121 
of floating Bodies, and the Stability of Ships . 
mg bodies, during their inclination from o° to 90°, pass through 
a position of equilibrium, in which the force of stability be- 
comes evanescent : in other bodies, no limit of this kind takes 
place ; a difference which depends partly on their forms, and 
partly on the disposition of the centres of gravity of the solids 
and of the immersed volumes. It may be satisfactory to con- 
sider, in a general view, the effects produced on the motion of 
ships by the different proportions of their stability while they 
are inclined round the longer'axes. If a vessel* should be of 
a cylindrical form, floating with its axis horizontal, the vertical 
sections must necessarily be equal circles : supposing the centre 
of gravity of such a cylinder to be situated out of the axis, the 
vessel will float permanently with its centre of gravity, and the 
centre of the section passing through it, in the same vertical 
line : if such a vessel should be inclined from the upright by 
external force, it will be impelled in a contrary direction by the 
force of stability, which increases exactly in the proportion of 
the sine of the angle of inclination : it is plain, therefore, that 
a vessel of this description, during its inclination by heeling, 
cannot arrive at any limit where the force of stability is eva- 
nescent; on the contrary, it must continually increase until the 
inclination is augmented to 90°, where it will have become 
greater than at any other angle. 
Let another case be assumed : suppose the form of the ves- 
sel to be a square parallelopiped, floating permanently with one 
of the flat surfaces upward ; when this solid has been inclined 
round the longer axis through 45 degrees, the stability will be 
evanescent, and the least inclination greater than that angle 
* This is evidently an hypothetical case, stated with a view of illustrating the 
subject, 
MDCCXCVI. R 
