of OXFO%p^S HI%E, ipt 
proportionabiy ; as if double the cize and ttnfion^ to half 
the diftance E F=l £ G or I Km the fame time (per Caf. 2. is" 
3.) and fo keeping touch in their vibrations^ they wiil ftrike 
unifons 1 to i vihration, 
Caf, 5, X.tiAB^C D Fig. 2. have as much greater ciz^ as lefs 
ten/ion j'twWl with the fame force vibrate to a greater diflance 
proportionabiy, in a time greater in a duplicat /ro/>or/io;2 ; 
as if double the cize^ and but half the tenfion^ to double the 
diftance EH— 2 E G ox I in quadruple the time (per Ca[, 
2. ^ 3.} and fo will ftrike 2.n under difdiapafon or 15'^ to C 
I to 4 vibrations ; as on the contrary C D to AB zn up- 
per^ 4 to I vibr* 
Whereby the way he gives notice, that when he fpeaks of firings 
(of a different cize') being moved by the fame or an equal force 
(which isalfo to be underftood in all the following cafes where not 
expreft) that he means it that way their gravity does propend, 
viz^ downward in thofe that are Horizontally ftreined, left their 
-proiper gravity might be thought to caufe a difference. 
203. Thus having abfolved his ftrft Hypothefis concerning f?r/;?^^ 
of equal length, he proceeds to his fecond^ and ftiews that if 
A B and C P, Fig, 3. be unequal in lengthy as in moft Lute-firings^ 
what vibrations and founds they will produce, according to their 
different cizes and tenfion alfo in the following Cafes, 
Caf I. Let AB> (i. e. be longer than) C Tab. 15. Fig. 3^ 
have the fame a:^ and tenfion^ it will with an equal /orc^?, 
z/i^r^/e proportionabiy to a grczter di fiance Qperprdtm. ^.J 
in a greater time Qer prdem, l.) as if twice as long to double 
• the diftance, LN=2LMi For AL. LNuCL. LM, (is' AN. 
CM::NL. ML, [per 4. 6^ Euc,'] ergo Arch, AN=Arc, CMD) 
and that in twice the time ; ftriking the air into an arch of a 
circle of double the Radius; by which double flower re- 
turn of its z/i^r^/io;25,'twill produce a found twice as grave^ 
or an under o^a7)e to CP. i to 2 vibrations, 
Caf 2. Let AB> CV Fig. ^, have the fame fi;^e, ^ndn tenfion 
zs much greater zs 'tis longer^ 'twill with an equal /orce, z/i- 
;' brate to the fame diftance LM (perpr<£m.d^. vel fer Caf i. Hyp, 
2, is" Caf 2. Hyp. I, ) in the lame time (T^er/r^e;;?. 1.) ftriking 
the air (with alike brilknefs) into an arch of a circle^ fo 
Oo 2 much 
