HYDROSTATICS. 335 



is fixed below the surface of a fluid, and when slightly displaced 

 from its highest position, it sinks till just immersed before rising: 

 prove that, when at rest in the highest position, the pressure on 

 the point of support was zero. 



1586. Two equal uniform rods AB, EC, freely jointed at P, 

 are capable of motion about A which is fixed at a given depth 

 below the surface of a uniform heavy fluid : find the position in 

 which both rods rest partly immersed; and prove that, if such a 

 position be possible, the ratio of the density of the rods to the 

 density of the fluid will be less than 1 : 3. 



1587. A hemisphere, a point in whose base is attached to 

 a fixed point by a fine string, rests with its centre in the surface 

 of a fluid and its base inclined at an angle a to the horizon : prove 

 that 



p 16 ( a) cos a 37rsin a 

 <r = 2ar (8 oos a - 3 sin a) ' 



p, a being the densities of the hemisphere and fluid respectively. 



1588. A cone is floating, with its axis vertical and vertex 

 downwards, in fluid with - th of its axis immersed; a u 



equal to the weight of the cone is placed upon the base after 

 which the cone sinks till just totally immersed before rising: 



n" + n f + n - 7. 



1589. A hollow cylinder whose axis is vertical contains a 

 quantity of fluid whose density varies as the depth, and a cone, 

 whose axis is coincident it, of the cylinder ami which is of 

 equal base, is allowed to sink slowly into the fluid with its \ 

 downwards. The coiie is in equilibrium when just immersed; 

 prove that the density of the cone is equal to the initial density 



'<iual to one twelfth of th ..f th< 



axis of the cone. 



