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

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Sect. VII.
of Natural Philoſophy
129

height of the hole above a plane parallel to the horizon were alſo 20 inches, a ſtream of water ſpringing out from thence would fall upon the plane. at the diſtance of 37 inches, very nearly, from a perpendicular let fall upon that plane from the hole. For without reſiſtance the ſtream would have fallen upon the plane at the diſtance of 40 inches. the latus rectum of the parabolic can being 80 inches.

Calse 4. If the effluent water tend upwards, it will ſtill iſſue forth with the ſame velocity. For the ſmall ſtream of water ſpringing upwards, aſcends with a perpendicular motion to GH ot GI the height of the ſtagnant water in the veſſel; excepting in ſo far as its aſcent is hindered a little by the reſiſtance of the air; and therefore it ſprings out with the ſame velocity that it would acquire in falling from that height. Every particle of the ſtagnant water is equally preſſed on all ſideſ, (by Prop. 19. Book 2.) and yielding to the preſſure, tends all ways with an equal force, whether it deſcends thro' the hole in the bottom of the veſſel, or guſhes out in an horizontal direction thro' an hole in the ſide, or paſſes into a canal, and ſprings up from thence thro' a little hole made in the upper part of the canal. And it may not only be collected from reaſoning, but is manifeſt alſo from the, well-known experiments juſt mentioned, that the velocity with which the water runs out is the very ſame that is aſſigned in this Propoſition.

Case 5. The velocity of the effluent water is the ſame, whether the figure of the hole be circular, or ſquare, 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 ariſes from its depth below the plane KL.

Case 6. If the lower part of the veſſel ABDC be immerſed into ſtagnant water, and the height of the ſtagnant water above the bottom of the veſſel be GR; the velocity with which the water that is in the veſſel