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30

Let now ye two branches be unequally large as in ye figure A B C D, ye washall never ye less be at ye same hight as E F in ye two branches, and ye water E B shall not force ye water C F;  for let ye base B G wch is supposed square be 16 times greater than the base C, and if it is possible let ye water descend from E unto I, and that it mount on ye other part unto D, that wch shall be descended from E to I, shall be equall to that wch is in F D, and ye two small cylinders F D, E I will have their hights reciprocall to their bases:  therefore 16:1:: ye hight F D: E I:  now ye cylinder E B being 16 times as great as ye cylinder C F it shall weigh 16 times more;  but ye space passed in ye same time by ye small cylinder, shall be 16 times as great as ye space passed by ye great cylinder, and their directions are ye same being perpendicular, therefore their swiftness should have been reciprocall to their weight, and they should have had an equal quantity of motion, wch is impossible; for by ye universal principall these cylinders of water ought to make an equilibrium, and ye one cannot move ye other since they are disposed to take an equall quantity of motion according to ye same direction.

[[image:  drawing of a "U" shaped pipe where the left tube is larger than the right tube.  The outline of the "U" is labeled A (top left), B (bottom left), C ( bottom right), D (top right).  The connecting tube at the bottom is labeled G.  There are three levels of liquid indicated by dotted lines (L, E, I)  in the larger left tube; and a horizontal line extends over to the smaller tube at a point labeled F]]

But if water is poured into ye narrow pipe unto D, it cannot stop but when ye other branch shall be full unto A; for let ye hight of F D be one inch and its base one inch and F C 10 inches, therefore all ye water C D shall be 11 cubic inches, and ye water C D descends an inch, ye water E B shall mount 1/10 of an inch, viz ye hight E L and ye space E L shall be ye measure of ye swiftness of ye water B E, as B F is that of ye water C D:  now 160 multiplyed by 1/10 gives ten for ye quantity of motion, and 11 multiply by 1 gives 11; therefore ye quantity of ye motion of ye water D C shall be greater than that of ye water B E, or wch is ye same thing, ye swiftness of ye water of ye little branch hath a greater reason to ye swiftness of ye great branch, than ye weight of ye last to ye weight of ye other;  and by ye universall principall ye water of ye small pipe will descend.  Ye same consequences will be drawn for ye other in equal heights untill that ye two surfaces of ye water of these branches may be even, and they will not stop one ye other before they be of ye same height.

One may moreover consider ye water in A G as if it was divided according to its length into 16 small square columnes each equal to ye small square column C D:  and because that each of these columns cannot mount higher or descend lower than ye other, one may judge ye same of ye small column C D, although they are not contiguous.

Hence it follows that if we put a floating body upon ye branch A B, and that the weight of that body may be equall to that of ye water wch occupies ye height A [[strikethrough]]?[[/strikethrough]] E when it should have been taken away, ye water of ye small branch shall remain always at ye height C D, and shall make an equilibrium between ye water C D and ye water C D joyned to ye weight or floting body for ye same reasons as above.

When ye little branch is very small as at half a line, or one third of a line, ye water mounts there higher than in ye other branch of an inch or two, wch happens also when th ye water a pipe glass, whose diameter is less than ye 4th of a line; for it is there elevated after ye same manner ye height of ye height of an inch or two above ye rest of ye surface of ye water, and all that water wch is elevated above ye rest level in ye small pipe or in those wch moderately large as of a line half a line insensibly equall to a gross drop of water wch being joyned to same, bodyes remains hanging without falling

The same effect is seen in ye experiment of ye bottle above, for if ye pipe is very slender, as of half a line, ye water will not descend [[strikethrough]] tow [[/strikethrough]] but towards L about an inch above E, and then ye particular cause of adhesion resists ye pipe; and ye slenderer ye pipe ye more elevated will ye point L be.

Transcription Notes:
mandc: Author started to write "water" at the end of first line but forgot to carry over the last syllable to the next line and wrote "washall" instead of "wa-ter shall." Beware of the confusion between some upper case letters: upper case D looks like lower case cursive "b" or a upper case D with a loop on top. Upper case "I" resembles "J." Upper case G resembles lower case g or y. For cleared diagram but slightly differenct labeling see scan 103 of page 72, and scan 118 of this book: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=11&pn=17&mode=imagepath Lower case "j" appears as "i" that is "judge" appears as "iudge."