EXAMPLES. 



not exceed ^-7, which term is always the distance be- 



tween the metacentre and the centre of buoyancy. 



If the centre of gravity of the body coincides with the 

 centre of buoyancy, we have e = 0, and (5) becomes 



S= P 



I2A 



d. 



(6) 



Hence, generally, the stability is -positive, negative, or 

 zero, according as the metacentre is above, beloir, or 

 coincident with the centre of gravity of the floating 

 body. 



A vertical line O'M through the centre of buoyancy is 

 called a line of support. 



COR. 3. From the above results we see that the stability 

 of a body is greater the broader it is and the lower its centre 

 of gravity is. (See Weisbach's Mechs., Vol. I., p. 750 ; also 

 Bland's Hydrostatics, p. 120.) 



EXAMPLES. 



1. Determine the stability of a homogeneous rectangular 

 parallelepiped floating in a fluid. 



Let HK be the line of flotation of 

 a vertical section passing through the 

 centre of gravity G; let b = the 

 breadth EF of the section of the par- 

 allelopiped, 7i = the height EC, and 

 y = the depth of immersion AC. 

 Then we have 



H 



A = by, and e = (h 



Fig. 24 



e being negative since the centre of buoyancy is below the 

 centre of gravity. Substituting in (5), we have 



