242 Mr. Willis on the Voivel Sounds, 



organ-pipe. By means of this, we can ascertain the note proper 

 to any cavity, such as the cone Z placed above it in the figure. 

 If this be transferred to the former plane its vowel will be ascer- 

 tained. 



As far as I have tried this, I have always found that any 

 two cavities yielding the identical note when applied to Fig. 12, 

 will impart the same vowel quality to a given reed at Fig. 11, 

 or indeed to any reed, provided the note of the reed be flatter 

 than that of the cavity, according to the principle explained 

 in No. 3*. 



The vowel distances in the first series, that is, those mea- 

 sured from a (No. 1.) are always rather less than those measured, 

 from the center points c, e, &c. This diminution varies with dif- 

 ferent reeds, and appears to be due to some disturbing effect of 

 the reed itself, or the short pipe annexed to it which I have not 

 been enabled as yet to examine so satisfactorily as I could wish. 

 For this reason I have preferred in the following table obtaining 

 the vowel lengths from the second and third series, by bisecting 

 their respective distances from each other measured across c, 

 which appear liable to no such alterations. These lengths, in 

 inches, occupy the third column. For want of a definite notation, 

 I have given in the second column the English word containing 

 the vowel in question. The fourth contains the actual note of 

 the musical scale corresponding to a stopped pipe of the vowel 

 length, supposing O to yield c" which it does as nearly as possible. 

 In effect its length = 4.7 inches which with Bernouilli's correction t 

 gives 4 inches for the length of the pitch pipe, and this will be 

 found to give c". 



* We can now connect the results of Figs, 4 and 5 with those of Fig. 6. If the cavity 

 Z, Fig. 4, be placed on Fig. 12, and the flat board EM slid over its mouth, a scale of 

 notes will be heard. H now any position of LM be taken by which Z is made to yield the 

 same note as a given cylinder, then both will yield the identical vowel upon Fig. 11. 



t Mm. Ac. Par. 1762, p. 46o. Biot, P%s. II. p. 134. 



