(.'imp. xxxn.] INTERFERENCE OF SOUND. 429 



sounds, one of which is produced by twelve vibrations 

 for every eight of the other, i.e. three for every two, 

 and is expressed thus, -|. In the same way the various 

 relations may be worked out, as shown in the accom- 

 panying list. 



octave, 

 fifth, 

 fourth, 

 major third. 



= minor third, 

 f = major sixth. 

 = minor sixth. 



With the same instrument the lowest C of the ordi- 

 nary pianoforte is determined by Helmholtz as due to 

 thirty-three vibrations per second, the middle C as due 

 to 264 vibrations per second. Taking the ordinary 

 scale, the relations are approximately given as 

 follows : 



CDEFGABC' 



(ut) Do Ee Mi Fa Sol La Si Do' (ut) 



2G4 297 330 352 396 440 495 528 



1 I f f ! f 2 



The upper two lines give the names of the notes, 

 as designated by letters, or the French or Italian 

 names, the tirst line of figures gives approximated 

 the number of vibrations per second, and the last 

 line gives the fraction which expresses the relation of 

 each note to the fundamental note. 



Interference of sound: Beats. By means 

 of the double siren of Helmholtz, another phenomenon 

 may be illustrated. The upper of the two boxes is 

 movable on an axis, and may be turned, by means of 

 a toothed wheel with a handle, either in the direction 

 of the rotating disc, or in the opposite direction. 

 Suppose the disc to be revolving, and the box to be 

 turned in the opposite direction, the holes in the lid 

 of the box will come opposite to the holes in the disc 

 more quickly than if the box were stationary, a 

 slightly greater number of pulses will be given to the 



