104 BELL SYSTEM TECHNICAL JOURNAL 



ductivity of the circle is its diameter; we may take the conductivity of 

 the ellipse as roughly equal to that of the circle of equal area.) In 

 some cases, however (as for example, long c), where teeth and lips 

 are nearly closed together, the conductivity is certainly less than it 

 appears on merely viewing the opening between the lips; hence a 

 smaller value must be used. The conductivity of the inner orifice is 

 even more uncertain, but in getting at this we are aided to some extent 

 b}^ a theoretical principle which will be given later. The diagrams at 

 least offer some guidance in placing the various conductivities in thei 

 order of relative magnitude. 



The most serious lack of data relates to the volumes Fi and V^. I 

 have made attempts to fill the mouth with water, and then measure 

 this volumetrically, but of course this gives no hint of the volume of the 

 pharynx. From these experiments, and other considerations, it seems 

 that for an adult male the total volume Vi -\- V2 should be something 

 over 100 cm.^ and nearly constant for all the vowel sounds. That is to 

 say, the change in V\ and F2 consists largely in a shift of volume from 

 Vi to Vi (or vice versa) by the movement of the tongue; a proposition 

 not so unreasonable anatomically, because competent advice states 

 that a muscle, in taking its various shapes, preserves the same volume. 

 Finally one would expect a somewhat larger total volume with the 

 mouth wide open, for certain sounds, but this is partially compensated 

 by the flattening of the cheeks in that position. 



For the purposes of this study we shall consider V\ + Vi = 120 cm.^ 

 as one of the given data. But it may be stated in passing that these 

 volumes should be much more accurately determined, preferably by 

 anatomical experts. 



It would be interesting to compare the results we shall obtain, for 

 the dimensions of the resonator systems, with the actual data of Paget's 

 resonators. But, on account of the four variables involved {Ki, K2, 

 V\, V»), there is no solution of a given case that is unique — that is to 

 say, there are several combinations of different elements possible which 

 will produce a given pair of natural frequencies. Hence such com- 

 parisons would often tell us little. Besides, in most cases it is im- 

 possible, from the figures given by Paget, to determine the sizes of his 

 resonators, though their shapes are well shown in his drawings. Paget 

 sometimes frankly imitated the structure of the mouth-pharynx 

 system — not necessarily to scale — but sometimes, as in producing 

 double (uncoupled) resonance by resonators in parallel, his models bore 

 no relation to the structure of the natural system. 



