y6 Mr. Atwood's Propositions determining the Positions 
it will continue permanently to float, we must have recourse 
to the theorem for expressing the perpendicular distance be- 
tween the two verticals, which pass through the centres of 
gravity of the solid and of the part immersed. For by put- 
ting this value = o, the resolution of an equation thence aris- 
ing, will give the sine of the inclination from the position of 
equilibrium at which these two vertical lines coincide; that is, 
when the centres of gravity of the solid and of the part im- 
mersed are again in the same vertical line : in this case the 
solid will be situated in a position of equilibrium, which, ac- 
cording to the observations in page 63, must be an equilibrium 
of stability. 
Let EFDC (fig. 6.) represent the vertical section passing 
through the centre of gravity G of an oblong solid or paralle- 
lopiped, the longer axis of which passes through the centre of 
gravity G in a direction perpendicular to the plane EFCD; 
LGS is drawn through G parallel to CE or DF ; this solid is 
placed on the surface of a fluid IABK, with the line SGL ver- 
tical ; and the specific gravity of the solid is such as causes it 
to sink to the depth under the fluid's surface SN. 
The volume immersed under the fluid's surface is the space 
ACDB, of which the centre of gravity is O ; and since the 
points G and O are situated in the same vertical line, the solid 
will be in a position of equilibrium, which, according to the 
present supposition, is assumed to be the equilibrium of insta- 
bility ; the solid will therefore spontaneously overset whenever 
external support is removed, and will change its position by re- 
volving round an horizontal axis which passes through the 
centre of gravity in a direction perpendicular to the plane 
CDFE. 
