^■~thrati07i Nodes of JlTuJical Strings. 34^ 



V. Divide the ftring AB by the points C, D, E, F, intfj 



five equal parts ; cut off, by means of two moveable bridges, 



the part DE; place upon C and F, and other points of the 



(tring AB, fmall bits of paper : rub the 



C D E F bow againft ED ; all the bits of paper 



A. — . — . — . — . — '.B will be thrown off* except thofe in C 



and F, and you will hear the tone cor- 



rcfponding to DE, which is to the tone of the whole ftring 



as 5 : X. 



From thefe few experiments, the following laws refpefting 

 vibration nodes may be deduced : — 



1 . The part of the firing apparently at reft is not perfeiSlly 

 fo, but only its vibration nodes. 



2. The original vibrating part of the ftring, which is 

 brought into immediate vibration by rubbing with the violin 

 bow, has no vibration nodes ; and therefore no ftring on the 

 violin, violoncello, harp, or harpfichord, can have any. All 

 the vibration nodes on thefe inftruments lie behind the 

 bridge. 



3. For vibration nodes to be poffible, a part of the ftring 

 muft: be apparently at reft; confcquently, the number which 

 exprefles the height of the tone emitted, as conjpared with 

 the tone of the whole ftring — i, muft be greater than one, 

 and muft therefore be expreflcd by an improper fraction. 



4. In order to determine the number of the vibration 



nodes of a ftring for the tone —-, where, as before ftiewn, a 

 muft be greater than b, we need only reduce the fraction 

 -7-, which exprefles the proportional height of the tone, to 



its loweft terms - — , and fubtracl the fmaller number a from 



9 

 the greater/).- the difference p — ^ w'ill be the number of the 



vibration nodes. This law follows very naturally from the 



preceding experiments. 



When the height of the tone to be produced is to tlie tone 



of 



