STABILITY OF EQUILIBRIUM. 57 



COB. 2. If the fluid be water, (5) becomes 



W = r 2 (Y* + 1) I 62.5 (Art. 10, Cor. 1). (6) 



5. Let the body be a cone floating with its base under 

 the fluid, and the axis a vertical. Find the depth of flota- 

 tion. ,/ 77 



Ans. a a\ / 1 -, 



6. A man whose weight is 150 Ibs. and density 1.1, just 

 floats in water by the help of a quantity of cork. Find the 

 volume of the cork in cubic feet, its density being .24, call- 

 ing the density of water 1. Ans. -gfo of a cubic foot. 



27. Stability of Equilibrium If a floating body is 

 in equilibrium, the centres of gravity and of buoyancy are 

 in the same vertical line (Art. 24, Cor. 1). Imagine the 

 body to be slightly displaced from its position of equilibrium 

 by turning it round through a small angle, so that the axis 

 of flotation shall be inclined to the vertical. If the body on 

 being released return to its original position, its equilibrium 

 is stable ; if, on the other hand, it fall away from that posi- 

 tion, its original position is said to be one of unstable equi- 

 librium ; when the body neither tends to return to its 

 original position, nor to deviate farther from it, the equilib- 

 rium is said to be one of indifference. 



The investigation of this problem in its utmost extent 

 would lead to very tedious and complex operations, which 

 would clearly be beyond the limits of this treatise ; we shall 

 therefore premise the three following hypotheses, in order 

 that we may obtain comparatively simple results : 



1. The floating body will be regarded as symmetrical 

 with respect to a vertical plane through its centre of gravity 

 when the whole is at rest, so that we need consider only the 

 problem for the area of a plane section of the body. 



