Castelli, Benedetto, Of the mensuration of running waters, 1661

Bibliographic information

Author: Castelli, Benedetto
Title: Of the mensuration of running waters
Date: 1661

Permanent URL

Document ID: MPIWG:9RRKX6H0
Permanent URL: http://echo.mpiwg-berlin.mpg.de/MPIWG:9RRKX6H0

Copyright information

Copyright: Max Planck Institute for the History of Science (unless stated otherwise)
License: CC-BY-SA (unless stated otherwise)
1
MATHEMATICAL
COLLECTIONS
AND
TRANSLATIONS:
THE SECOND
TOME.
THE SECOND PART,
Containing,
D. BENEDICTUS CASTELLUS, his DISCOURSE
of the MENSURATION of RUN­
NING WATERS.
His Geometrical DEMONSTRATIONS of
the Meaſure of RUNNING WATERS.
I. His LETTERS and CONSIDERATIONS
touching the Draining of FENNS, Diverſions of
RIVERS, &c.
V. D. CORSINUS, His RELATION of the ſtate of the
Inundations, &c. in the Territories of BOLOGNA,
and FERRARA.
By THOMAS SALUSBURY, Eſque
LONDON,
Printed by WILLIAM LEYBOURNE, MDCLXI.
1
[Empty page]
1
OF THE
MENSURATION
OF
RUNNING WATERS.
An Excellent Piece
Written in ITALIAN
BY
DON BENEDETTO CASTELLI,
Abbot of St. BENEDETTO ALOYSIO,
and Profeſſour of the Mathematicks to
Pope URBAN VIII. in ROME.
Engliſhed from the Third and beſt Edition, with
the addition of a Second Book not before extant:
By THOMAS SALUSBURY.
LONDON,
Printed by WILLIAM LEYBOURN, 1661.
1
[Empty page]
1
THE
AUTHOURS EPISTLE
TO
Pope VRBAN VIII.
I lay at the Feet of your Ho­
lineſſe theſe my Conſide­
rations concerning the
MENSURATION OF
RUNNING WATERS:
Wherein if I ſhall have ſucceeded, being a
matter ſo difficult and unhandled by Wri­
ters both Ancient Modern, the diſcovery of
any thing of truth hath been the Effect of
Your Holineſſes Command; and if through
inability I have miſſed the Mark, the ſame
1Command will ſerve me for an Excuſe with
Men of better Judgment, and more eſpeci­
ally with Your Holineſſe, to whom I humbly
proſtrate my ſelf, and kiſſe Your Sacred
Feet.
From ROME.
Your Holineſſes
Moſt humble Servant
BENEDETTO.
A Monk of Caſſino.
1
AN
ACCOUNT
OF THE
Authour and Work.
DON BENEDETTO CASTELLI,
the famous Authour of theſe enſuing
Diſcourſes of the Menſuration of
Running Waters, is deſcended from
the Worſhipful FAMILY of the
GASTELLII, and took his
firſt breath near to the lake THR A­
SIMENVS, (where Hanibal gave
a fatal overthrow to the Roman
Legions) in that ſweet and fertile part
of happy ITALY, called the Territory
of PERUGIA, a branch of the Dukedome of TUSCANY, which
at preſent ſubmitteth to the Juriſdiction of the Church, as being a
part of St. PETER'S Patrimony. His Parents, who were more
zealous of the good of his Soul than obſervant of the Propenſion 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
riſhing Order of Black-Friers, called from the place Moncks
of Monte Caſino, and from the Founder Benedictines. Na­
ture, that She might conſummate the Profuſion of her Fa­
vours upon him, ſent him into the World in an Age that was ſo
ennobled and illuminated with Eminent Scholars in all Kinds of
Literature, that hardly any Century ſince the Creation can boaſt
the like.
1
§. In particular, the SCIENCES MATHEMATI­
CAL had then got that Fame and Eſteem in the Learned World,
that all men of Spirit or Quality became either Students in, or
Patrons of thoſe Sublime Knowledges. On this occaſion the Curi­
oſity of our AUTHOUR being awakened, his Active Wit
could not endure to be any longer confined to the Slaviſh Tuition
of Hermetical Pedagogues; but in concurrence with the Genius
of the Age, he alſo betook himſelf to thoſe moſt Generous and
Liberal Studies. His helps in this his deſign were ſo many, and
ſo extraordinary, that had his Inclination been weaker, or his
Apprehenſion leſſer, he could hardly have failed attaining more
than a Common Eminency in theſe Sciences. For beſides the De­
luge of Learned and Vſeful Books, which the Preſſe at that
time ſent forth from all parts of EUROPE, he had the good
Fortune to fall into the Acquaintance, and under the Inſtruction
of the moſt Demonſtrative and moſt Familiar Man in the World,
the Famous GALILEO: whoſe ſucceſſe being no leſſe upon
this his Pupil than upon the reſt of thoſe Illuſtrious and Ingeni­
ous Perſons that reſorted from all parts to ſit under his Admi­
rable Lectures, he in a ſhort time attained to that Name in the
Mathematicks, that he was invited to ROME, Complemen­
ted, and Preferred by his then Holineſſe the Eighth URBAN,
upon his very firſt Acceſſion to the Papacy, which was in the
Year 1623.
§. This Pope being moved with a Paternal Providence for the
Concerns of his Subjects in that part of ITALY about BO­
LOGNA, FERRARA, and COMMACHIO, ly­
ing between the Rivers of PO and RENO, which is part of
Lo Stato della Chieſa, or the Church Patrimony, appoints this
our CASTELLI in the Year 1625, to accompany the Right
Honourable Monſignore GORSINI (a moſt obſervant and
intelligent perſon in theſe affaires, and at that time Superinten­
dent of the General Draines, and Preſident of ROMAGNA)
in the Grand Viſitation which he was then ordered to make con­
cerning the diſorders occaſioned by the Waters of thoſe parts.
§. CASTELLI, having now an Opportunity to employ,
yea more, to improve ſuch Notions as he had imbued from the
Lectures of his Excellent MASTER, falls to his work with
all induſtry: and in the time that his Occaſions detained him in
ROMAGNA he perfected the Firſt Book of this his Diſ­
courſe concerning the Menſuration of Running Waters. He con­
feſſeth that he had ſome years before applyed himſelf to this part
of Practical Geometry, and from ſeveral Obſervations collected
part of that Doctrine which at this time he put into Method, and
which had procured him the Repute of ſo much Skill that he began
1to be Courted by ſundry Princes, and great Prelates. In particu­
lar about the beginning of the Year 1623. and before his Invita­
tion to ROME he was employed by Prince Ferdinando I, Grand
Duke of TUSCANY, to remedy the Diſorders which at that
time happened in the Valley of PISA in the Meadows that lye
upon the Banks of Serchio and Fiume Morto: and in the pre­
ſence of the Grand Duke, Grand Dutcheſſe Mother, the Commiſ­
ſioners of Sewers, and ſundry other Perſons in a few hours he
made ſo great a progreſſe in that affair, as gave his Moſt Serene
Highneſſe high ſatisfaction, and gained himſelf much Honour.
§. No ſooner had he in his fore-mentioned Voiage to RO­
MAGNA (which was but few Moneths after, in the ſame
Year) committed his Conceptions to paper, but he communicated
them to certain of his Friends. In which number we finde Signo­
re Ciampoli Secretary of the Popes Private Affaires; whom in
the beginning of the Firſt Book he gratefully acknowledgeth to
have been contributary, in his Purſe, towards defraying the
charge of Experiments, and in his Perſon, 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 preſent the World with his
Firſt Diſcourſe, accompanied with a Treatiſe of the Geometrical
Demonſtrations of his whole Doctrine. What Reception it found
with the Judicious muſt needs be imagined by any one that hath
obſerved how Novelty and Facility in conjunction with Verity
make a Charm of irreſiſtable Operation.
§. New it was, for that no man before him had ever attemp­
ted to Demonſtrate all the three Dimenſions, to wit, the Length,
Breadth and Profundity, of this Fluid and Current Ele­
ment. And he detecteth ſuch groſſe Errours in thoſe few that
had untertook to write upon the Subject (of which he inſtan­
ceth in Frontinus and Fontana, as thoſe that include the rest)
and delivereth ſuch ſingular and unheard-of Paradoxes (for ſo
they ſound in Vulgar Eares) as cannot but procure unſpeakable
delight to his Reader.
§. Eafie it is likewiſe and True; and that upon ſo Familiar
Experiments and Manifeſt Demonſtrations, that I have oft que­
ſtioned with my ſelf which merited the greater wonder, he, for
diſcovering, or all men that handled the Argument before him
for not diſcovering a Doctrine of ſuch ſtrange Facility and Infal­
libility. But yet as if our Authour deſigned to oblige the whole
World to him by ſo excellent a Preſent, he ſelects a Subject that
he knew would be carreſſed by all perſons of Nobler Souls, upon
the accounts afore-named, and by all Mankind in General, as
gratifying them in their much adored Idol Utility. And to ren-
1der his Art the more profitable, he reduceth the lofty, and eaſie-to­
be-miſtaken 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
ſtribute Waters for the Flowing and Stercoration of Grounds,
ſtrengthening of Fortifications, ſerving of Aquaducts, preſer­
ving of Health (by cleanſing Streets, and ſcowring Sewers) and
maintaining of Commerſe (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 circumſtance
that may recommend my Authour, the Fortune of this his Trea­
tiſe hath been ſuch, that as if he intended a Plus ultra by it,
or as if all men deſpaired to out-do it, or laſtly, as if CA­
STELLI hath been ſo great a Maſter that none have preſu­
med to take Pencil in hand for the finiſhing of what he Pour­
foild, this ſmall Tract like the Arabian Phœnix (of which it is
ſaid Unica ſemper Avis) did for ſeveral years together continue
ſingle in the World, till that to verifie it to be truly Phœnician,
it renewed its Age by undergoing a ſecond Impreſſion. And as if
this did not make out the Immortal vertue of it, it hath had
Anno 1660 a third Circulation, and riſen in this laſt Edition as
it were from the Vrne of its Authour; and that ſo improved by
the Addition of a ſecond part, that it promiſeth to perpetuate
his Merits to all Poſterity. To be brief, the meer Fame of this
Work reſounded the Honourable Name of CASTELLI in­
to all the Corners of Italy, I may ſay of Europe; inſomuch,
that, in hopes to reap great benefit by his Art, the reſpective
Grandees of the adjacent Countries courted his Judgment and
Advice about their Draining of Fenns, Diverſion of Rivers,
Evacuation of Ports, Preventing of Inundations, &c. So that
every Summer he made one or more of theſe Journies or Viſitati­
ons. Particularly, the Senate of Venice conſulted him about their
Lake; to whom he delivered his Opinion in May 1641. and up­
on farther thoughts he preſented them with another Paper of Con­
ſiderations the 20 December following. Prince LEOPOLDO
of TUSCANY likewiſe requeſted his Advice in the begin­
ning of the enſuing year 1642, which occaſioned his Letter to
Father Franceſco di San Giuſeppe, bearing date February 1,
To which Signore Bartolotti oppoſing, he writes a ſecond Let­
ter, directed to one of the Commiſſioners of Sewers, vindicating
his former, and refuting Bartolotti, both which I here give
you.
