522 Dr. R. Konig on the Simultaneous 



holes. Notwithstanding this great difference in the number of 

 the primary impulses which the single periods produced upon 

 these different circles, they all equally, when their number 

 had become sufficiently .great, changed into a note ; and if 

 the circles, following the series from the seventh to the first, 

 were blown upon, they always allowed the deep note in the 

 interchanging series of the fourth and fifth to be clearly and 

 loudly heard beside the constantly unchanging high note. 



Although, therefore, such series of isolated impulses of 

 periodically changing intensity show a great likeness to clangs 

 producing beats (with regard to the possibility of the single 

 maxima of intensity changing to a note), they are still very 

 different from the latter. If, for example, a series of 96 iso- 

 chronous impulses increasing and decreasing sixteen times in 

 intensity imitates very closely the clang of two notes which allow 

 16 beats to be heard, the two primary notes should be percep- 

 tible which form this simultaneous sound — in this case 88 and 

 104, two notes in the interval 11 : 13 ; but in fact we cannot 

 hear them. The reason of this may certainly be looked for in 

 the fact that two notes near unison, whose number of vibra- 

 tions are a and b, periodically exhibit when sounded together an 



increase and decrease of vibrations of about , but that at 



z 



the change from one period to another a change of signs 

 takes place, so that the maxima of compression of the middle 

 vibrations are only isochronous in the imperfect periods, 

 while at the perfect periods the maxima of dilatation take their 

 place. 



I have endeavoured in two different ways, by means of 

 primary impulses^ approximately to obtain this result, and 

 first by producing the resultant compressions of all the fol- 

 lowing vibrations of the clang on the same circle of the disk 

 of a siren through holes of appropriate size. The clang of 

 two notes of 80 and 96 double vibrations produces a note of 



— = 88 vibrations, increasing and decreasing in intensity 



16 times ; and at each change from one beat to another the 

 change of signs causes the maximum of compression of the first 

 vibration of the following undulation to vary from the maximum 

 of compression of the last vibration of the preceding undulation 

 by half a vibration. I therefore divided the circle into 176 

 parts, and in parts 1, 3, 5, 7, and 9 bored five holes of different 

 sizes, the same thing in parts 12, 14, 16, 18, and 20, again in 

 parts 23, 25, 27, 29, and 31, and so on. If now a circle of 

 holes was blown upon through a tube of the diameter of the 



