SOUND 185 occurs at the instant it passes us ; the same phe- nomenon is yet more marked when the listener is on a train which passes another going in the opposite direction while the whistle of the latter is sounding. If we suppose each train to be moving at the rate of 30 m. an hour, and the pitch of the whistle while the trains are ap- proaching each other to be that of the C next above the treble, the pitch will fall about a tone while the trains are receding from each other.' The following simple considerations will afford the means of calculating the change in wave length produced by a known velocity given to a sounding body of a given pitch, and will also serve to solve the inverse problem, viz., the velocity of the sounding body which causes an observed change in its pitch. If the sound- ing body moves toward the ear over a space S in one second, it is evident that in these con- itions more vibrations or wave lengths will ter the ear by the number of wave lengths contained in S. If I represent the wave length produced by the vibrating body when it is sta- tionary, and V the wave length when it moves toward the ear, N the number of vibrations er second of the sounding body, and V the "ocity of sound per second, we shall have = y, and l'=l (y^g); and S, the velocity the sounding body per second, will be S=V . Perception of Sounds and their Anal- ly the Ear. The ear may be divided into three portions : the outer, the middle, and the inner ear. (See EAR.) The organ of Corti is enclosed in the ductus cochlearis of the inner ear, a canal of triangular section which forms an ascending spiral of two and a half turns around the modiolus. It is bounded on two of its sides by the seal, and on its third by the membranes lining the outer wall of the cochlea. The upper wall of the ductus coch- learis is formed by the rnembrana Reissneri, which separates it from the scala vestibuli, d its lower wall is the lamina spiralis and e elastic membrana basilaris, which sepa- it from the scala tympani. The ductus is losed at its upper end, and at its lower end it mmunicates with the sacculus hemisphericus a fine duct. The arch of Corti rests upon the embrana basilaris, which extends beyond the of the arch to the membranous outer wall the cochlea ; and over the arch spreads the embrana tectoria, covering the rods of Corti id the hair-cell chords as with a roof, but leav- g the outer portion of the elastic membrana ilaris exposed. The effect of theee anatom- al relations is to bring the sound vibrations act with the greatest advantage on the hair- 11 chords, which are supposed to be the parts f the inner ear that are tuned to the range of unds appreciated as musical by the human If a simple sonorous vibration enter the r ear, then one of these chords, vibrating chronously with it, will shake the nerve bril attached to this chord, and thus give the sensation of a simple sound ; but if a com- posite sonorous vibration enter the ear, several chords will enter into vibration, each vibrating to one of the definite simple vibrations form- ing the components of the compound sound. These hair-cell chords may be compared to the tuned strings in a pianoforte, which readily respond to a note sung over them. If the note be formed of a simple sound, then only one string of the piano will answer back. If the sound be composite, the strings will decom- pose it into its simple component sounds, and the position of these simple sounds in the musical scale can be determined by observing which of the strings of the piano have en- tered into vibration. This experiment shows how the ear is supposed to appreciate a sim- ple sound, and to decompose a compound sound into its simple sonorous sensations. The relation of the various parts of the inner ear is such as to cause the chords of the organ of Corti and their attached nerve filaments to make half as many vibrations in a given time as are made in the same time by the membrane of the drum of the ear. The rela- tions which the form of the scalse bears to the sonorous waves traversing them will be modi- fied according to the existence or non-existence of a communication between the scalse. On this point there seems to be some difference of opinion ; but in explaining the functions of the scalse, first on the supposition that the seal are continuous, and then on the assumption that they are not continuous, but closed at the place where the passage called the helicotrema is supposed to exist, it will be made highly probable that no communication exists between the scalffi, or at least if one exist it must be by a very contracted passage. E. Weber was the first to point out the peculiar molecular actions which exist when the dimensions of a body are very small compared with the length of the sonorous waves which traverse it ; and Helm- holtz based his investigations on " The Mech- anism of the Ossicles of the Ear " on the theory of Weber, which Helmholtz gives in these words : " The difference in displacement of two oscillating particles, whose distance from one another is infinitely small compared with the wave length, is itself infinitely small compared with the entire amplitude of displacement." It is evident that the sonorous compressions and dilatations which may exist in any body depend entirely on the differences in the phases of the vibrations constituting the sonorous wave, and when the body has a depth equal to half a wave length it can embrace the maximum amounts of condensation and of rarefaction. But condensation and rarefaction can alone produce lateral action on the walls of a straight canal traversed by sonorous vibrations; and hence, if the length of the canal be but a small fraction of the wave, there exists throughout the canal but little difference in phase of vibra- tion, and therefore but little lateral action. The united length of the scala3 is but a small
