290 The Statural Hiftory 



/?/? tenfion ; and the quicknefs or frequency of vibration, from the 

 greater or fmfter motion, and le/s compafs. 



202. This premifed, he proceeds to his firft Hypothefis, and 

 fhews, that if AB and C D, Tab. 15. F/g.i. be equal in length, 

 as in Viol firings, what founds and vibrations they will produce ac- 

 cording to their different bignefs and tenfion in the following 



&/ 1. LetAB=(i. e. beequalto) D, Tab. 15. Fig.i. have 

 the fame cize and tenfion, and be touched with an equal force, 

 they will vibrate to equal diftances EG=IK(perpr<emi[fam 3) 

 in the fame time (perpr<*m. 1.) whereby ftriking the ^4/V in- 

 to alike arches, or arftfai' of equal circles, with the fame brifk- 

 nefs, and alike quick or frequent returns of their vibrations, 

 they will produce the fame found, and fo be unifons, 1 to 1, 

 vibration. 



Caf 2. Let A B=C P, Fig. 1. have the fame cize and a greater 

 tenfion, 'twill with the fame force, vibrate proportionably to 

 alefs diftance (perpr^emif. 4.) in zjborter time (perpr*m.i.) 

 as, if double the tenfion, to half the diflance EF=[EG or 

 /ZF, in half the J/we ; ftriking the tfir into an drc/> of a great- 

 er circle (and that fo much the greater, as ^4 B is a chord of 

 fewer degrees to^GZ?, the lefs) which doing brifk and 

 fmartly with a quick return, becaufe of the little compafs it 

 fetches, 'twill beget a found fo much the more acute, as its 

 vibrations (are fhorter, and thereby) come thicker and oft- 

 ner ; i.e. of double the acute/ie/s, or an upper cflave to C 

 1/ 2 to 1 vibration. 



Caf. 3. Let ^4 B=C~D, Tab. 15. ^fg. 2. have a greater riband 

 the fame tenfion, it will with the fame /orce, vibrate to the 

 fame distance E'G~IK (per pr<*m.y.) but in a longer time 

 proportionably (perpr*m. 2. J as, if it be double in diame- 

 ter (and foin circumference, i. &. quadruple in bulk) in twice 

 the time ; ftriking a Note fo much the more grave, as its vi- 

 brations return flower and feldomer, and are thereby fewer, 

 i. e. twice as grave, or an under ofiave to CD, 1 to 2 vibra- 

 tions. 



Caf 4. Let A B=C P F/. 2. have as much greater a cize as 

 tenfion, it will, with an equal /orce, vibrate to a lefs diflance 



pro- 



