7i 
of floating Bodies , and the Stability of Ships. 
y/T to s/~\ and from the same solution it appears, that if 
the height bears a less proportion to the base than that of 
y/T to s/~, no value can be given to the specific gravity, 
which will cause the stability to vanish, because the quantity 
y/ -j- — f-r becomes impossible.; in which case the solid 
placed with the surface EF horizontal, must in all cases con- 
tinue to float permanently in that position, whatever may be 
the specific gravity, always supposed to be less than that of 
the fluid. 
(Fig. 4.) Similar determinations may be obtained from the 
same theorem respecting the equilibrium of the solid, when 
placed on a fluid with a plane angle upward, that is, with 
the diagonal line EGC vertical. Let EDCF represent a ver- 
tical section of a square parallelopiped floating on the surface 
of a fluid IABK -. making the side DC — a, the line GC = 
^7=, suppose that the specific gravity of the solid is to the 
specific gravity of the fluid as n to 1, and that the solid sinks in 
the fluid to the depth HC ; let G be the centre of gravity of 
the solid, and O the centre of gravity of the part immersed ; 
then the area ABC is to the area DEFC as n to 1 ; wherefore 
the space A B C = H B = an , and I IB = HC = a x \/ n ; 
AB = 2jv / iT; OC = — andGO = L— _ 
________ 3 ^23 
a X 3 — 8 X n 
^2x3 
Referring to the quantity expressing the perpendicular dis- 
tance between the two vertical lines passing through the 
centre of gravity of the solid, and the centre of gravity of 
the part immersed, when the angles of inclination from the 
