STABILITY OF EQUILIBRIUM. 59 



t. e., if the angle between GO and the vertical be very small, 

 the point M is called the metacentre, and the question of 

 stability is now reduced to the determination of this point. 

 A ship, or any other body, floats with stability when its 

 metacentre lies above its centre of gravity, and without sta- 

 bility when it lies below it; it is in indifferent equilibrium 

 when these two points coincide. Hence the danger of 

 taking the whole cargo out of a ship without putting in 

 ballast at the same time, or of putting the heaviest part of 

 a ship's cargo in the top of the vessel and the lightest in 

 the bottom, or the risk of upsetting .when several people 

 stand up at once in a small boat. 



One of the most important problems in naval architecture 

 is to secure the ascendancy, under all circumstances, of the 

 metacentre above the centre of gravity. This is done by a 

 proper form of the midship sections, so as to raise the meta- 

 centre as much as possible, and by ballasting, so as to lower 

 the centre of gravity.* 



The horizontal distance MN, of the metacentre M, from 

 the centre of gravity G of the body, is the arm of the couple 

 whose forces are P and P, the weight of the body and the 

 buoyant effort; and the moment of this couple, which 

 measures the stability of the body, is P> MN. Let GM = c, 

 and the angle OMO', through which the body rolls, = 6, 

 and denote the measure of the stability by S', then we have 



8= P-MN = PC sin0; (1) 



therefore, the stability of a body, in general, varies as 

 its weight, as the distance of its metacentre from its 

 centre of gravity, and as the angle of inclination ; 

 and hence, in the same body, for a given inclination, 

 it depends only upon the distance of its metacentre 

 from its centre of gravity. 



* Besant's Hydrostatics, p. 58. 



