THEORY OF VIBRATION OF THE LARYNX 217 



is constant on all its walls, including the surface of the trachea piston 

 f^/So = f.'Si. We then have 



f\ = zMn. (22) 



This reaction due to the trachea must be added to those of the glottis 

 given in (20). In like manner if the effective area of the vocal cords 

 is 52 a reaction h must be added to their force equation 



h = zMi,. (23) 



•Jo" 



Due to the steady component of air flow there is a static component 

 of pressure tending to force the cords outward. This is counter to 

 the static Bernoulli term and again, if second order effects of small 

 quantities be neglected, serves only to alter the equilibrium position 

 and may therefore be disregarded here. 



When the glottis plug of air is displaced inward a force is exerted 

 on the vocal cords tending to move them outward which is relieved 

 to a certain extent by a yield of the trachea piston. This force on 

 the vocal cords may be shown by reasoning similar to that above 

 to be 



Zo%i-^\. (24) 



Since this part of the system is linear, the reaction between glottis 

 and vocal cords through this channel is reciprocal so a force is exerted 

 on the glottis when the vocal cords are displaced of 



Zo%|i2. (25) 



It will be noticed that ^i is a variable because of the variation in 

 width of the glottis while vibrating. The effect of this variation in 

 these terms is obviously second order since ii is small and will therefore 

 be neglected. 



The reactions of the upper cavities might be similarly added, but 

 they are apparently relatively small and since they are at present not 

 quantitatively known, are disregarded in the general equations be- 

 cause of the increased complexity. Generally, however, Zo may be 

 thought of as representing the additive effects of both upper and 

 lower chambers. 



The complete force equations of the voice for small vibrations, 



