276 



NATURE 



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ratus on the principle of the wave-siren. Its mode of 

 operation will be best understood by reference to Fig. 

 5, taken by Dr. Kcenig's permission from his work, 

 "Ouelques Experiences d'Acoustique." Upon a strong 

 stage about 4 feet high is mounted a series of 16 brass 

 disks, cut at their edges into sinusoidal wave-forms, all 

 fixed upon a common axis, and capable of being rotated 

 by a band and treadle. The wave-forms cut against the i 

 contours of these 16 disks represent a harmonic series of 

 16 members of decreasing amplitude, there being just 16 

 times as many sinuosities on the largest as on the smallest 

 disk Against the edge of each of these wave-disks wind 

 can be blown by a special mouth-piece in the form of a 

 horizontally-placed slit connected by a tube to a powerful 

 wind-chest mounted upon the stand of the instrument. 

 We have, in fact, here sixtetn simple wave-sirens of dif- 

 ferent pitch all combined together in such a manner that 

 any one of them can be used separately. When the axis 

 is rotated the wave-disks pass in front of the slits through 

 which the wind is blown, and throw the issuing streams 

 of air into vibration. Each wave-disk thus sets up a 

 perfectly simple tone. We have therefore provide I in 

 this instrument a fundamental sound with its fifteen upper 

 partial tones. It is clear that any desired combination 



can be made by opening the appropriate stops on the 

 wind chest. In order to vary at will the phase in which 

 these elementary tones are combined, a very ingenious 

 arrangement is adopted. The brass tubes which ter- 

 minate in the fifteen mouth-pieces are connected by 

 flexible caoutchouc pipes to the wind-chest. The mouth- 

 piece tubes are mounted upon a plate in such a way that 

 they can slide up and down in curved slots concentric 

 with the disks. By the aid of templates cut out in comb- 

 fashion, and screwed to a lever handle, the mouth-pieces, 

 or any set of them, can be displaced at will ; thereby 

 introducing any required difference of phase. Fig. 6 

 shows the way in which the fifteen mouth-piece slits are 

 arranged with respect to the wave-disks ; there being two 

 series along two different radii, eight corresponding to 

 the even members of the series, and seven to the odd 

 members. They are set with the slits each opposite a 

 summit or crest of its wave-disk, so that all the slots are 

 closed simultaneously. This in Kcenig's nomenclature 

 corresponds to a phase of f ; the minimum condensations 

 of all the individual air-waves occurring simultaneously. 



Suppose now it is desired to change the phase in which 

 the waves are compounded, and to make all the maximnm 

 condensations occur simultaneously (i.e. d = 5) : all that 



is necessary is to move the mouth-pieces of the odd series 

 forward to the positions shown in Fig. 7, where all the 

 slits are seen to be opposite hollows of the wave-disks. 

 This is, of course, done by pushing up under the lower 

 series of tubes a comb-like template which moves e:tch 

 through half its own wave-length. 



The template that is used fur causing the difference of 

 phase to become zero, is shown in Fig. 8, attached to the 

 lever-handle. Here the first, or fundamental slit, being 

 always immovable, the fourth, eighth, and twelfth slits 

 will not require to be moved, but the intermediate 

 members will require shifting by {, j, or f of their wave- 

 length, according to their place in the series. When this 

 set of positions is attained, the condensation is increasing 

 simultaneously in all the sixteen waves, and reaches its 

 mean value in all at the same moment. 



The fourth method of placing the slits, so as to produce 

 difference of phase = -J in the combination, is shown in 

 Fig. 9. 



Having thus described the peculiar arrangements for 

 experimenting, we will briefly give Kcenig's principal 

 results. 



If first we take simply the fundamental and its octave 

 together, the total resultant sound has the greatest inten- 

 sity for a = ■;, and at the same time the whole character 

 of the sound becomes somewhat more grave, as if the 

 fundamental tone predominated more. The intensity is 

 least when d = f. If, however, attention is concen- 

 trated on the octave-note while the phase is changed, the 

 intensity of it appears to be about the same for d = \ and 

 </ = |, but weaker in all other positions. 



The compound tones formed only of odd numbers of 

 the harmonic series have always more power and bril- 

 liancy in tone for phase-differences of £ and -|, than for 

 o and h, but the quality for } is always the same as that 

 for J, and the quality for o is always the same as for i. 

 This peculiary corresponds precisely to the peculiarity of 

 the curves (see Fig. 4, b and d), in which the resultant 

 wave-forms are correspondingly identical. 



For compound tones corresponding to the whole series, 

 odd and even, there is, in every case, minimum intensity, 

 brilliancy, and stridence with d = J, and maximum when 

 d = £ ; the phases o and ^ being intermediate. A refer- 

 ence to Fig. 4, a and 6, will here show that the maxima of 



