the Stability of Ships. 21$ 
vessel is inclined from the perpendicular, through an angle 
equal to the angle OPQ. 
At whatever angle the vessel may be inclined from the per- 
pendicular, the total volume immersed must always remain the 
same, while the vessel's weight continues unaltered. Where- 
fore, the volume which has been immersed, or ASH, must be 
equal to the volume BSC, which has emerged from the water, 
in consequence of the vessel's inclination. For this reason, and 
because the side AH projects outward, while the side BC is 
parallel to the plane of the masts, it must necessarily happen, 
that the point S will not in this case bisect the line BA, as it 
did in the preceding construction, but will be removed nearer 
to the side AH, which has been immersed by the inclination 
of the vessel. Previously, therefore, to any consideration of 
the stability, it will be necessary to define the position of the 
point S in the line AB, so that a line CH, being drawn 
through S, at a given angle of inclination to AB, equal to that 
of the ship's inclination from the perpendicular, shall cut off 
the area ASH equal to the area BSC. 
Let the given angle of inclination, be OPO equal to ASH 
(fig. 4.) the angle QAH, at which the sides of the vessel are 
inclined outward from the plane of the masts above the water- 
line, is supposed to be given : this angle -|- 90° will be the angle 
SAH, which is therefore a known quantity : the remaining 
angle SHA, in the triangle ASH, will likewise be known. 
Through the extremity B of the line BA, (fig. 5.) equal to 
the vessel's breadth at the water-line, draw the indefinite line 
BU inclined to BA, at an angle ABU equal to OPQ : in BU, 
take any point O, and, in the line BO, set ofFBD to BO, as the 
cosine of the angle ABU to radius. In the line BD, take BE to 
BD, as the sine of the angle BAU is to radius : also take BF to 
F f 2. 
