1897 - 98 .] Dr Lloyd on Analysis of Tracings of Vowels. 101 
other on the 10th partial. But observe how much narrower in 
range are these reinforcements of i than those of aa , for these upper 
resonances of i affect only one or two high partials ; the neighbour- 
ing partials are not reinforced at all, though they are hardly two 
semitones removed. The two resonances are both comprised within 
a space of six semitones (7th to 10 th partials), and yet, within that 
narrow space, are sharply marked off from each other by the prac- 
tical absence of the 9th partial. This results from the nature of the 
cavity in which the resonance is generated. One of these resonances 
of i is certainly generated by the narrow tube formed between the 
tongue and the hard palate in the articulation of that vowel (Helm- 
holtz, Sensations of Tone , p. 108). Hence its narrowness of range ; 
for a tube will not respond to any tone which differs much from its 
own. But a rounded cavity has a range of resonance which increases 
with every increase in the size of its aperture or apertures. The 
articulation of aa consists of two such cavities, of rather wide aper- 
ture (see figures in Journ. of Anat., loc. cit.), and I believe, after 
actual measurements of the articulation, that the two reinforcements 
displayed in the phonograms of this vowel ( e.g ., fig. 3) can be satis- 
factorily traced to the proper resonances of these two cavities. 
Hence its two reinforcements are seen to spread over a whole 
octave (4th to 8th partials) and even then do not find space with- 
out some overlapping, for the 6th partial seems to be reinforced by 
both. The question has been warmly argued whether the Fourierian 
analysis accurately represents the facts of vowel-resonance or not. 
Does it follow, because a vibration can be analysed into a certain 
note and its partials, that the vowel objectively consists of those 
partials, and nothing more ? Hensen and Pipping say yes ; Her- 
mann says that the higher-pitched elements are not partials at all, 
but independent resonances. A middle opinion seems best to 
deserve adoption. It is as difficult to conceive the voice passing 
through the articulation of a given vowel without arousing the 
proper tone of the cavities passed through, as it is to conceive the 
voice passing through the same articulation without having its own 
partials reinforced or damped. In the Fourierian analysis we get 
both of these elements together; they cannot be discriminated. 
But the proper tones of the cavities must undoubtedly be present 
in some degree. It seems most probable, too, that they are suffi- 
