=The analysis of compound wave-forms= is supposed (after Helmholtz) to be effected through the different rates of sympathetic resonance of the different parts of the membranous cochlea. The basilar membrane is some twelve times broader at the apex of the cochlea than at the base where it begins, and is largely composed of radiating fibres which may be likened to stretched strings. Now the physical principle of sympathetic resonance says that when stretched strings are near a source of vibration those whose own rate agrees with that of the source also vibrate, the others remaining at rest. On this principle, waves of perilymph running down the scala tympani at a certain rate of frequency ought to set certain particular fibres of the basilar membrane vibrating, and ought to leave others unaffected. If then each vibrating fibre stimulated the hair-cell above it, and no others, and each such hair-cell, sending a current to the auditory brain-centre, awakened therein a specific process to which the sensation of one particular pitch was correlated, the physiological condition of our several pitch-sensations would be explained. Suppose now a chord to be struck in which perhaps twenty different physical rates of vibration are found: at least twenty different hair-cells or end-organs will receive the jar; and if the power of mental discrimination be at its maximum, twenty different 'objects' of hearing, in the shape of as many distinct pitches of sound, may appear before the mind. The rods of Corti are supposed to be _dampers_ of the fibres of the basilar membrane, just as the malleus, incus, and stapes are dampers of the tympanic membrane, as well as transmitters of its oscillations to the inner ear. There must be, in fact, an instantaneous _damping_ of the physiological vibrations, for there are no such positive after-images, and no such blendings of rapidly successive tones, as the retina shows us in the case of light. Helmholtz's theory of the analysis of sounds is plausible and ingenious. One objection to it is that the keyboard of the cochlea does not seem extensive enough for the number of distinct resonances required. We can discriminate many more degrees of pitch than the 20,000 hair-cells, more or less, will allow for.