of floating Bodies , and the Stability of Ships. 65 
points P, B, and N, will coincide ; on which account the 
evanescent area NXP will be = = A B — ; and if % 
2 O 
is put to represent a line drawn through the middle of the 
solid, on a level with the fluid's surface, and parallel to the 
longer axis, the evanescent portion of the solid intercepted 
between the two adjacent planes, will be A B x z: the per- 
pendicular distance of the centre of gravity of this evanescent 
solid from the point X, is -j AB. But it is required in the 
present instance to assign the distance from the horizontal 
line passing through the point X, of the centre of gravity of 
the entire volume immersed by the inclination, that is, the 
common centre of gravity of ail the evanescent solids 
corresponding to the entire length %. This distance may 
be obtained from the known rule of mechanics, which is, 
by multiplying each evanescent solid, considered as concen- 
tered in its centre of gravity, into the distance of that cen- 
tre from the given line, and dividing the sum of the pro- 
ducts by the sum of the solids; the result will be, the distance 
of the common centre of gravity from the horizontal line 
passing through the point X parallel to the axis ; and since 
the evanescent solid corresponding to the small lineal incre- 
ment z is - A B — , and the distance of its centre of gravity 
from the point X == or;—-, the product arising from mul- 
tiplying the solid into the distance of its centre of gravity, 
from the given horizontal line passing through X, will be 
~~ B 2 / X % ; an< ^ ^ ie SLim t ^ ose products corresponding 
K 
MDCCXC VI . 
