34 UNIVERSITY OF MISSOURI STUDIES 



We can measure the length of that part of the partition 

 which is jerked up and down, only by the aid of our knowledge 

 (if we have any) of the movement of the 

 Another difficulty ^^'''''^P- ^ow, the reader will recall among 

 in the theoretical o^'^ provisional assumptions the one that 

 determination of the width of the partition at any point near 

 tone intensity the windows is the same as at any point 



far away from them. But the anatomists 

 tell us that this assumption is incorrect ; that the partition is 

 about twelve (or more) times as wide at the end 

 as near the windows. Nevertheless we shall provisionally 

 make the assumption of proportionality between any 

 length of the partition being jerked up and down and 

 the extent of the movement of the stirrup which causes 

 the movement of this piece of the partition, in order to under- 

 stand first a simpler, though imaginary, case and to proceed 

 gradually to a comprehension of the actual, rather compli- 

 cated function of the partition. Let us be aware, however, 

 that, having thus simplified the actual conditions, we cannot 

 expect to find a perfect, but only an approximate harmony 

 between the results of a theoretical analysis and the direct 

 observations of an actual sound analysis by the ear. We 

 may find, indeed, with respect to tone intensity, rather se- 

 rious disagreements between the facts and the theory. But 

 these disagreements will disappear as soon as the theory takes 

 account of what, for simplicity's sake, we provisionally neg- 

 lect. 



Making the two provisional assumptions just mentioned, 

 we can theoretically measure the intensity of a tone sensa- 

 tion by the total length of that part of the 

 Tone intensity partition the nerve ends of which are ex- 



in our graphic cited with one definite frequency. In our 



representation graphic representation (Fig. 10) the inten- 



sity can then be measured by the vertical 

 distance between the horizontal coordinate and the top of the 

 curves which represent the down and up jerks. 



