35^ Vihratlon Nodes ofMuJical Strikes * 



of the whole firing as — , — parts of the firing mufl be 



tubbed with the bow in order to produce that tone, that is, 

 the firing is divided into a parts, and b parts mufl be cut off 

 and rubbed with the bow; therefore a—b ate parts of thd 



ftringj or of the whole fifing apparently at refl, the 



extreme points of which are capable of producing vibration 



t 

 nodes j and when — is bfought to its lowefl expfeflion, 



it gives a—^b vibration nodes. If — ■ be not in its lowefl 



terms, let its lowefl terms be -3— j fo that — = 3^, 



and A'hen e is the greatefl common divifor of a and by a, 

 will be = ep^ and b — eq\ therefore a. — b = e {p — q), 



r 



Now, if it fliould be required to apply this law to — , the 



number of the vibration nodes a — b muft be = e{^ — q)\ 



but if applied to -^, as above demonflrated, the number of 



P 

 the vibration nodes will be p — 'q; therefore ^(/)—- 5) = 



f — y, which can no otherwife be true than when ^ is = 1. 



that is, or-^- mufl be expreffed in its lowefl terms. 

 a b 



5. As the members of two fraSions not of the fame value 

 may have the fame difference as } and ^, the fame number 

 of vibration nodes may exifl where the tones are different, 

 and therefore each tone has not its own peculiar number of 

 vibration nodes. 



6. Vibration nodes are only poflible where the tones halve 

 a certain ratio to the fundamental tone. 



It mufl not, however, be cxpeiSled, that the experiment 

 can be made, for example, with a firing %6 inches in length, 

 in fuch a manner thdt you can divide it into 40 or 50 parts, 

 and rub one of them with the bow; for in this cafe the vi- 

 bration nodes, or points at refl, are at fb little diflance froto 



each 



