A. M. Mayer — Researches in Acoustics. 27 



compared. Thus, if we adopt the law of Weber, with the 

 least perceptible difference in the sensation of two sounds 

 equal to \ of their energy, as given by the experiments of 

 Yolkmann,* we find that if 1 and 4 are the absolute energies 

 of the sound- vibrations we get for the ratio of their corre- 

 sponding intensities of sensations 1 : 2*6, but, if the absolute 

 energies of the sounds are 10 to 40 (and their ratio is also 1 :4), 

 we get for their relative sensations 1 : 1'48. Or, what is the 

 same, on the curve expressing the law of Weber, or, of 

 Fechner, the ratio of the sensations of two sounds as given by 

 their corresponding ordinates, depends on the number of units 

 on the abscissas forming the ratio of the energies of these 

 sounds. 



Professors Cattell and Fullerton from extended experiments 

 " On the Perception of Small Differences,"f very carefully 



* Tii the investigations, of which I have knowledge, the experimenters have 

 used either noises, or, sounds of complex composition mingled with noise, and 

 the ways in which they have determined the relative energies of sounds, or, of 

 noise-producing vibrations, are open to criticism. 1 do not know of similar ex- 

 periments made with simple sounds, or, tones. 1 would suggest that the problem 

 of determining the differences in the energies of two simple sounds to give a per- 

 ceptible difference in the sensations they cause maybe solved as follows: A fork, 

 or, rod, is vibrated with a constant amplitude and this amplitude is measured with 

 a micrometer-microscope. A second fork, or, rod, placed alongside of the first 

 fork, or, rod. has a much smaller amplitude ot vibration, which can be varied, 

 and is also measured with a microscope. The second fcrk differs from the first 

 slightly in pitch, so that, say, three beats per second are given. The amplitude 

 of the second, or. of the first fork, is varied till the perception of beats just van- 

 ishes or just appears, while the ear is kept at a fixed distance from the forks. If 

 we take for the relative energies of the sound-giving vibrations the ratio of the 

 squares of the amplitudes of the forks, the least perceptible difference in sensa- 

 tion corresponding to the differences in the energies of the sounds may be com- 

 puted. As example: suppose the second fork has ^-- 6 of the amplitude of vibra- 

 tion of the first. Then the energy of the maximum sounds of the beats will be 



2 



20+1 =441, and the energy of the minimum sound of the beating will be 



2 



20—1 =361, and -||A = the ratio of the stimuli giving the least peiceptible 

 difference in sensation. Sound vibrations of different amplitudes and of different 

 pitch will have to be experimented with and the fork giving the greater ampli- 

 tude of vibration should, in successive experiments, be lower in pitch and then 

 higher in pitch than the fork giving the lesser amplitude of vibration, for reasons 

 set forth in my research. '' (I) On the obliteration of the sensation of one sound 

 by the simultaneous action on the ear of another more intense and lower sound. 

 (2) On the discovery of the fact that a sound even when intense cannot obliterate 

 the sensation of another sound lower than it in pitch." (This Journal, Nov., 1876: 

 Nature, Aug. 10, 1876). Such a research will be difficult and tedious and will 

 require many precautions in arranging the experiments. 



Any one may readily observe the phenomena described by sounding a fork 

 with a large amplitude of vibration and gradually bringing up to the ear a second 

 fork with a small amplitude of vibration, giving with the first three beats per 

 second. As the latter fork gradually approaches the ear the beats become 

 stronger, reaching a maximum of intensity, and then diminishing till they vanish 

 in the more intense sensation of the more iutense sound, to reappear when the 

 faintly vibrating fork has been brought closer to the ear. 



f Publications of the University of Pennsylvania. Philosophical Series, No. 2, 

 May, 1892. 



