82 HYDRAULICS AND ITS APPLICATIONS 



distances d, h and .i, are measured in the plane of the figure in each 

 case. 



ART. 11. EQUILIBRIUM OF FLOATING BODIES. 



When a body is freely floating in a liquid, the conditions of equilibrium 

 may be inferred by imagining the body removed and the space occupied 

 by it to be filled with the liquid. The reactions of the surrounding 



liquid will be unaltered by the 

 change, the whole being still in 

 equilibrium, and it is clear that 

 the resultant pressure of the 

 surrounding liquid is vertically 

 upwards, and is equal to the 

 weight of the displaced liquid, 

 and also that the line of action 

 of this resultant pressure passes 

 through the Centre of Gravity 

 of the displaced liquid. It 

 follows that for equilibrium the 

 weight of the floating body is 



equal to the weight of the liquid which it displaces, and that the Centres 

 of (iravity of the body and of the displaced liquid are in the same 

 vertical line. 



The Centre of Gravity of the displaced liquid is called the Centre of 

 Buoyancy. 



Stability of Equilibrium. If a floating body be slightly displaced from 

 its equilibrium position so that the line joining the C. G. and the Centre 

 of Buoyancy is no longer vertical, the forces now acting may tend to 

 restore the body to its original position ; to move it still further from 

 that position ; or to maintain it in equilibrium. In the first case the 

 equilibrium is said to be stable; in the second, unstable; and in the third, 

 neutral. 



Let G (Fig. 16) be the C. G. of the floating body ; H the Centre of 

 Buoyancy when in the equilibrium position ; and H' the C. B. in the 



FIG. 16. 



