THEORY OF VIBRATION OF THE LARYNX 213 



In this expression Rq is the resistance measured in the reference 

 position at which point the derivatives are taken, where ii and q- 

 are zero. The experiment mentioned above determines the signs ot 

 the coefficients of q-i and i\ as positive. If the flow were purely lami- 

 nar, i.e. due to viscosity only, the first would be negative and the 



second zero. 



The Reaction F^ 



By definition, £o = RJi, where £o is the force of the lung pressure 

 on the glottis and /i a corresponding linear velocity of fiow of air. 

 If a force Fi slightly greater than Eq act on the glottis and result in 

 a velocity I = h -\- i], 



zh, = ^- («' 



A combination of (7) and (8) constitutes an evaluation of Fi for sub- 

 stitution in the force equation (5). To a first order approximation 

 then : 



/^, =J?,/, + (i?. + /,^)/, + /,^^,.. (9) 



The coefficient of g-^ is dimensionally a stiffness and that of /'i a re- 

 sistance. In what follows they will be denoted by 



F, = RJ, + Rrii + K„q.. (10) 



Glottis Mass (L/) Reactions 



The kinetic energy of the air stream being proportional to the volume 

 integral of the square of the velocity is largely concentrated in the 

 glottis on account of the relatively high velocity at this point. On 

 account of the irregularity in shape and turbulence in the stream it 

 is impracticable to attempt an integration. If the velocity were so 

 small that the turbulence were absent an approximate value of the 

 air mass would be obtained by taking the mass of a cylinder of air 

 having the length of the slit and a diameter equal to its width. This 

 would make the mass L/ proportional to W~, or since the width is 

 proportional to displacement of the vocal cords, to q-i'. Owing, how- 

 ever, to turbulence and other non-linearities, the mass is probably 

 more nearly described as a tongue of air issuing from the glottis, 

 the inertia L/ of which varies as some power function of the width 

 and also of the velocity. - 



- It has been found since experimentally that the mass reaction is very nearly 

 that of a cylinder as described but reduced somewhat in diameter due to viscous 

 or turbulent drag at the tips of tiie "socal cords. 



