208 Prof. F. Elgar. The Variation of 



G and the vertical through the centre of buoyancy B,, then W X GZ 

 is the righting moment ; W being the weight of the ship. But 

 GZ=MG sin WOW l ; and therefore when WOW, is indefinitely 

 small, the righting moment is proportional to W x MG. While 

 G remains below M the moment is always a righting one, and 

 tends to restore the ship to the upright position, which in this case 

 is one of stable equilibrium ; but if it be above M the tendency is to 

 move the ship farther away from the upright till an inclined position 

 of stable equilibrium be reached, or to capsize her. The curve of 

 metacentres for a ship, which gives the height of the metacentre at 

 all draughts of water, indicates therefore the limit above which the 

 centre of gravity cannot be raised by changes in the amounts or 

 positions of any of the weights without causing her to become 

 unstable. Sufficient stability for practical working requirements and 

 for purposes of safety can only be secured by taking care that at the 

 various displacements and draughts of water a vessel may have in 

 different conditions of loading, the centre of gravity is always kept at 

 a proper depth below the corresponding points on the metacentric 

 curve. 



Such instability as may be due to deficiency, or absence, of meta- 

 centric height is not necessarily dangerous, and may not be sufficient 

 to cause a complete capsize. It will, of course, cause the vessel to 

 incline away from the upright, but a position of stable equilibrium 

 may soon be reached ; and the righting moments at greater inclina- 

 tions, and the range of stability, beyond that point may be so large as 

 to put all danger of upsetting out of the question if there are no 

 openings through which water may find its way inboard, and no large 

 weights free to shift. Many ships are in this condition when light, 

 and some approach it when laden. On the other hand, there are 

 vessels in which small metacentric height involves a serious risk of 

 capsizing. 



No fixed distance of centre of gravity below metacentre, or meta- 

 centric height, as it is commonly termed, can be adopted as a standard 

 for application to all ships, because such a measure of stability 

 is very imperfect and insufficient, and may by itself be misleading. 

 This is chiefly due to the reasons that the form and proportions of the 

 above- water part of the ship are not taken into consideration in the 

 metacentric calculations, and the tinder-water form not completely 

 so ; and that the value, as a general measure of stability, of a given 

 metacentric height is largely affected by the absolute heights in a 

 ship of the centre of gravity and metacentre. The initial stability is, 

 of course, constant for a given metacentric height whatever may be 

 the absolute positions of the points M and G, but the righting 

 moments at moderate and large angles of inclination, and the angle 

 at which such righting moments vanish, or change into upsetting 



