114 Proceedings of Royal Society of Edinburgh. [sess. 
below 150 v.d. Many examples are available of o analyses at 
higher pitches, but not one of them shows any sign of the existence 
of two separate resonances. Two analyses, however, of a lower 
pitch than 150 v.d. have been published, and both of them show 
that palpable cleavage in the reinforcements which is the constant 
sign of the presence of two separate resonances. They were both 
sung by Hermann at 132 v.d., and the two series of amplitudes are 
as follow : — 
Y.D. 123 4 56789 10 
132, . 6-7 107 18*4 14*6 18*1 4*7 2-5 1*3 1 0 0’5 
132, . 7-8 23-4 11-2 7 0 17*0 3*6 24 1-2 0*6 1*0 
To these, by the kindness of Dr Boeke, I am enabled to add two 
more ; one sung at 148 v.d. by Professor M ‘Kendrick of Glasgow, 
and the other at 128 v.d. by himself : — 
Y.D. 1 2 3 4 5 6 7 8 
148, . 1 M2 1*73 049 1*90 0*97 0-35 ... 
128, . 1 2*32 5-81 2*10 5*48 0*32 055 0-76 
The 4th partial in each of these four analyses shows a palpable 
falling-off in strength as compared with its neighbours on either 
side ; and there can be no doubt that this falling-off marks in each 
case the gap between an a-resonance of 300-400 v.d. and a /3 - 
resonance of 600-800 v.d. But when we attempt to evaluate these 
resonances more closely, the problem of the common partial arises 
in a more imperative form than ever. The o vowel, however low 
we may sing it, can hardly have more than two partials intermediate 
to the two culminations. In three out of the four cases above 
given, it has only one intermediate partial. What is to be done 
with this one partial in our calculations 1 To what extent must we 
ascribe it to the a-resonance and to the /3-resonance respectively ? 
And how comes it to pass that, in the first of these four analyses, 
this middle partial seems to derive great support from both reson- 
ances, whilst in the third example it is supported by neither, and 
almost vanishes ? 
There is one point in which the common partial differs from all 
others in an analysis : it is in being subject to strong influence from 
