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angles C A I,X I A : Therefore C I -f C A,: G I C A : : 
or the fum of the weight of the fcale and counter- 
poife is to their difference, as the tangent' of. ACK, 
half the angle of the lever, to the tangent of DAI 
=ECP, the inclination of the index to the perpen- 
dicular when the lever is at reft : and the angles at 
A and J, or the inclinations of the arms, will be the 
fum and difference of ACK and DAI. 
Hence the fcale and counterpoife being given, the 
inclination of the index may be found from the angle 
of the lever j or the angle of the lever from the in- 
clination of the index. 
The weight of the counterpoife being fixt, let that 
of the Icale vary uniformly ; it is required to find 
when the angular motion of the index is greateft. 
^ All, things remaining. as before, draw AS- perpen- 
dicular to Cl;-, and the variation of Cl will be the 
fame as that of" SI (the line CS being conftant) : 
For- a, like reafon the variation of the angle DAI is 
the fame with that of SAI. Now the variation of 
SI, is to that of the arch which meafures SAI, (AS 
being radius) asj AD to AS?;: if therefore Clror Sf 
flows uniformly, the fluxion ,of S Ad or DAI, or the 
angular motion of the index, will be greateft when 
Aids leaft, that is, when -AT' coincides with AS, or 
when. the inclination of the index is equal to DAS, 
or when the:- arm -carrying the fcale is parallel to the 
horizon. 
The angle DAS is the complement of ADS 
(—ACK). or of -half the-. angle of' tlae- leveri 
Again.CA:CS: or, radius, to the~. co.-fine. of the 
angle«of the lever as. th'e 'counterpoife to the weight 
