the Propagation of Sound. 447 



a known fact that, when a .sound-wave passes through a mass of 

 air, the mass of air oscillates, as a whole, backwards and forwards 

 (within small limits). It will therefore be necessary to explain 

 how this takes place in accordance with the kinetic theory. 

 Taking- the illustrative case of the row of spheres, we have 

 observed that when no wave is passing, each sphere is 1101% 

 mally oscillating backwards and forwards within definite 

 limits ; or all the alternate spheres, or half the row, move 

 forward, whilst the other half moves backwards. We have 

 observed that when a wave passes, each sphere, after it has 

 transferred the increment of velocity foward, returns back- 

 wards with its normal velocity; i. e. the sphere is only affected 

 with the increment of velocity when it moves fomvards, and not 

 when it moves backwards. The sphere therefore makes its 

 forward movement with a greater velocity than its backward 

 movement ; and accordingly the sphere gains more ground at 

 its forward movement than it loses at the backward movement 3 

 and as this occurs at each oscillation of the sphere, and the 

 sphere oscillates a great number of times backwards and for? 

 wards during the passage of the wave, there is a gradual gain 

 of ground by the sphere. The same applies to all the spheres 

 forming the first half of the wave, so that all the spheres 

 affected by the increment of velocity are pushed bodily foiv 

 ward, during the time that the increment of velocity forming 

 the first half of the wave passes. The same considerations 

 apply to the molecules of a mass of air, which are accordingly 

 pushed bodily forward during the time that the first half of a 

 wave of sound passes ; and thus the mass of air oscillates" 

 forward as a whole during the passage of the half-wave. 

 This forward movement of the mass of air is naturally ac- 

 companied by a condensation of the air. 



8. Precisely the same considerations (conversely) apply to 

 the decrement of velocity experienced in the second half of 

 the' wave. The spheres now make their forward movement 

 with a decrement of velocity and their backward movement at 

 their normal velocity; so that their forward movement is made 

 at a less velocity than their backward movement ; and thus 

 (conversely) ground is lost by the spheres, or they are shifted 

 bodily backwards during the time the decrement of velocity 

 forming the second half of the wave passes. The same ap- 

 plies to the molecules of a mass of air, which is accordingly 

 shifted bodily backwards during the passage of the decrement 

 of velocity constituting the second half of the sound-wave ; 

 and thus the mass of air oscillates backwards and forwards 

 during the time the complete w r ave traverses it. By the back-* 

 ward-shifting of the mass of air, a rarefaction ensues. 



