231 
the Stability of Ships . 
complicated, another solution is subjoined, by which the mea- 
sure of stability is exhibited in more simple terms. The inves- 
tigation is troublesome ; but the conciseness of the result, and 
the readiness with which it is applied to practical cases, com- 
pensate for the difficulty of obtaining it. 
Let the isosceles triangle BAF (Tab. X. fig. 11.), represent 
a vertical section of the vessel ; the base of which, BA, coin- 
cides with the water’s surface, when the vessel floats upright. 
Bisect BA in D, and join FD. Let G be the centre of gravity of 
the vessel, and take FE to FD as 2 to 3 ; E will be the centre of 
gravity of the immersed volume when the vessel floats upright. 
Draw the line CH, * intersecting the line BA at an angle 
ASH, equal to the given angle of the vessel’s inclination from 
the perpendicular, and cutting off the area ASH equal to 
the area BSC. When the vessel is inclined through the angle 
ASH, the line of intersection with the water’s surface will co- 
incide with CH. Bisect CH in the point N, and join FN : 
take FQ to FN as 2 to 3. Q is the centre of gravity of the 
area CFH, representing the volume immersed when the vessel 
is inclined. Through Q, draw QM perpendicular to CH ; and, 
through G, draw GZ perpendicular to QM. GZ is evidently 
the measure of the vessel’s stability. 
To obtain an analytical value of the line GZ, through Q, 
draw OQP parallel to CH ; through G, draw GR parallel to 
QM ; and, through E, draw ET perpendicular to QM. In this 
investigation it will be expedient, first, to express in general 
and known terms the line FW ; secondly, the line WQ, which 
is to MW as the sine of the vessel’s inclination to radius : this 
will give the value of MW, which being added to WF before 
* By the construction, p. 228. 