§. The Preferments which his Merits recommended him unto,
were firſt to be Abbot of Caſſino, from which he was removed
1Anno 1640, or thereabouts, unto the Abbey of Santo Benedet­
to Aloyſio; and much about the ſame time preferred to the Dig­
nity of Chief Mathematician to his grand Patron Pope URBAN
VIII. and Publique Profeſſour of Mathematicks in the Vni­
verſity of ROME.
§. Here a Stop was put to the Carier of his Fortunes, and be­
ing fuller of Honour than of Years, was by Death, the Importu­
nate Intrerupter of Generous Deſigns, prevented in doing that
farther Good which the World had good reaſon to promiſe it ſelf
from ſo Profound and Induſtrious a Perſonage, leaving many
Friends and Diſciples of all Degrees and Qualities to lament
his loſſe, and honour his Memory.
§. His ſingular Virtues and Abilities had gained him the
Friendſhip of very many; as to inſtance in ſome, he had con­
racted ſtrict Amity with Monſignore Maffei Barberino a Floren­
tine, Præfect of the Publique Wayes, and afterwards Pope with
the Name of URBAN VIII. as was ſaid before; with the
above-named Monſignore Corſini Superintendant of the General
Draines: with Monſignore Piccolomini Arch-Biſhop of Siena:
with Cardinal Serra: with Cardinal Caponi, who hath ſtudied
much and writ well upon this Subject; and with Cardinal Gae­
tano who frequently conſulted with him in his deſign of Drain­
ing the Fenns of ROMAGNA. Moreover Prince LEO­
POLDO, and his Brother the Grand Duke had very great
kindneſſe for him; which ſpeaks no ſmall attractions in him,
conſidering him as a favourite of the Family of Barberini, be­
tween whom and the Houſe of Medeci there is an inveterate
Fewd. Amongſt perſons of a lower Quality he acknowledgeth
Signore Ciampoli the Popes Secretary, Sig. Ferrante Ceſarini,
Sig. Giovanni Baſadonna Senator of Venice; and I find menti­
oned Sig. Lana, Sig. Albano, Padre Serafino, Pad. Franceſco
de San. Giuſeppe, and many others.
§. The Works in which he will ſurvive to all ſucceeding Ages
are firſt His ſolid and ſober Confutation of the Arguments of
Signore Lodovico dell Columbo, and Signore Vincentio di
Gratia againſt the Tract of Galileo Delle coſe che ſtanno ſopra
Aqua, wherein he vindicates bis ſaid Maſter with a Gratitude
that Tutors very rarely reap from the pains they take in Culti­
vating their Pupils. This Apology was firſt Printed Anno 1615.
and was a ſecond time publiſhed, as alſo thoſe of his Antago­
niſts, amongſt the Works of GALILEO, ſet forth by the
Learned Viviani 1656. He hath likewiſe writ ſeveral other
curious Pieces, as I am informed by the moſt Courteous Carolo
Manoleſſi of Bologna; amongſt others an excellent Treatiſe
concerning Colours, which he putteth me in hopes to ſee printed
1very ſpeedily. And laſt of all theſe Diſcourſes and Reflections
upon the Menſuration of Running Waters, with the addition of
a Second Book, three Epiſtles, and four Conſiderations upon
the ſame Argument, which conduce much to Illuſtrate his Do­
ctrine and Facilitate the Practice of it; and which with a Rela­
tion of Monſignore Corſini, make the ſecond part of my Firſt
Tome.
§. I might here ſally forth into the Citation of ſundry Au­
thours of Good Account, that have tranſmitted his Character
to Poſterity, but ſhall confine my ſelf to onely two; the one is
of his Maſter, the other of his Scholar; than whom there can­
not be two more competent Judges of his Accompliſhments. To
begin with his Maſter, the Quick-ſighted, and truly Lyncean
GALILEO, who ſpeaking of his Abilities in Aſtronomy ſaith

(a) Che la felicità del ſuo ingegno non la fà biſognoſa dell' o­
pera ſuo. And again, ſubmitting a certain Demonſtration,
which he intended to divulge, to the Judgment of this our Abbot, he

writes to him in this manner: (b) Queſto lo comunico a V. S.
per lettera prima che ad alcun altro, con attenderne principal­
mente il parer ſuo, e doppo quello de' noſtri Amici diſcoſti,
conpenſiero d' inviarne poi altre Copie ad altri Amici d' Italia,
e di Francia, quando io ne venga da lei conſigliato: e qui pre­
gandola a farci parte d' alcuna delle ſue peregrine ſpeculationi;
con ſinceriſſimo affetto, &c. And the moſt acute Mathematician
Signore Evangeliſta Terricelli, late Profeſſour to the Grand
Duke in immediate Succeſſion after GALILEO, maketh this

Honourable and Grateful Mention of him, and his Book: (c) O­
mitto magnum illum nutantis Maris motum; Prætereo etiam
omnem Fluminum, Aquarumque Currentium tum menſurum,
tum uſum, quarum omnis doctrina reperta primum fuit ab
Abbate BENEDICTO CASTELLIO Preceptore
meo. Scripſit ille Scientiam ſuam, & illam non ſolum demonſtra­
tione, verum etiam opere confirmavit, maxima cum Princi­
pum & populorum utilitatate, majore cum admiratione Phylo­
ſophorum. Extat illius Liber, vere aureus.
(a)Nella continu­
atione dell Nun­
tio ſiderio.
(b) Lettera al P.
Abbate D. B. Ca­
ſtelli D'Arcetro;
li. 3. Decemb.
1639.
(c) De Motu A­
quarum. Lib. 2.
Prop. 37. p. 191.
§. I have onely two particulars more to offer the Engliſh Rea­
der: The one concerns the Book, and it is this, That after the
general Aprobation it hath had in Italy, I cannot but think it
deſerveth the ſame Civil Entertainment with us, in regard that
it cometh with no leſſe Novelty, Facility, Verity, and Utility to
us than to thoſe whom the Authour favoured with the Original.
Our Rivers and Sewers through Publique Diſtractions and Pri­
vate Incroachments are in great diſorder, as thoſe Channels for
iuſtance which formerly were Navigable unto the very Walls of
1York and Salisbury, &c: Our Ports are choaked and obſtructed
by Shelfes and Setlements: Our Fenns do in a great part lie waſte
and unimproved: Now all theſe may be (and, as I find by the
Confeſſion of ſome whoſe Practiſes upon the Copy of the Firſt
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 ſets down. The truth is the Argument hath been paſt over
with an Vniverſal Silence; ſo that to this day I have not ſeen
any thing that hath been written Demonſtratively and with Ma­
thematical Certainty concerning the ſame, ſave onely what this
Learned Prelate hath delivered of his Own Invention in theſe
Treatiſes: who yet hath ſo fully and plainly handled the Whole
Doctrine, that I may affirm his Work to be every way abſolute. It
muſt be confeſt the Demonſtration of the Second Propoſition of the
Second Book did not well pleaſe the Authour, and had he lived
he would have ſupplyed that defect, but being prevented by
Death, the Reader muſt content himſelf with the Mechanical
Proof that he giveth you of the truth of ſo Excellent a Con­
cluſion.
§. The other particular that I am to offer is, that out of my de­
ſire to contribute what lyeth in me to the compleating of this Piece
for Engliſh Practice, I have exeeded my promiſe not onely in gi­
ving you the Second and following Books which were not extant at
the time of tendring my Overtures, but alſo 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 conſidered that I am the Tranſlator and not the
Printer. To conclude, according to your acceptance of theſe my
endeavours, you may expect ſome other Tracts of no leſſe Profit
and Delight. Farewell.
T. S.
1
ERRATA of the ſecond PART of the firſt TOME.
In PREFACE, I cad Ferdinando II. ibid. l' Aqua.
PAGE 2. LINE 26, for muſt read much. P. 3. l. 22, r. and let. l. 25. r. water, from l. 41.
r. Tappe, (as every where elſe). Page 4. l. 18. r cords. Page 6. l. 9. r. acquire, or.
Page 9. l. 1. r. irreperable. P. 10. l. 13. r. diſſimboguement. For Page 17. r. P. 15.
P. 15. l. 27, r. in. l. 36, r. is as. l. 38, r. Panaro. P. 17. l. 12, Giulio. l. 17. r. Meaſurers. l.
25, r. meaſured it,. r. neceſſarily. P. 23. l. 19. r. for help. for Page 31. r. P. 32. P. 24.
l. 14, r. to. l. 17, r. namly, of the. l. 23, r. eaſie. P. 25. l. 38. r. Cock. p. 29. l. 7. r. laſted,.
p. 31. l. 32. r. Soe. p. 41. l. 20. r. to the line. p. 48. l. 19. r. us the ^{*}. id. Figure falſe p. 52.
l. 30, and 31. for Theorem r. Propoſition. p. 53. l. 29. r. again. p. 57. l. 19, r. ſame if.
l. 44. r. bodily. p. 58. l. 9, r. gathering. l. 40. omit;. p. 60. l. 2. omit, if. p. 65. l. 1. r. tide
dele;. p. 66. l. 35. r. Stoppage of. p. 68. l. 12, for Lords the r. Lords. l. ult. for they
r. it. p. 69. l. 14. r. to one. id. carried dele to. p. 71. l. 20, r. and that. l. 25, r. Braces; it. l.
