Castelli, Benedetto - Of the mensuration of running waters

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1the leſſer; that is, to ſpeak more properly, The Water which
paſſeth through the greater Cock, hath alwaies a greater pro
portion to that which paſſeth through the leſſer, than the greater
Cock hath to the leſſer. All which I will declare by an exam
ple.

Let there be ſuppoſed for more plainneſs two Squares; (the
ſame may be underſtood of Circles, and other like Figures) The
firſt Square is, as we will ſuppoſe, quadruple to the other, and
theſe Squares are the mouths of two Cocks.; one of four inches,
the other of one: Now its manifeſt by what hath been ſaid, that
the Water which paſſeth by the leſs Cock, findeth its velocity
impeded in the circumference of the Cock; which impediment

1[Figure 1]
is meaſured by the ſaid circumfe
rence. Now it is to be conſider
ed, that if we would have the Wa
ter which paſſeth through the
greater Cock, to be onely qua
druple to that which paſſeth
through the leſſe, in equal ſpaces of time, it would be neceſſary,
that not onely the capacity and the meaſure of the greater Cock
be quadruple to the leſſer Cock, but that alſo the impediment be
quadrupled. Now in our caſe it is true, That the belly and
mouth of the Cock is quadrupled, and yet the impediment is not
quadrupled, but is onely doubled; ſeeing that the circumference
of the greater Square, is onely double to the circumference of
the leſier Square; for the greater circumference containeth eight
of thoſe parts, of which the leſſer containeth but four, as is ma
nifeſt by the deſcribed Figure; and for that cauſe there ſhall
paſs by the greater Cock, above four times as much Water, as
ſhall paſs by the leſſer Cock.

The like errour occurreth alſo in the other manner of meaſu
ring the Water of a Fountain, as may eaſily be collected from
what hath been ſaid and obſerved above.

APPENDIX VIII.

The ſame contemplation diſcovereth the errour of thoſe
Architects, who being to erect a Bridge of ſundry Arches
over a River, conſider the ordinary breadth of the River;
which being v. g. fourty fathom, and the Bridge being to conſiſt
of four Arches, it ſufficeth them, that the breadth of all the four
Arches taken together, be fourty fathom; not conſidering that
in the ordinary Channel of the River, the Water hath onely
two impediments which retard its velocity; namely, the touching
and gliding along the two ſides or ſhores of the River: but

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