Equilibrium of Floating Bodies. 335 



43 feet and two inches, and its depth 22 feet 9 inches. Whence 



- ') = 5,1 feet, differing little from the conclusion of a strict- 

 9 1 



er but very tedious process. 



451. Since the height of the metacentre is inversely as the 

 draught of a vessel, and directly as the square of its breadth, its 

 stability depends mainly on its spreading shape. This property 

 is an essential condition in the construction of life-boats. But 

 the lowering even of the centre of gravity has been found to be 

 sometimes insufficient to procure stability to new ships, which, 

 after various ineffectual attempts, were rendered serviceable, by 

 applying a sheathing of light wood along the outside, and thus 

 widening the plane of floating. 



452. It is not very difficult to determine the centre of buoy- 

 ancy, by guaging the immersed part of the hull. A cubic foot 

 of sea-water weighs 64 lb - avoirdupois, and 35 feet, therefore, 

 make a ton. The load of the vessel corresponding to every 

 draught of water may be hence computed. 



453. The height of the metacentre above the centre of grav- Fi g .220 

 ity in a loaded vessel, may be determined by simple observation. 



Let a long, stiff, and light beam be projected transversely from 

 the middle of the deck, and a heavy weight suspended from its 

 remote end, inclining the ship to a certain angle, which is easily 

 measured. Thus, if NL represent this lever, q the weight at- 

 tached, M the metacentre, and GMQ the inclination produced, 

 G being the centre of gravity, and GR a perpendicular drawn 

 from it to the vertical L </, the power of the weight q to in- 

 cline the vessel will be expressed by q X GR ; but p denoting 

 the entire weight of the vessel, the effort exerted at the metacen- 

 tre to keep the mast erect, will be represented by 



p x GQ, OY p x GM X sin GMQ. 

 Wherefore 



q X GR p x GM X sin GMQ, 



and consequently the elevation GM above the centre of gravity 

 C 1 /? 



is expressed by . sin GM Q- Now GR may, without any sen- 



