MATHEMATICAL
COLLECTIONS
AND
TRANSLATIONS:
THE SECOND
TOME.
THE SECOND PART,
Containing,
D. BENEDICTUS CASTELLUS,
of the MENSURATION of RUN
NING WATERS.
the Mea&longs;ure of RUNNING WATERS.
His LETTERS and CONSIDERATIONS
touching the Draining of FENNS, Diver&longs;ions of
RIVERS, &c.
Inundations, &c. in the Territories of BOLOGNA,
and FERRARA.
By
LONDON,
Printed by WILLIAM LEYBOURNE, MDCLXI.
OF THE
MENSURATION
OF
RUNNING WATERS.
An Excellent Piece
BY
DON BENEDETTO CASTELLI,
Abbot of St.
and Profe&longs;&longs;our of the Mathematicks to
Pope
Engli&longs;hed from the Third and be&longs;t Edition, with
the addition of a Second Book not before extant:
By
Printed by WILLIAM LEYBOURN, 1661.
THE
AUTHOURS EPISTLE
TO
Pope VRBAN VIII.
I lay at the Feet of your Ho
line&longs;&longs;e the&longs;e my Con&longs;ide
rations concerning the
MENSURATION OF
RUNNING WATERS:
Wherein if I &longs;hall have &longs;ucceeded, being a
matter &longs;o difficult and unhandled by Wri
ters both Ancient Modern, the di&longs;covery of
any thing of truth hath been the Effect of
Your Holine&longs;&longs;es Command; and if through
inability I have mi&longs;&longs;ed the Mark, the &longs;ame
Men of better Judgment, and more e&longs;peci
ally with Your Holine&longs;&longs;e, to whom I humbly
pro&longs;trate my &longs;elf, and ki&longs;&longs;e Your Sacred
Feet.
Your Holine&longs;&longs;es
A Monk of
AN
ACCOUNT
OF THE
Authour and Work.
DON BENEDETTO CASTELLI,
Di&longs;cour&longs;es of the
Running Waters,
the Wor&longs;hipful FAMILY of the
GASTELLII,
fir&longs;t breath near to the lake THR A
SIMENVS, (where
a fatal overthrow to the
of happy
at pre&longs;ent &longs;ubmitteth to the Juri&longs;diction of the Church, as being a
part ofPETER'S Patrimony.
zealous of the good of his Soul than ob&longs;ervant of the Propen&longs;ion of
his Genius, dedicated him (according to the Devotion of that Coun
try) to the Service of the Church; and entered him into the Flou
ri&longs;hing Order of Black-Friers, called from the place Moncks
of
ture, that She might con&longs;ummate the Profu&longs;ion of her Fa
vours upon him, &longs;ent him into the World in an Age that was &longs;o
ennobled and illuminated with Eminent Scholars in all Kinds of
Literature, that hardly any Century &longs;ince the Creation can boa&longs;t
the like.
§.
CAL
that all men of Spirit or Quality became either Students in, or
Patrons of tho&longs;e Sublime Knowledges. On this occa&longs;ion the Curi
o&longs;ity of our
could not endure to be any longer confined to the Slavi&longs;h Tuition
of Hermetical Pedagogues; but in concurrence with the Genius
of the Age, he al&longs;o betook him&longs;elf to tho&longs;e mo&longs;t Generous and
Liberal Studies. His helps in this his de&longs;ign were &longs;o many, and
&longs;o extraordinary, that had his Inclination been weaker, or his
Apprehen&longs;ion le&longs;&longs;er, he could hardly have failed attaining more
than a Common Eminency in the&longs;e Sciences. For be&longs;ides the De
luge of Learned and V&longs;eful Books, which the Pre&longs;&longs;e at that
time &longs;ent forth from all parts of
Fortune to fall into the Acquaintance, and under the In&longs;truction
of the mo&longs;t Demon&longs;trative and mo&longs;t Familiar Man in the World,
the Famous
this his
ous Per&longs;ons that re&longs;orted from all parts to &longs;it under his Admi
rable Lectures, he in a &longs;hort time attained to that Name in the
Mathematicks, that he was invited to
ted, and Preferred by his then Holine&longs;&longs;e the Eighth
Year
§.
Concerns of his Subjects in that part of
LOGNA, FERRARA,
ing between the Rivers of
Lo Stato della Chie&longs;a,
our
Honourable
intelligent per&longs;on in the&longs;e affaires, and at that time Superinten
dent of the General Draines, and Pre&longs;ident of
cerning the di&longs;orders occa&longs;ioned by the Waters of tho&longs;e parts.
§.
CASTELLI,
yea more, to improve &longs;uch Notions as he had imbued from the
Lectures of his Excellent
all indu&longs;try: and in the time that his Occa&longs;ions detained him in
ROMAGNA
cour&longs;e concerning the
fe&longs;&longs;eth that he had &longs;ome years before applyed him&longs;elf to this part
of Practical Geometry, and from &longs;everal Ob&longs;ervations collected
part of that Doctrine which at this time he put into Method, and
which had procured him the Repute of &longs;o much Skill that he beganIn particu
lar about the beginning of the Year 1623. and before his Invita
tion to
Duke of
time happened in the Valley of
upon the Banks of
&longs;ence of the Grand Duke, Grand Dutche&longs;&longs;e Mother, the Commi&longs;
&longs;ioners of Sewers, and &longs;undry other Per&longs;ons in a few hours he
made &longs;o great a progre&longs;&longs;e in that affair, as gave his Mo&longs;t Serene
Highne&longs;&longs;e high &longs;atisfaction, and gained him&longs;elf much Honour.
§.
MAGNA
Year) committed his Conceptions to paper, but he communicated
them to certain of his Friends. In which number we finde
re Ciampoli
the beginning of the Fir&longs;t Book he gratefully acknowledgeth to
have been contributary, in his Pur&longs;e, towards defraying the
charge of Experiments, and in his Per&longs;on, towards the debating
and compleating of Arguments upon this Subject. Some few years
after the Importunity of Friends, and the Zeal he had for the
Publique Good prevailed with him to pre&longs;ent the World with his
Fir&longs;t Di&longs;cour&longs;e, accompanied with a Treati&longs;e of the Geometrical
Demon&longs;trations of his whole Doctrine. What Reception it found
with the Judicious mu&longs;t needs be imagined by any one that hath
ob&longs;erved how
§.
New
ted to Demon&longs;trate all the three Dimen&longs;ions, to wit, the Length,
Breadth and Profundity, of this Fluid and Current Ele
ment. And he detecteth &longs;uch gro&longs;&longs;e Errours in tho&longs;e few that
had untertook to write upon the Subject (of which he in&longs;tan
ceth in
and delivereth &longs;uch &longs;ingular and unheard-of Paradoxes (for &longs;o
they &longs;ound in Vulgar Eares) as cannot but procure un&longs;peakable
delight to his Reader.
§.
Eafie
Experiments and Manife&longs;t Demon&longs;trations, that I have oft que
&longs;tioned with my &longs;elf which merited the greater wonder, he, for
di&longs;covering, or all men that handled the Argument before him
for not di&longs;covering a Doctrine of &longs;uch &longs;trange Facility and Infal
libility. But yet as if our Authour de&longs;igned to oblige the whole
World to him by &longs;o excellent a
he knew would be carre&longs;&longs;ed by all per&longs;ons of Nobler Souls, upon
the accounts afore-named, and by all Mankind in General, as
gratifying them in their much adored Idol
be-mi&longs;taken Speculations of the Theory, into certain and facile
Directions for Practice; teaching us how to prevent and repaire
the Breaches of Seas, and Inundations of Rivers; to draine
and recover Fenns and Marches; to divert, conveigh and di
&longs;tribute Waters for the Flowing and Stercoration of Grounds,
&longs;trengthening of Fortifications, &longs;erving of Aquaducts, pre&longs;er
ving of Health (by clean&longs;ing Streets, and &longs;cowring Sewers) and
maintaining of Commer&longs;e (by defending Bridges, cleering Ri
vers, and opening Ports and Channels) with innumerable other
Benefits of the like nature. And, that I may omit no circum&longs;tance
that may recommend my Authour, the Fortune of this his Trea
ti&longs;e hath been &longs;uch, that as if he intended a
or as if all men de&longs;paired to out-do it, or la&longs;tly, as if
STELLI
med to take Pencil in hand for the fini&longs;hing of what he
foild,
&longs;aid
&longs;ingle in the World, till that to verifie it to be trulyAnd as if
this did not make out the Immortal vertue of it, it hath had
Anno 1660
it were from the Vrne of its Authour; and that &longs;o improved by
the Addition of a &longs;econd part, that it promi&longs;eth to perpetuate
his Merits to all Po&longs;terity. To be brief, the meer Fame of this
Work re&longs;ounded the Honourable Name of
to all the Corners of
that, in hopes to reap great benefit by his Art, the re&longs;pective
Grandees of the adjacent Countries courted his Judgment and
Advice about their Draining of Fenns, Diver&longs;ion of Rivers,
Evacuation of Ports, Preventing of Inundations, &c. So that
every Summer he made one or more of the&longs;e Journies or Vi&longs;itati
ons. Particularly, the Senate of
Lake; to whom he delivered his Opinion in
on farther thoughts he pre&longs;ented them with another Paper of Con
&longs;iderations thePrince
ning of the en&longs;uing year 1642, which occa&longs;ioned his Letter to
Father
ter, directed to one of the Commi&longs;&longs;ioners of Sewers, vindicating
his former, and refuting
you.
§.
were fir&longs;t to be Abbot of
to Aloy&longs;io;
nity of Chief Mathematician to his grand Patron Pope
VIII.
ver&longs;ity of
§.
ing fuller of Honour than of Years, was by Death, the Importu
nate Intrerupter of Generous De&longs;igns, prevented in doing that
farther Good which the World had good rea&longs;on to promi&longs;e it &longs;elf
from &longs;o Profound and Indu&longs;trious a Per&longs;onage, leaving many
Friends and Di&longs;ciples of all Degrees and Qualities to lament
his lo&longs;&longs;e, and honour his Memory.
§.
Friend&longs;hip of very many; as to in&longs;tance in &longs;ome, he had con
racted &longs;trict Amity with
tine, Præfect of the Publique Wayes, and afterwards Pope with
the Name of
above-named
Draines: with
with Cardinal
much and writ well upon this Subject; and with Cardinal
tano
ing the Fenns of
POLDO,
kindne&longs;&longs;e for him; which &longs;peaks no &longs;mall attractions in him,
con&longs;idering him as a favourite of the Family of
tween whom and the Hou&longs;e of
Fewd. Among&longs;t per&longs;ons of a lower Quality he acknowledgeth
Signore Ciampoli Ferrante Ce&longs;arini,
Sig. Giovanni Ba&longs;adonna
onedLana, Sig.
Albano, Padre Serafino, Pad.
France&longs;co
de San. Giu&longs;eppe,
§.
are fir&longs;t His &longs;olid and &longs;ober Confutation of the Arguments of
Signore Lodovico dell Columbo,
Gratia
Aqua,
that Tutors very rarely reap from the pains they take in Culti
vating their Pupils. This Apology was fir&longs;t Printed
ni&longs;ts, among&longs;t the Works of
Learned
curious Pieces, as I am informed by the mo&longs;t Courteous
Manole&longs;&longs;i
concerningAnd la&longs;t of all the&longs;e Di&longs;cour&longs;es and Reflections
upon the
a Second Book, three Epi&longs;tles, and four Con&longs;iderations upon
the &longs;ame Argument, which conduce much to Illu&longs;trate his Do
ctrine and Facilitate the Practice of it; and which with a Rela
tion of
Tome.
§.
thours of Good Account, that have tran&longs;mitted his Character
to Po&longs;terity, but &longs;hall confine my &longs;elf to onely two; the one is
of his
not be two more competent Judges of his Accompli&longs;hments. To
begin with his
GALILEO,
pera &longs;uo.
which he intended to divulge, to the Judgment of this our Abbot, he
per lettera prima che ad alcun altro, con attenderne principal
mente il parer &longs;uo, e doppo quello de' no&longs;tri Amici di&longs;co&longs;ti,
conpen&longs;iero d' inviarne poi altre Copie ad altri Amici d' Italia,
e di Francia, quando io ne venga da lei con&longs;igliato: e qui pre
gandola a farci parte d' alcuna delle &longs;ue peregrine &longs;peculationi;
con &longs;inceri&longs;&longs;imo affetto, &c.
Signore Evangeli&longs;ta Terricelli,
Duke in immediate Succe&longs;&longs;ion after
mitto magnum illum nutantis Maris motum; Prætereo etiam
omnem Fluminum, Aquarumque Currentium tum men&longs;urum,
tum u&longs;um, quarum omnis doctrina reperta primum fuit ab
Abbate BENEDICTO CASTELLIO Preceptore
meo. Scrip&longs;it ille Scientiam &longs;uam, & illam non &longs;olum demon&longs;tra
tione, verum etiam opere confirmavit, maxima cum Princi
pum & populorum utilitatate, majore cum admiratione Phylo
&longs;ophorum. Extat illius Liber, vere aureus.
atione dell Nun
tio &longs;iderio.
Abbate D. B.
Ca
&longs;telli D'Arcetro;
li. 3. Decemb.
1639.
quarum. Lib. 2.
Prop. 37. p.
191.
§.
der: The one concerns the Book, and it is this, That after the
general Aprobation it hath had in
de&longs;erveth the &longs;ame Civil Entertainment with us, in regard that
it cometh with no le&longs;&longs;e
us than to tho&longs;e whom the Authour favoured with the Original. Our Rivers and Sewers through Publique Di&longs;tractions and Pri
vate Incroachments are in great di&longs;order, as tho&longs;e Channels for
iu&longs;tance which formerly were Navigable unto the very Walls of
by Shelfes and Setlements: Our Fenns do in a great part lie wa&longs;te
and unimproved: Now all the&longs;e may be (and, as I find by the
Confe&longs;&longs;ion of &longs;ome who&longs;e Practi&longs;es upon the Copy of the Fir&longs;t
Book onely of our Authour hath got them both Money and Repu
tation, in part have been) remedied by the Ways and Means he
here &longs;ets down. The truth is the Argument hath been pa&longs;t over
with an Vniver&longs;al Silence; &longs;o that to this day I have not &longs;een
any thing that hath been written Demon&longs;tratively and with Ma
thematical Certainty concerning the &longs;ame, &longs;ave onely what this
Learned Prelate hath delivered of his Own Invention in the&longs;e
Treati&longs;es: who yet hath &longs;o fully and plainly handled the Whole
Doctrine, that I may affirm his Work to be every way ab&longs;olute. It
mu&longs;t be confe&longs;t the Demon&longs;tration of the Second Propo&longs;ition of the
Second Book did not well plea&longs;e the Authour, and had he lived
he would have &longs;upplyed that defect, but being prevented by
Death, the Reader mu&longs;t content him&longs;elf with the Mechanical
Proof that he giveth you of the truth of &longs;o Excellent a Con
clu&longs;ion.
§.
&longs;ire to contribute what lyeth in me to the compleating of this Piece
for Engli&longs;h Practice, I have exeeded my promi&longs;e not onely in gi
ving you the Second and following Books which were not extant at
the time of tendring my Overtures, but al&longs;o in that I have added
a Map or Plat of all the Rivers, Lakes, Fenns, &c. mentioned
thorow out the Work. And if I have not kept touch in point of
Time, let it be con&longs;idered that I am the Tran&longs;lator and not the
Printer. To conclude, according to your acceptance of the&longs;e my
endeavours, you may expect &longs;ome other Tracts of no le&longs;&longs;e Profit
and Delight.
ERRATA of the
In PREFACE, I cad
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OF THE
MENSURATION
OF
Running Waters.
What, and of how great moment the confi
deration of
is &longs;o manife&longs;t, that the Prince of
pateticks
now much u&longs;ed Sentence:
tu, ignoratur natura.
true Philo&longs;ophers have &longs;o travailed in the
contemplation of the Cele&longs;tial motions,
and in the &longs;peculation of the motions of
Animals, that they have arrived to a wonderful height and &longs;ub
limity of under&longs;tanding. Under the &longs;ame Science of
is comprehended all that which is written by Mechanitians con
cerning Engines moving of them&longs;elves,
force of Air, and tho&longs;e which &longs;erve to move weights and im
men&longs;e magnitudes with &longs;mall force. There appertaineth to the
Science of
alteration not onely of Bodies, but of our Minds al&longs;o; and
in &longs;um, this ample matter of
lated, that there are few things which fall under mans no
tice, which are not conjoyned with
pending thereupon, or to the knowledge thereof directed;
and of almo&longs;t every of them, there hath been written and
compo&longs;ed by &longs;ublime wits, learned Treati&longs;es and In&longs;tructions.
our Lord Pope
the Waters of Rivers, (a matter difficult, mo&longs;t important, and
little handled by others) having concerning the &longs;ame ob&longs;erved
&longs;ome particulars not well ob&longs;erved, or con&longs;idered till now, but of
great moment both in publick and private affairs; I have thought
good to publi&longs;h them, to the end that ingenious &longs;pirits might
have occa&longs;ion to di&longs;cu&longs;&longs;e more exactly then hitherto hath been
done, &longs;o nece&longs;&longs;ary and profitable a matter, and to &longs;upply al&longs;o my
defects in this &longs;hort and difficult Tractate. Difficult I &longs;ay, for
the truth is, the&longs;e knowledges, though of things next our &longs;en&longs;es,
are &longs;ometimes more ab&longs;truce and hidden, then the knowledge of
things more remote; and much better, and with greater exqui&longs;it
ne&longs;s are known the motions of the Planets, and Periods of the
Stars, than tho&longs;e of Rivers and Seas: As that &longs;ingular light of
Philo&longs;ophie of our times, and my Ma&longs;ter
wi&longs;ely ob&longs;erveth in his Book concerning the Solar &longs;pots. And
to proceed with a due order in Sciences, I will take &longs;ome &longs;uppo
&longs;itions and cognitions &longs;ufficiently clear; from which I will after
wards proceed to the deducing of the principal conclu&longs;ions. But
to the end that what I have written at the end of this di&longs;cour&longs;e in
a demon&longs;trative and Geometrical method, may al&longs;o be under
&longs;tood of tho&longs;e which never have applyed their thoughts to the
&longs;tudy of Geometry; I have endeavoured to explain my conceit
by an example, and with the con&longs;ideration of the natural things
them&longs;elves, mu&longs;t after the &longs;ame order in which I began to doubt
in this matter; and have placed this particular Treati&longs;e here in
the beginning, adverting neverthele&longs;s, that he who de&longs;ires more
full and ab&longs;olute &longs;olidity of Rea&longs;ons, may overpa&longs;s this prefatory
di&longs;cour&longs;e, and onely con&longs;ider what is treated of in the demon&longs;tra
tions placed towards the end, and return afterwards to the con&longs;i
deration of the things collected in the
which demon&longs;trations notwith&longs;tanding, may be pretermitted by
him that hath not &longs;een at lea&longs;t the fir&longs;t &longs;ix Books of the Elements
of Euclid; &longs;o that he diligently ob&longs;erveth that which fol
loweth.
I &longs;ay therefore, that having in times pa&longs;t, on divers occa&longs;i
ons heard &longs;peak of the mea&longs;ures of the waters of Rivers, and
Fountains, &longs;aying, &longs;uch a River is two or three thou&longs;and feet of
water; &longs;uch a &longs;pring-water is twenty, thirty, or forty inches,
Although in &longs;uch manner I have found all to treat thereof in
word and writing, without variety, and as we are wont to &longs;ay,
a thing that admitted not of any doubt, yet how&longs;oever I re
mained &longs;till infolded in &longs;uch an ob&longs;curity, that I well knew I un
clearly to under&longs;tand. And my doubt aro&longs;e from my frequent
ob&longs;ervation of many Trenches and Channels, which carry
water to turn Mills, in which Trenches, and Channels, the
water being mea&longs;ured, was found pretty deep; but if afterwards
the &longs;ame water was mea&longs;ured in the fall it made to turn the
Wheel of the Mill, it was much le&longs;&longs;e, not amounting often to the
tenth part, nor &longs;ometimes to the twentieth, in&longs;omuch, that the
&longs;ame running water came to be one while more, another while le&longs;s
in mea&longs;ure, in divers parts of its Channel; and for that rea&longs;on this
vulgar manner of mea&longs;uring running Waters, as indeterminate and
uncertain, was by me ju&longs;tly &longs;u&longs;pected, the mea&longs;ure being to be de
terminate, and the &longs;ame. And here I freely confe&longs;&longs;e that I had fin
gular help to re&longs;olve this difficulty from the excellent & accurate
way of di&longs;cour&longs;ing, as in allother matters, &longs;o al&longs;o in this, of the
Right Honourable and Truly Noble Signior
of the Popes &longs;ecret affairs. Who moreover, not &longs;paring &longs;or the co&longs;ts
of the &longs;ame, generou&longs;ly gave me occa&longs;ion a few years pa&longs;t to try by
exact experiments that which pa&longs;t concerning this particular. And
to explain all more clearly with an example; we &longs;uppo&longs;e a Ve&longs;&longs;el
filled with Water, as for in&longs;tance a Butt, which is kept full, though
&longs;till water runneth out, and the Water run out by two Taps equal
of bigne&longs;&longs;e, one put in the bottom of the Ve&longs;&longs;el, and the other in
the upper part; it is manife&longs;t that in the time wherein from the
upper part &longs;hall i&longs;&longs;ue a determinate mea&longs;ure of water &longs;rom
the inferiour part there &longs;hall i&longs;&longs;ue four, five, and many more of
the &longs;ame mea&longs;ures, according to the difference of the height of
the Taps, and the di&longs;tance of the upper Tap from the Superfici
es and level of the water of the Ve&longs;&longs;el: and all this will alwayes
follow, though, as hath been &longs;aid, the Taps be equal, and the
water in di&longs;charging keep the &longs;aid Taps alwayes full. Where fir&longs;t
we note, that, although the mea&longs;ure of the Taps be equal, never
thele&longs;&longs;e there i&longs;&longs;ueth from them in equal times unequal quantities
of water, And if we &longs;hould more attentively con&longs;ider this bu&longs;i
ne&longs;&longs;e, we &longs;hould find, that the water by the lower Tap, run
neth and pa&longs;&longs;eth with much greater velocity, then it doth by the
upper, whatever is the rea&longs;on. If therefore we would have
&longs;uch a quantity of Water di&longs;charge from the upper tap, as
would di&longs;charge from the neather in the &longs;ame time, it is plain, that
either the upper Taps mu&longs;t be multiplyed in &longs;uch &longs;ort, that &longs;o
many more Taps in number be placed above than below, as the
neather tap &longs;hall be more &longs;wift than the upper, or the upper Tap
made &longs;o much bigger than the nether, by how much that be
neath &longs;hall be more &longs;wift than that above; and &longs;o then in equal
times, the &longs;ame quantity of Water &longs;hall di&longs;charge from the upper,
as doth from the neather part.
I will declare my &longs;elf by another example.
If we &longs;hould ima
gine, that two cords or lines of equal thickne&longs;s, be drawn through
two holes of equal bore; but &longs;o that the fir&longs;t pa&longs;s with quadruple
velocity to the &longs;econd: It is manife&longs;t, that if in a determinate
time, we &longs;hall by the fir&longs;t bore have drawn four Ells of the line,
in the &longs;ame time, by the &longs;econd hole we &longs;hall have drawn but one
Ell of cord onely; and if by the fir&longs;t there pa&longs;&longs;e twelve Ells, then
through the &longs;econd there &longs;hall pa&longs;&longs;e onely three Ells; and in
&longs;hort the quantity of cord &longs;hall have the &longs;ame proportion to the
cord, that the volocity hath to the velocity. And therefore we
de&longs;iring to compen&longs;ate the tardity of the &longs;econd cord, and main
taining the &longs;ame tardity to draw through the &longs;econd hole as much
cord as through the fir&longs;t, it will be nece&longs;&longs;ary to draw through the
&longs;econd bore four ends of cord; &longs;o that the thickne&longs;s of all the
cords by the &longs;econd hole, have the &longs;ame proportion to the thick
ne&longs;s of the cord which pa&longs;&longs;eth onely by the fir&longs;t, as the velocity
of the cord by the fir&longs;t hole hath reciprocally to the velocity of
the codrs by the &longs;econd hole. And thus its clear, that when
there is drawn through two holes equal quantity of cords in
equal time, but with unequal velocity, it will be nece&longs;&longs;ary, that
the thickne&longs;s of all the four cords &longs;hall have the &longs;ame reciprocal
proportion to the thickne&longs;s of the &longs;wifter cord, that the velo
city of the &longs;wifter cord hath to the velocity of the &longs;lower. The
which is verified likewi&longs;e in the fluid Element of Water.
And to the end that this principal fundamental be well under
&longs;tood, I will al&longs;o note a certain ob&longs;ervation made my me in the
Art of Wyer-drawing, or &longs;pinning Gold, Silver, Bra&longs;s, and Iron,
and it is this; That &longs;uch Artificers de&longs;iring more and more to
di&longs;gro&longs;&longs;e and &longs;ubtillize the &longs;aid Metals, having would about a
ket in a frame upon a &longs;tedfa&longs;t Axis, in &longs;uch &longs;ort that the Rocket
may turn about in it &longs;elf; then making one end of the thread to
pa&longs;&longs;e by force through a Plate of Steel pierced with divers holes,
greater and le&longs;&longs;er, as need requireth, fa&longs;tning the &longs;ame end of the
thread to another Rocket, they wind up the thread, which pa&longs;
&longs;ing through a bore le&longs;s than the thickne&longs;&longs;e of the thread, is of
force con&longs;trained to di&longs;gro&longs;&longs;e and &longs;ubtillize. Now that which is
inten&longs;ly to be ob&longs;erved in this bu&longs;ine&longs;s, is this, That the parts of
the thread before the hole, are of &longs;uch a thickne&longs;&longs;e, but the parts
of the &longs;ame thread after it is pa&longs;&longs;ed the hole, are of a le&longs;&longs;er thick
ne&longs;&longs;e: and yet neverthele&longs;&longs;e the ma&longs;&longs;e and weight of the thread
which is drawn forth, is ever equal to the ma&longs;&longs;e and weight of the
thread which is winded up. But if we &longs;hould well con&longs;ider the mat
ter, we &longs;hould finde, that the thicker the thread before the hole is,
than the thread pa&longs;&longs;ed the hole, the greater reciprocally is the
city of the parts before the hole: In&longs;omuch that if
the thickne&longs;&longs;e of the thread before the hole, were double to the
thickne&longs;&longs;e after the hole, in &longs;uch ca&longs;e the velocity of the parts of
the thread pa&longs;&longs;ed the hole, &longs;hould be double to the velocity of the
parts of the thread before the hole; and thus the thickne&longs;&longs;e
compen&longs;ates the velocity, and the velocity compen&longs;ates the thick
ne&longs;&longs;e. So that the &longs;ame occurreth in the &longs;olid Metals of Gold,
Silver, Bra&longs;s, Iron, &c. that eveneth al&longs;o in the fluid Element of
Water, and other liquids, namely, That the velocity beareth the
&longs;ame proportion to the velocity, that the thickne&longs;&longs;e of the Me
tal, or Water, hath to the thickne&longs;&longs;e.
And therefore granting this di&longs;cour&longs;e, we may &longs;ay, that as of
ten as two Taps with different velocity di&longs;charge equal quanti
ties of Water in equal times, it will be nece&longs;&longs;ary that the Tap
le&longs;&longs;e &longs;wift be &longs;o much greater, and larger, than the Tap more
&longs;wift, by how much the &longs;wifter &longs;uperates in velocity the &longs;lower;
and to pronounce the Propo&longs;ition in more proper terms, we &longs;ay;
That if two Taps of unequal velocity, di&longs;charge in equal times
equal quantities of Water, the greatne&longs;&longs;e of the fir&longs;t &longs;hall be to
the greatne&longs;&longs;e of the &longs;econd, in reciprocal proportion, as the ve
locity of the &longs;econd to the velocity of the fir&longs;t. As for example,
if the fir&longs;t Tap &longs;hall be ten times &longs;wifter than the &longs;econd Tap, it
will be nece&longs;&longs;ary, that the &longs;econd be ten times bigger and larger
than the fir&longs;t; and in &longs;uch ca&longs;e the Taps &longs;hall di&longs;charge equall
quantities of water in equal times; and this is the principal and
mo&longs;t important point, which ought to be kept alwayes in minde,
for that on it well under&longs;tood depend many things profitable,
and worthy of our knowledge.
Now applying all that hath been &longs;aid neerer to our purpo&longs;e, I
con&longs;ider, that it being mo&longs;t true, that in divers parts of the &longs;ame
River or Current of running water, there doth always pa&longs;&longs;e equal
quantity of Water in equal time (which thing is al&longs;o demon
&longs;trated in out fir&longs;t Propo&longs;ition) and it being al&longs;o true, that in di
vers parts the &longs;ame River may have various and different veloci
ty; it follows of nece&longs;&longs;ary con&longs;equence, that where the River
hath le&longs;&longs;e velocity, it &longs;hall be of greater mea&longs;ure, and in tho&longs;e
parts, in which it hath greater velocity, it &longs;hall be of le&longs;&longs;e mea
&longs;ure; and in &longs;um, the velocity of &longs;everal parts of the &longs;aid River,
&longs;hall have eternally reciprocall and like proportion with
their mea&longs;ures. This principle and fundamental well e&longs;tabli&longs;h
ed, that the &longs;ame Current of Water changeth mea&longs;ure, accor
ding to its varying of velocity; that is, le&longs;&longs;ening the mea&longs;ure,
when the velocity encrea&longs;eth, and encrea&longs;ing the mea&longs;ure, when
the velocity decrea&longs;eth; I pa&longs;&longs;e to the con&longs;ideration of many
on this &longs;ole Propo&longs;ition, the &longs;en&longs;e of which I have oft repeated,
that it might be well under&longs;tood.
And fir&longs;t, we hence conclude, that the &longs;ame Streams of a
Torrent, namely, tho&longs;e &longs;treams which carry equal quantity of
Water in equal times, make not the &longs;ame depths or mea&longs;ures in
the River, in which they enter, unle&longs;&longs;e when in the entrance in
to the River they acquire; or to &longs;ay better, keep the &longs;ame velo
city; becau&longs;e if the velocicities acquired in the River &longs;hall be
different, al&longs;o the mea&longs;ures &longs;hall be diver&longs;e; and con&longs;equently
the depths, as is demon&longs;trated.
And becau&longs;e &longs;ucce&longs;&longs;ively, as the River is more and more full,
it is con&longs;tituted ordinarily in greater & greater velocity: hence
it is that the &longs;ame &longs;treams of the Torrent, that enter into the Ri
ver, make le&longs;&longs;e and le&longs;&longs;e depths, as the River grows more and
more full; &longs;ince that al&longs;o the Waters of the Torrent being en
tered into the River, go acquiring greater and greater velocities,
and therefore dimini&longs;h in mea&longs;ure and height.
We ob&longs;erve al&longs;o, that while the main River is &longs;hallow, if there
fall but a gentle rain, it &longs;uddenly much increa&longs;eth and ri&longs;eth;
but when the River is already &longs;welled, though there fall again a
nother new violent &longs;hower, yet it increa&longs;eth not at the &longs;ame rate
as before, proportionably to the rain which fell: which thing
we may affirm particularly to depend on this, that in the fir&longs;t
ca&longs;e, while the River is low, it is found al&longs;o very &longs;low, and there
fore the little water which entereth into it, pa&longs;&longs;eth and runs with
little velocity, and con&longs;equently occupieth a great mea&longs;ure:
But when the River is once augmented, by new water being al&longs;o
made more &longs;wift, it cau&longs;eth the great Flood of water which fal
leth, to bear a le&longs;&longs;e mea&longs;ure, and not to make &longs;uch a depth.
From the things demon&longs;trated is manife&longs;t al&longs;o, that whil&longs;t a
Torrent entereth into a River, at the time of Ebbe, then the
Torrent moveth with &longs;uch a certain velocity, what ever it be,
the River; in which parts, the Torrent being mea&longs;ured, &longs;hall
have &longs;uch a certain mea&longs;ure: but the River &longs;welling and ri&longs;ing,
al&longs;o tho&longs;e parts of the Torrent augment in greatne&longs;&longs;e and mea
&longs;ure, though the Torrent, in that in&longs;tant, di&longs;-imbogue no more
water than it did before: &longs;o that the River being &longs;welled, we
are to con&longs;ider two mouths of the &longs;ame Torrent, one le&longs;&longs;e be
fore the ri&longs;ing, the other greater after the ri&longs;ing, which mouths
di&longs;charge equal quantities of water in equal times; therefore the
velocity by the le&longs;&longs;er mouth &longs;hall be greater than the velocity by
the greater mouth; and thus the Torrent &longs;hall be retarded from
its ordinary cour&longs;e.
From which operation of Nature proceedeth another effect
worthy of con&longs;ideration; and it is, that the cour&longs;e of the water
retarding, as hath been &longs;aid in tho&longs;e ultimate parts of the Tor
rent, if it &longs;hall happen that the Torrent grow torbid and mud
dy, and its &longs;treame be retarded in &longs;uch a degree, that it is not
able to carry away tho&longs;e minute grains of Earth, which com
po&longs;e the muddine&longs;&longs;e; in this ca&longs;e the Torrent &longs;hall clear away
the mud, and carry away the Sand at the bottome of its own
Chanel, in the extream parts of its mouth, which rai&longs;ed and
voided Sand, &longs;hall again afterwards be carried away, when the
River abating, the Torrent &longs;hall return to move with its primitive
velocity.
Whil&longs;t it is demon&longs;trated, that the &longs;ame water hath different
mea&longs;ures in its Chanel or cour&longs;e, according as it varieth in
velocity; &longs;o that the mea&longs;ure of the water is alwayes greater, where
the velocity is le&longs;&longs;er; and on the contrary, the mea&longs;ure le&longs;&longs;er,
where the velocity is greater: from hence we may mo&longs;t ele
gantly render the rea&longs;on of the u&longs;ual Proverb,
&longs;till waters:
River in tho&longs;e parts, wherein it is le&longs;s &longs;wift, and thence called
or
than in tho&longs;e parts, in which it is more &longs;wift, and therefore ordi
narily &longs;hall be al&longs;o more deep and dangerous for pa&longs;&longs;engers;
whence it is well &longs;aid,
&longs;aying hath been &longs;ince applied to things moral.
