338 THE MATHEMATICAL PRINCIPLES [BOOK II the vertex of this column be ; and the circle being diminished in infinitn/n the angle PHQ will be diminished in infinitum, and therefore the co lumn will lie within the hemi-spheroid. Therefore that column is less than that hemi-spheroid, or than two-third parts of the cylinder whose base is that little circle, and its altitude GH. Now the little circle sustains a force of water equal to the weight of this column, the weight of the ambient water being employed in causing its efflux out at the hole. COR. 9. The weight of water which the little circle PQ sustains, when it is very small, is very nearly equal to the weight of a cylinder of water whose base is that little circle, and its altitude