no Mr. Atwood's Propositions determining the Positions 
If SG = o, that is, if the centre of gravity of the solid co- 
incides with the point of equipoise S, otherwise called the 
metacentre,* or centre of equilibrium, the stability will be 
= o, or in other words, the solid will float in all posi- 
tions alike, without effort to restore the upright position 
when inclined, or to incline itself further; it being remem- 
bered that the angles of inclination are very small. When 
the centre of gravity is situated beneath the metacentre, 
the solid must always float with stability, the measure of 
which is W x SG‘ x s, in which case this force acts on the so- 
lid to turn it in a direction contrary to that in which it is 
inclined from the upright position ; but when the centre of 
gravity is placed above the metacentre, (fig. 2.) the quantity 
W x SG x s having passed through o, becomes a force which 
acts to turn the solid in the same direction in which it is in- 
clined, and will therefore constitute the equilibrium of insta- 
bility. The determination of the point S becomes, for these 
reasons, of consequence in estimating the stability of vessels 
and other bodies when the angles of inclination are very small, 
and is particularly of use in ascertaining whether a solid, when 
placed on a fluid in a given position of equilibrium, will float 
permanently in that position, or will overset. Because it de- 
pends on the stability or instability *f of floating when the angles 
of inclination are of evanescent magnitude, whether the solid 
will continue to float in a position of equilibrium or will re- 
volve on an axis until it settles in some other. These theorems, 
however, for the measure of stability being applicable only in 
those cases when the angles of inclination from the position 
of equilibrium are extremely small, when a ship or other body 
is inclined io°, 15 0 , or 20°, the stability of floating is to be ob~ 
* Bougver. Liv. i. sect. iii. chap. iy. f Page66. 
