the Stability of Ships . 207 
inclination, it is restrained to the condition that the inclina- 
tions from the upright shall be evanescent, or, in a practical 
sense, very small angles. In consequence of this restriction, 
the rule in question cannot be generally applied to ascertain 
the stability of ships at sea ; because the angles to which they 
are inclined, both by rolling and pitching, being of consider- 
able magnitude, the stability will depend, not only on the con- 
ditions which enter into M. Bouguer's solution, but also on 
the shape given to the sides of the vessel above and beneath 
the water-line or section, of which M. Bouguer's theorem 
takes no account. But it is certain that the quantity of sail a 
ship is enabled safely to carry, and the use of the guns in 
rough weather, depend in a material degree on the form of 
the sides above and beneath the water-line ; this observation 
referring to that portion of the sides only which may be im- 
mersed under, or may emerge above, the water's surface, in 
consequence of the vessel's inclination ; for, whatever portion 
of the sides is not included within these limits, will have no 
effect on the vessel's stability, the centres of gravity, volume 
of water displaced, and other elements not being altered. By 
the water-section is meant, the plane in which the water's sur- 
face intersects the vessel, when floating upright and quiescent ; 
and the termination of this section in the sides of the vessel is 
termed the water-line. A general theorem for determining 
the floating positions of bodies is demonstrated in a former 
paper, inserted in the Phil. Trans, for the year 1796, and ap- 
plied to bodies of various forms : the same theorem is there 
shewn to be no less applicable to the stability of vessels, taking 
into account the shape of the sides, the inclination from the 
upright, as well as every other circumstance by which the 
