Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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velocity of the parts of the thread paſſed the hole, than the volo
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city of the parts before the hole: Inſomuch that if
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verbi gratia
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the thickneſſe of the thread before the hole, were double to the
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thickneſſe after the hole, in ſuch caſe the velocity of the parts of
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the thread paſſed the hole, ſhould be double to the velocity of the
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parts of the thread before the hole; and thus the thickneſſe
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compenſates the velocity, and the velocity compenſates the thick
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neſſe. </
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<
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>So that the ſame occurreth in the ſolid Metals of Gold,
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Silver, Braſs, Iron, &c. </
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<
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>that eveneth alſo in the fluid Element of
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Water, and other liquids, namely, That the velocity beareth the
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ſame proportion to the velocity, that the thickneſſe of the Me
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tal, or Water, hath to the thickneſſe.</
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>And therefore granting this diſcourſe, we may ſay, that as of
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ten as two Taps with different velocity diſcharge equal quanti
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ties of Water in equal times, it will be neceſſary that the Tap
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leſſe ſwift be ſo much greater, and larger, than the Tap more
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ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
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and to pronounce the Propoſition in more proper terms, we ſay;
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That if two Taps of unequal velocity, diſcharge in equal times
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equal quantities of Water, the greatneſſe of the firſt ſhall be to
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the greatneſſe of the ſecond, in reciprocal proportion, as the ve
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locity of the ſecond to the velocity of the firſt. </
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<
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>As for example,
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if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
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will be neceſſary, that the ſecond be ten times bigger and larger
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than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
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quantities of water in equal times; and this is the principal and
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moſt important point, which ought to be kept alwayes in minde,
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for that on it well underſtood depend many things profitable,
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and worthy of our knowledge.</
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>Now applying all that hath been ſaid neerer to our purpoſe, I
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conſider, that it being moſt true, that in divers parts of the ſame
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River or Current of running water, there doth always paſſe equal
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quantity of Water in equal time (which thing is alſo demon
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ſtrated in out firſt Propoſition) and it being alſo true, that in di
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vers parts the ſame River may have various and different veloci
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ty; it follows of neceſſary conſequence, that where the River
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hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
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parts, in which it hath greater velocity, it ſhall be of leſſe mea
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ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
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ſhall have eternally reciprocall and like proportion with
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their meaſures. </
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>This principle and fundamental well eſtabliſh
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ed, that the ſame Current of Water changeth meaſure, accor
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ding to its varying of velocity; that is, leſſening the meaſure,
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when the velocity encreaſeth, and encreaſing the meaſure, when
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the velocity decreaſeth; I paſſe to the conſideration of many </
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