Page 87 - statbility for masters and mates

Simpson's Rules for areas and centroids 75
Using the extension of Simpson's Second Rule
This rule can be used to ®nd the area when the number of ordinates is such that if one be subtracted from the number of ordinates the remainder is divisible by 3.
Fig. 10.6(a)
AreaofFigure10.6(a) 38 h a 3b 3c d
Now consider a water-plane area which has been divided up using seven half-ordinates as shown in Figure 10.6(b).
The water-plane can be split into two sections as shown, each section having four ordinates.
Fig. 10.6(b)
1331

combined 1 3 3 2 3 3 1 multipliers
Area1 38 h a 3b 3c d
Area 2 38 h d 3e 3f g Areaof 12 WP Area1 Area2
;Areaof 12 WP 38 h a 3b 3c d 38 h d 3e 3f g
1331
or
Areaof 12 WP 38 h a 3b 3c 2d 3e 3f g