374 Dynamic Theory. 



square of its position multiplied by the number of spokes in the first 

 globe. Thus, if the first globe has 100, the second will have 400, the 

 third 900, the fourth 1,600, the fifth 2,500, &c. Now, imagine a blow 

 at the center of this system that is powerful enough to drive endwise all 

 the spokes in the first sphere a, distance of one inch. The force of the 

 blow is transferred from the first to the second tier. Each spoke in the 

 first tier having to move four spokes, in the second it is obvious the 

 force delivered to each spoke of the second tier will be only J as power- 

 ful as the original impact on the first spokes, and the distance they will 

 be moved, therefore, will be only ^ as great, or ^ of an inch. As be- 

 tween the second and third globes, the force of the movement of four 

 spokes in the former will be expended in moving nine in the latter, and 

 their endwise movement will be therefore | as far as that of the second 

 tier, or | of an inch. Nine spokes of the third tier transfer their en- 

 ergy of motion to sixteen in the fourth, so that the sixteen move -j^ of i, 

 or - 1 - of an inch, &c. The distance that these vibratory spokes thus 

 move is called the amplitude of the vibration, and this amplitude, trans- 

 lated in our auditory sense gives the sensation of loudness. It is plain 

 how this amplitude must become rapidly less as the distance from the 

 sonorous body increases. In fact, it diminishes in proportion to the 

 Square of the distance, and consequently the loudness of the sound 

 diminishes in the same ratio, and dies away with distance till the ampli- 

 tudes are too diminished to produce sensation. Obviously the end of 

 the spoke next the center will be driven further than the end away 

 from the center, the elasticity of the material allowing the spoke to 

 shorten. Thus, in the above example the spokes in the sphere No. 1 

 would shorten f of an inch, in No. 2 they would 'shorten the difference 

 between ^ and i of an inch, or j^ of an inch. In No. 3 they would 

 shorten |- =^ of an inch. IH No. 4, ^_^=^- o , &c. 



If the spokes of the sphere should be composed of any other sub- 

 stance than air as water, wood or iron, or partly of one substance and 

 partly of another, the same principles govern the propagation of the 

 vibrations, each substance, however, giving them the length and ampli- 

 tude due to its peculiar molecular constitution. It is evident that the 

 amplitude of the sound will be the same at the end of the first spoke in 

 all conductors, regardless of the material of the conductor. Therefore 

 a sound will be heard through steel at- a distance of 124 feet, as loud 

 as through air a distance of 8. 3 feet. The sound of a blow ( of the 

 pitch of C , say ) struck on a railroad track, will be conveyed to a lis- 

 tener standing beside the track at a distance of say 1090 feet, by two 

 mediums, the air and the steel rail. The sound by the air will be a 

 whole second in coming, and will have vibrated 132 times, and the 

 loudness of the sound will be reduced to ~ part of what it was at the 



