260 Dr. A. M. Mayer*s Researches in Acoustics. 



Madame Ema Seiler had made at my request. She made a 

 long series of experiments with the same apparatus I had 

 used. Her determinations, though agreeing with mine in 

 having approximately the same variation of the residual 

 sensation with the pitch, yet differed considerably in the 

 absolute quantities which she found for the durations of these 

 sensations. That the two 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-sensations from the one 

 alone to be studied. In the ability to analyse 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 those 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 con- 

 siderations regarding Helmholtz's Theory of Consonance " 

 (Proc. Amer. Acad., Boston, June 1891). They obtained 

 the smallest consonant intervals of simple sounds by blowing 

 sheets of air across the mouths of resonators. The reciprocals 

 of the differences of the frequency of the vibrations forming 

 the intervals thus found are plotted in the curve C C of 

 fig. 1. I and I' give their determinations of the durations 

 of the residual sensations of UT 3 and of UT 4 , deduced from 

 their observations of the coalescence of these sounds when 

 interrupted by a perforated disk rotating between a resonator 

 and its corresponding fork. 



