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48. being reduced we shall find 13A - 32 = to AA ye square of 6 1/2 half ye roots is 42 1/4, from wch takeing 32 there remains 10 1/4, whose root is 3 5/24, a little less, take that from 6 1/2, there remains 3 [[?]]/24 ad that to 6 1/2, it shall be ye roots; whence we see that ye water can never mount when ye pipe is void, but to 3 feet and 7/24 a little more althô we play ye (piston) [[space]] as much as we please but if ye pipe had been filled to 9 feet 18/24 we might conclude that ye water might mount to 12 feet by many strokes of ye (piston) [[/space]] Let us suppose now that ye pipe to ye (piston) [[space]] may be 14 feet, and that ye play of ye (piston) [[space]] may be 2 feet, 32 - A shall be to 32 as 14 - A to 16 - A, to find easily ye equation we must multiply 32 by 2 ye difference of 14 and 16: ye product is 64 for ye absolute number and 16A shall be ye number of ye roots and AA shall be equall to 16 A - 64, from wch taking 64 there remains nought, whose root is 0 wch takeen away added to 8, makes allways 8, wch marks that there is but one root and ye water cannot mount but to 8; but if we play ye (piston) a little heigher than these two feet, ye water will mount to 14 feet. The analogy is easy for ye (piston) [[space]] being mounted to 2 feet ye pipe shall be of 16 feet and ye water being at 8 feet there will remain 8 feet of air; but 32 is to 24 ye compliment of 8 feet to 32 as 8 feet of dilated air to feet of common air: therefore ye water will mount heigher than these 8 feet if ye (piston) [[space]] as played but 2 feet. Whence it may be seen that to make ye water mount by aspiration to a considerable height as to 20 feet, we must diminish ye largeness of ye pipe of ye pump and give sufficient play to ye (piston) [[space]] Suppose that ye surface of ye piston was 4 times as large as large as ye base of ye pipe one foot of ye elivation of ye piston, would be as much as 4 if is ye (piston) [[space]] was not larger: If therefore ye play is 1 1/2 foot it shall be ye same as if it was elevated to 6 feet being of ye same largeness: now ye 4 terms of ye equation being 32 - A: 32:: 20 - A: 26 - A there will be 6 times 32 viz 192 for one term of ye equation [[strikethrough]] being 32 - :A 12 [[/strikethrough]] and ye other 26 A it shall be therefore AA equall to 26 A less by 192, ye square of ye half ye roots is 169 less than 192: and by consequent in pumping a long time we shall make ye water mount to 20 feet. If in ye example above we take 8 feet for ye heightest term of ye water, when ye pipe is 14 feet and we play of ye (piston) [[space]] 2 feet, it is easy to prove that if we suppose 2 feet of water upon ye (souspape) [[valve]] [[space]] it will make [one end of mounting ye play of ye (piston) [[space]] to 2 feet; for there will remain 5 feet of air now there is a less [[?reason]] of 5 to 7 than of 27 if compliment of 5 to 32, to 32; and by consequent ye water will mount heigher than these 2 feet. Ye proportions shall be allways more inequall in taking 10 feet or 11 feet and if we take 7 feet instead of 8 feet, ye water will yet mount, for there still rest 7 feet of air; now 25 ye compliment of 7 to 32 is to 32 as 7 to 8 24/25; therefore if ye (piston) [[space]] goes to 2 feet it will make ye water mount heigher than 7 feet; it will mount also more easily if we pour upon it but to 6 feet: for there will be 8 feet of air: now 26 ye compliment is to 32 as 8 to 2 22/26 equilibrium ye (piston) [[space]] goes to 10 feet, it will also make ye water mount better than when it was at 7 feet and also better when it shall be at 5 feet etc: if we would know what play of ye (piston) [[space]] would be necessary to make ye water mount to 30 feet we might take a number a little greater than ye half of 30 as 16 ye compliment is 16 ye rest of ye air is 14, as 16 to 32 so is 14 to 28: it is necessary therefore that ye (piston) [[space]] be elevated 14 feet, or that if ye pipe is 2 inches Diameter that of ye (piston) [[space]] may be 7 1/2 inches; for ye square of 7 1/2 wch is a little more than 14 times 4 ye square of 2 inches, and then it will suffice that ye play of ye (piston) [[space]] may be one foot. But as to 18 feet ye elevation is yet more difficult, there must be 8 inches of b Diameter to ye (piston) [[space]] that its play being one foot it may elevate ye water heigher than these 18 feet. We may easily explain ye ye same force of ye spring of ye air ye following experiment, wch is sufficiently curious: Take a pipe AG stopped below [[,]] about 12 or 15 lines large [[diameter]], but a little streighter [[narrower]] towards A that one may exactly stop it with ones finger, fill it with water and put there some small figure of glass or of copper hollow within and pearced as is D with a small hole to put in a pin that ye air and ye water may not enter, and that its specific weight in respect of ye water may be so proportioned, that if we add a little weight it will go to ye bottom and if we take it away it will swim above as wax. Apply ye finger to ye open hole A and press it strongly, ye small figure will descend to B or lower and to ye bottom; take away ye finger, it will remount; and it being remounted as in E or C reput ye finger on again it will begin to redescend. Ye cause of these effects is that when ye water is pressed with ye finger we press also ye air wch is in ye figure, and it is condensed althô we do not condense ye water and by consequence
Transcription Notes:
mand: Again it looks like the translator left spaces to go back and put in proper english words for some words he was not familiar with [piston (French for piston); and souspape (French for valve)].
"Pipe" in this ms is translated differently than in the Desaguliers translation (link below) as "barrel."
illustration for the last paragraph is on the next page (53), and here: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=131&viewMode=images&mode=imagepath&pn=174&ww=0.0846&wh=0.2515&wx=0.5854&wy=0.3465
Desaguliers translation: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=131&viewMode=images&mode=imagepath&pn=5&wh=0.9198&wy=0.0802
