The curve S shows Madame Seiler's determination of the residual sonorous sensations; M shows mine. It is evident that the meandering, undecided curve, C, cannot be the expression of a law, and that the data I and I' cannot be combined with those contained in the curve S, or in the

curve M. In a general way the curve C shows that the

smallest consonant interval of two tones contracts as the pitch of the tones, forming the interval, rises.

The physicists Mr. Alexander J. Ellis and Professor J. A. Zahm have discussed the bearing of the law (as given by the experiments of 1874 and 1875) on the elucidation of many facts in consonance and dissonance, to which I referred in my paper of 1874*.

On the Duration of the Residual Sonorous Sensation.

The duration of a residual sonorous sensation is really the duration of the entire period in which a sensation of sound is perceived after the vibrations outside of the ear, giving rise to that sensation, have ceased to exist. While the total

* See Ellis's translation, of 1875, of Helmholtz's Die Lehre von den Tonempfindungen, pp. 173,701, 795, and Ellis's "Illustrations of Just and Tempered Intonation," Proc. Musical Assoc. of London, June 7, 1875; Zahm, 'Sound and Music,' Chicago, 1892.

Phil. Mag. S. 5. Vol. 37. No, 226. March 1894.

Τ

duration of the after-sensation produced by the stimulus of light can be measured, as in the case of an electric flash, the determination of the total duration of the after-sensation of a sound appears, in the light of our present knowledge and with the means of experiment at our command, to be a problem very difficult to solve.

The object of this research was not to determine the total duration of the after-sensation of a sound, but to measure that duration in which the after-sensation of a sound does not perceptibly diminish in intensity.

Fig. 2.

In fig. 2, D and E represent openings in a screen impervious to sound. The distance between the openings equals thrice the diameter of an opening. A tube, R, having the same interior diameter as the openings, is supposed to convey sound-vibrations against the screen, while the tube itself moves from left to right with its mouth sliding along the surface of the screen. In the position A, the sound is just about to traverse the opening D to the ear on the other side of the screen. As R progresses over the opening D, the sound traverses the opening till R has reached the position F B. Then, in the path of the tube from B to C, no sound traverses the screen. When the edge B of the tube has reached the position C, the sound is again just on the eve of traversing the screen through the opening E. As the distance A to B equals B to C, the periods during which the sound traverses the screen equal those in which it does not do so. If these alternations of sound and silence should succeed one another so rapidly that the sensation of the sound is uniform in its intensity, it may at first sight appear that during the time that the tube takes to go from B to C the after-sensation of the sound has not diminished in intensity. But is B to C to be taken as the measure of the duration of uniform sensation? As the tube R moves over D a sound with a varying intensity traverses the opening in the screen. We cannot suppose that the residual sensation caused by the stimulus of the sound traversing a minute opening in the screen equals that caused by the sound which traverses the screen when the circles R and D coincide. In such experiments, however, we are driven to take as the duration of the

undiminished residual sensation the time that the centre of the tube, R, takes to go from the centre of D to the centre of E.

In this illustration I have, for simplicity and conciseness, supposed the tube R to move over the openings D and E. In the actual experiments D and E are two of several holes in a disk, arranged in a circle, and the disk rotates while the tube R is fixed. Another tube placed in the prolongation of the tube R, on the other side of the disk, conveys the interrupted sound to the ear.

Evidently the manner in which the tube conveying the sound to the disk is open and closed by the revolving disk has to be considered in researches made with this apparatus. I give two cases whose discussion has led me to modify,

with marked efficiency, the apparatus, shown in fig. 3, which was used in the researches published in this Journal in 1875. In that apparatus the interruptions of sound were made by a perforated disk revolving in front of the mouth of a resonator, while the interrupted sound was conveyed to the ear by a tube attached to the small opening in the nipple of the resonator.

This mode of obtaining the interruptions of the sound is objectionable because the resonator is not in tune with the fork except when the former is fully opened, and also because

the perforated disk rotating across the mouth of the resonator gives rise to two secondary sounds and a resultant sound, fully described in my paper of 1875*. These sounds, from their intensity in this form of experiment, mask the proper sound of the fork, making the determination of the durations of the sonorous sensations both difficult and uncertain. Also, in these experiments the action of the interrupted sound on the ear is distressing, even injurious; for the hearing of one of my ears was permanently impaired by the experiments I made with this apparatus nineteen years ago.

In the apparatus presently to be described, the fork vibrates in front of the mouth of the resonator, and the interruptions in the flow of sound are caused by the perforated disk revolving in front of the small opening in the nipple of the resonator, as shown in fig. 7.

Discussion of the Effects of the Relative Sizes of the Openings in the Revolving Disk and of the Opening in the Tube conveying the Sound to the Disk.

First Case. Suppose that the opening of the nipple of the resonator and the openings in the disk have the same diameter. In the actual experiments these openings were 1 centim. in diameter. The nipple of the resonator had a tube of that diameter adapted to it.

Fig. 4 is the graphic representation of the results of computing the varying areas of the opening of the tube of the resonator, as an opening in the disk passes in front of it. This diagram is to be studied in connexion with fig. 2. The entire length on the axis of abscissas OX gives the space A to B of fig. 2, divided into sixteen parts. The ordinates of the curve give the relative areas of opening for corresponding positions on the axis of abscissas. The ordinate

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* See a paper by Lord Rayleigh, Acoustical Observations, III. Intermittent Sounds," Phil. Mag., April 1880, in which the author gives an explanation, in mode and in measure, of the secondary sounds and of the resultant sound, observed by me in these experiments.

marked 8 Y shows the full area of opening when the circles of the tube of the resonator and of the disk coincide. It will be observed that the tube is opened and closed slowly, and is only instantaneously fully opened at 8.

Second Case. The openings in the disk remain 1 centim. in diameter, but the opening in the nipple of the resonator is centim. in diameter. Fig. 5 shows the relations between the areas of opening of the nipple of the resonator and the

path A to B (fig. 6) of this opening, R, as it is supposed to move across the opening D in the disk. Fig. 5 is to be studied in connexion with fig. 6. Fig. 5 shows that the opening and closing of the nipple of the resonator take place rapidly, and that the nipple remains fully opened from 4 to 8, that is, during one-third the time that the opening in the disk takes to traverse the opening in the resonator. The advantages gained by this mode of experimenting are considerable. The periods of sound and of silence are sharply marked, and, as we shall now show, the fact that the hole in the resonator has half the diameter of the hole in the disk gives us the means of approaching nearer to the measure of the veritable time during which we have an after-sensation of uniform intensity.

Fig. 6.

In fig. 6 R represents the opening in the nipple of the resonator, supposed to pass over the opening D in the disk. In this case, as in fig. 2, the space A to B in which sound traverses the revolving disk is equal to the space B to C in which silence supervenes, for the distance separating two holes in the disk equals twice the diameter of a hole, or four