75 
ofjloatmg Bodies , and the Stability of Ships. 
the specific gravity, i — & it > H> & i + ^ i ~ i : 
or .zii, .281,-718, & .789, we find 
that if the specific gravity is less than .an, the square paral- 
lelopiped, when placed on the surface of the fluid with a flat 
surface upward and horizontal, floats permanently in that po- 
sition, but oversets if the specific gravity is greater than .211, 
and less than .789. We observe also, that when the solid is 
placed on the fluid with an angle upward, if the specific gra- 
vity is less than .281 it oversets ; if greater than .281 and less 
than .718, the solid floats permanently with the angle up- 
ward ; but if the specific gravity exceeds .718, the solid over- 
sets when placed on the fluid with an angle upward. 
It is therefore evident at what depth of floating, depending 
on the specific gravity, the solid when placed on the fluid in 
the positions which have been described, begins or ceases to 
float with stability. But a material inquiry remains to be 
considered, which is, to ascertain in what position a square 
parallelopiped will dispose itself, in respect to the fluid's sur- 
face, when the specific gravity is of any intermediate values 
between the limits which have been determined. To resolve 
this question the preceding results are evidently inadequate, 
since from these we only know in what cases, depending on 
the values of the specific gravity, the solid when placed on the 
fluid either with a flat surface or an angle upward will float 
permanently ; and in what cases it will overset. Suppose the 
latter event to take place, and that the solid, having been placed 
on the fluid in a position of unstable equilibrium, oversets or 
changes its position by revolving on its axis. To ascertain 
what position the solid so circumstanced will assume, in which 
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