io8 Mr. Atwood's Propositions determining the Positions 
by which agreement both the construction and investigation 
receive the most satisfactory confirmation. 
It has been observed in the course of the preceding pages, 
that the theorems* investigated to discover the floating posi- 
tions of bodies, are no less applicable to ascertain the stability 
of floating, or the resistance which the fluid's pressure opposes 
to any force applied to incline a floating body from its position 
of equilibrium. This latter branch of statics is a subject deserv- 
ing of every attention which science and practical experience 
can bestow upon it, from the immediate relation it bears to the 
motion and equilibrium of ships at sea. By this principle, the 
wind's impulses become effectual in propelling vessels, which, 
in default of stability, are rather inclined from the perpendicu- 
lar than moved forward by the force of the wind : and when a 
ship has been nearly overset by the violence of the elements, it 
is the power of stability which still sustains, and (if sufficient) 
at length restores it to the upright position. 
The stability of a floating body when inclined through any 
angle from the perpendicular, has been obtained by investi- 
gating a general value of the perpendicular distance GZf = 
ds ; (fig. 2.) for the distance between the two vertical 
lines, one of which passes through the centre of gravity of the 
solid, and the other through the centre of gravity of the vo- 
lume immersed. This principle is now to be applied to ascer- 
tain the stability of ships : this will be effected by finding either 
by construction or by calculation, the length of the line GZ : 
and if the vessel's weight should be W, the measure of stability 
will be GZ x W, by which it is plainly seen, that if any force 
M should be applied at a distance from the centre of gravity 
SG, (fig. 2.) and in a direction perpendicular to SG, to balance 
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