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39

Application of that Rule

  If there is fastened an empty vessel A B C D in ye water F E I L contained in some vessel, holding ye empty vessel so that it may be upright, and may not be over turned, there needs as much force to keep one part stopped at a certain deepth below

[[image: drawing of a smaller vessel A C D B inside a larger vessel G L I H, with a dotted line E F across both vessels labled N and O where it intersects the sides of the smaller vessel inside.  Inside the smaller vessel a weight M sits on the bottom C D of the smaller vessel.]]

The surface of ye water E F as that wch is necessary to sustain in ye air a weight M wch being put in the bottom of ye vessel A B C D may keep it in that situation, wch weight with that at ye empty vessel ought to be equal to ye weight of ye water wch should posses ye space N O D C, as hath been explained above:

  We may apply that effect to ye ice wch is formed in rivers round about ye piles wch sustain bridges, for supposeing that ye ice is a foot thick, and that it weighs with the air wherewith it is filled less by 1/12 than ye water, we may easily calculate to know what weight may hinder its elevation to ye top of ye water, as if it is 400 feet in surface, it shall ^[[be]] 400 cubic feet each at wch [[strikethrough]]or cubic feet of water[[/strikethrough]] shall weigh but 64 pounds instead of 70 for a cubic foot of water, and ye product of 6 ye difference of 64 and 70 being multiplied by 400 is 2400 pound: now if ye weight of ye piles of ye bridge is greater than 2400, ye ice shall not carry away ye piles; for there is yet more resistance that ye piles make by their bearing against ye firm earth where they are engaged, as to be rooted up:

  If there is no ice but from ye side upward, and it is extream long as A B, it may serve as a lever, as is seen in ye foregoing figure, by makeing it support upon ye left pile C B

[[image: cross section drawing of three piles E G C, their pointed tips extended down into the riverbed F H D, standing in water with ice on the top of the water represented as a frozen block A I B, represented by horizontal lines.]]

serve as a lever, as is seen in ye foregoing figure, by making its support upon ye left pile C B