^ The OSQitUral Hijlory 
much greater proportionably, as CD is the chord of fewer 
degrees^ and fo will produce alike founds or unijons. i to i 
vibration, 
Caf.'^. LaAB>CD^ F^g-d- have the fame d^c and a 
as much lefs^ as 'tis longer ; 'twill vibrate to a diftance^ and 
in a /i;;2e greater in a duplicate proportion Q^Tpr<£m, 4.<s>* i- 
z/g//er Caf. I, Hjp: 2. (isr Hjip.i.) as, if being double, 
it has but half the tenfion to quadruple the diftance L0=\ LM 
in quadruple the time^ and fo will produce a found 4 times 
2iSgrave^ or under difdiapafin to CD 1 to 4 vibr. 
Caf. 4. Let i45> /^i^. 15.^/^. 4. have a d:^easmuch 
greater as 'tis longer^ and the fame tenfion, 'twill vibrate to 
a greater diftance proportionably Q&er pr<£in.\, vel per Caf, i . 
//)'^. 2. J in a greater in ?i duplicate proportion (perpri£m, 
2. z/e/ per Caf, 3. //yj^?. i .) as if double in length and ciz^^ to 
double the diftance PR=2 PQJm quadruple the time ; and fo 
will ftrikean under difdiapafon or 1 5*'' to CD, i to 4 vibr. 
Caf.^, Let AB> CD^ Tab* 15. Fig, 5. have a ci:^e as much 
/f/s as *tis longer^ and the fame tenfion ; 'twill with the fame 
force^ vibrate to a greater diftance proportionably (perpr^em. 
4. vel Caf I. Hyp, 2.) as if twice as long to double the di- 
ftance 7X=2 /r, in the fame (/?er prdim,i.J and fo keep- 
ing pace in their vibrations will ftrike i to i . vibr. 
Caf 6. Let AB > ^^P, Fig. 4. have both ci^eand tenfion as much 
greater as 'tis longer^ 'twill vibrate to the fame diftance PQ^ 
(per proem. ^, vel Caf.2.Hjp,2.J in a longer /iwze proportion- 
ably (perpr<iem. 2.J as if double the ci^e, in twice the timey 
and fo will ftrike an under o£iave^ i to 2 vibrations, 
Caf 7. Let i45> Fig, 5. have both d:^e and tenfion as 
much /f/}, as 'tis longer ; 'twill vibrate to a diftance greater 
im duplicate proportion fp^r, Caf 3. J7j//. 2. J in a /i/we pro- 
portionably greater Cperpr^em. 2. J as if double the lengthy 
it has but half the d;^eand tenfion^ to quadruple the diftance 
Tr=^TVin twice the /i/we,and fo will ftrike an under o£Iave 
I to 2 vibr, 
Caf, 8. Let ^5 > CD, 4. have a cize as much greater., and 
a tenfion as much /e/y as 'tis /t);j'^er ; 'twill vibrate to a diftance 
greater in a duplicate proportion Cp^r Caf 3. //j/jf'. 2. J in a 
greater m2i triplicate proportion Qerpr^m, 2 J as if dou- 
ble 
