branous cochlea (CC), the latter being bounded above by the membrane of Reissner (R) and below by the basilar membrane (b).”*

The membranous cochlea does not extend to the tip of the bony cochlea; above its apex the scala vestibuli and scala tympani communicate. Both are filled with perilymph, so that when the stapes is pushed into the oval foramen, o, in Fig. 17, by the impact of an air-wave on the tympanic membrane, a wave of perilymph runs up the scala vestibuli to the top, where it turns into the scala tympani, down whose whorls it runs and pushes out the round foramen r, ruffling probably the membrane of Reissner and the basilar membrane on its way up and down.

The Terminal Organs.—“The membranous cochlea contains certain solid structures seated on the basilar membrane and forming the organ of Corti. This contains the end-organs of the cochlear nerves. Lining the sulcus

A

B

r

FIG. 22. The rods of Corti. 4, a pair of rods separated from the rest; B, a bit of the casilar membrane with several rods on it, showing how they cover in the tunnel of Cordi; i, inner, and e, outer rods; b, basilar membrane; r, reticular membrane.

spiralis, a groove in the edge of the bony lamina spiralis, are cuboidal cells; on the inner margin of the basilar membrane they become columnar, and then are succeeded by a row which bear on their upper ends a set of short stiff hairs, and constitute the inner hair-cells, which are fixed below by a narrow apex to the basilar membrane; nervefibres enter them. To the inner hair-cells succeed the

*Martin: op. cit.

rods of Corti (Co, Fig. 21), which are represented highly magnified in Fig. 22. These rods are stiff and arranged side by side in two rows, leaned against one another by their upper ends so as to cover in a tunnel; they are known respectively as the inner and outer rods, the former being nearer the lamina spiralis. The inner rods are more numerous than the outer, the numbers being about 6000 and 4500 respectively. Attached to the external sides of the heads of the outer rods is the reticular membrane (r, Fig. 22), which is stiff and perforated by holes. External to the outer rods come four rows of outer hair-cells, connected like the inner row with nerve-fibres; their bristles project into the holes of the reticular membrane. Beyond the outer hair-cells is ordinary columnar epithelium, which passes gradually into cuboidal cells lining most of the membranous cochlea. From the upper lip of the sulcus spiralis projects the tectorial membrane (t, Fig. 21) which extends over the rods of Corti and the hair-cells.”*

The hair-cells would thus seem to

be the terminal organs for 'picking FIG. 23.-Sensory epithelium

from ampulla or semicircular canal, and saccule. At n a nerve-fibre pierces the wall, and after branching enters

the two hair-cells, c. At ha

'columnar cell' with a long

hair is shown, the nerve-fibre base. The slender cells at

being broken away from its

f seem unconnected with

up' the vibrations which the airwaves communicate through all the intervening apparatus, solid and liquid, to the basilar membrarie. Analogous hair-cells receive the terminal nerve-filaments in the walls of the saccule, utricle, and ampullæ (see Fig. 23). The Various Qualities of Sound.-Physically, sounds consist of vibrations, and these are, generally speaking, aërial waves. When the waves are non-periodic the result is a

*Martin: op. cit.

noise; when periodic it is what is nowadays called a tone, or note. The loudness of a sound depends on the force of the waves. When they recur periodically a peculiar quality called pitch is the effect of their frequency. In addition to loudness and pitch tones have each their voice or timbre, which may differ widely in different instruments giving equally loud tones of the same pitch. This voice depends on the form of the aërial wave.

Pitch. A single puff of air, set in motion by no matter what cause, will give a sensation of sound, but it takes at least four or five puffs, or more, to convey a sensation of pitch. The pitch of the note c, for instance, is due to 132 vibrations a second, that of its octave c' is produced by twice as many, or 264 vibrations; but in neither case is it necessary for the vibrations to go on during a full second for the pitch to be discerned. "Sound vibrations may be too rapid or too slow in succession to produce sonorous sensations, just as the ultra-violet and ultra-red rays of the solar spectrum. fail to excite the retina. The highestpitched audible note answers to about 38,016 vibrations in a second, but it differs in individuals; many persons cannot hear the cry of a bat nor the chirp of a cricket, which lie near this upper audible limit. On the other hand, sounds of vibrational rate about 40 per second are not well heard, and a little below this they produce rather a 'hum’than a true tone-sensation, and are only used along with notes of higher octaves to which they give a character of greater depth."

The entire system of pitches forms a continuum of one dimension; that is to say, you can pass from one pitch to another only by one set of intermediaries, instead of by more than one, as in the case of colors. (See p. 41.) The whole series of pitches is embraced in and between the terms of what is called the musical scale. The adoption of certain arbitrary points in this scale as 'notes' has an ex

*Martin: op. cit.

planation partly historic and partly æsthetic, but too com. plex for exposition here.

The timbre' of a note is due to its wave-form. Waves are either simple ('pendular') or compound. Thus if a tuning-fork (which gives waves nearly simple) vibrate 132 times a second, we shall hear the note c. If simultaneously a fork of 264 vibrations be struck, giving the next higher octave, c', the aerial movement at any time will be the algebraic sum of the movements due to both forks; whenever both drive the air one way they reinforce one another; when on the contrary the recoil of one fork coincides with the forward stroke of another, they detract from each other's effect. The result is a movement which is still periodic, repeating itself at equal intervals of time, but no longer pendular, since it is not alike on the ascending and descending limbs of the curves. We thus get at the fact that non-pendular vibrations may be produced by the fusion of pendular, or, in technical phrase, by their composition.

Suppose several musical instruments, as those of an orchestra, to be sounded together. Each produces its own effect on the air-particles, whose movements, being an algebraical sum, must at any given instant be very complex; yet the ear can pick out at will and follow the tones of any one instrument. Now in most musical instruments it is susceptible of physical proof that with every single note that is sounded many upper octaves and other harmonics' sound simultaneously in fainter form. On the relative strength of this or that one or more of these Helmiholtz has shown that the instrument's peculiar voice depends. The several vowel-sounds in the human voice also depend on the predominance of diverse upper harmonics accompanying the note on which the vowel is sung. When the two tuning-forks of the last paragraph are sounded together the new form of vibration has the same period as the lower-pitched fork; yet the ear can clearly distinguish the resultant sound from that of the lower fork alone, as a note of the same pitch but of different timbre; and within

the compound sound the two components can by a trained ear be severally heard. Now how can one resultant waveform make us hear so many sounds at once?

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 pitchsensations 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