Deductions from the above:—1, _the velocity depends on the depth of the orifice from the surface, and is independent of the density of the liquid_. Water and mercury in vacuo would fall from the same height in the same time; and so escaping from an orifice at the same depth, below the surface, would pass out with equal velocity; but mercury, being 13·5 times as heavy as water, the pressure exerted at the aperture of a vessel filled with mercury, will be 13·5 times as great as the pressure exerted at the aperture of a vessel filled with water; 2, _the velocity of liquids is as the square roots of the depths of the orifices below the surfaces of the liquids_. NOTE.—Torricelli discovered, in the early part of the 17th century, the remarkable fact that a fluid issues from a small orifice with the same velocity (friction and atmospheric resistance excluded) which it would have acquired in falling through the depth from its surface. This was one of a long series of discoveries leading toward the now almost exact science of hydro-mechanics. Thus stating, the velocity of a liquid escaping from an orifice one foot below the surface to be _one_; from a similar orifice four feet below the surface, it will be _two_, and at nine feet _three_, at sixteen feet _four_, and so on. From comparative experiments made by a great number of observers, it is learned that the actual flow is only about two-thirds of the theoretical flow. See note. The form and constitution of liquid veins have been studied and found to be: 1.—That the fluid issuing vertically from an orifice made in a plane and thin horizontal wall, is always composed of two distinct parts, Fig. 97, the portion nearest the orifice is calm and transparent, like a rod of glass, gradually decreasing in diameter. The lower part, on the contrary, is always agitated, and takes an irregular form, in which are regularly distributed elongated swellings, called _ventres_, whose maximum diameter is greater than that of the orifice.