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pendlcular to it, cutting CL produced in F, then will 
LF reprefent the weight of the fkain, and D A F be 
the inclination of the index, when its variation is 
greateft. 
On FL as a diameter defcribe a femicircle, 
and let CA intcrfeft it again in a: Join L^, 
a F, then will L ^zF be a right angle as well as L AF; 
therefore with the given angle of the lever ACB and 
given fcale CL, we have the fame maximum FL, 
cither with the counterpoife CA, or Qa -, either of 
which gives the other j for C A : C L : : C F : C 
In like manner, if the angle of the lever, 
the counterpoife C A, and F L the weight of 
the fkain at the maximum are given, with 
Fig. 5, the center A and radius A E — : .1 FL defcribe 
a circle cutting B C produced in E and e, 
towards C fet off E L and e /, equal to the ra- 
dius aforefaid, and either CL or C / will be the 
weight of the fcale that will give the propofed maxi- 
mum. It is manifeft that^if AE or i- FL is lefs 
than AS, the problem is impoffible; therefore the 
maximum is limited, and muff be propofed fuch, 
that the weight of the fkain in that cafe be lefs than 
2 A S. 
Example: 
Let the femi-angle of the lever be 84° : 03^ 
the counterpoife one ounce, let the divifion 
for 50 to the pound, fland at the top of the graduated 
arch perpendicularly over the center of the lever, 
that is, let L D =: 44. oz. confequently L C or the 
fcale r=CD — LD, orCA — LDr:=i ^ 
