OfOXFO%'D^SHI%^E. 
hit in length and cize^ and but half fo much tended^ to qua-, 
druple the diflance PS=/[PQjn oftuple the time ; and fa 
will ftrike an under trifdiapafon^ or 2i 22^ i to 8. vibr, 
Caf. 9 Let AB > CD^ Fig. 5 . have a cize as much iefi^ and a ten- 
fion as much greater as 'tis longer ; 'twill vibrate to the fame 
diftance TVCf^T Caf 2. i^/?. 2. J in a time proportionably /e/f 
CperpYd^m* 2. velCaJ* 3. //y/. i.J as if half the in half 
the time ; and thereby will ftrike an upper o5iave^ 2 to i 
vibr. 
All which ^df/ey, may be thus briefly exprcfled (putting Tfor Ten- 
fion^ D for the Cize or Diameter^ and Z, for the length of the firing:} 
fuppofing ~=i to be the acutene/s of the found propofed (to 
which you compare the reft) the acutene/s in the other cafes com- 
pared to it, will be in the proportions following refpedtively. 
^^^fi^' 2. 3. 4. S. 
C ^"^7^ I. 2. 3. 4. 
HypOth. 2.^ T 2T ^, JT T 
6. 7. 8. 9- . ... 
2la:2D * 2LxjD * 2L^2D • ILxjo 
The reafon of which manner of expreflion, depends on this ; 
that (in Proportions expreffed after the manner of Fra^ions) 
i/2(:re^j//«^ that above the line, doth /Wej/e the value (and fo doth 
the increafe of Tenfion^ increafe the acutenefs :) But increafing that 
under the line, doth diminijb the value (and fo doth the increafe of 
the lengthy and the increafe of the ci:^e, diminij/j the acutenefs} in the 
hme proportion. Which may ferve for a brief demonftration of the 
whole. ' ' 
By which may be judged of, all other more mixt or compound 
Cifes^ which are infinite, according to the divers unequal pro- 
portions, of lengthy bignefs^ and tenfion ; but being all made out 
of, or founded on thefcj they will all hold true in Analogy to 
them. 
204. From many of which C^fes 'tis plain and eafie, that the 
Jjimpatbji znd confent of f rings lies not wholly in their like tenfon 
and 
