HYDROSTATICS. 333 



K>75. A hollow paraboloid, Laving a base perpendicular to 

 the axis and at a distance from the vertex equal to the latus 

 rectum, is placed with its axis vertical and vertex upwards, and 

 contains seven-eighths of its volume of heavy uniform fluid. Find 

 the angular velocity with which it must revolve about the axis 

 in order th;tt the surface of the fluid may be confocal with the 

 paraboloid; and prove that in this case the pressure on the base 

 will be greater than it was when the fluid was at rest in the ratio 



8 : 2^2-1. 



l."7G. If a uniform fluid be acted on by two central forces, 

 each varying as the distance from a fixed point and equal at equal 

 di stances from those points, one attractive and the other repulsive, 

 the surfaces of equal pressure will be planes. 



l.">77. In a uniform fluid under the action of two forces 

 tending to fixed points and varying inversely as the square of the 

 distance, one attractive and one repulsive, prove that one surface 

 of equal pressure is a sphere. 



1 '78. A mass of elastic fluid is confined within a hollow 

 sphere and repelled from the centre of the sphere by a force - ; 



prove that the whole pressure on the sphere : the whole pressure 

 which w.uld be exerted if no force acted :: 3& + /* : 3, the pres- 

 .ig k . density. 



1579. A quantity of uniform i no impressible fluid, not m 



on by gravity, just fills a hollow sphere, and is n>j m a 



point on the surface of th< sphere by a force equal to /z . distjr 

 the fluid iv volves about the diameter through the centre of force 

 with uniform angular velocity <o; find th- whole pressure on the 

 sphere, and prove that, if when the angular vel uinished 



one half the whole pressure is also diminished one half, <u f - G/z. 



1580. All space being supposed filled with an clastic fluid, 

 the whole mass of which is known, which is attracted to a given 



