ON THE PROPAGATION OF SOUND. 3t)9 



wards, and then either remains stationary, or returns back to its original 

 situation ; but in the case of a musical sound, is continually moved back- 

 wards and forwards, with a velocity always varying, and varying by differ, 

 ent degrees, according to the nature or quality of the tone ; for instance, 

 differently in the notes of a bell and of a trumpet. We may lirst suppose for 

 the sake of simplicity, a single scries of particles to be placed only in the same 

 line with the direction of the motion. It is obvious that if these particles were 

 absolutely incompressible, or infinitely elastic, and were also retained in 

 contact with each other by an infinite force of cohesion or of compression, 

 the whole series must move precisely at the same time, as well as in the same 

 manner. But in a substance which is both compressible and extensible or 

 expansible, the motion must occupy a certain time in being propagated to 

 the successive particles on either side, by means of the impulse of the first 

 particle on those which are before it, and by means of the diminution of 

 its pressure on those which are behind ; so that when the sound consists of a 

 series of alternations, the motion of some of the particles will be always in a 

 less advanced state than that of others nearer to its source; while at a greater 

 distance forwards, the particles will be in the opposite stage of the unduktion, 

 and still further on, they will again be moving in the same manner with the 

 first particle, in consequence of the effect of a former vibration. 



The situation of a particle at anytime maybe representedby supposing it to 

 mark its path, on a surface sliding uniformly along in a transverse direction. 

 Thus,if wefix asmall pencil in a vibrating rod, and draw a sheet of paper along, 

 against the point of the pencil, an undulated line will be marked on the paper, 

 and will correctly represent the progress of the vibration. Whatever the na- 

 ture of the sound transmitted through any medium may be, it may be shown that 

 the path thus described will also indicate the situation of the different particles 

 at any one time. The simplest case of the motion of the particles is that in which 

 they observe the same law with the vibration of a pendulum, which is always 

 found opposite to a point supposed to move uniformly in a circle: in this case 

 the path described will be the figure denominated a harmonic curve ; and it may 

 be demonstrated that the force, impelling any particle backwards or forwards, 

 will always be represented by the distance of the particle before or behind its 

 natural place; the greatest condensation and the greatest direct velocity, as 



VOL. I. 3 b 



