of floating Bodies, and the Stability of Ships. 85 
with a plane angle obliquely upward, when the specific gravity 
is between the limits — and — , or between the limits — and —. 
32 32’ 32 32 
It has been seen in a former investigation, that if the solid is 
placed on the fluid with an angle upward, and the specific gra- 
vity is it will just begin to float with stability, and ceases to 
float with stability when the specific gravity exceeds When 
the specific gravity is — = ^ or -=j- = p, it floats permanently 
with the surface of the fluid coincident with an extremity of 
one of the sides: if, therefore, the specific gravity is between the 
limits — and—, or between — and—, the solid will float per- 
32 32’ 32 32’ r 
manently, with the diagonal line inclined to the vertical. This 
angle may be determined by finding an equation which ex- 
presses the relation between the given specific gravity and the 
sine or tangent of the required angle to radius = 1. Let a 
square parallelopiped IVCF (fig. 10.) float with an angle 
obliquely upward, so that the diagonal line shall make an 
angle with the vertical ; suppose that angle to be OGT, the 
line GT being perpendicular to the horizon ; let the surface 
of the fluid coincide with the line DE perpendicular to GT ; 
take CB a mean proportional between EC and CD, and draw 
BA parallel to GV, intersecting the line GC in H ; so shall 
CH be the depth to which the solid sinks in the fluid when 
the diagonal line Cl is vertical, and consequently the area 
BXE is equal to the area XDA ; take CO = y CH ; O will 
be the centre of gravity of the volume ABC ; bisect EB in K, 
and AD in B ; draw XR and XK ; and take XM = f of XR, 
and HL = \ of XK ; M will be the centre of gravity of the 
