MECHANICS OF THE INNER EAR 3 1 



line), since this direction, according to definition, represents 

 the time. Our first crossing of a curve (in e) means a jerk 

 down; the next crossing (in /) a jerk up; and so forth. That 

 is, the odd crossings mean each a jerk down, the even crossings 

 each a jerk up. The time intervals can then be measured 

 with a rule. We find in this special case that the intervals are 

 all equal. We have thus graphically represented the exact 

 movement of the partition in a case where the movement of 

 the stirrup is of the form of a sinusoid. The same graphic 

 representation is applicable to any given curve, however com- 

 plicated it may appear. This method has universal validity. 

 We shall soon convince ourselves of its importance for the 

 analysis of a complicated curve. 



We can easily learn from the graphic representation be- 

 fore us that under the assumptions provisionally made the 

 stimulation of each nerve ending can 



hardly be influenced by the form of the 

 What movement J . .*.*.• 



c .. .• stirrup curve, that is, whether this curve 



produces the ' s a sinusoid, or made up of straight lines 



sensation of a connecting the maxima and minima, or of 



single tone (free any other shape, provided the maxima and 

 from overtones) ? m j n j ma re main unaltered. Let us sup- 

 pose that each "down" means a shock to 

 the nerve end and that the "ups" are indifferent as to ner- 

 vous excitation. We see immediately (Fig. 10) that the time 

 interval between two shocks at any point of the partition 

 must be exactly the same, since each down curve would be 

 exactly like any other down curve, whatever the shape of 

 the up curve. (This result would be the same if the "ups" 

 meant excitation of the nerve end and the "downs" were in- 

 different.) That is, the particular shape of the curve rep- 

 resenting the movement of the stirrup, has no significance 

 for the question whether a single tone will be heard or not. 

 If all the down curves are identical, a single tone only is 



