124 THE STUDY OF SPEECH CURVES. 



Only by careful adaptation can such a representation avoid being 

 utterly false. The same coefficient of friction (or suddenness) is used 

 throughout; although this is only an approximation, it brings us far 

 nearer the truth than the clearly false assumption that £ = 0. We can 

 assume that the fundamental T of the analysis arises from the glottal 

 tone Pi, that is, that the element with T coincides with the element P. 

 There may possibly have been some reinforcement by cavity resonance; 

 such a condition will reveal itself in a speech curve by a strong vibration 

 throughout the whole wave — a case that is very rare in the curves I have 

 collected. We can also assume that the main higher tones come from 

 the cavities, and can take one such tone for each maximum as indicated 

 above (p. 80). That is, we assign the centroid for a group such as ^7"^ 

 \T, ^T, etc., to some one cavity element, for example, Qs, etc. 



When the glottal puff is very sharp, it is approximately the effect 

 of an instantaneous impulse and the curve itself is composed practically 

 of the second member of (13). This gives us 



y = R,.e-'^'.sm (^t -q^') + R^.e-'.sm (^t-q/) + . . . (IG) 



for the curve. The analysis gives the results in (15) for which the means 

 are calculated (p. 79), the lowest being assigned to the vibration with Q,, 

 the next to Qi, etc. 



The supposition that the friction in all the cavities is the same has 

 some justification as far as the vowel elements are concerned; the various 

 cavities are parts of a comphcated one— thorax, larynx, phar>'nx, mouth, 

 nose — having walls of flesh, cartilage or bone covered with moist mem- 

 brane. The application to the glottal elements is made also because no 

 better assumption suggests itself. 



