378 



OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



or 



469. Let A B c K D represent a tranverse section of the hulk of a ship, 

 perpendicular to the longer axis, and passing through G its centre of 

 gravity, and suppose the vessel as it floats upon the surface of the 

 water to be upright and quiescent; then LK the axis of the section, 

 according to the seventh definition, is perpendicular to the horizon, 

 and in this state 

 the principal sec- 

 tion of the water 

 passes through the 

 line D c throughout 

 the whole length 

 of the vessel ; 

 which may 

 bly be better un- 

 derstood, if the 

 principal water 

 section be viewed 

 endways, with the eye at a great distance, it will appear as if it were 

 projected into the straight line DC. 



While the vessel retains its upright position and remains in a state 

 of rest, the transverse or shorter axis, is that which is represented by 

 the dotted line a b, and the place of the centre of gravity of the 

 immersed portion DKC, is somewhere in the line passing through g in 

 a direction parallel to the horizon ; for g is the place of the centre of 

 gravity of the section DKC, which falls below the principal section of 

 the water passing through DC. 



When the ship is caused to heel or to revolve about the longer axis 

 passing through G, until it moves through an angle equal to FPC; 

 then it is manifest, that the principal section of the water, or the plane 

 in the ship which passes through the line DC, will be transferred into 

 the position EF ; but the section of the water will intersect the sides 

 of the vessel, in the direction of a plane passing through DC, which is 

 inclined to the former plane passing through EF in an angle equal to 

 the angle FPC. The plane which passes through the line DC in a 

 direction parallel to the plane of the horizon, may therefore be termed 

 the secondary section of the water, merely to distinguish it from that 

 which formerly passed through EF, and which we denominated the 

 principal section. 



The principal and secondary sections of the water must therefore 

 intersect one another in the line denoted by the point P, or rather in 

 the line which being viewed endways, is projected into the point P, 



