Castelli, Benedetto - Of the mensuration of running waters

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1the fourth Theorem of this, with its Table, and the uſe there
of annexed.

COROLLARIE

Hence it followeth, that when a River increaſeth in quick
height by the addition of new water, it alſo increaſeth in ve
locity; ſo that the velocity hath the ſame proportion to the velo
city that the quick height hath to the quick height; as may be
demonſtrated in the ſame manner.

PROPOS. III. PROBLEME II.

Achanel of Water being given whoſe breadth exceeds not
twenty Palms, or thereabouts, and whoſe quick beight
is leſs than five Palms, to meaſure the quantity of the
Water that runneth thorow the Chanel in a time
given.

Place in the Chanel a Regulator, and obſerve the quick
height in the ſaid Regulator; then let the water be turned
away from the Chanel by a Chanellet of three or four Palms
in breadth, or thereabouts: And that being done, meaſure the
quantity of the water which paſſeth thorow the ſaid Chanellet,
as hath been taught in the ſecond Propoſition; and at the ſame
time obſerve exactly how much the quick height ſhall be abated
in the greater Chanel, by means of the diverſion of the Chancl
let; and all theſe particulars being performed, multiply the quick
height of the greater Chanel into it ſelf, and likewiſe multiply
into it ſelf the leſſer height of the ſaid bigger Chanel, and the
leſſer ſquare being taken, from the greater, the remainder ſhall
have the ſame proportion to the whole greater ſquare, as the wa
ter of the Chanellet diverted, hath to the water of the bigger
Chanel: And becauſe the water of the Chanellet is known by
the Method laid down in the firſt Theorem, and the terms of the
Theorem being alſo known, the quantity of the water which run
neth thorow the bigger Chanel, ſhall be alſo known by the Gol
den Rule, which was that that was deſired to be known. We
will explain the whole buſineſs by an example.

Let a Chanel be, for example, 15 Palms broad, its quick height
before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
inches; but after the diverſion, let the quick height of the Chanel
be onely 22 inches. Therefore the greater height to the leſſer,
is as the number 11. to 12. But the ſquare of 11. is 121, and the
ſquare of 12. is 144, the difference between the ſaid leſſer

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