ofOXFO%p~SHt%E. z$i 



proportionally ; as if double the cize and tenfwn, to half 

 the diftance E F*4 E C or IK in the fame time (per Caf 2 . is 1 

 3 .) and fo keeping touch in their vibrations, they will ftrike 

 unifons 1 to 1 vibration. 

 Caf. 5. Let A B=C D Fig. 2. have as much greater cize as lefs 

 tenfwn, 'twill with the fame force vibrate to a greater diftance 

 proportionally, in a time greater in a duplicat proportion ; 

 as if double the cize, and but half the tenfwn, to double the 

 diftance E Hz EC or / K, in quadruple the time (per Caf. 

 2. isr 3.) an d fo will ftrike an under difdiapafon or 15 th to C 

 D, 1 to 4 vibrations ; as on the contrary C D to A B an up- 

 per., 4 to 1 w'^r. 



Whereby the way he gives notice, that when he fpeaks of firings' 

 (of a different ci^e) being moved by the fame or an equal force 

 (which is alfo 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 

 proper gravity might be thought to caufe a difference. 



203. Thus having abfolved hisftrft Hypothefis concerning firings 

 of equal length, he proceeds to his fecond, and (hews that if 

 A B and C D, Fig. 3. be unequal in length, as in moft Lute-ftrings i 

 what vibrations and founds they will produce, according to their 

 different cizes and tenfwn alfo in the following Cafes* 



Caf 1. Let AB> (i. e. be longer than) CD, Tab. 15. Fig* %i 

 have the fame cize and tenfion, it will with an equal force, 

 vibrate proportionably to a greater diftance Qerpr^m.^.J 

 in a greater time (perprxm. 1.) as if twice as long to double 

 the diftance, LN=iLM\ For AL.LNnCL. LM. ((y 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 vibrations^twill produce a found twice asgrdz/e, 

 or an under oclane to CD. 1 to 2 vibrations. 



Caf 2. Let AB> CD Fig. 3. have the fame cize, and a i tenfwn 

 as much greater as 'tis longer, 'twill with an equal force, vi- 

 brate to the fame diftance LM(perpr*m.(\. velper Caf 1. Hyp. 

 2. isfCaf.2. Hyp.!.) in the lame time Cperpreem. 1.) ftriking 

 the air (with alike brilknefs) into an arch of a circle, fo* 



Oo 2 much 



