Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1weigh equally it would be neceſſary to hang it nearer to the
Perpendicular C, as v. gr. in E: and look how many times the Di­
ſtance C A ſhall contain A E, ſo many times ſhall the Metal
weigh more than the Water.
Let us therefore ſuppoſe that the
Weight in B be Gold, and that weighed in the Water it with­
draws the Counterpoiſe D into E; and then doing the ſame with
pure Silver, let us ſuppoſe that its Counterpoiſe, when afterwards
it is weighed in the Water, returneth to F: which point ſhall be
nearer to the point C, as Experience ſheweth, becauſe the Silver
is leſs grave than the Gold: And the Diſtance that is between
A and F ſhall have the ſame Difference with the Diſtance A E,
that the Gravity of the Gold hath with that of the Silver.
But if
we have a Mixture of Gold and Silver, it is clear, that by reaſon it
participates of Silver, it ſhall weigh leſs than the pure Gold, and
by reaſon it participates of Gold, it ſhall weigh more than the
pure Silver: and therefore being weighed in the Air, and deſiring
that the ſame Counterpoiſe ſhould counterpoiſe it, when that
Mixture ſhall be put into the Water it will be neceſſary to draw
the ſaid Counterpoiſe more towards the Perpendicular C, than the
point E is, which is the term of the Gold; and more from C
than F is, which is the term of the pure Silver; Therefore it ſhall
fall between the points E and F: And the proportion into which
the Diſtance EF ſhall be divided, ſhall exactly give the proportion
of the two Metals which compound that Mixture.
As for exam­
ple: Let us ſuppoſe the Mixture of Gold and Silver to be in B,

counterpoiſed in
the Air by D,
which Counter­
poiſe when the
Compound Me­
tal is put into the Water returneth into G: I ſay now, that the
Gold and the Silver which compound this Mixture are to one ano­
ther in the ſame proportion, as the Diſtance F G is to the Diſtance
G E.
But you muſt know that the Diſtance G F terminated in
the mark of the Silver, ſhall denote unto us the quantity of the
Gold, and the Diſtance G E, terminated in the mark of the Gold,
ſhall ſhew us the quantity of the Silver: inſomuch that if F G
ſhall prove double to G E, then that Mixture ſhall be two parts
Gold, and one part Silver: and in the ſame method proceeding in
the examination of other Mixtures, one ſhall exactly find the
quantity of the ſimple Metals.
To compoſe the Ballance, therefore, take a Rod at leaſt a yard
long, (and the longer it is, the exacter the Inſtrument ſhall be)
and divide it in the midſt, where place the Perpendicular: then
adjuſt the Arms that they may ſtand in Equilibrium, by filing or