80 Mr. Atwood’s Propositions determining the Positions 
its axis till it settles in some other position wherein the equi- 
librium is permanent. 
From the present proposition we shall be enabled to ascer- 
tain what that position is. Thus, let the specific gravity n = 
.24, which is between the limits .211 and .789; and will con- 
sequently place the solid with a flat surface upward and hori- 
zontal, in an equilibrium of instability. By referring to the 
equation s* = ~ ”” 2 ~ * , and substituting .24 for n, we find 
, 1 , a 12 n — 12 n z — 2 .1888 , co , 
tHat 5 = , 2 »- , = T1888’ a,ld 5 = the SUie ° f 2 3 29'. 
From this calculation it appears, that the solid after having 
overset from its position of unstable equilibrium, with the flat 
surface upward and horizontal, and having revolved through 
an angle of 23 0 29', will settle in a position of permanent equi- 
librium at that angular distance from its original situation ; 
for by the solution, when the solid has revolved through that 
angle, the centres of gravity of the solid and of the part im- 
mersed are again situated in the same vertical line, and con- 
sequently the solid is then situated in a position of equili- 
brium, which must be the equilibrium of stability, because the 
original position from which the solid inclined, was that of 
instability ; and it has been observed previously, that when a 
solid changes its position by revolving on an axis on the sur- 
face of a fluid, any position of equilibrium is always succeeded 
by a position of equilibrium which is of a contrary descrip- 
tion. 
If the angle of inclination from the upright position with a 
flat surface horizontal should be given, the specific gravity of 
the solid may be inferred from the preceding equation, which 
will cause the solid to float in a position of equilibrium at 
