54 EXAMPLES. 



gravity of the floating body and the centre of buoyancy is 

 called the axis of flotation. 



The weight gpv of the body acting downwards, and the 

 buoyant effort gp'v' acting upwards (Art. 24, Sch.), form a 

 couple, by which the body rotates till the directions of these 

 forces coincide, i.e., till the centre of gravity of the body 

 and the centre of buoyancy come into the same vertical line. 



EXAMPLE. 



1. A piece of oak containing 32 cubic inches, floats in 

 water ; how much water will it displace, the density of 

 the oak being 0.743 times that of water ? 



Ans. 23.776 cu. in. 



26. Depth of Flotation.* The depth to which a 

 body sinks below its plane of flotation is called its 

 Depth of Flotation. When the form and weight of a 

 floating body are known, its depth of flotation can be calcu- 

 lated. 



Denoting the volume and density of the body by v and p, 

 and of the displaced fluid by v and p', respectively, we have 



[Art. 25, (1)]. 



gpv = gp'v' ; 



- 

 - p , 



(1) 



by which the depth of flotation can be determined, when- 

 ever v' can be determined in terms of that depth. 



EXAMPLES. 



1. Let the solid be a right cylinder, whose axis a is verti- 

 cal, and the radius of whose base is r; let x denote the 

 depth of flotation. Then we have 



Called also depth of immersion. 



