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PIERHEADS, QUAYS, AND LANDING-STAGES.
203
sect at a point which we will designate M. The technical name for this
point of intersection is the metacentre.1
It will be noticed that there is a very striking difference in the position
of the metacentre in the two figures. In one case it lies above the centre of
gravity of the pontoon ; in the other case, it lies below it. The former
arrangement produces a righting moment; the latter, an overturning
moment.
The metacentre of a floating body has a variable position dependent upon
(a) the shape of the body and (6) its centre of gravity, and also (c) upon the
centre of buoyancy; but, from what has been pointed out, it follows, as a
general rule, that a pontoon is stable or unstable according as the metacentre
lies above or below the centre of gravity.
It would not be strictly correct to say that overturning would absolutely
ensue in the latter event, as through the variation in the centre of buoyancy
an intermediate position might be reached in which the conditions of equili-
brium are satisfied.
It will be well, therefore, to go through the process of determining the
complété range of position of the metacentre, and to construct a diagram
showing all the changes in position of the centre of buoyancy corresponding
to various degrees of inclination.
(I.) Case of the unballasted pontoon immersed to half its depth.—Let us take
the case of a symmetrical pontoon of rectangular cross section floating so as
to have a moiety of its volume immersed. Fig. 179 represents such a case:
GHNP is the pontoon, and RT the water surface level in the initial position,
while FS, IIP, and VX are other water-lines corresponding to changes of
inclination in the pontoon.
1 Bouguer, who introdueed the tenn a eentury and a half ago, employed it to designate
a point in a ship’s vertical axis above which the centre of gravity of the vessel might not be
raised without producing an inclination in the axis. The metacentre must not be confused
with any of a series of points on a curve distinguished by Bouguer as the nietacentric. The
metacentric may be defined as the locus of the intersections of successive vertical through
adjacent centres of buoyancy as a ship undergoes a series of slight inclinations. In
other words, it is the evolute of the curve of buoyancy, or the locus of its centre of
curvature.