29. r. Braces. l. 44, r. the Brent. p. 72. l. 23. r. Serene Highneſſe. p. 73. l. 24, r. deliberation:.
l. 26, for ſumme r. Moddel. l. 40. r. Months. p. 79. l. 18. r. that into. p. 82. l. 22. dele;. p.
85. l. 9, 10. dele a free drame. p. 88. l. 5. r. Palmes. p. 89. l. 8. r. Princes. p. 92. l. 3. r. Diſ­
courſes. p. 93. l. 31. r. Tautologie. p. 94. l. 9. r. miracle;. p. 97. l. 13. r, weighty. p. 101.
l. 21. r. Marrara. p. 107. l. 28, r. Patrimony. l. 40, r. above. p. 111. l. 16. r. ſaid. For p. 432.
r. p. 114. p. 114. l. 35. r. of 200, l. 41. r. cloſed. p. 115. l. 29. r. conſtant;.
1
OF THE
MENSURATION
OF
Running Waters.
LIB. I.
What, and of how great moment the confi­
deration of Motion is in natural things,
is ſo manifeſt, that the Prince of Peri­
pateticks pronounced that in his Schools
now much uſed Sentence: Ignorato mo­
tu, ignoratur natura. Thence it is that
true Philoſophers have ſo travailed in the
contemplation of the Celeſtial motions,
and in the ſpeculation of the motions of
Animals, that they have arrived to a wonderful height and ſub­
limity of underſtanding. Under the ſame Science of Motion
is comprehended all that which is written by Mechanitians con­
cerning Engines moving of themſelves, Machins moving by the
force of Air, and thoſe which ſerve to move weights and im­
menſe magnitudes with ſmall force. There appertaineth to the
Science of Motion all that which hath been written of the
alteration not onely of Bodies, but of our Minds alſo; and
in ſum, this ample matter of Motion is ſo extended and di­
lated, that there are few things which fall under mans no­
tice, which are not conjoyned with Motion, or at leaſt de­
pending thereupon, or to the knowledge thereof directed;
and of almoſt every of them, there hath been written and
compoſed by ſublime wits, learned Treatiſes and Inſtructions.
1And becauſe that in the years paſt I had occaſion by Order of
our Lord Pope Vrban 8. to apply my thoughts to the motion of
the Waters of Rivers, (a matter difficult, moſt important, and
little handled by others) having concerning the ſame obſerved
ſome particulars not well obſerved, or conſidered till now, but of
great moment both in publick and private affairs; I have thought
good to publiſh them, to the end that ingenious ſpirits might
have occaſion to diſcuſſe more exactly then hitherto hath been
done, ſo neceſſary and profitable a matter, and to ſupply alſo my
defects in this ſhort and difficult Tractate. Difficult I ſay, for
the truth is, theſe knowledges, though of things next our ſenſes,
are ſometimes more abſtruce and hidden, then the knowledge of
things more remote; and much better, and with greater exquiſit­
neſs are known the motions of the Planets, and Periods of the
Stars, than thoſe of Rivers and Seas: As that ſingular light of
Philoſophie of our times, and my Maſter Signore Galileo Galilei
wiſely obſerveth in his Book concerning the Solar ſpots. And
to proceed with a due order in Sciences, I will take ſome ſuppo­
ſitions and cognitions ſufficiently clear; from which I will after­
wards proceed to the deducing of the principal concluſions. But
to the end that what I have written at the end of this diſcourſe in
a demonſtrative and Geometrical method, may alſo be under­
ſtood of thoſe which never have applyed their thoughts to the
ſtudy of Geometry; I have endeavoured to explain my conceit
by an example, and with the conſideration of the natural things
themſelves, muſt after the ſame order in which I began to doubt
in this matter; and have placed this particular Treatiſe here in
the beginning, adverting nevertheleſs, that he who deſires more
full and abſolute ſolidity of Reaſons, may overpaſs this prefatory
diſcourſe, and onely conſider what is treated of in the demonſtra­
tions placed towards the end, and return afterwards to the conſi­
deration of the things collected in the Corollaries and Appendices;
which demonſtrations notwithſtanding, may be pretermitted by
him that hath not ſeen at leaſt the firſt ſix Books of the Elements
of Euclid; ſo that he diligently obſerveth that which fol­
loweth.
I ſay therefore, that having in times paſt, on divers occaſi­
ons heard ſpeak of the meaſures of the waters of Rivers, and
Fountains, ſaying, ſuch a River is two or three thouſand feet of
water; ſuch a ſpring-water is twenty, thirty, or forty inches, &c.
Although in ſuch manner I have found all to treat thereof in
word and writing, without variety, and as we are wont to ſay,
conſtanti ſermone, yea even Artiſts and Ingeneers, as if it were
a thing that admitted not of any doubt, yet howſoever I re­
mained ſtill infolded in ſuch an obſcurity, that I well knew I un­
1derſtood nothing at all, of that which others pretended full and
clearly to underſtand. And my doubt aroſe from my frequent
obſervation of many Trenches and Channels, which carry
water to turn Mills, in which Trenches, and Channels, the
water being meaſured, was found pretty deep; but if afterwards
the ſame water was meaſured in the fall it made to turn the
Wheel of the Mill, it was much leſſe, not amounting often to the
tenth part, nor ſometimes to the twentieth, inſomuch, that the
ſame running water came to be one while more, another while leſs
in meaſure, in divers parts of its Channel; and for that reaſon this
vulgar manner of meaſuring running Waters, as indeterminate and
uncertain, was by me juſtly ſuſpected, the meaſure being to be de­
terminate, and the ſame. And here I freely confeſſe that I had fin­
gular help to reſolve this difficulty from the excellent & accurate
way of diſcourſing, as in allother matters, ſo alſo in this, of the
Right Honourable and Truly Noble Signior Ciampoli, Secretary
of the Popes ſecret affairs. Who moreover, not ſparing ſor the coſts
of the ſame, generouſly gave me occaſion a few years paſt to try by
exact experiments that which paſt concerning this particular. And
to explain all more clearly with an example; we ſuppoſe a Veſſel
filled with Water, as for inſtance a Butt, which is kept full, though
ſtill water runneth out, and the Water run out by two Taps equal
of bigneſſe, one put in the bottom of the Veſſel, and the other in
the upper part; it is manifeſt that in the time wherein from the
upper part ſhall iſſue a determinate meaſure of water ſrom
the inferiour part there ſhall iſſue four, five, and many more of
the ſame meaſures, according to the difference of the height of
the Taps, and the diſtance of the upper Tap from the Superfici­
es and level of the water of the Veſſel: and all this will alwayes
follow, though, as hath been ſaid, the Taps be equal, and the
water in diſcharging keep the ſaid Taps alwayes full. Where firſt
we note, that, although the meaſure of the Taps be equal, never­
theleſſe there iſſueth from them in equal times unequal quantities
of water, And if we ſhould more attentively conſider this buſi­
neſſe, we ſhould find, that the water by the lower Tap, run­
neth and paſſeth with much greater velocity, then it doth by the
upper, whatever is the reaſon. If therefore we would have
ſuch a quantity of Water diſcharge from the upper tap, as
would diſcharge from the neather in the ſame time, it is plain, that
either the upper Taps muſt be multiplyed in ſuch ſort, that ſo
many more Taps in number be placed above than below, as the
neather tap ſhall be more ſwift than the upper, or the upper Tap
made ſo much bigger than the nether, by how much that be­
neath ſhall be more ſwift than that above; and ſo then in equal
times, the ſame quantity of Water ſhall diſcharge from the upper,
as doth from the neather part.
1
I will declare my ſelf by another example. If we ſhould ima­
gine, that two cords or lines of equal thickneſs, be drawn through
two holes of equal bore; but ſo that the firſt paſs with quadruple
velocity to the ſecond: It is manifeſt, that if in a determinate
time, we ſhall by the firſt bore have drawn four Ells of the line,
in the ſame time, by the ſecond hole we ſhall have drawn but one
Ell of cord onely; and if by the firſt there paſſe twelve Ells, then
through the ſecond there ſhall paſſe onely three Ells; and in
ſhort the quantity of cord ſhall have the ſame proportion to the
cord, that the volocity hath to the velocity. And therefore we
deſiring to compenſate the tardity of the ſecond cord, and main­
taining the ſame tardity to draw through the ſecond hole as much
cord as through the firſt, it will be neceſſary to draw through the
ſecond bore four ends of cord; ſo that the thickneſs of all the
cords by the ſecond hole, have the ſame proportion to the thick­
neſs of the cord which paſſeth onely by the firſt, as the velocity
of the cord by the firſt hole hath reciprocally to the velocity of
the codrs by the ſecond 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 neceſſary, that
the thickneſs of all the four cords ſhall have the ſame reciprocal
proportion to the thickneſs of the ſwifter cord, that the velo­
city of the ſwifter cord hath to the velocity of the ſlower. The
which is verified likewiſe in the fluid Element of Water.
And to the end that this principal fundamental be well under­
ſtood, I will alſo note a certain obſervation made my me in the
Art of Wyer-drawing, or ſpinning Gold, Silver, Braſs, and Iron,
and it is this; That ſuch Artificers deſiring more and more to
diſgroſſe and ſubtillize the ſaid Metals, having would about a
Rocket or Barrel, the thread of the Metal, they place the Roc­
ket in a frame upon a ſtedfaſt Axis, in ſuch ſort that the Rocket
may turn about in it ſelf; then making one end of the thread to
paſſe by force through a Plate of Steel pierced with divers holes,
greater and leſſer, as need requireth, faſtning the ſame end of the
thread to another Rocket, they wind up the thread, which paſ­
ſing through a bore leſs than the thickneſſe of the thread, is of
force conſtrained to diſgroſſe and ſubtillize. Now that which is
intenſly to be obſerved in this buſineſs, is this, That the parts of
the thread before the hole, are of ſuch a thickneſſe, but the parts
of the ſame thread after it is paſſed the hole, are of a leſſer thick­
neſſe: and yet nevertheleſſe the maſſe and weight of the thread
which is drawn forth, is ever equal to the maſſe and weight of the
thread which is winded up. But if we ſhould well conſider the mat­
ter, we ſhould finde, that the thicker the thread before the hole is,
than the thread paſſed the hole, the greater reciprocally is the
1velocity of the parts of the thread paſſed the hole, than the volo­
city of the parts before the hole: Inſomuch that if verbi gratia
the thickneſſe of the thread before the hole, were double to the
thickneſſe after the hole, in ſuch caſe the velocity of the parts of
the thread paſſed the hole, ſhould be double to the velocity of the
parts of the thread before the hole; and thus the thickneſſe
compenſates the velocity, and the velocity compenſates the thick­
neſſe. So that the ſame occurreth in the ſolid Metals of Gold,
Silver, Braſs, Iron, &c. that eveneth alſo in the fluid Element of
Water, and other liquids, namely, That the velocity beareth the
ſame proportion to the velocity, that the thickneſſe of the Me­
tal, or Water, hath to the thickneſſe.
