2 A. 31. Mayer — Researches in Acoustics. 



series of observations should differ was to be expected from 

 the known variation of the sonorous sensations among different 

 observers ; but the principal cause of the difference is to be 

 attributed to the apparatus, fig. 3, used in these experiments. 

 This apparatus generated sounds in addition to the one to be 

 specially observed, so that the determinations were difficult to 

 make except by one whose hearing was peculiarly trained and 

 naturally gifted in the power of excluding other sound sensa- 

 tions from the one alone to be studied. In the ability to 

 analyze composite sounds Madame Seiler was noted, and I had 

 no doubt at the time of the publication of her results that 

 they were more worthy than mine to form the basis of a 

 physiological law. This I stated in my paper of 1875, and 

 the experiments described in the present paper, made with 

 improved methods, show that the opinion then entertained 

 was correct. 



That there is a physiological law which gives the relation 

 between the pitch of a sound and the duration of its residual 

 sensation is shown by the numerous experiments contained in 

 this paper. But those published in 1874 and 1875 sufficed to 

 establish that fact ; yet these experiments have never been 

 repeated by physiologists. 



I have waited nineteen years in the hope that others would 

 make similar experiments, so that the combination of the 

 results of various experimenters would give an expression of 

 the law which might be regarded as general and accepted as 

 expressing the average residual sensations of sounds. 



It is true that Professor C. R. Cross and H. M. Goodwin 

 published a series of similar experiments in " Some considera- 

 tions regarding Helmholtz's Theory of Consonance." (Proc. 

 Amer. Acad. Boston, June, 1891.) They obtained the smallest 

 consonant intervals by blowing sheets of air across the mouths 

 of resonators. The reciprocals of the differences of the fre- 

 quency of the vibrations forming the intervals, thus found, 

 are plotted in the curve, C, C, of fig. 1. I and V give their deter- 

 minations of the durations of the residual sensations of UT 3 and 

 UT 4 , deduced from their observations of the coalescence of 

 these sounds when interrupted by a perforated disk rotating 

 between the resonator and its corresponding fork. 



The curve, S, shows Madame Seller's determination of the 

 residual sonorous sensations ; M, shows mine. It is evident 

 that the meandering, undecided curve, C, cannot be the ex- 

 pression of a law, and that the data I and V cannot be com- 

 bined 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. 



