'[ 209 ] 
The divifions are fet on the ring by an inftrument 
made on purpofe, which will very readily cut them, 
tho’ unequal, with great exaftnefs, on any circle large 
orfmall. 
To prove- the beam, put a weight into the fcalc 
(that of 28 to the pound is the beft in this cafe) and 
fee if it brings the index down to the proper divifion 
on the. ring: if it carries it too far, the angle of the 
beam ACB is too great; if the contrary, too little ; 
and the arms.C A, C B, muft be fet a little in, or out, 
till the angle is right : or the angle of the beam may 
be firft found exjjerimentally, by the rule hereafter 
given, and the divifions calculated to it, which is not 
much trouble ; for having a table ready made for the 
intended angle; the alterations in that table occafion’d 
by a fmall variation from that angle will be eafily 
found by the. rules at the end of the following The-- 
ory. 
When the balance is to be ufed, a weight of of 
a. pound avoirdupoife is to be put on the hook: The 
fcrew G muft then be turned, till the index E points 
at the divifion of 50 : The machine is then properly 
adjufted, and the weight may.be taken off, and a 
fkain put on. 
jtjq 2 Let A CB be a bent lever moveable about 
the angular point C, B a fcale at the end of 
the arm B, A a counterpoife at the end of the other 
arm A; Given the angle of the. lever, the length of 
the arms, the refpe< 5 live weights of the fcale and 
counterpoife, to find the pofition of the lever when at 
reft. 
Produce the arm B C to I,- fo that C I may be to 
CB as the weight of the fcale to the counterpoife; 
VoL. LV. E e join 
