k for bulk, and that the way to test the
bulk of such an irregular object as a crown was to immerse it in water.
The experiment was made. A lump of pure gold of the weight of the crown
was immersed in a certain receptacle filled with water, and the overflow
noted. Then a lump of pure silver of the same weight was similarly
immersed; lastly the crown itself was immersed, and of course--for the
story must not lack its dramatic sequel--was found bulkier than its
weight of pure gold. Thus the genius that could balk warriors and armies
could also foil the wiles of the silversmith.

Whatever the truth of this picturesque narrative, the fact remains that
some, such experiments as these must have paved the way for perhaps
the greatest of all the studies of Archimedes--those that relate to the
buoyancy of water. Leaving the field of fable, we must now examine these
with some precision. Fortunately, the writings of Archimedes himself
are still extant, in which the results of his remarkable experiments are
related, so we may present the results in the words of the discoverer.

Here they are: "First: The surface of every coherent liquid in a state
of rest is spherical, and the centre of the sphere coincides with the
centre of the earth. Second: A solid body which, bulk for bulk, is of
the same weight as a liquid, if immersed in the liquid will sink so that
the surface of the body is even with the surface of the liquid, but will
not sink deeper. Third: Any solid body which is lighter, bulk for bulk,
than a liquid, if placed in the liquid will sink so deep as to displace
the mass of liquid equal in weight to another body. Fourth: If a body
which is lighter than a liquid is forcibly immersed in the liquid, it
will be pressed upward with a force corresponding to the weight of a
like volume of water, less the weight of the body itself. Fifth: Solid
bodies which, bulk for bulk, are heavier than a liquid, when immersed in
the liquid sink to the bottom, but become in the liquid as much lighter
as the weight of the displaced water itself differs from the weight of
the solid." These propositions are not difficult to demonstrate, once
they are conceived, but their discovery, combined with the discovery
of the laws of statics already referred to, may justly be considered as
proving Archimedes the most inventive experimenter of antiquity.

Curiously enough, the discovery which Archimedes himself is said to have
considered the most important of