NOTE.—_Theoretical and actual flow._—_The actual flow from an orifice_, is the volume of liquid which escapes from it in a given time. _The theoretical flow_, is a volume equal to that of a cylinder which has for its base the orifice, and for its height the velocity, furnished by the discovery of Torricelli. That is, the theoretical flow is the product of the area of the orifice multiplied by the theoretical velocity. It is observed that the vein escaping from an orifice, contracts quite rapidly, so that its diameter is soon only about two-thirds of the diameter of the orifice. If there was no contraction of the vein after leaving the orifice, and its velocity was the theoretical velocity, the actual flow would be the same as that indicated by theory. But its section is much less than at the orifice, and its velocity is not so great as the theoretical velocity, so that the actual flow is much less than the theoretical flow; and in order to reduce this to the first, it is necessary to multiply it by a fraction. 2.—In the lower part of the vein, the liquid is not continuous; for if we employ an opaque liquid, as mercury, we can see through the vein, Fig. 98. The apparent continuity in a vein of water is owing to the fact that the globules which constitute it succeed each other at a distance inappreciable to the eye. [Illustration: FIGS. 97, 98.] _The time it takes by a vessel to empty itself_ is to the time required, when it is kept constantly full, to discharge the same quantity of water, as 2 to 1, and the spaces described by the surface in its descent in a column of equal size throughout, are as the odd numbers, 9, 7, 5, 3, 1. Thus these spaces measure equal times. Since liquids are not perfectly mobile, and their exit at an orifice must be retarded by cohesion and friction, the results thus far given are much modified in practice. When a liquid flows through an orifice in a vessel, eddies are formed about the sides of the orifice, preventing the escape of a jet equivalent to its full size; and owing to these, and to acceleration of velocity, _if the jet be downward_, it rapidly contracts in its diameter. At a distance outside about equal to diameter of the opening, it is contracted to 2/3 or 5/7 its original area; and this part has been called the “contracted vein.” It has been shown, that below this the stream still contracts, though less rapidly. These swellings separate more widely as they descend with increased rapidity; but falling through great heights, the whole may finally be dissipated in a mist.