Likewi&longs;e, from the things demon&longs;trated may be concluded,
that the windes, which &longs;top a
Current, retard its cour&longs;e and ordinary velocity &longs;hall nece&longs;&longs;arily
amplifie the mea&longs;ure of the &longs;ame River, and con&longs;equently &longs;hall
be, in great part, cau&longs;es; or we may &longs;ay, potent con-cau&longs;es of
making the extraordinary inundations which Rivers u&longs;e to make. And its mo&longs;t certain, that as often as a &longs;trong and continual wind
&longs;hall blow again&longs;t the Current of a River, and &longs;hall reduce the
water of the River to &longs;uch tardity of motion, that in the time
wherein before it run five miles, it now moveth but one, &longs;uch a
River will increa&longs;e to five times the mea&longs;ure, though there &longs;hould
not be added any other quantity of water; which thing indeed
hath in it &longs;omething of &longs;trange, but it is mo&longs;t certain, for that
look what proportion the waters velocity before the winde, hath
to the velocity after the winde, and &longs;uch reciprocally is the mea
&longs;ure of the &longs;ame water after the winde, to the mea&longs;ure before
the winde; and becau&longs;e it hath been &longs;uppo&longs;ed in our ca&longs;e that the
velocity is dimini&longs;hed to a fifth part, therefore the mea&longs;ure &longs;hall
be increa&longs;ed five times more than that, which it was before.
We have al&longs;o probable the cau&longs;e of the inundations of
which befel at
and without great thaws of the Snows; which therefore much
puzzled the wits of tho&longs;e times. But we may with much pro
bability affirm, That the River ro&longs;e to &longs;uch a height and excre&longs;
cence, by the retardation of the Waters dependant on the
boi&longs;trous and con&longs;tant Winds, that blew in tho&longs;e times, as is no
red in the memorials.
It being mo&longs;t manife&longs;t, that by the great abundance of Water
the Torrents may increa&longs;e, and of them&longs;elves alone exorbitantly
&longs;well the River; and having demon&longs;trated that al&longs;o without new
Water, but onely by the notable retardment the River ri&longs;eth and
increa&longs;eth in mea&longs;ure, in proportion as the velocity decrea&longs;eth:
hence it is apparent, that each of the&longs;e cau&longs;es being able of it &longs;elf,
and &longs;eparate from the other to &longs;well the River; when it &longs;hall
happen that both the&longs;e two cau&longs;es con&longs;pire the augmentation of
pable innundations.
From what hath been demon&longs;trated, we may with facility re
&longs;olve the doubt which hath troubled, and &longs;till po&longs;eth the mo&longs;t
diligent, but incautelous ob&longs;ervers of Rivers, who mea&longs;uring
the Streams and Torrents which fall into another River; as tho&longs;e
for in&longs;tance, which enter into the
ber
ferring the mea&longs;ures of the Rivers and Brooks, which fall into
di&longs;imbogue into
equal, as, it &longs;eems to them, they ought to be, and this is becau&longs;e
they have not well noted the mo&longs;t important point of the varia
tion of velocity, and how that it is the mo&longs;t potent cau&longs;e of won
derfully altering the mea&longs;ures of running Waters; but we mo&longs;t
facilly re&longs;olving the doubt, may &longs;ay that the&longs;e Waters dimini&longs;h
the mea&longs;ure, being once entered the principal Channel, becau&longs;e
they increa&longs;e in velocity.
Through the ignorance of the force of the velocity of the Wa
ter, in altering its mea&longs;ure, & augmenting it when the velocity
dimini&longs;heth; and dimini&longs;hing it when the velocity augmenteth:
The Architect
and to cau&longs;e to be mea&longs;ured by his Nephew, all the Brooks and
Rivers which di&longs;charged their Waters into
the Innundation; which happened at
and publi&longs;hed a &longs;mall Treati&longs;e thereof, wherein he &longs;ummeth up
the mea&longs;ures of the extraordinary Water which fell into
and made account that it was about five hundred Ells more than
ordinary; and in the end of that Treati&longs;e concludeth, that to re
move the Innundation wholly from
to make two other Channels, equal to that at pre&longs;ent, and that
le&longs;&longs;e would not &longs;uffice; and finding afterwards that the whole
Stream pa&longs;&longs;ed under the Bridge
of is of a far le&longs;s mea&longs;ure then five hundred Ells) concludeth,
that under the &longs;aid Bridge pa&longs;t a hundred fifty one Ells of Water
compre&longs;&longs;ed, (I have &longs;et down the preci&longs;e term of compre&longs;t Wa
ter, written by
The fir&longs;t of which is to think that the mea&longs;ures of the&longs;e Wa
ters compre&longs;&longs;ed in the Channels of tho&longs;e Brooks and Rivers,
is mo&longs;t fal&longs;e, when ever tho&longs;e waters reduced into
not the &longs;ame velocity which they had in the place in which
tana
from the things which we have above explained; for, if the Wa
ters reduced into
&longs;ure; and if they decrea&longs;e in velocity, they increa&longs;e in mea
&longs;ure.
Secondly, I con&longs;ider that the mea&longs;ures of tho&longs;e Brooks and
Rivers, which enter into
not between them&longs;elves really the &longs;ame, when their velocities are
not equal, though they have the &longs;ame names of Ells and Feet;
for that its po&longs;&longs;ible that a di&longs;inboguement of ten Ells requadrated
(to &longs;peak in the phra&longs;e of
might di&longs;charge into
and twenty times le&longs;s Water, than another mouth equal to the
fir&longs;t in greatne&longs;s, as would occur when the fir&longs;t mouth were four,
ten, or twenty times le&longs;s &longs;wift than the &longs;econd. Whereupon,
whil&longs;t
tho&longs;e Brooks and Rivers into a total aggregate, he commits the
&longs;ame error with him, which would add into one &longs;umme diver&longs;e
moneys of diver&longs;e values, and diver&longs;e places, but that had the
&longs;ame name; as if one &longs;hould &longs;ay ten Crowns of
four Crowns of Gold, thirteen Crowns of
of
&longs;umme with forty Crowns of Gold, or forty Crowns of
Thirdly, It might happen that &longs;ome River or Current in the
parts nearer
more Water than ordinary; and however, its a thing very clear,
that whil&longs;t the &longs;tream came from the &longs;uperior parts, that &longs;ame
Brook or River would be augmented in mea&longs;ure, as hath been
noted in the fourth
have inculcated, and noted that &longs;ame River or Current as con
curring to the Innundation, although it were therein altogether
unconcerned.
Moreover, in the fourth place we mu&longs;t note, That it might
&longs;o fall out, that &longs;uch a River not onely was unintere&longs;&longs;ed in the
Innundation, though augmented in mea&longs;ure, but it might I &longs;ay
happen, that it was in&longs;trumental to the a&longs;&longs;waging the Innunda
tion, by augmenting in the mea&longs;ure of its own Channel; which
matter is &longs;ufficiently evident; for if it be &longs;uppo&longs;ed that the Ri
ver in the time of flood, had not had of it &longs;elf, and from its pro
per &longs;prings more Water than ordinary, its a thing certain, that
the Water of
vel it &longs;elf with the Water of
ber,
&longs;ome of the water of
undation, le&longs;&longs;e abundance of water would have come to
and yet neverthele&longs;&longs;e the mea&longs;ure of that River would have been
increa&longs;ed.
Fifthly,
to remove the Inundation from
make two other Chanels of Rivers, that were as large as that,
which is the pre&longs;ent one, and that le&longs;s would not &longs;uffice, which,
I &longs;ay, is a fallacy: and to convince him ea&longs;ily of his errour, it
&longs;ufficeth to &longs;ay, that all the Streams being pa&longs;&longs;ed under the Bridge
ly of the capacity of the &longs;aid Bridge, provided that the water
there might run with the &longs;ame velocity, as it did under the Bridge
at the time of Inundation; and on the contrary, twenty Cur
rents of capacity equal to the pre&longs;ent one, would not &longs;uffice, if
the water &longs;hould run with twenty times le&longs;s velocity, than it made
at the time of the Inundation.
Sixthly, to me it &longs;eemeth a great weakne&longs;&longs;e to &longs;ay, that there
&longs;hould pa&longs;&longs;e under the Bridge
ells of water compre&longs;&longs;ed; for that I do not under&longs;tand that wa
ter is like Cotton or Wool, which matters may be pre&longs;t and trod,
as it happeneth al&longs;o to the air, which receiveth compre&longs;&longs;ion in
&longs;uch &longs;ort, that after that in &longs;ome certain place a quantity of air
&longs;hall be reduced to its natural con&longs;titution; and having taken up
all the &longs;aid place, yet neverthele&longs;&longs;e compre&longs;&longs;ing the fir&longs;t Air
with force and violence, it is reduced into far le&longs;s room, and will
admit four or &longs;ix times as much air, as before, as is experimen
tally ^{*} &longs;een in the Wind-Gun, invented in our dayes by
ting conden&longs;ation, is al&longs;o &longs;een in the portable Fountains of the
&longs;ame
by force of the Air compre&longs;&longs;ed, which whil&longs;t it &longs;eeks to reduce
its &longs;elf to its natural con&longs;titution, in the dilation cau&longs;eth that vi
olence. But the water can never, for any thing I know, crowd,
or pre&longs;s &longs;o, as that if before the compre&longs;&longs;ion it held or po&longs;&longs;e&longs;t a
place, being in its natural con&longs;titution, I believe not, I &longs;ay, that it
is po&longs;&longs;ible, by pre&longs;&longs;ing and crowding to make it po&longs;&longs;e&longs;s le&longs;s room,
for if it were po&longs;&longs;ible to compre&longs;s the Water, and make it to oc
cupy a le&longs;s place, it would thence follow, that two Ve&longs;&longs;els of e
qual mea&longs;ure, but of unequal height, &longs;hould be of unequal capa
city, and that &longs;hould hold more water which was higher; al&longs;o a
Cylinder, or other Ve&longs;&longs;el more high than broad, would containe
more water erected, than being laid along; for that being erect
large demon&longs;trated
by that mo&longs;t excel
lent and lonour
able per&longs;onage Mr.
&longs;trious experiment
of his Pneumatical
Engine.
And therefore, in our ca&longs;e, according to our principles we will
&longs;ay, that the water of that Stream pa&longs;seth all under the &longs;aid
Bridge
con&longs;equence to be le&longs;s in mea&longs;ure.
And here one may &longs;ee, into how many errours a man may run
through ignorance of a true and real Principle, which once known
and well under&longs;tood, takes away all mi&longs;ts of doubting, and ea
&longs;ily re&longs;olveth all difficulties.
Through the &longs;ame inadvertency of not regarding the variation
of velocity in the &longs;ame Current, therea re committed by Ingi
neers and Learned men, errours of very great moment (and I
could thereof produce examples, but for good rea&longs;ons I pa&longs;s
them over in &longs;ilence) when they think, and propo&longs;e, by deriving
new Channels from great Rivers, to dimini&longs;h the mea&longs;ure of the
water in the River, and to dimini&longs;h it proportionally, according
to the mea&longs;ure of the Water which they make to pa&longs;s through
the Channel, as making
the derived water is to run wa&longs;te, ten foot deep, they think they
have dimini&longs;hed the mea&longs;ure of the Water in the River five hun
dred feet, which thing doth not indeed &longs;o fall out; and the rea
&longs;on is plain; for that the Chanel being derived, the re&longs;t of the
main River, dimini&longs;heth in velocity, and therefore retains a grea
ter mea&longs;ure than it had at fir&longs;t before the derivation of the Cha
nel; and moreover, if the Chanel being derived, it &longs;hall not
con&longs;erve the &longs;ame velocity which it had at fir&longs;t in the main Ri
ver, but &longs;hall dimini&longs;h it, it will be nece&longs;&longs;ary, that it hath a grea
ter mea&longs;ure than it had before in the River; and therefore
to accompt aright, there &longs;hall not be &longs;o much water derived into
the Channel, as &longs;hall dimini&longs;h the River, according to the quanti
ty of the water in the Channel, as is pretended.
This &longs;ame con&longs;ideration giveth me occa&longs;ion to di&longs;cover a mo&longs;t
ordinary errour, ob&longs;erved by me in the bu&longs;ine&longs;&longs;e of the wa
ter of
Reverend and Illu&longs;trious Monfignor
whom hath been a very great help to me in the&longs;e contemplations;
its very true, I have been much perplexed, whether I &longs;hould
commit this particular to paper, or pa&longs;&longs;e it over in &longs;ilence, for
that I have ever doubted, that the opinion &longs;o common and
onely make this my conjecture to be e&longs;teemed far from true,
but al&longs;o to di&longs;credit with the World the re&longs;t of this my Treati&longs;e:
Neverthele&longs;&longs;e I have at la&longs;t re&longs;olved not to be wanting to my
&longs;elf, and to truth in a matter of it &longs;elf, and for other con&longs;e
quences mo&longs;t important; nor doth it &longs;eem to me requi&longs;ite in
difficult matters, &longs;uch as the&longs;e we have in hand, to refigne our
&longs;elves to the common opinion, &longs;ince it would be very &longs;trange if
the multitude in &longs;uch matters &longs;hould hit on the truth, nor ought
that to be held difficult, in which even the vulgar do know the
truth and right; be&longs;ides that I hope morever to prove all in &longs;uch
&longs;ort, that per&longs;ons of &longs;olid judgment, &longs;hall re&longs;t fully per&longs;waded,
&longs;o that they but keep in mind the principal ground and foundation
of all this Treati&longs;e; and though that which I will propo&longs;e, be a par
ticular, as I have &longs;aid, pertaining onely to the intere&longs;ts of
yet neverthele&longs;&longs;e from this particular Doctrine well under&longs;tood,
good judgement may be made of other the like ca&longs;es in general.
I &longs;ay then, for greater per&longs;pecuity, and better under&longs;tanding
of the whole, That about thirteen miles above
of its Arms it cometh clo&longs;e to
P
branches, and that which continueth on the right hand, is called
the P
of
tofore augmented and rai&longs;ed, it followeth that it re&longs;teth wholly
deprived of the Water of the great P
greater &longs;welling; for in that ca&longs;e, this P
&longs;trained with a Bank near to
overflowings of the main P
Lords of
break out, to cut the bank; by which cutting, there di&longs;
gorgeth &longs;uch a Torrent of Water, that it is ob&longs;erved, that the
main P
all per&longs;ons that I have &longs;poken with hitherto, moved by this ex
periment, think that it is of great profit and benefit to keep ready
this Vent, and to make u&longs;e of it in the time of its fullne&longs;&longs;e. And
indeed, the thing con&longs;idered &longs;imply, and at the fir&longs;t appearance,
it &longs;eemeth that none can think otherwi&longs;e; the rather, for that
many examining the matter narrowly, mea&longs;ure that body of
Water which runneth by the Channel, or Bed of the P
ra,
P
runneth by the P
hath been &longs;aid in the beginning of the Treati&longs;e, and how much
knowledge of them is nece&longs;&longs;ary to conclude the true quantity of
the running Water, we &longs;hall finde it manife&longs;t, that the benefit of
this Vent is far le&longs;&longs;e than it is generally thought: And mereover,
we &longs;hall finde, if I deceive not my &longs;elf, that there follow from
thence &longs;o many mi&longs;chiefs, that I could greatly incline to believe,
that it were more to the purpo&longs;e wholly to &longs;top it up, than to
maintain it open: yet I am not &longs;o wedded to my opinion, but
that I am ready to change my judgement upon &longs;trength of better
rea&longs;ons; e&longs;pecially of one that &longs;hall have fir&longs;t well under&longs;tood
the beginning of this my di&longs;cour&longs;e, which I frequently inculcate,
becau&longs;e its ab&longs;olutely impo&longs;&longs;ible without this adverti&longs;ement to
treat of the&longs;e matters, and not commit very great errours.
I propo&longs;e therefore to con&longs;ideration, that although it be true,
that whil&longs;t the water of the main P
Bank and Dam then cut of the P
waters having a very great fall into the Channel of
precipitate into the &longs;ame with great violence and velocity, and
with the &longs;ame in the beginning, or little le&longs;&longs;e, they run towards
the P
&longs;pace of &longs;ome few hours, the P
perior Waters not finding &longs;o great a diclivity there, as they had
at the beginning of the cutting, they fall not into the &longs;ame with
the former velocity, but with far le&longs;&longs;e, and thereby a great deal
le&longs;&longs;e Water begins to i&longs;&longs;ue from the great P
gently compare the velocity at the fir&longs;t cutting, with the velocity
of the Water after the cutting made, and when the P
&longs;hall be full of Water, we &longs;hall finde perhaps that to be fifteen or
twenty times greater than this, and con&longs;equently the Water
which i&longs;&longs;ues from the great P
&longs;hall be onely the fifteenth or twentieth part of that which i&longs;&longs;ued
at the beginning; and therefore the Waters of the main P
return in a &longs;mall time almo&longs;t to the fir&longs;t height. And here I will
pray tho&longs;e who re&longs;t not wholly &longs;atisfied with what hath been &longs;aid,
that for the love of truth, and the common good, they would
plea&longs;e to make diligent ob&longs;ervation whether in the time of great
Floods, the &longs;aid Bank or Dam at
hours the main P
its height; that they would ob&longs;erve I &longs;ay, whether, a day or two
being pa&longs;t, the Waters of the main P
height; for if this &longs;hould follow, it would be very clear, that the
benefit which re&longs;ulteth from this diver&longs;ion or Vent, is not &longs;o great
as is univer&longs;ally pre&longs;umed; I &longs;ay, it is not &longs;o great as is
pre&longs;umed; becau&longs;e, though it be granted for true, that
the Waters of the main P
few hours: If the ri&longs;ing of P
were of &longs;hort duration, as it ordinarily befalleth in the overflow
ings of Torrents, in &longs;uch a ca&longs;e the profit of the Vent would be
of &longs;ome e&longs;teem: But becau&longs;e the &longs;wellings of P
thirty, or &longs;ometimes for forty dayes, therefore the gain which
re&longs;ults from the Vent proveth to be incon&longs;iderable. It remain
eth now to con&longs;ider the notable harms which follow the &longs;aid
Sluice or Vent, that &longs;o reflection being made, and the profit and
the detriment compared, one may rightly judge, and choo&longs;e that
which &longs;hall be mo&longs;t convenient. The fir&longs;t prejudice therefore
which ari&longs;eth from this Vent or Sluice, is; That the Channels of
from
thereby. Secondly, The Waters of the P
free ingre&longs;&longs;e into the upper Valleys, they fill them to the great
damage of the Fields adjacent, and ob&longs;truct the cour&longs;e of the
ordinary Trenches in the &longs;ame Valleys; in&longs;omuch that all the
care, co&longs;t, and labour about the draining, and freeing the upper
Valleys from Water, would al&longs;o become vain and ineffectual. Thirdly, I con&longs;ider that the&longs;e Waters of the P
pa&longs;&longs;ed downwards towards the Sea, at the time that the main P
was in its greater excre&longs;cences and heights, it is manife&longs;t by expe
rience, that when the great P
pa&longs;&longs;ed by the P
finally come to turn the current upwards towards
fir&longs;t iu the intermediate time, almo&longs;t fixed and &longs;tanding, and
therefore depo&longs;ing the muddine&longs;&longs;e, they fill up the Channel of
the River or Current of
followeth from this &longs;ame diver&longs;ion another notable damage, and
it is like to that which followeth the breaches made by Rivers;
near to which breaches in the lower parts, namely below the
breach, there is begot in the Channel of the River, a certain ridge
or &longs;helf, that is, the bottom of the River is rai&longs;ed, as if &longs;ufficiently
manife&longs;t by experience; and thus ju&longs;t in the &longs;ame manner cutting
the Bank at
followeth the ri&longs;ing in the lower parts of the main P
the mouth of
judge that under&longs;tandeth the&longs;e matters. And therefore both for
the &longs;mall benefit, and &longs;o many harms that en&longs;ue from maintain
ing this diver&longs;ion, I &longs;hould think it were more &longs;ound advice to
keep that Bank alwaies whole at
nient place, and not to permit that the Water of the Grand P
&longs;hould ever come near to
In the Grand Rivers, which fall into the Sea, as here in
Po, Adige,
excre&longs;cencies, its ob&longs;erved that far from the Sea, they need
Banks of a notable height; which height goeth afterwards by
degrees dimini&longs;hing, the more it approacheth to the Sea-coa&longs;ts:
in &longs;uch &longs;ort, that the P
miles at
higher than the ordinary Water marks; but ten or twelve miles
from the Sea, the Banks are not twelve feet higher than the &longs;aid
ordinary Water-marks, though the breadth of the River be the
&longs;ame, &longs;o that the excre&longs;cence of the &longs;ame Innundation happens
to be far greater in mea&longs;ure remote from the Sea, then near; and
yet it &longs;hould &longs;eem, that the &longs;ame quantity of Water pa&longs;&longs;ing by
every piace, the River &longs;hould need to have the &longs;ame altitude of
Banks in all places: But we by our Principles and fundamentals
may be able to render the rea&longs;on of that effect, and &longs;ay; That
that exce&longs;&longs;e of quantity of Water, above the ordinary Water,
goeth alwaies acquiring greater velocity; the nearer it approach
eth the Sea, and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equenly
in height. And this perhaps might have been the cau&longs;e in great
part, why the
forth of its Channel below
From the &longs;ame Doctrine may be rendred a mo&longs;t manife&longs;t rea
&longs;on why the falling Waters go le&longs;&longs;ening in their de&longs;cent, &longs;o
that the &longs;ame falling Water, mea&longs;ured at the beginning of
its fall, is greater, and bigger, and afterwards by degrees le&longs;&longs;eneth
in mea&longs;ure the more it is remote from the beginning of the fall. Which dependeth on no other, than on the acqui&longs;ition, which
it &longs;ucce&longs;&longs;ively makes of greater velocity; it being a mo&longs;t fami
liar conclu&longs;ion among Philo&longs;ophers, that grave bodies falling,
the more they remove from the beginning of their motion, the
more they acquire of &longs;wiftne&longs;&longs;e; and therefore the Water, as a
grave body, falling, gradually velocitates, and therefore de
crea&longs;eth in mea&longs;ure, and le&longs;&longs;eneth.
And on the contrary, the &longs;pirtings of a Fountain of Water,
which &longs;pring on high, work a contrary effect; namely
and bigge; and the rea&longs;on is mo&longs;t manife&longs;t, becau&longs;e in the be
ginning they are very &longs;wift, and afterwards gradually relent
their impetuo&longs;ity, and motion, &longs;o that in the beginning of the
excur&longs;ion that they make, they ought to be &longs;mall, and after
wards to grow bigger, as in the effect is &longs;een.
APPENDIX. I.
Into the errour of not con&longs;idering how much the different
velocities of the &longs;ame running water in &longs;everal places of
its current, are able to change the mea&longs;ure of the &longs;ame
water, and to make it greater, or le&longs;&longs;e, I think, if I be not
deceived, that
have faln in the Second Book which he writ, of the Aqueducts
of the City of
^{*}
thought that &longs;o much difference might proceed from the negligence
of the Mea&longs;ures; and when afterwards with his own indu&longs;try he
mea&longs;ured the &longs;ame water at the beginnings of the Aqueducts,
finding it neer 10000.
riis
Partakers; which in part might be &longs;o, for it is but too true, that
the publique is almo&longs;t alwayes defrauded; yet neverthele&longs;&longs;e, I
verily believe withal, that be&longs;ides the frauds of the&longs;e Officers,
the velocities of the water in the place wherein
red, it might be different from tho&longs;e velocities, which are
found in other places before mea&longs;ured by others; and there
fore the mea&longs;ures of the waters might, yea ought nec&longs;&longs;arily to
be diffcrent, it having been by us demon&longs;trated, that the mea
&longs;ures of the &longs;ame running water have reciprocal proportion to
their velocities. Which
ing the water
one
head of the fountain 22755.
thought, that in all the&longs;e places there pa&longs;t different quantities of
water; namely, greater at the fountain head then that which was
beareth many &longs;en
&longs;es, but in this
place &longs;ignifieth a
certain Regi&longs;ter of
the quantities of
the Waters in the
&longs;everal publique A
qu ducts of
which word I find
frequently u&longs;ed in
the Law-books of
antient Civilians:
Andby errogation
we are to under
&longs;tand the di&longs;tribu
tion or delivering
out of tho&longs;e &longs;tores
of Water.
APPENDIX II.
Alike mi&longs;take chanced lately in the Aqueduct of
Paola,
effectively ought to be allowed; and it hath been given in
and there was a mea&longs;ure thereof made at the beginning of the
Aqueduct; which mea&longs;ure proved afterwards much le&longs;&longs;e and
&longs;hort, con&longs;idered and taken in
contents and great di&longs;orders, and all becau&longs;e this property of
Running-Waters, of increa&longs;ing in mea&longs;ure, where the velocity
decrea&longs;ed; and of dimini&longs;hing in mea&longs;ure, where the velocity
augmented, was not lookt into.
APPENDIX III.
Alike errour, in my judgement, hath beeen committed by
all tho&longs;e learned men, which to prevent the diver&longs;ion of
the
which it at pre&longs;ent runneth, judged, that the
greater excre&longs;cence about 2000 feet, and the P
1000 feet broad, they judged, I &longs;ay, that letting the
P
ri&longs;e, they concluded afterwards mo&longs;t exorbitant di&longs;orders, either
of extraordinary Inundations, or el&longs;e of immen&longs;e and intolera
ble expences to the people in rai&longs;ing the Banks of P
and with &longs;uch like weakne&longs;&longs;es, often vainly di&longs;turbed the minds
of the per&longs;ons concerned: But now from the things demon&longs;tra
ted, it is manife&longs;t, That the mea&longs;ure of the
be different from the mea&longs;ure of
velocity of the
of
po&longs;ition.
APPENDIX IV.
No le&longs;s likewi&longs;e are tho&longs;e Ingeneers and Arti&longs;ts deceived,
that have affirmed, That letting the
would be no ri&longs;e at all in the Water of P
is, That letting
&longs;ometimes greater, &longs;ometimes le&longs;&longs;e, as the P
or &longs;lower Current; &longs;o that if the P
velocity, the ri&longs;e will be very &longs;mall; and if the &longs;aid P
&longs;low in its cour&longs;e, then the ri&longs;e will be notable.
APPENDIX V.
And here it will not be be&longs;ides the purpo&longs;e to adverti&longs;e, That
the mea&longs;ures, partments, and di&longs;tributions of the Waters
of Fountains, cannot be made exactly, unle&longs;s there be con
which particular not being thorowly ob&longs;erved, is the cau&longs;e of
continual mi&longs;cariages in &longs;uch like affairs.
APPENDIX VI.
Like con&longs;ideration ought to be had with the greater diligence,
for that an errour therein is more prejudicial; I &longs;ay, ought to
be had by tho&longs;e which part and divide Waters; for the
watering of fields, as is done in the Territories of
gama, Crema, Pavia, Lodigiano, Cremona,
For if they have not regard to the mo&longs;t important point of the
variation of the velocity of the Water, but onely to the bare
Vulgar mea&longs;ure, there will alwaies very great di&longs;orders and pre
judices en&longs;ue to the per&longs;ons concerned.
APPENDIX VII.
It &longs;eemeth that one may ob&longs;erve, that whil&longs;t the Water run
neth along a Channel, Current, or Conduit, its velocity is
retarded, withheld, and impeded by its touching the Bank or
&longs;ide of the &longs;aid Channel or Current; which, as immoveable, not
following the motion of the Water, interrupteth its velocity:
From which particular, being true, as I believe it to be mo&longs;t
true, and from our con&longs;iderations, we have an occa&longs;ion of di&longs;
covering a very nice mi&longs;take, into which tho&longs;e commonly fall
who divide the Waters of Fountains. Which divi&longs;ion is wont
to be, by what I have &longs;een here in
The fir&longs;t of which is with the mea&longs;ures of like figures, as Cir
cles, or Squares, having cut through a Plate of metal &longs;everal
Circles or Squares, one of half an inch, another of one inch,
another of two, of three, of four,
wards adju&longs;t the Cocks to di&longs;pence the Waters. The other
manner of dividing the Waters of Fountains, is with rectangle
paralellograms, of the &longs;ame height, but of different Ba&longs;es, in &longs;uch
&longs;ort likewi&longs;e, that one paralellogram be of half an inch, another
of one, two, three,
dividing the Water, it &longs;hould &longs;eem that the Cocks being placed
in one and the &longs;ame plain, equidi&longs;tant from the level, or &longs;uperior
&longs;uperficies of the water of the Well; and the &longs;aid mea&longs;ures be
ing mo&longs;t exactly made, the Water ought con&longs;equently al&longs;o to
be equally divided, and parted according to the proportion of
the mea&longs;ures. But if we well con&longs;ider every particular, we &longs;hall
finde, that the Cocks, as they &longs;ucce&longs;&longs;ively are greater, di&longs;charge
alwaies more Water than the ju&longs;t quantity, in compari&longs;on of
pa&longs;&longs;eth through the greater Cock, hath alwaies a greater pro
portion to that which pa&longs;&longs;eth through the le&longs;&longs;er, than the greater
Cock hath to the le&longs;&longs;er. All which I will declare by an exam
ple.
Let there be &longs;uppo&longs;ed for more plainne&longs;s two Squares; (the
&longs;ame may be under&longs;tood of Circles, and other like Figures) The
fir&longs;t Square is, as we will &longs;uppo&longs;e, quadruple to the other, and
the&longs;e Squares are the mouths of two Cocks.; one of four inches,
the other of one: Now its manife&longs;t by what hath been &longs;aid, that
the Water which pa&longs;&longs;eth by the le&longs;s Cock, findeth its velocity
impeded in the circumference of the Cock; which impediment
is mea&longs;ured by the &longs;aid circumfe
rence. Now it is to be con&longs;ider
ed, that if we would have the Wa
ter which pa&longs;&longs;eth through the
greater Cock, to be onely qua
druple to that which pa&longs;&longs;eth
through the le&longs;&longs;e, in equal &longs;paces of time, it would be nece&longs;&longs;ary,
that not onely the capacity and the mea&longs;ure of the greater Cock
be quadruple to the le&longs;&longs;er Cock, but that al&longs;o the impediment be
quadrupled. Now in our ca&longs;e it is true, That the belly and
mouth of the Cock is quadrupled, and yet the impediment is not
quadrupled, but is onely doubled; &longs;eeing that the circumference
of the greater Square, is onely double to the circumference of
the le&longs;ier Square; for the greater circumference containeth eight
of tho&longs;e parts, of which the le&longs;&longs;er containeth but four, as is ma
nife&longs;t by the de&longs;cribed Figure; and for that cau&longs;e there &longs;hall
pa&longs;s by the greater Cock, above four times as much Water, as
&longs;hall pa&longs;s by the le&longs;&longs;er Cock.
The like errour occurreth al&longs;o in the other manner of mea&longs;u
ring the Water of a Fountain, as may ea&longs;ily be collected from
what hath been &longs;aid and ob&longs;erved above.
APPENDIX VIII.
The &longs;ame contemplation di&longs;covereth the errour of tho&longs;e
Architects, who being to erect a Bridge of &longs;undry Arches
over a River, con&longs;ider the ordinary breadth of the River;
which being g.
of four Arches, it &longs;ufficeth them, that the breadth of all the four
Arches taken together, be fourty fathom; not con&longs;idering 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 &longs;ides or &longs;hores of the River: but
with eight of the &longs;ame impediments, bearing, and thru&longs;ting upon
two &longs;ides of each Arch (to omit the impediment of the bottom,
for that it is the &longs;ame in the River, and under the Bridge) from
which inadvertency &longs;ometimes follow very great di&longs;orders, as
quotidian practice &longs;hews us.
APPENDIX IX.
It is al&longs;o worthy to con&longs;ider the great and admirable benefit
that tho&longs;e fields receive, which are wont to drink up the Rain
water with difficulty, through the height of the water in the
principal Ditches; in which ca&longs;e the careful Husbandman cutteth
away the reeds and ru&longs;hes in the Ditches, through which the
waters pa&longs;s; whereupon may be pre&longs;ently &longs;een, &longs;o &longs;oon as the
reeds and ru&longs;hes are cut, a notable Ebb in the level of the water
in the Ditches; in&longs;omuch that &longs;ometimes it is ob&longs;erved, that the
water is abated after the &longs;aid cutting a third and more, of what it
was before the cutting. The which effect &longs;eemingly might de
pend on this, That, before tho&longs;e weeds took up room in the
Ditch, and for that cau&longs;e the water kept a higher level, and the
&longs;aid Plants being afterwards cut and removed, the water came to
abate, po&longs;&longs;e&longs;&longs;ing the place that before was occupied by the
weeds: Which opinion, though probable, and at fir&longs;t &longs;ight &longs;a
tisfactory, is neverthele&longs;s in&longs;ufficient to give the total rea&longs;on of
that notable abatement which hath been &longs;poken of: But it is ne
ce&longs;&longs;ary to have recour&longs;e to our confideration of the velocity in
the cour&longs;e of the water, the chiefe&longs;t and true cau&longs;e of the vari
ation of the mea&longs;ure of the &longs;ame Running-Water; for, that
multitudes of reeds, weeds, and plants di&longs;per&longs;ed through the cur
rent of the Ditch, do chance notably to retard the cour&longs;e of the
water, and therefore the mea&longs;ure of the water increa&longs;eth; and
tho&longs;e impediments removed, the &longs;ame water gaineth velocity,
and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equently in
height.
And perhaps this point well under&longs;tood, may be of great
profit to the fields adjacent to the
but if the River
Territories were kept well clean&longs;ed from weeds, their waters
would be at a lower level, and con&longs;equently the drains of the
fields would run into them more readily; it being alwayes to be
held for undoubted, that the mea&longs;ure of the water before the
clean&longs;ing, hath the &longs;ame proportion to the mea&longs;ure after clean
&longs;ing, that the velocity after the clean&longs;ing hath to the velocity
before the clean&longs;ing: An dbecau&longs;e tho&longs;e weeds being clean&longs;ed
nece&longs;&longs;ary that the &longs;aid water abate in mea&longs;ure, and become
lower.
