EQUILIBRIUM OF AN- IMMERSED SOLID. 53 



That is, the wholly immersed solid will descend, re- 

 main at rest, or ascend, according as its density is 

 greater than, equal to, or less than the density of the 

 fluid. 



In the first case the solid will descend to the bottom, and 

 press it with a force equal to the excess of its weight above 

 that of an equal bulk of fluid. 



In the third case the solid will rise to the surface, and be 

 but partially immersed, the volume v' of the fluid displaced 

 by the solid having the same weight as the entire solid. 



[An egg, placed in a vessel of fresh water, sinks to the 

 bottom of the vessel, its mean density being a little greater 

 than that of the water. If, instead of fresh water, salt 

 water is employed, the egg floats at the surface of the liquid, 

 which is a little denser than the egg. If fresh water is 

 carefully poured on the salt water, a mixture of the two 

 liquids takes place where they are in contact ; and if the 

 egg is put in the upper part, it will descend, and, after a 

 few oscillations, remain at rest in a layer of liquid of which 

 it displaces a volume whose weight is equal to its own.] 



COR. From (1) we have 



v : v' :: p' : p; 



therefore, if a homogeneous solid float in a fluid, its 

 whole volume is to the volume of the displaced fluid as 

 the density of the fluid is to the density of the solid. 



Sen. When the floating solid and fluid are both homo- 

 geneous, the centre oi gravity of the part immersed will 

 coincide with the centre of buoyancy. 



The section of a floating body formed by the plane of the 

 surface of the fluid in which the body floats is called the 

 plane of flotation. The line passing through the centre of 



