241 
the Stability of Ships . 
should be placed above the metacentre, suppose at g, the same 
force of the fluid’s pressure, by turning the vessel round an axis 
passing through g, must immerse further the portion of the side 
A a; and this immersion, being continued, will cause the vessel to 
overset. Another property of this point has been demonstrated 
by M. Euler, * and other authors ; which is, that when the 
angles of a vessel’s inclination are evanescent, or very small, 
the effect of stability, to restore the vessel to the upright po- 
sition, will be as the sine of the angle of inclination GWZ 
and the line WG jointly : at the same small angles of incli- 
nation, the stability of different vessels will be in proportion 
to the line WG, or distances of the metaeentre above the 
centre of gravity. 
Let the curve EQ q (Tab. XI. fig. 1 6 .) represent the line traced 
by the successive centres of gravity of the immersed volumes, 
while the vessel is inclined from the upright through any angle 
ASH. M. Bouguer demonstrates, that a tangent to this curve in 
any point Q, will be parallel to the water’s surface CH, corre- 
sponding to that point : if, therefore, through any two adjacent 
points Q and q, in the curve EQ q, lines QM, q N, are drawn per- 
pendicular to the lines CH, c h , respectively, the intersection of 
those lines in the point X will be the centre of curvature, and 
XQ, X q, will be the radii of a circle, which has the same cur- 
vature with the curve EQ in the point Q. For the same rea- 
sons, the line WE (fig. 15, 16.) is the radius of a circle which 
has the same curvature with the curve EQ in the point E. The 
point W has been denominated the metacentre corresponding 
to the upright position of the vessel, when the line WGE is 
perpendicular to the water’s surface. M. Bouguer denomi- 
* Theory of the Construction of Vessels, chap. S, book i. f To radius — i. 
MDCCXCVIII. I | 
