7 6 Proceedings of Royal Society of Edinburgh. [sess. 
Koenig investigated the subject with the aid of his manometric 
flame apparatus. This method is useful, because it shows the 
different forms of the sound wave without change of period, corre- 
sponding to a tone of determinate pitch when the vowels are sung 
upon that tone. The flame picture shows the forms taken by the 
flame when the three notes ut 15 sol 1} and ut 2 are sung with the 
vowels a, o, and ou. 
Each of these pictures is composed of two groups of teeth repro- 
duced again and again, and thus showing a regular periodic vibra- 
tory movement. The three pictures of ut contain eight groups of 
teeth, while those of sol contain twelve, and those of ut 2 sixteen. 
As the length of all these pictures correspond to the same duration 
of a vibratory state, it is evident that the period of the vibratory 
movement, or the length of the wave characteristic of a tone of 
determinate pitch, is independent of the vowel upon which the 
sound is emitted. But the form of the wave characteristic of the 
tone of given pitch varies much with the vowel upon which it is 
sung. This alteration of the form of the wave, while the period is 
