of floating Bodies , and the Stability of Ships. 83 
upright position, which is the angle KDC in the present 
case; substituting for n its value the equation will now 
become s* = ‘j or because s' = -^7, ■ = 
6tZ^Z\ > or 6t ’ ~ — t' = 6t — 3^ — 2 + «/'— gi 4 — *£, 
or 4fl =z6t — 2 ; which equation being resolved, gives £ = 
JL=±z — that is, t = — or i = i. By this solution it appears, 
4 4 2 
that there are two angles at which the solid may be inclined 
from its upright position of unstable equilibrium with the flat 
surface upward, so as to rest permanently on the surface of the 
fluid,whenthat surface passes through one extremity of the base : 
1st, when the angle of inclination is KDC = 26° 33', 31^,4, 
or about 26° 34', of which the tangent is to radius as 1 to 2 ; 
and secondly, (fig. 8. ) when the angle of inclination KDC == 45 0 , 
of which the tangent is equal to the radius. When the solid 
floats permanently on the fluid at the angle of inclination 
KDC = 26° 34' from the upright position, the part immersed, 
or KCD, is to the whole volume ABCD as 1 to 4; and there- 
fore the specific gravity of the solid is to that of the fluid as 1 
to 4, or resuming the former notation applied to the present 
case, the specific gravity of the solid or n = when that of 
the fluid is = 1 . That the position of equilibrium here de- 
termined is that of stability, appears from attending to the 
limiting value of the specific gravity, determined in page 6 g, 
where it is shewn that when the square parallelopiped is 
placed on the surface of a fluid with one of the flat surfaces 
horizontal, and the specific gravity of the solid is greater than 
.211, so as not to exceed .78 g, the equilibrium will be that of 
instability, and consequently the solid will overset. It has 
Ms 
