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41. fall perpendicularly, will be determined to go by ye radins of ye Hemisphere H E and L E with greater swiftness than ye like small bodies wch should be in O or M G. The same thing will happen if ye hole is in P instead of E: for ye small bodies wch should be in ye Hemisphere K R S run there as soon as ye finger is taken away; it is for this reason that if we peice [[for pierce]] a vessel of wine a finger above ye grounds [[sediment]], and that ye hole is sufficiently great; ye parts of ye ground, wch are near mount to pass there and do render ye wine troubled; when ye holes E or P are very small, ye hemisphere doth not extend so far as when they are great. Rule III Bodys whose specific weight is greater than that of water, fall to ye bottom. Explication. Let A be ye body heavier than ye water, will descend after ye same manner in ye water [[image: cross section drawing of a vessel filled with liquid D B C (dash lines) supporting a floating object A. Horizontal dotted line indicates the level the liquid in the vessel crossing through the floating object which is about half submerged.]] as in ye air if it doth not descend less swift, ye water B wch shall immediately below shall be pushed down by that body which [[?spiking]] ye other lower shall push it to ye side towards C and D in ye circumference and ye whose water of the vessel shall be put in motion; and when ye body is descended as in B it shall make other Tourbidions to fill that place it shall quit till it toucheth ye bottom Rule IV Bodys whose specific weight is greater than that of water, loose in ye water as much of their weight as is ye water whose place they occupy. Hang ye body A B, in ye water by ye cord C D, suppose ye part E was entirely taken away so ye rest weighs as much as ye water wch should fill ye space A B if that body was taken away, it is evident [[image: cross section drawing of a vessel with water level indicated by a horizontal dotted line. A square A B is submerged in the water suspended on a cord C D. Inside the square A B there is a smaller square labeled E.]] that it will then make an equilibrium with as water situated at ye side; and by consequence will not weigh upon ye cord C D, no more than if we had dipt it in ye water without ye body: therefore if we suppose that ye part E is added so if ye whole body shall not weigh upon C D but so much as ye point E; whence follows what has been proposed: from hence we may find a means to examine ye specific weight all those bodies wch weigh more than ye water, both in respect of ye water and of other bodys; for example let ye body A B be of gold; it is necessary to weigh it in ye water with a balance, they join, to one of ye scales by a cord and put an equal weight in ye other scale, they afterwards dip it entirely in ye water, and if 1/8 of ye weight made an equilibrium in ye air must be taken away to continue that equilibrium when it is in ye water we may know that ye specific weight of ye gold is to that of water as 18 to 1, and if ye body is of lead and that we must take away 1/11 of ye weight that it may make an equilibrium in ye water; we may know that ye specific weight of water in regard of lead is as on to 11 and thence that that of gold in regard of lead is 18 to 11; whence we may know if a piece of gold falsified without observation; for if in a like experiment it looses in ye water 1/12 or 1/14 of its weight we may judge that it hath other metals mixed within a sufficiently great quantity, as 1/3 or 1/2 and that is falsified but if looseth but 1/17 little mixture. but if we suspend in a vessel with a cord a great cylindric body of glass or metals so that it almost fills it without touching the sides or ye bottom, and we pour water to fill up ye void places to ye height of ye cylindric body; then ye wch could
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