APPENDIX. X.
We having above ob&longs;erved &longs;ome errors that are commit
ted in di&longs;tributing the waters of Fountains, and tho&longs;e
that &longs;erve to water fields; it &longs;eemeth now fit, by way of
a clo&longs;e to this di&longs;cour&longs;e, to adverti&longs;e by what means the&longs;e divi
&longs;ions may be made ju&longs;tly and without error. I therefore think
that one might two &longs;everal wayes exqui&longs;itly divide the water of
Fountains; The fir&longs;t would be by diligently examining, Fir&longs;t,
how much water the whole Fountain di&longs;chargeth in a determi
nate time, as for in&longs;tance: How many Barrels, or Tuns it carri
eth in a &longs;et time; and in ca&longs;e you are afterwards to di&longs;tribute
the water, di&longs;tribute it at the rate of &longs;omany Barrels or Tuns, in
that &longs;ame time; and in this ca&longs;e the participants would have
their punctual &longs;hares: Nor could it ever happen to &longs;end out more
water, than is reckoned to be in the principal Fountain; as befel
dern Aqueducts, to the publick and private detriment.
The other way of dividing the &longs;ame waters of a Fountain, is
al&longs;o &longs;ufficiently exact and ea&longs;ie, and may be, by having one one
ly &longs;ize for the Cock or Pipe, as &longs;uppo&longs;e of an inch, or of half an
inch; and when the ca&longs;e requireth to di&longs;pence two, three, and
more inches, take &longs;o many Cocks of the &longs;aid mea&longs;ure as do eva
cuate the water, which is to be emitted; and if we are to make
u&longs;e onely of one greater Cock, we being to place one to di&longs;
charge for example four inches; and having the former &longs;ole mea
&longs;ure of an inch, we mu&longs;t make a Cock that is bigger, its true, than
the Cock of one inch; but not &longs;imply in a quadruple propor
tion, for that it would di&longs;charge more than ju&longs;t &longs;o much water,
as hath been &longs;aid above; but we ought to examine diligently
how much water the little Cock emitteth in an hour; and then
enlarge, and contract the greater Cock, &longs;o, that it may di&longs;
charge four times as much water as the le&longs;&longs;er in the &longs;ame time;
and by this means we &longs;hall avoid the di&longs;order hinted in the
&longs;eventh Appendix. It would be nece&longs;&longs;ary neverthele&longs;s, to ac
commodate the Cocks of the Ci&longs;tern &longs;o, that the level of the
water in the Ci&longs;tern may alwayes re&longs;t at one determinate mark
above the Cock, otherwi&longs;e the Cocks will emit &longs;ometimes
greater, and &longs;ometimes le&longs;&longs;e abundance of water: And becau&longs;e
it may be that the &longs;ame water of the Fountain may be &longs;ometimes
more abundant, &longs;ometimes le&longs;s; in &longs;uch ca&longs;e it will be nece&longs;&longs;ary
ter, di&longs;charge into the publick Fountains, that &longs;o the particular
participants may have alwayes the &longs;ame abundance of
water.
APPENDIX XI.
Much more difficult is the divi&longs;ion of the waters which
&longs;erve to water the fields, it not being po&longs;&longs;ible to ob&longs;erve
&longs;o commodiou&longs;ly, what quantity of water the whole
Ditch &longs;ends forth in one determinate time, as may be done in
Fountains: Yet neverthele&longs;s, if the &longs;econd propo&longs;ition by us a
little below demon&longs;trated, be well under&longs;tood, there may be
thence taken a very &longs;afe and ju&longs;t way to di&longs;tribute &longs;uch waters. The Propo&longs;ition therefore by us demon&longs;trated is this: If there
be two Sections, (namely two mouths of Rivers) the quantity of
the water which pa&longs;&longs;eth by the fir&longs;t, hath a proportion to that
which pa&longs;&longs;eth by the &longs;econd, compounded of the proportions of
the fir&longs;t Section to the &longs;econd, and of the velocity through
the fir&longs;t, to the velocity through the &longs;econd: As I will declare
for example by help of practice, that I may be under&longs;tood by
all, in a matter &longs;o important. Let the two mouths of the
Rivers be A, and B, and let
the mouth A be in mea&longs;ure
and content thirty two feet,
and the mouth B, eight feet. Here you mu&longs;t take notice,
that it is not alwayes true, that
the Water which pa&longs;&longs;eth by A,
hath the &longs;ame proportion to that which pa&longs;&longs;eth by B, that the
mouth A hath to the mouth B; but onely when the velocityes
by each of tho&longs;e pa&longs;&longs;ages are equal: But if the velocityes &longs;hall
be unequal, it may be that the &longs;aid mouths may emit equal
quantity of Water in equal times, though their mea&longs;ure be un
equal; and it may be al&longs;o, that the bigger doth di&longs;charge a great
er quantity of Water: And la&longs;tly, it may be, that the le&longs;s mouth
di&longs;chargeth more Water than the greater; and all this is mani
fe&longs;t by the things noted in the beginning of this di&longs;cour&longs;e, and
by the &longs;aid &longs;econd Propo&longs;ition. Now to examine the propor
tion of the Water that pa&longs;&longs;eth by one Ditch, to that which pa&longs;
&longs;eth by another, that this being known, the &longs;ame Waters and
mouths of Ditches may be then adju&longs;ted; we are to keep ac
count not onely of the greatne&longs;s of the mouths or pa&longs;&longs;ages of the
Water, but of the velocity al&longs;o; which we will do, by fir&longs;t find
ing two numbers that have the &longs;ame proportion between them
in our example: Then this
being done, let the velocity
of the Water by the pa&longs;&longs;a
ges A and B, be examined
(which may be done keeping
account what &longs;pace a piece
of Wood, or other body that
&longs;wimmeth, is carried by the &longs;tream in one determinate time; as
for in&longs;tance in 50 pul&longs;es) and then work by the golden Rule, as
the velocity by A, is to the velocity by B, &longs;o is the number 8, to
another number, which is 4. It is clear by what is demon&longs;tra
ted in the &longs;aid &longs;econd Propo&longs;ition, that the quantity of water,
which pa&longs;&longs;eth by the mouth A, &longs;hall have the &longs;ame proportion of
that which pa&longs;&longs;eth by the mouth B, that 8 hath to 1. Such pro
portion being compo&longs;ed of the proportions of 32 to 8, and of 8 to
4; namely, tothe greatne&longs;s of the mouth A, to the greatne&longs;s of the
mouth B, and of the velocity in A, to the velocity in B. This being
done, we mu&longs;t then contract the mouth which di&longs;chargeth more
then its ju&longs;t quantity of water, or enlarge the other which di&longs;char
geth le&longs;s, as &longs;hal be mo&longs;t commodious in practice, which to him that
hath under&longs;tood this little that hath been delivered, will be very
afie.
APPENDIX XII.
The&longs;e opperations about Water, as I have hitherto on &longs;un
dry occa&longs;ions ob&longs;erved, are involved in &longs;o many difficul
ties, and &longs;uch a multiplicity of mo&longs;t extravagant accidents,
that it is no marvel if continually many, and very important er
rours be therein committed by many, and even by Ingeneers
them&longs;elves, and Learned-men; and becau&longs;e many times they
concern not onely the publique, but private intere&longs;ts: Hence it
is, that it not onely belongeth to Arti&longs;ts to treat thereof, but very
oft even the vulgar them&longs;elves pretend to give their judgement
therein: And I have been troubled many times with a nece&longs;&longs;ity
of treating, not onely with tho&longs;e, which either by practice, or
particular &longs;tudy, under&longs;tood &longs;omewhat in the&longs;e matters; but al&longs;o
with people wholly void of tho&longs;e notions, which are nece&longs;&longs;ary for
one that would on good grounds di&longs;cour&longs;e about this particular;
and thus many times have met with more difficulty in the thick
skulls of men, than in precipitous Torrents, and va&longs;t Fennes. And in particular, I had occafion &longs;ome years pa&longs;t to go &longs;ee the
Gave or Emi&longs;&longs;ary of the Lake of
by
Time decayed, and rendred unu&longs;eful, it was repaired with in
herino,And being
nece&longs;&longs;itated, that I might be able to walk in the Cave, and for
other cau&longs;es, I let down the Sluices of the &longs;aid Cave, at the mouth
of the Lake: No &longs;ooner were they &longs;topt, but a great many of the
people of the Towns and Villages coa&longs;ting upon the
flocking thither, began to make grievous complaints, that if tho&longs;e
Sluices were kept &longs;hut, not onely the Lake would want its due
Vent, but al&longs;o the parts adjacent to the Lake would be over
flown to their very great detriment. And becau&longs;e at fir&longs;t appea
rance their motion &longs;eemed very rea&longs;onable, I found my &longs;elf hard
put to it, &longs;eeing no way to per&longs;wade &longs;uch a multitude, that the
prejudice which they pretended I &longs;hould do them by keeping
the Sluices &longs;hut for two dayes, was ab&longs;olutely in&longs;en&longs;ible; and that
by keeping them open, the Lake did not ebb in the &longs;ame time &longs;o
much as the thickne&longs;s of a &longs;heet of Paper: And therefore I was
nece&longs;&longs;itated to make u&longs;e of the authority I had, and &longs;o followed
my bu&longs;ine&longs;s as cau&longs;e required, without any regard to that Rab
ble tumultuou&longs;ly a&longs;&longs;embled. Now when I am not working with
Mattock or Spade, but with the Pen and Di&longs;cour&longs;e, I intend to
demon&longs;trate clearly to tho&longs;e that are capable of rea&longs;on, and that
have well under&longs;tood the ground of this my Treati&longs;e, that the
fear was altogether vain which tho&longs;e people conceited. And
therefore I &longs;ay, that the Emi&longs;&longs;ary or Sluice of the Lake of
gia,
pa&longs;&longs;ing thorow it with the &longs;ame velocity as now; to examine
how much the Lake may abate in two days &longs;pace, we ought to
con&longs;ider, what proportion the &longs;uperficies of the whole Lake hath
to the mea&longs;ure of the Section of the Emi&longs;&longs;ary, and afterwards to
infer, that the velocity of the water by the Emi&longs;&longs;ary or Sluice,
&longs;hall have the &longs;ame proportion to the abatement of the Lake,
and to prove thorowly and clearly this di&longs;cour&longs;e, I intend to
demon&longs;trate the following Propo&longs;ition.
Suppo&longs;e a Ve&longs;&longs;el of any bigne&longs;&longs;e, and that it hath an Emi&longs;&longs;ary
or Cock, by which it di&longs;chargeth its water. And look what pro
portion the &longs;uper&longs;icies of the
ve&longs;&longs;el hath to the mea&longs;ure of
the &longs;ection of the cock, &longs;uch pro
portion &longs;hall the velocity of the
Water in the Cock have to the
abatement of the Lake Let the
Ve&longs;&longs;el be A B C D, H I L B, through which the Water runneth,
the &longs;uperficies of the Water in the Ve&longs;&longs;el A D, and the &longs;ection
of the Cock H L: and let the Water in the Ve&longs;&longs;el
be &longs;uppo&longs;ed to have falne in one determinate time from A to F.
in proportion to the mea&longs;ure of the &longs;ection of the Emi&longs;&longs;ary
H L, as the velocity of the Emi&longs;&longs;ary or Cock to the line A F;
which is manife&longs;t, for that the Water in the Ve&longs;sel moving by
the line A F; as far as F, and the whole ma&longs;s of Water A G
di&longs;charging it &longs;elf, and in the &longs;ame time the &longs;ame quantity of
Water being di&longs;charged by the &longs;ection of the Emi&longs;&longs;ary H L; it
is nece&longs;&longs;ary by what I have demon&longs;trated in the third Propo&longs;ition,
and al&longs;o explained in the beginning of this Treati&longs;e, that the ve
locity by the Emi&longs;&longs;ary or Cock be in proportion to the velocity
of the abatement, as the &longs;uperficies of the Ve&longs;&longs;el to the mea
&longs;ure of the &longs;ection of the Emi&longs;&longs;ary, which was to be demon
&longs;trated.
That which hath been demon&longs;trated in the Ve&longs;&longs;el, falls out ex
actly al&longs;o in our Lake of
the immen&longs;ity of the &longs;uperficies of the Lake is in proportion to
the &longs;uperficies of the Emi&longs;sary or Sluice, as many millions to
one, as may be ea&longs;ily calculated; it is manife&longs;t, that &longs;uch abate
ment &longs;hall be imperceptible, and almo&longs;t nothing, in two dayes
&longs;pace, nay in four or &longs;ix: and all this will be true, when we
&longs;uppo&longs;e that for that time there entreth no other Water into the
Lake from Ditches or Rivolets, which falling into the Lake would
render &longs;uch abatement yet le&longs;s.
Now we &longs;ee, that it's nece&longs;sary to examine &longs;uch abatements
and ri&longs;ings, with excellent rea&longs;ons, or at lea&longs;t, with accurate ex
periments, before we re&longs;olve and conclude any thing; and how
farre the vulgar are di&longs;tant from a right judgment in &longs;uch
matters.
APPENDIX XIII.
For greater confirmation of all this which I have &longs;aid, I
will in&longs;tance in another like ca&longs;e, which al&longs;o I met with here
tofore, wherein, for that the bu&longs;ine&longs;s was not rightly un
der&longs;tood, many di&longs;orders, va&longs;t expences, and con&longs;iderable mi&longs;
chiefs have followed. There was heretofore an Emi&longs;sary or
Sluice made to drain the Waters, which from Rains, Springs, and
Rivolets fall into a Lake; to the end, the &longs;hores adjoyning on
the Lake, &longs;hould be free from the overflowing of the Waters;
but becau&longs;e perhaps the enterprize was not well managed and
carried on, it fell out, that the Fields adjacent to the &longs;aid Chanel
could not drain, but continued under water; to which di&longs;orders
a pre&longs;ent remedy hath been u&longs;ed, namely, in a time convenient
to &longs;top up the Sluice, by meanes of certain Floodgates kept on
purpo&longs;e for that end; and thus abating the Level of the Water
have been haply drained. But on the other part, the proprietors
bordering on the Lake oppo&longs;ed this, grievou&longs;ly complaining, that
whil&longs;t the Floodgates are &longs;hut, and the cour&longs;e of the Water of
the Sluice hindered, the Lake overflowes the Lands adjacent, by
meanes of the Rivers that fell into it, to their very great damage;
and &longs;o continuing their &longs;uits, they got more of vexation than &longs;a
tisfaction. Now, being asked my opinion herein, I judged it
requi&longs;ite (&longs;ince the point in controver&longs;ie was about the ri&longs;ing
and falling of the Lake) that the &longs;aid abatement, when the
Floodgates are open, and increa&longs;e when they are &longs;hut &longs;hould be
exactly mea&longs;ured, and told them, that it might be ea&longs;ily done at
a time when no extraordinary Waters fell into the Lake, neither
of Rain, or otherwi&longs;e; and the Lake was undi&longs;turbed by winds
that might drive the Water to any &longs;ide, by planting neer to an
I&longs;let, which is about the middle of the Lake, a thick po&longs;t, on
which &longs;hould be made the marks of the Lakes ri&longs;ing and falling
for two or three dayes. I would not, at that time, pawn, or re
&longs;olutely declare, my judgment, in regard I might be, by divers
accidents mi&longs;led. But this I told them, that (by what I have
demon&longs;trated, and particularly that which I have &longs;aid above
touching the Lake of
that the&longs;e ri&longs;ings and fallings would prove imperceptible, and
incon&longs;iderable; and therefore, that in ca&longs;e experience &longs;hould
make good my rea&longs;on, it would be to no purpo&longs;e for them to
continue di&longs;puting and wrangling, which cau&longs;eth, (according
to the Proverb)
La&longs;tly, it importing very much to know what a Rain conti
nued for many dayes can do in rai&longs;ing the&longs;e Lakes, I will here in
&longs;ert the Copy of a Letter, which I writ formerly to
lilæo Galilæi,
wherein I have delivered one of my conceits in this bu&longs;ine&longs;&longs;e, and
it may be, by this Letter, I may, more &longs;trongly, confirm what I
have &longs;aid above.
GALILÆI,
Great Duke of TVSCANY.
In &longs;atisfaction of my promi&longs;e, in my former Letters of
repre&longs;enting unto you &longs;ome of my Con&longs;iderations
made upon the Lake
pa&longs;t, being in
Convention, having under&longs;tood that the Lake
the great drought of many Moneths was much abated, It came
into my head, to go privately and &longs;ee this novelty, both for my
particular &longs;atisfaction, as al&longs;o that might I be able to relate the
whole to my Patrons, upon the certitude of my own &longs;ight of the
place. And &longs;o being come to the Emi&longs;&longs;ary of the Lake, I found
that the Level of the Lakes &longs;urface was ebbed about five Ro
man Palmes of its wonted watermark, in&longs;omuch that it was lower
than the tran&longs;ome of the mouth of the Emi&longs;&longs;ary, by the length
of ----------------------------this de&longs;cribed line, and there
fore no Water i&longs;&longs;ued out of the Lake, to the great prejudice of
all the places and villages circumjacent, in regard that the Wa
ter which u&longs;ed to run from the &longs;aid Lake turned 22 Mills, which
not going, nece&longs;&longs;itated the inhabitants of tho&longs;e parts to go a
dayes journey and more, to grinde upon the
ned to
&longs;tant, and even, which la&longs;ted for the &longs;pace of eight hours, or
thereabouts; and it came into my thoughts to examine, being
in
Rain, &longs;uppo&longs;ing (as it was probable enough) that the Rain had
been univer&longs;al over all the Lake; and like to that which fell in
linder, about a palme high, and half a palme broad; and having
put in water &longs;nfficient to cover the bottome of the Gla&longs;&longs;e, I no
ted diligently the mark of the height of the Water in the Gla&longs;&longs;e,
and afterwards expo&longs;ed it to the open weather, to receive the
Raine-water, which fell into it; and I let it &longs;tand for the
&longs;pace of an hour; and having ob&longs;erved that in that time the Wa
ter was ri&longs;en in the Ve&longs;&longs;el the height of the following line---,
I con&longs;idered that if I had expo&longs;ed to the &longs;ame rain &longs;uch other ve&longs;
&longs;els equal to that, the Water would have ri&longs;en in them all accor
ding to that mea&longs;ure: And thereupon concluded, that al&longs;o in all
be rai&longs;ed in the &longs;pace of an hour the &longs;ame mea&longs;ure. Yet here I
con&longs;idered two difficulties that might di&longs;tutb and altar &longs;uch an
effect, or at lea&longs;t render it inob&longs;erveable, which afterwards well
weighed, and re&longs;olved, left me (as I will tell you anon) in the
conclu&longs;ion the more confirmed; that the Lake ought to be in
crea&longs;ed in the &longs;pace of eight hours, that the rain la&longs;ted eight
times that mea&longs;ure. And whil&longs;t I again expo&longs;ed the Gla&longs;s to re
peat the experiment, there came unto me an Ingeneer to talk
with me touching certain affairs of our Mona&longs;tary of
di&longs;cour&longs;ing with him, I &longs;hewed him the Gla&longs;s out at my Cham
ber-window, expo&longs;ed in a Court-yard; and communicated to
him my fancy, relacing unto him all that I had done. But I
&longs;oon perceived that this brave fellow conceited me to be but of
a dull brain, for he &longs;milling &longs;aid unto me; Sir, you deceive
your &longs;elf: I am of opinion that the Lake will not be increa&longs;
ed by this rain, &longs;o much as the thickne&longs;&longs;e of a ^{*}
Hearing him pronounce this his opinion with freene&longs;s and
confidence, I urged him to give me &longs;ome rea&longs;on for what he
&longs;aid, a&longs;&longs;uring him, that I would change my judgement, when I
&longs;aw the &longs;trength of his Arguments: To which he an&longs;wered, that
he had been very conver&longs;ant about the Lake, and was every day
upon it, and was well a&longs;&longs;ured that it was not at all increa&longs;ed. And
importuning him further, that he would give me &longs;ome rea&longs;on
for his &longs;o thinking, he propo&longs;ed to my con&longs;ideration the great
drought pa&longs;&longs;ed, and that that &longs;ame rain was nothing for the
great parching: To which I an&longs;wered, I believe Sir that the &longs;ur
face of the Lake, on which the rain had fallen was moi&longs;tned; and
therefore &longs;aw not how its drought, which was nothing at all,
could have drunk up any part of the rain. For all this he per
&longs;i&longs;ting in his conceit, without yielding in the lea&longs;t to my allega
tion; he granted in the end (I believe in civility to me) that
my rea&longs;on was plau&longs;ible and good, but that in practi&longs;e it could
not hold. At la&longs;t to clear up all, I made one be called, and
&longs;ent him to the mouth of the Emi&longs;&longs;ary of the Lake, with order
to bring me an exact account, how he found the water of the
Lake, in re&longs;pect of the Tran&longs;ome of the Sluice. Now here,
Signore
the matter in hand to concern me in my honour; but believe me
(and there are witne&longs;&longs;es of the &longs;ame &longs;till living) that my me&longs;&longs;en
ger returning in the evening to
that the water of the Lake began to run through the Cave; and
that it was ri&longs;en almo&longs;t a fingers breadth above the Tran&longs;ome:
In&longs;omuch, that adding this mea&longs;ure, to that of the lowne&longs;s of
the &longs;urface of the Lake, beneath the Tran&longs;ome before the rain,
to a hair tho&longs;e four fingers breadth that I had judged it to be. Two dayes after I had another bout with the Ingeneer, and re
lated to him the whole bu&longs;ine&longs;s, to which he knew not what to
an&longs;wer.
pence.
Now the two difficulties which I thought of, able to impede
my conclu&longs;ion, were the&longs;e following: Fir&longs;t, I con&longs;idered that
it might be, that the Wind blowing from the &longs;ide where the
Sluice &longs;tood, to the Lake-ward; the mole and ma&longs;s of the Wa
ter of the Lake might be driven to the contrary &longs;hore; on which
the Water ri&longs;ing, it might be fallen at the mouth of the Emi&longs;&longs;a
ry, and &longs;o the ob&longs;ervation might be much ob&longs;cured. But this
difficulty wholly vani&longs;hed by rea&longs;on of the Aires great tranqui
lity; which it kept at that time, for no Wind was &longs;tirring on any
&longs;ide, neither whil&longs;t it rained, nor afterwards.
The &longs;econd difficulty which put the ri&longs;ing in doubt, was, That
having ob&longs;erved in
which the rain-water, falling from the hou&longs;e, is conveyed
through the Common-&longs;hores: And that they are not thereby
ever filled, but that they &longs;wallow all that abundance of water,
that runs into them by tho&longs;e conveyances which &longs;erve them with
water; in&longs;omuch that tho&longs;e conveyances which in time of
drought maintain the Pond, when there comes new abundance
of water into the Pond, they drink it up, and &longs;wallow it: A like
effect might al&longs;o fall out in the Lake, in which there being many
veins (as it is very likely) that maintain and feed the Lake; the&longs;e
veins might imbibe the new addition of the Rain-water, and &longs;o
by that means annuall the ri&longs;ing; or el&longs;e dimini&longs;h it in &longs;uch &longs;ort, as
to render it inob&longs;ervable. But this difficulty was ea&longs;ily re&longs;olved
by con&longs;idering my Treati&longs;e of the mea&longs;ure of Running-Waters;
fora&longs;much as having demon&longs;trated, that the abatement of a Lake
beareth the reciprocal proportion to the velocity of the Emi&longs;&longs;a
ry, which the mea&longs;ure of the Section of the Emi&longs;&longs;ary of the Lake,
hath to the mea&longs;ure of the &longs;urface of the Lake: making the
calculation and account, though in gro&longs;s; by &longs;uppo&longs;ing that its
veins were &longs;ufficiently large, and that the velocity in them were
notable in drinking up the water of the Lake; yet I found never
thele&longs;s, that many weeks and moneths would be &longs;pent in drink
ing up the new-come abundance of water by the rain, &longs;o that
I re&longs;ted &longs;ure, that the ri&longs;ing would en&longs;ue, as in effect it did.
And becau&longs;e many of accurate judgement, have again cau&longs;ed
me to que&longs;tion this ri&longs;ing, &longs;etting before me, that the Earth be
ing parched by the great drought, that had &longs;o long continued, it
might be, that that Bank of Earth which environed the brink of
the Lake, being dry, and imbibing great abundance of Water
height: I &longs;ay therefore, that if we would rightly con&longs;ider this
doubt here propo&longs;ed, we &longs;hould, in the very con&longs;ideration of it,
&longs;ee it re&longs;olved; for, it being &longs;uppo&longs;ed that that li&longs;t or border of
Banks which was to be occupied by the increa&longs;e of the Lake, be
a Brace in breadth quite round the Lake, and that by rea&longs;on of
its dryne&longs;s it &longs;ucks in water, and that by that means this propor
tion of water co-operates not in rai&longs;ing of the Lake: It is ab&longs;o
lutely nece&longs;&longs;ary on the other hand, that we con&longs;ider, That the
Circuit of the water of the Lake being thirty miles, as its com
monly held, that is to &longs;ay, Ninety thou&longs;and Braces of
in compa&longs;s; and therefore admitting for true, that each Brace of
this Bank drink two quarts of water, and that for the &longs;pieading
it require three quarts more, we &longs;hall finde, that the whole agre
gate of this portion of water, which is not imployed in the rai&longs;ing
of the Lake, will be four hundred and fifty thou&longs;and Quarts of
water; and &longs;uppo&longs;ing that the Lake be &longs;ixty &longs;quare miles, three
thou&longs;and Braces long, we &longs;hall finde, that to di&longs;pence the water
po&longs;&longs;e&longs;t by the Bank about the Lake, above the total &longs;urface of
the Lake, it ought to be &longs;pread &longs;o thin, that one &longs;ole quart of
water may over-&longs;pread ten thou&longs;and &longs;quare Braces of &longs;urface:
&longs;uch a thinne&longs;s, as mu&longs;t much exceed that of a leaf of beaten
Gold, and al&longs;o le&longs;s than that skin of water which covers the Bub
bles of it: and &longs;uch would that be, which tho&longs;e men would have
&longs;ub&longs;tracted from the ri&longs;ing of the Lake: But again, in the &longs;pace
of a quarter of an hour at the beginning of the rain, all that
Bank is &longs;oaked by the &longs;aid rain, &longs;o that we need not for the
moi&longs;tning of it, imploy a drop of that water which falleth into
the Lake. Be&longs;ides we have not brought to account that abun
dance of water which runs in time of rain into the Lake, from
the &longs;teepne&longs;s of the adjacent Hills and Mountains; which would
be enough to &longs;upply all our occa&longs;ions: So that, neither ought
we for this rea&longs;on to que&longs;tion our pretended ri&longs;ing. And this
is what hath fallen in my way touching the con&longs;ideration of the
After which, perhaps &longs;omewhat ra&longs;hly, wandring beyond my
bounds, I proceeded to another contemplation, which I will re
late to you, hoping that you will receive it, as collected with
the&longs;e cautions requi&longs;ite in &longs;uch like affairs; wherein we ought
not too po&longs;itively to affirm any thing of our own heads for cer
tain, but ought to &longs;ubmit all to the &longs;ound and &longs;ecure delibera
tion of the Holy Mother-Church, as I do this of mine, and all
others; mo&longs;t ready to change my judgement, and conform my
&longs;elf alwaies to the deliberations of my Superiors. Continu
ter in the gla&longs;s tried before, it came into my minde, that the
forementioned rain having been very gentle, it might well be,
that if there &longs;hould have faln a Rain fifty, an hundred, or a thou
&longs;and times greater than this, and much more inten&longs;e (which
would in&longs;ue as oft as tho&longs;e falling drops were four, &longs;ive or ten
times bigger than tho&longs;e of the above-mentioned rain, keeping
the &longs;ame number) in &longs;uch a ca&longs;e its manife&longs;t, that in the &longs;pace
of an hour the Water would ri&longs;e in our Gla&longs;s, two, three, and
perhaps more Yards or Braces; and con&longs;equently, if &longs;uch a
Raine &longs;hould fall upon a Lake, that the &longs;aid Lake would
ri&longs;e, according to the &longs;ame rate: And likewi&longs;e, if &longs;uch a
Rain were univer&longs;all, over the whole Terre&longs;triall Globe, it
would nece&longs;&longs;arily, in the &longs;pace of an hour, make a ri
&longs;ing of two, or three braces round about the &longs;aid Globe,
And becau&longs;e we have from Sacred Records, that in the
time of the Deluge, it rained fourty dayes and fourty nights;
namely, for the &longs;pace of 960 houres; its clear, that if the &longs;aid
Rain had been ten times bigger than ours at
of the Waters above the Terre&longs;trial Globe would reach and pa&longs;s
a mile higher than the tops of the Hills and Mountains that are
upon the &longs;uperficies of the Earth; and they al&longs;o would concur
to increa&longs;e the ri&longs;e. And therefore I conclude, that the ri&longs;e of
the Waters of the Deluge have a rational congruity with natural
Di&longs;cour&longs;es, of which I know very well that the eternal truths of
the Divine leaves have no need; but however I think &longs;o clear an
agreement is worthy of our con&longs;ideration, which gives us occa
&longs;ion to adore and admire the greatne&longs;&longs;e of God in his mighty
Works, in that we are &longs;ometimes able, in &longs;ome &longs;ort, to mea&longs;ure
them by the &longs;hort Standard of our Rea&longs;on.
Many Le&longs;&longs;ons al&longs;o may be deduced from the &longs;ame Doctrine,
which I pa&longs;&longs;e by, for that every man of him&longs;elf may ea&longs;ily know
them, having once &longs;tabli&longs;hed this Maxime; That it is not po&longs;&longs;i
ble to pronounce any thing, of a certainty, touching the quantity
of Running Waters, by con&longs;idering only the &longs;ingle vulgar mea
&longs;ure of the Water wichout the velocity; and &longs;o on the contrary,
he that computes only the velocity, without the mea&longs;ure, &longs;hall
commit very great errours; for treating of the mea&longs;ure of Run
ning Waters, it is nece&longs;&longs;ary, the water being a body, in handling
its quantity, to con&longs;ider in it all the three dimen&longs;ions of breadth,
depth, and length: the two fir&longs;t dimen&longs;ions are ob&longs;erved by all
in the common manner, and ordinary way of mea&longs;uring Running
Waters; but the third dimen&longs;ion of length is omitted; and hap
ly &longs;uch an over&longs;ight is committed, by rea&longs;on the length of Run
&longs;eth to move away, and as infinite is judged incomprehen&longs;ible;
and &longs;uch as that there is no exact knowledge to be had thereof;
& &longs;o there comes to be no account made thereof; but if we &longs;hould
make &longs;trict reflection upon our con&longs;ideration of the velocity of
Water, we &longs;hould find, that keeping account of the &longs;ame, there
is a reckoning al&longs;o made of the length; fora&longs;much as whil&longs;t we
&longs;ay, the Water of &longs;uch a Spring runs with the velocity of pa&longs;&longs;ing
a thou&longs;and or two thou&longs;and paces an hour: this in &longs;ub&longs;tance is
no other than if we had &longs;aid, &longs;uch a Fountain di&longs;chargeth in an
hour a Water of a thou&longs;and or two thou&longs;and paces long. So
that, albeit the total length of Running water be incomprehen
&longs;ible, as being infinite, yet neverthele&longs;&longs;e its rendered intelligible
by parts in its velocity. And &longs;o much &longs;ufficeth to have hinted
about this matter, hoping to impart on &longs;ome other occa&longs;ion other
more accurate Ob&longs;ervations in this affair.
GEOMETRICAL
DEMONSTRATIONS
OF THE
MEASURE
OF
Running Waters.
BY
D. BENEDETTO CASTELLI,
Abbot of CASSINA, and Mathematician to
P.
DEDICATED
DON THADDEO BARBERINI,
PRINCE OF
PALESTRINA,
AND
GENERAL of the HOLY CHURCH.
Printed
OF THE
MENSURATION
OF
Running Waters.
SUPPOSITION I.
Let it be &longs;uppo&longs;ed, that the banks of the Rivers of which
we &longs;peak be erected perpendicular to the plane of the up
per &longs;uperficies of the River.
SUPPOSITION II.
We &longs;uppo&longs;e that the plane of the bottome of the River, of
which we &longs;peak is at right angles with the banks.
SUPPOSITION III.
It is to be &longs;uppo&longs;ed, that we &longs;peak of Rivers, when they are at
ebbe, in that &longs;tate of &longs;hallowne&longs;&longs;e, or at flowing in that &longs;tate
of deepne&longs;&longs;e, and not in their tran&longs;ition from the ebbe to the
flowing, or fr m the flowing to the ebbe.
FIRST.
If a River &longs;hall be cut by a Plane at right angles to the &longs;urface
of the water of the River, and to the banks of the River,
that &longs;ame dividing Plane we call the Section of the River; and
this Section, by the Suppo&longs;itions above, &longs;hall be a right angled
Parallelogram.
SECOND.
We call tho&longs;e Sections equally Swift, by which the water runs
with equal velocity; and more &longs;wift and le&longs;s &longs;wift that
Section of another, by which the water runs with greater or le&longs;&longs;e
velocity.
AXIOME I.
Sections equal, and equally &longs;wift, di&longs;charge equal quantities
of Water in equal times.
AXIOME II.
Sections equally &longs;wift, and that di&longs;charge equal quantity of
Water, in equal time, &longs;hall be equal.
AXIOME III.
Sections equal, and that di&longs;charge equal quantities of Water
in equal times, &longs;hall be equally &longs;wift.
AXIOME IV.
When Sections are unequal, but equally &longs;wift, the quanti
ty of the Water that pa&longs;&longs;eth through the fir&longs;t Section,
&longs;hall have the &longs;ame proportion to the quantity that pa&longs;
&longs;eth through the Second, that the fir&longs;t Section hath to the &longs;econd
Section. Which is manife&longs;t, becau&longs;e the velocity being the
&longs;ame, the difference of the Water that pa&longs;&longs;eth &longs;hall be according
to the difference of the Sections.
