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



consonant intervals, the periods of silence, or 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 residual 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 the 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 here are in doubt as 

 to the relative intensities of the sensations given by two 

 sound-vibrations whose amplitudes are 2 : 1, and whose 

 energies are as 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 corre- 

 sponding 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 compared. Thus, if we 

 adopt the law of Weber, with the least perceptible difference in 

 the sensation of two sounds equal to J of their energy, as given 

 by the experiments of Volkmann *, we find that if 1 and 4 



* In the investigations on this subject of which T hp.ve knowledge, 

 the experimenters have used either noises, or soundsfof complex composi- 

 tion mingled with noise, and the ways in which they have determined 

 the relative energies of sounds, or noise-producing vibrations, are open to 

 criticism. I do not know of similar experiments made with simple 

 sounds or tones. I would suggest that the problem of determining the 

 difference in the energies of two simple sounds to give a perceptible 

 difference in the sensations they cause may be solved as follows : — A fork 

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

 accurately measured with a micrometer-microscope. A second fork, or 

 rod, placed alongside of the first fork or rod, has a much smaller amplitude 

 of vibration, which can be varied, and is also measured with a micro- 

 scope. The second fork 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 vanishes, or 

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



