506 NICHOLLS'S SEAMANSHIP AND NAUTICAL KNOWLEDGE
the ship to small inclinations, and assumes that the line of action through
the centre of buoyancy passes through the metacentre. This is practi-
cally so for small angles not exceeding 12 degrees, but may not be the
case at bigger angles in a ship-shaped body.
Metacentric Height.—We must know, in the metacentric system of
stability, the positions G and M relatively to the keel, or, at least, the
distance between them which is called the metacentric height (GM)\
also the angle of heel, called 6, and the weight of displacement of
the ship. The height of the metacentre is assumed to be constant at
a given draught, but the position of the centre of gravity moves up
and down when weights in the ship are raised and lowered with a
consequent decrease and increase in her G M. The arm GZ becomes
smaller with every reduction in the distance G M, and the length of this
arm, as we have been endeavouring to point out, is a determining factor
in the law of moments.
The metacentre acting through Z is the fulcrum, the ship's dis-
placement acting through G is the power or weight, and, as before,
armxpower=moment, or, ffZxTF=foot-tons and expresses the
energy of the ship to return to a position of equilibrium.
Example.—If 6rZ=2 feet and weight of ship=5000 tons, the moment
will be 2 X 5000=10,000 foot-tons. This is equivalent to a 1 ton weight
suspended at the end of a lever 10,000 feet, nearly 2 miles, long, or,
of 10,000 tons weight at the end of a lever 1 foot long.
When weights are kept low the G M and G Z are big ar>d the ship
is said to be stiff, she is hard to incline, but when forcibly heeled over an
excessive righting moment is brought into operation which brings the ship
upright in a violent manner, making the motion uncomfortable for those
on board and straining the hull unnecessarily. Should the weights
be high so that GM and G Z become very small: the ship is said to be
tender, she is easily heeled over and is slow and sluggish in returning to
the upright. She would be quite a comfortable ship at sea if she did not
capsize. The cargo when being loaded should be distributed to produce
a condition between these extremes so that the ship will be of good
behaviour at sea. In theory this is quite simple; in practice, however,
it is more complicated.
' The metacentric height (G M) is found by actually heeling the ship
in her light condition, that is, with no ballast, cargo, bunker coal,
stores or water on board—just the completed ship with steam up. This
initial GM having been supplied by the builder, also the corresponding