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all the elements ; hence the whole pressure on the bottom 

 of the canal is 



that is to say, it is equal to the weight of a cylinder of 

 fluid, whose base is the area of the part A of the bottom, 

 and whose altitude is the same as that of the superincum 

 bent fluid. 



The bottom is not pressed by the whole weight of the 

 incumbent fluid, but only that part which is described 

 above ; and it will be the same whether the fluid rises per 

 pendicularly above A in a rectilinear direction, or whether 

 it be contained in crooked cavities and canals, whether 

 these passages be regular or irregular, wide or narrow. 



If a body of the same specific gravity as the fluid, and 

 incapable of condensation, be immersed in the fluid, it will 

 neither acquire motion by the pressure of the fluid, nor 

 any change of figure. Any portion of a fluid at rest may 

 clearly be supposed to become solidified without affecting 

 the equilibrium. Let a part of the fluid equal and similar 

 to the body about to be immersed become solid ; removing 

 it we may replace it by this body, and the equilibrium 

 will still subsist. It also follows that the resultant of all 

 the pressures exerted by the fluid on the solid is a force 

 equal to the weight of the fluid displaced acting upwards 

 through the centre of gravity of the volume of the body. 

 If, therefore, a solid be immersed in a liquid, it will remain 

 at rest if it be of the same density as the fluid. But if it 

 be of greater density, it will be no longer sustained by 

 the resultant pressures, and will sink to the bottom. If it 

 be of less density, it will rise to the surface, being acted 

 on upwards by a greater force than its own weight. Hence, 

 Newton concludes, bodies placed in fluids have a twofold 

 gravity ; one true and absolute, the other apparent, vulgar, 



