t 
of floating Bodies, and the Stability of Ships. 73 
Respecting this determination it seems remarkable, that 
there should be only one value of specific gravity, as a limit 
between the stability and instability of floating ; whereas 
there were two specific gravities, each of which was a limit in 
the case when the solid was placed on the fluid with a flat 
surface upward. This difficulty admits of very satisfactory 
explanation ; when the flat surface is placed upward, the con- 
ditions on which the solution is founded are not at all altered, 
to whatever depth the solid may sink : but in the present 
case, when the solid is placed on the fluid with a plane angle 
upward, the conditions on which the solution has been inves- 
tigated imply, that as the specific gravity is increased, the 
section of the solid formed by the fluid's surface shall conti- 
nually increase also ; and on that ground the result justly gives 
one limit only between the stability and instability of floating ; 
but since in reality the section of the solid by the fluid’s sur- 
face increases only until the specific gravity becomes one half 
of that of the fluid, and afterwards decreases, it is evident, 
that if there should be another limit corresponding to the case 
when the specific gravity is greater than one-half, it must be 
discovered by a separate investigation. Let, therefore, the 
square parallelopiped EDCF (fig. 5.) of which the specific 
gravity is greater than that of the fluid being 1, be placed 
on the fluid with the diagonal line EC vertical: IABK repre- 
sents the surface of the fluid, and HC the depth to which the 
solid sinks ; G is the centre of gravity of the solid, and O 
the centre of gravity of the part immersed. If one of the 
sides DE is made = a, and the specific gravity put = n, then 
the area ABDCFA — an; and the area EAB = a — an = 
EH ; wherefore EH = a y s/ 1 — n = AH ; AB = 2 a x 
L 
MDCCXCVI. 
