55 
of floating Bodies, and the Stability of Ships. 
several positions of equilibrium through which the solid may 
be conceived to pass, while it revolves round the axis of mo- 
tion ; and secondly, by determining in which of those posi- 
tions the equilibrium is permanent, and in which of them it is 
momentary and unstable. 
In proceeding to investigate the principles which are the ob- 
jects of the present inquiry, it will be convenient in the first 
instance to consider the floating body to be some homogeneal 
solid of regular figure, and uniform shape and dimensions, in 
respect of the axis of motion throughout. If such a solid is 
supposed to be cut through by vertical planes in a direction 
perpendicular to the axis of motion, the sections of these 
planes with the solid will be areas precisely equal and similar. 
Let EDHF (Tab. III. fig. 1.) represent the vertical section 
of such a solid, which passes through the centre of gravity G 
in a direction perpendicular to the axis of motion. The solid 
floats on the surface of a fluid I ABL ; consequently ADHB 
represents the part immersed under the fluid's surface ; O is 
the centre of gravity of the part immersed, and the line GOC 
is assumed perpendicular to the horizontal line AB. We are 
in the next place to suppose that this solid is inclined round 
the axis of motion from its former position, through an angle 
KGS (fig. 2.) ;* so that the line KC which was before ver- 
* When this inclination takes place, the centre of gravity G, through which the 
axis of motion passes, is not necessarily fixed, but must evidently in most cases change 
its place, since the total volume immersed before the inclination is always equal to that 
which is immersed after the inclination ; and from this cause such change of place en- 
sues : but the motion of the axis, and of the point G, is wholly independent of' the 
reasoning in this and the subsequent constructions and investigations ; the object of 
which is to ascertain the angular motion round the said axis, and the several conse- 
quences thereof, and is no ways connected with the motion of the axis itself. This note 