AXIOME V.
If the Sections &longs;hall be equal, and of unequal velocity, the
quantity of the Water that pa&longs;&longs;eth through the fir&longs;t, &longs;hall
have the &longs;ame proportion to that which pa&longs;&longs;eth through the
&longs;econd, that the velocity of the fir&longs;t Section, &longs;hall have to the
velocity of the &longs;econd Section. Which al&longs;o is manife&longs;t, becau&longs;e
the Sections being equal, the difference of the Water which
pa&longs;&longs;eth, dependeth on the velocity.
A Section of a River being given, we may &longs;uppo&longs;e another
equal to the given, of different breadth, heigth, and ve
locity.
PROPOSITION I.
tities of Water in equal times, although the Secti
ons them&longs;elves he unequal.
Let the two Sections be A and B, in the River C, running
from A, towards B; I &longs;ay, that they di&longs;charge equal quan
tity of Water in equal times; for if greater quantity of Wa
ter &longs;hould pa&longs;s through A, than pa&longs;&longs;eth through B, it would
follow that the Water in the intermediate &longs;pace of the River C,
would increa&longs;e continually, which is manife&longs;tly fal&longs;e, but if
more Water &longs;hould i&longs;&longs;ue through the Section B, than entreth at
the Section A, the Water in the intermediate &longs;pace C, would
grow continually le&longs;s, and alwaies ebb, which is likewi&longs;e fal&longs;e;
therefore the quantity of Water that pa&longs;&longs;eth through the Secti
on B, is equal to the quantity of Water which pa&longs;&longs;eth through
the Section A, and therefore the Sections of the &longs;ame River di&longs;
charge,
PROPOSITION II.
which pa&longs;&longs;eth by one Section, is to that which pa&longs;
&longs;eth by the &longs;econd, in a Proportion compounded of
the proportions of the fir&longs;t Section to the &longs;econd, and
of the velocitie through the first, to the velocitie
of the &longs;econd.
I Et A, and B be two Sections of a River; I &longs;ay, that the
quantity of Water which pa&longs;&longs;eth through A, is to that which
pa&longs;&longs;eth through B, in a proportion compounded of the pro
portions of the fir&longs;t Section A, to the Section B; and of the velo
city through A, to the velocity through B: Let a Section be
equal to the Section B, and let it be G, and as the Section A is
to the Section B, &longs;o let the line F be to the line D; and as the
velocity A, is to the velocity by B, &longs;o let the line D be to the
line R: Therefore the Water which pa&longs;&longs;eth thorow A, &longs;hall be
to that which pa&longs;&longs;eth through G (in regard the Sections A and
G are of equal bigne&longs;s, but of unequal velocity) as the velocity
through A, to the velocity through G; But as the velocity
through A, is to the velocity through G, &longs;o is the velocity through
A, to the velocity through B; namely, as the line D, to the
line R: therefore the quantity of the Water which pa&longs;&longs;e the
through A, &longs;hall be to the quantity which pa&longs;&longs;eth through G, as
the line D is to the line R; but the quantity which pa&longs;&longs;eth
through G, is to that which pa&longs;&longs;eth through B, (in regard the
Sections G, and B, are equally &longs;wift) as the Section G to the Se
ction B; that is, as the Section A, to the Section B; that is, as
the line F, to the line D: Therefore by the equal and perturbed
proportionality, the quantity of the Water which pa&longs;&longs;eth through
A, hath the &longs;ame proportion to that which pa&longs;&longs;eth through B,
that the line F hath to the line R; but F to R, hath a proportion
compounded of the proportions of F to D, and of D to R; that
is, of the Section A to the Section B; and of the velocity through
A, to the velocity through B. Therefore al&longs;o the quantity of
Water which pa&longs;&longs;eth through the Section A, &longs;hall have a propor
tion to that which pa&longs;&longs;eth through the Section B, compounded of
the proportions of the Section A, to the Section B; and of
the velocity through A, to the velocity through B: And
therefore in two Sections of Rivers, the quantity of Water which
pa&longs;&longs;eth by the fir&longs;t,
The &longs;ame followeth, though the quantity of the Water which
pa&longs;&longs;eth through the Section A, be equal to the quantity of
Water which pa&longs;&longs;eth through the Section B, as is manife&longs;t by the
&longs;ame demon&longs;tration.
PROPOSITION III.
quantities of Water in equal times, the Sections
have to one another, reciprocal proportion to their
velocitie.
Let the two unequal Sections, by which pa&longs;s equal quantities
of Water in equal times be A, the greater; and B, the le&longs;&longs;er:
I &longs;ay, that the Section A, &longs;hall have the &longs;ame Proportion
to the Section B, that reciprocally the velocity through B, hath to
the velocity through A; for &longs;uppo&longs;ing that as the Water that
pa&longs;&longs;eth through A, is to that which pa&longs;&longs;eth through B, &longs;o is the
line E to the line F: therefore the quantity of water which pa&longs;
&longs;eth through A, being equal to that which pa&longs;&longs;eth through B,
the line E &longs;hall al&longs;o be equal to the line F: Suppo&longs;ing moreover,
That as the Section A, is to the Section B, &longs;o is the line F, to the
line G; and becau&longs;e the quantity of water which pa&longs;&longs;eth
through the Section A, is to that which pa&longs;&longs;eth through the
Section B, in a proportion compo&longs;ed of the proportions of the
Section A, to the Section B, and of the velocity through A, to the
velocity through B; therefore the line E, &longs;hall be the line to F, in
a proportion compounded of the &longs;ame proportions; namely, of
the proportion of the Section A, to the Section B, and of the ve
locity through A, to the velocity through B; but the line E, hath
to the line G, the proportion of the Section A, to the Section B,
therefore the proportion remaining of the line G, to the line F,
&longs;hall be the proportion of the velocity through A, to the velocity
through B; therefore al&longs;o the line G, &longs;hall be to the line E, as
the velocity by A, to the velocity by B: And conver&longs;ly, the ve
locity through B, &longs;hall be to the velocity through A, as the line
E, to the line G; that is to &longs;ay, as the Section A, to the Section B,
and therefore in two Sections, &c. which was to be demon&longs;trated.
Hence it is manife&longs;t, that Sections of the &longs;ame River (which
are no other than the vulgar mea&longs;ures of the River) have
betwixt them&longs;elves reciprocal proportions to their veloci
ties; for in the fir&longs;t Propo&longs;ition we have demon&longs;trated that the
Sections of the &longs;ame River, di&longs;charge equal quantities of Water
in equal times; therefore, by what hath now been demon&longs;trated
the Sections of the &longs;ame River &longs;hall have reciprocal proportion
to their velocities; And therefore the &longs;ame running water chan
geth mea&longs;ure, when it changeth velocity; namely, increa&longs;eth the
mea&longs;ure, when it decrea&longs;eth the velocity, and decrea&longs;eth the
mea&longs;ure, when it increa&longs;eth the velocity.
On which principally depends all that which hath been &longs;aid
above in the
pendixes
heeded.
PROPOSITION IV.
fir&longs;t in its own Chanel &longs;hall be to the height that it
&longs;hall make in the &longs;econd Chanel, in a proportion
compounded of the proportions of the breadth of
the Chanel of the &longs;econd, to the breadth of the
Chanel of the fir&longs;t, and of the velocitie acquired in
the Chanel of the &longs;econd, to that which it had in
its proper and first Chanel.
Let the River A B, who&longs;e height is A C, and breadth C B,
that is, who&longs;e Section is A C B; let it enter, I &longs;ay, into a
nother River as broad as the line E F, and let it therein make
the ri&longs;e or height D E, that is to &longs;ay, let it have its Section in
the River whereinto it falls D E F; I &longs;ay, that the height A C
hath to the height D E the proportion compounded of the pro
portions of the breadth E F, to the breadth C B, and of the ve
locity through D F, to the velocity through A B. Let us &longs;up
po&longs;e the Section G, equal in velocity to the Section A B, and in
breadth equal to E F, which carrieth a quantity of Water e
qual to that which the Section A B carrieth, in equal times,
and con&longs;equently, equal to that which D F carrieth. Moreover,
as the breadth E F is to the breadth C B, &longs;o let the line H be to
&longs;o let the line I be to the line L; becau&longs;e therefore the two
Sections A B and G are equally &longs;wift, and di&longs;charge equal quan
tity of Water in equal times, they &longs;hall be equal Sections; and
therefore the height of A
breadth of G, to the breadth of A
that is, as the line H to the line I: but becau&longs;e the Water which
pa&longs;&longs;eth through G, is equal to that which pa&longs;&longs;eth through D E F,
therefore the Section G, to the Section D E F, &longs;hall have the re
ciprocal proportion of the velocity through D E F, to the velo
city through G; but al&longs;o the height of G, is to the height D E,
as the Section G, to the Section D E F: Therefore the height of
G, is to the height D E, as the velocity through D E F, is to the
velocity through G; that is, as the velocity through D E F, is to
the velocity through A
line L; Therefore, by equal proportion, the height of
is, A C, &longs;hall be to the height D E; as H to L, that is, com
pounded of the proportions of the breadth E F, to the breadth
C
A which was
to be demon&longs;trated.
PROPOSITION V.
in a certain time; and after that there come into it
a Flood, the quantity of Water which is di&longs;char
ged in as much time at the Flood, is to that which
was di&longs;charged before, whil&longs;t the River was low,
in a proportion compounded of the proportions of
the velocity of the Flood, to the velocity of the first
Water, and of the height of the Flood, to the
height of the first Water.
Suppo&longs;e a River, which whil&longs;t it is low, runs by the Section
AF; and after a Flood cometh into the &longs;ame, and runneth
through the Section D F, I &longs;ay, that the quantity of the Wa
ter which is di&longs;charged through D F, is to that which is di&longs;charged
through A F, in a proportion compounded of the proportions of
the velocity through D F, to the velocity through A F, and of
the height D
is to the velocity through A F, &longs;o let the line R, to the line S;
and as the height D
the line T; and let us &longs;uppo&longs;e a Section L M N, equal to D F
in height and breadth; that is L M equal to D
to
fore the quantity of Water which runneth through D F, &longs;hall be
to that which runneth through LN, as the velocity through DF,
is to the velocity through L N, that is, to the velocity through
D
runneth through D
have the proportion of R to S; but the quantity which runneth
through L N, to that which runneth through
the Section A F; that is, as D B, to A B; that is as the line S, to
the line T: Therefore by equal proportion, the quantity of the
water which runneth through D F, &longs;hall be in proportion to that
which runneth through A F, as R is to T; that is, compounded of
the proportions of the height D B, to the height A B, and of the
velocity through
if a River di&longs;charge a certain quantity,
mon&longs;trated.
ANNOTATION.
The &longs;ame might have been demon&longs;trated by the &longs;econd
Propo&longs;ition above demon&longs;trated, as is manife&longs;t.
PROPOSITION VI.
River at divers times, the heights made in the Ri
ver by the Torrent, &longs;hall have between them
&longs;elves the reciprocal proportion of the velocities
acquired in the River.
Let A and B, be two equal &longs;treams of the &longs;ame Torrent,
which falling into a River at divers times, make the heights
C D, and F G; that is the &longs;tream A, maketh the height
C D, and the &longs;tream B, maketh the height F G; that is, Let
their Sections in the River, into which they are fallen, be C E,
and FH; I &longs;ay, that the height C D, &longs;hall be to the height F G,
in reciprocal proportion, as the velocity through F H, to the ve
locity through C E; for the quantity of water which pa&longs;&longs;eth
through A, being equal to the quantity which pa&longs;&longs;eth through B,
in equal times; al&longs;o the quantity which pa&longs;&longs;eth through C E, &longs;hall
be equal to that which pa&longs;&longs;eth through F H: And therefore the
proportion that the Section C E, hath to the Section F H; &longs;hall
be the &longs;ame that the velocity through F H, hath to the velocity
through C E; But the Section C E, is to the Section F H, as
C D, to F G, by rea&longs;on they are of the &longs;ame breadth: Therefore
C D, &longs;hall be to F G, in reciprocal proportion, as the velocity
through F H, is to the velocity through C E, and therefore if two
equal &longs;treams of the &longs;ame Torrent,
mon&longs;trated.
OF THE
MENSURATION
OF
Running Waters.
Having, in the clo&longs;e of my Treati&longs;e of the
Men&longs;uration of Running Waters promi&longs;ed
to declare upon another occa&longs;ion other par
ticulars more ob&longs;cure, and of very great
concern upon the &longs;ame argumement: I now
do perform my promi&longs;e on the occa&longs;ion
that I had the pa&longs;t year 1641. to propound
my thoughts touching the &longs;tate of the Lake
of
concernment of that mo&longs;t noble and mo&longs;t admirable City; and
indeed of all
truly &longs;ay of all the whole World. And being to proceed according
to the method nece&longs;&longs;ary in Sciences, I wil propo&longs;e, in the fir&longs;t place
certain Definitions of tho&longs;e Terms whereof we are to make u&longs;e
in our Di&longs;cour&longs;e: and then, laying down certain Principles we
will demon&longs;trate &longs;ome Problemes and Theoremes nece&longs;&longs;ary for
the under&longs;tanding of tho&longs;e things which we are to deliver; and
moreover, recounting &longs;undry ca&longs;es that have happened, we will
prove by practice, of what utility this contemplation of the
Mea&longs;ure of Running Waters is in the more important affairs both
Publique and Private.
DEFINITION I.
Two Rivers are &longs;aid to move with equal velocity, when in e
qual times they pa&longs;&longs;e &longs;paces of equal length.
DEFINITION II.
Rivers are &longs;aid to move with like velocity, when their propor
tional parts do move alike, that is, the upper parts alike to
the upper, and the lower to the lower; &longs;o that if the upper
part of one River &longs;hall be more &longs;wift than the upper part of ano
ther; then al&longs;o the lower part of the former &longs;hall be more &longs;wift
than the part corre&longs;pondent to it in the &longs;econd, proportionally.
DEFINITON III.
To mea&longs;ure a River, or running Water, is in our &longs;en&longs;e to finde
out how many determinate mea&longs;ures, or weights of Water
in a given time pa&longs;&longs;eth through the River, or Channel of the
Water that is to be mea&longs;ured.
DEFINITION IV.
If a Machine be made either of Brick, or of Stone, or of
Wood, &longs;o compo&longs;ed that two &longs;ides of the &longs;aid Machine be
placed at right angles upon the ends of a third &longs;ide, that is
&longs;uppo&longs;ed to be placed in the bottom of a River, parallel to the
Horizon, in &longs;uch a manner, that all the water which runneth
through the &longs;aid River, pa&longs;&longs;eth thorow the &longs;aid Machine: And
if all the water coming to be diverted
that runneth through the &longs;aid River, the
upper &longs;uperficies of that third &longs;ide placed
in the bottom do remain uncovered
and dry, and that the dead water be not
above it; This &longs;ame Machine &longs;hall be
called by us ^{*} REGULATOR: And that third &longs;ide of the
Machine which &longs;tandeth Horizontally is called the bottom of
the Regulator; and the other two &longs;ides, are called the banks of
the Regulator; as is &longs;een in this fir&longs;t Figure: A B C D, &longs;hall be
the Regulator; B C the bottom; and the other two &longs;ides A B,
and C D are its banks.
DEFINITION V.
By the quick height, we mean the Perpendicular from the upper
&longs;uperficies of the River, unto the upper &longs;uperficies of the bot
tom of the Regulator; as in the foregoing Figure the line. G H.
DEFINITION VI.
If the water of a
&longs;ides of a Regulator, that Rightangled Parallelogram compre
hended between the banks of the Regulator, and the bottom,
and the &longs;uperficies of the Water is called a Section of the
River.
ANNOTATION.
Here it is to be noted, that the River it &longs;elf may have &longs;undry
and divers heights, in &longs;everal parts of its Chanel, by rea&longs;on of
the various velocities of the water, and its mea&longs;ures; as hath
been demon&longs;trated in the fir&longs;t book.
SUPPOSITION I.
It is &longs;uppo&longs;ed, that the Rivers equal in breadth, and quick
height, that have the &longs;ame inclination of bed or bottom, ought
al&longs;o to have equal velocities, the accidental impediments being
removed that are di&longs;per&longs;ed throughout the cour&longs;e of the water,
and ab&longs;tracting al&longs;o from the external windes, which may velo
citate, and retard the cour&longs;e of the water of the River.
SUPPOSITION II.
Let us &longs;uppo&longs;e al&longs;o, that if there be two Rivers that are in
their beds of equal length, and of the &longs;ame inclination, but of
quick heights unequal, they ought to move with like velocity,
according to the &longs;en&longs;e explained in the &longs;econd definition.
SUPPOSITION III.
Becau&longs;e it will often be requi&longs;ite to mea&longs;ure the time exactly
in the following Problems, we take that to be an excellent
way to mea&longs;ure the time, which was &longs;hewed me many years &longs;ince
by
A &longs;tring is to be taken three Roman feet long, to the end of
which a Bullet of Lead is to be hanged, of about two or three
ounces; and holding it by the other end, the Plummet is to be
removed from its perpendicularity a Palm, more or le&longs;s, and then
let go, which will make many &longs;wings to and again, pa&longs;&longs;ing and
repa&longs;&longs;ing the Perpendicular, before that it &longs;tay in the &longs;ame: Now
it being required to mea&longs;ure the time that is &longs;pent in any what
&longs;oever operation, tho&longs;e vibrations are to be numbred, that are
made whil&longs;t the work la&longs;teth; and they &longs;hall be &longs;o many &longs;econd
minutes of an hour, if &longs;o be, that the &longs;tring be three Roman feet
long, but in &longs;horter &longs;trings, the vibrations are more frequent, and
in longer, le&longs;s frequent; and all this &longs;till followeth, whether the
Plummet be little or much removed from its Perpendicularity, or
whether the weight of the Lead be greater or le&longs;&longs;er.
The&longs;e things being pre-&longs;uppo&longs;ed, we will lay down &longs;ome fa
que&longs;tions more &longs;ubtil and curious; which will al&longs;o prove profi
table, and not to be &longs;leighted in this bu&longs;ine&longs;s of Waters.
PROPOSITION I. PROBLEME I.
of which pa&longs;sing through a Regulator, is three
Palms; and the height one Palm, little more or
le&longs;s, to mea&longs;ure what water pa&longs;&longs;eth through the
Regulator in a time given.
Fir&longs;t, we are to dam up the Chanel; &longs;o that there pa&longs;s not any
water below the Dam; then we mu&longs;t place in the &longs;ide of the
Chanel, in the parts above the Regulator three, or four, or five
Bent-pipes, or Syphons, according to the quantity of the water
that runneth along the Chanel; in &longs;uch &longs;ort, as that they may
drink up, or draw out of the Chanel all the water that the Cha
nel beareth (and then &longs;hall we know that the Syphons drink up
all the water, when we &longs;ee that the water at the Dam doth nei
ther ri&longs;e higher, nor abate, but alwaies keepeth in the &longs;ame Le
vel.) The&longs;e things being prepared, taking the In&longs;trument to
mea&longs;ure the time, we will examine the quantity of the water that
i&longs;&longs;ueth by one of tho&longs;e Syphons in the &longs;pace of twenty vibrations,
and the like will we do one by one with the other Syphons; and
then collecting the whole &longs;umme, we will &longs;ay, that &longs;o much is
the water that pa&longs;&longs;eth and runneth thorow the Regulator or
Chanel (the Dam being taken away) in the &longs;pace of twenty &longs;e
cond minutes of an hour; and calculating, we may ea&longs;ily reduce
it to hours, dayes, months, and years: And it hath fallen to my
turn to mea&longs;ure this way the waters of Mills and Fountains, and I
have been well a&longs;&longs;ured of its exactne&longs;s, by often repeating the
&longs;ame work.
CONSIDERATION.
And this method mu&longs;t be made u&longs;e of in mea&longs;uring the waters,
that we are to bring into Conducts, and carry into Cities
and Ca&longs;tles, for Fountains; and that we may be able afterwards
to divide and &longs;hare them to particular per&longs;ons ju&longs;tly; which will
prevent infinite &longs;uits and controver&longs;ies that every day happen in
the&longs;e matters..
PROPOSITION II. THEOREM I.
through its Regulator, &longs;hall have a given quick
height, and afterwards by new water &longs;hall increa&longs;e
to be double, it &longs;hall al&longs;o increa&longs;e double in ve
locitie.
Let the quick height of a River in the Regulator A B C D,
be the perpendicular F B, and afterwards, by new water that
is added to the River, let the water be &longs;uppo&longs;ed to be rai&longs;
ed to G, &longs;o that G B may be double to E B. I &longs;ay, that all the
water G C &longs;hall be double in velocity to
that of E C: For the water G F, having
for its bed the bottom E F, equally in
clined as the bed B C, and its quick
height G E being equal to the quick
height E C, and having the &longs;ame breadth
B C, it &longs;hall have of it &longs;elf a velocity e
qual to the velocity of the fir&longs;t water
F C: but becau&longs;e, be&longs;ides its own moti
on, which is imparted to it by the motion of the water E C, it
hath al&longs;o over and above its own motion, the motion of E C. And
becau&longs;e the two waters G C, and E C, are alike in velocity, by
the third Suppo&longs;ition; therefore the whole water G C &longs;hall be
double in velocity to the water E C; which was that which we
were to demon&longs;trate.
ving by &longs;everal letters to his friends confe&longs;&longs;ed him&longs;elf un&longs;atisfi
ed therewith; and that he intended not to publi&longs;h the
upon. But being overtaken by Death, he could not give the
fini&longs;hing touch either to this, or to the rest of the &longs;econd Book. In
con&longs;ideration of which, it &longs;eemed good to the Publi&longs;her of the
&longs;ame, rather to omit it, than to do any thing contrary to the mind of
the Authour. And this he hints, by way of adverti&longs;ement, to
tho&longs;e that have Manu&longs;cript Copies of this Book, with the &longs;aid de
mon&longs;tration. For this time let the Reader content him&longs;elf with
the knowledge of &longs;o ingenious and profitable a Conclu&longs;ion; of the
truth of which he may, with &longs;mall expence and much plea&longs;ure, be
a&longs;&longs;ured by means of the experiment to be made in the &longs;ame man
ner, with that which is laid down in the &longs;econd Corollary of
of annexed.
Hence it followeth, that when a River increa&longs;eth in quick
height by the addition of new water, it al&longs;o increa&longs;eth in ve
locity; &longs;o that the velocity hath the &longs;ame proportion to the velo
city that the quick height hath to the quick height; as may be
demon&longs;trated in the &longs;ame manner.
PROPOS. III. PROBLEME II.
twenty Palms, or thereabouts, and who&longs;e quick beight
is le&longs;s than five Palms, to mea&longs;ure the quantity of the
Water that runneth thorow the Chanel in a time
given.
Place in the Chanel a Regulator, and ob&longs;erve the quick
height in the &longs;aid 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, mea&longs;ure the
quantity of the water which pa&longs;&longs;eth thorow the &longs;aid Chanellet,
as hath been taught in the &longs;econd Propo&longs;ition; and at the &longs;ame
time ob&longs;erve exactly how much the quick height &longs;hall be abated
in the greater Chanel, by means of the diver&longs;ion of the Chancl
let; and all the&longs;e particulars being performed, multiply the quick
height of the greater Chanel into it &longs;elf, and likewi&longs;e multiply
into it &longs;elf the le&longs;&longs;er height of the &longs;aid bigger Chanel, and the
le&longs;&longs;er &longs;quare being taken, from the greater, the remainder &longs;hall
have the &longs;ame proportion to the whole greater &longs;quare, as the wa
ter of the Chanellet diverted, hath to the water of the bigger
Chanel: And becau&longs;e the water of the Chanellet is known by
the Method laid down in the fir&longs;t Theorem, and the terms of the
Theorem being al&longs;o known, the quantity of the water which run
neth thorow the bigger Chanel, &longs;hall be al&longs;o known by the Gol
den We
will explain the whole bu&longs;ine&longs;s by an example.
Let a Chanel be, for example, 15 Palms broad, its quick height
before its diver&longs;ion by the Chanellet &longs;hall be &longs;uppo&longs;ed to be 24
inches; but after the diver&longs;ion, let the quick height of the Chanel
be onely 22 inches. Therefore the greater height to the le&longs;&longs;er,
is as the number 11. to 12. But the &longs;quare of 11. is 121, and the
&longs;quare of 12. is 144, the difference between the &longs;aid le&longs;&longs;er
to the whole water, as 23. to 144: which is well near as 1 to
6 6/23: and that is the proportion that the quantity of the water
which runneth through the Chanellet &longs;hall have, to all the water
that runneth thorow the great Chanel. Now if we &longs;hould finde
by the Rule mentioned above in the fir&longs;t Propo&longs;ition, that the
quantity of the water that runneth through the Chanellet, is g.
an hour, it is manife&longs;t, that the water which runneth through the
great Chanel in the &longs;aid time of 35 min. &longs;ec.
&longs;hall be about 600
Barrels.
And becau&longs;e very often in applying the Theory to Practice
it happeneth, that all the nece&longs;&longs;ary particulars in the The
ory cannot &longs;o ea&longs;ily be put in execution; therefore we will
here add another way of performing the &longs;ame Problem, if it &longs;hould
chance to happen that the Chanellet could not commodiou&longs;ly be
diverted from the great Chanel, but that it were ea&longs;ier for the
water of another &longs;maller Chanel to be brought into the greater
Chanel; which water of the &longs;maller Chanel might be ea&longs;ily mea
&longs;ured, as hath been &longs;hewen in the fir&longs;t Probleme; or in ca&longs;e that
there did fall into a greater Chanel, a le&longs;&longs;er Chanel that might
be diverted and mea&longs;ured. Therefore I &longs;ay in the fir&longs;t ca&longs;e, If
we would mea&longs;ure the quantity of the water that runneth in a
certain time thorow the greater Chanel, into which another le&longs;&longs;er
Chanel that is mea&longs;urable may be brought, we mu&longs;t fir&longs;t exactly
mea&longs;ure the Chanellet, and then ob&longs;erve the quick height of the
greater Chanel, before the introduction of the le&longs;&longs;er; and having
brought in the &longs;aid Chanellet, we mu&longs;t agnin find the propor
tion that the water of the Chanellet hath to all the water of the
great Ghanel; for the&longs;e terms of the proportion being known, as
al&longs;o the quantity of the water of the Chanellet, we &longs;hall al&longs;o
come to know the quantity of the water that runneth thorow
the great Chanel. It is likewi&longs;e manife&longs;t, that we &longs;hall obtain
our intent, if the ca&longs;e were that there entered into the great
Chanel, another le&longs;&longs;er Chanel that was mea&longs;urable, and that
might be diverted.
CONSIDERATION.
It would be nece&longs;&longs;ary to make u&longs;e of this Doctrine in the di
&longs;tribution of the waters that are imploy'd to overflow the fields,
as is u&longs;ed in the
and differences ari&longs;e, which not being to be determined with in
telligible rea&longs;ons, come oftentimes to be decided, by force of
armes; and in&longs;tead of flowing their Grounds with Waters, they
cruelly flow them with the &longs;hedding of humane blood, impiou&longs;ly
inverting the cour&longs;e of Peace and Ju&longs;tice, &longs;owing &longs;uch di&longs;orders
and feuds, as that they are &longs;ometimes accompanied with the ru
ine of whole Cities, or el&longs;e unprofitably charge them with vain,
and &longs;ometimes prejudicial expences.
PROPOS. IV. THEOR. II.
Water which the River di&longs;chargeth after the in
crea&longs;e, hath the Proportion compounded of the
Proportions of the Quick height to the Quick
height, and of the velocity to the velocity.
Let there be a River, which whil&longs;t it is low, runneth thorow
the Regulator D F, with the Quick height A B, and after
wards let a Flood come; and then let it run with the height
D B, I &longs;ay, that the quantity of the Water that is di&longs;charged
through D F, to that which di&longs;chargeth through A F, hath the
proportion compounded of the proportions of the velocity
through D F to the velocity through A F, and of the height
D B to the height A B. As the velocity through D F is to the
velocity through A F, &longs;o let the line R be to the line S; and as
the height D B is to the height A B; &longs;o let the line S be to the
line T. And let a Section be &longs;uppo&longs;ed L M N equal to the
Section D F in height and length, but let it be in velocity equal
to the Section AF. Therefore the quantity of the Water that run
neth through D F to that which runneth through L N, &longs;hall be
the velocity through L N, that is, to the velocity through
therefore the quantity of Water which runneth through D
to that which pa&longs;&longs;eth through L N, &longs;hall have the proportion
that R hath to S; but the quantity of the Water that runneth
through L N, to that which runneth through
being equally &longs;wift) &longs;hall have the proportion that the Section
L N hath to the Section A F, that is, that the height
the height
proportion, the quantity of the Water which runneth by D F,
to that which runneth by A F, &longs;hall have the proportion of R to
T, that is, &longs;hall be compounded of the proportions of the height
D
the velocity through A F. And therefore if a River increa&longs;e in
quick height, the quantity of the Water that runneth after the
increa&longs;e, to that which runneth before the increa&longs;e, hath the
proportion compounded, &c. Which was to be demon&longs;trated.
Hence it followeth, that we having &longs;hewn, that the quantity of
the Water which runneth, whil&longs;t the River is high, to that
which ran, whil&longs;t it was low, hath the proportion compounded
of the velocity to the velocity, and of the height to the height. And it having been demon&longs;trated, that the velocity to the velo
city is as the height to the height; it followeth, I &longs;ay, that the
quantity of the Water that runneth, whil&longs;t the River is high, to
that which runneth, whil&longs;t it is low, hath duplicate proportion of
the height to the height, that is, the proportion that the &longs;quares
of the heights have.
Vpon which things dependeth the rea&longs;on of that which I have
&longs;aid, in my &longs;econd Con&longs;ideration, that if by the diver&longs;ion of
5/9 of the Water that entereth by the Rivers into the Moor or
Fen, the Water be abated &longs;uch a mea&longs;ure, that &longs;ame &longs;hall be
only one third of its whole height; but moreover diverting the 4/9, it
&longs;hall abate two other thirds, a mo&longs;t principal point; and &longs;uch,
that its not having been well under&longs;tood, hath cau&longs;ed very great
di&longs;orders, and there would now, more than ever, follow extream
dammage, if one &longs;hould put in execution the diver&longs;ion of the
and other Rivers; and it is manife&longs;t, that in the &longs;ame manner,
wherewith it hath been demon&longs;trated, that the quantity of the
Water increa&longs;ing quadruple, the height would increa&longs;e onely
&longs;eth triple; &longs;o that, by adding to units all the odde numbers, ac
cording to their Series, the heights increa&longs;e according to the na
tural progre&longs;&longs;ion of all the numbers, from units. As for exam
ple, there pa&longs;&longs;ing thorow a Regulator &longs;uch a certain quantity of
Water in one time; adding three of tho&longs;e mea&longs;ures, the quick
height is two of tho&longs;e parts, which at fir&longs;t was one; and con
tinuing to adde five of tho&longs;e &longs;aid mea&longs;ures, the height is three of
tho&longs;e parts which at fir&longs;t were one; and thus adding &longs;even, and
then nine, and then 11. and then 13, &c. the heights &longs;hall be 4.
then 5, then 6. then 7, &c. And for the greater facility of the
Work, we have de&longs;cribed the following Table, of which we will
declare the u&longs;e: The Table is divided into three Series or Pro
gre&longs;&longs;ions of Numbers: the fir&longs;t Series containeth all the Num
bers in the Natural Progre&longs;&longs;ion, beginning at a Unit, and is called
the Series of the Heights; the &longs;econd containeth all the odde
numbers, beginning at an unit, and is called the Series of the
Additions: the third containeth all the &longs;quare numbers, begin
ning at an unit, and is called the Series of Quantity.
Fir&longs;t, if we &longs;uppo&longs;e the whole quick height of a River of Run
ning Water to be divided into any number of equal parts, at
plea&longs;ure, and would abate the &longs;ame one fift, by means of a divi
&longs;ron; let there be found in the Table in the Series of heights the
number 5. the denominator of the part which the River is to a
bate, and take the number that is immediately under it in the
row of Additions, which is 9. which let be &longs;ub&longs;tracted from the
number 25. placed underneath the &longs;ame in the row of Quanti
ties, the remainder 16. &longs;ignifieth that of the 25. parts of Water
that ran in the River, whil&longs;t it was 5 mea&longs;ures high, there do
onely run 16. parts; &longs;o that to make it abate 1/5 it is nece&longs;&longs;ary to
take 9/25 from the Water that the whole River did carry; &longs;o that
with &longs;ub&longs;tracting &longs;omewhat more than one third of the Water of
the River, it is abated but only one fift.
2. And thus, in the &longs;econd place, if on the contrary, one would
know how much water is to be added to the &longs;aid River to make
it increa&longs;e one fift more in height, &longs;o as that it may run in the
6 be found in the row of heights, and let the number 11. &longs;tand
ing under the &longs;ame be taken and added to the number 25.
that is placed under the number 9. in the Additions, and 5. in
the heights, and you &longs;hall have 36; which is the quantity of the
water that runneth with the height of the River, when it is high
6 of tho&longs;e parts, whereof it was before but 5.
3. But if it &longs;hould be de&longs;ired, to know how much water it is
requi&longs;ite to add to make the River ri&longs;e &longs;o, as that it may run in
height 8. of tho&longs;e parts of which before it ran but 5; one
ought to take the &longs;um of the number of the Series of Additions
&longs;tanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
and this &longs;hall be the &longs;umme that mu&longs;t be added to 25: So that
to make the River to run 8. of tho&longs;e parts in height, of which it
before did run 5, it will be nece&longs;&longs;ary to add 39. of tho&longs;e parts,
of which the River before was 25.
