of floating Bodies , and the Stability of Ships. 87 
diagonal line obliquely upward, being inclined to the vertical 
at an angle of 15 0 ; the equilibrium is that of stability, because 
when the diagonal is Vertical, the solid floats in a position of 
unstable equilibrium, the specific gravity 0.261 being less 
than. — or .281, the limiting value which separates the cases 
of permanent and unstable equilibrium when the solid is placed 
on the fluid with a diagonal line vertical. 
It is curious to observe the conclusions which arise in the 
extreme case when the angle of inclination from the vertical 
is assumed =t o ; and consequently the angle XEC ±= 45 0 ; 
for in this case CB == CE — a\ t = 1 ; and BH — - 4 = ; 
therefore u or the area BXE *■ = — . L . x . ? — _£fl • and since 
2 4 
b — PO = — ^ 4 =, it follows that bu = ; and izba = 
^ 3V2 3 v" 2 
= y/ 2a 3 s ; which quantities being substituted for their 
values, the equation s/ n — -—- 4 - — -will become s/ n = 
iz bu -f 2 V ztl a z s 
3 a s 
— — — — - 7— ; and therefore n == — , agreeinp- 4 ' 
2 2 a 3 s -f z V 2 a 3 s 4^2 3 2& & 
precisely with the specific gravity inferred by a different me- 
thod from the same data. 
The equation \/ n = (the line CE = a be- 
ing assumed = 1) expresses the relation between the specific 
gravity of the solid and the fraction representing the sine of the 
angle of inclination from the upright position : if, therefore, that 
# Because the point of intersection X coincides with H when the angle BXE va- 
nishes, 
f Page 72. 
