352 Prof. Riicker and Mr. Edser on the 



that in some cases the difference-tones of the lower harmonics 

 correspond either to the fundamentals or to some of their upper 

 partials. In the case of the fourth (3 : 4) , however, Konig 

 remarks that the 5th partials would give a difference-tone (5) 

 which could be distinguished from the lower partials, and that 

 the difference-tone of the 7th partials would give the summa- 

 tion-tone. Now we have already proved (Exp. IV.) that the 

 summation- tone produced bj two notes separated by the 

 interval of a fourth (9 : 12) is objective ; and if this is due to 

 the difference-tone of the 7th partials, there seems to be no 

 reason why the difference-tone of the 5th partials should not 

 be objective also, and probably more intense. 



We therefore increased t^e velocity of revolution to 4*27 

 per second, the 9 and 12 rows of holes being opened as before. 

 The frequencies of the two notes were thus 38*43 and 51*24. 

 The pitch was determined by keeping the 12 holes nearly 

 stationary when viewed 51 times a second by aid of the 25*5 

 fork. The first difference-tone was 12*81, and the difference- 

 tone of the 5th partials was 64*05. When the speed corre- 

 sponding to this difference-tone was attained there were occa- 

 sional flickers of the bands, so that it is possible that it has 

 an objective existence. But, on the other hand, the effect 

 was less than that produced by the summation-tone. The 

 bands never disappeared for any considerable length of time, 

 as they did when the fork responded to the summation-tone, 

 and the experiment left no doubt in our minds that the greater 

 effect was produced by the summation-tone. 



Experiment VI. 



The same point was also investigated in another way. If 



the summation-tone of two notes of frequencies p and q 



corresponds to the difference-tone of the nth. partial, we 



must have ■ , 



(p + q) =n(p-q), 



where n is an integer. If, however, the 9 and 16 rows of 

 holes were opened, 



p + q=2b, p — q=7; 



so that the summation-tone could not be produced by partials 

 of the same order. The 10th partial of the higher note 

 beating with the 15th of the lower note (160 — 135 = 25) 

 would indeed have the same frequency as the summation-tone, 

 but it appears to us absurd to suppose that so improbable a 

 combination should produce appreciable results. It is true that 

 lower partials may give beat-tones near to the summation- tone. 



