of floating Bodies , and the Stability of Ships. 
79 
to be 
d = 
2a x 2 -f t x 
3 X Vi |/ 1 2 X 2 acn 
ds, or f X ' 2 — ds; or since 
!, the said distance = 
6 cn x 
a 1 t x 2 4- t 
by substituting for t its value — 
6 cn x v' i t z 
- — the distance 
or 
ben x 
— 1 — .fLili . j n expression a denotes half the breadth 
PQ ; but as it may be more convenient to represent the whole 
breadth AB or PQ by the letter a , the expression will in this 
case be = - lEEdLL ; which quantity be- 
mg put = o, we obtain 5 = lac ,„, _ 1M ,„ + — , or s = 
~ 120 . From this equation the angle of inclination 
from the original position of equilibrium may be found, from 
having given the specific gravity ; or conversely, the specific 
gravity may be found from having given the angle of inclina- 
tion through which the solid must revolve, so as to be situated 
in a second position of equilibrium. As the instances given to il- 
lustrate the propositions already investigated have been adapted 
to the case of a square parallelopiped, the present result may 
be exemplified on the same supposition. Assuming then the 
height of the solid to be equal to the base, a will become 
= c in the preceding expression, and consequently / = 
We have seen in a foregoing proposition, that if the specific 
gravity of this square solid should be greater than .211 so as 
not to exceed .789, the solid placed on the fluid with a flat 
surface upward, would be situated in an equilibrium of instabi- 
lity, and consequently must change its position by revolving on 
