43 2 PHYSIOLOGICAL PHYSICS. [Chap. xxxn. 



direction, and the extent of movement will be greatly 

 increased ; when they are in opposite phases, the par- 

 ticles will be urged in one direction by one and in the 

 opposite by the other, and will, therefore, assume the 

 mean position, very nearly the position of rest ; the 

 movement will be arrested. To apply this to sonorous 

 waves, when the two waves coincide the condensation 

 of one is added to that of the other, with the result of 

 increased condensation, the rarefaction of one to the 

 rarefaction of another, with the result of increased 

 rarefaction. Then, owing to the difference of period, 

 they do not coincide ; gradually the difference increases 

 till the rarefaction of one coincides with the conden- 

 sation of another (they are in opposite phases), and 

 the result is abolition of the sound (interference], 

 After a few more vibrations the condensations again 

 coincide, and there is intensification of the sound. 

 Thus, when two notes are produced by nearly the 

 same number of vibrations, they alternately add to 

 one another and subtract from one another, the sound 

 alternately grows louder and then fades away, to grow 

 loud again, and again fade ; beats are produced. The 

 more nearly alike they are the fewer will be the beats, 

 and the more they differ, within limits, the more fre- 

 quent the beats. The beats, in short, represent the 

 difference between the number of vibrations of the 

 two notes ; so that the number of vibrations of the 

 lower note + the number of beats per second will 

 give the number of vibrations per second of the higher 

 note. 



IMssoiiaiice. This physical phenomenon of 

 interference is found to have a physiological side. 

 When the two notes are very near one another we 

 see the beats are few, and the ear readily distinguishes 

 each separately, when there are no more, for instance, 

 than four to six in a second. When the two notes are 

 farther apart the beats become partly fused by the 



