THE SENSE OF HEARING. 147 



have no relation to our auditory organ, could yield no sound ; we should 

 see, but not hear them. The sound, indeed, as we before remarked, pro- 

 ceeds not as such from the string, but is produced indirectly by the string 

 through the action of its vibrations upon the organism of the ear ; and for this 

 mediate or indirect action there is needed a material medium with movable 

 particles, a conductor capable of propagating the vibrations of the string by 

 corresponding movements of its own constituent parts. How this propagation 

 is effected by the air is easily shown. We must conceive the air, surrounding 

 the string and filling the space between that and our ear, to be composed of in- 

 finitely small particles movable among one another, and we will suppose the ear 

 to be placed on the side next to c'. If the string, now, be supposed to oscillate 

 from the position a c" b towards a c' h, it drives before it the particles of air next 

 to it; it is evident, too, that, were the air a firm and cohesive body, the string 

 could not execute its movement unless it propelled in a mass the whole of the 

 air lying in its passage. But as the air is an elastic compressible body, the string, 

 instead of driving before it at once the entire mass, presses upon and condenses 

 only the parts immediately next to it, these in turn press upon the neighboring 

 parts, and thus the impulse is progressively propagated from one portion of air 

 to another. When the string has arrived at its limitary position a c' h, the dis- 

 placement of successive portions of air and the compression which attends it 

 have been propagated to a certain distance, so that the air to that extent is in a 

 compressed state, forming a tvave of condensation. Did the string remain mo- 

 tionless ai » c' h, then, while the movement of propagation was still continued 

 among the particles at the further end of the wave, those nearest to the stiing 

 would come to a state of rest, then the next, and so on, till finally all the particles 

 in the first wave would cease to move, the last of them precisely at the moment 

 when the condensation on the further side has reached the limit to which it was 

 carried during tlie forward movement of the string — that is to say, when the 

 wave of condensation has reached its full length. But the string stops not at 

 its greatest convexity; it springs back by virtue of its elasticity, and again 

 passing the line of equilibrium, forms just such a curvature as before, occupying 

 the second limitary position a c" b During this recoil there occurs in the 

 stratum of air lying to the left of the string, and which had been condensed by 

 its forward movement, the opposite condition of rarefaction, because a void space 

 is left behind the returning string which the air must occupy. The several 

 particles of air follow the string, first, those immediately contiguous to it, then 

 in succession those more remote, so that, as is readily seen, the direction of the 

 movement which the particles now execute is the opposite of that Avhicii had 

 taken place on the advance of the string, while the direction in which this move- 

 ment is propagated from particle to particle is the same. When the string has 

 reached the position a c" b, the propagated displacement of the particles and the 

 rarefaction attending it have extended through a certain tract on the same side 

 with the previous condensation; the air within this tract is in a rarefied state, 

 forming a wave of rarefaction, which, succeeding the wave of condensation, ad- 

 vances, like that, from space to space, and to the same distance. In the mean 

 time, the string again springs forward, again compresses the particles of air 

 before it, and in this way the wave of rarefaction is replaced by a new wave of 

 condensation. Thus these waves proceed from the string to the ear in constant 

 succession and regular interchange, alternating as often in a definite time as the 

 string vibrates from side to side; and a particular particle of air, whatever its 

 distance from the string, continues, as long as the string vibrates, to oscillate 

 forward and backward according as it happens to be in a wave of condensation 

 or one of rarefaction. We shall only add that the velocity with which the dis- 

 placement of the particles of air is propagated always remains the same, no 

 matter how great the number of the vibrations of the string, or how wide its ex- 

 cursions ; and that the magnitude of the displacement of each several particle 



