a 4,o 
Mr. Atwood’s Disquisition on 
other conditions remaining the same, if the position of the sides 
should be reversed, in the manner described in the proposition, 
the stability, at equal angles of inclination, will remain the same. 
It may be proper in this place to remark, that the metacentric 
curve, described by M. Bouguer,* and M. Clairbois,^ and ap- 
plied to the preceding cases, does not appear to have any relation 
to the stability of vessels, except in the single point where the 
curve intersects the vertical axis ; and therefore can be applica- 
ble only in the case when the angle of the vessel’s inclination 
from the upright is evanescent. Let FBC, DAH, (fig. 15. ) repre- 
sent the sides of a vessel, BA coinciding with the water’s sur- 
face when the vessel floats upright : bisect BA in S, and draw 
ISE perpendicular to BA. Let E be the centre of gravity of the 
volume immersed. Suppose the vessel to be inclined through 
a very small angle AS a , so that the water’s surface shall now 
coincide with the line ba\ and let the centre of gravity of the 
volume immersed be Q. Through 0, draw the line QWz per- 
pendicular to ba, intersecting the line IE in the point W. This 
point is called by M. Bouguer the metacentre. One of the prin- 
cipal properties of this point is, that whenever the centre of gra- 
vity of the vessel is situated beneath it, any where in the line WE, 
( suppose at G, ) the vessel will float permanently, with the line 
IE vertical; but that, if the centre of gravity is placed above the 
metacentre, suppose at g, the vessel will overset, from that po- 
sition ; for, drawing GZ, gz, perpendicular to Qz, if the vessel 
should be inclined through a small angle AS a, so as to immerse 
the portion of the side A a , the force of pressure acting in the 
direction of the line QZ, to turn the vessel round an axis passing 
horizontally through G, will elevate the parts adjacent to A, so as 
to restore the upright position : whereas, if the centre of gravity 
* Traite du Navire, p. 270. 4 Clajrhois, p. 289, et seq. 
