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57.

[[image:  Diagram of two cylinders with different points marked alphabetically]]

weights to try ye force of ye shock of that air.  Ye experiments are found conformed to ye demonstration above, viz that if ye air is blown with a bellows into ye pipe L I that it hinders ye weight M and ye cylinder A D from descending then that rushed air makes ye same effect as if ones finger was put at ye point L to hinder ye air from going out, and as in that estate ye finger would bare its part of ye weight in joyned to that of ye cylinder A D, and ye rest should be sustained by ye of ye base G H to ye height of C D, to ye hole L so that if ye whole weight was 100 and ye base G H was 100 times as great as ye hole L ye air blowed into ye pipe would sustain ye 100 part of ye whole weight:  Therefore reciprocally we take away if ye blast of ye air wch should go out with ye same swiftness as ye wind of ye bellows wch would hinder its going out, will make an equilibrium with a weight equall to that of 100 [[?point or ?part]].

  It follows for these reasons, that if two cylinders full of air of ye same height having their bases in equall are charged by equall weights being disposed as ye cylinder A B C D and having ye holes equall thrô wch ye air ought to go out, ye weights that ye air going out will elevate shall be one to ye other in a reason reciprocal of their bases;  for let ye two cylinders A B C D, a b c d put each in another cylinder full of water, as it hath been explained in ye figure preceding, and let ye two weights M and m be equally placed upon in equall cylinders, and ye weights elevated be P and p viz P for m and p for M, for as much as ye base G H is to ye hole L as ye weight m to ye weight P elevated by ye air wch goeth out thrô L to ye weight M or m;  in equall reason.  Ye proportion being trebled, ye base G H shall be to ye base g h as ye weight p to ye weight P.  But if ye weights wch charge ye cylinders are proportionall to their bases, they elevate equall weights by ye shoc of ye air wch they make to go out thrô equall holes, as if ye base G H is 24 and ye base g h 12 and that ye weight M may be 12 pounds and ye weight m 6 ye hole L being 4 ye same as 6, ye weights P and p are each of 2 pound, of wch ye proof is easy:

     Consequence
   of ye former demonstration
 
  It follows that ye time of ye runing out of ye air of ye small cylinder shall be to ye time of ye running out of ye air of ye great cylinder, when they are charged with equall weights in a proportion compounded of that of ye base G H to that of ye base g h and ye subduple of ye same base G H to ye same base g h;  for if ye swiftness were equall, ye times would be one to another as bases:  But ye weight elevated being in a reason reciprocall of ye bases and ye swiftness being by ye third rule in a subduple reason of ye weights elevated, ye swiftness will be reciprocally in a subduple reason of ye bases that is to say that ye swiftness by I shall be to ye swiftness by L in a subduple proportion of ye base G H to ye base g h;  and by consequence ye time of ye runing out of ye air of ye great cylinder shall be to ye time of ye runing out of ye air of ye little cylinder in ye proportion compounded of that of ye base G H to ye base g h, and of ye subduple of ye same base one to ye other;  wch is found conformed to experience:  For a cylinder of 8 inches 7 lines diameter at ye base, and another of 5 inches 6 lines being charged each with 44 ounces ye great one is void in 47 half seconds and ye little one in 12:  Now ye bases G H and g h are one to ye other as ye squares of their diameters G H and g h;  and 74 

Transcription Notes:
mandc: Reviewed. Changed: J to I, B to D, upper to lower case [note that the drawing to the left uses upper case letters, the drawing to the right lower case letters]. Image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=174&ww=0.1315&wh=0.1957&wx=0.4793&wy=0.7462