%po The 5\(amral Hijlory 
/^y? tenfion ; and the quicknefs or frequency of vibration, from the 
greater ox fmfter motion, and lefs compafs. 
202. This premifed, proceeds to his firft Hyfothefis-, and 
(liews, that if AB and C D^Tab. 15. Fig.i, be equal in length, 
as in Viol firings^ what founds and vibrations they will produce ac- 
cording to their different bignefs and tenfion in the following 
Cafes* 
Cafi. Let>4^=Ci. e. be equal to) ^P,r^3. 15. Fi^. I. have 
the fame cize and tenfion^ and be touched with an equal/ore^?, 
they will vibrate to equal diftances EG=IKQ)erprd^milfam 3) 
in the fame time (perprcem, i.) whereby ftrikingthe Air in- 
to alike arches^ or /7rc/?ty of equal circles^ with the fame brifk- 
nefs, and alike quick or frequent returns of their vibrations, 
they will produce the fame found, and fo be unifons^ i to 1 
vibration. 
Caf 2. Let A B=C 1>, Fig. i. have the fame cize and z greater 
tenfion^ 'twill with the hmeforce^ vibrate proportionably to 
a lefs diftance (^fer pr<£mif 4.) mzfiorter time (perprdem.i .) 
as, if double the tenfion^ to the dijiance EF~lEG or 
in half the time ; flriking the dfir into an arch of a great- 
er circle (and that fo much the greater^ as i4 5 is a chord of 
fewer degrees to^G^, the/e/i) which doing brifk and 
fmartly with a quick return, becaufe of the little compafs it 
fetches, 'twill beget a found fo much the more acute^ as its 
vibrations (are fhorter, and thereby) come thicker and ofc- 
ner ; i.e. of double the acutenefs^ or an upper o^ave to C 
2 to I vibration. 
Caf. 3. Let A B=CI>^ Tab. 15. Fig, 2. have a greater cz:^e and 
the fame tenfion^ it will with the fame/orce, vibrate to the 
fame distance EG=IK (per pr^^m.'^.') but in a longer time 
proportionably (perpr^m. 2. J as, if it be double in diame- 
ter (and foin circumference, i. £. quadruple in bulk') in twice 
the time ; itriking a iVb/e fo much the more grave^ as its vi- 
brations return (iowex md feldomer, and are thereby fewer, 
I. e. twice as grave, or an under o5fave to CD, i to 2 vibra- 
tions. 
Caf 4. Let A B=C D Fig. 2. have as much greater a cize as 
tenfion, it will, with an equal force, vibrate to a lefs difiance 
pro- 
