7 8 Proceedings of Royal Society of Edinburgh. [sess. 
tone. This tone is usually compound, the constituents being 
partial tones. 
4. Only one form of vibration, like that of a pendulum, or the 
limbs of a tuning-fork, can give rise to a simple tone, destitute of 
partials. This is a simple pendular vibration, and the sensation is 
a simple tone. 
5. A compound tone is the sensation produced by the simul- 
taneous action of several simple tones, with definite ratio of pitch. 
Such a compound tone corresponds physically to a wave of more or 
less complex form. i 
6. Such a compound wave is capable of being analysed into a 
number of simple pendular vibrations, and each pendular vibration 
corresponds to a simple tone, having a pitch determined by the 
periodic time of the corresponding motion of the air (Ohm’s law). 
7. It is evident that such combinations of simple waves may 
give rise to an infinite variety of wave forms ; but, according to 
Fourier’s theorem,* “Any given regular periodic form of vibration 
can always be produced by the addition of simple vibrations, 
having vibrational numbers, which are once, twice, thrice, four 
times, etc., as great as the vibrational number of the given 
motion.” 
8. If we know the amplitudes of the simple vibrations and the 
difference of these , then any regularly periodic motion can be shown 
to be the sum of a certain number of pendular vibrations ; in other 
words, the compound wave may be analysed into its constituents. 
[Dr M ‘Kendrick then described the method of applying the 
Fourierian analysis, as given in the paper by Dr R. J. Lloyd in 
the Proceedings of the Royal Society of Edinburgh , 1898.] 
Phonograms. — We are nowin a position to examine the methods 
that have been adapted to obtain graphic tracings of the wave 
forms, or “ phonograms ” corresponding to vowel-tones, so as to sub- 
mit these to the Fourierian analysis. 
Donders,t in 1870, was the first to apply the phonautograph of 
Leon Scott £ (invented in 1856) to the investigation of the curves 
* Donkin, Acoustics,' ‘ Fourier’s Theorem proved,” pp. 65 to 71 ; “illus- 
trated,” pp. 56 to 65 ; see also Everett, Vibratory Motion and Sound. 
t Donders, De Physiologic der sprachlclanken in het bijzonder van die der 
nederlandische taal, Utrecht, 1870. 
i E. Leon Scott, Compt. rendus, t. 53, p. 108. 