And therefore granting this diſcourſe, we may ſay, that as of­
ten as two Taps with different velocity diſcharge equal quanti­
ties of Water in equal times, it will be neceſſary that the Tap
leſſe ſwift be ſo much greater, and larger, than the Tap more
ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
and to pronounce the Propoſition in more proper terms, we ſay;
That if two Taps of unequal velocity, diſcharge in equal times
equal quantities of Water, the greatneſſe of the firſt ſhall be to
the greatneſſe of the ſecond, in reciprocal proportion, as the ve­
locity of the ſecond to the velocity of the firſt. As for example,
if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
will be neceſſary, that the ſecond be ten times bigger and larger
than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
quantities of water in equal times; and this is the principal and
moſt important point, which ought to be kept alwayes in minde,
for that on it well underſtood depend many things profitable,
and worthy of our knowledge.
Now applying all that hath been ſaid neerer to our purpoſe, I
conſider, that it being moſt true, that in divers parts of the ſame
River or Current of running water, there doth always paſſe equal
quantity of Water in equal time (which thing is alſo demon­
ſtrated in out firſt Propoſition) and it being alſo true, that in di­
vers parts the ſame River may have various and different veloci­
ty; it follows of neceſſary conſequence, that where the River
hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
parts, in which it hath greater velocity, it ſhall be of leſſe mea­
ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
ſhall have eternally reciprocall and like proportion with
their meaſures. This principle and fundamental well eſtabliſh­
ed, that the ſame Current of Water changeth meaſure, accor­
ding to its varying of velocity; that is, leſſening the meaſure,
when the velocity encreaſeth, and encreaſing the meaſure, when
the velocity decreaſeth; I paſſe to the conſideration of many
1particular accidents in this admirable matter, and all depending
on this ſole Propoſition, the ſenſe of which I have oft repeated,
that it might be well underſtood.
COROLLARIE I.
And firſt, we hence conclude, that the ſame Streams of a
Torrent, namely, thoſe ſtreams which carry equal quantity of
Water in equal times, make not the ſame depths or meaſures in
the River, in which they enter, unleſſe when in the entrance in­
to the River they acquire; or to ſay better, keep the ſame velo­
city; becauſe if the velocicities acquired in the River ſhall be
different, alſo the meaſures ſhall be diverſe; and conſequently
the depths, as is demonſtrated.
COROLLARIE II.
And becauſe ſucceſſively, as the River is more and more full,
it is conſtituted ordinarily in greater & greater velocity: hence
it is that the ſame ſtreams of the Torrent, that enter into the Ri­
ver, make leſſe and leſſe depths, as the River grows more and
more full; ſince that alſo the Waters of the Torrent being en­
tered into the River, go acquiring greater and greater velocities,
and therefore diminiſh in meaſure and height.
COROLLARIE III.
We obſerve alſo, that while the main River is ſhallow, if there
fall but a gentle rain, it ſuddenly much increaſeth and riſeth;
but when the River is already ſwelled, though there fall again a­
nother new violent ſhower, yet it increaſeth not at the ſame rate
as before, proportionably to the rain which fell: which thing
we may affirm particularly to depend on this, that in the firſt
caſe, while the River is low, it is found alſo very ſlow, and there­
fore the little water which entereth into it, paſſeth and runs with
little velocity, and conſequently occupieth a great meaſure:
But when the River is once augmented, by new water being alſo
made more ſwift, it cauſeth the great Flood of water which fal­
leth, to bear a leſſe meaſure, and not to make ſuch a depth.
COROLLARIE IV.
From the things demonſtrated is manifeſt alſo, that whilſt a
Torrent entereth into a River, at the time of Ebbe, then the
Torrent moveth with ſuch a certain velocity, what ever it be,
1paſſing by its extreameſt parts, wherewith it communicateth with
the River; in which parts, the Torrent being meaſured, ſhall
have ſuch a certain meaſure: but the River ſwelling and riſing,
alſo thoſe parts of the Torrent augment in greatneſſe and mea­
ſure, though the Torrent, in that inſtant, diſ-imbogue no more
water than it did before: ſo that the River being ſwelled, we
are to conſider two mouths of the ſame Torrent, one leſſe be­
fore the riſing, the other greater after the riſing, which mouths
diſcharge equal quantities of water in equal times; therefore the
velocity by the leſſer mouth ſhall be greater than the velocity by
the greater mouth; and thus the Torrent ſhall be retarded from
its ordinary courſe.
COROLLARIE V.
From which operation of Nature proceedeth another effect
worthy of conſideration; and it is, that the courſe of the water
retarding, as hath been ſaid in thoſe ultimate parts of the Tor­
rent, if it ſhall happen that the Torrent grow torbid and mud­
dy, and its ſtreame be retarded in ſuch a degree, that it is not
able to carry away thoſe minute grains of Earth, which com­
poſe the muddineſſe; in this caſe the Torrent ſhall clear away
the mud, and carry away the Sand at the bottome of its own
Chanel, in the extream parts of its mouth, which raiſed and
voided Sand, ſhall again afterwards be carried away, when the
River abating, the Torrent ſhall return to move with its primitive
velocity.
COROLLARIE VI.
Whilſt it is demonſtrated, that the ſame water hath different
meaſures in its Chanel or courſe, according as it varieth in
velocity; ſo that the meaſure of the water is alwayes greater, where
the velocity is leſſer; and on the contrary, the meaſure leſſer,
where the velocity is greater: from hence we may moſt ele­
gantly render the reaſon of the uſual Proverb, Take heed of the
ſtill waters: For that if we conſider the ſelf ſame water of a
River in thoſe parts, wherein it is leſs ſwift, and thence called ſtill
or ſmooth water, it ſhall be, of neceſſity, of greater meaſure
than in thoſe parts, in which it is more ſwift, and therefore ordi­
narily ſhall be alſo more deep and dangerous for paſſengers;
whence it is well ſaid, Take heed of the ſtill Waters; and this
ſaying hath been ſince applied to things moral.
1
COROLLARIE VII.
Likewiſe, from the things demonſtrated may be concluded,
that the windes, which ſtop a River, and blowing againſt the
Current, retard its courſe and ordinary velocity ſhall neceſſarily
amplifie the meaſure of the ſame River, and conſequently ſhall
be, in great part, cauſes; or we may ſay, potent con-cauſes of
making the extraordinary inundations which Rivers uſe to make.
And its moſt certain, that as often as a ſtrong and continual wind
ſhall blow againſt the Current of a River, and ſhall reduce the
water of the River to ſuch tardity of motion, that in the time
wherein before it run five miles, it now moveth but one, ſuch a
River will increaſe to five times the meaſure, though there ſhould
not be added any other quantity of water; which thing indeed
hath in it ſomething of ſtrange, but it is moſt certain, for that
look what proportion the waters velocity before the winde, hath
to the velocity after the winde, and ſuch reciprocally is the mea­
ſure of the ſame water after the winde, to the meaſure before
the winde; and becauſe it hath been ſuppoſed in our caſe that the
velocity is diminiſhed to a fifth part, therefore the meaſure ſhall
be increaſed five times more than that, which it was before.
COROLLARIE VIII.
We have alſo probable the cauſe of the inundations of Tyber,
which befel at Rome, in the time of Alexander the Sixth, & of
Clement the Seventh; which innundations came in a ſerene time,
and without great thaws of the Snows; which therefore much
puzzled the wits of thoſe times. But we may with much pro­
bability affirm, That the River roſe to ſuch a height and excreſ­
cence, by the retardation of the Waters dependant on the
boiſtrous and conſtant Winds, that blew in thoſe times, as is no­
red in the memorials.
COROLLARIE. IX.
It being moſt manifeſt, that by the great abundance of Water
the Torrents may increaſe, and of themſelves alone exorbitantly
ſwell the River; and having demonſtrated that alſo without new
Water, but onely by the notable retardment the River riſeth and
increaſeth in meaſure, in proportion as the velocity decreaſeth:
hence it is apparent, that each of theſe cauſes being able of it ſelf,
and ſeparate from the other to ſwell the River; when it ſhall
happen that both theſe two cauſes conſpire the augmentation of
1the River, in ſuch a caſe there muſt follow very great and irre­
pable innundations.
COROLLARIE X.
From what hath been demonſtrated, we may with facility re­
ſolve the doubt which hath troubled, and ſtill poſeth the moſt
diligent, but incautelous obſervers of Rivers, who meaſuring
the Streams and Torrents which fall into another River; as thoſe
for inſtance, which enter into the Po, or thoſe which fall into Ti­
ber; and having ſummed the total of theſe meaſures, and con­
ferring the meaſures of the Rivers and Brooks, which fall into
Tiber, with the meaſure of Tiber, and the meaſures of thoſe which
diſimbogue into Po, with the meaſure of Po, they find them not
equal, as, it ſeems to them, they ought to be, and this is becauſe
they have not well noted the moſt important point of the varia­
tion of velocity, and how that it is the moſt potent cauſe of won­
derfully altering the meaſures of running Waters; but we moſt
facilly reſolving the doubt, may ſay that theſe Waters diminiſh
the meaſure, being once entered the principal Channel, becauſe
they increaſe in velocity.
COROLLARIE XI.
