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especially if the portions of the body be so equally divided by 

 the obstacle, that two or more are left capable of vibrating 

 in like times ; and having also seen how easily sympathetic 

 vibrations are induced, we shall readily comprehend that 

 vibration will be communicated from one part of the body 

 to the other or others. Thus, when a string is vibrated, and 

 the finger is slightly applied exactly at the middle of the 

 string, the portion touched by the finger cannot vibrate, 

 but the string is divided into two halves, each of which 

 are capable of vibrating in like times, and the string will, 

 therefore, vibrate in two portions, producing the octave of 

 the fundamental note. 



In like manner, if the string be touched at the 3rd, 4th, 

 5th, 6th, or any multiple part of the whole, it will in 

 vibrating divide itself into as many parts, vibrating in unison, 

 separated by points at rest, which are termed nodal points. 



A column of air divides itself into difi'erent vibrating 

 portions more readily than a string ; thus with the flute, 

 when an aperture is opened at the 1st, 3rd, or 4th of the 

 tube, nodal points are produced in like manner as when a 

 string is touched, and similar harmonic tones are produced ; 

 and the like harmonies are also produced when the air is 

 more strongly introduced into the instrument, the primary 

 vibrations being more accordant with the production of high 

 than low notes ; the column of air in the flute may thus 

 be divided into as many as eight parts. 



The vibrations of glass goblets op metallic vessels of 

 similar shapes do not appear to give the strictly funda- 

 mental vibrations, but only the harmonic corresponding to 

 the 4th in the series on a string ; for the hemispherical 

 form does not so readily permit vibration to take place 

 by the change of the entire form, as by a change of form 

 in four or more segments alternating with each other. This 

 appears the more probable, as we cannot produce the vibra- 



