EQUILIBEIUM OF FLOATING BODIES 



35 



FIG. 19. 



important, although the stability in a longitudinal direction may be 

 seriously affected by the flooding of one or more watertight compartments. 

 In the case of vessels of the submarine type, the longitudinal stability 

 becomes of the greatest importance, lack of such stability causing 

 a tendency to dive suddenly. 

 The metacentric height for 

 fore and aft displacements 

 may be experimentally deter- 

 mined just as for rolling 

 displacements. 



The position of the rneta- 

 centre may be determined 

 theoretically as follows, if the 

 positions G and H of the 

 C. G. of the vessel and of the centre of buoyancy are known. 

 Let A = area of section of vessel made by the plane of water line, or 



plane of flotation. 

 K = radius of gyration of this area about a longitudinal axis 



through its Centroid. 

 V = volume of water displaced by vessel. 



Let G, H, H', M, have the 

 meanings previously 

 attached to them. 

 be the elevation of the 

 line of intersection of 

 the planes of flotation 

 in the equilibrium and 

 displaced positions 

 (Fig. 16). 



Then if a small angular dis- 

 placement 6 be given to the 

 vessel, the volume displaced, 

 being proportional to the 



FIG. 16. 



weight of the vessel, does not change. 



/. Volume of wedge a o a' = volume of b o b', 



Again if y be the depth, perpendicular to the paper, of any element 8 x 

 of the wedge at a distance x from o, the volume of this element 

 = y x d x. 



Volume of wedge a o a' = / x y d x 



