26 A. M. Mayer — Researches in Acoustics. 



parison of the durations of the residual sonorous sensations 

 thus determined may be readily compared with those given 

 (by the curve I), of the residual sensations as determined by 

 the blending of sounds interrupted by rotating perforated 

 disks. 



The ordinates of the curve I and F of fig. 1L are obtained 

 in fractions of a second by changing the numbers 1. 2 and 3 

 on the left of fig. 11 into -01, '02 and -03. 



These two curves of fig. 11 present the same general char- 

 acter of a rapid upward flexure at the points corresponding to 

 about 600 v. d. 



The durations of the sound- sensations thus deduced from 

 the smallest consonant intervals average about -J greater than 

 those given by the beats of interrupted sounds. It may be 

 supposed that the durations of the sonorous sensations deduced 

 from the smallest consonant intervals of simple tones are 

 greater than those determined by s*ounds interrupted by the 

 perforated disks because in the resultant actions of the vibra- 

 tions of the tones, forming the smallest- consonant intervals, 

 the periods of silence, or, of the periods of great diminution 

 of sound, are a fraction of the periods of sound, or, of the 

 periods of maximum intensity of sound. To test this opinion 

 I combined the sinusoids corresponding to the two tones of 

 various smallest consonant intervals. On taking, as the re- 

 sidual duration of the sound, not the time from maximum to 

 maximum of vibration (as in the deduction of the durations 

 from the smallest consonant intervals), but the interval of time 

 during which much diminished intensity of sound exists, as 

 shown in the combined curves, I found that the durations of 

 sonorous sensations were thus reduced, on the average, about 

 ■J-, whereas, the reduction in time should be only -J to make 

 these durations agree with those determined by the rotating 

 perforated disks. The explanation suggested is therefore not 

 tenable. 



For the period of much diminished intensity of sound I 

 took that length (in time) of the resultant curve which is 

 bounded, at each end, by an amplitude of vibration |- of the 

 maxima amplitudes of the curve. We are here in doubt as to 

 the relative intensities of the sensations given by two sound- 

 vibrations whose amplitudes are 2 : 1 and whose energies are 

 4: 1. We at once face an obstacle which, from our want of 

 knowledge, is insurmountable ; for, assuming that either the 

 law of Weber, or the formula of Fechner deduced from it, 

 correctly gives the relations existing between the intensity of 

 a stimulus and its corresponding sensation, we cannot apply 

 either of these laws, because we do not know the absolute 

 energies of the sound-vibrations whose sensations are to be 



