MECHANICS OF THE INNER EAR 35 



We discussed above the result of a simple back and forth 

 movement of the stirrup. Let us now do the same with a 



more complicated movement. Figure 11 

 Analysis of the represents the new stirrup movement 

 combination which we are going to study. This curve 



2 and 3 is approximately the one represented by the 



equation 

 y = (1 — cos 2x20 + (1 — cos2,r30 ; 

 which justifies us in saying that it represents physically the 

 sum of two tones of the vibration ratio 2 : 3. Let us apply 



Fig. II. The combination 2 and 3. First characteristic phase 



the same graphic method to this case. We have first to trans- 

 plant the part of the curve from the first minimum to the fol- 

 lowing maximum, A to B, into figure 12. Now, when the stirrup 

 reverses its motion, the parts of the partition near the windows 

 begin to be jerked up. Therefore, the curve from the maximum B 

 to the next minimum C has to be turned upside down and then 

 transplanted. The following part of the curve, from C to D, must 

 be transplanted in its original upright position, but placed on the 



