Fig. 43.
Note 180, [p. 138]. Elliptical shell. If fig. 6 be a section of an elliptical shell, then all sounds coming from the focus S to different points on the surface, as m, are reflected back to F, because the angle T m S is equal to t m F. In a spherical hollow shell, a sound diverging from the centre is reflected back to the centre again.
Note 181, [p. 142]. Fig. 44 represents musical strings in vibration; the straight lines are the strings when at rest. The first figure of the four would give the fundamental note, as, for example, the low C. The second and third figures would give the first and second harmonics; that is, the octave and the 12th above C, n n n being the points at rest; the fourth figure shows the real motion when compounded of all three.
Fig. 44.
Note 182, [p. 143]. Fig. 45 represents sections of an open and of a shut pipe, and of a pipe open at one end. When sounded, the air spontaneously divides itself into segments. It remains at rest in the divisions or nodes n nʹ, &c., but vibrates between them in the direction of the arrow-heads. The undulations of the whole column of air give the fundamental note, while the vibrations of the divisions give the harmonics.
Fig. 45.
Note 183, [p. 144]. Fig. 1, [plate 1], shows the vibrating surface when the sand divides it into squares, and fig. 2 represents the same when the nodal lines divide it into triangles. The portions marked a a are in different states of vibration from those marked b b.
Note 184, [p. 145]. [Plates 1] and [2] contain a few of Chladni’s figures. The white lines are the forms assumed by the sand, from different modes of vibration, corresponding to musical notes of different degrees of pitch. [Plate 3] contains six of Chladni’s circular figures.