394 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



consequently, if this line be divided into six equal parts of 1.925 feet 

 each, and perpendicular ordinates be erected thereon, they will be 

 found to measure as follows, viz. 



No. of ordinates 

 Feet - - - 



0.15 



Therefore, if a' denote the area of the curvilinear space fxi ; then 

 by the second of the preceding approximating rules, we have 



S 4- 0, the sum of the extreme ordinates, 



4p = 4(.15 4- .43 4- .23) = 3.24, the second term of the series, 



2Q = 2(.30 4- .38) 1.36, the third and last term ; 



hence, by addition, we get 

 S _|_ 4? 4- 2 Q = 4- 3.24 + 1 .36 = 4.6 ; 



but one third of the common interval is 0.642 of a foot nearly ; con- 

 quently, by multiplication, the area of the curvilinear space fxi, 

 becomes 



a 1 = .642 X 4.6 = 2.9532 square feet, 



which being added to the area of the triangle above determined, the 

 area of the compound space fk i x becomes 



a 4- a' = 121.927 4- 2.953= 124.88 square feet. 



Again, if we put b to denote the area of the triangle hke, and b' 

 the area of the curvilinear space hye; then, by proceeding in a 

 manner similar to the above, the area of the mixed space hkey 

 becomes 



b 4- b' = 1 33.68 square feet. 



Now, if in this way, the values of a 4- a' and b 4- b' be calculated 

 for each of the 34 vertical sections, the several results will be as exhi- 

 bited in the following table. 



