Prof. A. M. Mayer's Researches in Acoustics. 359 



cing the maximum dissonances a constant fraction of the num- 

 bers of beats which give continuous sensations. Thus I find 

 that ^o °f tne latter numbers give me the most disagreeable sen- 

 sations ; another observer has placed the fraction as high as - 6 l . 

 I imagine that we do not greatly depart from an average judg- 

 ment in stating that about ^ of the number of beats, through- 

 out the musical scale, which produce continuous sensations, cor- 

 respond to the numbers of beats giving the greatest dissonant 

 effects. Thus we can go from the law connecting the pitch of a 

 sound with the duration of its residual sonorous sensation to the 

 law giving the numbers of beats throughout the musical scale 

 which produce the most dissonant sensations. 



3. Application of the above Laws in a new Method of Sonorous 

 Analysis, by means of a perforated rotating disk. 



It is an interesting deduction from the laws we have estab- 

 lished that a composite sound can be analyzed by means of a 

 rotating disk with sectors cut out of it. Thus, on rotating a 

 large perforated disk with great velocity before a reed-pipe and 

 placing the ear close to the disk (or in connexion with the gutta- 

 percha funnel, by means of the rubber tube), we shall have the 

 composite sound reaching the ear in a series of impacts which suc- 

 ceed 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 har- 

 monic can no longer blend, and we perceive the harmonic beat- 

 ing on the ear alone. This can be readily confirmed by the aid 

 of a resonator. A further slight lowering of the velocity brings 

 out the beats of the next lower harmonic, and so on until the 

 velocity has been so diminished that even the beats of the lowest, 

 or fundamental, harmonic are perceived; and then all of the 

 component sounds of the reed are beating in unison ; but yet 

 the effects they produce on the ear are very different ; for the 

 higher harmonics, notwithstanding their feebler intensities, must 

 be heard more distinctly, because their intermittences are furthest 

 removed from the numbers that cause their sensations to blend. 

 In other words, the highest harmonics, in the phase of the expe- 

 riment above described, approach nearer than the lower to the 

 numbers of beats required to cause them to give their greatest 

 dissonant effects. This method of sonorous analysis was arrived 

 at as a deduction from our laws ; and subsequent experiments con- 

 firmed the assumption that a sonorous analysis could be thus 

 effected. This curious discovery has its analogue in the case of 

 light ; for when a disk with alternate white and black sectors is 

 rotated so slowly that distinct flashes of white light are perceived, 

 the retina is thrown into states of successive increasing and de* 