Through the ignorance of the force of the velocity of the Wa­
ter, in altering its meaſure, & augmenting it when the velocity
diminiſheth; and diminiſhing it when the velocity augmenteth:
The Architect Giovanni Fontana, endeavoured to meaſure, and
and to cauſe to be meaſured by his Nephew, all the Brooks and
Rivers which diſcharged their Waters into Tiber, at the time of
the Innundation; which happened at Rome in the year 1598,
and publiſhed a ſmall Treatiſe thereof, wherein he ſummeth up
the meaſures of the extraordinary Water which fell into Tiber,
and made account that it was about five hundred Ells more than
ordinary; and in the end of that Treatiſe concludeth, that to re­
move the Innundation wholly from Rome, it would be neceſſary
to make two other Channels, equal to that at preſent, and that
leſſe would not ſuffice; and finding afterwards that the whole
Stream paſſed under the Bridge Quattro-Capi, (the Arch where­
of is of a far leſs meaſure then five hundred Ells) concludeth,
that under the ſaid Bridge paſt a hundred fifty one Ells of Water
compreſſed, (I have ſet down the preciſe term of compreſt Wa­
ter, written by Fontana) wherein I finde many errors.
The firſt of which is to think that the meaſures of theſe Wa­
ters compreſſed in the Channels of thoſe Brooks and Rivers,
1ſhould maintain themſelves the ſame in Tiber, which by his leave,
is moſt falſe, when ever thoſe waters reduced into Tiber, retain
not the ſame velocity which they had in the place in which Fon­
tana and his Nephew meaſured them: And all this is manifeſt
from the things which we have above explained; for, if the Wa­
ters reduced into Tiber increaſe in velocity, they decreaſe in mea­
ſure; and if they decreaſe in velocity, they increaſe in mea­
ſure.
Secondly, I conſider that the meaſures of thoſe Brooks and
Rivers, which enter into Tiber at the time of Innundation, are
not between themſelves really the ſame, when their velocities are
not equal, though they have the ſame names of Ells and Feet;
for that its poſſible that a diſinboguement of ten Ells requadrated
(to ſpeak in the phraſe of Fontana) of one of thoſe Brooks,
might diſcharge into Tiber at the time of Innundation, four, ten,
and twenty times leſs Water, than another mouth equal to the
firſt in greatneſs, as would occur when the firſt mouth were four,
ten, or twenty times leſs ſwift than the ſecond. Whereupon,
whilſt Fontana ſummes up the Ells and Feet of the meaſures of
thoſe Brooks and Rivers into a total aggregate, he commits the
ſame error with him, which would add into one ſumme diverſe
moneys of diverſe values, and diverſe places, but that had the
ſame name; as if one ſhould ſay ten Crowns of Roman money,
four Crowns of Gold, thirteen Crowns of Florence, five Growns
of Venice, and eight Crowns of Mantua, ſhould make the ſame
ſumme with forty Crowns of Gold, or forty Crowns of Mantua.
Thirdly, It might happen that ſome River or Current in the
parts nearer Rome, in the time of its flowing, did not ſend forth
more Water than ordinary; and however, its a thing very clear,
that whilſt the ſtream came from the ſuperior parts, that ſame
Brook or River would be augmented in meaſure, as hath been
noted in the fourth Corollary; in ſuch ſort, that Fontana might
have inculcated, and noted that ſame River or Current as con­
curring to the Innundation, although it were therein altogether
unconcerned.
Moreover, in the fourth place we muſt note, That it might
ſo fall out, that ſuch a River not onely was unintereſſed in the
Innundation, though augmented in meaſure, but it might I ſay
happen, that it was inſtrumental to the aſſwaging the Innunda­
tion, by augmenting in the meaſure of its own Channel; which
matter is ſufficiently evident; for if it be ſuppoſed that the Ri­
ver in the time of flood, had not had of it ſelf, and from its pro­
per ſprings more Water than ordinary, its a thing certain, that
the Water of Tiber riſing and increaſing; alſo that River, to le­
vel it ſelf with the Water of Tiber, would have retained ſome of
1its Waters in its own Chanel, without diſcharging them into Ty­
ber, or elſe would have ingorged and ſwallowed (if I may ſo ſay)
ſome of the water of Tyber; and in this caſe, at the time of In­
undation, leſſe abundance of water would have come to Rome,
and yet nevertheleſſe the meaſure of that River would have been
increaſed.
Fifthly, Fontana deceiveth himſelf, when he concludeth, that
to remove the Inundation from Rome, it would be neceſſary to
make two other Chanels of Rivers, that were as large as that,
which is the preſent one, and that leſs would not ſuffice, which,
I ſay, is a fallacy: and to convince him eaſily of his errour, it
ſufficeth to ſay, that all the Streams being paſſed under the Bridge
Quattro-Capi, as he himſelf atteſts, a Channel would ſuffice on­
ly of the capacity of the ſaid Bridge, provided that the water
there might run with the ſame velocity, as it did under the Bridge
at the time of Inundation; and on the contrary, twenty Cur­
rents of capacity equal to the preſent one, would not ſuffice, if
the water ſhould run with twenty times leſs velocity, than it made
at the time of the Inundation.
Sixthly, to me it ſeemeth a great weakneſſe to ſay, that there
ſhould paſſe under the Bridge Quattro-Capi, an hundred fifty one
ells of water compreſſed; for that I do not underſtand that wa­
ter is like Cotton or Wool, which matters may be preſt and trod,
as it happeneth alſo to the air, which receiveth compreſſion in
ſuch ſort, that after that in ſome certain place a quantity of air
ſhall be reduced to its natural conſtitution; and having taken up
all the ſaid place, yet nevertheleſſe compreſſing the firſt Air
with force and violence, it is reduced into far leſs room, and will
admit four or ſix times as much air, as before, as is experimen­
tally ^{*} ſeen in the Wind-Gun, invented in our dayes by M. Vin,

cenzo Vincenti of Vrbin, which property of the Air of admit­
ting condenſation, is alſo ſeen in the portable Fountains of the
ſame M. Vincenzo: which Fountains ſpirt the Water on high,
by force of the Air compreſſed, which whilſt it ſeeks to reduce
its ſelf to its natural conſtitution, in the dilation cauſeth that vi­
olence. But the water can never, for any thing I know, crowd,
or preſs ſo, as that if before the compreſſion it held or poſſeſt a
place, being in its natural conſtitution, I believe not, I ſay, that it
is poſſible, by preſſing and crowding to make it poſſeſs leſs room,
for if it were poſſible to compreſs the Water, and make it to oc­
cupy a leſs place, it would thence follow, that two Veſſels of e­
qual meaſure, but of unequal height, ſhould be of unequal capa­
city, and that ſhould hold more water which was higher; alſo a
Cylinder, or other Veſſel more high than broad, would containe
more water erected, than being laid along; for that being erect­
1ed, the water put therein would be more preſſed and crowded.
* And as is at
large demonſtrated
by that moſt excel­
lent and lonour­
able perſonage Mr.
Botle in the indu­
ſtrious experiment
of his Pneumatical
Engine.
And therefore, in our caſe, according to our principles we will
ſay, that the water of that Stream paſseth all under the ſaid
Bridge Quattro-Capi, for that being there moſt ſwift, it ought of
conſequence to be leſs in meaſure.
And here one may ſee, into how many errours a man may run
through ignorance of a true and real Principle, which once known
and well underſtood, takes away all miſts of doubting, and ea­
ſily reſolveth all difficulties.
COROLLARIE. XII.
Through the ſame inadvertency of not regarding the variation
of velocity in the ſame Current, therea re committed by Ingi­
neers and Learned men, errours of very great moment (and I
could thereof produce examples, but for good reaſons I paſs
them over in ſilence) when they think, and propoſe, by deriving
new Channels from great Rivers, to diminiſh the meaſure of the
water in the River, and to diminiſh it proportionally, according
to the meaſure of the Water which they make to paſs through
the Channel, as making v.g a Channel fifty foot broad, in which
the derived water is to run waſte, ten foot deep, they think they
have diminiſhed the meaſure of the Water in the River five hun­
dred feet, which thing doth not indeed ſo fall out; and the rea­
ſon is plain; for that the Chanel being derived, the reſt of the
main River, diminiſheth in velocity, and therefore retains a grea­
ter meaſure than it had at firſt before the derivation of the Cha­
nel; and moreover, if the Chanel being derived, it ſhall not
conſerve the ſame velocity which it had at firſt in the main Ri­
ver, but ſhall diminiſh it, it will be neceſſary, that it hath a grea­
ter meaſure than it had before in the River; and therefore
to accompt aright, there ſhall not be ſo much water derived into
the Channel, as ſhall diminiſh the River, according to the quanti­
ty of the water in the Channel, as is pretended.
COROLLARIE XIII.
This ſame conſideration giveth me occaſion to diſcover a moſt
ordinary errour, obſerved by me in the buſineſſe of the wa­
ter of Ferara, when I was in thoſe parts, in ſervice of the moſt
Reverend and Illuſtrious Monfignor Corſini; the ſublime wit of
whom hath been a very great help to me in theſe contemplations;
its very true, I have been much perplexed, whether I ſhould
commit this particular to paper, or paſſe it over in ſilence, for
that I have ever doubted, that the opinion ſo common and
1moreover confirmed with a moſt manifeſt experiment, may not
onely make this my conjecture to be eſteemed far from true,
but alſo to diſcredit with the World the reſt of this my Treatiſe:
Nevertheleſſe I have at laſt reſolved not to be wanting to my
ſelf, and to truth in a matter of it ſelf, and for other conſe­
quences moſt important; nor doth it ſeem to me requiſite in
difficult matters, ſuch as theſe we have in hand, to refigne our
ſelves to the common opinion, ſince it would be very ſtrange if
the multitude in ſuch matters ſhould hit on the truth, nor ought
that to be held difficult, in which even the vulgar do know the
truth and right; beſides that I hope morever to prove all in ſuch
ſort, that perſons of ſolid judgment, ſhall reſt fully perſwaded,
ſo that they but keep in mind the principal ground and foundation
of all this Treatiſe; and though that which I will propoſe, be a par­
ticular, as I have ſaid, pertaining onely to the intereſts of Ferara;
yet nevertheleſſe from this particular Doctrine well underſtood,
good judgement may be made of other the like caſes in general.
