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of the fcale, when the angular motion of the Index is 
Let now the weight of the fcale as well as the 
counterpoife be fixt, but into it let there be fuccef- 
fively put variable weights or fkains of thread, to be 
denominated by the number of them which (at that 
lize) go to the pound : Let the weight of thefe fkains 
vary at each fucceffive change in fuch a manner, that 
the number which goes to the pound may be in- 
creafed each time by unity : It is required to find 
when the angular variation of the index, in one ex- 
change, will be greateft. 
All things as before, let C L reprefent the 
’ fixt weight of the fcale, L I the variable one 
of ths fkain, C 1 that of both together. Call A S, j : 
SL, d: put p ■=. one pound, x the number by which 
any one fkain is denominated, 
confequently 
A 
weights LI; whence S I =LI-L S = whofe 
fluxion (putting the uniform fluxion of x to be unity) 
is — - : but the fluxion of S I is to that of the arch 
XX 
which meafures S A I, as A P to A S% or as A S’+ 
SP to AS", or as ss-\--~d : ss, that is ss-X-^-d^ ; 
ss : : — ^ to the variation of the index fought ; whence 
that variation is greatefl when x — ^- — that is 
° isX- da 
when — or the weight of the fkain =— where- 
Fig. 4 . if .CA reprefent the counterpoife, and 
CL the fcale, join AL and draw AF per- 
pendicular 
