216 



Professor Silvanus P. Thompson 



[June 13, 



Oue other example I will give you of a beat-tone belonging to 

 the second period. The two primary notes are given by the forks 

 ut^ = 1024 and re^ = 2304. The beat-tone which you hear is 

 uf.. = 256, which corresponds to the positive remainder. 



I may here mention that a mathematical investigation,* which 

 only appeared a month ago from the pen of Professor W. Voigt, 

 entirely confirms the views of Dr. Koenig as to the non-existence of 

 the supposed summational tones, and the existence of those which 

 accord with the two remainders. 



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

 obtained. These may be considered as abbreviations of the much 

 more extended tables drawn up by Dr. Koenig, which hang upon the 

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



d'Acoustique.' 



TABLE II. 



Sounds of Pkimary Beats. 



Primary Tones. 



Uts 

 1024 



2304 



Eatio. 



8 : 9 

 8 : 15 

 8 : 12 

 8 : 11 

 8 : 13 



4 : 9 



Inferior Beat-tone. Superior Beat-tone. 



256 



1024 



i 768 

 ( mi 



in.. 



.280 



256 



So far we have been dealing with primary beats and beat- tones ; 

 but there are also secondary beats and secondary beat-tones, which 

 are produced by the interference of primary beat-tones. An example 

 of a secondary beat is afforded by the following experiment. 

 Recurring to the preceding table of experiments, it may be observed 

 that when the two shrill notes uIq, sol^, giving the interval of the 

 fifth, are sounded together, the inferior and superior beat-tones are 

 both present, and of the same pitch. If, now, one of the two forks 

 is lightly loaded with pellets of wax to put it out of adjustment, we 



♦ " Ueber den Zusammenklaiig zweier einfacher Tone." ' Gcttinger Nach- 

 richten,' No. 5, 1890. 



