110 BELL SYSTEM TECHNICAL JOURNAL 



dilemma here, as to which pair of solutions (5 or 5a) to apply, since 

 solutions are possible in which the two cavities Vi and Fo are of compa- 

 rable size in this case. It is nearly certain, however, that the front 

 cavity, Vi, is greater than Fo in this case, but it is not certain that the 

 highest possible value of ^ (m = 1) is the one to use. A compromise 

 was made, setting ix = .80, and using equations (5a) for the solution. 

 We shall see later that a resonator built according to these specifica- 

 tions performs sufficiently well to justify these assumptions. With 

 this sound we have finished with equations (6) and (5a) and for the 

 last time we have Vi > V^. 



For the last 5 sounds (short e to long e) the maximum possible 

 coupling factors range from 1.75 to 9.4; it has been found advisable to 

 shade these and use factors ranging from 1.25 to 5.0. A choice now 

 has to be made between solutions (5) and (5a) ; and since the tongue 

 comes so far forward in these cases, we adopt at once the first solution, 

 according to (5), which leads to the relation Fi < V-z in all these cases. 



Discussion of the Results 



The calculated results are shown in the chart, Fig. 5. Because of the 

 speculative character of some of the assumptions made it is reasonable 

 to call attention only to certain outstanding features of the chart. 

 Among the first seven (loosely-coupled) systems the sound u (as in 

 put), if placed second, would seem definitely out of order, because of the 

 magnitude of the coupling factor, or (what is the same thing) the 

 greater separation of the characteristic frequencies. There is no es- 

 cape from the larger inner orifice for this system, and the effect which 

 it produces. This sound simply does not conform to the habits of its 

 (assumed) neighbors; otherwise the first seven sounds form a coherent 

 group. In classifying short u Paget takes the dilemma by the horns, 

 and places \t first, that is, preceding all the other sounds of this group. 

 This arrangement is adopted in Fig. 5. 



There will be noticed in the chart a tendency to expand the total 

 volume, Fi + F2, for the rounder and more open sounds. This is in 

 a deliberate attempt to allow for the effect of opening the mouth a 

 little wider in these cases. 



The last 5 sounds (from short e to long e) form a fairly coherent 

 group, except for the non-conforming member er. Paget places er 

 preceding short a in the series; it seems to the writer a hybrid of the 

 short e (or long a) and the r sound, but its low frequency resonance 

 (ca. 500) requires a large volume for either Fi or F2, and this can only 

 be back of the tongue ( F2) because of the contraction of Vi when the 

 tip of the tongue is raised for the r sound. If we let iCx = 1.5 cm., and 