I ſay then, for greater perſpecuity, and better underſtanding
of the whole, That about thirteen miles above Ferara, near to
Stellata, the main of Po, branching it ſelf into two parts, with one
of its Arms it cometh cloſe to Ferara, retaining the name of the
Po of Ferara; and here again it divideth it ſelf into two other
branches, and that which continueth on the right hand, is called
the Po of Argenta, and of Primaro; and that on the left the Po
of Volana. But for that the bed of the Po of Ferara being here­
tofore augmented and raiſed, it followeth that it reſteth wholly
deprived of the Water of the great Po, except in the time of its
greater ſwelling; for in that caſe, this Po of Ferara being re­
ſtrained with a Bank near to Bondeno, would come alſo in the
overflowings of the main Po, to be free from its Waters: But the
Lords of Ferara are wont at ſuch time as the Po threateneth to
break out, to cut the bank; by which cutting, there diſ­
gorgeth ſuch a Torrent of Water, that it is obſerved, that the
main Po in the ſpace of ſome few hours abateth near a foot, and
all perſons that I have ſpoken with hitherto, moved by this ex­
periment, think that it is of great profit and benefit to keep ready
this Vent, and to make uſe of it in the time of its fullneſſe. And
indeed, the thing conſidered ſimply, and at the firſt appearance,
it ſeemeth that none can think otherwiſe; the rather, for that
many examining the matter narrowly, meaſure that body of
Water which runneth by the Channel, or Bed of the Po of Fera­
ra, and make account, that the body of the Water of the great
Po, is diminiſhed the quantity of the body of the Water which
runneth by the Po of Ferara. But if we well remember what
hath been ſaid in the beginning of the Treatiſe, and how much
1the variety of the velocities of the ſaid Water importeth, and the
knowledge of them is neceſſary to conclude the true quantity of
the running Water, we ſhall finde it manifeſt, that the benefit of
this Vent is far leſſe than it is generally thought: And mereover,
we ſhall finde, if I deceive not my ſelf, that there follow from
thence ſo many miſchiefs, that I could greatly incline to believe,
that it were more to the purpoſe wholly to ſtop it up, than to
maintain it open: yet I am not ſo wedded to my opinion, but
that I am ready to change my judgement upon ſtrength of better
reaſons; eſpecially of one that ſhall have firſt well underſtood
the beginning of this my diſcourſe, which I frequently inculcate,
becauſe its abſolutely impoſſible without this advertiſement to
treat of theſe matters, and not commit very great errours.
I propoſe therefore to conſideration, that although it be true,
that whilſt the water of the main Po is at its greateſt height, the
Bank and Dam then cut of the Po of Ferara, and the ſuperior
waters having a very great fall into the Channel of Ferara, they
precipitate into the ſame with great violence and velocity, and
with the ſame in the beginning, or little leſſe, they run towards
the Po of Volana, and of Argenta on the ſea coaſts; yet after the
ſpace of ſome few hours, the Po of Ferara being full, and the ſu­
perior Waters not finding ſo great a diclivity there, as they had
at the beginning of the cutting, they fall not into the ſame with
the former velocity, but with far leſſe, and thereby a great deal
leſſe Water begins to iſſue from the great Po; and if we dili­
gently compare the velocity at the firſt cutting, with the velocity
of the Water after the cutting made, and when the Po of Ferara
ſhall be full of Water, we ſhall finde perhaps that to be fifteen or
twenty times greater than this, and conſequently the Water
which iſſues from the great Po, that firſt impetuoſity being paſt,
ſhall be onely the fifteenth or twentieth part of that which iſſued
at the beginning; and therefore the Waters of the main Po will
return in a ſmall time almoſt to the firſt height. And here I will
pray thoſe who reſt not wholly ſatisfied with what hath been ſaid,
that for the love of truth, and the common good, they would
pleaſe to make diligent obſervation whether in the time of great
Floods, the ſaid Bank or Dam at Bondeno is cut, and that in few
hours the main Po diminiſheth, as hath been ſaid about a foot in
its height; that they would obſerve I ſay, whether, a day or two
being paſt, the Waters of the main Po return almoſt to their firſt
height; for if this ſhould follow, it would be very clear, that the
benefit which reſulteth from this diverſion or Vent, is not ſo great
as is univerſally preſumed; I ſay, it is not ſo great as is
preſumed; becauſe, though it be granted for true, that
the Waters of the main Po, abate at the beginning of
1the Vent, yet this benefit happens to be but temporary and for a
few hours: If the riſing of Po, and the dangers of breaking forth
were of ſhort duration, as it ordinarily befalleth in the overflow­
ings of Torrents, in ſuch a caſe the profit of the Vent would be
of ſome eſteem: But becauſe the ſwellings of Po continue for
thirty, or ſometimes for forty dayes, therefore the gain which
reſults from the Vent proveth to be inconſiderable. It remain­
eth now to conſider the notable harms which follow the ſaid
Sluice or Vent, that ſo reflection being made, and the profit and
the detriment compared, one may rightly judge, and chooſe that
which ſhall be moſt convenient. The firſt prejudice therefore
which ariſeth from this Vent or Sluice, is; That the Channels of
Ferara, Primaro, and Volana filling with Water, all thoſe parts
from Bondeno to the Sea ſide are allarmed and endangered
thereby. Secondly, The Waters of the Po of Primaro having
free ingreſſe into the upper Valleys, they fill them to the great
damage of the Fields adjacent, and obſtruct the courſe of the
ordinary Trenches in the ſame Valleys; inſomuch that all the
care, coſt, and labour about the draining, and freeing the upper
Valleys from Water, would alſo become vain and ineffectual.
Thirdly, I conſider that theſe Waters of the Po of Ferara being
paſſed downwards towards the Sea, at the time that the main Po
was in its greater excreſcences and heights, it is manifeſt by expe­
rience, that when the great Po diminiſheth, then theſe Waters
paſſed by the Po of Ferara begin to retard in their courſe, and
finally come to turn the current upwards towards Stellata, reſting
firſt iu the intermediate time, almoſt fixed and ſtanding, and
therefore depoſing the muddineſſe, they fill up the Channel of
the River or Current of Ferara. Fourthly and laſtly, There
followeth from this ſame diverſion 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 ſhelf, that is, the bottom of the River is raiſed, as if ſufficiently
manifeſt by experience; and thus juſt in the ſame manner cutting
the Bank at Bondeno, there is at it were a breach made, from which
followeth the riſing in the lower parts of the main Po, being paſt
the mouth of Pamaro; which thing, how pernitious it is, let any one
judge that underſtandeth theſe matters. And therefore both for
the ſmall benefit, and ſo many harms that enſue from maintain­
ing this diverſion, I ſhould think it were more ſound advice to
keep that Bank alwaies whole at Bondeno, or in any other conve­
nient place, and not to permit that the Water of the Grand Po
ſhould ever come near to Ferara.
1
COROLLARIE XIV.
* Arteſia.
In the Grand Rivers, which fall into the Sea, as here in Italy
Po, Adige,^{*} and Arno, which are armed with Banks againſt their
excreſcencies, its obſerved that far from the Sea, they need
Banks of a notable height; which height goeth afterwards by
degrees diminiſhing, the more it approacheth to the Sea-coaſts:
in ſuch ſort, that the Po, diſtant from the Sea about fifty or ſixty
miles at Ferara, ſhall have Banks that be above twenty feet
higher than the ordinary Water marks; but ten or twelve miles
from the Sea, the Banks are not twelve feet higher than the ſaid
ordinary Water-marks, though the breadth of the River be the
ſame, ſo that the excreſcence of the ſame Innundation happens
to be far greater in meaſure remote from the Sea, then near; and
yet it ſhould ſeem, that the ſame quantity of Water paſſing by
every piace, the River ſhould need to have the ſame altitude of
Banks in all places: But we by our Principles and fundamentals
may be able to render the reaſon of that effect, and ſay; That
that exceſſe of quantity of Water, above the ordinary Water,
goeth alwaies acquiring greater velocity; the nearer it approach­
eth the Sea, and therefore decreaſeth in meaſure, and conſequenly
in height. And this perhaps might have been the cauſe in great
part, why the Tyber in the Innundation Anno 1578. iſſued not
forth of its Channel below Rome towards the Sea.
COROLLARIE XV.
From the ſame Doctrine may be rendred a moſt manifeſt rea­
ſon why the falling Waters go leſſening in their deſcent, ſo
that the ſame falling Water, meaſured at the beginning of
its fall, is greater, and bigger, and afterwards by degrees leſſeneth
in meaſure the more it is remote from the beginning of the fall.
Which dependeth on no other, than on the acquiſition, which
it ſucceſſively makes of greater velocity; it being a moſt fami­
liar concluſion among Philoſophers, that grave bodies falling,
the more they remove from the beginning of their motion, the
more they acquire of ſwiftneſſe; and therefore the Water, as a
grave body, falling, gradually velocitates, and therefore de­
creaſeth in meaſure, and leſſeneth.
COROLLARIE XVI.
And on the contrary, the ſpirtings of a Fountain of Water,
which ſpring on high, work a contrary effect; namely
1in the beginning they are ſmall, and afterwards become greater
and bigge; and the reaſon is moſt manifeſt, becauſe in the be­
ginning they are very ſwift, and afterwards gradually relent
their impetuoſity, and motion, ſo that in the beginning of the
excurſion that they make, they ought to be ſmall, and after­
wards to grow bigger, as in the effect is ſeen.
APPENDIX. I.
Into the errour of not conſidering how much the different
velocities of the ſame running water in ſeveral places of
its current, are able to change the meaſure of the ſame
water, and to make it greater, or leſſe, I think, if I be not
deceived, that Ginlio Frontino a noble antient Writer, may
have faln in the Second Book which he writ, of the Aqueducts
of the City of Rome: Whilſt finding the meaſure of the Water
^{*}Commentaries leſſe than it was in erogatione 1263. Quinaries, he

thought that ſo much difference might proceed from the negligence
of the Meaſures; and when afterwards with his own induſtry he
meaſured the ſame water at the beginnings of the Aqueducts,
finding it neer 10000. Quinaries bigger than it was in Commenta­
riis he judged, that the overplus was imbeziled by Miniſters and
Partakers; which in part might be ſo, for it is but too true, that
the publique is almoſt alwayes defrauded; yet nevertheleſſe, I
verily believe withal, that beſides the frauds of theſe Officers,
the velocities of the water in the place wherein Frontino meaſu­
red, it might be different from thoſe velocities, which are
found in other places before meaſured by others; and there­
fore the meaſures of the waters might, yea ought necſſarily to
be diffcrent, it having been by us demonſtrated, that the mea­
ſures of the ſame running water have reciprocal proportion to
their velocities. Which Frontino not well conſidering, and find­
ing the water in Commentariis 12755. Quinaries in erogati­
one 14018, and in his own meaſure ad capita ductuum, at the
head of the fountain 22755. Quinaries, or thereabouts, he
thought, that in all theſe places there paſt different quantities of
water; namely, greater at the fountain head then that which was
in Erogatione, and this he judged greater than that which was
in Commentariis.
