Stability with Draught of Water in Ships. 213 



depth of immersion. What is usually done in practice, is to ascertain 

 the position of the centre of gravity for such conditions of loading as 

 may often be expected to occur ; or to determine the limits between 

 which it will lie in certain extreme circumstances. This variable and 

 uncertain factor, of height of centre of gravity, is one of the greatest 

 practical difficulties that have to be overcome in fully or accurately 

 determining and regulating a ship's stability. The difficulty is not 

 the same in all cases. In war-ships, for instance, and many which 

 merely carry passengers and light baggage, the centre of gravity may 

 either be regarded as fixed, or to vary with the draught of water in 

 a specific manner which may be readily determined. On the other 

 hand, many mercantile vessels employed in the carrying trade are 

 laden with cargoes which, together with the coals that are required 

 for consumption upon a voyage, weigh twice their own total weight. 

 In such cases, the position of the centre of gravity of the laden ship 

 is largely dependent upon stowage, a,nd the stability may be entirely 

 dependent upon it. The consumption of coal at sea introduces a 

 cause of variation in position of cenbre of gravity, and metacentric 

 height, which operates during a voyage ; so that the stability may be 

 materially altered after a steamer has left port, by reason of the con- 

 sumption of coal. Such alteration frequently has the effect of 

 diminishing the stability : and there are cases of steamers whose 

 gross weight when fully laden is reduced at sea from this cause by 

 over 25 per cent., and some in which the metacentric height is 

 reduced by 1^ feet. These large changes in the amount and distri- 

 bution of a ship's weights some of which take place at sea 

 sometimes make the problem of regulating the stability of a ship, so 

 as to prevent its ever becoming deficient or excessive during her 

 voyages, a very difficult and extremely delicate one. 

 ' The curve of metacentres and the positions of the centre of gravity 

 for all possible draughts of water and conditions of loading are not 

 sufficient, when obtained, for enabling the condition of a ship in 

 respect of stability to be completely determined. Atwood showed, in 

 two papers communicated to the Royal Society in 1796 and 1798, that 

 much more than this is required. In his second paper, read on the 8th 

 March, 1798, he says, " M. Bouguer, in his treatise entitled ' Traite du 

 Navire,' has investigated a theorem for estimating the exact measure 

 of the stability of floating bodies. This theorem, in one sense, is 

 general, not being confined to bodies of any particular form ; but in 

 respect to the angles of inclination, it is restrained to the condition 

 that the inclinations from the upright shall be evanescent, or, in a 

 practical sense, very small angles. In consequence of this restriction, 

 the rule in question cannot be generally applied to ascertain the 

 stability of ships at sea, because the angles to which they are inclined, 

 both by rolling and pitching, being of considerable magnitude, the 



