the Stability of Ships. £75 
If the total area DOA (fig. 26. ) should be measured by one 
computation, suppose from Rule 11. the 
Area would be found - = 2176.875 
Correct area - - - - =2.222.222 
Difference or error of the approximation = 45-347 
If this area should be computed according to 
the Rule 1. the error of the approximation will be 
found ------ 74-54 
It is easily shewn, that these errors, which are far from in- 
considerable, arise almost wholly from the mensuration of the 
area OXE, (fig. 26. ) adjacent to the vertex O. For, by measur- 
ing that area, according to the Rule 11. from three ordinates 
l = o, £ = 37.495, i = 40.889, the area is found to be 318.115 
Whereas the correct area OXE = iox 40.889 x J- = 3^3-457 
Difference or error from computing the area OXE 
by Rule 11. - - - — 45- 34 2 
Scarcely differing from - - - = 45-347 
which was found to be the error from computing the entire 
area DOA by this rule. 
If the area between the ordinates a and k be measured by 
the Rule in. it is found to be - - = 2055.390 
Area between the ordinate £ and /, by the proper- 
ties of the figure, is = 37.495 x 5 x J- - = 166.640 
Entire area DOA - = 2222.030 
Correct area - = 2222.222 
i n 1 
Difference or error of this approximation = .192 
From these computations it is evident, that the rules here 
given, when employed with attention to the necessary limita- 
N n 2 
1 
