Dr. A. M. Mayer's Researches in Acoustics. 285 



when two sounds of different pitch blend, there is no reason 

 why the duration of their residual sensation, as given by the 

 reciprocal in column C, should refer to the lower sound more 

 than to the higher. Therefore we have taken these recipro- 

 cals from column C as expressing the durations of sounds 

 having the mean pitch of the two associated sounds forming 

 the interval. The residual sensations thus found were 

 projected in a curve, drawn to a large scale. From this 

 curve were obtained the durations of the residual sonorous 

 sensations of the tones of the musical scale. These durations 

 are given in column H of Table I. 



In column I of Table I. are given these durations as 

 computed by the formula 



D= (Nt30 + 21 ) ,000L 



In column K are given the differences between the dura- 

 tions computed by the formula and the durations given in 

 column H. The differences show that the formula expresses 

 closely the durations of the residual sensations thus deduced 

 from the determinations of the smallest consonant intervals, 

 except in the case of UT 3 ; for which tone the computed 

 number of vibrations to be added to it to form the higher 

 tone of its smallest consonant interval, as shown in Table II., 

 is 5' 2 vibrations less than the number really required. 



In fig. 11 these durations, as determined from the smallest 

 consonant intervals, are plotted in the curve F, so that the 

 comparison of the durations of the residual sonorous sensa- 

 tions 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 curves I and F of fig. 11 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 iig. 11 present the same general 

 character of a rapid upward flexure at the points corre- 

 sponding to the pitch of about 600 v.d. 



The durations of the sound-sensations as deduced from the 

 smallest consonant intervals of the forks average about J 

 greater than those given by the beats of interrupted sounds. 

 It may be supposed that the durations of the sonorous sensa- 

 tions deduced from the smallest consonant intervals of simple 

 tones are greater than those determined by sounds inter- 

 rupted by the perforated disks, because in the resultant 

 actions of the vibrations of the tones, forming the smallest 



