84 Mr. Atwood's Propositions determining the Positions 
been just shewn, that after the body has revolved through an 
angle of 26° 34' it will be again in a position of equilibrium, 
which must therefore be the equilibrium of stability. Similar 
consequences follow from supposing the specific gravity = \ ; 
in this case if the solid is placed on the fluid with a flat sur- 
face upward, the equilibrium will be that of instability ; and 
it appears from the preceding solution, that after revolving 
through an angle of 45 0 , (fig. 8.) it will again be in a position 
of equilibrium, which therefore will be stable and permanent. 
By a similar investigation, the angle of inclination ABK (fig. 9. ) 
from the original position of equilibrium may be found when 
the solid floats permanently, and the fluid’s surface intersects 
one of the extremities of the upper side of the square AB : for 
the notation remaining, by putting the tangent of the angle 
of inclination ABK = t, the area ABK = area KCDB = 
2a ~ a wherefore the specific gravity or n— 2 ~ which 
i 1 
quantity being substituted for n in the equation ■ fa * == 
— - 12?; - 2 there will arise the equation — - -- = v! ~ ~ % 
exactly the same as in the former case ; and by solving this 
equation it appears that t = =*= -j, and consequently the spe- 
cific gravity of the solid, or n — — ~ 1 = | or m = A 
The only inquiry remaining to complete the investigation 
respecting the floating positions of the square parallelopiped, 
is to ascertain in what position the solid will float permanently 
* Because s being the sine, and t being the tangent of the angle ABK, it follows that 
