844 



DR. KCENIG S RESEARCHES ON 



beats will both be present. We shall have four tones altogether — two 

 primary tones and two beat tones. The forks 1 select are ut^ = 2048, 

 as before, and a fork which is tuned to vibrate exactly 11 times as 

 rapidly at ut^ — it is the eleventh harmonic of that note, but does not cor- 

 respond precisely to any note of the diatonic scale. It has 2816 vibra- 

 tions, and is related to ute as 11 : 8. The two remainders, will now be 

 768 and 1280, which are the respective frequencies of sol^, and m^5. 

 Dr. Kceiiig will first sound those notes on two other forks, that you 

 may know beforehand what to listen for. Now, on striking the two 

 shrill forks in rapid succession, the two beat tones are heard. 



If I select, instead of the eleventh harmonic, the thirteenth harmonic 

 of wf 3, vibrating 3328 times in the second, to be sounded along with 

 nta, the same two beat tones will be produced as in the preceding case ; 

 but m?5 = 1280 is now the inferior one, corresponding to the positive re- 

 mainder, whilst sok = 't^^^ is the superior tone, corresponding to the 

 negative remainder. It is certainly a striking corroboration of Dr. 

 Koenig's view that the beat tones actually heard in these last two ex- 

 periments should come out precisely alike, though on the old view, 

 that the combinational tones were simply the summational and differ- 

 ential tones, one would have been led to expect the sounds in the two 

 experiments to be quite different. 



One other example I will give you of a beat tone belonging to the 

 second i)eriod. The two primary notes are given by the forks ut^ = 

 1024 and rCf, =2304. The beat tone which you hear is uf^ = 250, which 

 corresponds to the positive remainder. 



It will be convenient to draw up in tabular form the results just 

 obtained. These maybe considered as abbreviations of the much more 

 extended tables drawn up by Dr. Kcenig, which hang npon llie walls, 

 and which are to be found in his book, " Quelques Experiences 

 d'Acoustique." 



Table II. — Sounds of primanj heats. 



