Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/151

Sect. VII. height of the hole above a plane parallel to the horizon were alo 20 inches, a tream of water pringing out from thence would fall upon the plane. at the ditance of 37 inches, very nearly, from a perpendicular let fall upon that plane from the hole. For without reitance the tream would have fallen upon the plane at the ditance of 40 inches. the latus rectum of the parabolic can being 80 inches.

If the effluent water tend upwards, it will till iue forth with the ame velocity. For the mall tream of water pringing upwards, acends with a perpendicular motion to GH ot GI the height of the tagnant water in the veel; excepting in o far as its acent is hindered a little by the reitance of the air; and therefore it prings out with the ame velocity that it would acquire in falling from that height. Every particle of the tagnant water is equally preed on all ide, (by Prop. 19. Book 2.) and yielding to the preure, tends all ways with an equal force, whether it decends thro' the hole in the bottom of the veel, or guhes out in an horizontal direction thro' an hole in the ide, or paes into a canal, and prings up from thence thro' a little hole made in the upper part of the canal. And it may not only be collected from reaoning, but is manifet alo from the, well-known experiments jut mentioned, that the velocity with which the water runs out is the very ame that is aigned in this Propoition.

The velocity of the effluent water is the ame, whether the figure of the hole be circular, or quare, or triangular; or any other figure equal to the circular. For the velocity of the effluent water does not depend upon the figure of the hole, but aries from its depth below the plane KL.

If the lower part of the veel ABDC be immered into tagnant water, and the height of the tagnant water above the bottom of the veel be GR; the velocity with which the water that is in the veel