+ Commentarius
beareth many ſen­
ſes, but in this
place ſignifieth a
certain Regiſter of
the quantities of
the Waters in the
ſeveral publique A­
qu ducts of Rome;
which word I find
frequently uſed in
the Law-books of
antient Civilians:
Andby errogation
we are to under­
ſtand the diſtribu­
tion or delivering
out of thoſe ſtores
of Water.
APPENDIX II.
Alike miſtake chanced lately in the Aqueduct of Acqua­
Paola, which Water ſhould be 2000 Inches, and ſo many
effectively ought to be allowed; and it hath been given in
1ſo to be by the Signors of Bracciano to the Apoſtolick-Chamber;
and there was a meaſure thereof made at the beginning of the
Aqueduct; which meaſure proved afterwards much leſſe and
ſhort, conſidered and taken in Rome, and thence followed diſ­
contents and great diſorders, and all becauſe this property of
Running-Waters, of increaſing in meaſure, where the velocity
decreaſed; and of diminiſhing in meaſure, where the velocity
augmented, was not lookt into.
APPENDIX III.
Alike errour, in my judgement, hath beeen committed by
all thoſe learned men, which to prevent the diverſion of
the Reno of Bologna into Po by the Channels, through
which it at preſent runneth, judged, that the Reno being in its
greater excreſcence about 2000 feet, and the Po being near
1000 feet broad, they judged, I ſay, that letting the Reno into
Po, it would have raiſed the Water of Po two feet; from which
riſe, they concluded afterwards moſt exorbitant diſorders, either
of extraordinary Inundations, or elſe of immenſe and intolera­
ble expences to the people in raiſing the Banks of Po and Reno,
and with ſuch like weakneſſes, often vainly diſturbed the minds
of the perſons concerned: But now from the things demonſtra­
ted, it is manifeſt, That the meaſure of the Reno in Reno, would
be different from the meaſure of Reno in Po; in caſe that the
velocity of the Reno in Po, ſhould differ from the velocity
of Reno in Reno, as is more exactly determined in the fourth Pro­
poſition.
APPENDIX IV.
No leſs likewiſe are thoſe Ingeneers and Artiſts deceived,
that have affirmed, That letting the Reno into Po, there
would be no riſe at all in the Water of Po: For the truth
is, That letting Reno into Po, there would alwaies be a riſing; but
ſometimes greater, ſometimes leſſe, as the Po ſhall have a ſwifter
or ſlower Current; ſo that if the Po ſhall be conſtituted in a great
velocity, the riſe will be very ſmall; and if the ſaid Po ſhall be
ſlow in its courſe, then the riſe will be notable.
APPENDIX V.
And here it will not be beſides the purpoſe to advertiſe, That
the meaſures, partments, and diſtributions of the Waters
of Fountains, cannot be made exactly, unleſs there be con­
1fidered, beſides the meaſure, the velocity alſo of the Water;
which particular not being thorowly obſerved, is the cauſe of
continual miſcariages in ſuch like affairs.
APPENDIX VI.
Like conſideration ought to be had with the greater diligence,
for that an errour therein is more prejudicial; I ſay, ought to
be had by thoſe which part and divide Waters; for the
watering of fields, as is done in the Territories of Breſcia, Ber­
gama, Crema, Pavia, Lodigiano, Cremona, and other places:
For if they have not regard to the moſt important point of the
variation of the velocity of the Water, but onely to the bare
Vulgar meaſure, there will alwaies very great diſorders and pre­
judices enſue to the perſons concerned.
APPENDIX VII.
It ſeemeth that one may obſerve, that whilſt the Water run­
neth along a Channel, Current, or Conduit, its velocity is
retarded, withheld, and impeded by its touching the Bank or
ſide of the ſaid 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 moſt
true, and from our conſiderations, we have an occaſion of diſ­
covering a very nice miſtake, into which thoſe commonly fall
who divide the Waters of Fountains. Which diviſion is wont
to be, by what I have ſeen here in Rome, performed two wayes;
The firſt of which is with the meaſures of like figures, as Cir­
cles, or Squares, having cut through a Plate of metal ſeveral
Circles or Squares, one of half an inch, another of one inch,
another of two, of three, of four, &c. with which they after­
wards adjuſt the Cocks to diſpence the Waters. The other
manner of dividing the Waters of Fountains, is with rectangle
paralellograms, of the ſame height, but of different Baſes, in ſuch
ſort likewiſe, that one paralellogram be of half an inch, another
of one, two, three, &c. In which manner of meaſuring and
dividing the Water, it ſhould ſeem that the Cocks being placed
in one and the ſame plain, equidiſtant from the level, or ſuperior
ſuperficies of the water of the Well; and the ſaid meaſures be­
ing moſt exactly made, the Water ought conſequently alſo to
be equally divided, and parted according to the proportion of
the meaſures. But if we well conſider every particular, we ſhall
finde, that the Cocks, as they ſucceſſively are greater, diſcharge
alwaies more Water than the juſt quantity, in compariſon of
1the leſſer; that is, to ſpeak more properly, The Water which
paſſeth through the greater Cock, hath alwaies a greater pro­
portion to that which paſſeth through the leſſer, than the greater
Cock hath to the leſſer. All which I will declare by an exam­
ple.
Let there be ſuppoſed for more plainneſs two Squares; (the
ſame may be underſtood of Circles, and other like Figures) The
firſt Square is, as we will ſuppoſe, quadruple to the other, and
theſe Squares are the mouths of two Cocks.; one of four inches,
the other of one: Now its manifeſt by what hath been ſaid, that
the Water which paſſeth by the leſs Cock, findeth its velocity
impeded in the circumference of the Cock; which impediment
1[Figure 1]
is meaſured by the ſaid circumfe­
rence. Now it is to be conſider­
ed, that if we would have the Wa­
ter which paſſeth through the
greater Cock, to be onely qua­
druple to that which paſſeth
through the leſſe, in equal ſpaces of time, it would be neceſſary,
that not onely the capacity and the meaſure of the greater Cock
be quadruple to the leſſer Cock, but that alſo the impediment be
quadrupled. Now in our caſe it is true, That the belly and
mouth of the Cock is quadrupled, and yet the impediment is not
quadrupled, but is onely doubled; ſeeing that the circumference
of the greater Square, is onely double to the circumference of
the leſier Square; for the greater circumference containeth eight
of thoſe parts, of which the leſſer containeth but four, as is ma­
nifeſt by the deſcribed Figure; and for that cauſe there ſhall
paſs by the greater Cock, above four times as much Water, as
ſhall paſs by the leſſer Cock.
The like errour occurreth alſo in the other manner of meaſu­
ring the Water of a Fountain, as may eaſily be collected from
what hath been ſaid and obſerved above.
APPENDIX VIII.
The ſame contemplation diſcovereth the errour of thoſe
Architects, who being to erect a Bridge of ſundry Arches
over a River, conſider the ordinary breadth of the River;
which being v. g. fourty fathom, and the Bridge being to conſiſt
of four Arches, it ſufficeth them, that the breadth of all the four
Arches taken together, be fourty fathom; not conſidering that
in the ordinary Channel of the River, the Water hath onely
two impediments which retard its velocity; namely, the touching
and gliding along the two ſides or ſhores of the River: but
1the ſame water in paſſing under the Bridge, in our caſe meeteth
with eight of the ſame impediments, bearing, and thruſting upon
two ſides of each Arch (to omit the impediment of the bottom,
for that it is the ſame in the River, and under the Bridge) from
which inadvertency ſometimes follow very great diſorders, as
quotidian practice ſhews us.
APPENDIX IX.
It is alſo worthy to conſider the great and admirable benefit
that thoſe 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 caſe the careful Husbandman cutteth
away the reeds and ruſhes in the Ditches, through which the
waters paſs; whereupon may be preſently ſeen, ſo ſoon as the
reeds and ruſhes are cut, a notable Ebb in the level of the water
in the Ditches; inſomuch that ſometimes it is obſerved, that the
water is abated after the ſaid cutting a third and more, of what it
was before the cutting. The which effect ſeemingly might de­
pend on this, That, before thoſe weeds took up room in the
Ditch, and for that cauſe the water kept a higher level, and the
ſaid Plants being afterwards cut and removed, the water came to
abate, poſſeſſing the place that before was occupied by the
weeds: Which opinion, though probable, and at firſt ſight ſa­
tisfactory, is nevertheleſs inſufficient to give the total reaſon of
that notable abatement which hath been ſpoken of: But it is ne­
ceſſary to have recourſe to our confideration of the velocity in
the courſe of the water, the chiefeſt and true cauſe of the vari­
ation of the meaſure of the ſame Running-Water; for, that
multitudes of reeds, weeds, and plants diſperſed through the cur­
rent of the Ditch, do chance notably to retard the courſe of the
water, and therefore the meaſure of the water increaſeth; and
thoſe impediments removed, the ſame water gaineth velocity,
and therefore decreaſeth in meaſure, and conſequently in
height.
And perhaps this point well underſtood, may be of great
profit to the fields adjacent to the Pontine Fens, and I doubt not
but if the River Ninfa, and the other principal Brooks of thoſe
Territories were kept well cleanſed from weeds, their waters
would be at a lower level, and conſequently the drains of the
fields would run into them more readily; it being alwayes to be
held for undoubted, that the meaſure of the water before the
cleanſing, hath the ſame proportion to the meaſure after clean­
ſing, that the velocity after the cleanſing hath to the velocity
before the cleanſing: An dbecauſe thoſe weeds being cleanſed
1away, the courſe ef the water notably increaſeth, it is therefore
neceſſary that the ſaid water abate in meaſure, and become
lower.
