Page:EB1911 - Volume 21.djvu/492

Rh from these measurements the depth of the impressions on the same spot or in other words he derives from these measurements the curve of the vibrations of the tone which produced the impression

. 4.

(Archiv f. d ges. Physiol. Bonn, Bd. 1, S. 297; also Proc. Roy. Soc. Edin., 1898).

From a communication to the Dutch Otorhinolaryngological Society Dr Boeke has permitted the author to select the accompanying illustrations, which will give the reader a fair conception of the nature of the marks on the wax cylinder produced by various tones. Fig. 2 shows portions of the curves obtained by Hermann, and enlarged by Boeke one and a half times. The numbers 1 to 4 refer to periods of the vowel (as in "hard"), sung by Hermann on the notes c e g c′. Numbers 5 to 8 show the curves of the vowel o (as in "go" ) sung to the same notes. The number of vibrations is also noted. Boeke measured the marks for the same vowels by his method, from the same cylinder, and constructing the curves, found the relative lengths to be the same. In fig 3 we see the indentations produced by the same vowels, sung by Hermann on the notes c e g c′, on the same phonograph cylinder, but delineated by Boeke after his method. The curves are also shown in linear fashion beside each group of indentations From these measurements the curves were calculated and reproduced, as in fig. 4. Thus the curves of the same vowel sounds on the same cylinder are shown by two methods, that of Hermann and that of Boeke.

. 5.

In fig. 5 we see the indentations on the vowel a, sung by Dr Boeke, aged 55, on the notes c d e f g a b c′, and near the frequencies of 128, 144, 160, 170 6, 192, 213 3, 240 and 256 The numbers 33 to 40 show the marks produced by the same vowel, sung by his son, aged 13. It will be seen that the boy sang the notes exactly an octave higher. Fig. 6 shows the marks produced by some musical

. 6.

sounds. Each shows on the right-hand side the curve deduced from the marks, and under it a graphical representation of the results of its harmonic analysis after the theorem of Fourier, in which the ordinates represent the amplitude of the subsequent harmonic constituents No 41 is the period of the sound of a pitch-pipe giving a′ (425 double vibrations per second), No 42 the period of a Dutch pitch-pipe, also sounding a′ (424·64 double vibrations per second). No 43 is a record of the period of a sound produced by blowing between two strips of indiarubber to imitate the vocal cords, with a frequency of 453 double vibrations per second. No. 44 is that of a telephone pipe used by Hermann (503 double vibrations per second). Nos. 45 and 46 show the marks of a cornet sounding the notes a ≠ 400 double vibrations per second, and e of 300 double vibrations per second. In fig. 7 are shown a number of vowel curves for the vowels O, OE, A, E and I. Each curve has on the right-hand side a graphical representation of its harmonic analysis. The curves are in live vertical columns, having on the

. 7.