24 ,6 Mr . Atwood’s Disquisition on 
of curvature, which he demonstrates to increase continually 
with the inclination of the vessel : he shews, that the centres of 
curvature thus found, or successive metacentres, according to M. 
Bouguer s construction, ascend as the vessel is inclined; a cir- 
cumstance which, according to his principle, imparts security 
from oversetting. On the contrary, in the other instance, when 
the sides of a vessel are inclined to an angle which is above the 
water’s surface, (fig. 12.) from a similar mode of reasoning he con- 
cludes, that the metacentre descends as the vessel is more and 
more inclined; which, according to his proposition, would 
endanger the safety of the vessel, when inclined to considerable 
angles. 
This determination is evidently inconsistent with the solu- 
tions of Case vi. and vii. preceding, by which it appears, that 
the stability acting to restore vessels thus constructed to the 
upright position, under the conditions that have been stated, 
will be precisely the same at all equal inclinations from the 
upright, whether the sides are inclined at an angle beneath or 
above the water-line; all the other conditions being the same 
in both cases. 
The solution of these questions being connected with a prin- 
ciple of some consequence in the practice of naval architecture, 
the preceding observations have been offered with a view of 
stating distinctly the opinions which are contradictory to the 
solutions of Case vi. and vii. referring to the authors who have 
treated on the subject, in order that a judgment may be formed 
by persons conversant in naval architecture, whether the pro- 
positions advanced by M. Bouguer and M. Clairbois, or the 
solutions of Case vi. and Case yn. here given, may be relied 
on, as founded on the genuine principles of geometry and me- 
chanics ; for error must exist on one side or the other. 
