350 r)R- K(knig's researches on 



far these pressures correspond to the values of the ordiuates of the 

 curves. This question, which involves the validity of the entire i)rin- 

 ciple of the wave-siren, can not here be considered in detail. Suffice it 

 to say that for present purposes the results are amply convincing. 



The wave disk (Fig. 3) has been clamped upon the whirling-table, 

 which an assistant sets into rotation at a moderate speed. Dr. Krenig 

 blows first through a small pipe through one of the rows of holes, then 

 through the other. The two low notes sound out separately, just a 

 major tone apart. Then he blows through the ])ipe with a slotted mouth- 

 piece against the waved edge : at ontie you hear the two low notes inter- 

 fering, and making beats. On increasing the sjjeed of rotation the two 

 notes become shrill, and the beats blend into a beat-tone. Notice the 

 pitch of that beat-tone : it is precisely the same as that which he now 

 produces by blowing through the small pipe against the ring of <S holes. 

 With the other wave-disk, having 184 and G4 holes in tlie two primary 

 circles, giving a wave form corresponding to the interval 8: 23, the 

 effects are of the same kind, and when driven at the same speed gives 

 the same beat-tone as the former wave-disk. It will be noted that in 

 each of these two cases the frequency of the beat-tone is neither the 

 difference nor the sum of the frequencies of the two primary tones. 



A final proof, if such were needed, is afforded by an experiment,which 

 though of a striking character, will not necessarily be heard by all per- 

 sons present, being only well heard by those who sit in certain posi- 

 tions. If a shrill tuning-fork is excited by a blow of the steel mallet, 

 and held opposite a tiat wall, part of the waves which it emits strike on 

 the surface, and are reflected. This reflected system of waves, as it 

 passes out into the room, interferes with the direct system. As a result, 

 if the fork, held in the hand, be moved toward the wall or from it, a 

 series of maxima and minima of sound will successively reach an ear 

 situated in space at any point near the line of motion, and will be heard 

 as a series of beats; the rapidity with which they succeed one another 

 being proportional to the velocity of the movement of the fork. The 

 fork Dr. Kcenig is using is ufr„ which gives well marked beats, slow 

 when he moves his arn» slowly, quick when he moves it quickly. There 

 are limits to the speed at which the human arm can be moved, and the 

 quickest speed that he can give to his, fails to make the beats blend to 

 a tone. But if he will take sole, vibrating J A times as fast, and strike 

 it, and move it away from the wall with the fastest speed that his arm 

 will i)ermit, the beats blend into a short low growl, a non-uniform tone 

 of low pitch, but still having true continuity. 



The first portion of my account of Dr. K<enig's researches may then 

 be sutnmarized by saying that in all circumstances where beats, either 

 natural orartilicial, can be produced with sufficient rapidity, they blend 

 to form a beat-tone of a pitch corresponding to their frequency. 



