1897-98.] Dr Lloyd on Analysis of Tracings of Voivels. 115 
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 clearly remembered that these stimuli are 
mutually and entirely independent (they are in fact successive, the 
one operating in the intra-velar and the other in the extra-velar 
cavity of o), and that it is a matter of pure chance whether, in 
any phonogram analysed, these two stimulations operate to exag- 
gerate or to conceal each other in the tabulated numerical strength 
of the partial. 
Briefly, it is a question of phase. The partials into which a 
sound is analysed by the Fourierian process are simple or pendular 
vibrations. If one of them enters successively into two vibrating 
cavities, each of which severally has power to give reinforcement, 
the resultant reinforcement need not be the sum of the two reinforce- 
ments : it may be their difference, or it may be anything inter- 
mediate. The first result will only follow when the two reinforce- 
ments are precisely identical in phase ; the second will follow 
when they are precisely opposite in phase ; and the third in all 
other (that is to say, in the great majority of) cases. On the 
average, it will be about one-half the sum of the two several 
reinforcements. 
This view explains the extraordinary fluctuations in the strength 
of the intermediate partial, but it helps us very little in the 
problem of evaluation. It shows us that if the intermediate partial 
is very strong, and we use it for its full value in calculating both of 
the resonances, we shall get the a-resonance too high and the /?- 
resonance too low, and the radical ratio — too small : whilst, if the 
intermediate partial is very weak, all these results will be precisely 
reversed. 
The following table contains a rough evaluation of the four o 
analyses just given : a common partial has had to be used in three 
cases, and it has been used in each case for its full value in calcu- 
lating both resonances ; and it will be noted at once that, where 
the common partial is strong, the radical ratio is unduly low, and 
vice versa : — 
