112 Proceedings of Royal Society of Edinburgh. [sess. 
Note in this last table that the vowel which is the highest 
pitched of the ten is also the one vowel whose resonances refuse to 
be easily evaluated, because their effects overlap, and we can discern 
but a vague line of demarcation in the phonogram. It was for 
exactly the same reason that the two highest pitches of Herr von 
Duinen’s sung vowels, and they only, were useless for evaluation 
of resonances. Compare figs. 8 and 9, and observe that while the 
difference of these two resonances of aa reaches 500 to 800 v.n., 
these three cases occur where the sung pitch (and therefore the 
interval between the successive partials) is only 264, 297, and 214’5 
v.d., respectively, — being in the last case certainly less than half the 
difference between the resonances ( v . supra). 
The second of these three instances (the last of Herr von 
Duinen’s vowels) is naturally the strongest. It furnishes, indeed, a 
concrete instance, just as striking as the case already noted to he 
theoretically possible, where the intermediate partial, receiving 
reinforcement from both resonances, comes out stronger in the 
analysis than either of the two partials on which the two reson- 
ances, if their effects could he disentangled, would he respectively 
seen to culminate. This striking analysis is displayed graphically 
in fig. 10 ; and the relative positions of Herr von Duinen’s reson- 
ances, as deduced from the other analyses, are indicated by the 
letters a and /3. 
f 7 ” 
1-0 2-68 2-96 6 '50 1-20 0'56 0*38 0*36 0’03 0’24 0‘37 0*24 
Fig. 10. 
But without the lower-pitched analyses we could not have had the 
least suspicion that fig. 10 is the work of two resonances, much less 
could we have evaluated them. 
If this difficulty thus arises in a vowel where there is a difference 
