SOUND 187 head. The following experiment illustrates very well the foregoing explanation of the mode of audition. A membrane, loosely stretched on a frame, is placed in a vertical position near a reed pipe, which, as we have already seen, gives a highly composite sound. Strings of various lengths and diameters, loaded at their centres, are fastened to the membrane and stretched to a fixed support. On sounding the reed pipe, only those strings in tune with the harmonics, or simple sounds, existing in the sound of the reed pipe, will enter into vibration ; similarly, when the sound of the same reed pipe enters the ear and vibrates the basilar membrane, the only hair-cell chords which enter into vibration are those which are in tune with the elementary vibrations existing in the composite sonorous vibr'ation produced by the reed pipe. And it is to be observed that as the loaded string makes one vibration to two of the membrane, so the hair- cell chord makes only one vibration to two of the basilar membrane or of the membrane of the drum of the ear. If it be true that when simple vibrations impinge on the ear the tympanic and basilar membranes vibrate twice, while the co- vibrating body only vibrates once, it follows that if the same simple vibra- tions be sent directly to the co-vibrating parts of the ear, without the intervention of the basilar membrane, we shall perceive a sound which is the octave of the one experienced when the same simple vibrations entered the ear through the tympanic membrane. Hence it appears that this hypothesis can be brought to the test of experiment in the following manner: If we vibrate a fork near the ear, and closely apprehend the character of its sound, we experience a sensation which cer- tainly does not contain that corresponding to the higher octave of the fork. Now press the foot of the fork firmly against the zygo- matic process, close to the ear, directing it somewhat backward, and we shall distinctly hear the higher octave of the fork singing in concert with its real note. If the auditory canal be now closed by gently placing the tip of the finger over it, we shall perceive the higher octave with an intensity almost equal to that of the fundamental note. The same sensation, though less intense, may be obtained by placing the fork on any part of the tem- poral bone. One can also perceive distinctly the higher octave when the fork is placed on the parietal bone, about two inches in front and an inch or so to the side of the foramen, with its foot directed toward the opposite in- ner ear, while the auditory canal of this ear is gently closed with the finger. In these cir- cumstances the higher octave is often heard, with some persons, to the almost entire ex- clusion of the lower, or of the proper note of the fork. These experiments have been made on the ears of several accomplished musicians, and the results have invariably agreed with those described above. Duration of residual Sonorous Sensations. For a long time it has been known that the sensation of light en- dures an appreciable time after the cessation of the entrance of light into the eye. The du- rations of the residual sensations correspond- ing to lights of different colors and intensi- ties have been generally determined by find- ing the number of flashes of a given light in a second required to blend and produce a con- tinuous sensation. The durations of the resid- ual sonorous sensations had never been made the subject of investigation until the writer began the study of these phenomena, and suc- ceeded in determining the law connecting the pitch of a sound with the duration of its re- sidual sonorous sensation. The manner of determining the data of this law is similar to the method employed in the study of the ana- logical phenomena of light. Intermittent so- norous pulses were sent into the ear by means of perforated revolving disks, and the rota- tion of the disk was brought just to that ve- locity required to blend the separated pulses. It was thus found that if we represent by N the number of vibrations per second producing a given sound, and by D the duration of the residual sonorous sensation of this sound, then, the law connecting the pitch, or number of vibrations per second, with the duration of the sonorous sensation, will be expressed by D =(NT + 24) -0001. This is the expression of the law given in the article HARMONY. Besides the application of this law to the elu- cidation of the fundamental facts of musical harmony, there are other and new classes of phenomena which it has served to point out. For instance, as the duration of the residual sonorous sensation is less as the pitch of the sound is higher, it follows that at the instant of the cessation of the aerial vibration, pro- ducing a given composite sound, the timbre of this sound must instantly begin to change ; for the residual sensations of the higher harmonics will disappear one after another, in the order of descending pitch, until there remains in the ear only the sensation corresponding to that of the lowest or fundamental harmonic. The knowledge of the law given above led to a new method of analyzing a composite sound by means of a perforated rotating disk. Thus, on rotating with great velocity a large disk, with sections cut out of it, before a reed pipe, and placing the ear close to the disk, we have the composite sound reaching the ear in a series of impacts which succeed each other so rapidly that even those of the highest harmonic of the reed blend into a continuous sensation ; but on gradually lowering the velocity of rotation, the impacts of this highest harmonic can no longer blend, and we perceive this harmonic beating alone on the ear. This fact can more readily be confirmed by the aid of the resonator corresponding to this harmonic. A further slight lowering of the velocity of rotation brings out the beats of the next lower har-
