68 UNIVERSITY OF MISSOURI STUDIES 



The thirty-fourth section of the partition moves down at 

 D, and up again at O ; down at P, and up again at S. That 

 is, the nerve ends of this section receive 

 Do we hear any two stimuli during the period. We may 

 difference tones? expect to hear, therefore, the tone 2 of the 

 relative intensity one. The three follow- 

 ing sections of the partition move down at H and up again 

 at O. The nerve ends on these sections receive, therefore, 

 one stimulus during the period. The next two sections move 

 down at H and up again at S. The nerve ends here receive 

 one stimulus during the period. The fortieth section moves 

 down at L and up again at S. The nerve ends here receive 

 one stimulus during the period. We must hear, then, the 

 tone 1 of the relative intensity six. The tones 2 (weak) and 1 

 (strong) are the only difference tones in this case which we 

 can derive from our theory with some degree of certainty. 



Summarizing now the results derived from our represen- 

 tation of the movements of the partition in the case of the 

 ratio 4:9, we find that we must expect to 

 The relative hear the tones 9, 4. 2 and 1, with the rel- 



intensities ative intensities nine, twenty-two, one and 



compared six : leaving out of discussion the doubt- 



ful sensation of the intensity two which 

 may be conveyed to our mind by the tenth and eleventh sec- 

 tions. Now, it is quite natural to ask the question whether 

 we hear these tones with just these relative intensities. Un- 

 fortunately, no exact answer to this question is possible, 

 because this matter, owing to technical difficulties and other 

 circumstances, has never been experimentally subjected to 

 accurate measurement. It is known, however — what also ap- 

 pears in the above statement of our results — that in a com- 

 bination of two tones the higher one loses in intensity, com- 

 pared with the lower one. Yet it is doubtful if this loss in 

 intensity is so great as the number nine indicates, compared 



