230 PHYSIOLOGY CHAP. 



For this purpose Konig constructed an apparatus which con- 

 sisted of a certain number of resonators, provided with manometric 

 flames, and tuned to the tones of which the number of vibrations 

 stand in the same proportion as the natural series of numbers 

 1, 2, 3, 4 Each resonator communicafes by a rubber tube with a 

 manometer capsule ; the burners of these capsules are arranged 

 under one another beside a four-sided mirror, which can be turned 

 with great rapidity round an axis parallel with the direction of 

 the flames. 



When a sound is made near this apparatus all the resonators 

 capable of vibrating in unison with the elementary tones contained 

 in the compound tone cause the respective flames to vibrate, and 

 the images reflected in the revolving mirror present characteristic 

 indentations. On the other hand, the resonators of which the 

 notes are not contained in the tone struck remain silent, and the 

 respective flames are unaffected, as shown on the revolving mirror 

 by the appearance of a continuous streak of light. The analysis 

 of compound tones by these manometric flames is a less sensitive 

 method than the direct application of resonators to the tympanum. 

 It only serves in recognising the lower partial tones, because the 

 flames are incapable of vibrating with sufficient rapidity to indicate 

 the rapid oscillations of the higher partials. 



The analysis of compound tones into their respective simple 

 component tones is merely the experimental confirmation of a 

 mathematical theorem formulated by Fourier (1822), long before 

 anything was known of the harmonics of the compound tones. 

 He proved that every periodic movement of any form can be 

 resolved into a certain number of simple pendular movements, the 

 periods of which are all multiples of that of the whole movement. 

 The analysis of compound into simple elementary tones by means 

 of resonators shows that Fourier's theorem is not a mathematical 

 fiction, but an expression of actual fact. 



As almost all the tones of the various musical instruments, 

 including the human larynx, are compound, and comprise a 

 quantity of partial tones which differ in number and intensity, 

 the differences in timbre or quality in all probability depend 

 upon this fact. 



Compound tones of different timbre may, even when they 

 express the same fundamental tone, be graphically represented by 

 a different complex form of vibration. But it would be inaccurate 

 to say that the perception of the quality of musical instruments 

 depends on the ability of our ear to recognise the different forms 

 of sound-vibration as such. In effect, the complex curve of any 

 given tone undergoes considerable changes in form, owing to 

 simple displacements of the phases of its partial tones (Fig. 93). 

 Eepeated experiments show, however, contrary to the opinion of 

 It. Konig, that such displacements of phase do not sensibly affect 



