130 UNIVERSITY OF MISSOURI STUDIES 



not, is a question which at present must be left entirely open, 

 like so many others, because of lack of experimental data. 



Whenever we have spoken of "amplitudes" we have 

 meant exclusively the amplitudes of stirrup movement. In 

 order to make use of our theory in experi- 

 Sounding bodies "^"^^^ investigations we must remember 

 and stirrup ^^^ ^^'^^ that the stirrup movements result 



movement from movements of the tympanum, trans- 



mitted by a rather complicated system of 

 levers, the auditory ossicles. It is quite probable that the 

 vibratory movements of the stirrup — even when these move- 

 ments are highly complex — are approximately like those re- 

 ceived by the hammer, the ossicle attached to the tympanum. 

 But no one knows as yet how close or remote this approxima- 

 tion is. We certainly have no right to regard this approxima- 

 tion as infinitely close, save by way of a provisional assump- 

 tion. 



The movements of the tympanum result from rhythmical 

 changes of the density of the external air. These density 

 changes, in experimental investigations, are sometimes pro- 

 duced by the vibrations of gaseous bodies, as in labial organ pipes ; 

 more frequently, however, by the vibrations of solid bodies, par- 

 ticularly of tuning forks on resonance boxes. Now, we must not 

 think that by graphically recording — which is a comparatively 

 easy method — the vibrations of a tuning fork, we obtain a record 

 of the exact form of the resulting air waves. It has been 

 experimentally and mathematically proved that the form of 

 the resulting air waves must be more or less different from 

 the form of the vibratory movement of the fork or other solid 

 body. The cause of this alteration of the form is to be found 

 in the fact that the layer of air which adjoins the solid body 

 and therefore directly receives the impulses from that body, 

 is unsymmetric with respect to its elastic properties, because 



