points at distances apart corresponding to the length of the wabble-waves; thus dividing the string into vibrating parts, as in Fig. 6.
These make their own little swift air-waves, while the whole string is making its large and comparatively slow ones, and thus produce what are called overtones—waves within waves. These form the feather-wave trimming spoken of, and shown in Fig. 4. These over-vibrations chord
Fig. 7.
or harmonize with the vibrations of the whole string, and are drowned in it, forming a conglomerate air-wave. They are two, three, four, five, six, seven, eight, etc., times the vibration of the whole string, and it is according to which of these over-vibrations is the fullest, that the sound takes its peculiar quality. Sounds without overtones are dull; with too many, harsh and grating; and, with the first six in fair proportion, are rich and sweet. Fig. 7 represents in musical language the overtones of the note C of 132 vibrations; number 1 being the
Fig. 8.
whole string, the other numbers denoting the overtones up to the eighth, the first six being those that give richness to the tone, and of these, one or another being the most prominent according to the source from which the note comes.
We have said that the over-tones are drowned in the tone—only stamping or trimming it, but they can be picked out. Let us see now how we can pick these overtones out of the conglomerate.
It is found that a column of air one-fourth the wave-length, of any note's air-waves, will resound to that note and to no other. Let us take our A-fork again with 440 vibrations per second, making a wave-length of 30 inches, and when vibrating hold it over a tall jar as in Fig. 8. The column of air may not be the right length. By pouring in water a point will be reached at which the jar will burst into the tone A with the fork. By pouring in more water it stops. A certain length only will resound A. Measur-
