the Stability of Ships. 293 
mated in the direction of the line NW, perpendicular to the 
plane Ff : let the line PO be denoted by the letter b. 
The solid contents of the entire volume displaced are next 
to be measured, from having first obtained the areas of the 1 2 
horizontal sections, intersecting the vertical axis at the common 
interval of 2 feet, and dividing the immersed volume into 1 1 
horizontal segments. The areas of the several horizontal sec- 
tions are measured by Rule hi. from having given the ordinates 
drawn in the said sections, parallel to the water's surface from 
head to stern, at the common interval of 5 feet. 
The mensuration of the area of the horizontal section 12, 
which coincides with the water's surface, from the ordinates; 
entered in the annexed * table, is as follows : 
According to the Rule in. 
S = 23.73 
p = 206.41 
Q = 41 1" 
the area of half the horizontal section 
is=S+sP + 3gx-^ = 3316.3, 
and the total area of the horizontal 
section 12 = 6633.6 square feet. 
The areas of the 12 horizontal sec- 
tions, computed by Rule in. from the 
ordinates, as expressed in the table 
inserted in the Appendix, are as fol- 
lows.. 
Ordinates, in the Appendix,. 
Vertica 
Sections 
Qrdinatesof 
the Hori- 
zontal Sec- 
tion 1C. 
Feet. 
Vertica 
| Sections 
Ordinates of 
the Hori- 
zontal Sec- 
tion 12. 
Feet. 
1 
IO.78 
1 9 
2I.48 
2 
16.00 
20 
21.32 
3 
18.40 
21 
21.22 
4 
19.84 
22 
2I.O5 
5 
20.54 
23 
20.82 
6 
20.94 
24 
20.61 
7 - 
21.20 
25 
20.44 
8 
2:1 3 8 
26 
20.15 
‘ 9 
21.48 
27 
i 9- 8 5 
10 
21.50 
28 
19.5 8 
11 
21.56 
2 9 
19-25 
32 
21.58 
30 
18.77 
] 3 
21.56 
3 i 
18.21 
14 
21.56 
32 
17.52 
15 
21.56 
33 
16.50 
l6 
21.55 
34 
12.95 
17 
18 
21-53 
21.51 
674.19 
* See Table of 
