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52.

[[image:  Three dimensional drawing of two thick, vertical tubes, the taller one on the left labeled A (top), B (bottom), with an opening at the top G; and E at the bottom.  The shorter one on the right (half as tall as A B) is labeled C (top), D (bottom), with an opening at the top H, and F at the bottom. Dotted lines indicate the tubes have an opening top to bottom.]]

For let a large uniforme pipe A B be full of water hold up B with ye finger, it is evident that ye same swiftness wch ye water takes to go out is equal to that wch is in A, and that all ye cylinder of water falls all in one peice, as if it was sollid;  and by consequent follows ye same rules in respect of ye swiftness at its fall as a cylinder o ice of ye same back viz that begining with a very small force it is augmented in descending according to ye odd numbers, 1 3 5 7 &c that is to say that if in ye 4th of a second it should descend 1 foot ye 4th following it would descend 3 feet in ye 3, 5 feet, &c whence it follows that ye water wch was in A being arrived to B shall go out swifter than that wch went out first.

Galileus hath spoken well of ye acceleration of ye swiftness of bodys wch fall in ye free air;  this is as I conceive it.  If there is some very light body wch dasheth against another body 100 times more heavy, it will give it ye 100th part of its swiftness and striking it ye second time it will give it yet another 100th part, so that if ye body strikeing hath 101 degrees of swiftness ye body strock shall take one degree at ye first shock and its quantity of motion shall be 100 and beeing stroke a second time with ye same swiftness of 101 degrees by ye light body, it will receive a new degree of swiftness, wch joyned to ye other shall make 2 degrees:  Ye third shock shall add yet to it one degree, and so on as it is proved in ye tract at ye shock of bodys.  Ye same thing will happen if any feeble power draws to it a very heavy body drawing it by bits now let a body be drawn or pushed by a matter very light it ought to happen that if at ye first moment of it effort it passes a line by an uniform swiftness, that [[strikethrough]] out [[/strikethrough]] at ye 2d shock and at ye 2d moment it will pass 2, at ye 3d moment 3 &c:

  Now if we take many numbers together begining at a unite as 1, 2, 3, 4, &c to 20 and we count 20 moments;  ye sum of that progression shall be 210;  and if we count 40 moments according to that progression till forty ye sum of these last numbers shall be 820, wch is near ye quadruple of 210 ye summ of ye 20 first numbers:  But at infinity that last summ shall be precisely ye quadruple of ye first, since ye proportion that is wanting always diminisheth:  whch Galileus hath also concluded in his treatise of ye acceleration of bodys wch fall:  But if ye motion is made cross a fluid body very heavy, ye acceleration shall be speedily stopped, and ye falling body is reduced to an uniform swiftness;  as also if it is a very light body wch falls thrô ye free air, as he hath proved in ye treatise of percussion:

[[image:  drawing of a rectangle representing a vessel half full of liquid atop a J shaped tube which which pierces the bottom of the vessel. The top of the open tube in the vessel is labeled C. The level of the liquid is labeled B.  Above B there is a dash mark through the right side of the vessel labeled L.  The bottom of the vessel is labeled B.  The bottom of the J has a horizontal dotted line E H F G level with the opening of the tube G.]]

We may judge also of ye gentleness of ye going out of ye first drops of water when ye [[strikethrough]] [[?]] [[/strikethrough]] ^[[pipes]] are uniformly large by ye following experiment.  Take a crooked pipe of 2 or 3 feet heigh as C D G equally large thrô out, pour water thrô C till it runs out at G, stop ye end G, an continue to fill ye pipe to C, put afterwards ye other finger upon that end, and open ye end G, ye water shall not run out if ye pipe is but 3 or 4 lines large take away ye finger wch ye end C, and clap it on again very reddily, ye water shall not spout thrô G but to 4 or 5 lines heigh, but if ye pipe C D is very much larger than ye hole G, for example if it is 9 lines large and ye end 2 or 3 lines, and that you open and shut with ye same rediness ye small hole in G, ye drops of water wch go out at G, do spout very near to ye height C ye may know also ye same slowness of ye water at its first going out of ye pipe as A B (in ye figure of page 125) and its acceleration, if you fill with water that pipe, and it sustaining it with your finger, you sustain also a small stone with another finger at ye same hand:  for suddainly drawing away ye hand:  you will see ye stone and ye bottom of ye water descend with ye same swiftness to 12 or 15 feet

  There is made also a very curious experiment to prove this rule, in ye following manner:

Transcription Notes:
mandc: reviewed and provided detailed image descriptions.