MECHANICS OF THE INNER EAR 37 



nerve ends between x\ and x 3 receive one shock. The nerve 

 ends located farther towards the apex of the cochlea do not 

 receive any stimulation and do not, therefore, concern us. How 

 many tones should we expect then to hear in this case? The 

 answer is as easy as simple: Three different tones, since shocks 

 of three different frequencies are received by the several nerve 

 ends. And the musical relationship, the pitch, as we say, of 

 these tones is determined by the relative frequencies found, 

 which are 3 and 2 and 1. The relative intensity of these tones 

 is to be measured, in accordance with our remarks in the pre- 

 ceding paragraph, by the relative lengths x Q x„ x : x s , and 

 x,x r 



A movement of the stirrup, not probably exactly like, 



but similar to the one just discussed could be produced by 



sounding simultaneously with approxi- 



_ . matelv equal intensities two tuning forks 



Two important ; , .,.,,. 



facts- Sound representing the ratio of vibration rates 



analysis and 3 :2 - ^ ' s weu known that we hear in such 



production of a case three different tones, 3 and 2, which 



subjective we may call "objective" or primary tones, 



difference tones and j which we may call a "subjective" or 

 difference tone. Some further facts con- 

 cerning such subjective or difference tones will be mentioned 

 subsequently for those readers who are not familiar with the 

 conditions under which they make their appearance. The 

 appropriateness of calling the subjective tones in question 

 "difference tones" will then become apparent. The fact that 

 our theory of the function of the inner ear and actual obser- 

 vation in this case agree so nicely, is highly satisfactory to 

 us and ought to encourage us to proceed further in applying 

 the theory to other special cases of movements of the stirrup. 

 Let us keep in mind that our theory thus far has explained in 

 a special case two most fundamental observations: 1. That 

 our organ of hearing is capable of analyzing a compound 



