245 
the Stability ..of Ships * 
ing position of the vessel, when the centre of gravity is situated 
out of the vertical axis in the line XQ, and Q is the centre of 
gravity of the volume displaced. The measure of stability, when 
the inclination is any small angle, will be the sine of that angle 
and the line XG jointly ; comparing, therefore, the stability of 
the vessel when the centre of gravity is situated in the line 
WGE, with the stability when the centre of gravity is in the 
line XGQ, the proportion of the two stabilities, at equal small 
angles of inclination, will be as the line WG is to the line XG; 
if the centre of gravity G should coincide with the point E in 
the first case, and with the point Q in the latter case, a con- 
dition often adopted by M. Bouguer, the stabilities will be in 
the proportion of the lines WE to XQ, or in a triplicate ratio 
of the lines BA, CH. 
Such is the result of the examination proposed, from which 
the only inference is, that while the centre of gravity remains 
situated in the vertical axis WE, (the position it occupies in 
vessels of every description,) the line XQ cannot be assumed 
to measure or estimate the stability and security of a vessel at 
sea, when inclined to the larger angles from the upright. M. 
Clairbois, to illustrate the principles of M. Bouguer, adopts 
two instances, which are the same with Case vi. (fig. 9.) and 
Case vn. (fig. 12.) in these pages. In the former case, the sides 
coincide with those of an isosceles wedge; the breadth BA at the 
water-line being the base, and the angle BWA situated under 
the water’s surface. As the vessel thus formed is gradually in- 
clined from the perpendicular, he shews,* that the curve traced 
by the centre of gravity of the successive volumes immersed is 
an hyperbola. Of this curve he calculates the successive radii 
* Clairbois, p. 291; 295, 
