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55.

ye same effect as ye air;  that is to say shall make an equilibrium by its shock with a weight wch shall be ye weight P as ye hole K to ye whole base B C because that then ye weight of ye inclosed water will contribute nothing sensible to ye force of ye spout, since it is allways below;  and that if a spout of water of ye same largeness and swiftness should strike [[? ?]] directly in K that wch goes thrôu that hole it would stop and make an equilibrium with it, and would sustain one part of ye weight P according to ye proportion of ye hole K to ye surface B C:  Whence follows a paradox enough surprising viz that ye air and ye water wch go out successively thrô ye same hole K, whatever weights we put up on ye base A B, elevate ye same weights by their shock, althô ye water be a matter much more dense and heavy than that of air:  But it happen also in recompense that ye air goeth out much swifter than ye water for we have found by many experiments, that when ye cylinder is full of air, it is void in about 24 times a less time than when it is full of water.

  For example if ye air is emptied in 2 seconds ye water shall not be emptied but in 29 seconds whence we may conclude that to ye end a spout of [[strikethrough]] water [[/strikethrough]] air may make ye same effect by its shock as a spout of water of a like largeness, it is necessary that its swiftness be about 24 times greater than that of ye water.

How ye same effect ought to happen, if A B C D is a cylindric vessel full of water, and open at ye top:  For ye water wch ought to spout thrô ye hole N, being stopped by another spout that meets it directly at ye point N, that spout will sustain one part of ye water of ye whole cylinder;  viz ye cylinder wch hath for its base ye hole N, and ye rest of ye base will sustain ye rest of ye water:  Therefore that spout being taken away, ye spout wch will go out thrô ye hole N, shall make an equilibrium by its shock with a weight wch shall be equall to ye weight of that small cylinder, wch hath for its base ye hole N, and ye height equall to A B, if ye cylinder A B C D is wholly full.

     RULE III
  The spouts of water equally large, wch go out thrô ye small holes made at ye bottom of many pipes full of water of different heights make an equilibrium with weights wch are are to ye other in proportion of ye heights of ye pipes:

Explication.

  Let there be a great pipe A B and a lesser C D [[?perced]] at ye points E and F with equall holes (fig p: 51 and ye I) it hath been above that ye water spouting thrô ye hole E shall make an equilibrium with a weight equall to ye weight of ye cylinder of water E G, and that ye spout wch goeth thrô F shall make an equilibrium with a weight equall to ye cylinder of water F H:  Now these small cylinders having equall bases by ye supposition will have their weights in proportion to their heights:  Whence it follows that ye weights with wch these spouts make an equilibrium shall be one to ye other as ye heights A B C D;  by consequent it is evident at ye first swiftness of a spout in going out ought to be such that if first drop of water wch goeth out be disposed to be elevated as heigh as ye upper surface of ye water:  For supposing that if water was in ye large cylinder A B C D at D, and that there was a cylinder of ice at ye largeness as ye hole F, wxh goeth not but from F to G and wch was suspended from that point directly upon ye hole F at ye distance of 1/2 a line or there abouts, and that we permit ye water to go of a suddain, it will make ye cylinder F G mount heigher by the shock since it can make an equilibrium with a cylinder of ye same largeness and height, F E:  Therefore if ye water should spout but to G from ye point F, it could not stay at ye elevation since ye force of ye water following would push it heigher, if it was firm as a cylinder of ice whence we may judge that ye first drop would be elevated to A E without ye resistance of ye air joyned to that that ye water wch goeth thrô F being charged on heigh to make an equilibrium with ye water A D, ye first drop that is elevated ought to have ye force to mount to ye [[strikethrough]] stop [[/strikethrough]] top of ye superior water of ye reservatory, if we make an abstraction of ye resistance of ye air:  As is explained in ye first discurs, whence it is made evident that in ye elevating to an equilibrium, it spouts also heigher than ye superior water by reason of swiftness acquired by ye great motion that ye spout takes to be elevated to the height of the superior water;:

[[image:  three dimensinal diagram of cylinder annotated A B C D, spout from the bottom annotated F, smaller cylinder annotated E G at top, F at bottom, a board or plank o L lying on top of the cylinder extending over to and above the smaller cylinder E G F.]]

Transcription Notes:
mandc: reviewed and changed Q to P, B to D, find to since. Page 51 of the ms is scan 55, and refers to Rule I and to this illustration on ms page 52 (scan 56): http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=174&ww=0.0731&wh=0.1861&wx=0.7907&wy=0.4337 Illustration at bottom of page: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=174&ww=0.1395&wh=0.1782&wx=0.7708&wy=0.6139