Hydraulic and Pneumatic Mechanics

III. Horizontal and intermediate Intermediate jets are those projected at an angle between the horizontal and vertical planes. jets preserve the same ratio of length as the heights of the tubes above the same horizontal level. 154
IV. The height of vertical jets is always the same at any elevation of the tube above the horizontal level. 155
V. A vertical jet never equals the height of its source. 156
VI. The vertical jet of a four-foot tube is nearly equal to five-sixths of its tube. ibid. original: "ibid." An abbreviation for "ibidem," meaning the same page as the previous entry.
VII. Vertical jets are longer when the tubes are longer; however, they do not grow in the same proportion as the tubes. ibid.
VIII. Given the height of the tube and its elevation above the horizontal level, to find the length of the horizontal and intermediate jet. 157
IX. Given the length of a horizontal or intermediate jet, to find the height of the tube, provided its elevation above the horizontal level is known. ibid.
X. From the known height of the source scaturigo: The source, head, or rising point of water in a hydraulic system. of one fountain leaping horizontally from a tube, to find the height of the source of any other elevated equally above the horizontal level. 158

CHAPTER V.

PROPOSITION
I. Through equal openings at an equal distance from the top of the tube, whether in the base or in the side, equal quantities of water flow in an equal time. 160
II. Waters flowing down from openings at an equal distance from the top of the tube are related to each other as the openings are. ibid.
III. Water flows down through the openings of a vessel with the same force or velocity as it does through tubes of equal openings and heights. 161
IV. The velocities of water flowing down through equal openings of the same vessel, at unequal distances from the top of the vessel, are in the subduplicate ratio subduplicate ratio: A mathematical relationship where values are proportional to the square roots of other values. of the distance. 162
V. Waters flowing through equal openings at unequal distances from the top of the vessel are in the subduplicate ratio of the distances. ibid.
VI. When a side opening of a vessel is divided into equal parts by horizontal lines, to find the ratios of the waters flowing from them. 163
VII. When a side opening of a vessel is divided into unequal parts by horizontal lines, to find the ratios of the waters flowing out from them. 164
VIII. Given unequal openings on the same horizontal level, to seek out original: "venari." Schott uses this term to mean investigating or mathematically pursuing a solution. the ratios of the waters. ibid.
IX. Given the openings of the same vessel, where one is higher and the other is lower, between the same parallel perpendicular lines, to find the ratios of the waters. 165