02 Mr. Atwood's Propositions determining the Positions 
equilibrium, when the line GZ = o ; that is, when the two cen- 
tres of gravity, G and Q, are again situated in the same vertical 
line ; or in other words, when the solid is again in a position 
of equilibrium. By this method of proceeding, the several 
positions of equilibrium may be determined ; it only, there- 
fore, remains to discover in which of these positions the equi- 
librium is permanent, and in which of them it is momentary 
and unstable. This, circumstance will depend on the species 
of equilibrium in which the solid is originally placed previously 
to the inclination, which, for the sake of more clearly stating 
the principles of stability, may be supposed known, although 
the rules for ascertaining this point have not yet been consi- 
dered, but will appear in the pages which next follow. As- 
suming then the species of equilibrium, in which a solid is ori- 
ginally placed on the surface of a fluid, to be known, let that 
equilibrium be supposed permanent, or the equilibrium of 
stability ; and let the solid be conceived to be inclined round 
the axis of motion, through a given angle A, till it becomes 
situated again in a position of equilibrium ; in which case the 
centres of gravity of the solid, and of the part immersed, will 
again be in the same vertical line. Since during this inclina- 
tion, the fluid's pressure acts with a force proportional to the 
line RT or GZ, (fig. 2.) to diminish the angular distance from 
the original position of equilibrium, it follows that the same 
force must act on the solid, so as to augment the inclination, 
or angular distance from the second position of equilibrium, 
in which the solid is situated after it has revolved through the 
entire angle A, or any part thereof, from its original situation ; 
from which observations it is evident, that the second position 
of equilibrium must be that of instability :* and by the same 
* It appears from the observations in page 49, that whenever a solid floats in a posi- 
