SM084     Equilibrium conditions for a liquid     circa 1905     Hydrostatics

            For a liquid to remain at rest in a vessel the following two conditions must be satisfied.

(a)   Its surface must everywhere be perpendicular to the resultant of the forces acting on the liquid molecules.

(b)   Every molecule of the mass of the liquid must be subject in every direction to equal and opposite forces.

           Now when there are communicating vessels of different shapes filled with liquid there will be equilibrium when the above conditions are met in each of the vessels.   Taking a section of the vessel, the pressure acting downwards is equal to that acting upwards.   This pressure is equal to the weight of a column of liquid whose base is the section being considered and whose height is the distance of the centre of gravity of this section to the surface of the liquid.   Therefore, any horizontal plane in the liquid will have a resultant force acting downward, only proportional to the height of the plane.   It follows that whatever the shape of the vessel each level of liquid will be the same height from the base.