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HYDROSTATICS. 



Ix these questions a fluid is supposed to be uniform, heavy, 

 and incompressible, unless otherwise stated: and all cones, cylin- 

 ders, paraboloids, are supposed to be surfaces of revolution, and 

 their bases circles. 



1544. A cylinder is filled with equal volumes of n different 

 fluids which do not mix ; the density of the uppermost is p, of the 

 next 2p, and so on, that of the lowest being np ; prove that the 

 whole pressures on the corresponding portions of the curve surface 

 are in the ratios 



l f : 2' : 3 f : ... : n'. 



1545. A hollow cylinder containing a weight IF of fluid is 

 -o that its axis makes an angle a with the horizon : prove 



that the resultant pressure on the curve surface is IF cos a, and 

 that its direction makes an angle a with the vertical. 



151 il V..IUIIH-S of thrvc fluids are mixed and tin- mix- 



ture separated into three parts; to each of these parts is th.-n 

 added it* own volume of one of the original fluids an. 1 the densi- 

 ties of the mixtures so formed are in the ratios 3 : I : , ].>vr 

 that the densities of the fluids are aa 1 : 2 : 3. 



1547. A thin tube in the form of an ! is 



till.-d with equal volumes of three fluids \\hirl- d> nd mi\ 



IP Id with one sideyertir.il tin tl.n-c points of junction of 

 the fluids bisect the sides : prove that the densities of the fluids 

 are in arithmetical progress 