4. Likewi&longs;e the &longs;ame Table giveth the quantity of water
that runneth from time to time through a River, that increa&longs;eth
by the addition of new water to the &longs;ame in one of its heights, the
quantity of its water be known. As for example: If we knew that
the River in one minute of an hour di&longs;chargeth 2500. of tho&longs;e mea
&longs;ures of water, and runneth in height 5. parts in the Regulator, and
afterwards &longs;hould &longs;ee that it runneth 8 Palms high, finding in the
row of quantity the number placed under 8. which is 64. we would
&longs;ay that the River heightned, carrieth of water 64. of tho&longs;e parts
whereof it carried before but 25; and becau&longs;e before it carried
2500. mea&longs;ures, by the Golden Rule we will &longs;ay, that the River
carrieth 6400. of tho&longs;e mea&longs;ures, of which before it carried 2500.
In this progre&longs;s of Nature, is one thing really curious, and that
at fir&longs;t &longs;ight &longs;eemeth to be &longs;omewhat Paradoxal, that we pro
ceeding ordinately in the diver&longs;ions and additions, with additi
ons and diver&longs;ions &longs;o unequal, the abatings do notwith&longs;tanding
alwaies prove equal, and &longs;o do the ri&longs;ings: And who would ever
think that a River in height, g.
ing an hundred mea&longs;ures in a minute of an hour, is to abate but
one Palm, onely by the diver&longs;ion of 19. of tho&longs;e mea&longs;ures; and
then again, that the bui&longs;ine&longs;s cometh to that pa&longs;s, that it abateth
likewi&longs;e a Palm by the diver&longs;ion of three onely of tho&longs;e mea&longs;ures,
nay, by the diver&longs;ion of but one mea&longs;ure? and yet it is mo&longs;t
certain: And this truth meets with &longs;o manife&longs;t proofs in experi
ence, that it is very admirable! And for the full &longs;atisfaction of
tho&longs;e, who not being able to comprehend &longs;ubtil demon&longs;trati
ons, desire to be clearly inform'd by the matters of fact, and to
&longs;ee with their bobily eyes, and touch with their hands, what their
under&longs;tanding and rea&longs;on cannot reach unto: I will hear add
another very ea&longs;ie way to reduce all to an experiment, the
which I make u&longs;e frequently, to the admiration of &longs;uch as &longs;ee it.
I prepared an hundred Siphons, or, if you will, bowed Pipes,
all equal; and placed them at the brim of a Ve&longs;&longs;el, wherein the
water is kept at one and the &longs;ame level (whether all the Syphons
work, or but a certain number of them) the mouths by which
the water i&longs;&longs;ueth being all placed in the &longs;ame level, parallel to
the Horizon; but lower in level than the water in the Ve&longs;&longs;el; and
gathered all the water falling from the Syphons into another
Ve&longs;&longs;el &longs;tanding lower than the former, I made it to run away
thorow a Chanel, in &longs;uch manner inclined, that wanting water
from the Syphons, the &longs;aid Chanel remained quite dry.
And this done, I mea&longs;ured the quick height of the Chanel
with care, and afterwards divided it exactly into 10 equal parts,
and cau&longs;ing 19. of tho&longs;e Syphons to be taken away, &longs;o that the
Chanel did not run water, &longs;ave onely with 81 of tho&longs;e Syphons,
I again ob&longs;erved the quick height of the water in the &longs;ame &longs;ite
ob&longs;erved before, and found that its height was dimini&longs;hed pre
ci&longs;ely the tenth part of all its fir&longs;t height; and thus continuing to
take away 17. other Syphons, the height was likewi&longs;e dimini&longs;h
ed 1/1. of all its fir&longs;t quick height; and trying to take away 15.
Syphons, then 13, then 11, then 9, then 7, then 5, and then 3.
alwaies in the&longs;e diver&longs;ions, made in order as hath been &longs;aid, there
en&longs;ued &longs;till an abatement of 1/1. of the whole height.
And here was one thing worthy of ob&longs;ervation, that the water
encrea&longs;ing in [
rent in different &longs;ites of the Chanel, that is &longs;till le&longs;&longs;er, the more
one approached to the Out-let; notwith&longs;tanding which the abate
ment followed in all places proportionably, that is in all its &longs;ites
the fir&longs;t part of the height of that &longs;ite dimini&longs;hed: And more
over the water i&longs;&longs;ued from the Chanel, and dilated into a broader
cour&longs;e, from which likewi&longs;e having divers Out-lets and Mouths;
yet neverthele&longs;s in that breadth al&longs;o the quick heights &longs;ucce&longs;&longs;ive
ly varied and altered in the &longs;ame proportions. Nor did I here
de&longs;i&longs;t my ob&longs;ervation, but the water being dimini&longs;hed, that i&longs;&longs;u
ed from the Syphons, and there being but one of them left that
di&longs;charged water; I ob&longs;erved the quick height that it made in the
above-&longs;aid &longs;ites, (the which was likewi&longs;e 1/1. of all the fir&longs;t height)
there being added to the water of that Syphon, the water of
three other Syphons; &longs;o that all the water was of 4 Syphons,
and con&longs;equently quadruple to the fir&longs;t Syphon; but the quick
height was onely double, and adding five Siphons, the quick
height became triple, and with adding &longs;even Syphons, the height
increa&longs;ed quadruple; and &longs;o by adding of 9. it increa&longs;ed quin
tuple, and by adding of 11. it increa&longs;ed &longs;extuple, and by ad
and by adding of 17. nonuple, and la&longs;tly by adding 19. Syphons;
&longs;o that all the water was centuple to the water of one Syphon,
yet neverthele&longs;s the quick height of all this water was onely de
cuple to the fir&longs;t height conjoyned by the water that i&longs;&longs;ued from
one onely Syphon.
For the more clear under&longs;tanding of all which, I have made
the following Figure; in which we have the mouth A, that
maintaineth the water of the Ve&longs;&longs;el B C in the &longs;ame level; though
it continually run; to the brim of the Ve&longs;&longs;el are put 25. Sy
phons (and there may be many more) divided into 5 Cla&longs;&longs;es,
D E F G H, and the fir&longs;t D, are of one onely Syphon; the &longs;econd
E, of three Syphons; the third F, of five; the fourth G, of 7; the
fifth H, of 9; and one may &longs;uppo&longs;e the &longs;ixth of 11, the &longs;eventh
of 13 Syphons, and &longs;o of the other Cla&longs;&longs;es, all containing in con
&longs;equent odd numbers &longs;ucce&longs;&longs;ively (we are content to repre&longs;ent in
the Figure no more but the five forenamed Cla&longs;&longs;es to avoid con
fu&longs;ion) the gathered water D E F G H, which runneth thorow
the Chanel I K L, and falleth into the out-let M N O P; and &longs;o
much &longs;ufficeth for the explanation of this experiment.
PROPOS. V. PROB. III.
quantity of the Water that runneth thorow the River
in a time a&longs;&longs;igned.
By what we have &longs;aid already in the two preceding Pro
blems, we may al&longs;o re&longs;olve this that we have now before
us; and it is done, by diverting in the fir&longs;t place from the
great River a good big mea&longs;urable Chanel, as is taught in the
&longs;econd Probleme, and ob&longs;erving the abatement of the River,
cau&longs;ed by the diver&longs;ion of the Chanel; and finding the proporti
on that the Water of the Chanel hath to that of the River, then
let the Water of the Chanel be mea&longs;ured by the &longs;econd Pro
bleme, and work as above, and you &longs;hall have your de&longs;ire.
CONSIDERATION. I.
And although it &longs;eemeth as if it might prove difficult, and
almo&longs;t impo&longs;&longs;ible to make u&longs;e of the Regulator number, if
one be about to mea&longs;ure the water of &longs;ome great River,
and con&longs;equently would be impo&longs;&longs;ible, or at lea&longs;t very difficult
to reduce the Theory of the fir&longs;t Probleme into practice: Yet ne
verthele&longs;s, I could &longs;ay that &longs;uch great conceits of mea&longs;uring the
water of a great River, are not to come into the minds of any
but great Per&longs;onages, and potent Princes; of whom it is expected
for their extraordinary concerns, that they will make the&longs;e kinde
of enquiries; as if here in
Velino, Chiana, Arno, Serchio, Adice,
ly difficult to apply the
height of the
it would turn to account to be at &longs;ome charge, to come to the
exact and true knowledge of the quantity of water which that
bur&longs;ments might afterwards be avoided, that would oft times be
made in vain; and prevent the di&longs;gu&longs;ts, which &longs;ometimes happen
among&longs;t Princes: Upon this ground I think it will be well to
&longs;hew al&longs;o the way how to make u&longs;e of the
great
with good ones, and tho&longs;e made without great co&longs;t or labour,
which will &longs;erve our turn.
For upon &longs;uch like
Mills, or the like. Now in the&longs;e Ca&longs;es it is &longs;ufficient, that one
erect upon the two extreames of the Weare two Pila&longs;ters either
of Wood or Brick, which with the bottome of the Weare do
compo&longs;e our Regulator, wherewith we may make our de&longs;ired
operation, yea the Chanel it &longs;elf diverted &longs;hall &longs;erve, without
making any other diver&longs;ion or union. And in brief, if the bu
fine&longs;&longs;es be but managed by a judicious per&longs;on, there may wayes
and helps be made u&longs;e of, according to occa&longs;ion, of which it
would be too tedious to &longs;peak, and therefore this little that hath
been hinted &longs;hall &longs;u&longs;&longs;ice.
CONSIDERATION II.
From what hath been declared, if it &longs;hall be well under
&longs;tood, may be deduced many benefits and conveniences,
not onely in dividing of Running Waters for infinite u&longs;es
that they are put to in turning of Corne-Mills, Paper-Mills,
Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw
ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills,
and &longs;uch other Machines; but al&longs;o in ordering Navigable Cha
nels, diverting Rivers and Chanels of Waters, or terminating
and limiting the &longs;izes of Pipes for Fountains: In all which af
fairs there are great errours committed, to the lo&longs;&longs;e of much
expence, the Chanels and Pipes that are made, &longs;ometimes not
being &longs;ufficient to carry the de&longs;igned Waters, and &longs;ometimes they
are made bigger than is nece&longs;&longs;ary; which di&longs;orders &longs;hall be
avoided, if the Engineer be advi&longs;ed of the things above&longs;aid: and
in ca&longs;e that to the&longs;e Notions there be added the knowledge of
Philo&longs;ophy and Mathematicks, agreeable to the &longs;ublime Di&longs;co
veries of
by
whole bu&longs;ine&longs;&longs;e of Motion, one &longs;hall then come to the know
ledge of particular notions of great curio&longs;ity in the Theoricks,
and of extraordinary benefit in the Practicks that daily occur in
the&longs;e bu&longs;ine&longs;&longs;es.
And to &longs;hew, in effect, of what utility the&longs;e Notions are, I
have thought fit to in&longs;ert, in this place, the Con&longs;iderations by
me made upon the Lake of
at large, by the experience of the la&longs;t year 1641. the mo&longs;t Se
rene Being
therefore at
mo&longs;t Illu&longs;trious and mo&longs;t Excellent
nuou&longs;ly deliver my opinion touching the &longs;tate of the Lake
of
ral times, in the end I had order to &longs;et down the whole
bu&longs;ine&longs;&longs;e in writing, who having afterwards read it privately,
the &longs;aid
mo&longs;t Serene PRINCE, and I received order to repre&longs;ent the
&longs;ame to the full
of
CONSIDER ATIONS
Concerning the
LAKE
OF
VENICE.
BY
D. BENEDETTO CASTELLI,
Abbot of S.
Pope
ROME.
Though the principal cau&longs;e be but one
onely, that in my judgment threatneth
irreparable ruine to the Lake of
now &longs;tands; Yet neverthele&longs;&longs;e, I think
that two Heads may be con&longs;idered. And this Con&longs;ideration may peradven
ture &longs;erve us for to facilitate and explain
the opportune remedies, though not to
render the &longs;tate of things ab&longs;olutely unchangeable and eternal:
an enterprize impo&longs;&longs;ible, and e&longs;pecially in that which having had
&longs;ome beginning, ought likewi&longs;e nece&longs;&longs;arily to have its end; or
at lea&longs;t to prevent the danger for many hundreds of years; and
po&longs;&longs;ibly it may, in the mean time, by the mutation it &longs;elf be
brought into a better condition.
I &longs;ay therefore, that the pre&longs;ent di&longs;order may be con&longs;idered
under two Heads; One is the very notable di&longs;covery of Land
that is ob&longs;erved at the time of low Water, the which, be&longs;ides
the ob&longs;tructing of Navigation in the Lake and al&longs;o in the
Chanels, doth likewi&longs;e threaten another mi&longs;chief and di&longs;order
drying up that mudde, e&longs;pecially in the times of hot Summers,
doth rai&longs;e thence the putrified and pernicious vapours, fogs, and
exhalations that infect the Air, and may render the City unha
bitable.
The &longs;econd Head is the great Stoppage that daily is grow
ing in the Ports, e&longs;pecially of
which matters I will hint certain general points, and then
will proceed to the more particular and important affairs.
And fir&longs;t, I &longs;ay, that I hold it altogether impo&longs;&longs;ible to effect
any thing, though never &longs;o profitable, which doth not bring with
it &longs;ome mi&longs;chief; and therefore the good and the hurt ought to
be very well weighed, and then the le&longs;&longs;e harmful part to be im
braced.
Secondly, I propo&longs;e to con&longs;ideration, that the &longs;o notable di&longs;
covery of Earth & Mud, hath not been long ob&longs;erved, as I under
&longs;tand, from old per&longs;ons that can remember pa&longs;&longs;ages for fifty
years pa&longs;t; which thing being true, as to me it &longs;eemeth mo&longs;t
true, it &longs;hould appear that it could not but be good to reduce
matters to that pa&longs;&longs;e that they were at formerly, (laying a&longs;ide
all affection or pa&longs;&longs;ion that &longs;elf-flattering minds have entertained
for their own conceits) or at lea&longs;t it &longs;hall be nece&longs;&longs;ary &longs;peedily to
con&longs;ult the whole.
Thirdly, I hold that it is nece&longs;&longs;ary to weigh, whether from the
fore&longs;aid di&longs;covery of Land, it followeth, that onely the Earth ri
&longs;eth, as it is commonly thought by all, without di&longs;pute; or whe
ther the Waters are abated and faln away; or el&longs;e whether it
proceedeth from both the one and other cau&longs;e. And here it would
be &longs;ea&longs;onable to enquire, what &longs;hare the &longs;aid cau&longs;es may have,
each con&longs;idered apart in the fore&longs;aid effect. For, in the fir&longs;t
ca&longs;e, if the Earth have been rai&longs;ed, it would be nece&longs;&longs;ary to
con&longs;ider of taking it down, and removing it: But if the Wa
ters have failed or abated, I believe that it would be extreamly ne
ce&longs;&longs;ary to re&longs;tore and rai&longs;e them: And if both the&longs;e rea&longs;ons have
con&longs;pired in this effect, it will be nece&longs;&longs;ary to remedy them each
apart. And I do, for my part, think, that the &longs;o notable appea
rance of Shelves at the time of low Water, proceeds principally
from the decrea&longs;e and abatement of the Waters, which may
confidently be affirmed to need no other proof, in regard that the
its Water into the Lake.
As to the other point of the great Stoppage of Ports, I hold,
that all proceedeth from the violence of the Sea, which being
&longs;ometimes di&longs;turbed by windes, e&longs;pecially at the time of the wa
ters flowing, doth continually rai&longs;e from its bottome immen&longs;e
into the Lake; it not having on its part any &longs;ttength of current
that may rai&longs;e and carry them away, they &longs;ink to the bottom, and
&longs;o they choke up the Ports. And that this effect happeneth in
this manner, we have mo&longs;t frequent experiences thereof along the
Sea-coa&longs;ts: And I have ob&longs;erved in
&longs;hores,
leth into the Sea, there is alwaies &longs;een in the Sea it &longs;elf, at the place
of the rivets out-let, the re&longs;emblance, as it were, of an half-Moon,
or a great &longs;helf of &longs;ettled &longs;and under water, much higher then the
re&longs;t of the &longs;hore, and it is called in
in
of the river, one while on the right &longs;ide, another while on the
left, and &longs;ometimes in the mid&longs;t, according as the Wind fits. And
a like effect I have ob&longs;erved in certain little Rillets of water,
along the Lake of
&longs;mall and great.
Now who&longs;o well con&longs;idereth this effect, plainly &longs;eeth that it
proceeds from no other, than from the contrariety of the &longs;tream
of the River, to the
great abundance of &longs;and which the Sea continually throws upon
the &longs;hore, cometh to be driven into the Sea by the &longs;tream of the
river; and in that place where tho&longs;e two impediments meet
with equal force, the &longs;and &longs;etleth under water, and thereupon is
made that &longs;ame Shelf or
water, and that any con&longs;iderable &longs;tore, it &longs;hall be thereby cut
and broken; one while in one place, and another while in ano
ther; as hath been &longs;aid, according as the Wind blows: And
through that Chanel it is that Ve&longs;&longs;els fall down into the Sea, and
again make to the river, as into a Port. But if the Water of
the river &longs;hall not be continual or &longs;hall be weak, in that ca&longs;e the
force of the Sea-Wind &longs;hall drive &longs;uch a quantity of &longs;and into
the mouth of the Port, and of the river, as &longs;hall wholly choak it
up. And hereupon there are &longs;een along the Sea-&longs;ide, very many
Lakes and Meers, which at certain times of the year abound with
waters, and the Lakes bear down that enclo&longs;ure, and run into
the Sea.
Now it is nece&longs;&longs;ary to make the like reflections on our Ports
of
&longs;en&longs;e are no other than Creeks, mouths, and openings of the &longs;hore
that parts the Lake from the main Sea; and therefore I hold that
if the Waters in the Lake were plentiful, they would have
&longs;trength to &longs;cowr the mouths of the Ports thorowly, & with great
force; but the Water in the Lake failing, the Sea will with
out any oppo&longs;al, bring &longs;uch a drift of &longs;and into the Ports; that if
unprofitable, and impo&longs;&longs;ible for Barks and great Ve&longs;&longs;els.
Many other con&longs;iderations might be propounded concerning
the&longs;e two heads of the &longs;toppage of the Ports, and of the appea
rance of the Ouze and Mud in the Lakes, but &longs;o much &longs;hall &longs;uf
fice us to have hinted, to make way for di&longs;cour&longs;ing of the opera
tions about the oportune remedies.
Yet before that I propound my opinion, I &longs;ay, That I know
very well that my propo&longs;al, at fir&longs;t &longs;ight, will &longs;eem ab&longs;urd and in
convenient; and therefore, as &longs;uch, will perhaps be rejected by
the mo&longs;t: and &longs;o much the rather, for that it will prove directly
contrary to what hath hitherto been, and as I hear, is intended to
be done. And I am not &longs;o wedded to my opinions, but that I
do con&longs;ider what others may judge thereof: But be it as it will,
I am obliged to &longs;peak my thoughts freely, and that being done,
I will leawe it to wi&longs;er men than my &longs;elf; when they &longs;hall have
well con&longs;idered my rea&longs;ons, to judge and deliberate of the
agendum:
mo&longs;t equitable and inexorable Tribunal of Nature, who not
caring in the lea&longs;t to plea&longs;e either one party or another, will be
alwaies a punctual and inviolable executrix of her eternal De
crees, again&longs;t which neither humane deliberations, nor our vain
de&longs;ires; &longs;hall ever have power to rebell. I added by word of
mouth that which followeth.
Though your Highne&longs;s intere&longs;t your &longs;elf in this Noble Col
ledge, and cau&longs;e it to be confirmed in the ^{*} Senate by univer&longs;al
Vote, that the Winds do not blow, that the Sea doth not fluctuate,
that the Rivers do not run; yet &longs;hall the Winds be alwaies deaf,
the Sea &longs;hall be con&longs;tant in its incon&longs;tancy, and the Rivers mo&longs;t
ob&longs;tinate: And the&longs;e &longs;hall be my Judges, and to their determi
nation I refer my &longs;elf.
particular Coun
cil, the Senators of
which have great
Authority.
By what hath been &longs;aid, in my opinion, that is made very clear
and manife&longs;t, which in the beginning of this di&longs;cour&longs;e I glanced
at; namely, That the whole di&longs;order, although it be divided into
two heads, into the di&longs;covery of the Mud, and of the &longs;toppage
Ports, yet neverthele&longs;s, by the application of one onely remedy,
and that in my e&longs;teem very ea&longs;ie, the whole &longs;hall be removed:
And this it is; That there be re&longs;tored into the Lake as much
Water as can be po&longs;&longs;ible, and in particular from the upper parts
of
po&longs;&longs;ible. And that this is the true and real remedy of the prece
dent di&longs;orders, is manife&longs;t: For in the pa&longs;&longs;age that this Water
&longs;hall make thorow the Lakes, it &longs;hall of it &longs;elf by degrees clear
the Chanels in &longs;undry parts of them, according to the currents
that it &longs;hall &longs;ucce&longs;&longs;ively acquire, and in this manner being di&longs;
and in the Chanels much higher, as I &longs;hall prove hereafter; a
thing that will make Navigation commodious; and that, which
moreover is of great moment in our bu&longs;ine&longs;&longs;e; tho&longs;e Shelves
of Mud which now di&longs;cover them&longs;elves at the time of Low
Waters &longs;hall be alwayes covered, &longs;o that the putrefaction of
the Air &longs;hall al&longs;o be remedied.
And la&longs;tly, this abundance of Water being alwayes to di&longs;
charge it &longs;elf into the Sea by the Ports, I do not doubt, but that
their bottomes will be &longs;coured. And that the&longs;e effects mu&longs;t fol
low, Nature her &longs;elf &longs;eemeth to per&longs;wade, there remaining onely
one great doubt, whether that abundance of Water that &longs;hall be
brought into the Lake may be really &longs;ufficient to make the Wa
ters ri&longs;e &longs;o much as to keep the Shelves covered, and to facilitate
Navigation, which ought to be at lea&longs;t half a ^{*} Brace, or there
abouts. And indeed it &longs;eemeth at fir&longs;t &longs;ight to be impo&longs;&longs;ible,
that the &longs;ole Water of the ^{*}
per&longs;ed over the &longs;ame, can occa&longs;ion &longs;o notable an height of water;
and the more to confirm the difficulties, one might &longs;ay, reducing
the rea&longs;on to calculation, that in ca&longs;e the
ces broad, and two and an half high, and the breadth of the
Lake were 20000. Braces, it would &longs;eem nece&longs;&longs;ary that the
height of the water of the
the Lake would be but onely 1/200 of a Brace in height, which is
imperceptible, and would be of no avail to our purpo&longs;e; nay
more, it being very certain that the
and foul, this would occa&longs;ion very great mi&longs;chief, filling and
contracting the Lake, and for that rea&longs;on this remedy ought, as
pernicious, to be totally excluded and condemned.
is 11/16 of our yard.
that name.
I here confe&longs;&longs;e that I am &longs;urprized at the forme of the Argu
ment, as if I were in a certain manner convinced, that I dare not
adventure to &longs;ay more, or open my mouth in this matter; but
the &longs;trength it &longs;elf of the Argument, as being founded upon
the means of Geometrical and Arithmetical Calculation, hath
opened me the way to di&longs;cover a very crafty fraud that is couch
ed in the &longs;ame Argument, which fraud I will make out to any
one that hath but any in&longs;ight in
And as it is impo&longs;&longs;ible, that &longs;uch an argument &longs;hould be produced
by any but &longs;uch as have ta&longs;ted of the&longs;e, in &longs;uch affairs, mo&longs;t pro
fitable, and mo&longs;t nece&longs;&longs;ary Sciences; &longs;o do not I pretend to make
my &longs;elf under&longs;tood, &longs;ave onely by &longs;uch, to whom I will evince
&longs;o clearly, as that more it cannot be de&longs;ired, the errour and fraud
wherein tho&longs;e Ancients and Moderns have been, and alwayes
are intangled, that have in any way yet handled this matter of
con&longs;idering the Mea&longs;ure and Quantity of the Waters that move.
about to &longs;ay touching this particular, that I am content that all
the re&longs;t of my Di&longs;cour&longs;e be rejected; provided, that that be per
fectly under&longs;tood, which I am hereafter to propo&longs;e, I holding
and knowing it to be a main Principle, upon which all that is
founded that can be &longs;aid either well or hand&longs;omely on this parti
cular. The other Di&longs;cour&longs;es may have an appearance of being
probable, but this hits the mark as full as can be de&longs;ired, arriving
at the highe&longs;t degree of certainty.
I have, &longs;eventeen years &longs;ince, as I repre&longs;ented to the mo&longs;t Se
rene Prince, and to the Right Honourable the Pre&longs;ident of the
Lords the Commi&longs;&longs;ioners of the ^{*}Sewers, written a Treati&longs;e of the
Mea&longs;ure of the waters that move, in which I Geometrically de
mon&longs;trate and declare this bu&longs;ine&longs;&longs;e, and they who &longs;hall have
well under&longs;tood the ground of my Di&longs;cour&longs;e, will re&longs;t fully &longs;a
tisfied with that which I am now about to propo&longs;e: But that all
may become rhe more ea&longs;ie, I will more briefly explicate and
declare &longs;o much thereof as I have demon&longs;trated in the Di&longs;cour&longs;e,
which will &longs;uffice for our purpo&longs;e: And if that &longs;hould not be
enough, we have alwayes the experiment of a very ea&longs;ie and
cheap way to clear up the whole bu&longs;ine&longs;&longs;e. And moreover I
will take the boldne&longs;&longs;e to affirm, that in ca&longs;e there &longs;hould not for
the pre&longs;ent any deliberation be made concerning this affair, ac
cording to my opinion; yet neverthele&longs;&longs;e it will be, at &longs;ome
time or other; or if it be not, things will grow wor&longs;e and
wor&longs;e.
Savii dell'
Acque,
lar Council that
take care of the
Lakes and other
Aquatick affairs.
For more clear under&longs;tanding, therefore, it ought to be known,
that it being required, as it is generally u&longs;ed, to mea&longs;ure the wa
ters of a River, its breadth and its depth is taken, and the&longs;e two
dimen&longs;ions being multiplied together, the product is affirmed to
be the quantity of that River: As for example, if a River &longs;hall
be 100. feet broad, and 20. feet high, it will be &longs;aid, that that
River is 2000 feet of Water, and &longs;o if a Ditch &longs;hall be 15. feet
broad, and 5. feet high, this &longs;ame Ditch will be affirmed to be
75. feet of Water: And this manner of mea&longs;uring Running
Water hath been u&longs;ed by the Ancients, and by Moderns, with
no other difference, &longs;ave onely that &longs;ome have made u&longs;e of the
Foot, others of the Palme, others of the Brace, and others of
other mea&longs;ures.
Now becau&longs;e that in ob&longs;erving the&longs;e Waters that move, I fre
quently found, that the &longs;ame Water of the &longs;ame River was in
&longs;ome &longs;ites of its Chanel pretty big, and in others much le&longs;&longs;e,
not arriving in &longs;ome places to the twentieth, nor to the hundreth
part of that which it is &longs;een to be in other places; therefore this
vulgar way of mea&longs;uring the Waters that move, for that they did
began de&longs;ervedly to be &longs;u&longs;pected by me, as difficult and defective,
being alwayes various, and the mea&longs;ure, on the contrary, being
to be alwayes determinate, and the &longs;ame; it is therefore written,
that
nabile e&longs;t apud Deum,I con&longs;idered that in the Terri
tory of
Waters are divided to overflow the Grounds, by the like way of
mea&longs;uring them, there were committed grievous and mo&longs;t impor
tant errours, to the great prejudice of the Publique and of Pri
vate per&longs;ons, neither they that &longs;ell, nor they that buy under
&longs;tanding the true quantity of that which is &longs;old and bought: In
regard that the &longs;ame &longs;quare mea&longs;ure, as is accu&longs;tomed in tho&longs;e
parts, a&longs;&longs;igned one particular per&longs;on, carried to &longs;ometimes above
twice or thrice as much water, as did the &longs;ame &longs;quare mea&longs;ure a&longs;
&longs;igned to another. Which thing proveth to be the &longs;ame incon
venience, as if the mea&longs;ure wherewith Wine and Oil is bought
and &longs;old, &longs;hould hold twice or thrice as much Wine or Oil at one
time as at another. Now this Con&longs;ideration invited my minde
and curio&longs;ity to the finding out of the true mea&longs;ure of Running
Waters. And in the end, by occa&longs;ion of a mo&longs;t important bu
&longs;ine&longs;&longs;e that I was imployed in &longs;ome years &longs;ince, with great in
ten&longs;ene&longs;&longs;e of minde, and with the &longs;ure direction of
have di&longs;covered the mi&longs;take, which was, that we being upon the
bu&longs;ine&longs;&longs;e of taking the mea&longs;ure of the Waters that move, do make
u&longs;e of two dimen&longs;ions onely, namely, breadth and depth, keep
ing no account of the length. And yet the Water being, though
running, a Body, it is nece&longs;&longs;ary in forming a conceit of its quan
tity, in relation to another, to keep account of all the three Di
men&longs;ions, that is of length, breadth, and depth.
Here an objection hath been put to me, in behalf of the ordi
nary way of mea&longs;uring Running Waters, in oppo&longs;ition to what
I have above con&longs;idered and propo&longs;ed: and I was told, Its true,
that in mea&longs;uring a Body that &longs;tands &longs;till, one ought to take all
the three Dimen&longs;ions; but in mea&longs;uring a Body that continually
moveth, as the Water, the ca&longs;e is not the &longs;ame: For the length
is not to be had, the length of the water that moveth being infi
nite, as never fini&longs;hing its running; and con&longs;equently is incom
prehen&longs;ible by humane under&longs;tanding, and therefore with rea&longs;on,
nay upon nece&longs;&longs;ity it cometh to be omitted.
In an&longs;wer to this, I &longs;ay, that in the above&longs;aid Di&longs;cour&longs;e, two
things are to be con&longs;idered di&longs;tinctly; Fir&longs;t, whether it be po&longs;&longs;ible
to frame any conceit of the quantity of the Body of the Water
with two Dimen&longs;ions onely. And &longs;econdly, whether this length
be to be found. As to the fir&longs;t, I am very certain that no man, let
ceit of the quantity of the Body of Water, without the third
Dimen&longs;ion of length: and hereupon I return to affirm, that the
vulgar Rule of mea&longs;uring Running water is vain and erroneous. This point being agreed on, I come to the &longs;econd, which is, Whe
ther the third Dimen&longs;ion of length may be mea&longs;ured. And I &longs;ay,
that if one would know the whole length of the water of a
Fountain or River, thereby to come to know the quantity of all
the Water, it would prove an impo&longs;&longs;ible enterprize, nay the
knowing of it would not be u&longs;eful. But if one would know how
much water a Fountain, or a River carrieth in a determinate time
of an hour, of a day, or of a moneth, &c. I &longs;ay, that it is a very
po&longs;&longs;ible and profitable enquiry, by rea&longs;on of the innumerable
benefits that may be derived thence, it much importing to know
how much Water a Chanel carrieth in a time given; and I have
demon&longs;trated the &longs;ame above in the beginning of this Book; and
of this we &longs;tand in need in the bu&longs;ine&longs;&longs;e of the Lake, that &longs;o we
may be able to determine how much &longs;hall be the height of the
&longs;ions of a Body being given, the Body is known; and the quan
tity of a Body being given, if you have but two dimen&longs;ions, the
third &longs;hall be known. And thus diving farther and farther into
this Con&longs;ideration, I found that the Velocity of the cour&longs;e of the
water may be an hundred times greater or le&longs;&longs;er in one part of
its Chanel than in another. And therefore although there &longs;hould
be two mouths of Waters equal in bigne&longs;&longs;e; yet neverthele&longs;s it
might come to pa&longs;&longs;e, that one might di&longs;charge an hundred or a
thou&longs;and times more water than another: and this would be, if
the water in one of the mouths &longs;hould run with an hundred or a
thou&longs;and times greater velocity, than the other; for that it
would be the &longs;ame as to &longs;ay, that the &longs;wifter was an hundred or
a thou&longs;and times longer, than the &longs;lower: and in this manner I
di&longs;covered that to keep account of the velocity, was the keeping
account of the Length.
And therefore it is manife&longs;t, that when two Mouths di&longs;charge
the &longs;ame quantity of Wa r in an equal velocity, it is nece&longs;&longs;ary
that the le&longs;s &longs;wift Mouth be &longs;o much bigger than the more &longs;wift;
as the more &longs;wift exceedeth in velocity the le&longs;s &longs;wift; as for
example.
In ca&longs;e two Rivers &longs;hould carry equal quantity of water in
equal times, but that one of them &longs;hould be four times more
&longs;wift than the other, the more &longs;low &longs;hould of nece&longs;&longs;ity be four
times more large. And becau&longs;e the &longs;ame River in any part
thereof alwaies di&longs;chargeth the &longs;ame quantity of Water in equal
times (as is demon&longs;trated in the fir&longs;t Propo&longs;ition of the fir&longs;t
Book^{*} of the mea&longs;ure of Running Watets;) but yet doth not
run thorowout with the &longs;ame velocity: Hence it is, that the vul
gar mea&longs;ures of the &longs;aid River, in divers parts of its Chanel, are
alwaies divers; in&longs;omuch, that if a River pa&longs;&longs;ing through its cha
nel had &longs;uch velocity, that it ran 100 Braces in the 1/60 of an hour
and afterwards the &longs;aid River &longs;hould be reduced to &longs;o much tardi,
ty of motion, as that in the &longs;ame time it &longs;hould not run more than
one Brace, it would be nece&longs;&longs;ary that that &longs;ame River &longs;hould be
come 100. times bigger in that place where it was retarded; I
mean, 100. times bigger than it was in the place where it was
&longs;wifter. And let it be kept well in mind, that this point rightly
under&longs;tood, will clear the under&longs;tanding to di&longs;cover very many
accidents worthy to be known. But for this time let it &longs;uffice,
that we have onely declared that which makes for our purpo&longs;e,
referring apprehen&longs;ive and &longs;tudious Wits to the peru&longs;al of my
aforenamed Treati&longs;e; for therein he &longs;hall finde profit and delight
both together.
the Demon&longs;trati
ons following, at
the end of the fir&longs;t
Book
Now applying all to our principal intent, I &longs;ay, That by what
hath been declared it is manife&longs;t, that if the
ces broad, and 2 1/2 high, in &longs;ome one part of its Chanel, that after
wards the &longs;ame Water of the
&longs;ing thorow the &longs;ame to the Sea, it &longs;hould lo&longs;e &longs;o much of its ve
locity, that it &longs;hould run but one Brace, in the time wherein
whil&longs;t it was in its Chanel at the place afore&longs;aid, it ran 100. Bra
ces. It would be ab&longs;olutely nece&longs;&longs;ary, that increa&longs;ing in mea
&longs;ure, it &longs;hould become an hundred times ^{*} thicker; and therefore
if we &longs;hould &longs;uppo&longs;e that the Lake were 20000. Braces, the
being brought into the Lake, &longs;hould be 100. times 100. Brates;
that is, &longs;hall be 10000. Braces in thickne&longs;s, and con&longs;equently &longs;hall
be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a
Brace, as was concluded in the Argument.
