342 DR. K(enig's researches on 



slightly, and then bow it, at oiu;o you hear beats. It was in studying 

 the beats of those hiiiher ])eri()ds that Dr. Ko'nii; made the observation 

 that, whereas the beats of an imperfect unison are heard as alternate 

 silences and sounds, the beats of the (imperfect) higher periods — twelfth 

 tone, double octave, etc. — consist maiidy in variations in the loudness 

 of the lower of the two primary tones, an observation which was inde- 

 pendently made by Mr. Bosanquet, of Oxford. 



Passing from the beats themselves, T approach the question, What 

 becomes of the beats when they occur too rapidly to produce on the 

 ear a discontinuous sensation ? On this matter there have been several 

 contlicting opinions, some holding, with Lagrange and Young, that 

 they blend into a separate tone; others, with von Helmholtz, main- 

 taining that the combinational tones can not be so explained and arise 

 from a different cause. Let it be observed that, even if beat-tones exist, 

 it is quite possible for beats and beat-tones to be simultaneously heard. 

 A similar coexistence of a continuous and a discontinuous sensation 

 is afforded by the familipr experiment of producing a tone by pressing 

 a card against the perii)hery of a rapidly rotating toothed wheel. There 

 is a certain speed at which the individual impulses begin to blend into 

 a continuous low tone, while yet there are distinguishable the discon- 

 tinuous impulses, the degree of distinctness of the two co existing 

 sounds being dependent on the manner in which the card is pressed 

 against the wheel, that is to say, on the nature of the individual im- 

 pulses themselves. The opponents of the view that beats blend into a 

 tone state idainlj- enough that, in their opinion, a mere succession of 

 alternate sounds and silences cannot blend into a tone different from 

 that of the beating tone. Uaving said that the beats can not blend, 

 they then add that they do not blend ; for, say they, the combinational 

 tones are a purely subjective phenomenon. Lastly, they say that even 

 if the beats blend they will not so explain the existence of combinational 

 tones, because the combinational tones have frequencies which do not 

 correspond to the number of the beats. 



In the teeth of all these views and opinions, Dr. Kcenig — without 

 dogmatizing as to how or why it is — emphatically afrirms that beats do 

 produce 6crtY tones; and lie has pursued the matter down to a i)oint that 

 leaves no room for doubting the general truth of the fact. The alleged 

 discrepancy between the freiiuency of the observed combinational tones 

 and that of the beats disappears when closely scrutinized. Those who 

 count the beats by merely taking the difierenee between the frequen- 

 cies of the two i)riniary tones, instead of calculating the two remain- 

 ders, will assuredly find that their numbers do not agree in pitch with 

 the actual sounds heard. But that is the fault of their miscalculation. 

 Those who use harmonium reeds or i)olyi»honic sirens instead of tuning 

 forks to ])roduce their i)rimary tones must not expe(;t from such impure 

 sources to reproduce the effects to be obtained from pure tones. And 

 those who say that the beats calculated truly from the two remainders 



