of floating Bodies , and the Stability of Ships. 53 
To put this matter in a clear point of view, let a case be 
assumed. Suppose two vessels to be of the same weight and 
dimensions in every respect, except that the sides of one of 
these vessels shall project more than those of the other, the 
projections commencing from the line coincident with the 
water’s surface. According to the theorems of Bouguer and 
other writers, the stability will be the same in both ships, which 
is in fact true, on the supposition that their inclinations from 
the perpendicular are extremely small angles : but when the 
ships heel to 15 0 or 20°, the stabilities of the two vessels must 
evidently be very different. Even supposing the stability of a 
ship A to be greater than that of a ship B, when the angles of 
heeling are very small, it may happen in cases easily supposable 
that when both ships are heeled to a considerable angle of in- 
clination, the stability of the ship B shall exceed that of the 
ship A. Admitting, therefore, that the theory of statics can be 
applied with any effect to the practice of naval architecture, it 
seems to be necessary that the rules investigated for determin- 
ing the stability of vessels should be extended to those cases 
in which the angles of inclination are of any magnitude likely 
to occur in the practice of navigation. 
When a solid is placed on the surface of a lighter fluid, at 
the proper depth corresponding to the relative gravities, it 
cannot change its position by the combined actions of its 
weight and the fluid’s pressure, except by revolving on some 
horizontal axis which passes through the centre of gravity. 
Various axes may be drawn through the centre of gravity of 
a floating body in a direction parallel to the horizon : but 
since the motion of the solid respecting one axis only, can be 
the subject of the same investigation (except in extreme cases 
