96 UNIVERSITY OF MISSOURI STUDIES 



time from B to C would have to be made room for by the third 

 and fourth sections, which, then, by necessity would extend 

 farther to the right than in proportion to the stirrup movement 

 from B to C. To take this into account would extraordinarily 

 complicate the graphic representation without offering, at 

 present, a correspondingly great advantage. This additional 

 extension of the third and fourth sections to the right could 

 be but slight since the amount of fluid in question would be 

 but slight. This becomes clear from a glance at figure 27. 

 We have learnt from this figure that some pressure added to 

 a given pressure does not cause a proportional, but a much 

 smaller increment to be added to the previous displacement of 

 the partition; and thus the amount of fluid in question may be 

 entirely neglected without depriving us of the right to regard 

 our representation as an approximation to the actual positions 

 of the partition sections. 



We may, then, under the third, fourth, and sixth pro- 

 visional assumptions, regard the relative intensities of the 

 tones as proportional to the ordinate dif- 

 The relative ferences in the table belonging to figure 



intensities of 26. We find in the table the value 1473 as 



2 and 1 expressing the ordinate difference of C and 



D, the value 1125 of D and E, 1125 

 of E and F, and 1473 of F and G, the sum of these last three being 

 372i3. Therefore, under the above simplifying assumptions, 

 the relative intensity of the tone 2 compared with 1 is about 

 as fifteen to thirty-seven. 



Let us now apply our theory to the ratio of the vibration 

 rates 5 : 8. The curve in figure 30 represents the function 

 f{x) ^= sin5;ir -\- sin8;t:. 



The table below contains all the abscissa and ordinate 



_, , . values of the maxima and minima as well 



The combma- .... 



tion 5 and 8 ^^ °^ inflection points of the curve. 



Equal ampli- The inflection points are computed as the 



tudes of stirrup maxima and minima of the first derivative 



movement curve, represented by the function 



