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(from the Laboratories of King's College, University of London).

A. Experimental. 1. Introductory. 2. Experimental methods and general results. 3. Effects produced by forks of different pitch. 4. The buzz. 5. Anomalous effects due to resonance. 6. The 'inertia' of judgment. 7. Influences of adaptation. 8. The lateral error. 9. Summary of factors determining individual differences of judgment.

B. Theoretical. 10. The difficulties of the theory t/tat the phases of sound vibrations are directly transmitted to the brain. 11. Our alternative explanation. 12. The intra-cranial conduction of tones from ear to ear. 13. The retardation in phase during intra-cranial conduction. 14. The meeting of the direct and the bone-conducted waves. 15. Its application of our explanation to binaural beats and to the localisation of low tones under ordinary conditions of hearing. 16. General conclusions.

A. Eocperimental.

1. A brief notice of the experiments which we describe in this paper has already been published'. They were begun in February 1907, having been suggested to us by Lord Rayleigh's account* of his investigations in the same field of research. We wish now to present our data in fuller detail, giving special consideration to those results which are of psychological interest, and to those which throw light on the localisation of low-pitched tones under ordinary conditions of hearing.

At the outset we proposed to ourselves the following problem. If the two ends of a long curved rubber tube be inserted one into each ear of an observer, what changes will occur in the apparent position of the sound of a vibrating tuning-fork, as the fork is moved (with its stem always touching the rubber tube) from the middle point of the tube towards one ear or the other? Have the differences of phase between the vibrations reaching the two ears any influence upon the apparent direction of the sound?

1 We wish to thank Lord Rayleigh for the interest he has taken in these experiments and for several suggestions which he has offered us. We would also express our obligation to the Drapers' Company, by whose liberal grant to the Physical Research Laboratory of the College the expenses involved in this investigation were defrayed.

a Proc. Roy. Soc. 1908, A. Vol. Lxxx. pp. 2G0-266.

» Phil. Mag. 1907, Ser. 6, Vol. xni. pp. 214-231, 316-319.

We were not then aware that thirty years ago a similar problem had been made the subject of a very rough experiment by Sylvan us Thompson1. This investigator introduced the ends of a curved copper wire, 3 feet long, into the ears of an observer, and set the stem of a vibrating tuning fork on the middle point of the wire, whereupon " the sound...appeared to come from the ends of the wire in the ears." He then slid the stem of the fork along the wire through a distance of about an inch and a third, whereupon "the sound appeared to come, not from the two ends of the wire, but from the back."

Under the improved experimental conditions which we are about to describe, we have been able to trace the influence of the differences of phase between the vibrations reaching the two ears in a more thorough and successful manner than was done, either in the above-mentioned experiment by Thompson, or in the more careful experiments which were published by More and Frya while our investigations were in progress. Probably owing to their mode of procedure, all three observers failed to demonstrate the striking series of changes in localisation which are to be met with,—changes of localisation from the middle of the head, across to one ear, back to the middle of the head and across to the other ear, as the tuning-fork is gradually moved from a symmetrical position nearer and nearer to one and the same ear.

2. Instead of using a rubber tube, we joined together pieces of brass

and glass tubing of the same calibre by means of very short pieces of

equally wide rubber tubing. And instead of moving the fork along the

tube, we introduced a hollow brass T-piece, the horizontal arm of which

could just slide freely within two slightly larger tubes, its short vertical

arm receiving the sound of the tuning-fork. This arrangement is made

clear in Fig. 1, where the (partially dotted) tube ATB is the T-piece

sliding within the closely fitting brass tubes SG, VF. From the points

G and F the sound was conducted by glass tubes, joined as we have

just described. These tubes were supported on wooden stools and

ended in the ear caps, P and Q, which consisted of wooden discs lined with

1 Phil. Mag. 1878, Ser. 6, Vol. vi. pp. 386, 387. a Phil. Mag. 1907, Ser. 6, Vol. mi. pp. 452-468.

annular soft pads so that they could be pressed against the observer's head II. The ear caps were supported on the retort stands, M and N, which were clamped to a large table. The length of each of the arms, SGP, VFQ, in most of our experiments, was 317 centimetres, their diameter was approximately 2 centimetres. As a rule, the observer sat facing the tuning-fork; but a large wooden screen, SS, was interposed between the head of the observer and the T-piece, so that the position of the latter was completely hidden from him. A graduated scale DE was fixed beside the T-piece, so that the position of the point T, i.e. the point of entrance of the sound from the tuning-fork K could be accurately recorded. It will be seen that the point of entrance of the sound could be varied through a range of 60 centimetres, on either side of the middle point 100.


By aid of this apparatus, we have been able to show that the result of slightly moving the point T from the middle (symmetrical) position, say towards V, is to shift the apparent position of the tone of the fork from the middle line to that side of the head, Q, towards which the T-piece is moved. And we find that, as the T-piece is moved still further towards V, this lateral displacement of the tone is reduced; a position of T is reached when the tone is again localised midway between the two ears. If the T-piece be again moved nearer to V, the tone passes over to the opposite ear P; and if it be still further moved in the same direction, the localisation of the tone again changes, passing through every gradation until it is localised once more at Q.

These series of changes in localisation can be repeated several times, as the point T approaches the point V, the number of the reversals depending on the wave length (X) of the tone employed and upon the available distance SV. As the point T is moved towards V, the tone is found to be localised on the observer's left (i.e. at Q) when the distance from T to the middle point of the scale (100) lies either

\ X 3X.

between 0 and T, or between - and -r-, while it is localised on his 4 2 4

right when this distance lies either between j an(l « or between


— and \; the same holds for simple multiples of X. The converse

effects are observed when the point T is moved towards 8.

In all these experiments one of us acted as observer, while the other varied the position of the T-piece, sounding the tuning-fork at each position and asking the observer where he localised the tone. On two occasions only we obtained the help of two other subjects, in order to confirm our results. We shall presently give a more detailed account of the experiences of the observer at different positions of the point T. For the present it is sufficient to say that we found it possible to grade our answers in the following manner, 'full-right' (R), 'half-right'

(j\ , 'middle or half-right '(f).' middle' (M), 'middle or half-left'

(j), 'half-left' (5-J, 'full-left' (L) according to the definiteness of the

lateral or medial localisation. The following may be regarded as a typical series of observations:

Fork 384. Observer with back to foak.


Such results we have conveniently expressed in the form of curves (Figs. 2—6), the coordinates of which are (i) the scale readings of the

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position of the T-piece and (ii) the localisation effects. We allow a 'full-right' to count as 1, a ' half-right' as £, a * middle or half-right' as

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