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The areas of the base and a side being equal, and thedepths of their centres of gravity :■ 2 : 1, (66) the pressureon the base is to that on a side :: 2 : 1 ; therefore the pres-sure on the base is to that on the four sides :: 2 : 4 :: 1 : 2,or, (51) the weight of the fluid is to the pressure on the foursides :: | ; t>.

Cor. The pressure on the sides and base is equal tothree times the weight of the fluid.

(9) If on the side of a vessel a number of circles be de-scribed, the pressures on which are proportional to theirdiameters: the ratio of their distances from the surface maybe found.

For the pressure oc area x depth of centre of gravity (65)oc R 1 x D.

But by the supposition it oc R-It 1 x D oc R,

and Doc—.

Cou. If the pressure oc R n , D oc R“ *.

(10) A circle being just immersed vertically in a fluid;draw from the lowest point that chord on which the pressureshall be the greatest.

From B the lowest point, draw the vertical diameter BA,and let BC be the chord, which bisect in G; and draw GE,CD perpendicular to AB.

Let BE — x; .'. BD = 9.x, BC = \Z4rx,and AE = 2r — x;

whence (65), (2 r — x) 4r\r = max.

or 2rxl — x^ — max.

.'. rx~^dx — 4-ari dx =0.

and x = •§•»’.

(11) If two spheres be just immersed in any fluid; tocompare the pressures upon them.

Since (65) the pressures are as the surfaces x the depthsof their centres of gravity, they arc as li 2 x R oc R’.