so8 Mr . Atwood's Disquisition on 
stability can be influenced. To infer, from this theorem, the 
stability of vessels in particular cases, the form of the sides, 
and the angle of inclination from the perpendicular, must be 
given. These conditions admit of great variety, considering 
the shape of the sides, both above the water-line and beneath 
it ; for we may first assume a case, which is one of the most 
simple and obvious ; this is, when the sides of a vessel are pa- 
rallel to the plane of the masts, both above and beneath the 
water-line ; or, secondly, the sides may be parallel to the masts 
under the water-line, and project outward, or may be inclined 
inward, above the said line ; or they may be parallel to the 
masts above the water-line, and inclined either inward or out- 
ward beneath it ; some of these cases, as well as those which 
follow, being not improper in the construction of particular 
species of vessels, and the others, although not suited to prac- 
tice, will contribute to illustrate the general theory. The 
sides of a vessel may also coincide with the sides of a wedge, 
inclined to each other at a given angle ; which angle, formed 
at an imaginary line, where the sides, if produced, would inter- 
sect each other, may be situated either under or above the 
water 's surface. To these cases may be added, the circular 
form of the sides, and that of the Apollonian or conic para- 
bola. The sides of vessels may also be assumed to coincide 
with curves of different species and dimensions, some of which 
approach to the forms adopted in the practice of naval archi- 
tecture, particularly in the larger ships of burden. And lastly, 
the shape of the sides may be reducible to no regular geome- 
trical law ; in which case, the determination of the stability, 
in respect to a ship's rolling, requires the mensuration of the 
ordinates of the vertical sections which intersect the longer 
