380 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



When the curves D E and c F are dissimilar between themselves, and 

 dissimilarly situated in respect of the intersecting lines DC and EF ; 

 then it is manifest, that the point p cannot fall in the middle of either, 

 but must occur to the right or to the left, according as it is influenced 

 by the nature of the curves, which define the exterior contour or bound- 

 ary of the vessel. 



Suppose therefore, that the intersection takes place at the point p, 

 a little to the right of the place where the two water lines are sup- 

 posed to bisect one another ; and through the pointy, let the straight 

 line <?/be drawn parallel to EF, and meeting the sides of the vessel in 

 the points e and/; then is e/the line through which the secondary 

 section of the water passes, on the supposition that it intersects the 

 principal section in the straight line passing through p, parallel to the 

 longer axis of the vessel. 



470. Now, in order to determine the position of the point p, it will 

 be expedient to conceive the volumes which become immersed under, 

 and elevated above the fluid's surface, in consequence of the inclination, 

 and of which fpc and epv are transverse sections, to be divided into 

 segments by vertical and parallel planes cutting the longer axis of the 

 vessel at right angles, and at the distance of a few feet from each 

 other, the distances being regulated by the dimensions of the vessel, 

 and the nature of the curves by which it is bounded ; they may in 

 general, however, be from 3 to 5 feet in large vessels, and from 2 to 

 3 feet in smaller ones ; but in all cases, they must be chosen accord- 

 ing to circumstances. 



i 7P 



Each of these segments will be of a wedge-like form, contained 

 between two vertical and parallel planes fpc, f'p'c'; two inclined 

 planes cpp'c', fpp'f, making with each other an angle fpc or 

 f'p'c' equal to the angle of the vessel's inclination, and the portion of 

 the ship's side which is represented by fee 1 'f r . 



The horizontal distance between the planes fpc and f'p'c', is the 

 line pp', which being produced both ways to the head and stern of 

 the vessel, forms the line in which the two sections of the water cut 



