288 LECTURE XXXI. 



suspends the bell being supported by some very soft substance, such as 

 cork or wool. As the air is gradually admitted, the sound becomes stronger 

 and stronger, although it is still much weakened by the interposition of 

 the glass : not that glass is in itself a bad conductor of sound, but the 

 change of the medium of communication from air to glass, and again from 

 glass to air, occasions a great diminution of its intensity. It is perhaps on 

 account of the apparent facility with which sound is transmitted by air, 

 that the doctrine of acustics has been usually considered as immediately 

 dependent on pneumatics, although it belongs as much to the theory of the 

 mechanics of solid bodies as to that of hydrodynamics. 



A certain time is always required for the transmission of an impulse 

 through a material substance, even through such substances as appear to 

 be the hardest and the least compressible. It is demonstrable that all 

 minute impulses are conveyed through any homogeneous elastic medium, 

 whether solid or fluid, with uniform velocity, which is always equal to 

 that which a heavy body would acquire by falling through half the height 

 of the modulus of elasticity, that is, in the case of the air, half the height 

 of the atmosphere, supposed to be of equal density ; so that the velocity of 

 sound passing through an atmosphere of a uniform elastic fluid must be 

 the same with that of a wave moving on its surface. In order to form a 

 distinct idea of the manner in which sound is propagated through an 

 elastic substance, we must first consider the motion of a single particle, 

 which, in the case of a noise, is pushed forwards, and then either remains 

 stationary, or returns back to its original situation ; but in the case of a 

 musical sound, is continually moved backwards and forwards, with a 

 velocity always varying, and varying by different 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 first suppose for the sake of sim- 

 plicity, a single series of particles to be placed only in the same line with 

 the direction of the motion. It is obvious that if these particles were ab- 

 solutely 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 par- 

 ticles 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 undulation, 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 any time may be represented by supposing 

 it to mark its path on a surface sliding uniformly along in a transverse dJ- 

 rection. Thus, if we fix a small pencil in a vibrating rod, and draw a 

 sheet of paper along, against the point of the pencil, an undulated line will 



