! S3 



iTil 



the Propagation of Sound. 445 



simultaneously in the opposite direction, the balls continually 

 rebounding from each other and maintaining an equilibrium 

 by their collisions. In the annexed diagram I, II, III, IV, V, 

 may serve to illustrate the different j^ 

 phases of the movement. The balls 1, r 

 2, 3, 4 may be supposed to be controlled 

 by the two plane surfaces A and B, I 

 from which the end ones rebound, the _[[j~ 

 whole row thus maintaining an equili- 

 brium. Each ball simply performs an -*- V 

 oscillatory movement within the limits ~V 

 of space bounded by the dotted lines 

 in the diagram — all the odd balls (or half the row) moving 

 simultaneously in one direction, whilst all the even balls (or 

 the other half of the row) move simultaneously in the reverse 

 direction. To assume the balls to move simultaneously merely 

 serves to simplify the conceptions without altering in the least 

 the true conditions of the case. In the actual fact, of course, 

 in the case of a gas, some of the molecules would be moving 

 obliquely to such an imaginary line ; but since the molecules 

 maintain an equilibrium by their collisions, it cannot alter the 

 case in the least if we assume for simplicity the motions to be 

 straight; or, indeed, the resolved component of the motions in 

 the direction of the line can be taken. The row of colliding 

 balls, like the colliding molecules of a gas, thus maintain a 

 perfect equilibrium, the row not tending bodily as a wiiole to 

 be propelled in any particular direction, but simply tending 

 to open out or expand, and to separate the controlling sur- 

 faces A and B. The oscillatory form of motion of the balls 

 fulfils that condition, that the row of balls, as a whole, main- 

 tains a fixed position while its parts are in motion, just as 

 a portion of a gas maintains a fixed position while its parts 

 are in motion. 



5. To illustrate now the way a wave is propagated by a 

 gas, we may suppose that a forward and backward motion 

 is communicated to the plane A in the form of a vibratory 

 motion ; also the plane B may be supposed removed and the 

 row of spheres extended indefinitely from the plane A, the 

 movement of vibration of the plane being also supposed slow 

 compared with the normal velocity of the spheres. In that 

 case the sphere 1 would strike against the plane A a number 

 of times during one forward swing of the plane. On the 

 commencement of the first forward swing of the plane, the 

 plane advancing towards the sphere 1, the latter receives a 

 small increment of Velocity, which it transfers by collision 

 to sphere 2, the two spheres simply exchanging velocities 



