and GM is called the metacentric height; and the ship must be
ballasted, so that G lies below M. If G was above M, the tangent drawn
from G to the evolute of B, and normal to the curve of buoyancy, would
give the vertical in a new position of equilibrium. Thus in H.M.S.
"Achilles" of 9000 tons displacement it was found that moving 20 tons
across the deck, a distance of 42 ft., caused the bob of a pendulum 20
ft. long to move through 10 in., so that
240 20
GM = --- × 42 × ---- = 2.24 ft.; (2)
10 9000
also
cot [theta] = 24, [theta] = 2°24´. (3)
In a diagram it is conducive to clearness to draw the ship in one
position, and to incline the water-line; and the page can be turned if
it is desired to bring the new water-line horizontal.
Suppose the ship turns about an axis through F in the water-line area,
perpendicular to the plane of the paper; denoting by y the distance of
an element dA if the water-line area from the axis of rotation, the
change of displacement is [sum]ydA tan[theta], so that there is no
change of displacement if [sum]ydA = 0, that is, if the axis passes
through the C.G. of the water-line area, which we denote by F and call
the centre of flotation.