164 OUTLINES OF NATURAL PHILOSOPHY.

246. The same being supposed, as in the lastproposition, the whole pressure sustained by anyportion whatever of the bottom or sides of the ves-sel, is equal to the weight of a column of the fluidhaving for its base the surface pressed on (extend-ed into a plane if necessary), and for its altitudethe mean depth of the incumbent fluid.

Cote’s Ilydrostatical Lectures. Bossut, Hydrodyn.vol. i. § 26.

The mean depth of any portion of the surface of thebottom or sides of the vessel, is the same with thedistance of the centre of gravity of that portion be-low the surface of the fluid.

The strength of the walls necessary to resist the pres-sure of a fluid of any given depth, is determinedby this proposition.-

If the figure of the vessel be such as is represented,(fig. 20.) the pressure on every point of the bot-tom is the same as if it were filled with fluid everywhere to the height FEG. Hence the pressure ofa fluid on the bottom of a vessel may be verygreat, while the weight of the fluid is very small;and hence also the addition of a small quantity ofwater in the neck or tube IIE, may increase thepressure on CD in a very great proportion. Thisis called the Hydrostatic Paradox.

247. A body immersed into a fluid is pressedupwards by a force equal to the weight of thefluid it displaces, and the direction of that force

passes