SEC. VII.] OF NATURAL PHILOSOPHY. 339 middle of the canal ; and produce CA to K, so K I JL f that AK may be to CK in the duplicate of the -^ 'jg'"" e ratio, which the excess of the orifice of the canal EF above the little circle PQ bears to the cir cle AB. Then it is manifest (by Case 5, Case 6, and Cor. 1, Prop. XXXVI) that the velocity of the water passing through the annular space between the little circle and the sides of the ves sel will be the very same which the water would acquire by falling, and in its fall describing the altitude KG or IG. And (by Cor. 10, Prop. XXXVI) if the breadth of the vessel be infinite, so that the lineola HI may vanish, arid the altitudes IG, HG become equal ; the force of the water that flows down and presses upon the circle will be to the weight of a cylinder whose base is that little circle, and the altitude iIG, as EF2 to EF2 —