Now one may &longs;ee into what a gro&longs;s errour of 99. in 100. one
may fall through the not well under&longs;tanding the true quantity
of Running Water, which being well under&longs;tood, doth open a
direct way to our judging aright in this mo&longs;t con&longs;iderable affair.
And therefore admitting that wich hath been demon&longs;trated,
I fay, that I would (if it did concern me) greatly encline to con
&longs;ult upon the returning of the
being mo&longs;t evident, that the
much &longs;wifter than the
certainly follow thereupon, that the thickne&longs;s of the Water of
in the Lake.
1. From which operation doth follow in the fir&longs;t place, that
the Lake being filled and increa&longs;ed by tbe&longs;e Waters, &longs;hall be
more Navigable, and pa&longs;&longs;ible, than at pre&longs;ent we &longs;ee it to be.
2. By the current of the&longs;e Waters, the Chanels will be &longs;cour
ed, and will be kept clean from time to time.
3. There will not appear at the times of low-waters &longs;o many
Shelves, and &longs;uch heaps of Mud, as do now appear.
4. The Ayr will become more whole&longs;om, for that it &longs;hall not
be &longs;o infected by putrid vapours exhaled by the Sun, &longs;o long as
the Miery Ouze &longs;hall be covered by the Waters.
5. La&longs;tly, in the current of the&longs;e advantagious Waters,, which
mu&longs;t i&longs;&longs;ue out of the Lake into the Sea, be&longs;ides tho&longs;e of the Tyde,
the Ports will be kept &longs;coured, and clear: And this is as much as
I &longs;hall offer for the pre&longs;ent, touching this weighty bui&longs;ine&longs;s; al
waies &longs;ubmitting my &longs;elf to &longs;ounder judgements.
Of the above-&longs;aid Writing I pre&longs;ented a Copy at
full Colledge, in which I read it all, and it was hearkned to with
very great attention; and at la&longs;t I pre&longs;ented it to the Duke, and
left &longs;ome Copies thereof with &longs;undry Senators, and went my way,
promi&longs;ing with all inten&longs;ene&longs;s to apply my pains with reiterated
&longs;tudies in the publick &longs;ervice; and if any other things &longs;hould come
into my minde, I promi&longs;ed to declare them &longs;incerely, and &longs;o took
leave of When I was
returned to
ning in my mind, I hapned to think of another admirable and
mo&longs;t important conceit, which with effectual rea&longs;ons, confirmed
by exact operations, I with the Divine a&longs;&longs;i&longs;tance, made clear and
manife&longs;t; and though the thing at fir&longs;t &longs;ight &longs;eemed to me a mo&longs;t
extravagant Paradox, yet notwith&longs;tanding, having &longs;atisfied my
&longs;elf of the whole bu&longs;ine&longs;s, I &longs;ent it in writing to the mo&longs;t Illu&longs;tri
ous and mo&longs;t Noble Ba&longs;adonna
well con&longs;idered my Paper, carried it to the Council; and after
that tho&longs;e Lords had for many months maturely con&longs;idered
thereon, they in the end re&longs;olved to &longs;u&longs;pend the execution of the
diver&longs;ion which they had before con&longs;ulted to make of the River
thing by me blamed in this &longs;econd Paper, as mo&longs;t prejudicial,
and harmful. The writing &longs;pake as followeth.
CONSIDERATIONS
Concerning the
LAKE
OF
VENICE.
If the di&longs;cour&longs;ing well about the truth of
things, Mo&longs;t Serene Prince, were as the
carrying of Burdens, in which we &longs;ee
that an hundred Hor&longs;es carry a greater
weight than one Hor&longs;e onely; it would
&longs;eem that one might make more account
of the opinion of many men, than of
one alone; But becau&longs;e that di&longs;cour&longs;ing
more re&longs;embleth running, than carrying
Burdens, in which we &longs;ee that one Barb alone runneth fa&longs;ter
than an hundred heavy-heel'd Jades; therefore I have ever more
e&longs;teemed one Conclu&longs;ion well managed, and well con&longs;idered by
one under&longs;tanding man, although alone, than the common and
Vulgar opinions; e&longs;pecially, when they concern ab&longs;truce and
arduous points: Nay in &longs;uch ca&longs;es the opinions moulded and
framed by the mo&longs;t ignorant and &longs;tupid Vulgar, have been ever
&longs;u&longs;pected by me as fal&longs;e, for that it would be a great wonder if
in difficult matters a common capacity &longs;hould hit upon that
which is hand&longs;om, good, and true. Hence I have, and do hold
in very great veneration the &longs;umme of the Government of the
mo&longs;t Serene, and eternal Republick of
as being in nature a Common-wealth, it ought to be governed by
the greater part; yet neverthele&longs;s, in arduous affairs, it is alwaies
directed by the Grave Judgement of few, and not judged blindly Tis true, that he that propoundeth Pro
po&longs;itions far above the reach of common capacity, runneth a
great hazard of being very often condemned without further Pro
ce&longs;s, or knowledge of the Cau&longs;e; but yet for all that, the truth
is not to be de&longs;erted in mo&longs;t weighty affairs, but ought rather to
be explained in due place and time with all po&longs;&longs;ible per&longs;picuity;
that &longs;o being well under&longs;tood, and con&longs;idered, it may come after
wards for the Common good to be embraced.
This which I &longs;peak in general, hath often been my fortune in
very many particulars, not onely when I have kept within the
bounds of meer &longs;peculation, but al&longs;o when I have chanced to de
&longs;cend to Practice, and to Operations: and your Highne&longs;s know
eth very well what befel me the la&longs;t Summer 1641. when in obe
dience to your Soveraign Command, I did in full Colledge repre
&longs;ent my thoughts touching the &longs;tate of the Lake of
there not being &longs;uch wanting, who without &longs;o much as vouch
&longs;afing to under&longs;tand me, but having onely had an inkling, and
bad apprehen&longs;ion of my opinion, fell furiou&longs;ly upon me, and by
violent means both with the Pen and Pre&longs;s, full of Gall, did abu&longs;e
me in reward of the readine&longs;s that I had expre&longs;t to obey and
&longs;erve them: But I was above mea&longs;ure encouraged and plea&longs;ed, to
&longs;ee that tho&longs;e few who vouch&longs;afed to hear me, were all either
thorowly per&longs;waded that my opinion was well grounded, or at
lea&longs;t &longs;u&longs;pended their prudent verdict to more mature deliberati
on. And though at the fir&longs;t bout I chanced to propo&longs;e a thing
that was totally contrary to the mo&longs;t received and antiquated
opinion, and to the re&longs;olutions and con&longs;ultations taken above an
hundred years ago: Moved by the&longs;e things, and to &longs;atisfie al&longs;o
to the promi&longs;e that I had made of tendering unto them what
&longs;hould farther offer it &longs;elf unto me touching the &longs;ame bu&longs;ine&longs;s; I
have re&longs;olved to pre&longs;ent to the Throne of your Highne&longs;s, another
Con&longs;ideration of no le&longs;s importance, which perhaps at fir&longs;t &longs;ight
will appear a &longs;tranger Paradox; but yet brought to the Te&longs;t and
Touch-&longs;tone of experience, it &longs;hall prove mo&longs;t clear and evident. If it &longs;hall be accounted of, &longs;o that it &longs;ucceedeth to the benefit of
your Highne&longs;s, I &longs;hall have obtained my defire and intent: And
if not, I &longs;hall have &longs;atisfied my &longs;elf, and &longs;hall not have been
wanting to the Obligation of your mo&longs;t faithful Servant, and na
tive &longs;ubject.
That which I propounded in the Mouths pa&longs;s, touching the
mo&longs;t important bu&longs;ine&longs;s of the Lake, though it did onely expre&longs;
ly concern the point of the diver&longs;ion of the Mouth of the Lake,
already made and put in execution; yet it may be under&longs;tood
and applyed al&longs;o to the diver&longs;ion under debate, to be made of
the other five Rivers, and of the
Now touching this, I had the fortune to offer an admirable
accident that we meet with when we come to the effect, which
I verily believe will be an utter ruine to the Lake of
nice.
I &longs;ay therefore, that by diverting the&longs;e five Rivers that re
main, although their water that they di&longs;charge for the pre&longs;ent in
to the Lake is not all taken together 4/5 parts of what the
alone did carry, yet neverthele&longs;&longs;e the abatement of the water of
the Lake which &longs;hall en&longs;ue upon this la&longs;t diver&longs;ion of four parts,
which was the whole water, &longs;hall prove double to that which hath
happened by the diver&longs;ion of
that are to be diverted carry four: A wonder really great, and
altogether unlikely; for the reducing all this Propo&longs;ition to be
under&longs;tood, is as if we &longs;hould &longs;ay, that there being given us
three Rivers, of which the fir&longs;t di&longs;chargeth five parts, the &longs;econd
three, and the third one, and that from the diver&longs;ion of the
fir&longs;t, there did follow &longs;uch a certain abatement or fall; from
the taking away of the &longs;econd there ought to follow al&longs;o &longs;o
much more abatement; And la&longs;tly, from the withdrawing of
the third the water ought to fall &longs;o much more, which is wholly
impo&longs;&longs;ible: And yet it is mo&longs;t certain, and be&longs;ides the demon
&longs;tration that per&longs;wades me to it, which I &longs;hall explain in due
time, I can &longs;et before your eyes &longs;uch an experiment as is not to
be denied by any one, although ob&longs;tinate: and I will make it
plainly &longs;een and felt, that by taking away only four parts of the
five, which &longs;hall have been taken away, the abatement proveth
double to the abatement en&longs;uing upon the diverting fir&longs;t of the
five onely; which thing being true, as mo&longs;t certainly it is, it
will give us to under&longs;tand how pernicious this diver&longs;ion of five
Rivers is like to prove, if it &longs;hall be put in execution.
By this little that I have hinted, and the much that I could
&longs;ay, let your Highne&longs;&longs;e gather with what circum&longs;pection this bu
&longs;ine&longs;&longs;e ought to be managed, and with how great skill he ought
to be furni&longs;hed who would behave him&longs;elf well in the&longs;e difficult
affairs.
I have not at this time explained the demon&longs;tration, nor have
I &longs;o much as propounded the way to make the Experiment, that
I am able to make in confirmation of what I have &longs;aid, that &longs;o
by &longs;ome one or others mi&longs;-apprehending the Demon&longs;tration,
and maiming the Experiment, the truth may not happen to &longs;hine
with le&longs;&longs;e clarity than it doth, when all mi&longs;ts of difficulty are re
moved: and if &longs;o be, no account &longs;hould be made of the Rea&longs;ons
by me alledged, and that men &longs;hould &longs;hut their eyes again&longs;t the
Experiments that without co&longs;t or charge may be made, I do de
to the Fields of the main Land, and extraordinary &longs;ummes
&longs;hall be expended to no purpo&longs;e. The Lake undoubtedly will
become almo&longs;t dry, and will prove impa&longs;&longs;ible for Navigation,
with a manife&longs;t danger of corrupting the Air: And in the la&longs;t
place there will unavoidably en&longs;ue the choaking and &longs;toppage of
the Ports of
Upon the 20th.
of
Con&longs;ideration to the mo&longs;t Excellent
ting him with a Copy thereof among&longs;t other Writings, which I
have thought good to in&longs;ert, although they &longs;eem not to belong
directly to our bu&longs;ine&longs;&longs;e of the Lake.
The way to examine the MUD and SAND
that entereth and remaineth in the
LAKE of
SIGNORE GIO. BASADONNA.
Two very con&longs;iderable Objections have been made a
gain&longs;t my opinion concerning the Lake of
was that, of which I have &longs;poken at large in my fir&longs;t
Con&longs;ideration, namely, that the
the Lake, cannot have been the occa&longs;ion of the notable fall of
the Waters in the Lake, as I pretend, and con&longs;equently, that
the turning
dy, in regard that the water of
of the Lake over which the water of
&longs;pread being con&longs;idered, it is found that the ri&longs;e proveth in
&longs;en&longs;ible.
The &longs;econd Objection was, that the
therefore if it &longs;hould fall muddy into the Lake, the Sand would
&longs;ink and fill up the &longs;ame.
Touching the fir&longs;t Query, enough hath been &longs;aid in my fir&longs;t
Con&longs;ideration, where I have plainly di&longs;covered the deceipt of the
Argument, and &longs;hewn its fallacy; It remaineth now to examine
things that I propo&longs;ed in this affair was, that I held it impo&longs;&longs;ible
to do any act, though never &longs;o beneficial, that was not al&longs;o ac
companied by &longs;ome inconvenience and mi&longs;chief; and therefore
we are to con&longs;ider well the profit, and the lo&longs;&longs;e and prejudice;
and they both being weighed, we &longs;hall be able to choo&longs;e the le&longs;
&longs;er evil: Secondly, I admit it to be mo&longs;t true, that
times muddy, but it is al&longs;o true, that for the greater part of the
year it is not muddy. Thirdly, I do not &longs;ee nor under&longs;tand
what &longs;trength this objection hath, being taken &longs;o at large, and in
general; and methinks that it is not enough to &longs;ay, that the
ne&longs;&longs;e in the Lake, but we ought moreover to proceed to particu
lars, and &longs;hew how much this Mud is, and in what time this
choaking up of the Ports may be effected. For the Rea&longs;ons are
but too apparent and particular, that conclude the ruine of the
Lake, and that in a very &longs;hort time, (for mention is made of
dayes) the Waters diver&longs;ion being made, and moreover we
have the circum&longs;tance of an Experiment, the &longs;tate of things be
ing ob&longs;erved to have grown wor&longs;e &longs;ince the &longs;aid diver&longs;ion. And
I have demon&longs;trated, that in ca&longs;e the Diver&longs;ion of the
the other Rivers &longs;hould be put in execution, the Lake would in a
few dayes become almo&longs;t dry; and the Ports would be lo&longs;t, with
other mi&longs;chievous con&longs;equences. But on the other &longs;ide, al
though that we did grant the choaking of them, we may very
probably &longs;ay, that it will not happen, &longs;ave onely in the &longs;ucce&longs;&longs;ion
of many and many Centuries of years. Nor can I think it pru
dent coun&longs;el to take a re&longs;olution and imbrace a De&longs;igne now, to
obtain a benefit very uncertain, and more than that, which only
&longs;hall concern tho&longs;e who are to come very many Ages after us,
and thereby bring a certain inconvenience upon our &longs;elves, and
upon our children that are now alive and pre&longs;ent.
Let it be alledged therefore, (although I hold it fal&longs;e) that by
the diver&longs;ions of the Rivers the Lake may be kept in good con
dition for &longs;everal years to come.
But I &longs;ay confidently, and hope to demon&longs;trate it; That the
Diver&longs;ions will bring the Lake, even in our dayes, to be almo&longs;t
dry, and at lea&longs;t will leave &longs;o little water in it, that it &longs;hall cea&longs;e
to be Navigable, and the Ports &longs;hall mo&longs;t infallibly be choaked
up. I will therefore &longs;ay upon experience, in an&longs;wer to this Ob
jection, that it is very nece&longs;&longs;ary fir&longs;t well to di&longs;cour&longs;e, and ratio
nally to particularize and a&longs;certain the be&longs;t that may be this
point of the quantity of this &longs;inking Mud or Sand.
Now I fear I &longs;hall make my &longs;elf ridiculous to tho&longs;e, who mea
&longs;uring the things of Nature with the &longs;hallowne&longs;&longs;e of their brains
will &longs;ay unto me,
ponderavitYet neverthele&longs;s I will propound a way whereby,
at lea&longs;t in gro&longs;s, one may find out the &longs;ame.
Take a Ve&longs;&longs;el of Cylindrical Figure, holding two barrels of
water, or thereabouts; and then fill it with the water of
at its Mouth or Fall into the Lake; but in the Lake at the time
that the
muddy for eight or ten hours, to give the mud time to go as far
as S.
another Ve&longs;&longs;el, like, and equal to the fir&longs;t, and fill it with the wa
ter of the Lake towards S.
ration ought to be made at the time when the waters go out,
and when the Sea is calm) and then, when the waters &longs;hall have
&longs;etled in the afore&longs;aid Ve&longs;&longs;els, take out the clear water, and con
&longs;ider the quantity of Sand that remains behind, and let it be &longs;et
down, or kept in mind: And I am ea&longs;ily induced to think, that
that &longs;hall be a greater quantity of Sand which &longs;hall be left in the
fir&longs;t Ve&longs;&longs;el, than that left in the &longs;econd Ve&longs;&longs;el. Afterwards
when the
repeated, and ob&longs;erve the quantity of Sand in the afore&longs;aid Ve&longs;
&longs;els; for if the Sand in the fir&longs;t Ve&longs;&longs;el &longs;hould be mo&longs;t, it would
be a &longs;ign, that in the revolution of a year the
Sand in the Lake: And in this manner one may calculate to a
&longs;mall matter what proportion the Sand that entreth into the Lake,
hath to that which remains: And by that proportion one may
judge how expedient it &longs;hall be for publick benefit. And if at
&longs;everal times of the year you carefully repeat the &longs;ame operati
ons, or rather ob&longs;ervations, you would come to a more exact
knowledge in this bu&longs;ine&longs;s: And it would be good to make the
&longs;aid operations at tho&longs;e times, when the Lake is di&longs;turbed by
&longs;trong high Winds, and made muddy by its own Mud, rai&longs;ed by
the commotion of the Waters.
This notion would give us great light, if the &longs;ame ob&longs;ervations
&longs;hould be made towards the Mouth of
waters flow and ebb, in calm &longs;ea&longs;ons; for &longs;o one &longs;hould come to
know whether the waters of the Lake are more thick at the going
out, than at the entrance. I have propounded the foregoing
way of mea&longs;uring Sands and Mud, to &longs;hew that we are not &longs;o
generally, and incon&longs;iderately to pronounce any &longs;entence, but
proceed to &longs;tricter inquiries, and then deliberate what &longs;hall be
mo&longs;t expedient to be done. Others may propo&longs;e more exqui
&longs;ite examinations, but this &longs;hall &longs;erve me for the pre&longs;ent.
I will add onely, that if any one had greater curio&longs;ity (it would
be profitable to have it) in inve&longs;tigating more exactly the quan
I have &longs;hewen in the beginning of this Book: When he &longs;hall
have found the proportion of the quantity of water to the quan
tity of Sand or Mud, he &longs;hall come to know how much Sand the But to
perform the&longs;e things, there are required per&longs;ons of di&longs;cretion, and
fidelity, and that are imployed by publick Order; for there
would thence re&longs;ult eminent benefit and profit.
To the Reverend Father,
S. GIUSEPPE.
In execution of the command that you laid upon me in your
former Letters, by order from the mo&longs;t Serene, my Lord,
ing the di&longs;imboguement of the River called
ther it ought to be let into the Sea, or into
I chanced 18. years &longs;ince to be pre&longs;ent, when the &longs;aid Mouth was
opened into the Sea, and that of
done to remedy the great Innundation that was made in all that
Country, and Plain of
and the Mountains of
Plain continued long under water, in&longs;omuch that not onely in the
Winter, but al&longs;o for a great part of the Summer, tho&longs;e fields
were overflowed; and when that the Mouth of
effectually opened into the Sea, the place was pre&longs;ently freed from
the waters. and drained, to the great &longs;atisfaction of the Owners
of tho&longs;e Grounds. And here I judge it worth your notice, that
for the generality of tho&longs;e that po&longs;&longs;e&longs;s e&longs;tates in tho&longs;e parts, they
de&longs;ired that the Mouth of
Sea, and tho&longs;e who would have it open into
that have no other concernment there, &longs;ave the hopes of gaining
by having the di&longs;po&longs;e of Commi&longs;&longs;ions, and the like, &c,
But for the more plain under&longs;tanding of that which is to be
&longs;aid, it mu&longs;t be known, That the re&longs;olution of opening the &longs;aid
Mouth into
again propo&longs;ed, as your Letters tell me, Since that, it manife&longs;t
ly appearing, that
the Sea, the Plain hathbeen kept dry; and it being al&longs;o true, that
abundance of &longs;and into the Mouth, or Out-let of
that it wholly &longs;topt it up: e&longs;pecially when the waters on
&longs;ide were low and &longs;hallow, And they think, that turning the
Lake of
continually its own Mouth with the force of its waters open to the
Sea, and con&longs;equently al&longs;o
Out-let clear and open; and in this manner they think, that the
Plain of The bu
&longs;ine&longs;s pa&longs;&longs;eth for current, at fir&longs;t &longs;ight; but experience proveth
the contrary, and Rea&longs;on confirmeth the &longs;ame: For the height
of the water of tho&longs;e Plains, was regulated by the height of the
waters in the Mouth of
Mouth being high, the waters al&longs;o do ri&longs;e in the fields; and when
the waters at the Mouth are low, the waters of the fields do like
wi&longs;e abate: Nor is it enough to &longs;ay, That the Out-let or Vent
of
would determine high; for
ever it more and more aboundeth with water, and ri&longs;eth, it is ne
ce&longs;lary that al&longs;o
quently &longs;hall keep the waters in the Plains higher. Nay, it hath
happened &longs;ometimes (and I &longs;peak it upon my own &longs;ight) that
which ca&longs;e will ever happen, when&longs;oever the
to be lower than the level of tho&longs;e of
the waters of
morto
been ob&longs;erved to be carried by this return as farr as the Walls of
&longs;waged, which come in with great fury, and go out by little and
little, there do pa&longs;s very many days, and moneths, nay &longs;ome
times one being never able to find the waters of
when at the &longs;hallowe&longs;t, &longs;o low as the Sea in level; (which is the
lowe&longs;t place of the waters) it thence doth follow, that the wa
ters of
as they determine in
the &longs;ame Tis true indeed,
that the Mouth of
the inconvenience of being &longs;topt up by the force of Winds: But
in this ca&longs;e, it is nece&longs;&longs;ary to take &longs;ome pains in opening it; which
may ea&longs;ily be done, by cutting that Sand a little which &longs;tayeth
in the Mouth, after that the Wind is laid; and it is enough if you
make a Trench little more than two Palms in breadth; for the
water once beginning to run into it, it will in a few hours carry
Trench that will drain away all the water of the Plains in very lit
tle time. And I have found by practice, that there having been
a great quantity of Sand driven back, by the fury of the South
We&longs;t-Wind, into the Mouth of
little gutter to be made in the Morning, &longs;omewhat before Noon,
a Mouth hath been opened of 40. Braces wide, and notably deep,
in&longs;omuch that the water, which before had incommoded all the
Champian ran away in le&longs;s than three dayes, and left the Coun
try free and dry, to the admiration of all men. There was pre
&longs;ent upon the place, at this bu&longs;ine&longs;s, on the &longs;ame day that I
opened the Mouth, the mo&longs;t Serene great Duke, the mo&longs;t Serene
Arch-Dutche&longs;s Mother, all the Commi&longs;&longs;ioners of Sewers, with
many other Per&longs;ons and Pea&longs;ants of tho&longs;e parts; and they all &longs;aw
very well, that it was never po&longs;&longs;ible that a little Bark of eight
Oars, which was come from
Duke, &longs;hould ever be able to ma&longs;ter the Current, and to make
up into
to cau&longs;e the &longs;aid Mouth towards the Sea to be &longs;topt; and that
into
that it &longs;hould be left open towards the Sea, as it was done. And
if at this day it &longs;hall return into
will be nece&longs;&longs;ary to open it again into the Sea. And there was
al&longs;o charge and order given to a per&longs;on appointed for the pur
po&longs;e, that he &longs;hould take care to open the &longs;aid Mouth, as hath
been &longs;aid upon occa&longs;ion. And thus things have &longs;ucceeded very
well unto this very time. But from the middle of
this fir&longs;t of
South-We&longs;t-Winds, with frequent and abundant Rains; it is no
wonder that &longs;ome innundation hath happened; but yet I will
affirm, that greater mi&longs;chiefs would have followed, if the Mouth
had been opened into
is very clear and intelligible to all &longs;uch as have but competent in
&longs;ight, and indifferent skill in the&longs;e affairs. But that which I am
now about to propo&longs;e farther, will, I am very certain, be under
&longs;tood by your &longs;elf, but it will &longs;eem &longs;trange and unlikely to many
others. The point is, that I &longs;ay, That by rai&longs;ing the level of
penitrate into
cau&longs;e the waters to ri&longs;e three, or perhaps more Braces upon the
fields towards
farther from the Sea-&longs;ide; and thus there will follow very great
Innundations, and con&longs;iderable mi&longs;chiefs. And to know that
this is true, you are to take notice of an accident, which I give
warning of in my di&longs;cour&longs;e of the Mea&longs;ure of Running Waters:
cident is this, That there coming a Land-Flood, for example,
into
wthin
ces; this &longs;ame height becometh alwaies le&longs;&longs;er and le&longs;&longs;er, the more
we approach towards the Sea-&longs;ide; in&longs;omuch, that near to the
Sea the &longs;aid River &longs;hall be rai&longs;ed hardly half a Brace: Whence
it followeth of nece&longs;&longs;ary con&longs;equence, that &longs;hould I again be at
the Sea-&longs;ide, and knowing nothing of what hapneth, &longs;hould &longs;ee
the River
of a Brace; I could certainly infer, that the &longs;ame River was rai&longs;ed
in And that which I &longs;ay of
Which thing
being true, it is nece&longs;&longs;ary to make great account of every &longs;mall
ri&longs;ing, that
ling into
being to di&longs;gorge its Waters into
onely a quarter of a Brace; we might very well be &longs;ure, that fart
from the Sea, about
much greater, and &longs;hall become two or three Braces: And be
cau&longs;e the Countrey lyeth low, that &longs;ame ri&longs;e will cau&longs;e a conti
nual Innundation of the Plains, like as it did before; I cau&longs;ed the
Mouth to be opened into the Sea. And therefore I conclude
that the Mouth of
into
diligence to keep it open after the manner afore&longs;aid, &longs;o &longs;oon as
ever the Wind &longs;hall be laid. And if they &longs;hall do otherwi&longs;e, I
confidently affirm, that there will daily follow greater damages;
not onely in the Plains, but al&longs;o in the whole&longs;omne&longs;s of the
Air; as hath been &longs;een in times pa&longs;t. And again, It ought with
all care to be procured, that no waters do by any means run or
fall from the Trench of
Waters being to di&longs;charge into
much higher than is imagined, according to that which I have de
mon&longs;trated in my con&longs;ideration upon the &longs;tate of the Lake of
&longs;tandeth much, and I &longs;ubmit all to the mo&longs;t refined judgment of
our mo&longs;t Serene Prince
humility to ki&longs;s in my name, and implore the continuance of his
Princely favour to me; and &longs;o de&longs;iring your prayers to God for
me, I take my leave.
1642.
D. BENEDETTO CASTELLI.
The an&longs;wer to a Letter written by BAR
TOLOTTI, touching the
difficultyes ob&longs;erved.
beginneth at the fir&longs;t Head.
And fir&longs;t I &longs;ay, Whereas I &longs;uppo&longs;e that the level of the
chio
at &longs;uch time as the waters of
to the Sea; but I did never &longs;ay that things could never be brought
to that pa&longs;s, as that the level of
Drain of
ther grant, that its po&longs;&longs;ible, that the
thorow
that it might have happened, that
&longs;uch a fall into
Mills: But then I add withall, that the Plains of
City it &longs;elf mu&longs;t be a meer Lake.
2.
leth by the South-We&longs;t, or other Winds, the level of
the place marked A in the Platt, di&longs;tant about 200. Braces, ri&longs;eth
very little: But that
more up into Land ri&longs;eth very much, and that certain Fi&longs;hermen
confirm this, and &longs;hew him the &longs;ignes of the ri&longs;ing of the Water. I grant it to be very true, and I have &longs;een it with my own eyes:
But this cometh to pa&longs;s, when the Mouth of
up by the Sea; as I &longs;hall &longs;hew by and by. And this ri&longs;ing near
the Sea-&longs;ide, is of no con&longs;iderable prejudice to the fields. And
this is as much as I find to be true in the a&longs;&longs;ertion of
tolotti,
it needs none) That the level of
ny miles farther upwards it ri&longs;eth much; nor did I ever affirm the
contrary.
3. Concerning the difficulty of opening the Mouth of
morto
namely, That at the entrance upon the opening of the Mouth, it
is nece&longs;&longs;ary to make a deep Trench: But I &longs;ay, that at that time
it is difficult to open it, unle&longs;s upon great occa&longs;ions; for that the
and the fields drained.
4. As to the particular of the Cau&longs;es that you tell me men
pre&longs;s &longs;o much unto the mo&longs;t
Prince, I have not much to &longs;ay, becau&longs;e it is not my profe&longs;&longs;ion;
nor have I con&longs;idered of the &longs;ame: Yet I believe, that when the
Prince and his Highne&longs;&longs;e &longs;ee the benefit of his People and Sub
jects in one &longs;cale of the Ballance, and the accomodation of
Hunt&longs;men in the other, his Highne&longs;&longs;e will incline to the profit
of his &longs;ubjects; &longs;uch have I alwayes found his Clemency and
Noblene&longs;&longs;e of minde. But if I were to put in my vote upon
this bu&longs;ine&longs;&longs;e, I would &longs;ay, that the points of Spears, and the
mouths of Guns, the yelping of Dogs, the wilyne&longs;&longs;e of Hunt&longs;
men, who run thorow and narrowly &longs;earch all tho&longs;e Woods,
Thickets and Heathes, are the true de&longs;troyers of Bucks and
Boares, and not a little Salt-water, which &longs;etleth at la&longs;t in &longs;ome
low places, and &longs;preadeth not very far. Yet neverthele&longs;&longs;e, I will
not enter upon any &longs;uch point, but confine my &longs;elf &longs;olely to the
bu&longs;ine&longs;&longs;e before me.
5. That Experiment of joyning together the water of
morto,
tage the Level E hath upon the Level I, doth not give me full
&longs;atisfaction, taken &longs;o particularly, for it may come to pa&longs;&longs;e, that
&longs;ometimes E may be higher, and &longs;ometimes A lower, and I do
not que&longs;tion but that when
of Water, the level of
ter, the contrary will follow, if the Mouth &longs;hall be opened to
the Sea. And here it &longs;hould &longs;eem to me, that it ought to be
con&longs;idered, that there is as much advantage from E to the Sea
through the little Trench opened anew into
the Sea by the Mouth of
is that we are to regard in our ca&longs;e) is, that the cour&longs;e of the
Waters thorow the Trench is three times longer than the cour&longs;e
of the Mouth of
Plat which you &longs;ent me, which I know to be very exactly drawn,
for that the &longs;ituation of tho&longs;e places are fre&longs;h in my memory. Here I mu&longs;t give notice, that the waters of
ning thorow the Trench in
morto
declivity &longs;hall, for two cau&longs;es, be le&longs;&longs;e than the pendency of tho&longs;e
waters through the Mouth towards the Sea, that is, becau&longs;e of
the length of the line through the Trench, and becau&longs;e of the
height of their entrance into
great import in di&longs;charging the waters which come &longs;uddenly, as
Mea&longs;ure of Running Waters And this was the Rea&longs;on why all
the Countrey did grow dry upon the opening of the Mouth into
the Sea. And here I propo&longs;e to con&longs;ideration that which the Pea
&longs;ants about
doth no con&longs;iderable harm by continuing there five or &longs;ix, yea, or
eight dayes. And therefore the work of the Countrey is to o
pen the Mouth of
being come, they may have the Trench free and ready, when that
the Water cometh it may have a free drain, and may not &longs;tay
there above eight or nine dayes, for then the overflowings be
come hurtful. It is to be de&longs;ired al&longs;o, that if any Propo&longs;ition is
produced touching the&longs;e affairs, it might be propounded the mo&longs;t
di&longs;tinctly that may be po&longs;&longs;ible, and not con&longs;i&longs;t in generals, e&longs;pe
cially when the Di&longs;pute is of the ri&longs;ings, of velocity, of tardity,
of much and little water; things that are all to be &longs;pecified by
mea&longs;ures.
6. Your Letter &longs;aith, in the next place, that
lotti
wayes be kept open, it would be better to let it continue as it is:
the which, that I may not yield to him in courte&longs;ie, I confe&longs;&longs;e,
for the keeping it &longs;topt on all &longs;ides would be a thing mo&longs;t per
nicious. But admitting of his confe&longs;&longs;ion I again reply, that
ume morto
to the Sea; becau&longs;e although &longs;ometimes the Mouth to Sea
wards be &longs;topt up, yet for all that, the rai&longs;ing of the Bank above
the Plains (which is all the bu&longs;ine&longs;&longs;e of importance) &longs;hall be ever
le&longs;&longs;er, if we make u&longs;e of the Mouth leading to the Sea, than u
&longs;ing that of
7. I will not omit to mention a kinde of &longs;cruple that I have
concerning the po&longs;ition of Bartolotti,
that the two Mouths A and D are equal to the like Mouths into
the Sea; Now it &longs;eems to me, that the Mouth A of
into
er, and is regulated by the height of
of
minate in the Sea it &longs;elf, the lowe&longs;t place. And this I believe
was very well peroeived by Bartolotti,
he pa&longs;t it over without declaring it: and we &longs;ee not that the
Mouth D falleth far from the Sea, which Mouth ought to be let
into the Sea it &longs;elf, and &longs;o the advantage of the
Sea more clearly appeareth.
