78 UNIVERSITY OF MISSOURI STUDIES 



which moves up and down four times is therefore 15.86 units. 

 The intensity of the tone 2 is one fluid unit. The length of 

 the partition section corresponding to this fluid unit is 43.8'0^ — 

 42.28c=:.&2. The fluid quantity for the tone 1 is six fluid units. 

 We have to read off from the table the values corresponding 

 to 9+2q-22i+l+6'=40 and to 9+2+22+1=34 fluid units. These 

 values are 45.73 and 42.80. The length of that section of the 

 partition which produces the tone 1 is therefore 2.9® units of 

 the partition. 



The relative intensities of the four tones 9, 4, 2, and 1, 

 would then be, not as nine to twenty-two to one to six, but as 

 24.1 to 15.9 to .5 to 2.9 ; and the tone about 

 The relative which we could not reach a definite con- 



intensities of the elusion would have the relative intensity 

 tones 9, 4, 2, 2.3 instead of two. For the sake of better 



srid 1 comparison let us express the relative in- 



tensities in percentages. The table shows 

 in one column the tone intensities in case we regard the par- 

 tition as of uniform width and in another column the intensi- 

 ties in case we regard the partition as tapering and possess- 

 ing those properties upon which the present computation is 

 based. 



We must not, of course, regard the result found in the 

 second column of intensities as any more final than that in 

 the first column. We have assumed that 

 This result the initial section of the partition tapers 



not final uniformly so that, the initial width being 



w, its width is 6w at a distance of hQw. But 

 we do not know that it tapers just this way. We have further 

 assumed that the areas described by cross-sections of the par- 

 tition in moving from one limit of position to the other, are 

 geometrically similar. But we do not know whether they are 

 or not. We have further assumed that the total movement of 

 the partition in this case extends just to the distance of 45.72w. 



