212
HARBOUR ENGINEERING.
or, geometrically, thus (fig. 184): —Through the point W, in which the
diagonal NG intersects the primary water-line RT, draw the line YZ. Then
YZ is the new water-line, and VX = Dj.
It follows, exactly as before, that the curve of buoyancy for the latest
condition of things is a parabola, the vertex of which is in JX at a distance
from the point X, and which passes through the points m and n in the lines
HN and GP, where Nm=Pn=2Dr
We have now traced the curve of buoyancy through rather more than
half of its path, and the remaining portion lies symmetrically about the same
axes, so that it is quite easy to draw the entire curve. A moiety is shown
in fig. 185. In the left hand quadrant the parabolic arc extends from A
to a, to be succeeded by a hyperbolic curve from a to b. From 5 to B the
curve is parabolic once'more.
Hence, the complété locus of the centre of buoyancy is a curve made up
of fouqparabolas and four hyperbolas.