of floating Bodies, and the Stability of Ships. 101 
FH = - ; FB = -; BH — — — A — ; and since by the 
construction KH : HI : l : n, and KH = BF= y, it follows that 
HI — ifp, and HO = ; consequently OB == HB — HO 
4^ — 3 P 2 a — 3/> — 4<* v' n (^(\ * / A a — 3 P — A a ^ n 
__ — — g ; VAJ _ V § 
x V~p : and because ON == 4 ' a ~ 4 — ■ * , it appears that CO 
will be to ON, that is, the tangent of the angle of inclination 
CNO,will be to radius as \/ 4 x >/ p to ^ 
or as 
y 
X P 
4 a — 3 p ■ 
— to l. When therefore the angle CNO 
becomes equal to 90°, that is, when the solid floats with 
the axis in a vertical position, the tangent of inclination 
= v/ 
\a _ _ 4a V n 
becomes infinite, or, which is the same 
thing, 4 < a — 3 p — 4 as/n — o, and consequently \/n = 
precisely coinciding with the limit deduced by a different 
method* of investigation. 
But another inquiry is here suggested. It is evident that 
this construction is applicable only while the solid floats 
in such a manner that the whole of the base AD shall be 
extant above the fluid’s surface. To know in what cases 
this condition takes place, it will be necessary to investigate 
what must be the value of the solid’s specific gravity, and the 
proportion of the axis to the parameter when the solid floats 
permanently, so that the surface of the fluid shall pass through 
one of the extremities of the base A. The result will shew 
the limit, or limits, if there are more than one, which sepa- 
* Page 96. 
