of floating Bodies, and the Stability of Ships. 107 
and BY = 22! = — * X£L= and YD = ON 
P 5° 
1 6a — 15/) — 4 x -v^ — 1 5 /» 34^: 4- i$p 4- 4 V' 2a X ^8a -- 1 5 />. 
50 50 
and since HN = HD* — ND, we shall obtain HN 
HD 
== HA = *2 
2 
and TS = 
\/Sap — V%ap — isp z 
V 50 
'/ ap + v' 1 6ap — 30 
10 
HN 
17a — 30ft 4- 2 V zq x V'Sa — i$p. 
5 o ' 
parameter of ATD 
wherefore since TH = — , and NX = TH — TS, it follows 
that NX = - 17 a ~ 3°P + 2 ^ 2a x ' /%a ~ l 5P 
2 50 
8a 4- 30/1 
Vza x ^ 8 a — 15 p # 
__ 
; or finally, OX = ON — NX = 
34a + i;/> 4- 4 x v / 2« x 8 a — 1 5/> 
50 
26a - i 5 i> 4 - 6 x Vs 
+ 3 Qp — 2 X x f 8 a — 1 5^ 
So 
5/> 
5° 
By a computation similar to the preceding it is found, that 
the line PF = — - lit - 6 V JL * v * a ~ Hi 
5° 
It is therefore a consequence, from the geometrical con- 
struction assumed as true, that the parabolic conoid will float 
permanently with the extremity of the base in contact with 
the fluid s surface ; if the specific gravity of the solid is to 
that of the fluid, either in the proportion of 
26a — 
15 p 4 - 6 x v" 2a X v^8a — 1 
5 P 
5 ° 
26 a — 
15P — 6 -X v^aa x 8a — I ^p 
1 
to a x , or in that of 
s° 
proportions which were deduced from analytical investigation :f 
* HD = HA r= 
f Page 104. 
