^88 
Mr. Atwood's Disquisition on 
water-section = 22.75 feet. The line DR = 22 feet, is divided 
into 11 equal parts, and, through the points of division, 12 ordi- 
1 
nates* are drawn, parallel to the line BA, at the common dis- 
tance of 2 feet. 
The vessel is supposed to be inclined round the longer axis, 
at an angle of 30°, and the line NDW is drawn through the 
point D, inclined to BA, at an angle ADW= 30°: proceeding 
according to the solution which has been given, by measuring 
the line DW ±= 22 .6 feet, DA = 21.58 feet, the area of the 
triangle ADW = 21-58 * 2 --— = 121.92 square feet. Also, by 
mensuration, the line WA = 11.55: this line being divided 
into six equal parts, of 1.925 each, if ordinates are drawn at 
the points of division, perpendicular to the line WA, they are 
found to be as here stated. 
By computing according to the 
Rule 11. from the 7 ordinates given, 
of which the two extremes are = o, 
the area of the curve space AW h 
— 2.95, which being added to the 
area ADW= 121.92, the area of 
the entire figure ADWZ> =124.87. 
By similar calculations, the area 
of the figure BDN c is found to be 
= 133 - 68 * 
The areas of the figures ADW£ 
and BDN c, being measured in 
each of the 34 vertical sections, 
are found to be as follows. 
* The numerical measures of these lines are inserted in the table of ordinates ; (see 
Appendix ;) the numbers are entered in the 12th vertical section. It is not necessary 
to express them in the figure. 
Ordinates. lumbers. Products. 
Pts. or a Foot. 
a 
== 0.00 1 
0.00 
b 
= 0.15 4 
0.60 
c 
= 0.30 2 
0.60 
d 
= °-43 4 
1.72 
e 
= 0.38 2 
0.76 
f 
== 0.23 4 
0.92 
g 
= 0.00 1 
0.00 
Sum 
4.60 
4 common interval 
— 
.642 ; and the area 
AW b — 4,0 x .64a 
= 2.95 
