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70. equall ye threed of ye pendulum must be shorter towards A than towards G. It is manifest that we cannot find precisely ye same quantity of water in all ye experiments, and we shall always find some small difference too many causes, viz that it is difficult to begin to count ye seconds at ye same moment ye water begins to run, that we cannot draw back ye vessel precisely when ye 30 second is ended, that ye holes thrô wch ye water runs is not perfectly perpendicular or is not exactly an inch, or that ye thread of ye pendulum may a little shorten or lengthen itself during ye experiment, or lastly that ye height of ye water is a little more or less than a line to ye place of ye small plate M; all wch things hinder ye precise exactness: But between ye greatest and least is found this measure of 13 pints 3/8. If we would know ye water wch smaller circular holes give as of 6 or 4 lines diameter, we must place them so that their center 3 may be 7 lines below ye surface of ye water of ye vessel, for if ye height of each hole was placed at a line distance from ye surface, they would give much less water than according to ye proportion of their greatness. But if they are disposed so that ye center of their holes might be at ye same distance from ye surface of ye water they give water near according to that proportion these are ye experiments wch have been made. Experiment II The water was many times made to run from ye same vessel thrô a hole of 6 lines whose center was alway at 7 lines distance from ye surface of ye water during ye whole running, and there was going between ye greatest and ye least 15 semi septierss in one minute, altho ye surface of that hole was but 1/4 of a circular linch and that according to that portion ye ought to go out in one minute but ye fourth of 13 pints 3/8 according to ye 4th rule of ye equilibrium by ye shoc. That difference proceeds from many causes. I That althô ye water of ye vessel was a line heigh above ye hole of an inch there remained near to ye hole but 1/2 of a line during its whole runing; wch might be easily know by a particular reflection or ye light wch was made in that place where ye water was lower than in ye rest of ye vessel, and that wch runs, ought to come from ye neighboring parts, as hath been explained above, and there being very little elevated near ye hole, it must be almost all depressed, to pass, wch diminisheth ye force of ye pressure of ye water and retards ye swiftness of its running: 2° That there coming little water from on heigh it must in requitall be that it comes from far to succeed that wch runs, wch also regards its swiftness. But ye same thing doth not happen to a hole of 6 lines because that not being to give but 1/4 as much water as ye inch, and its hole being surmounted to 4 lines thickness of water there is not made any considerable depression; and by consequence ye water is pressed by these 4 entire lines, besides that ye water wch ought to succeed that wch runs doth not come so far as when that is an inch; and also that ye top of ye water wch is directly above ye hole of an inch, was 7 lines above its center, it would be necessary it should be in ye rest of ye vessel near 8 lines: There is yet another cause wch is that ye swiftness of ye runnings, being in a subduple proportion of ye height of ye waters, as hath been said, if there is a vessel as A B perced at ye bottom with an horizontal hole as a b c d, and with another vertical E F G H, equal one to ye other, and that ye water be elevated in ye vessel to ye precise height of C F there ought to go out at that verticall hole but 2/3 as much water as there will go out thrô that wch is at ye bottom of ye vessel at ye same time if ye water is maintained at ye same height C F wch is proved in this manner: The water wch goeth thrô ye base of ye verticall hole EH, hath its swiftness in respect of that wch goeth thrô L I in a subduple proportion of ye height E G to ye height E L, and ye same in respect of all ye horizontall,
Transcription Notes:
mandc: Reviewed. Corrected "semi septiers" is Demi-septiers (Quartens) or quarters of a pint.
