1. Helmholtz's. Die Lehre von den Tonempfindungen 173, 701, 795–173, 701, 795. See Ellis's translation, of 1875and Ellis's “Illustrations of Just and Tempered Intonation,” Proc. Musical Assoc. of London, June 7, 1875; Zahm, ‘Sound and Music,’ Chicago, 1892
2. XXXVI. Acoustical observations. III
3. 1882. Quelques Expériences d'Acoustique 89, 107, 113–89, 107, 113. Paris Seepar Rudolph Kænig
4. 1876. Phil. Mag., Dec. In the investigations on this subject 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 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 microscope. 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, If we take for the relative intensities of the sound-giving vibrations the ratio of the squares of the amplitudes of the forks, the least perceptible difference in sensation corresponding to the differences in the energies of the sounds may be computed. As example, suppose the second fork has 1/20 of the amplitude of vibration of the first.