57 
of floating Bodies , and the Stability of Ships. 
QS parallel to GO; through E draw EY perpendicular to 
SQ; and through G draw %GZ perpendicular to SQ. Then, 
since the point Q is the centre of gravity of the part immersed, 
the pressure of the fluid will act in the direction of the verti- 
cal line OS, with a force equal to the body's weight, and by 
the principles of mechanics will have precisely the same effect 
to turn the solid round its axis as if the same force was ap- 
plied immediately at the point Z, acting in the same direction 
QS. Since, therefore, the effect of the fluid's pressure acting 
in the direction of a vertical line which passes through the 
centre of gravity Q, no way depends on the absolute position 
of that point, but on the perpendicular distance GZ, between 
the two vertical lines GO and SO only, in proceeding to ascer- 
tain, by geometrical construction, the several positions which 
bodies assume on a fluid’s, surface, and their stability of float- 
ing, the determination of the absolute position of the point 
Q, or centre of gravity of the immersed part, will not be ne- 
cessary ; the perpendicular distance GZ between the two ver- 
tical lines which pass through the centres of gravity of the 
solid, and of the part immersed, being sufficient for obtaining 
all the results that are required. 
The part immersed, before the inclination of the solid took 
place, is ADHB; when the solid has been inclined through 
the angle KGS, the part immersed is WRMP, which is the 
volume I R M N diminished by the space I W X, and aug- 
mented by the space NXP. But since the volume immersed 
under the fluid’s surface must always be of the same magni- 
tude while the solid’s weight continues unaltered, it follows, 
that whatever additional space is immersed under the surface 
in consequence of the inclination, an equal space must be ele- 
MDCCXCVI. I 
