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the axis passing through the pentre of gravity ofthe vessel, and the line of support, which is avertical line drawn through the centre of gravityof the immersed part of the vessel. Thus letA B (fig. 10, plate 8) be the line of floatationwhen the body is upright, and C D that corre-sponding to any angle of heel; G the centre ofgravity of the whole vessel, and G 1 that of thepart immersed. Through G 1 draw G 1 E parallelto C D, and make G 1 E a fourth proportional tothe area immersed, that of either of the equaltriangles A K C or B D K, and the distance p pbetween the two centres of gravity of the twotriangles, projected on the oblique line C D.From E draw and prolong E M, perpendi-cular to G 1 E, until it meet the vertical axis ofthe vessel in M. Then the point M is the meta-centre. When M, the metacentre, is above G,the centre of gravity of the body, the stability ispositive : when M is coincident with G, the sta-bility is nothing, as in the case of a cylinderfloating horizontally without load: and whenM is lower than G, the stability is negative, andtends to overset the body, as is the case with acylinder with a load fixed at some distanceabove it.

Reducing the rectangular figure to a trapezoid,abed, we perceive, (beside the advantages arising.