Mr. Atwood's Disquisition on 
nates the point X the mfetacentre corresponding to the position 
when the vessel has been inclined from the upright through the 
angle ASH; and the curve WX is termed the metacentric 
curve, being the line traced by the successive metacentres, or 
intersections, of the lines QM, q N, drawn perpendicular to the 
lines in which the vessel is intersected by the water's surface, 
while it is gradually inclined. Consequently, according to this 
construction, the metacentric curve WX is the evolute, of 
which the curve EQ q is the involute. 
The construction and properties of the metacentric curve 
being a subject of geometrical reasoning, considered purely as 
such, are liable neither to ambiguity nor error ; but, on what 
grounds these properties are applied to measure the stability of 
vessels, or to estimate their security from oversetting, when 
much inclined from the upright, is not explained by M. Bou- 
guer, M. Clairbois, or any other author I have had an op- 
portunity of consulting : yet the opinions expressed by these 
authors on the subject in question, have been adopted by many 
persons as established principles ; and, being of some import- 
ance in the practice, as well as theory, of naval architecture, it 
cannot be thought superfluous to pay some farther attention to 
them. 
M. Bouguer,* having demonstrated the property of the me- 
tacentre, which gives security from spontaneously oversetting, 
to a vessel, whenever the centre of gravity is situated beneath 
it, proceeds to observe, that his theorem, being founded on 
supposing the angles of the vessel's inclination as evanescent, 
or extremely small, such as a vessel may experience in smooth 
water, cannot be relied on for ascertaining the safety of ships. 
* Traiii du Havire t p. 269. 
