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



movement of acoustic waves, but only to their difference in 

 frequency. 



(iii) The ears cannot be turned toward different directions 

 as the eyes can be, independently of the movements of the 

 head, at least in man. There seems no reason, however, to 

 doubt that the faculty of moving the pinnae of the ears is 

 useful to animals in their perception of the direction of a 

 sound. It is a matter of common knowledge that horses, 

 asses, cats, and dogs do thus use their pinnae in ascertaining 

 the direction of a sound. In these cases, however, it is 

 doubtful whether there is any muscular sense of convergence 

 to give (as with the eye) a perception of distance. 



3. There are four physical characteristics of waves of sound 

 by which one sound is discriminated from another, viz.: — 



(i) Intensity, or loudness, depending upon extent or energy 

 of the vibratory motions. 



(ii) Pitch, or frequency, depending upon the rapidity of 

 the vibratory motions. 



(iii) Phase of the vibratory motions, as to whether moving 

 backward or forward or at any other state. 



(iv) Quality, or timbre, depending upon the degree of com- 

 plexity of the vibratory motion. 



The third of these physical characteristics is one for which the 

 single ear possesses no direct means of perception. The author 

 of this paper discovered in 1877*, however, that in binaural 

 audition a perception of difference of phase did exist ; and the 

 same discovery was made independently in the succeeding 

 December by Prof. Graham Bell and Sir William Thomson. 

 The existing theories of the acoustic perception of space, which 

 will now be examined, are founded upon the perceptions of 

 these four physical characteristics. 



4. Theories of Steinhauser and of Graham Bell. — A verv 

 complete and careful theory of binaural audition was pub- 

 lished in 1877 by Prof. Anton Steinhauser t, who worked out 

 on geometrical principles the laws which determine the rela- 

 tive intensity with which a sound will reach the two ears when 

 starting from any given point of space. The intensities are 

 equal in the two ears when the sonrce of sound is in the 

 median plane, and is a maximum when in front, a minimum 

 when behind the head, since the ears are set angularly (so as 

 to catch sounds from the front of the head) in planes which 

 determine, according to Steinhauser, the conditions of best 

 hearing. The formula deduced by Steinhauser is the follow- 



* Rep. Brit. Assoc. 1877, p. 37; Phil. Mag. [5] vol. iv. Oct. 1877, 

 p. 274. 



t Vienna, 1877: Phil. Mag. [6] vol, vij. pp. 181, 861. 



