OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 391 



the nature of its bounding curves ; but the arithmetical operations, as 

 applied to any particular case, are unavoidably tedious, and necessa- 

 rily extend to considerable length ; they are, however, very far from 

 being difficult, as the ensuing process will fully testify. 



478. By referring to the table of ordinates, it will appear, that the 

 greatest, or principal transverse section, intersects the longer axis, at 

 about the distance of 60 feet, or 12 intervals from the section nearest 

 to the head of the ship ; we shall therefore delineate that section, and 

 in order that nothing may be wanting to the proper understanding of 

 the subject, we shall also delineate the plane of floatation, which cor- 

 responds to the twelfth horizontal section in the preceding table of 

 ordinates. 



The ordinate in the table opposite the twelfth vertical and under 

 the twelfth horizontal section, is 21.58 feet, and the whole vertical 

 distance between the keel and the plane of floatation, is 22.75 feet; 

 therefore, draw 

 the horizontal 

 line a a which 

 make equal to 

 43.16 feet, and 

 bisect a a per- 

 pendicularly by 

 AK equal to 

 22.75 feet. 



Divide the 

 vertical axis A K 



into twelve parts, eleven of which are 2 feet each, and the first or 

 lowermost only three fourths of a foot, or nine inches ; then, through 

 the several points of division 1, 2, 3, 4, 5, 6, &c. and parallel to aa, 

 draw the several ordinates, taken from the twelfth horizontal row in 

 the preceding table, which set off both ways, and through the extre- 

 mities of the several ordinates, let the curve line ana be drawn, which 

 will represent the boundary of the principal lateral section, so far as 

 it is immersed below the fluid's surface. 



And exactly in the same manner may the whole of the 34 vertical 

 sections, into which the longer axis is divided, be delineated ; but the 

 above being sufficient for illustration, we shall next proceed to describe 

 the twelfth horizontal section which is coincident with the water's 

 surface, and of which the greatest ordinate is 21.58 feet, correspond- 

 ing to a A in the above vertical section. 



479. Since the body of the vessel is divided at intervals of 5 feet into 

 34 vertical sections, it follows, that between the first section adjacent 



