HYDROSTATICS. 171 



251. The same being supposed, as in the last 

 proposition, the whole pressure sustained by any 

 portion whatever of the bottom or sides of the ves- 

 sel, is equal to the weight of a column of the fluid 

 having for its base the surface pressed on (extend- 

 ed into a plane if necessary), and for its altitude 

 the mean depth of the incumbent fluid. 



COTE'S Hydrostatical Lectures^ Lect. in. BOSSUT, 

 Hylrodyn. vol. i 26. 



The mean depth of any portion of the surface of the 

 bottom or sides of the vessel, is the same with the 

 distance 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 determined 

 by this proposition. 



If the figure of a vessel containing a fluid be such as 

 is represented, fig. 21. the pressure on every point 

 of the bottom is the same as if it were entirely fill- 

 ed with the fluid to the height FEG. Hence the 

 pressure of a fluid on the bottom of a vessel may 

 be very great, while the weight of the fluid is very 

 small ; because the water in the narrow tube HE 

 will press on the bottom CD with a force greater 

 than its own weight in the proportion that the area 

 of the bottom is greater than the horizontal section 

 of the tube. 



This proposition is called the Hydrostatic Paradox. 



The 



