the Stability of Ships . 
when agitated by the winds and -waves in open sea, where the 
inclinations from the upright must often become considerable. 
In order to extend the application of his theorem to the larger 
angles of inclination, he proposes to examine whether the me- 
tacentre ascends or descends as the vessel is gradually inclined .* 
To effect this, the curve line EQ<? (fig.16.) is to be traced, by find- 
ing the successive centres of gravity of the volumes immersed 
while the vessel is inclined ; and, from this curve the metacen- 
tric curve WX is to be defined : the point where the metacentric 
curve meets the vertical axis in W, is the metacentre corre- 
sponding to the position when the vessel floats upright and 
quiescent He observes, that if the metacentre X ascends from 
its original position W, while the vessel is inclined gradually 
from the perpendicular, the vessel will be secure from overset- 
ting ; but will be insecure, if that point should descend while 
the vessel is inclined. No demonstration of this proposition is 
given, either by M. Bouguer, or by M. Clairbois, who un- 
dertakes to explain the principles delivered in this chapter of 
M. Bouguer's work, -f If the proposition has been suggested 
by some analogies which subsist between the construction of 
the lines EW, QX, and other lines similarly drawn, they will 
be insufficient to establish the truth of it. The analogies are 
such as the following. W being the metacentre, and E the 
centre of gravity of the volume displaced, when the vessel floats 
upright, WE is the radius of curvature to the curve EQ q, at 
the point E ; X being also the metacentre, constructed accord- 
ing to the method which has been described, when the vessel 
has been inclined through an angle ASH, and Q the centre of 
gravity of the corresponding volume immersed; XQ is the 
* Traite duNavire, p. 271. f Clairbois sur V Architecture Navale, p. 289, et seq . 
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