Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
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the leſſer; that is, to ſpeak more properly, The Water which
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paſſeth through the greater Cock, hath alwaies a greater pro
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portion to that which paſſeth through the leſſer, than the greater
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Cock hath to the leſſer. </
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<
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>All which I will declare by an exam
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ple.</
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>Let there be ſuppoſed for more plainneſs two Squares; (the
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ſame may be underſtood of Circles, and other like Figures) The
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firſt Square is, as we will ſuppoſe, quadruple to the other, and
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theſe Squares are the mouths of two Cocks.; one of four inches,
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the other of one: Now its manifeſt by what hath been ſaid, that
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the Water which paſſeth by the leſs Cock, findeth its velocity
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impeded in the circumference of the Cock; which impediment
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is meaſured by the ſaid circumfe
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rence. </
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>Now it is to be conſider
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ed, that if we would have the Wa
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ter which paſſeth through the
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greater Cock, to be onely qua
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druple to that which paſſeth
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through the leſſe, in equal ſpaces of time, it would be neceſſary,
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that not onely the capacity and the meaſure of the greater Cock
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be quadruple to the leſſer Cock, but that alſo the impediment be
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quadrupled. </
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>Now in our caſe it is true, That the belly and
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mouth of the Cock is quadrupled, and yet the impediment is not
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quadrupled, but is onely doubled; ſeeing that the circumference
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of the greater Square, is onely double to the circumference of
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the leſier Square; for the greater circumference containeth eight
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of thoſe parts, of which the leſſer containeth but four, as is ma
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nifeſt by the deſcribed Figure; and for that cauſe there ſhall
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paſs by the greater Cock, above four times as much Water, as
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ſhall paſs by the leſſer Cock.</
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>The like errour occurreth alſo in the other manner of meaſu
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ring the Water of a Fountain, as may eaſily be collected from
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what hath been ſaid and obſerved above.</
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>APPENDIX VIII.</
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>The ſame contemplation diſcovereth the errour of thoſe
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Architects, who being to erect a Bridge of ſundry Arches
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over a River, conſider the ordinary breadth of the River;
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which being
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v. </
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<
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fourty fathom, and the Bridge being to conſiſt
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of four Arches, it ſufficeth them, that the breadth of all the four
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Arches taken together, be fourty fathom; not conſidering that
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in the ordinary Channel of the River, the Water hath onely
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two impediments which retard its velocity; namely, the touching
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and gliding along the two ſides or ſhores of the River: but </
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