216 BELL SYSTEM TECHNICAL JOURNAL 



stiffness Kj. is included in K^ to simplif\' notation. This leaves (18) 

 and (19) finally: 



= L, ^ + R,H + Gu + K.,q,, (20) 



= Lo^ + Roi. + K.q. - Gi\. (21) 



It should be noted that these equations represent all first order 

 internal reactions of the idealized model of the larynx. The series 

 expansions have been carried out, to show to what approximations 

 these equations hold. It should also be pointed out that the effects 

 of mechanical hysteresis of the parts, which make the relative posi- 

 tions of the parts dependent on the previous history of their motion, 

 have not been considered. A consideration of hysteresis complicates 

 the theory considerably and is ignored for the same reason and with 

 the same justification and limitations that it is ignored in the ele- 

 mentary treatment of electrical circuits containing coils with magnetic 

 material and condensers with electrostatic hysteresis. 



External Reactions of the Trachea and \'ocal Cavith^s on 



THE Larynx 



So far the modifying effect of the trachea and lungs, as well as the 

 upper vocal cavities, on the motion have not been considered. Before 

 using the equations it is necessary to evaluate these reactions and 

 add them in their proper places. 



Imagine a weightless piston fitted into the trachea just below the 

 vocal cords such that the volume of air thus enclosed in the larynx 

 is so small in comparison to that of the trachea and lungs that its 

 compressibility may be neglected. If the vocal cords are held rigid 

 and the plug or piston of air in the glottis is forced inward, a reaction 

 in addition to the resistance and inertia of the glottis will be encoun- 

 tered due to the impeding effect of the trachea piston, which impe- 

 dance is determined by the constants of the lower chambers. If a 

 small force /o act on the trachea, causing a small velocity, to, and 

 we assume linearity of response /o = Zoio where Zo is a constant which 

 may, due to a positive inertia reactance or a stiffness, contributed 

 by air compression in the lungs, involve either a time derivative or 

 integral of displacement. For the present consider it to be a gener- 

 alized impedance operator. Due to the relative incompressibility of 

 the air in the larynx, the volume displaced by the trachea piston is 

 i^So = iiS]. Since also the instantaneous pressure inside the larynx 



