mirror we obtain a beautiful interlacing of the two sinuous lines, Fig. 24. [Illustration: FIG. 23.] [Illustration: FIG. 24.] § 5. _The Waves of Sound_ How are we to picture to ourselves the condition of the air through which this musical sound is passing? Imagine one of the prongs of the vibrating fork swiftly advancing; it compresses the air immediately in front of it, and when it retreats it leaves a partial vacuum behind, the process being repeated by every subsequent advance and retreat. The whole function of the tuning-fork is to carve the air into these condensations and rarefactions, and they, as they are formed, propagate themselves in succession through the air. A condensation with its associated rarefaction constitutes, as already stated, a sonorous wave. In water the length of a wave is measured from crest to crest; while, in the case of sound, the _wave-length_ is the distance between two successive condensations. The condensation of the sound-wave corresponds to the crest, while the rarefaction of the sound-wave corresponds to the _sinus_, or depression, of the water-wave. Let the dark spaces, _a_, _b_, _c_, _d_, Fig. 25, represent the condensations, and the light ones, _a′_, _b′_, _c′_, _d′_, the rarefactions of the waves issuing from the fork A B: the wave-length would then be measured from _a_ to _b_, from _b_ to _c_, or from _c_ to _d_. [Illustration: FIG. 25.] § 6. _Definition of Pitch: Determination of Rates of Vibration_ When two notes from two distinct sources are of the same pitch, their rates of vibration are the same. If, for example, a string yield the same note as a tuning-fork, it is because they vibrate with the same rapidity; and if a fork yield the same note as the pipe of an organ or the tongue of a concertina, it is because the vibrations of the fork in the one case are executed in precisely the same time as the vibrations of the column of air, or of the tongue, in the other. The same holds good for the human voice. If a string and a voice yield the same note, it is because the vocal chords of the singer vibrate in the same time as the string vibrates. Is there any way of determining the actual number of vibrations corresponding to a musical note? Can we infer from the pitch of a string, of an organ-pipe, of a tuning-fork, or of the human voice, the number of waves which it sends forth in a second? This very beautiful problem is capable of the most complete solution. § 7. _The Siren: Analysis of the Instrument_