62 



UNIVERSITY OK MISSOURI STUDIES 



rule : Find the smallest difference between the larger num- 

 ber of the ratio and any multiple of the smaller number. The 

 table contains a few instances of this class: 



Let me repeat that the above rules do not pretend to 

 represent scientific laws in the strict sense of the word. They 



are stated here chiefly for a practical pur- 

 The use of pose. If the reader who is unfamiliar with 



such laws difference tones will use the above "laws" 



as directions for observation and obtain 

 a first hand knowledge of the phenomena of difference tones, 

 he will be more interested in the theoretical discussions which 

 are to follow, and able to decide for himself in what di- 

 rections the mechanical theory is yet most undeveloped and 

 most wanting in details. 



Let us applv our theory now to the combination of two 

 sinusoids of the relative periods nine and four, that is, of the 



relative frequencies 4 and 9. The com- 

 The combination pound curve, representing the function 

 4 and 9 / 1 x > = 1.99 -4- sin4a- -f- sin9x 



is shown in figure 22. The period is made 

 to begin and to end with the lowest ordinate value of the 

 function, zero, because this has certain technical advantages. 



