Of OX FO%!D~S HI%E. r 9; 



ble in length and cize, and but half fo much tended, to qua^ 

 druple the distance PS=$PQJn octuple the time ; and fo 

 willftrike an under trifdiapafon, or a 22 d , i to 8. vibr. 

 Cafe 9 Let AB > CD, Fig. 5 . have a cize as much lefs, and a ten* 

 fion as much greater as 'tis longer ; 'twill vibrate to the fame 

 diftance TVCper Caf 2. /%>. 2.J in a time proportionably /*/5 

 Cperpram. 2. velCaJ. 3. #j//>. i.J as if half the cize in half 

 the time ; and thereby will ftrike an upper oclave, 2 to 1 

 vibr. 



All which <*/, may be thus briefly expreffed (putting 7" for Ten- 



fion, D for the Cize or Diameter, and L for the /o?gM of the firing:) 



fuppofing ^=1 to be the acutene/s of the found propofed (to 



which you compare the reft) the acutenefs in the other cafes com- 

 pared to it, will be in the proportions following refpectively. 



u *,a <; C ^ J - 2 - a- 4. 5. 



Hypoth.i.2j_^ aT j 2T t _iT ^ 



4 , C^L 2. 3. 4. 5. 



Eypoth.z.X t _, 2T _, v. _X_ _^ T 



ZL*2D + * 2L*D '* 



6. 7. 8* 9 



aT . iT ._, \\ j 2T 



51 _. 



*" ^ r"~ ~~ ~ 



2L*2D 2LxjD 2L*2D 2L*jD 



The reafon of which manner of expreffion, depends on this * 

 that (in Proportions expreffed after the manner of Fraftions) 

 increasing that above the line, doth increafe the value (and fo doth 

 the increafe of Tenfion, increafe the acutenefs :) But increafing that 

 under the line, doth diminijh the value (and fo doth the increafe of 

 the length, and the increafe of the cize, diminijb the Acutenefs) in the 

 fame proportion. Which may ferve for a brief demonfiration of the 

 whole. 



By which may be judged of, all other more mixt or compound 

 Cafes, which are infinite, according to the divers unequal pro- 

 portions, of length, bignefs, and ten/ion ; but being all made out 

 of, or founded on thefe 7 they will all hold true in Analogy to 

 them. 



204. From many of which Cafes 'tis plain and eafie, that the 

 Jympathy and confent of firings lies not wholly in their like ten/ion 



and 



