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.
_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.
NOTE.—The annular swellings contain air and arise from a periodical succession of pulsations near the orifice, which must be produced by very small oscillations of the entire mass of the liquid, so that the velocity of the flow is periodically variable. The sucking, whistling noise which is often heard in the descent of water through an orifice is caused by air drawn in by the whirling motion. See Fig. 103.
If an orifice in a vessel looks downward, and the column of liquid over it be short, this will simply drop out by its own weight, starting at a velocity of o. But if a considerable depth of liquid be above, its gravity produces a corresponding pressure on its base, or on that liquid which is near it; so that, if a plug be removed from an orifice in or close to the base, the liquid starts at once into rapid motion.