86 Proceedings of Royal Society of Edinburgh . [sess. 
from both resonances at one time. All the other partials are 
situated so much nearer to the one resonance than to the other 
that they may be regarded as being under the sole influence of the 
former. The common partial, on the other hand, receives a 
stimulus from each, and it must be remembered that these stimuli 
are mutually independent, as the one operates in the oral and the 
other in the pharyngeal cavity, and that it is a matter of chance 
whether, in any phonogram analysed, these two stimulations operate 
to exaggerate or to conceal each other in the tabulated numerical 
strength of the partial. Thus it comes to be a question of phase. 
Dr Lloyd has evaluated the a- and /3-resonances of the vowel o, as 
above given, and stated the result in the following table : — 
Sung by 
Y.D. 
Partials Reinforced, 
a jB 
Mean Resonance. 
a & 
Radical 
Ratio. 
Hermann, 
132 
2-4 
4-7 
421 
653 
1-553 
Hermann, 
132 
1-3 
4-7 
290 
672 
2-318 
M‘Kendrick, 
148 
1-4 
4-7 
365 
812 
2-221 
Boeke, . 
128 
2-4 
4-6 
391 
615 
1-573 
These four available instances give an average of 368 v.d. for 
a-resonance, of 688 v.d. for /3-resonance, and of 1 *91 6 for the 
radical ratio. A sounder method would be to take from one voice 
a sufficient number of o analyses to constitute . an average, thus 
eliminating the chances which cause the common partial to vary 
to such a noticeable degree. 
It would appear, also, on some vowel-tones that the intensity of 
the fundamental or prime tone is weaker than one of the upper 
partials. Helmholtz laid special emphasis on this observation, and 
he put the statement conversely, namely, that vowel-tones differ 
from those of ordinary musical instruments in that one of the 
upper partials is more marked than the prime. Hermann also 
supports this view • and, in a communication to myself, Boeke 
expressly states that his analyses bring out the same fact. On the 
other hand, Auerbach * maintains that the prime tone is always 
the strongest. Lord Rayleigh t is also of this opinion, while he 
admits that in the vowel a the fundamental is not heard so loudly 
as in other vowels. Hermann suggests that when the prime tone 
is heard of very weak intensity, it may exist only in the ear, but 
* Auerbach, Poggendorff’s Annal., Bd. viii. , 1876, p. 177. 
t Rayleigh, Theory of Sound, 1896, vol. ii. p. 477. 
