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56.

Having filled with water ye reservatory A B C D of 15 inches heigh above ye hole of ye spout in F till it may pass above ye edges about a line:  for [[strikethrough]] about [[/strikethrough]] as it hath been said it doeth not run over when it is about a line and a half or 2 lines above particularly if ye edges of ye reservatory are rubbed with grease, we put upon ye top a rule of O L in an horizontal situation, wch was by consequence about a line lower than ye upper surface of ye water;  and we observe that permitting ye water to spout a little obliquely thrô ye hole F, and keping ye pipe A B C D always full to a line above ye base of that rule, ye height of ye spout would go to that rule, wch would be known by a little water wch would stick to it, wch had yet force enough to be elevated a little heigher as one fourth of a line:  But when ye water was but even with ye reservatory, and could not pass over ye brimes, there would no water stick to ye rule, because ye air would resist a little ye force of ye spout.

  But if ye pipe was 2 feet heigh there was need of some what less than 2 lines that ye spout might not go to ye rule:  But when ye reservatory was of a less height at 7 or 8 inches, and that ye holes were of 3 or 4 lines diameter, ye spouts would be allways elevated sensibly as heigh as ye surface of ye water because that little air they have to pass thrô cannot sensibly diminish their force.

  How by ye doctrine of Galileus a drop of water wch is elevated to ye height of 2 or 3 feet when in falling down again it is come to ye point whence it begott to be elevated, it ought to take at that point ye same swiftness wch had elevated it;  whence it follows that we may take it for a [[space]] or law of nature that ye water wch spouts at ye bottom of a reservatory thrô a small hole, hath ye same swiftness as a gross drop of water should have had in falling from ye height of ye surface of ye water to ye hole fitted for it, abstracting from it ye resistance of ye air.

    Consequence

  It follows that ye swiftness of ye water wch goeth out at ye bottom of reservatorys wch are of an equall height, are one to ye other in a subduple proportion of these heights;  for since ye swiftness of each spout ought to elevate them to ye height of their reservatory, and that by what Galileus hath demonstrated, ye bodys wch are moved with different swiftnesses, are elevated to ye heights wch are one to ye other in a double proportion of their swiftness;  it follows that ye swiftnesses are one to ye other in a subduple proportion of ye heights.

    RULE IV
 Spouts of water equally large wch have inequall swiftness, sustain by their shock weights weights wch are one to ye other in a proportion double of these swiftness.

     Explication

  For as much as ye water may be considered as composed of an infinite number of small imperceptible parcells, it ought to happen that when they go twise as swift, there is twise as many wch shock at ye same time, and for that reason ye spout wch goeth twise as swift as another, makes twise as great an effort by ye sole quantity of ye small bodys wch shock and because it goeth twise as swift it makes yet twise as much effort by its motion;  and by consequence these two efforts together ought to produce a quadruple effort, and ye same in respect of other proportions.  We moreover prove this rule in ye following manner (fig: p 51 and ye I: A B is a cylinder 4 times as heigh as ye cilinder C B, ye hole E is equall to ye hole F, ye two cylinders are full of water:  Now for as much as ye spout going out at E ought to sustain a weight equall to ye weight to ye small cylinder of water G E, and that ye spout thrô F ought to sustain a weight equall to ye weight of ye small cylinder H F, and that ye small cylinder G E is 4 times ye small cylinder H F;  it follows that ye weights elevated shall be as 4 to one;  but by ye consequent of ye preceeding rule, ye swiftness of ye spout thrô F is to that of ye point thrô E in a subduple proportion of ye height F H to ye height E G, and by consequence it shall be as 1 to 2:  Therefore a double swiftness of a spout of ye same largeness shall sustain a weight quadruple and so in respect of other proportions;  whence it follows that a spout of air wch goeth 24 times as swift as another shall sustain a weight 576 times greater, since 576 is ye square of 24;  and because a spout of water wch goeth 24 times slower, sustains ye same weight we may judge that ye air is 576 times more rarefied than ye water since that going with ye same swiftness ye spout of water sustain a weight of 576 times greater.

  We may know by experience ye force of ye shock of ye air with ye following engine as well as with that of ye second rule:  A B C D is a cylindrik vessel of Tinn well soddered open in C B, and inverted in another cylinder E F G H at ye bottom of wch there is a small pipe well soddered L I wch enters into ye inverted cylinder and passeth a little above ye water N K wch is in ye cylinder F H ye base A B is with many different weights to make that cylinder descend, and at ye same time make ye air go out with violence thrô ye pipe JL at ye base of which is filled a ballance as that at ye figure above marked 2, charged at one end with different 

Transcription Notes:
mandc: Reviewed. The translator frequently uses the word "rule" to describe what looks to be a board, beam or plank (O L). The translator came upon a problem in the third paragraph where he needed the phrase "rule of law or nature" so he left a blank space rather than use "rule" ambiguously. French: r?le de droit ou de la nature. Droit (right) may have stumped him so he left a blank. Swiftness in this text means velocity. For ms page 51 see scan 55-56.