Perception of Sound Direction. 219 



conducted with the aid of two forks and resonators of this 

 pitch, gave an answer in the negative. The localization was as 

 easy and as distinct at pitch 512 as at pitch 256. But it is 

 quite possible that 512 is not sufficiently near the particular 

 pitch for which the retardation would have the value of 

 precisely half a period. 



The calculations for a spherical obstacle already quoted give 

 some information upon this point. From the values of 

 F + i'G corresponding to fi= + 1 for the case of 2ttc/\=1, it 

 appears that there is approximate opposition of phase. A 

 closer examination and comparison of the three cases shows 

 that exact opposition will occur at a somewhat higher 

 value, say 2wc/\==l*l. Calculating from this and taking 

 2-rrc at 2 i'eet, I find at the temperature of the observations a 

 pitch about a minor third above 512, as that corresponding to 

 a phase-difference of half a period. 



Naturally, iri its application to the head, the calculation is 

 not very trustworthy, and I thought it important to make sure 

 by actual experiment that there is no pitch in this region for 

 which the discrimination of right and left is at all uncertain. 

 Tuning-forks not being available, I fell back upon " singing- 

 flames," i. e. tubes, usually of metal and about 1 inch in 

 diameter, maintained in vibration by hydrogen flames. In 

 order to eliminate overtones, the tubes were provided near 

 their centres with loosely-fitting rectangular blocks about 

 two diameters long, held in position by the friction of 

 attached springs. In this way and with the precaution of not 

 sounding them more loudly than was necessary, the tones were, 

 it is believed, sufficiently pure. Trials were made in the open 

 air on many occasions, the pitch ranging in all from d' tog"' ', 

 and there was never the smallest suspicion of a difficulty in 

 discriminating right and left. In the region from c" to g" 

 of special interest, the pitch was varied by half semitones 

 with the aid of sliding prolongations of the tube. During 

 most of the observations the listener was placed upon the 

 rotating stool and was in ignorance of the real position of 

 the source. This precaution is of course desirable ; but after 

 a good deal of practice I found that I was able to trust the 

 direct sensual impression. In the case of right or left the 

 impression is always distinct and always correct ; but in 

 trving to discriminate front and back there is usually no 

 distinct impression, and when there is it often turns out to 

 be wrong. 



We may fairly conclude that in this region of pitch (above 

 c" = 512) the discrimination of right and left is not made 

 upon the evidence of phase-differences, or at any rate not upon 



