Galilei, Galileo, Mechanics, 1665

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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,
29[Figure 29]
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.

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