222 Professor Silvanus P. TJiompson [June 13, 



and 8 : 23. A number of sncli wave-disks corresponding to other 

 intervals lie upon the table ; these two will, however, suffice. In the 

 first of these the curve is that which would be obtained by setting 

 out around the periphery a series of 120 simple sinusoidal waves, 

 and a second set of 64 waves, and then compounding them into one 

 resultant wave. In order to permit of a comparison being made with 

 the simple component sounds, two concentric rings of holes have 

 been also pierced with 120 and 64 holes respectively. Regarding 

 these two numbers as the frequency of two primary tones, there 

 ought to result beats of frequency 8 (being the negative remainder 

 corresponding to the superior beat). An interior set of 8 holes is 

 also pierced, to enable a comparison to be made. To experiment 

 with such wave-disks they are mounted upon a smoothly running 

 whirling-table, and wind from a suitable wind-chest is blown against 

 the waved edge from behind, through a narrow slit set radially. In 

 this way the air-pressures in front of the wave-edge are varied by 

 the rush of air between the teeth. It is a question not yet decided 

 how far these pressures correspond to the values of the ordinates of the 

 curves. This question, which involves the validity of the entire prin- 

 ciple of the wave-siren, cannot 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 sjDeed. I blow 

 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 

 seventh aj)art. Then I blow through the pipe with a slotted 

 mouth-piece against the waved edge ; at once you hear the two low 

 notes interfering, and making beats. On increasing the speed 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 I now produce by blowing through the small pipe against 

 the ring of 8 holes. A\ ith the other wave-disk, having 184 and 64 

 holes in the 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 it 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 persons present, being only well heard by those who sit in 

 certain positions. If a shrill tuning-fork is excited by a blow of the 

 steel mallet, and held opposite a flat 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, interfere 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 



