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54.

[[image: three dimensional drawing of a round container like a barrel A B C D, with a weight P sitting on top of the lid A D.  There are five dotted lines across the container: A C (top), F E, H I, L M, and B C.  The sides of the container are slightly concave between the dotted lines.  The space between F E and H I is the letter Z.  Between D and E thereis a spout K. There is another spout N out the bottom B C.]]

[[image 2]] three dimensional drawing of a balance beam Q R supported on a bar C H in to vertical beams. Above point R is a vertical tube M N.  On the opposite end of the balance beam is q weight Q, and under that is a block O.]]

This proposition may be demonstrated and at ye same time ye force of ye air in this sort.  A B C D is a hollow cylinder whose two bases A D, B C are of wood, and ye rest of copper, sustained and extended by many circles of wood arrangers F E, H I, L M, so that we can bring down ye base B C wch is supposed immoveable in ye a hole made in ye base B C thrô wch ye inclosed air in ye cylinder may go out;  that cylinder is charged with a weight P placed upon ye surface A D and if we fit below ye cylinder a ballance as that of ye figure marqued 2, so that ye rule Q R being situated horizontally ye point R wch is near to its extremity may be very near ye hole N, and directly below its center:  this being supposed of say that if we put a weight Q upon ye other end as ye ballance whose support C D is supposed to turn easily upon ye points C and D, and that ye air, wch ye weight P in descending makes to go out with much violence thrô ye hole N, dasheth against ye extremity of ye ballance towards R makes an equilibrium with ye weight Q supposed equally distant from ye support C D, that weight shall be Q to ye weight P in ye same proportion as ye surface of ye one where N is to ye entire surface of ye base B C:  for if by means of a bellows whose hath its hole equall to ye hole N, ye air is pushed against that hole with a force equall to that of ye air wch ye weight P makes to go out, there shall be made an equilibrium between their two forces on ye weight P shall not descend because there will be no air go out thrô ye hole;  and then ye air pushed by ye bellows filling that hole will sustain its part of ye weight P, as ye other parts of ye base B C sustain ye rest of ye weight, and then ye [[strikethrough]] pushed [[/strikethrough]] part wch ye pressed air will sustain shall be to ye entire weight P in ye proportion of ye hole N to ye entire largeness of ye weight B C;  therefore reciprocally ye air going out at that hole after we have taken away ye bellows, shall make an equilibrium by its shock with a weight wch shall be to ye weight P as ye hole N to ye base B C.  But if we stop ye hole N, and open another of ye same largeness as at ye point K, ye air will go out with ye same swiftness as by ye hole N, if ye base A B is charged with ye same weight P, and will make an equilibrium with ye same weight by its shock:

  But if ye cylinder is successively charged with divers weights to make ye surface A B descend more or less swift, ye air wch will go out thrô ye hole N, shall make an equilibrium by its shock with weights wch are one to ye other in ye same proportion as ye weights wch successively charge ye base A D:  ye reason is that ye proportion of ye great weight P to ye small wch makes an equilibrium, is always ye same as that of ye base B C to ye hole N;  whence it follows that ye small weights shall be one to ye other in ye same proportion as ye great weights that shall be put upon ye surface A D.  But if we fill ye same cylinder with water, ye spout wch shall be made thrô ye hole K by ye effort of ye weight P, shall make 

Transcription Notes:
mandc: reviewed and gave more detailed image descriptions. The top image is a sort of bellows structure. The bottom image resembles a teeter-totter or lever set in an H frame and a pipe impinging on one end of the board and a weight on the other end. Changed a few letters, J to I, D to P, 2 to Q, ball to base, etc.