Castelli, Benedetto, Of the mensuration of running waters, 1661

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              derſtood nothing at all, of that which others pretended full and
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              clearly to underſtand. </s>
              <s>And my doubt aroſe from my frequent
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              obſervation of many Trenches and Channels, which carry
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              water to turn Mills, in which Trenches, and Channels, the
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              water being meaſured, was found pretty deep; but if afterwards
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              the ſame water was meaſured in the fall it made to turn the
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              Wheel of the Mill, it was much leſſe, not amounting often to the
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              tenth part, nor ſometimes to the twentieth, inſomuch, that the
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              ſame running water came to be one while more, another while leſs
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              in meaſure, in divers parts of its Channel; and for that reaſon this
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              vulgar manner of meaſuring running Waters, as indeterminate and
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              uncertain, was by me juſtly ſuſpected, the meaſure being to be de­
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              terminate, and the ſame. </s>
              <s>And here I freely confeſſe that I had fin­
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              gular help to reſolve this difficulty from the excellent & accurate
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              way of diſcourſing, as in allother matters, ſo alſo in this, of the
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              Right Honourable and Truly Noble Signior
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              Ciampoli,
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              Secretary
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              of the Popes ſecret affairs. </s>
              <s>Who moreover, not ſparing ſor the coſts
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              of the ſame, generouſly gave me occaſion a few years paſt to try by
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              exact experiments that which paſt concerning this particular. </s>
              <s>And
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              to explain all more clearly with an example; we ſuppoſe a Veſſel
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              filled with Water, as for inſtance a Butt, which is kept full, though
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              ſtill water runneth out, and the Water run out by two Taps equal
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              of bigneſſe, one put in the bottom of the Veſſel, and the other in
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              the upper part; it is manifeſt that in the time wherein from the
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              upper part ſhall iſſue a determinate meaſure of water ſrom
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              the inferiour part there ſhall iſſue four, five, and many more of
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              the ſame meaſures, according to the difference of the height of
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              the Taps, and the diſtance of the upper Tap from the Superfici­
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              es and level of the water of the Veſſel: and all this will alwayes
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              follow, though, as hath been ſaid, the Taps be equal, and the
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              water in diſcharging keep the ſaid Taps alwayes full. </s>
              <s>Where firſt
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              we note, that, although the meaſure of the Taps be equal, never­
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              theleſſe there iſſueth from them in equal times unequal quantities
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              of water, And if we ſhould more attentively conſider this buſi­
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              neſſe, we ſhould find, that the water by the lower Tap, run­
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              neth and paſſeth with much greater velocity, then it doth by the
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              upper, whatever is the reaſon. </s>
              <s>If therefore we would have
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              ſuch a quantity of Water diſcharge from the upper tap, as
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              would diſcharge from the neather in the ſame time, it is plain, that
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              either the upper Taps muſt be multiplyed in ſuch ſort, that ſo
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              many more Taps in number be placed above than below, as the
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              neather tap ſhall be more ſwift than the upper, or the upper Tap
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              made ſo much bigger than the nether, by how much that be­
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              neath ſhall be more ſwift than that above; and ſo then in equal
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              times, the ſame quantity of Water ſhall diſcharge from the upper,
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              as doth from the neather part.</s>
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