8. That which
Bartolotti
Waters, at &longs;uch time as the Waters are out, and when Winds
choak up
more readily to believe that Bartolotti
that the Mouth of
by this he acknowledgeth that the Mouth towards the Sea doth
in &longs;uch &longs;ort drain the Countrey of the Waters, as that they be
come very low; and therefore upon every little
ters turn their cour&longs;e: And from the motions, being exceeding
&longs;low, is inferred, that the abundance of Sea-water that com
eth into Bat
tolotti
9. After that
Bartolotti
bove, namely, that when the Windes blowing &longs;trongly do &longs;top
up
wards, the time being Rainy, and the Mouth of
up, the Waves of the Sea pa&longs;&longs;e over the Bank of
that time, &longs;aith
benefit of
&longs;hall &longs;tand alwayes open; and
&longs;tantly run out, as al&longs;o the Rains and Rain-waters, although the
hurtful Tempe&longs;t &longs;hould la&longs;t many dayes, &c. And I reply, that
all the Art con&longs;i&longs;ts in this; for the benefit of tho&longs;e Fields doth
not depend on, or con&longs;i&longs;t in &longs;aying, that
open, and
ne&longs;&longs;e of profit lyeth and con&longs;i&longs;teth in maintaining the Waters
low in tho&longs;e Plaines, and tho&longs;e Ditches, which &longs;hall never be ef
fected whil&longs;t the World &longs;tands, if you let
chio
&longs;o much rea&longs;on and nature proveth, and (which importeth) Ex
perience confirmeth.
10. In the tenth place I come to con&longs;ider the an&longs;wer that
was made to another Propo&longs;ition in the Letter which I writ to
Father
to clear this whole bu&longs;ine&longs;&longs;e. I &longs;aid in my Letter, That great
account is to be made of every &longs;mall ri&longs;ing and ebbing of the
Waters neer to the Sea in
fallings, although that they be &longs;mall neer to the Sea-&longs;ide, yet ne
verthele&longs;&longs;e, they operate and are accompanied by notable ri&longs;ings
and fallings within Land, and far from the Sea-&longs;ide, and I have
declared by an example of
that made it increa&longs;e above its ordinary height within
&longs;even Braces, that this height of the &longs;ame Flood becometh &longs;till
le&longs;&longs;er, the neerer we approach to the Sea-coa&longs;ts. Nor &longs;hall the
&longs;aid River be rai&longs;ed hardly half a Brace; whereupon it nece&longs;&longs;
rily followeth, that if I &longs;hould return to the Sea-&longs;ide, and not
knowing any think of that which happeneth at
fidently affirm the &longs;aid River to be rai&longs;ed in
ven Braces, &c. From &longs;uch like accidents I conclude in the &longs;ame
Letter, that it is nece&longs;&longs;ary to make great account of every little
ri&longs;e that Now cometh
&longs;elf better, under&longs;tandeth not my Propo&longs;ition) and &longs;peaketh that
which indeed is true, but yet be&longs;ides our ca&longs;e: Nor have I ever
&longs;aid the contrary; and withall doth not apply it to his purpo&longs;e. Nay I &longs;ay, that if he had well applyed it, this alone had been a
ble to have made him change his opinion. And becau&longs;e he &longs;aith,
that I &longs;aid, that it is true, when the abatement proceedeth from
&longs;ome cau&longs;e above, as namely by Rain, or opening of Lakes;
But when the cau&longs;e is from below, that is, by &longs;ome &longs;top, as for
in&longs;tance &longs;ome Fi&longs;hers Wears or Locks, or &longs;ome impediment re
mote from the Sea, although at the Level it &longs;hall ri&longs;e &longs;ome Braces
where the impediment is, yet that ri&longs;ing &longs;hall go upwards; and
here he fini&longs;heth his Di&longs;cour&longs;e, and concludeth not any thing
more. To which I &longs;ay fir&longs;t, that I have al&longs;o &longs;aid the &longs;ame in the
Propo&longs;ition, namely, that a Flood coming (which maketh
to ri&longs;e in
cau&longs;e whether it be Rain or the opening of Lakes, as be&longs;t plea
&longs;eth
the Sea-coa&longs;ts it &longs;hall not cau&longs;e a ri&longs;ing of full half a Brace; and
therefore &longs;eeing
ther of Rain, or of opening of Lakes half a Brace) it may be
inferred, that at
which variety, well con&longs;idered, explaineth all this affair in favour
of my opinion: For the ri&longs;ing that is made by the impediment
placed below, of Fi&longs;hing Weares and Locks, operateth at the be
ginning, rai&longs;ing the Waters that are neer to the impediment;
and afterwards le&longs;s and le&longs;s, as we retire upwards from the im
pediment: provided yet that we &longs;peak not of a Flood that com
meth by acce&longs;&longs;ion, but onely of the ordinary Water impeded. But there being a new acce&longs;&longs;ion, as in our ca&longs;e, then the Water
of the Flood, I &longs;ay, &longs;hall make a greater ri&longs;ing in the parts &longs;uperi
our, far from the impediment; and the&longs;e impediments &longs;hall
come to be tho&longs;e that &longs;hall overflow the Plains, as happened
eighteen or nineteen years ago, before the opening of
morto
morto
ca&longs;e that befell me in
&longs;ide. where I drained a Bog or Fen, of the nature of the Wa
ters of
&longs;ite towards the Sea abating only three Palmes, and yet in the But the bu&longs;ine&longs;&longs;e
would be long, and not &longs;o ea&longs;ily to be declared, and I am cer
tain that Bartolotti
judgment, and withall would know that remitting that impedi
ment anew, which I had left for le&longs;&longs;e than three Palmes towards
the Sea, the Waters in the Fen would return with the fir&longs;t Floods
and Raines to the &longs;ame height as before, as likewi&longs;e
will do if it &longs;hall be let again into
or Province lying
round the City,
heretofore called
Here I intreat your Honour to do me the favour to importune
my meaning in the afore&longs;aid Letter to Bartolotti,
that if he will under&longs;tand this point, he will be no longer &longs;o te
nacious in his opinion.
Next that the&longs;e Lords in the Commi&longs;&longs;ion of Sewers, with the
Right Honourable the Marque&longs;&longs;e of S.
do approve of my judgment, doth very much rejoyce me; but
becau&longs;e that I know that they do it not in de&longs;ign to complement
me, but onely to &longs;erve his Highne&longs;s our Grand Duke, I freely
profe&longs;s that I will pretend no farther obligations from them there
in, than I account my &longs;elf to owe to tho&longs;e who&longs;e opinions are
contrary to mine, for that I know that they have the &longs;ame end. The definitive &longs;entence of this whole bu&longs;ine&longs;s is, that they give
the&longs;e Plains, the&longs;e Draines, and the&longs;e Waters farre fetcht ap
pellations.
11. As to the quantity of the Water that
chargeth into the Sea, there are very great di&longs;putes about it, and
I have been pre&longs;ent at &longs;ome of them. But let your Honour be
lieve me, that as this is not continual, but only during a few
dayes, &longs;o it will never be of any great prejudice to the&longs;e Fields;
and if your Lord&longs;hip would be a&longs;certained thereof, you may
plea&longs;e to go to
Sea, in the time of the&longs;e &longs;trong Windes, and ob&longs;erve the cur
rent from thence upwards, for you &longs;hall finde it extream &longs;low,
and con&longs;equently will know that the quantity of the Water that
is repuls'd is very &longs;mall. And this &longs;eems to be contradicted by the
rule of Ri&longs;ings proceeding from cau&longs;es below, which occa&longs;ion no
con&longs;iderable alteration far from the Sea.
I am nece&longs;&longs;itated to go to morrow out of
nence Cardinal
therefore I &longs;hall not farther inlarge, but for a clo&longs;e to this tedious
Di&longs;cour&longs;e, I conclude in few words, that
means to be let into
ate cour&longs;es to be taken, for they will alwayes be prejudicial; but When
it is &longs;topt up by the fury of the Sea waves, I affirm that it is a
ca&longs;ion to open it, it is ea&longs;ily done. As for the re&longs;t your Lord&longs;hip
may plea&longs;e to keep account of all the particulars that occur, for
the memory of things pa&longs;t is our Tutre&longs;&longs;e in tho&longs;e that are to
come. If occa&longs;ion &longs;hall offer, I intreat you to bow humbly in
my name to His Highne&longs;s the Grand Duke, and the mo&longs;t Serene
Prince
you &longs;erve I rinces of extraordinary merit; And to whom I my
&longs;elf am al&longs;o exceedingly obliged. In the controver&longs;ies that ari&longs;e
re&longs;pect the pious end of &longs;peaking the Truth, for then every
thing will &longs;ucceed happily. I ki&longs;s the hands of
of Bartolotti,
D.
Vpon this occa&longs;ion I will here in&longs;ert a Di&longs;cour&longs;e that I made
upon the Draining and improvement of the
for that I think that what&longs;oever may be done well and to pur
po&longs;e in this matter hath ab&longs;olute dependance on the perfect know
ledge of that &longs;o important Propo&longs;ition, by me demon&longs;trated and
explained in my Treati&longs;e of the
ters,
change Mea&longs;ures, according as it altereth and changeth the ve
locity of its cour&longs;e; &longs;o that the mea&longs;ure of the thickne&longs;&longs;e of a
River in one Site, to the mea&longs;ure of the &longs;ame River in another
Site, hath the &longs;ame proportion reciprocally that the velocity in
this &longs;ite hath to the velocity in the fir&longs;t &longs;ite. And this is a Truth
&longs;o con&longs;tant and unchangeable, that it altereth not in the lea&longs;t
point on any occurrences of the Waters that change: and
being well under&longs;tood, it openeth the way to the knowledge of
&longs;undry adverti&longs;ements in the&longs;e matters, which are all re&longs;olved by
this &longs;ole Principle; and from it are derived very con&longs;iderable be
nefits; and without the&longs;e it is impo&longs;&longs;ible to do any thing with
ab&longs;olute perfection
A
CONSIDERATION
Upon the
DRAINING
OF THE
Pontine Fenns. BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO, and Profe&longs;&longs;or
of the
Univer&longs;ity of
Among&longs;t the enterprizes by me e&longs;teemed, if not ab
&longs;olutely impo&longs;&longs;ible, , at lea&longs;t exceeding difficult,
one was that famous one of Draining the
Fenns
never to apply my minde thereunto, although
by my Patrons I &longs;hould be commanded to the
&longs;ame: accounting that it was an occa&longs;ion rather of lo&longs;ing repu
tation by the mi&longs;carriage of the attempt, than of gaining fame by
reducing things to a better pa&longs;s then they now are at. Yet never
thele&longs;s, having of late years ob&longs;erved the place, and &longs;ailed through
tho&longs;e Chanels, and tho&longs;e Waters; after I had made &longs;ome reflection
thereupon, I thought that the enterprize was not &longs;o difficult as
I had at fir&longs;t conceited it to be; and I am the more confirmed in
this opinion, upon the inducement of that which I have written
Waters; &longs;o that talking with &longs;everal per&longs;ons, I adventured to
affirm, in di&longs;coures, that this improvement might po&longs;&longs;ibly be
brought into a good e&longs;tate.
Now I have re&longs;olved to &longs;et down my thoughts in writing, and
to honour this my Paper with the Noble Name of your Lord&longs;hip,
to render it the more credible and con&longs;picuous at the fir&longs;t view,
if it &longs;hould chance that the Subject I treat of, were not of &longs;uch
moment, as that it did de&longs;erve to be valued for any other rea&longs;on. Pardon me, Sir, if I have been too bold, and continue me in the
number of your Servants.
The enterprize of Draining a great part of the Territories of
the
the antient
times by I do not doubt in the lea&longs;t, but that it will
be po&longs;&longs;ible yet to reduce things to a very good pa&longs;s; and if I be not
mi&longs;taken, with a very &longs;mall charge in compari&longs;on of the profit that
would be received from tho&longs;e rich Grounds. This improvement
was of great expence in the time of
&longs;on the thing was not rightly under&longs;tood, there were made many
Drains; a great part of which were unprofitable and vain: and
among&longs;t &longs;o many operations, there hapned &longs;ome to be made that
&longs;ucceeded, as was de&longs;ired; but not being under&longs;tood, they were
held in no account; and thus the bu&longs;ine&longs;s being neglected, the
waters are returned into the &longs;ame &longs;tate as they were at fir&longs;t, be
fore the improvement. Here I have by familiar di&longs;cour&longs;es
with my friends, explained this enterprize undertaken by
tus
the Fable of
&longs;uch enchantment, that men fought with him alwayes in vain;
for though in the Combate he were cut in pieces, tho&longs;e divided
Members pre&longs;ently re-united, and returned to the fight more
fierce then ever. But the
him, after a long di&longs;pute, at the end he cut his head &longs;heer off
from the &longs;houlders at one blow; and nimbly alighting from his
Hor&longs;e, took the Mon&longs;trous head, and mounting again, as he rid
away he fell to &longs;have the Pole of that Mon&longs;ter, and &longs;o he lo&longs;t
the Lock of Hair, in which alone the enchantment lay; and then
the horrible Head in an in&longs;tant manife&longs;ted &longs;igns of death, and the
trunk which ran, &longs;eeking to reunite to it anew, gave the la&longs;t ga&longs;p,
and in this manner the enchantment ended. The Book of Fate
&longs;erved admirably to the
&longs;tand that Charm; for by &longs;having his whole head, the enchanted
hairs came to be cut off among&longs;t the re&longs;t: In the &longs;ame manner, I
&longs;ay, that it hath &longs;ometimes happened in Draining tho&longs;e Fields;
was light upon, on which the improvement and remedy to the
di&longs;order did depend. And to us my fore-named Treati&longs;e &longs;hall
&longs;erve for a Rule, which being well under&longs;tood, &longs;hall make us to
know wherein con&longs;i&longs;teth, and whereon dependeth this mi&longs;carri
age, and con&longs;equently it will be ea&longs;ie to apply thereunto a &longs;ea&longs;o
nable remedy.
And fir&longs;t I &longs;ay, That there is no doubt but that the waters
continue &longs;o high on tho&longs;e Plains becau&longs;e they are &longs;o high in the
principal River, which ought to receive them, and carry them
into the Sea. Now the Cau&longs;es of the height of the River, may
in my judgement be reduced to one alone; which is that by me
&longs;o often mentioned for the mo&longs;t Potent one, and declared in my
afore-named Tractate; to wit, The tardity of the motion of the
waters, which doth alwayes infallibly, and preci&longs;ely cau&longs;e the
&longs;elf &longs;ame Running Water to change the mea&longs;ure of its thickne&longs;s
at &longs;uch a rate, that the more it encrea&longs;eth in velocity, the more
it decrea&longs;eth in mea&longs;ure; and the more it decrea&longs;eth in velocity,
the more it encrea&longs;eth in mea&longs;ure: As for example; If a River
run in &longs;uch a place with the velocity of moving a mile in the
&longs;pace of an hour, and afterwards the &longs;ame River in another place
doth encrea&longs;e in velocity, &longs;o as to make three miles an hour;
that &longs;ame River &longs;hall dimini&longs;h in thickne&longs;s two thirds: And on
the contrary, If it &longs;hall dimini&longs;h in velocity &longs;o, as that it runneth
but half a mile in the &longs;ame time, it &longs;hall encrea&longs;e the double in
thickne&longs;s and mea&longs;ure. And in a word, look what proportion
the velocity in the fir&longs;t place, hath to the velocity in the &longs;econd,
and &longs;uch hath reciprocally the mea&longs;ure of the thickne&longs;s in the
&longs;econd place, to the mea&longs;ure in the fir&longs;t; as I have clearly demon
&longs;trated in my Treati&longs;e: Which I repeat &longs;o frequently, that I
fear the Profe&longs;&longs;ors of Polite Learning will charge me with Tua
tologie, and vain Repetition. But I am &longs;o de&longs;irous in this mo&longs;t
important point to be well under&longs;tood, becau&longs;e it will then be
ea&longs;ie to comprehend all the re&longs;t; and without this it is impo&longs;&longs;ible
(I will not &longs;ay difficult, but ab&longs;olutely impo&longs;&longs;ible) to under&longs;tand,
or ever to effect any thing to purpo&longs;e. And the better to ex
plain the example, let it be &longs;uppo&longs;ed,
That the water of a River A D,
runneth high at the level of A F,
with &longs;uch a certain velocity; and let
it, by the &longs;ame water, be velocitated
three times more; I &longs;ay, that it will
abate 1/3, and &longs;hall &longs;tand at the level
in B E; and if it &longs;hall more veloci
tate, it will abate the more at the Sea; But if it &longs;hould retard
the &longs;aid level A F; although that the &longs;elf &longs;ame quantity of water
runneth all the while. By the above-named &longs;olid Principle I
re&longs;olve extravagant Problems in my Treati&longs;e, and a&longs;&longs;ign the Rea
&longs;ons of admirable effects of Running Waters: But as for what
concerneth our purpo&longs;e of the
&longs;es very plain and clear; for which, by the trampling of Cattle
which pa&longs;s thorow the
bly, that it is as it were a miracle for tho&longs;e Reeds, Flags, and
Weeds that &longs;pring up, encrea&longs;e, and &longs;pread all over the River,
&longs;top and impede that velocity of the waters which they would
have by means of their declivity. But that pa&longs;&longs;age of tho&longs;e Bea&longs;ts,
treading down tho&longs;e Weeds unto the bottom of the River, in &longs;uch
&longs;ort, as that they no longer hinder the Current of the Water;
and the &longs;ame Waters increa&longs;ing in their cour&longs;e, they do dimi
ni&longs;h in mea&longs;ure and height; and by this meanes the Ditches of the
Plains empty into the &longs;ame &longs;ucce&longs;sfully, and leave them free
from Waters, and Drained. But the&longs;e Weeds in a &longs;hort
time &longs;prouting up anew, and rai&longs;ing their &longs;talkes thorow the
body of the Waters, they reduce things to the &longs;ame evil
&longs;tate, as before, retarding the velocity of the Water, ma
king it to increa&longs;e in height, and perhaps do occa&longs;ion grea
ter mi&longs;chiefs; &longs;eeing that tho&longs;e many knots which each plant
&longs;hoots forth, begets a greater multitude of Stalks, which much
more incumbering the Water of the River, are a greater impe
diment unto its velocity, and con&longs;equently make the height
of the waters to encrea&longs;e &longs;o much the more, and do more mi&longs;chief
than before.
Another head to which the&longs;e harms may be reduced, but pro
ceeding from the &longs;ame Root, which hath a great part in this
di&longs;order, is the impediment of tho&longs;e Wears in the River which
are made by heightning the bed of the &longs;ame, for placing of fi&longs;h
ing-nets; of which
a voyage thorow tho&longs;e waters to
Wears are &longs;uch impediments, that &longs;ome one of them makes the
water of the River in the upper part to ri&longs;e half a Palm, and
&longs;ometimes a whole Palm, and more; &longs;o that when they are all
gathered together, the&longs;e impediments amount to more than &longs;even,
or po&longs;&longs;ibly than eight Palms.
There concurreth for a third mo&longs;t Potent Cau&longs;e of the waters
continuing high in the evacuating, or Draining Chanel, and con
&longs;equently on the Plains; The great abundance of water that i&longs;&longs;u
eth from
Banks when they are abundant; but encrea&longs;ing above its Chanel,
they unite with tho&longs;e of the Evacuator, and di&longs;per&longs;ing thorow
ter than is conceived, according to what hath been demon
&longs;trated in the Second Con&longs;ideration upon the
Nor is it to any purpo&longs;e to &longs;ay, that if we &longs;hould mea&longs;ure
all the Waters that disimbogue from
them into one &longs;umme, we &longs;hould not finde them to be &longs;uch,
as that they &longs;hall be able to make the Waters of the Fens
to increa&longs;e, by rea&longs;on of the great expan&longs;ion of them, over
which that body of water is to di&longs;tend: for to this in&longs;tance we
an&longs;wer wich that which we have given notice of in the Fir&longs;t Con
&longs;ideration touching the
ment that is cau&longs;ed by the And more
over, if I &longs;hall adde thereto that which I write in the Second
Con&longs;ideration, it will be very apparent how greatly harmfull
and prejudicial the&longs;e excurfions of Waters from
may be, which are not kept under, and confined within the
River: Therefore, proceeding to the provi&longs;ions, and ope
rations that are to be accounted Principall, I reduce them to
three Heads.
In the fir&longs;t place it is nece&longs;&longs;ary to throw down tho&longs;e Weares,
and to take the Pi&longs;ciaries quite away, ob&longs;erving a Maxime, in
my judgment, infallible, that Fi&longs;hing and Sowing are two things
that can never con&longs;i&longs;t together; Fi&longs;hing being on the Water, and
Sowing on land.
Secondly, it will be nece&longs;&longs;ary to cut under Water in the bot
tome of the River tho&longs;e Weeds and Plants that grow and in
crea&longs;e in the River, and leave them to be carried into the Sea by
the Stream; for by this means the&longs;e Reeds &longs;hall not &longs;pring up
and di&longs;tend along the bottome of the River, by means of the
Bea&longs;ts treading upon them; And the &longs;ame ought to be done
often, and with care, and mu&longs;t not be delaied till the mi&longs;
chief increa&longs;e, and the Champain Grounds be drowned, but
one ought to order matters &longs;o, as that they may not drown. And I will affirm, that otherwi&longs;e this principal point would be
come a mo&longs;t con&longs;iderable inconvenience.
Thirdly, it is nece&longs;&longs;ary to make good the Banks of
on the left hand, and to procure that tho&longs;e Waters may run in
the Chanel, and not break forth. And it is to be noted, that
it is not enough to do one or two of tho&longs;e things, but we are to
put them all in execution; for omitting any thing, the whole
machine will be out of tune, and &longs;poiled. But proceeding with
due care, you &longs;hall not only Drain the
means of this la&longs;t particular the Current of
&longs;cowr its own Chanel of its &longs;elf, even to the carrying part of it
away: and haply with this abundance of water that it &longs;hall
into the Sea. And it would, la&longs;t of all, be of admirable bene
fit to clean&longs;e
with it is overgrown.
And with this I conclude, that the Improvement or Drain
po&longs;&longs;ible to be made con&longs;i&longs;teth in the&longs;e three particulars. Fir&longs;t,
in taking away the Fi&longs;hing Weares, leaving the Cour&longs;e
of the Waters free. Secondly, in keeping the Principal
Rivers clear from Weeds and Plants. Thirdly, in keeping
the water of All which are
things that may be done with very little charge, and to the
manife&longs;t benefit of the whole Country, and to the rendering
the Air whol&longs;omer in all tho&longs;e Places adjoyning to the
tine Fens.
A
CONSIDERATION
Upon the
DRAINING
Of the Territories of
Bologna, Ferrara,
AND
Romagna.
BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO,
to P.
Univer&longs;ity of
The weghty bu&longs;ine&longs;&longs;e of the Draining of
the Territories of
and
handled and declared in writing from
the excellent memory of the Right Ho
nourable and Noble
who was heretofore Deputed Commi&longs;
&longs;ary General, and Vi&longs;itor of tho&longs;e Wa
ters; I am not able to make &longs;uch ano
ther Di&longs;cour&longs;e upon the &longs;ame Subject, but will only &longs;ay &longs;ome
what for farther confirmation of that which I have &longs;aid in this
Book upon the
on the Draining of tho&longs;e Plains of
vers
with, there have, in times pa&longs;t, very gro&longs;&longs;e Errours been com
mitted, through the not having ever well under&longs;tood the true
mea&longs;ure of Running waters; and here it is to be noted, that the
bu&longs;ine&longs;&longs;e is, that in
Lake, by diverting the
without con&longs;ideration had how great abatement of water might
follow in the Lake, if the
in the fir&longs;t Con&longs;ideration upon this particular, from which act
there hath in&longs;ued very bad con&longs;equences, not only the difficulty
of Navigation, but it hath infected the whol&longs;omne&longs;&longs;e of the Air,
and cau&longs;ed the &longs;toppage of the Ports of
contrary, the &longs;ame inadvertency of not con&longs;idering what ri&longs;ing of
the Water the
leys of
the certain cau&longs;e that &longs;o many rich and fertile Fields are drown
ed under water, converting the happy habitations and dwellings
of men into mi&longs;erable receptacles for Fi&longs;hes: Things which
doubtle&longs;&longs;e would never have happened, if tho&longs;e Rivers had been
kept at their height, and
and the other Rivers into that of
there having &longs;ufficient been &longs;poken by the above-named Cor&longs;ini
which after the Rivers &longs;hould be regulated, as hath been &longs;aid, I
verily believe would be of extraordinary profit, I much doubt in
deed that I &longs;hall finde it a hard matter to per&longs;wade men to be of
my mind, but yet neverthele&longs;s I will not que&longs;tion, but that tho&longs;e,
at lea&longs;t, who &longs;hall have under&longs;tood what I have &longs;aid and demon
&longs;trated concerning the manners and proportions, according to
which the abatements and ri&longs;ings of Running waters proceed,
that are made by the Diver&longs;ions and Introductions of Waters,
will apprehend that my conjecture is grounded upon Rea&longs;on. And although I de&longs;cend not to the exactne&longs;&longs;e of particulars, I
will open the way to others, who having ob&longs;erved the requi&longs;ite
Rules of con&longs;idering the quantity of the waters that are intro
duced, or that happen to be diverted, &longs;hall be able with punctu
ality to examine the whole bu&longs;ine&longs;&longs;e, and then re&longs;olve on that
which &longs;hall be expedient to be done.
Reflecting therefore upon the fir&longs;t Propo&longs;ition, that the
Ri&longs;ings of a Running Water made by the acce&longs;&longs;ion of new water
into the River, are to one another, as the Square-Roots of the
quantity of the water that runneth; and con&longs;equently, that the
&longs;ame cometh to pa&longs;s in the Diver&longs;ions: In&longs;omuch, that a River
running in height one &longs;uch a certain mea&longs;ure, to make it encrea&longs;e
double in height, the water is to be encrea&longs;ed to three times as
ple, the height &longs;hall be double; and if the water were centuple,
the height would be decuple onely, and &longs;o from one quantity
to another: And on the contrary, in the Diver&longs;ions; If of the
100. parts of water that run thorow a River, there &longs;hall be di
verted 19/160, the height of the River dimini&longs;heth onely 1/10, and con
tinuing to divert 17/100, the height of the River abateth likewi&longs;e 1/10,
and &longs;o proceeding to divert 15/100 and then 13/100, and then 11/100, and
then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by
each of the&longs;e diver&longs;ions, the height of the Running Water di
mini&longs;heth the tenth part: although that the diver&longs;ions be &longs;o une. qual.
Reflecting I &longs;ay upon this infallible Truth, I have had a
conceit, that though the
from the Valleyes, and there was onely left the
gation,
leth into the Valleys; yet neverthele&longs;s, the water in tho&longs;e &longs;ame
Valleyes would retain a tenth part of that height that became
conjoyned by the concour&longs;e of all the Rivers: And therefore I
&longs;hould think that it were the be&longs;t re&longs;olution to maintain the
nel of Navigation
be&longs;ides that it would be of very great ea&longs;e in the Navigation of
&longs;equently the Navigation would be continuate from
the Sea-&longs;ide.
But to manage this enterprize well, it is nece&longs;&longs;ary to mea&longs;ure
the quantity of the Water that the Rivers di&longs;charge into the Val
leys, and that which the
ner as I have demon&longs;trated at the beginning of this Book; for this
once known, we &longs;hall al&longs;o come to know, how profitable this di
ver&longs;ion of the
prove; which yet would &longs;till be unprofitable, if &longs;o be that all
the Rivers that di&longs;charge their waters into the Valleys, &longs;hould
not &longs;ir&longs;t be Drained, according to what hath been above ad
verti&longs;ed.
Abbot CASTELLI,
himfelf to the Relation ofCor&longs;ini,
&longs;ervations and Precepts of the &longs;aid Abbot; as is &longs;een in the pre
&longs;ent Di&longs;cour&longs;e. I thought it convenient for the compleating of the
Work of our Aulhour, upon the&longs;e &longs;ubjects, to in&longs;ert it in this
place.
A
Relation of the Waters in the Territories
of
BY
The Right Honourable and Illu&longs;trious,
nore
perintendent of the general DRAINS,
and Pre&longs;ident of
The
advice of Ago&longs;tino Spernazzati
the latter end of the time of
&longs;tanding the oppo&longs;ition of the
therein, diverted from their Chanels, for the more commodious
clean&longs;ing of the P
ro,
re&longs;tored, they might carry the Muddy-water thence into the Sea,
and re&longs;tore to the City the Navigation which was la&longs;t, as is ma
nife&longs;t by the Brief of the &longs;aid
dinal San Clemence,
The work of the &longs;aid clean&longs;ing, and introducing of the &longs;aid
P
ned betwixt them, proved &longs;o difficult, that after the expence of
va&longs;t &longs;umms in the &longs;pace of 21. years, there hath been nothing
done, &longs;ave the rendring of it the more difficult to be effected.
Interim, the Torrents with their waters, both muddy and
clear, have damaged the Grounds lying on the right hand of the
P
will &longs;peak in the fir&longs;t place, as of that which is of greater impor
tance, and from which the principal cau&longs;e of the mi&longs;chiefs that
re&longs;ult from the re&longs;t doth proceed.
This
in circumference about fourteen miles given it before, and part
of that of
cle; from whence, having depo&longs;ed the matter of its muddine&longs;s,
it i&longs;&longs;ued clear by the Mouths of
the P
Chanel on the right hand neer to
By the breaches on this &longs;ide it &longs;treamed out in great abun
dance from the upper part of
Pro&longs;pero, San Vincenzo,
incultivable: it made al&longs;o tho&longs;e places above but little fruitful,
by rea&longs;on of the impediments that their Draines received, finding
the Conveyances called
Motta
&longs;elves.
But by the Mouths in the inclo&longs;ing Bank or Dam at
S.
ancient Navigation of
the moderne of the mouth of
merce between
in any durable way renewed, whil&longs;t that this exceeds its due
bounds, and what ever moneys &longs;hall be imployed about the &longs;ame
&longs;hall be without any equivalent benefit, and to the manife&longs;t
and notable prejudice of the ^{*} Apo&longs;tolick Chamber.
Exchequer.
Thence pa&longs;&longs;ing into the Valley of
er, not only by the ri&longs;ing of the water, but by the rai&longs;ing of the
bottome, by rea&longs;on of the matter &longs;unk thither after Land
floods, and dilateth &longs;o, that it covereth all the Meadows there
abouts, nor doth it receive with the wonted facility the Drains of
the upper Grounds, of which the next unto it lying under the wa
ters that return upwards by the Conveyances, and the more re
mote, not finding a pa&longs;&longs;age for Rain-waters that &longs;ettle, become
either altogether unpro&longs;itable or little better.
From this Valley, by the Trench or Ditch of
new pa&longs;&longs;age it falleth into the P
ceive it clear, that &longs;o it may &longs;ink farther therein, and receiving
it muddy, becau&longs;e it hath acquired a quicker cour&longs;e, there will
ari&longs;e a very contrary effect.
Here therefore the &longs;uperficies of the water keeping high, until
it come to the Sea, hindereth the Valleys of
the River
turned, tho&longs;e of
the
in their Waters by their u&longs;ual In-lets, yet many times, as I my
&longs;elf have &longs;een in the
whereupon, being conjoyned with the muddine&longs;&longs;e of tho&longs;e Ri
vers that fall into the &longs;ame, they &longs;well, and dilate, and overflow
&longs;ome grounds, and deprive others of their Drains in like manner
Point of S.
the Valleys and P
and Valley many are in a very bad condition, and tho&longs;e that are
&longs;ome con&longs;iderable &longs;pace above not a little damnified.
In fine, by rai&longs;ing the bottom or &longs;and of the Valleys, and the
bed of
with waters, the Valleys of
are very bad) and ^{*}
danger, that may in time, if it be not remedied, become irrepa
rable, and at pre&longs;ent feeleth the incommodity of the Waters,
which penetrating thorow the pores of the Earth do &longs;pring up in
the &longs;ame, which they call
to the prejudice of
portant to the
plat of Ground al
mo&longs;t &longs;urrounded
with Bogs or wa
ters, like an I&longs;land
Which particulars all appear to be atte&longs;ted under the hand of
a Notary in the
His Holine&longs;&longs;e, and are withall known to be true by the ^{*}
them&longs;elves, of whom (be&longs;ides the reque&longs;t of the
greater part beg compa&longs;&longs;ion with &longs;undry
dies, a&longs;well for the mi&longs;chiefs pa&longs;t, as al&longs;o for tho&longs;e in time to
come, from which I hold it a duty of Con&longs;cience, and of Cha
rity to deliver them.
rara.
Pope
was the &longs;aid Introduction of the
than benefit to that City, of which I &longs;peak not at pre&longs;ent, be
cau&longs;e I think that there is need of a readier and more acco
modate remedy.
So that I &longs;ee not how any other thing can be &longs;o much con&longs;ide
rable as the removal of
^{*} inclo&longs;ing it from Valley to Valley untill it come to the Sea, as
the Dukes of
re&longs;i
right hand of the P
openly, prote&longs;t again&longs;t it; and becau&longs;e that before the Chanel
were made as far as the Sea, many hundreds of years would be
&longs;pent, and yet would not remedy the dammages of tho&longs;e who
now are agrieved, but would much increa&longs;e them, in regard the
Valleys would continue &longs;ubmerged, the Drains &longs;topped, and the
other Brooks ob&longs;tructed, which would of nece&longs;&longs;ity drown not a
few Lands that lie between Valley and Valley; and in fine, in
regard it hath not from
ty miles a greater fall then 19, 8, 6, feet, it would want that force
which they them&longs;elves who propound this project do require it to
it is intended to be let into
made by hand.
