Note 19 — PART III.—Continued. LETTERS WRITTEN AFTER HIS RETURN TO THE U. S. DOWN TO THE TIME OF HIS DEATH. 1790-1826. (continued 12)

These ordinates are arithmetical progressionals, each of which is double the root of its abscissa, plus unit. The equation, therefore, expressing the law of the curve is y = 2 N x + 1; that is, the velocity of the water of any depth will be double the root of that depth, plus unit. Were the line a e a wall, and b f e g d h e i troughs, along which water spouted from apertures at b c d e, their intersections with the curve at f g h i would mark the point in each trough to which the water would flow in a second of time, abating for friction.