Mr. Atwood’s Disquisition on 
Let t = 100, s = sin. i >f to rad. = 1. d = 13, V = 3600. 
According to these conditions, GZ = 2.63. If, therefore, the 
vessel’s weight should be 1000 tons, the stability will be equi- 
valent to the weight of 1000 tons, acting to turn the vessel at 
the distance of 2.63 from the axis passing through G, or equi- 
valent to a weight of ,52.5 tons, acting at a distance of 50 from 
the axis. 
CASE XI. 
The vertical sections of a vessel are terminated by the arcs 
of a conic parabola. 
Let the parabola BLA (fig. 20.) represent a vertical section 
of a vessel, floating with the axis DL perpendicular to BA, 
which coincides with the water’s surface. G is the centre of 
gravity of the vessel. Suppose a ship, so formed, to be inclined 
from the upright through a given angle MOL The breadth 
BA, and depth from the water-line, DL, being given, it is re- 
quired to construct the measure of the vessel’s stability. 
The principal parameter being given from the conditions of 
the construction, from the vertex L set off LF, equal to a fourth 
part of the parameter : F is the focus of the parabola. In the 
line LF, take LI to LF, as the tangent of the given angle 
MOI to radius; and, in the line LI, take LX to LI, in the 
same proportion of the tangent of the angle MOI to radius. 
Through the point X, draw XV perpendicular to XL, inter- 
secting the curve in the point V ; set off LN equal to XL : 
join N-V, which produce indefinitely, in the direction NVW ; 
angles of inclination that are evanescent, the stability of all vessels, at equal inclina- 
tions, thus calculated, whatever be their forms, would be the same as if the vertical 
sections were circular ; the breadths at the water-line, position of the centres of gravity.. 
■ 
and other elements, being the same. 
