CHAPTER IV. 



OF THE PRESSURE OF INCOMPRESSIBLE FLUIDS ON CIRCULAR 



PLANES AND ON SPHERES IMMERSED IN THOSE FLUIDS, THE 



EXTREMITY OF THE DIAMETER OF THE FIGURE BEING IN EACH 

 CASE IN EXACT CONTACT WITH THE SURFACE OF THE FLUID. 



PROBLEM XIV. 



98. Suppose a circular plane to be immersed perpendicularly 

 in an incompressible fluid, in such a manner, that the extremity 

 of the diameter is just in contact with the surface : 



It is required to draw from the lowest point of the circular 

 plane, that chord on which the pressure shall be a maximum. 



Let ABC be the circular plane immersed in the fluid according to 

 the conditions of the problem ; draw the ver- 

 tical diameter BC touching the surface of the 

 fluid in the point B, and let CA be the chord 

 required. 



Bisect the chord CA in the point m, and 

 through the point m thus determined, draw 

 mn parallel to BC the vertical diameter, meeting the surface of the 

 fluid in n j then is n m the perpendicular depth of the centre of gravity 

 of the chord AC, below the surface of the fluid in which it is immersed ; 

 draw also AE and mD respectively perpendicular to the diameter BC. 



Now, we have already demonstrated in the first Problem, that the 

 pressure upon a physical line, is equal to the product of its length by 

 the perpendicular depth of its centre of gravity, and again by the 

 specific gravity of the fluid ; consequently, we have 



p = AC x nm X s. 

 Put d~ BC, the diameter of the immersed circular plane, 



I =. mn, the perpendicular depth of the centre of gravity of the 

 chord AC, 



