330 Hydrostatics. 



]2/i = 100, 

 or 



h : a :: 10 : 12, 



that is, a parallelepiped of half the density of the fluid, and hav- 

 ing its height te one side of a square base, as 10 to 12, would 

 float indifferently. 



446. But if the relative density of the parallelepiped were 

 either greater or less than |, its equilibrium would become stable. 

 Thus, if we suppose A equal to J, we shall have the distance 

 of the metacentre above the centre of buoyancy, as follows, 

 namely, 



BM = jfrh = 12 x ! f x 10 = " = 3 ' 6 inches ' 



and for the distance of the centre of gravity above the centre of 

 buoyancy, 



BG = h ^~^ = fc = J 10 = 3,3 inches; 



so that the centre of gravity is about 0,3 of an inch below the 

 metacentre. Therefore the equilibrium would be stable. 



. In like manner, if we substitute f instead of ^ in the above 

 equations, or, which is the same thing, take half of each of the 

 above results, we shall have half of 0,3, or 0,15 of an inch, for 

 the distance of the centre of gravity below the metacentre. 



447. These principles are well illustrated by the masses of 

 ice which appear on the rivers of the colder climates at the 

 opening of spring. Being ordinarily much broader than they 

 are thick, they have a stable equilibrium in their natural position 

 with their broad surface horizontal. But when by striking 

 against each other, or by passing over a fall, they are thrown 

 up sidewise, their equilibrium becomes unstable, and they soon 

 return to their former position. Moreover a piece of ice of a 

 cubical form will still preserve its balance, since its specific grav- 

 ity does not come within the limits already pointed out, of an 

 unstable equilibrium.! 



t The specific gravity of ice is 0,92, or compared with sea-water 

 as unity 0,89. 



