of Edinburgh, Session 1877-78. 
717 
sities of the mouth than to the requirements of the ear ; for, as stated 
above, one voice will give a simple harmonic curve for u, while 
another gives (at the same pitch) a double curve for a sound which is 
intended for the same letter in the same language, and which is at least 
generically the same vowel. This fact suggests that the mouth, 
being unable to shape itself so as to continue the simple form of the 
letter, adapts itself in some way so as to produce what may perhaps 
be termed an imitation. It is by no means impossible that this 
imitation may in some cases be produced by a recurrence to the 
form used for the same letter at a higher pitch. If this be so, then 
the hypothesis of a constant cavity for a given vowel sound would 
be true for the letter u when pronounced on notes an octave or a 
twelfth apart, although not for intermediate notes. 
When we examine the sound o we find less necessity for insisting 
on recurrence or any tuning of the mouth cavity. A fair approach 
to the phenomena observed might be obtained by assuming a constant 
mouth cavity, having a pitch of maximum resonance near 6'b, as 
stated by Helmholtz, and reinforcing tones over a large range of 
nearly two octaves — from f" to /, or thereabouts. There are, how- 
ever, some peculiarities in the constituents which suggest that the o 
cavity may also be adjustable. Our results are not inconsistent 
with the assumption that the cavity is slightly altered or tuned so 
as to bring the maximum resonance approximately into unison with 
that upper partial of the prime sung which lies nearest to &'{?. This 
hypothesis would allow us to diminish the very large range of rein- 
forcement which the constant cavity theory requires, although even 
an adjustable cavity must still reinforce tones over a considerable 
range. Further experiments are required to determine how the 
mouth actually produces the results obtained, but is clear that the 
idea of relation between the constituents must be combined 
with that of absolute pitch in any complete vowel theory. The 
relation may, however, depend for some vowels, though hardly 
for u, on the simple range over which the reinforcement 
acts. The pitch of maximum resonance in the o cavity given 
by Helmholtz is V b, and this, on either hypothesis, agrees well 
with our results. It is either the pitch of maximum resonance of 
the constant cavity, or the pitch near which the upper and strongest 
resonance is to be found, where the cavity is tuned. It may be 
VOL. ix. 5 B 
