Suspension Bridges and other Structures, 391 



phenomena on philosophical principles — the case is in close ana- 

 logy with the phenomena of vibration in a musical string. The 

 string of an ^olian harp, acted on by the wind, vibrates in 

 numerical divisions exactly like this beam, and in doing so, it 

 gives out the beautiful tones called natural harmonies ; and by 

 an intimate acquaintance with the principles of producing these 

 tones, some performers on stringed instruments have attained 

 celebrity. The laws of vibration of elastic cords, will explain 

 by analogy the vibrations of the framings alluded to. 



If A and B represent the two ends of a string which is struck 

 or put in vibration, while it is prevented by a touch of the 

 finger from vibrating at r/i, it will divide itself into two equal 

 parts at w, each of which will sound an octave to the open note. 

 If the finger be placed at m"\ fig. 6, the string will divide 

 itself into three parts, and each will vibrate in the tone which is 

 called the fifth above the other. If, next, the finger be placed 

 at m""y fig. 7, the string will divide spontaneously into four 

 parts, and the note sounded by each part will be that which is 

 called the internal of a fourth from its predecessor. The next 

 step taking one-fifth of the length of the string would stop it 

 in five divisions, and the note produced would be that which 

 is called an interval of one-third. 



Now, the remarkable circumstance worthy of great attention 

 in this inquiry is this, that, unless the vibrating body be fixed 

 by a stop at one of these simple numerical divisions, 2, 3, 4, 5, 

 it will either not vibrate at all, or through a very minute space 

 only, and will return to rest almost instantly after the dis- 

 turbing cause ceases to act, instead of continuing to perform 

 equal timed oscillations. 



Application to Suspension Bridges. — This case is in strict 

 analogy with the case of the vibrations of a suspension bridge, 

 and shews us the means of counteracting and suppressing its 

 vibrations in the most efficient and simple manner. 



Every one who has noticed the vibrations of a suspension 

 bridge in a gale of wind, must have observed that its oscilla- 

 tions are performed in a certain measured time, and are pro- 

 pagated from one part to another until the whole structure is in 

 ^a state of equal timed vibration. 



It is also matter of common observation, that any equal 



