of Difference of Phase of Sound- Waves. 455 



producing a difference in phase of the waves which entered 

 the two ears. It was easy to produce such an effect, but an 

 exact relation between phase-difference and direction was 

 more difficult to obtain, although, allowing for personal 

 variations, something has been accomplished. 



A listener seated himself at the centre of a large circle 

 marked on the floor of a room. The circle was divided by 

 radii every 22^°. so that 0° was directly behind him and 

 180° in front, +90° being to his right and -90° to his left. 

 A glass funnel, 13'5 cm. in diameter, was mounted hori- 

 zontally on a table about seven feet behind him. Heavy 

 rubber tubing, 1*2 cm. internal diameter, connected the 

 funnel to a glass Y tube, on the other two branches of which, 

 rubber tubing of the same size was fitted. These branch 

 tubes ended in glass tubes bent so as to fit into the ears of 

 the listener. Each of the branch tubes was cut in two in 

 the middle and, by inserting pieces of glass tubing, their 

 lengths were readily altered without the listener being at all 

 aware of it. Fourteen different students of the college 

 assisted, and to be sure they might not be biassed in their 

 judgments, they remained unacquainted with the purpose of 

 the experiment. In experimenting, a tuning-fork or the. 

 voice singing an open vowel at the same pitch was sounded 

 at the mouth of the funnel. The listener was then asked re- 

 locate the direetiou from which the sound appeared to come ; 

 this direction was compared with the angles of the circle, and 

 the relative lengths of the branch tubes were measured. 



The results, in general terms, prove that when the branch 

 tubes were of exactly equal length, the sound seemed to come 

 from behind, but if one were longer than the other, by say 

 two centimetres, the direction of the sound was shifted to 

 the right or left; when the tube to the left ear was the 

 longer the sound came from the right, and vice versa. How- 

 ever the different observers might vary as to the exact angle, 

 they were unanimous so far. Some objections to the ex- 

 periments are obvious, but they can be discussed better after 

 the results are displayed in detail. 



In the following two tables of results, the capital letters 

 stand for the different listeners. 8<fi is the difference in 

 phase of the two waves of sound when they reach the ears, 

 expressed in eighths of the wave-length of the tone used. 

 The angles give the apparent direction of the sound for 

 various phase-differences noted by each listener. Since no 

 mistakes were made in respect to the general directions, right 

 and left, it is not necessary to distinguish the angles with 

 plus and minus signs, if we remember only that 0° signifies 



