388 



OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



.7 



Let enfm be the space in question, including the angle of the 

 vessel's inclina- 

 tion ; draw the 

 lines me and nf 

 cutting off the 

 curvilinear areas 

 mre and nsf; 

 bisect the sides 

 me, pe in the 

 points u and TT, 

 and draw the 

 lines pu and mir 



intersecting each other in l\ /is the centre of gravity of the triangular 

 space mpe. Suppose z to be the centre of gravity of the curvilinear 

 segment mre, and through the points I and z, draw lq and zy respec- 

 tively perpendicular to mn, the line of floatation in the inclined posi- 

 tion of the vessel. 



Again, bisect the sides w/and/p in the points w, $, and draw pw 

 and n(f> intersecting each other in the point o\ o is the centre of 

 gravity of the triangular space npf. Let v be the centre of gravity 

 of the curvilinear area n sf, and through the points o and v, draw the 

 straight lines ot and vx respectively perpendicular to the water line 

 mpn; then, in the line tx intercepted by the perpendiculars ot and 

 vx, take tc such, that it shall be to 0: in the same proportion, as the 

 curvilinear space nsf, is to the compound space pnsf, and by the 

 property of the centre of gravity, c will be the point in mn, where it 

 is intersected by the perpendicular through the common centre of the 

 triangular and curvilinear spaces npf and n sf. 



Through the point p in all the sections, let a line PQ be drawn at 

 right angles to mn ; then, the same plane will pass through all these 

 lines, and cp will be the perpendicular distance of this plane, from 

 the centre of gravity of the mixed space pnsf. Therefore, if the 

 products arising from multiplying each area, into the distance pc of 

 its centre of gravity from the plane passing through PQ, be truly cal- 

 culated in all the sections contained between the head and stern of 

 the vessel ; then, by the principle announced and demonstrated in 

 Proposition (A), Chapter I, the distance of the centre of gravity of 

 the volume, whose sections are represented by all the areas pnsf, 

 from the vertical plane passing through PQ can easily be ascertained. 



Let pR be that distance, and by a similar mode of computation, 

 suppose that pE is found to be the corresponding distance of the 



