zpz The Statural Hi/lory 



much greater proportionally, as CD is the chord of fewer 

 degrees, and fo will produce alike founds or unifons. i to i 

 vibration. 

 Caf 3 . Let AB > CD, Fig. 3 . have the fame cize and a tenfion 

 as much /<?/$, as 'tis longer ; 'twill vibrate to a difiance, and 

 in a /Z777e greater in a duplicate proportion Cper proem. 4. &> 1 .. 

 w/jter C^ r*Hjfp. 2. &> C0/2. Hjp.i.) as, if being double, 

 it has but half the tenfion to quadruple the difiance L0=/\. LM 

 in quadruple the //Ve, and fo will produce 2 found 4 times 

 as grave, or an under difdiapafon to CD 1 to 4 z/i^r. 

 Gj/! 4. Let AB> CD, Tab. 15. Fig. 4. have a a^asmuch 

 greater as 'tis longer, and the fame tenfion. 'twill vibrate to 

 a greater difiance proportionably (per proem. ^. velper Caf. 1. 

 Hj>/>. 2. J in a ///* greater in a duplicate proportion (per proem. 

 2. W/er &/ 3. H)/>. 1 .) as if double in length and c, to 

 double the diftance PR 2 Pfljn quadruple the time ; and fo 

 will ftrike an under difdiapafon or 1 5 th to CD. 1 to 4 vibr. 

 Caf. 5. Let AB> CD, Tab. 15. Fig. 5. havead^as much 

 lefs as *tis longer, and the fame /e//o ; 'twill with the fame 

 force, vibrate to a greater diftance proportionably (per proem. 

 4. w/ Caf. 1 . #?/>. 2.) as if twice as long to double the di- 

 ftance TX=2 TV, in the fame time (per proem. 2. J and fo keep- 

 ing pace in their vibrations will ftrike unifons, 1 to 1 . vibr. 

 Caf. 6. Let AB> CD, Fig. 4. have both cize and tenfion as much 

 greater as 'tis longer, 'twill vibrate to the fame difiance PQ^ 

 (per proem. 4. z/e/ Caf 2. Hyp. 2. J in a longer /zwze proportion- 

 ably (per proem. 2.J as if double the cize, in twice the time, 

 and fo will ftrike an under oftave, 1 to 2 vibrations. 

 Caf. 7. Let AB> CD, Fig. 5. have both cize and tenfion as 

 much /e/J, as 'tis longer ; 'twill vibrate to a diftance greater 

 i. in a duplicate proportion Qer. Caf. 3. /jite, 2. J in a ///we pro- 



portionably greater Cper pram. 2. J as if double the length, 

 it has but half the cize and tenfion, to quadruple the diftance 

 TT$TV'm twice the /ie,and fo will ftrike an under oftave 

 1 to 2 vibr. 

 Caf 8. Let AB > CD, Fig. 4. have a a'^e as much greater, and 

 a /e/?otf as much lefs as 'tis /eager ; 'twill vibrate to a diftance 

 greater in a duplicate proportion Cper Caf. 3. ##>. 2. J in a 

 time greater in a triplicate proportion Cper proem. 2. J as if dou- 

 ble 



