273 
the Stability of Ships . 
And, since r = 5, the area between the ordinates 
b and I — S -(- 2 P -f^Qx j » = 1971,220 
Area IKOD between the ordinates a and b = 250.000 
area BDO 
Correct area BDO 
= 2221.220 
= 2222.222 
Difference or error of the approximation = 1.002 
In applying these rules, it is necessary to observe, that if 
the ordinates are drawn perpendicular to the axis of the curve, 
whenever the area to be measured, or any part of it, is adjacent 
to the vertex O, the area found by these rules will be the least 
exact : in such cases, it will be requisite to assume an abscissa 
near the vertex O, perpendicular to the axis : by erecting equi- 
distant ordinates upon it, parallel to the axis, the area will be 
found, with the same exactness as in the other cases, which will 
appear by the following computations. 
DOA (fig. 2 6.) is a semiparabola, similar and equal to DOB. 
Let the line DO = 50 be divided into 1 o equal parts, each 
— 5 ; and, through the points of division, let the succes- 
sive ordinates b, c, d, &c. be drawn perpendicular to DO: 
according to the preceding observations, if the entire area DOA 
should be computed by either of the three rules, the result 
would be less exact than in the former cases. To obtain an 
approximate value of the area, sufficiently near the truth, a por- 
tion of the area adjacent to the vertex O, suppose XEO, is to 
be separately computed. If OX be = 10, the line XE will 
~ 40.8890, which being divided into six equal parts, each of 
them will = 6815: let the ordinates p , q, s, t } &c. be erected at 
the points of division, perpendicular to XE : 
N n 
MDCCXCVIII. 