So that making the Line of the bottome neer to
would ri&longs;e to tho&longs;e prodigious termes that they do make bigger,
and they may thence expect tho&longs;e mi&longs;chiefs, for which they
will not admit of introducing it into the &longs;aid P
Among&longs;t the wayes therefore that I have thought of for effect
ing that &longs;ame remotion, and which I have cau&longs;ed to be viewed by
skilful men that have taken a level thereof, (with the a&longs;&longs;i&longs;tance of
the venerable Father, Benedetto Ca&longs;telli
much fidelity and hone&longs;ty, and no le&longs;s expert in &longs;uch like affairs
touching waters, than perfect in the
onely, the re&longs;t being either too tedious, or too dangerous to the
City, have &longs;eemed to me worthy, and one of them al&longs;o more than
the other, to offer to your Lord&longs;hip.
The one is to remit it into the Chanel of
it goeth of its own accord to the Sea.
The other is to turn it into
times it hath done, it will carry it to the Sea happily.
As to what concerns the making choice of the fir&longs;t way, that
which &longs;eemeth to per&longs;wade us to it is, that we therein do nothing
that is new, in that it is but re&longs;tored to the place whence it was
removed in the year 1522. in the time of Pope
agreement made in way of contract, between
that are either out of date, or el&longs;e have been too long time
deferred.
In like manner the facility wherewith it may be effected, let
ting it run into the divided P
rara,
and from thence thorow the Trench made by the
along by
thick Banks, that will &longs;erve at other times for it, and for the wa
ters of P
That what ever its Fall be, it would maintain the &longs;ame, not
having other Rivers, which with their Floods can hinder it; and
that running confined between good Banks, without doubt it
would not leave
would be &longs;ufficient if it came to
the Ebbing and Flowing of the Sea, it would run no hazard of
having its Chanel filled up from thence downwards.
That there might thence many benefits be derived to the City,
by means of the Running Waters, and al&longs;o no mean Navigation
might be expected.
On the contrary it is objected, That it is not convenient to
the peril that would thence redound to this City.
And that going by
the Mouth
by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, &longs;o
that it would come to fall but 4. inches & an half, or thereabouts
in a mile; whereas the common opinion of the skilfull (to the
end that the Torrents may not depo&longs;e their &longs;and that they bring
with them in Land-Floods) requireth the twenty fourth part of
the hundredth part of their whole length, which in our ca&longs;e,
accounting according to the mea&longs;ure of the&longs;e places, is 16. inches
a ^{*} mile; whereupon the &longs;inking of the Mud and Sand would
mo&longs;t certainly follow, and &longs;o an immen&longs;e heightning of the Line
of the Bottom, and con&longs;equently a nece&longs;&longs;ity of rai&longs;ing the Banks,
the impo&longs;&longs;ibility of maintaining them, the danger of breaches
and decayes, things very prejudicial to the
of
Tower of
tho&longs;e of the Sluices of
&longs;aid
ters that &longs;hould enter into the
guardo,
becau&longs;e they belong to the Duke of
diverting the waters of that place at his plea&longs;ure to the work of
turning Mills.
the&longs;e places is
&longs;omewhat bigger
than ours.
The greater part of which Objections, others pretend to prove
frivolous, by &longs;aying, that its running there till at the la&longs;t it was
turned another way, is a &longs;ign that it had made &longs;uch an elevation
of the Line, of its Bed as it required; denying that it needeth
&longs;o great a declivity as is mentioned above; and that for the fu
ture it would ri&longs;e no more.
That the &longs;aid Dra ns and Ditches did empty into the &longs;ame,
whil&longs;t P
&longs;o when onely
That there would no Breaches follow, or if they did, they
would be onely of the water of
be taken away (in tho&longs;e parts they call damming up of Breaches,
and mending the Bank,
&longs;tion whether they would procure more inconvenience than bene
fit, for that its Mud and Sand might in many places, by filling
them up, occa&longs;ion a &longs;ea&longs;onable improvement.
Now omitting to di&longs;cour&longs;e of the &longs;olidity of the rea&longs;ons on the
one&longs;ide, or on the other, I will produce tho&longs;e that move me to
&longs;u&longs;pend my allowance of this de&longs;ign.
The fir&longs;t is, that although I dare not &longs;ub&longs;cribe to the opinion
of tho&longs;e that require 16. inches Declivity in a mile to
prevent its depo&longs;ing of Mud; yet would I not be the Author that
&longs;hould make a trial of it with &longs;o much hazard, for having to &longs;a
tisfie my &longs;elf in &longs;ome particulars cau&longs;ed a Level to be taken of
the Rivers
we found that they have more Declivity by much than Arti&longs;ts re
quire, as al&longs;o the
Chappel of
Line falleth five feet and five inches. So that I hold it greater
prudence to depend upon that example, than to go contrary to a
common opinion, e&longs;pecially &longs;ince, that the effects cau&longs;ed by
it &longs;elf do confirm me in the &longs;ame, for when it was for&longs;aken by
the P
Chanel with Sand, or becau&longs;e its too long journey did increa&longs;e
it, it al&longs;o naturally turned a&longs;ide, and took the way of the &longs;aid
P
way, it only began (as relations &longs;ay) to make Breaches, an evi
dent &longs;ign that it doth depo&longs;e Sand, and rai&longs;e its Bed; which a
greeth with the te&longs;timony of &longs;ome that were examined in the
having Running Water, and &longs;ome kind of pa&longs;&longs;age for Boats,
and yet neverthele&longs;s affirm that it for want of Running Water
had made too high Stoppages and Shelfes of Sand; &longs;o that if
it &longs;hould be re&longs;tored to the Cour&longs;e that it for&longs;ook, I much fear
that after a &longs;hort time, if not &longs;uddenly, it would leave it a
again.
The &longs;econd I take from the ob&longs;ervation of what happened to
brought by Cardinal
that notwith&longs;tanding that it had Running Waters in much grea
ter abundance than
that Chanel it rai&longs;ed its Bed well neer five feet, as is to be &longs;een
below the Sluice made by Cardinal
yea, the &longs;aid Cardinal
&longs;hould appear to have been of no danger nor damage, was con
&longs;trained at its Overflowings, to give it Vent into
it might not break in upon, and prejudice the City; which dan
ger I &longs;hould more fear from
abundance of Water and Sand
Thirdly, I am much troubled (in the uncertainty of the &longs;uc
ce&longs;s of the affair) at the great expence thereto required; For in
regard I do not approve of letting it in, neer to the Fortre&longs;&longs;e,
for many re&longs;pects, and carrying it by
Month
under Water; but from the Mouth
would al&longs;o be nece&longs;&longs;ary to make new Scowrings of the Chanel;
to the end, that the Water approaching (by wearing and carry
ing away the Earth on both &longs;hores, might make a Bed &longs;ufficient
for its Body, the depth made for
I conceive; and if it &longs;hould &longs;uffice, when could the people of
thereof?
Fourthly, it &longs;erves as an Argument with me, to &longs;ee that the
very individual per&longs;ons concerned in the Remotion or Diver&longs;ion
of the &longs;aid Torrent, namely, the
and that the whole City of
at pre&longs;ent receive damage by it, cannot indure to hear thereof. The rea&longs;on that induceth the&longs;e la&longs;t named to be &longs;o aver&longs;e thereto,
is, either becau&longs;e that this undertaking will render the introducti
on of the Water of
the danger thereof; The others decline the Project, either for
that they know that
or becau&longs;e they fear that it is too much expo&longs;ed to tho&longs;e mens re
vengeful Cutting of it who do not de&longs;ire it &longs;hould; and if a
man have any other wayes, he ought, in my opinion, to forbear
that, which to &longs;uch as &longs;tand in need of its Removal, is le&longs;&longs;e &longs;ati&longs;
factory, and to &longs;uch as oppo&longs;e it, more prejudicial.
To conclude, I exceedingly honour the judgment of Cardinal
a particular Study, Ob&longs;ervation, and Experience of the&longs;e Wa
ters for the &longs;pace of three years together, doth not think that
dinal S.
&longs;ite under&longs;tanding, we ought to make great account. But if e
ver this &longs;hould be re&longs;olved on, it would be materially nece&longs;&longs;ary
to unite the Quick and Running Waters of the little Chanel of
beginning tho&longs;e of
Springs or Heads of
ing its Sand, and the matter of its Muddine&longs;s into the Sea; and
then there would not fail to be a greater evacuation and &longs;cowr
ing; but withall the Proprietors in the I&longs;let of
of
of Purlings or Sewings of the Water from the River thorow
the Boggy Ground thereabouts.
I &longs;hould more ea&longs;ily incline therefore to carry it into
at
ou&longs;ly enumerates in a &longs;hort, but well-grounded Tract of his: not
ches occa&longs;ion &longs;ome inconvenience; e&longs;pecially, in the beginning:
but becau&longs;e I hold this for the incomodities of it, to be a far le&longs;s
evil than any of the re&longs;t; and becau&longs;e that by this means there is
no occa&longs;ion given to them of
deprived of the hope of ever &longs;eeing the P
of their City: To whom, where it may be done, it is but rea&longs;on
that &longs;atisfaction &longs;hould be given.
It is certain that P
great Valley made by the
carry, as the Ma&longs;ter-Drain to the Sea, that is the grand receptacle
of all Waters; tho&longs;e particular &longs;treams which de&longs;cend from
them.
That the
Mella,
the &longs;aid P
That although P
did not ob&longs;truct its pa&longs;&longs;age; &longs;o that it neither is, nor ought to
&longs;eem &longs;trange, if one for the greater common good &longs;hould turn it
into the &longs;ame.
Now at
by the levels that were taken by my Order; of all which I &longs;hould
be&longs;t like the turning of it to
above
lower, as &longs;hall be judged lea&longs;t prejudicial, when it cometh to the
execution, and this for two principal rea&longs;ons: The one becau&longs;e
that then it will run along by the confines of the Church P tri
mony, without &longs;eparating
is, Becau&longs;e the Line is &longs;horter, and con&longs;equently the fall greater;
for that in a &longs;pace of ten miles and one third, it falleth twenty &longs;ix
feet, more by much than is required by Arti&longs;ts; and would go
by places where it could do but little hurt, notwith&longs;tanding that
the per&longs;ons interre&longs;&longs;ed &longs;tudy to amplifie it incredibly.
On the contrary, there are but onely two objections that are
worthy to be examined; One, That the Drains and Ditches of
S.
others that enter into P
encrea&longs;ing of the waters in the P
about the Tran&longs;om of the
to a terrible height, at which it would not be po&longs;&longs;ible to make, or
keep the Banks made, &longs;o that it would break out and drown
the Meadowes, and cau&longs;e mi&longs;chiefs, and damages un&longs;peakable
and irreparable; as is evident by the experiment made upon
into P
out into the territories of
that might be done, it would thereupon en&longs;ue, that there being
let into the Chanel of P
we account tho&longs;e of
greate&longs;t heights) the &longs;uperficies of it would ri&longs;e at lea&longs;t four feet,
in&longs;omuch that either it would be requi&longs;ite to rai&longs;e its Banks all the
way unto the Sea, to the &longs;ame height, which the trea&longs;ures of the
&longs;ity of enduring exce&longs;&longs;ive Breaches. To the&longs;e two Heads are the
Arguments reduced, which are largely amplified again&longs;t our opi
nion; and I &longs;hall an&longs;wer fir&longs;t to the la&longs;t, as mo&longs;t material.
I &longs;ay therefore, that there are three ca&longs;es to be con&longs;idered:
Fir&longs;t, PSecondly,
low. Thirdly,
As to the fir&longs;t and &longs;econd, there is no difficulty in them; for if
P
into it, and there &longs;hall need no humane Artifice about the Banks:
And if
the Chanel of it; and al&longs;o from thence no inconvenience &longs;hall
follow. The third remains, from which there are expected ma
ny mi&longs;chiefs; but it is a mo&longs;t undoubted truth, that the excre&longs;cen
cies of
are to continue but &longs;even, or eight hours at mo&longs;t, and &longs;o would
never, or very rarely happen to be at the &longs;ame time with tho&longs;e of
P
miles di&longs;tance from thence. But becau&longs;e it &longs;ometimes may hap
pen, I reply, that when it cometh to pa&longs;s,
P
the Chanel of
where it runneth at pre&longs;ent, and wherewith there is no doubt, but
that the per&longs;ons concerned will be well plea&longs;ed, it being a great
benefit to them, to have the water over-flow their grounds once
every four or five years, in&longs;tead of &longs;eeing it anoy them continu
ally. Yea, the Vent may be regulated, re&longs;erving for it the Cha
nel in which
by a Dam at
&longs;trong Sluices, that may upon all occa&longs;ions be opened and &longs;hut. And for my part, I do not que&longs;tion but that the Proprietors
them&longs;elves in
receiving, and confining it in the time of the Vents, might carry
the Sand into the P
ed any &longs;toppage by Mud and Sand, &longs;ince that it is &longs;uppo&longs;ed that
there will but very &longs;eldom be any nece&longs;&longs;ity of u&longs;ing it; &longs;o that
it.
And in this manner all tho&longs;e Prodigies vani&longs;h that are rai&longs;ed
with &longs;o much fear from the enterance of the Water of
&longs;welled into P
an&longs;wer; yet neverthele&longs;&longs;e we do not take that quantity of Wa
ter, that is carried by
med: For that P. D.
than accurately ob&longs;erved the mea&longs;ures of this kind, noting that
the breadth and depth of a River is not enough to re&longs;olve the
que&longs;tion truly, but that there is re&longs;pect to be had to the velocity
of the Waters, and the term of time, things hitherto not con&longs;i
dered by the Skilful in the&longs;e affairs; and therefore they are not
able to &longs;ay what quantity of Waters the &longs;aid Rivers carry, nor
to conclude of the ri&longs;ings that will follow thereupon. Nay, it
is mo&longs;t certain, that if all the Rivers that fall into
above thirty, &longs;hould ri&longs;e at the rate that the&longs;e compute
do, an hundred feet of Banks would not &longs;uffice, and yet they
have far fewer: So that this confirmes the Rule of R. P. D.
detto,
of
compounded of the proportion of the breadth of the Chanel of
in
argument that there cannot in it, by this new augmentation of
Waters follow any alteration that nece&longs;&longs;itates the rai&longs;ing of its
Banks, as appeareth by the example of
&longs;o far from &longs;welling P
carried away many Shelfs and many I&longs;lets that had grown in its
Bed, for want of Waters &longs;ufficient to bear away the matter of
Land-floods in &longs;o broad a Chanel; and as is learnt by the trial
made by us in
in the River &longs;tanding marks, and &longs;hutting the &longs;aid Sluice, we could
&longs;ee no &longs;en&longs;ible abatement, nor much le&longs;s after we had opened it
&longs;en&longs;ible increa&longs;ment; by which we judge that the &longs;ame is to &longs;uc
ceed to P
portion to
Rivers in which the Ob&longs;ervation was made. So that there is no
longer any occa&longs;ion for tho&longs;e great rai&longs;ings of Banks, and the
danger of the ruptures as well of
&longs;o the fear le&longs;t that the Sluices which empty into P
ceive ob&longs;truction: which if they &longs;hould, yet it would be over in
a few hours. And as to the Breaches of
in 1623. I know not why, &longs;eeing that it is confe&longs;&longs;ed that the P
was not, at that time, at its height, one &longs;hould rather charge it The truth is, that the
Bank was not made of proof, &longs;ince that the &longs;ame now continu
eth whole and good, and
was, when it brake more than a foot and half of its Banks above
the Water, and to &longs;pare; but it broke thorow by a Moles wor
king, or by the hole of a Water-Rat, or &longs;ome &longs;uch vermine;
and by occa&longs;ion of the badne&longs;s of the &longs;aid Banks, as I finde by
the te&longs;timony of &longs;ome witne&longs;&longs;es examined by my command, that
I might know the truth thereof. Nor can I here forbear to &longs;ay,
that it would be better, if in &longs;uch matters men were more candid
and &longs;incere. But to &longs;ecure our &longs;elves neverthele&longs;&longs;e, to the ut
mo&longs;t of our power, from &longs;uch like Breaches which may happen
at the fir&longs;t, by rea&longs;on of the newne&longs;&longs;e of the Banks, I pre&longs;uppo&longs;e
that from P
be a high and thick Fence made with its Banks, &longs;o that there
would be no cau&longs;e to fear any what&longs;oever acce&longs;&longs;ions of Water,
although that concurrence of three Rivers, which was by &longs;ome
more ingeniou&longs;ly aggravated than faithfully &longs;tated by that which
was &longs;aid above were true; to whom I think not my &longs;elf bound
to make any farther reply, neither to tho&longs;e who &longs;ay that
a&longs;cend upwards into
who would introduce a &longs;mall branch of the &longs;aid P
Chanel of
onely, but al&longs;o all the other Brooks of which we complained;
and becau&longs;e that withal it is impo&longs;&longs;ible, that a River &longs;o capacious
as
hath no proportion to it.
I come now to the bu&longs;ine&longs;&longs;e of the Ditches and Draines; and
as to the Conveyance of
ted to turn it into
harm, and though it were not removed, yet would it by a Trench
under ground pur&longs;ue the cour&longs;e that it now holdeth, and al&longs;o
would be able to di&longs;-imbogue again into the &longs;aid new Chanel of
would continue at a lower level than that which
when it came to
empty it &longs;elf for &longs;ome time.
The Conveyance or Drain of
Chanel of
Trenches, without any prejudice where they run at pre&longs;ent, or
without any more works of that nature, they may be turned into
the &longs;aid new Chanel, although with &longs;omewhat more of incon
venience; and withall, the Chanel of
be a &longs;ufficient receptacle for any other Sewer or Drain what&longs;oe
ver, that &longs;hould remain there.
All which Operations might be brought to perfection with
150. thou&longs;and Crowns, well and faithfully laid out; which &longs;umm
the
benefit.
Let me be permitted in this place to propo&longs;e a thing which I
have thought of, and which peradventure might occa&longs;ion two
benefits at once, although it be not wholly new. It was in the
time of
neer, to cut the
&longs;ufficient evacuation to derive the water thereof into the P
that time effected, either by rea&longs;on of the oppo&longs;itions of tho&longs;e,
who&longs;e po&longs;&longs;e&longs;&longs;ions were to be cut thorow, or by rea&longs;on of the
great &longs;um of money that was nece&longs;&longs;ary for the effecting of it: But
in viewing tho&longs;e Rivers, we have ob&longs;erved, that the &longs;edge cutting
might ea&longs;ily be made below
Bank called
skilful Arti&longs;ts &longs;hall judge meet unto the P
above 160. Perches in length, would be fini&longs;hed with onely
12000. Crowns.
Fir&longs;t; it is to be believed, that the waters running that way,
would not fail to open that Mouth into the Sea, which at pre
&longs;ent is almo&longs;t choakt up by the Shelf of Sand, which the new
Mouth of
again bring into u&longs;e the Port
And haply experience might teach us, that the &longs;uperficies of
P
acce&longs;&longs;ion of
Whereupon, if it &longs;hould &longs;o fall out, tho&longs;e Princes would have
no rea&longs;on to complain; who &longs;eem to que&longs;tion, le&longs;t by this new
acce&longs;&longs;ion of water into PWhich I thought not fit to omit to repre&longs;ent to your Lord&longs;hip;
not, that I propo&longs;e it to you as a thing ab&longs;olutely certain, but that
you might, if you &longs;o plea&longs;ed, lay it before per&longs;ons who&longs;e judge
ments are approved in the&longs;e affairs.
I return now from where I degre&longs;t, and affirm it as indubita
ble, that
it at this day is; and that it cannot go into any other place but
that, whither
at pre&longs;ent plea&longs;eth me better than any other; or into
whence it was taken away; the vigilance of Men being able to
obviate part of tho&longs;e mi&longs;chiefs, which it may do there.
But from its Removal, be&longs;ides the alleviation of the harm
of that which is occa&longs;ioned by the other Brooks, to the right hand
of the
water of
ner, that the Valleys would have a greater Fall into the &longs;ame,
and con&longs;equently it would take in, and &longs;wallow greater abun
dance of water; and by this means the Ditches and Draines
of the Up-Lands would likewi&longs;e more ea&longs;ily Fall into them; e&longs;
pecially if the &longs;couring of
by which the waters of
if al&longs;o that of
might enter as much water into the &longs;aid P
from it by the removal of
the water of the Valleys would a&longs;&longs;wage double: Nor would the
people of
cau&longs;e to complain; for that there would not be given to them
more water than was taken away: Nay &longs;ometimes whereas they
had Muddy waters, they would have clear; nor need they to fear
any ri&longs;ing: And furthermore, by this means a very great quan
tity of ground would be re&longs;tored to culture; For the effecting of
all which, the &longs;umm of 50. thou&longs;and Crowns would go very far,
and would &longs;erve the turn at pre&longs;ent touching tho&longs;e Brooks, car
rying them a little farther in the mean time, to fill up the greater
cavities of the Valleys, that we might not enter upon a va&longs;ter
and harder work, that would bring with it the difficulties of other
operations, and &longs;o would hinder the benefit which the&longs;e people
expect from the paternal charity of His Holine&longs;s.
TO
The Right Honourable,
MONSIGNORE
D. Ferrante Ce&longs;arini.
My Treati&longs;e of the MENSURATION of RUN
NING WATERS, Right Honourable, and
mo&longs;t Noble Sir, hath not a greater Preroga
tive than its having been the production of the
command of Pope
line&longs;s was plea&longs;ed to enjoyn me to go with
impo&longs;ed upon him in the year 1625. of the Waters of
Bologna, Romagna,
applying my whole Study to my &longs;ervice and duty, I publi&longs;hed in
that Treati&longs;e &longs;ome particulars till then not rightly under&longs;tood and
con&longs;idered (that I knew) by any one; although they be in them
&longs;elves mo&longs;t important, and of extraordinary con&longs;equence. Yet
I mu&longs;t render thanks to Your Lord&longs;hip for the honour you have
done to that my Tract; but wi&longs;h withal, that your E&longs;teem of it
may not prejudice the univer&longs;al E&longs;teem that the World hath of
Your Honours mo&longs;t refined judgement.
As to that Point which I touch upon in the Conclu&longs;ion, name
ly, That the con&longs;ideration of the Velocity of Running Water &longs;up
plyeth the con&longs;ideration of the ^{*} Length omitted in the common
way of mea&longs;uring Running Waters; Your Lord&longs;hip having com
manded me that in favour of
very of the di&longs;order that commonly happeneth now adayes in
the di&longs;tribution of the Waters of Fountains, I &longs;hould demon
&longs;trate that the knowledge of the Velocity &longs;erveth for the finding
of the Length: I have thought fit to &longs;atisfie your Command by
relating a Fable; which, if I do not deceive my &longs;elf, will make
out to us the truth thereof; in&longs;omuch that the re&longs;t of my Treati&longs;e
&longs;hall thereby al&longs;o become more manife&longs;t and intelligible, even to
mi&longs;printed.
In the dayes of yore, before that the admirable Art of Wea
ving was in u&longs;e, there was found in
Trea&longs;ure, which con&longs;i&longs;ted in an huge multitude of pieces of Er
me&longs;in, or Damask, I know not whether; which, as I take it,
amounted to near two thou&longs;and pieces; which were of &longs;uch a
nature, that though their Breadth and Thickne&longs;s were finite and
determinate, as they u&longs;e to be at this day; yet neverthele&longs;s, their
Length was in a certain &longs;en&longs;e infinite, for that tho&longs;e two thou&longs;and
pieces, day and night without cea&longs;ing, i&longs;&longs;ued out with their ends
at &longs;uch a rate, that of each piece there i&longs;&longs;ued 100. Ells a day, from
a deep and dark Cave, con&longs;ecrated by the Super&longs;tition of tho&longs;e
people, to the fabulous
times (I take it to have been, in that &longs;o much applauded and
de&longs;ired Golden age) it was left to the liberty of any one, to cut
off of tho&longs;e pieces what quantity they plea&longs;ed without any diffi
culty: But that felicity decaying and degenerating, which was
altogether ignorant of
pernicious, the Original of all evils, and cau&longs;e of all di&longs;cords;
there were by tho&longs;e people &longs;trong and vigilant Guards placed
upon the Cave, who re&longs;olved to make merchandize of the Stuffes;
and in this manner they began to &longs;et a price upon that ine&longs;tima
ble Trea&longs;ure, &longs;elling the propriety in tho&longs;e pieces to divers Mer
chants; to &longs;ome they &longs;old a right in one, to &longs;ome in two, and to
&longs;ome in more. But that which was the wor&longs;t of all, There was
found out by the in&longs;atiable avarice of the&longs;e men crafty inventions
to deceive the Merchants al&longs;o; who came to buy the afore&longs;aid
commodity, and to make them&longs;elves Ma&longs;ters, &longs;ome of one
&longs;ome of two, and &longs;ome of more ends of tho&longs;e pieces of &longs;tuff;
and in particular, there were certain ingenuous Machines placed
in the more &longs;ecret places of the Cave, with which at the plea&longs;ure
of the Guards, they did retard the velocity of tho&longs;e Stuffs, in
their i&longs;&longs;uing out of the Cave; in&longs;omuch, that he who ought to have
had 100. Ells of Stuff in a day, had not above 50, and he who
&longs;hould have had 400, enjoyed the benefit of 50. onely; and &longs;o all
the re&longs;t were defrauded of their Rights, the &longs;urplu&longs;age being &longs;old,
appropriated, and &longs;hared at the will of the corrupt Officers: So
that the bu&longs;ine&longs;s was without all order or ju&longs;tice, in&longs;omuch that
the Godde&longs;s
every one of their benefit, and with a dreadful Earthquake for
ever clo&longs;ing the mouth of the Cave, in puni&longs;hment of &longs;o much
impiety and malice: Nor did it avail them to excu&longs;e them&longs;elves,
by &longs;aying that they allowed the Buyer the Breadth and Thick
ne&longs;s bargained for; and that of the Length, which was infinite,
Prie&longs;t of the Sacred
length, which they were defrauded of, in that the velocity of the
ftuffe was retarded, as it i&longs;&longs;ued out of the Cave: and although
the total length of the Piece was infinite, for that it never cea
&longs;ed coming forth, and &longs;o was not to be computed; yet never
thele&longs;s its length con&longs;idered, part by part, as it came out of the
Cave, and was bargained for, continued &longs;till finite, and might
be one while greater, and another while le&longs;&longs;er, according as the
Piece was con&longs;tituted in greater or le&longs;&longs;er velocity; and he added
withall, that exact Ju&longs;tice required, that when they &longs;old a piece
of &longs;tuff, and the propriety or dominion therein, they ought not
only to have a&longs;certained the breadth and thickne&longs;&longs;e of the Piece,
but al&longs;o to have determined the length, determining its ve
locity.
The &longs;ame di&longs;order and confu&longs;ion, that was repre&longs;ented in the
Fable, doth come to pa&longs;&longs;e in the Hi&longs;tory of the Di&longs;tribution of
the Waters of Conduits and Fountains, &longs;eeing that they are &longs;old
and bought, having regard only to the two Dimen&longs;ions, I mean
of Breadth and Height of the Mouth that di&longs;chargeth the Wa
ter; and to remedy &longs;uch an inconvenience, it is nece&longs;&longs;ary to de
termine the length in the velocity; for never &longs;hall we be able to
make a gue&longs;&longs;e at the quantity of the Body of Running Water,
with the two Dimen&longs;ions only of Breadth and Height, without
Length.
And to the end, that the whole bu&longs;ine&longs;s may be reduced
to a mo&longs;t ea&longs;ie practice, by which the waters of Aqueducts
may be bought and &longs;old ju&longs;tly, and with mea&longs;ures alwayes ex
act and con&longs;tant.
Fir&longs;t, the quantity of the Water ought diligently to be exa
mined, which the whole principal ^{*} Pipe di&longs;chargeth in a time
certain, as for in&longs;tance, in an hour, in half an hour, or in a le&longs;&longs;e
interval of time, (for knowing which I have a mo&longs;t exact and
ea&longs;ie Rule) and finding that the whole principal pipe di&longs;char
geth g.
more hours, in &longs;elling of this water, it ought not to be uttered by
the ordinary and fal&longs;e mea&longs;ure, but the di&longs;tribution is to be
made with agreement to give and maintain to the buyer ten or
twenty, or a greater number of Tuns, as the bargain &longs;hall be
made, in the &longs;pace of an hour, or of &longs;ome other &longs;et and deter
minate time. And here I adde, that if I were to undertake to
make &longs;uch an adju&longs;tment, I would make u&longs;e of a way to divide
and mea&longs;ure the time with &longs;uch accuratene&longs;&longs;e, that the &longs;pace of
an hour &longs;hould be divided into four, &longs;ix, or eight thou&longs;and parts
Ma&longs;ter Galilæo Galilæi,
rene
admirably to our purpo&longs;e and occa&longs;ion; &longs;o that we &longs;hall
thereby be able to know how many Quarts of Water an A
queduct will di&longs;charge in a given time of hours, moneths, or
years. And in this manner we may con&longs;titute a Cock that &longs;hall
di&longs;charge a certain and determinate quantity of water in a time
given.
And becau&longs;e daily experience &longs;hews us, that the Springs of A
queducts do not maintain them alwayes equally high, and full
of Water, but that &longs;ometimes they increa&longs;e, and &longs;ometimes de
crea&longs;e, which accident might po&longs;&longs;ibly procure &longs;ome difficulty in
our di&longs;tribution: Therefore, to the end that all manner of &longs;cru
ple may be removed, I conceive that it would be convenient to
provide a Ci&longs;tern, according to the occa&longs;ion, into which there
might alwayes fall one certain quantity of water, which &longs;hould
not be greater than that which the principal pipe di&longs;chargeth in
times of drought, when the Springs are bare of water, that &longs;o in
this Ci&longs;tern the water might alwayes keep at one con&longs;tant height. Then to the Ci&longs;tern &longs;o prepared we are to fa&longs;ten the Cocks of
particular per&longs;ons, to whom the Water is &longs;old by the Reverend
Apo&longs;tolique Chamber, according to what hath been ob&longs;erved
before; and that quantity of Water which remaineth over and
above, is to be di&longs;charged into another Ci&longs;tern, in which the
Cocks of the Waters for publick &longs;ervices, and of tho&longs;e which
people buy upon particular occa&longs;ions are to be placed. And
when the bu&longs;ine&longs;&longs;e &longs;hall have been brought to this pa&longs;&longs;e, there
will likewi&longs;e a remedy be found to the &longs;o many di&longs;orders that
continually happen; of which, for brevity &longs;ake, I will in&longs;tance
in but four only, which concern both publique and private bene
fit, as being, in my judgment, the mo&longs;t enormous and intole
rable.
The fir&longs;t inconvenience is, that in the common way of mea&longs;u
ring, di&longs;pen&longs;ing, and &longs;elling the Waters of Aqueducts, it is not
under&longs;tood, neither by the Buyer nor Seller, what the quantity
truly is that is bought and &longs;old; nor could I ever meet with any
either Engineer or Architect, or Arti&longs;t, or other that was able to
decypher to me, what one, or two, or ten inches of water was. But by our above declared Rule, for di&longs;pen&longs;ing the Waters of
Aqueducts we may very ea&longs;ily know the true quantity of Water
that is bought or &longs;old, as that it is &longs;o many Tuns an hour, &longs;o ma
ny a day, &longs;o many in a year, &c.
The &longs;econd di&longs;order that happeneth, at pre&longs;ent, in the di&longs;tri
lieth in the power of a &longs;ordid Ma&longs;on to take unju&longs;tly from one,
and give unde&longs;ervedly to another more or le&longs;&longs;e Water than be
longeth to them of right: And I have &longs;een it done, of my
own experience. But in our way of mea&longs;uring and di&longs;tri
buting Waters, there can no fraud be committed; and put
ting the ca&longs;e that they &longs;hould be committed, its an ea&longs;ie mat
ter to know it, and amend it, by repairing to the Tribunal
appointed.
Thirdly, it happens very often, (and we have examples there
of both antient and modern) that in di&longs;pen&longs;ing the Water after
the common and vulgar way; there is &longs;ometimes more Water di&longs;
pended than there is in the Regi&longs;ter, in which there will be regi
&longs;tred, as they &longs;ay, two hundred inches (for example) and there
will be di&longs;pen&longs;ed two hundred and fifty inches, or more. Which
pa&longs;&longs;age happened in the time of
Frontino
where he ob&longs;erveth that they had
naries
naries.
modernly until our times. But if our Rule &longs;hall be ob&longs;erved,
we &longs;hall incur no &longs;uch di&longs;order, nay there will alwayes be given
to every one his &longs;hare, according to the holy end of exact ju&longs;tice,
which
manife&longs;t, that His Divine Maje&longs;ty hateth and abominateth
dus & pondus, Men&longs;ura & men&longs;ura,
eth by the mouth of 20. Pondus
& Pondus, Men&longs;ura & Men&longs;ura, utrumque abominabile e&longs;t apud
Deum.
dividing and mea&longs;uring of Waters, commonly u&longs;ed, is expre&longs;ly
again&longs;t the Law of God. Since that thereby the &longs;ame mea&longs;ure
is made &longs;ometimes greater, and &longs;ometimes le&longs;&longs;er; A di&longs;order &longs;o
enormous and execrable, that I &longs;hall take the boldne&longs;s to &longs;ay, that
for this &longs;ole re&longs;pect it ought to be condemned and prohibited like
wi&longs;e by human Law, which &longs;hould Enact that in this bu&longs;ine&longs;s there
&longs;hould be imployed either this our Rule, or &longs;ome other that
is more exqui&longs;ite and practicable, whereby the mea&longs;ure
might keep one con&longs;tant and determinate tenor, as we make it,
and not, as it is now, to make
Men&longs;ura.
And this is all that I had to offer to Your mo&longs;t Illu&longs;trious
Lord&longs;hip, in obedience to your commands, re&longs;erving to my &longs;elf
the giving of a more exact account of this my invention, when
the occa&longs;ion &longs;hall offer, of reducing to practice &longs;o holy, ju&longs;t, and
of Aqueducts in particular: which Rule may al&longs;o be of great
benefit in the divi&longs;ion of the greater Waters to over-flow
Grounds, and for other u&longs;es: I humbly bow,
and
D.
Benedetto Ca&longs;telli,
Ca&longs;in.
FINIS.
A TABLE
Of the mo&longs;t ob&longs;ervable matters in this Treati&longs;e of the
MENSURATION of RUNNING
WATERS.
The END of the TABLE of the Second Part
of the Fir&longs;t TOME.