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47.

We shall find ye like equilibrium of ye spring of ye in pipes full of water and air, supposing that ye greatest weight of atmosphere is equall to ye weight of 31 feet of water, as is found by experience:  for ye Barometer being at 27 inches 8 lines, ye Barometer of water was at 31 feet 1 inch;  and being at 28 inches ye other was at 31 feet 4 inches:  and if it had been at 28 inches 7 lines as it sometimes happens ye water would have been at 32 feet.  If ye pipe is 40 feet and we would reduce ye water to 16 feet, we must put 12 feet of air above ye water;  for ye air dilating itself double and possesing 24 feet, shall make an equilibrium by its spring, with ye half of ye weight of ye atmostphere, and ye 16 feet of water wch remain make an equilibrium with ye other half.  It is supposed that one small part of ye pipe being plonged or dipped in ye water, to make ye experiment after ye same manner as that of mercury;  there remains 40 feet above

  Whence is seen manifestly that if we plonge into a deep water an inverted bottel full of air, having weights around its neck sufficient to make it go to ye bottom, when it descends but little and little ye water by little and little enters and mounts up into its neck;  and when it shall be descended 32 feet deep ye water wch will enter there will reduce ye air to half ye extent wch it had in ye bottle before it was plonged therein wch I have explained more longely in ye essay of ye nature of ye air.

  We may therefore see ye error of them wch believe that in a pump;  we may make ye water mount to 32 feet by drawing with ye (piston) [[space]] find according to ye play of ye (piston) [[space]] it cannot be elevated but to a determinale height:  for let there be for example a body or pipe of a pump uniform of 20 feet having above ye 20 feet a (piston) [[space]] of ye same longeness wch cannot be elevated and depressed but ye space of one foot; I say that if there is a (souspape) [[valve]] [[space]] at ye bottom of ye pump and we play ye (piston) to 11 feet or that we pair upon ye (piston) [[space]] ye water cannot be elevated to 12 feet. for let it be elevated if it be possible to 11 feet on that we pour upon ye  (piston) [[space]] water to eleven feet heigh and we repair ye (piston) [[space]] there will remain 9 feet of air to ye (piston) [[space]] and that air wch is rarefied in elevating ye (piston) [[space]] one [[strikethrough]] part [[/strikethrough]] foot, cannot be rarefied but as 9 to 10;  and because that 21 ye compliment of 11 feet to 32 wch is ye weight of ye atmostphere, is to 32 as 9 to 13 5/7 it is necessary to keep ye water at 11 feet that ye (piston) [[space]] be elevated to 4 feet 5/7 to make an equilibrium between ye weight of ye atmosphere and ye diminished spring of ye inclosed air joyned to ye weight of 11 feet of water, as hath been explained above whence it follows that by elevating ye (piston) [[space]] one foot only, ye (souspape) [[valve]] [[space]] will not open and ye water will not mount any heigher than 11 feet.

  To give ye rules for these elevations of water in ye pumps, we may follow an algebraic calculation in this manner.  We will call A ye height whether ye water ought to mount in ye pipe of ye pump by ye play of ye (piston) [[space]] abstracting ye weight from that (souspape) [[valve]] [[space]]  Let ye pipe of ye pump above ye surface of ye water wch we would elevate be 12 feet, and suppose that we would elevate it to these 12 feet by one only stroke of ye (piston) [[space]] we shall make this Analogy:  as 20 ye complement of 12 feet to 32, is to 32 so is 12 foot of ordinary air to a fourth proportional that 4th proportionall shall be 19 1/5 whence you will see that ye pipe of ye pump must be very large to elevate ye (piston) [[space]] to 19 1/5 feet above ye 12 feet to make ye water mount to 12 feet by one only stroke of ye (piston) [[space]] but ye play at ye (piston) [[space]] was limited to 2 feet, we may say as 32 - A is to 32, so is 12 - A to 4 - A, ye first term is ye compliment at ye unknown height whether ye water will mount, to 32 feet of water wch is ye weight to ye Atmostphere, ye third term is ye 12 feet less by that height, and ye 4th is ye 2 feet where ye (piston) [[space]] is elevated joyned to 12 feet less by ye same height:  Now ye product of 14 - A by 32 - A is 448 - 46A + AA, and ye product of ye two midle terms is 384 - 32A, ye equation being reduced there will be an equallity between AA and 14 A - 64 and because we cannot take away from 49 ye square of ye 1/7 half of ye roots, 64 is that mark wch continueing to pump we shall at many times make ye water mount to ye (piston) [[space]] and to know how it will mount at ye first stroke, we must [[?suppose]] that ye (piston) [[space]] may be elevated these two feet:  There will be therefore and uniform pipe of 14 feet and following that wch hath been said in ye essay of Logic and ye treatise of ye nature of ye air, we shall make this calculation: Ye inclosed air was 12 feet + A is to A as 32 to 2 - A, ye equation being reduced we shall find that AA shall be equall to 24 - 10 A, and at last that ye value of ye root shall be somewhat short of A 4/7 wch taken from 2 there will remain 1 3/7 and by consequence ye water will not mount by ye first stroke of ye piston [[space]] but to 1 foot 3/7 a little more

  If it had been supposed that ye play of ye (piston) [[space]] was one foot, we might know by ye same calculation whether ye water would be elevated by ye first stroke of ye (piston) [[space]] and if we would know whether it may be elevated after many strokes, we must say as 32 - A is to 32, so is 12 - A is to 13 - A, ye equaission 

Transcription Notes:
para 3: Difficult to determine whether she is writing "C piston)" or (piston). mandc: This page appears to have been "a work in progress" that was never completed. Transcriber also left many gaps in the text, understandable due to the disjointed spaces. I believe it is (piston). Piston is French for piston, and the translator might not have been familiar with the term and meant to look it up. I see a faint close parenthesis after the word. This and following para's look like the author (Mariotte was a man, translator of this ms apparently unknown) intended to go back and fill in the blanks after drawing the illustration or looking up words, but I find no matching drawing. Too hard box? "Line" is an old English unit of measurement: 1/4 of a barleycorn or about 1/10th of an inch. I beleive what looks like "sonspape" is really "souspape" French for valve. In another translation "souspape" is translated as valve or "clack." "Clack" in the OED is a noise. It could be that the translator didn't know the best English word so noted a mnemonic French word and left a space to remind himself to look up the English word later and cross out the mnemonic.