SECT. XVII. BELLS HARMONICS. 147 



interior surface of the tube are perfectly similar to those in the 

 exterior, but they occupy intermediate positions. If a small 

 ivory ball be put within the tube, it will follow these nodal lines 

 when the tube is made to revolve on its axis. 



All solids which ring when struck, such as bells, drinking 

 glasses, gongs, &c., have their shape momentarily and forcibly 

 changed by the blow, and from their elasticity, or tendency to 

 resume their natural form, a series of undulations take place, 

 owing to the alternate condensations and rarefactions of the 

 particles of solid matter. These have also their harmonic tones, 

 and consequently nodes. Indeed, generally, when a rigid system 

 of any form whatever vibrates either transversely or longitudin- 

 ally, it divides itself into a certain number of parts which per- 

 form their vibrations without disturbing one another. These 

 parts are at every instant in alternate states of undulation ; and, 

 as the points or lines where they join partake of both, they 

 remain at rest, because the opposing motions destroy one 

 another. 



The air, notwithstanding its rarity, is capable of transmitting 

 its undulations when in contact with a body susceptible of 

 admitting and exciting them. It is thus that sympathetic undu- 

 lations are excited by a body vibrating near insulated tended 

 strings, capable of following its undulations, either by vibrating 

 entire, or by separating themselves into their harmonic divi- 

 sions. If two chords equally stretched, of which one is twice or 

 three times longer than the other, be placed side by side, and if 

 the shorter be sounded, its vibrations will be communicated by 

 the air to the other, which will be thrown into such a state of 

 vibration that it will be spontaneously divided into segments 

 equal in length to the shorter string. When a tuning-fork 

 receives a blow and is made to rest upon a piano-forte during its 

 vibration, every string which, either by its natural length or by 

 its spontaneous subdivisions, is capable of executing correspond- 

 ing vibrations, responds in a sympathetic note. The same effect 

 will be produced by the stroke of a bell near a piano or harp. 

 Some one or other of the notes of an organ are generally in 

 unison with one of the panes or with the whole sash of a window, 

 which consequently resounds when those notes are sounded. A 

 peal of thunder has frequently the same effect. The sound of 

 very large organ-pipes is generally inaudible till the air be set in 



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