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46.

Demonstration

[[image: Drawing of a long verticl tube A B, standing in a small vessel C D E, containing a liquid (ditted line F G, about 1/4th of the way down the tube is the letter H, and half way down the letter L, and at the bottom of the tube Z.]]

Let ye pipe A B be 38 inches Z B one inch;  A H ye inclosed air above ye mercury H B of what [[strikethrough]] ye inched [[/strikethrough]] extent you please sustained with your finger in B;  I say first of all that if ye finger is taken away ye mercury will descend;  for as much as ye air A H is condensed after ye same manner as that of ye place where ye experiment is made, it ought to make [[strikethrough]] by its experiment is made [[/strikethrough]] by its spring an equilibrium with ye whole weight of ye atmosphere, as hath been proved and being joyned with ye with ye weight of ye mercury in Z H, these two powers together would surpass ye weight of ye atmosphere and it is necessary that ye air, A H dilate itself and that one part of ye mercury descend;  but it will not descend entirely descend ye air A H would be dilated very much, and in that estate it could not make an equilibrium with ye weight of ye atmosphere:  whence it follows that one part of ye mercury ought to remain in ye pipe.  I say therefore that if H A is 9 inches it will be dilated and will push back ye mercury so that it will remain elevated 16 inches above ye upper surface of ye mercury F Z G let that elevation be Z L.  Now there will than be an equilibrium between ye weight of ye whole column of air of ye atmosphere and ye spring at ye dilated air A L joyned to ye weight of 16 inches of mercury Z L; and because ye compliment of 16 to 28 is 12, ye dilated air A L shall make an equilibrium by its spring to ye weight of 12 inches of mercury which remain for ye weight of ye atmosphere beyond ye 16 inches;  but as 28 to 12 so A L of 21 inches is to 9;  whence it follows that ye mercury ought to remain at 16 inches heigh above ye mark Z, when we have 9 inches of air in ye pipe above ye mercury, because that ye air is condensed in proportion to ye weight, wherewith it is charged.  But so ye mercury in another experiment stay at 21 inches, we may judge following ye same rule, that since these 21 inches of mercury make an equilibrium with 3/4 of ye weight of ye air, ye forth remaining wch ought to halve ye value of 7 inches, shall be sustained by ye spring of ye rarefied air contained in ye pipe according to ye [[strikethrough]] pipe [[/strikethrough]] distinction of ye equilibrium of springs:  now 28 inches of mercury ye entire weight of ye atmosphere is to 7 inches as 16 inches of dilated air is to 4 inches of air, wherefore we may judge that we must leave 4 inches of air in ye pipe above ye mercury, that it may [[strikethrough]] dilated [[/strikethrough]] remain at 21 inches and ye air may be dilated to 16 inches.  But if we would reduce ye mercury to 14 inches wch is ye half of ye weight of ye atmosphere in ye same pipe above mark Z, we must consider that there will remain 23 inches to A, and that ye dilated air of 23 inches ought to make an equilibrium with its spring to ye remaining weight of ye atmosphere.  We must therefore say that as 28 is to 14, ye compliment of 14 to 28, so 23 of dilation wch fills ye pipe above 14 inches, is to 11 1/2, whence we know that we must leave 11 inches and 1/2 of air above ye mercury in ye pipe before ye experiment, and it will manifestly appear that ye spring of ye inclosed air making then an equilibrium but with half ye weight of ye air of ye atmosphere since ye 14 inches of mercury make an equilibrium with ye rest, it shall be rarefied in a double proportion:  and by all these experiments we may judge by observeing ye same rule explaned above, what quantity of air we must leave in a great or small pipe, that ye mercury may stay at what height we please.  For if ye pipe should be only six inches above ye mark Z we shall find ye same proportions in making ye same calculation, as for example if 2 inches is ye given height of ye mercury, and that we had found that as 28 is to 26 ye complement of 2 to 28, so 4 ye space of ye dilated air above ye 2 inches of mercury is to 3 5/7;  3 inches 5/7 shall be quantity we must leave in ye pipe, that ye mercury may stop at 2 inches heigh in a pipe of 7 inches, [[strikethrough]] playced [[/strikethrough]] plonged one inch into ye mercury of ye vessel:

  But if ye quantity at ye inclosed air in ye pipe were given, and we would know to what height ye mercury would remain after ye experiment; we may observe an algeraic calculation, applyed to ye same rules, as I have taught in ye essay of logic, and in ye treatise of ye nature of ye air.

Transcription Notes:
mandc: Read "spring" as force or pressure.