre- 

 vious perceptions of rotational movement must, however, be 

 admitted as entering into the mental process of judging of 

 angular position. 



(b) The theory of Steinhauser leads to the mathematical 

 deduction that perception of direction is the most exact for 

 sounds situated in the plane of best hearing, or in the median 

 plane and in front of the head. The experiments of Graham 

 Bell, on the other hand, as well as those of Mach and of Lord 

 Eayleigh, are conclusive that the perception of " the direction 

 of a sound is more accurately denned as it approximates to 

 the axial line of the ears.''' 



(c) Steinhauser's theory and his fundamental formula given 

 above in § 4 assume that the ratio between the tangents of 

 the angles will be the same in our perception as the ratio 

 between the angles themselves. This is only true when both 

 are small, and when therefore the source of sound is nearly 

 in the median plane. Unfortunately for the theory, for very 

 small angles the perception ceases to be accurate, especially 

 for small angles near the median plane. 



(d) Steinhauser's theory assumes the pinnse to act as reflec- 

 tors and funnels; he further assumes the magnitude of the 

 " effective surface " to be equal for sounds coming at all 

 angles, which is by no means proven or even probable. 



(e) It is a mathematical consequence of Steinhauser's 

 theory, that if the plane of the effective surface of the pinna 

 makes an angle of less than 30° with the line of sight, a sound 

 will be heard louder when opposite one ear than when placed 



