of Difference of Phase of Sound- Waves. 453 



complex tones similar in all respects, save the phase relations 

 o£ their harmonics. His experiments with his rotating 

 6 " phase-disks " have been repeated in many laboratories, and 

 most observers agree with Helmholtz that there was no 

 certainty in distinguishing the tones. In fact the theory of 

 audition elaborated by Helmholtz apparently excludes the 

 recognition of the phase of the wave by the auditory nerves. 

 While this may be true of the sensation in a single ear, the 

 experiments described in this paper make it probable that 

 phase relations of sounds do influence binaural audition and 

 enable us to locate sounds. 



If we accept Helmholtz's theory of sound perception, we 

 are, in explaining our method of locating sounds, compelled 

 to rely on the ability of the mind to judge the intensity and 

 complexity of the waves which enter the ears. That is, 

 sounds coming from the right or left are louder or more 

 complex in one ear than in the other, and by comparing the 

 relative intensities or complexities of the two, we determine 

 with considerable accuracy the direction of a sound. 



The effect of the complexity of the wave we know little 

 about from direct experiment and it is probably of minor 

 importance in the general problem, as one can locate pare 

 tones quite accurately. However, it seems natural to suppose 

 the sound heard by the averted ear is weaker than the im- 

 pression made on the other, and that the mind is capable by 

 comparison to judge the location of the sound. But the work 

 of Lord Rayleigh has raised very grave objections to this as 

 an adequate method of locating sounds in all cases. We can 

 dismiss at once the fact that one ear is a little further from 

 the sound source than the other, because we can as readily 

 determine the direction of sounds coming from a great dis- 

 tance as of those from near by. But the intensity of sounds 

 is affected by obstacles in their path, and it is true that the 

 head is generally more in the path of the wave to one ear 

 than to the other. Although the head may be thus inter- 

 posed, the calculations of Lord Rayleigh, ' Theory of Sound,' 

 vol. ii. p. 4:4:2, show that it is too small an obstacle to affect 

 appreciably the intensity of the long waves given out by 

 grave tones. And this can be verified experimentally. If 

 these two functions of sound-waves are inadequate, we are 

 compelled to fall back on the only other property of a wave, 

 its phase. 



In one case, at least, we do know that the mind takes 

 notice of the phase relations. Professor S. P. Thompson 

 proved this by applying the receivers of two telephones, each 

 to an ear. When the telephone disks vibrated so as to give 



