428 PHYSIOLOGICAL PHYSICS. [Chap, xxxii. 



concentric circles, the outer circle containing eighteen 

 holes, the next twelve, the next ten, and the inner- 

 most eight. By means of four stops any one of these 

 circles of holes may be opened or closed at pleasure. 

 Thus only the set of eighteen may be open, or the set 

 of twelve, and of ten, or all of them, may be opened, 

 which would mean forty-eight shocks to the air with 

 each revolution. The rotating disc has, of course, 

 a hole for each one of the lid. This improvement in 

 the siren is due to Dove. Helmholtz takes two such 

 boxes, and fixes one a little way above the other, 

 a.nd upside clown so that they face one another. 

 Both may have the same number of holes in the lids, 

 arranged with stops in the same way ; but in Helm- 

 holtz's siren the upper box has four concentric series 

 of sixteen, fifteen, twelve, and nine holes respectively. 

 The rotating disc of both is on one axis, so that if one 

 rotates, the other does also. The inlet tube of the 

 upper box is bent down, that of the lower one bent 

 up ; thus they meet one another in a common pipe to 

 which the tube from the bellows is attached, and so 

 both can be worked simultaneously and with the 

 same blast. Of course, by stopping all the holes of 

 one box only one may be worked at a time. Now with 

 such a siren it is possible to make one box produce 

 in the same time double the number of vibrations of 

 the other. In such a case the sound produced by one 

 box is found to be the octave of that produced by 

 the other. An octave is, therefore, a note produced 

 by double the number of vibrations of the note of 

 which it is the octave. Double the number of the 

 vibrations of the octave will produce its octave, or the 

 second octave of the original note, and so on. Again, 

 twelve holes of one box may be opened, and eight of the 

 other, when the two musical notes produced will be 

 perceived by trained ears to be a fifth. The musical 

 interval of a fifth is shown, thus, to be due to two 



