2 gz Mr. Atwood's Disquisition on 
Suppose the volume immersed, by the 
inclination on the side ADW b, to be di- 
vided into very thin laminae, or solids, the 
bases of which are the areas of the succes- 
sive figures ADH 5 , and the thickness a 
small increment of the longer axis ; by ap- 
plying the Rule hi. to the products in the 
adjacent table, corresponding to the figures 
ADW b , we shall obtain the sum of all 
the products, arising from multiplying each 
of these thin solids into the perpendicular 
distance of its centre of gravity from the 
plane F/ = S+2P+3Q x ^- = 254,367; 
which sum of products being divided by 
the solid contents of the said volume, or 
18509, will be the distance DO, of the 
centre of gravity of the volume ADW b 
from the plane Ff = = 13.78 ; and, 
by a similar calculation, the distance DP 
from the plane F /, of the centre of gravity 
of the volume on the side BDN r, caused 
to emerge by the inclination, will be 
= 13-54 = DP - 
The sum of these two lines, DQ+DP; 
or PQ, will be = 27.32 feet, which is the 
distance of the centres of gravity of the 
volumes immersed and emerged, in con- 
sequence of the vessel's inclination, esti- 
Vertical 
Sections 
Products on 
the Side 
ADH b 
Products on 
the Side 
BDC c 
1 
359 
1 43 
2 
9 2 9 
562 
3 
12 6 9 
1010 
4 
1522 
2342 
5 
1683 
! 54 2 
6 
1699 
166 g 
7 
1723 
1 76b 
8 
1747 
^53 
9 
1 739 
187s 
10 
173 1 
1892 
11 
1736 
1912 
12 
1742 
*93 1 
13 
1742 
'93 1 
14 
1742 
1 93 1 
15 
1727 
1 93 ° 
16 
1713 
i 9 2 9 
17 
1724 
1915 
18 
1736 
1901 
19 
17 1 9 
1866 
20 
1702 
1832 
21 
i6bo 
1798 
22 
1618 
1764 
2 3 
'59' 
1 7°5 
24 
1564 
I646' 
25 
j 5 i6 ' 
1584 
2 6 
1468 
1522 
27 
3 4 1 5 
1434 
28 
’ 3 6 3 
1346 
29 
1290 
1220 
30 
1199 
1088 
S 1 
1114 
88l 
3 3 
101c 
6 73 
33 
9 1 9 
4*5 
34 
708 
102 
50119 
49.908 