APPENDIX. X.
We having above obſerved ſome errors that are commit­
ted in diſtributing the waters of Fountains, and thoſe
that ſerve to water fields; it ſeemeth now fit, by way of
a cloſe to this diſcourſe, to advertiſe by what means theſe divi­
ſions may be made juſtly and without error. I therefore think
that one might two ſeveral wayes exquiſitly divide the water of
Fountains; The firſt would be by diligently examining, Firſt,
how much water the whole Fountain diſchargeth in a determi­
nate time, as for inſtance: How many Barrels, or Tuns it carri­
eth in a ſet time; and in caſe you are afterwards to diſtribute
the water, diſtribute it at the rate of ſomany Barrels or Tuns, in
that ſame time; and in this caſe the participants would have
their punctual ſhares: Nor could it ever happen to ſend out more
water, than is reckoned to be in the principal Fountain; as befel
Giulio Frontino, and as alſo it frequently happeneth in the Mo­
dern Aqueducts, to the publick and private detriment.
The other way of dividing the ſame waters of a Fountain, is
alſo ſufficiently exact and eaſie, and may be, by having one one­
ly ſize for the Cock or Pipe, as ſuppoſe of an inch, or of half an
inch; and when the caſe requireth to diſpence two, three, and
more inches, take ſo many Cocks of the ſaid meaſure as do eva­
cuate the water, which is to be emitted; and if we are to make
uſe onely of one greater Cock, we being to place one to diſ­
charge for example four inches; and having the former ſole mea­
ſure of an inch, we muſt make a Cock that is bigger, its true, than
the Cock of one inch; but not ſimply in a quadruple propor­
tion, for that it would diſcharge more than juſt ſo much water,
as hath been ſaid 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, ſo, that it may diſ­
charge four times as much water as the leſſer in the ſame time;
and by this means we ſhall avoid the diſorder hinted in the
ſeventh Appendix. It would be neceſſary nevertheleſs, to ac­
commodate the Cocks of the Ciſtern ſo, that the level of the
water in the Ciſtern may alwayes reſt at one determinate mark
above the Cock, otherwiſe the Cocks will emit ſometimes
greater, and ſometimes leſſe abundance of water: And becauſe
it may be that the ſame water of the Fountain may be ſometimes
more abundant, ſometimes leſs; in ſuch caſe it will be neceſſary
1to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa­
ter, diſcharge into the publick Fountains, that ſo the particular
participants may have alwayes the ſame abundance of
water.
APPENDIX XI.
Much more difficult is the diviſion of the waters which
ſerve to water the fields, it not being poſſible to obſerve
ſo commodiouſly, what quantity of water the whole
Ditch ſends forth in one determinate time, as may be done in
Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
little below demonſtrated, be well underſtood, there may be
thence taken a very ſafe and juſt way to diſtribute ſuch waters.
The Propoſition therefore by us demonſtrated is this: If there
be two Sections, (namely two mouths of Rivers) the quantity of
the water which paſſeth by the firſt, hath a proportion to that
which paſſeth by the ſecond, compounded of the proportions of
the firſt Section to the ſecond, and of the velocity through
the firſt, to the velocity through the ſecond: As I will declare
for example by help of practice, that I may be underſtood by
all, in a matter ſo important. Let the two mouths of the
Rivers be A, and B, and let
2[Figure 2]
the mouth A be in meaſure
and content thirty two feet,
and the mouth B, eight feet.
Here you muſt take notice,
that it is not alwayes true, that
the Water which paſſeth by A,
hath the ſame proportion to that which paſſeth by B, that the
mouth A hath to the mouth B; but onely when the velocityes
by each of thoſe paſſages are equal: But if the velocityes ſhall
be unequal, it may be that the ſaid mouths may emit equal
quantity of Water in equal times, though their meaſure be un­
equal; and it may be alſo, that the bigger doth diſcharge a great­
er quantity of Water: And laſtly, it may be, that the leſs mouth
diſchargeth more Water than the greater; and all this is mani­
feſt by the things noted in the beginning of this diſcourſe, and
by the ſaid ſecond Propoſition. Now to examine the propor­
tion of the Water that paſſeth by one Ditch, to that which paſ­
ſeth by another, that this being known, the ſame Waters and
mouths of Ditches may be then adjuſted; we are to keep ac­
count not onely of the greatneſs of the mouths or paſſages of the
Water, but of the velocity alſo; which we will do, by firſt find­
ing two numbers that have the ſame proportion between them­
1ſelves, as have the mouths, which are the numbers 32 and 8
in our example: Then this
3[Figure 3]
being done, let the velocity
of the Water by the paſſa­
ges A and B, be examined
(which may be done keeping
account what ſpace a piece
of Wood, or other body that
ſwimmeth, is carried by the ſtream in one determinate time; as
for inſtance in 50 pulſes) and then work by the golden Rule, as
the velocity by A, is to the velocity by B, ſo is the number 8, to
another number, which is 4. It is clear by what is demonſtra­
ted in the ſaid ſecond Propoſition, that the quantity of water,
which paſſeth by the mouth A, ſhall have the ſame proportion of
that which paſſeth by the mouth B, that 8 hath to 1. Such pro­
portion being compoſed of the proportions of 32 to 8, and of 8 to
4; namely, tothe greatneſs of the mouth A, to the greatneſs of the
mouth B, and of the velocity in A, to the velocity in B. This being
done, we muſt then contract the mouth which diſchargeth more
then its juſt quantity of water, or enlarge the other which diſchar­
geth leſs, as ſhal be moſt commodious in practice, which to him that
hath underſtood this little that hath been delivered, will be very
afie.
APPENDIX XII.
Theſe opperations about Water, as I have hitherto on ſun­
dry occaſions obſerved, are involved in ſo many difficul­
ties, and ſuch a multiplicity of moſt extravagant accidents,
that it is no marvel if continually many, and very important er­
rours be therein committed by many, and even by Ingeneers
themſelves, and Learned-men; and becauſe many times they
concern not onely the publique, but private intereſts: Hence it
is, that it not onely belongeth to Artiſts to treat thereof, but very
oft even the vulgar themſelves pretend to give their judgement
therein: And I have been troubled many times with a neceſſity
of treating, not onely with thoſe, which either by practice, or
particular ſtudy, underſtood ſomewhat in theſe matters; but alſo
with people wholly void of thoſe notions, which are neceſſary for
one that would on good grounds diſcourſe about this particular;
and thus many times have met with more difficulty in the thick
skulls of men, than in precipitous Torrents, and vaſt Fennes.
And in particular, I had occafion ſome years paſt to go ſee the
Gave or Emiſſary of the Lake of Perugia, made many years agon
by Braccio Fortobraccio, but for that it was with great ruines by
Time decayed, and rendred unuſeful, it was repaired with in­
1duſtry truly heroicall and admirable, by Monſignor Maffei Bar­
herino, then Prefect for the Wayes, and now Pope. And being
neceſſitated, that I might be able to walk in the Cave, and for
other cauſes, I let down the Sluices of the ſaid Cave, at the mouth
of the Lake: No ſooner were they ſtopt, but a great many of the
people of the Towns and Villages coaſting upon the Lake
flocking thither, began to make grievous complaints, that if thoſe
Sluices were kept ſhut, not onely the Lake would want its due
Vent, but alſo the parts adjacent to the Lake would be over
flown to their very great detriment. And becauſe at firſt appea­
rance their motion ſeemed very reaſonable, I found my ſelf hard
put to it, ſeeing no way to perſwade ſuch a multitude, that the
prejudice which they pretended I ſhould do them by keeping
the Sluices ſhut for two dayes, was abſolutely inſenſible; and that
by keeping them open, the Lake did not ebb in the ſame time ſo
much as the thickneſs of a ſheet of Paper: And therefore I was
neceſſitated to make uſe of the authority I had, and ſo followed
my buſineſs as cauſe required, without any regard to that Rab­
ble tumultuouſly aſſembled. Now when I am not working with
Mattock or Spade, but with the Pen and Diſcourſe, I intend to
demonſtrate clearly to thoſe that are capable of reaſon, and that
have well underſtood the ground of this my Treatiſe, that the
fear was altogether vain which thoſe people conceited. And
therefore I ſay, that the Emiſſary or Sluice of the Lake of Peru­
gia, ſtanding in the ſame mannner as at preſent, and the water
paſſing thorow it with the ſame velocity as now; to examine
how much the Lake may abate in two days ſpace, we ought to
conſider, what proportion the ſuperficies of the whole Lake hath
to the meaſure of the Section of the Emiſſary, and afterwards to
infer, that the velocity of the water by the Emiſſary or Sluice,
ſhall have the ſame proportion to the abatement of the Lake,
and to prove thorowly and clearly this diſcourſe, I intend to
demonſtrate the following Propoſition.
Suppoſe a Veſſel of any bigneſſe, and that it hath an Emiſſary
or Cock, by which it diſchargeth its water. And look what pro­
portion the ſuperſicies of the
veſſel hath to the meaſure of
4[Figure 4]
the ſection of the cock, ſuch pro­
portion ſhall the velocity of the
Water in the Cock have to the
abatement of the Lake Let the
Veſſel be A B C D, H I L B, through which the Water runneth,
the ſuperficies of the Water in the Veſſel A D, and the ſection
of the Cock H L: and let the Water in the Veſſel
be ſuppoſed to have falne in one determinate time from A to F.
1I ſay that the proportion of the ſuperficies of the Veſſel A D is
in proportion to the meaſure of the ſection of the Emiſſary
H L, as the velocity of the Emiſſary or Cock to the line A F;
which is manifeſt, for that the Water in the Veſsel moving by
the line A F; as far as F, and the whole maſs of Water A G
diſcharging it ſelf, and in the ſame time the ſame quantity of
Water being diſcharged by the ſection of the Emiſſary H L; it
is neceſſary by what I have demonſtrated in the third Propoſition,
and alſo explained in the beginning of this Treatiſe, that the ve­
locity by the Emiſſary or Cock be in proportion to the velocity
of the abatement, as the ſuperficies of the Veſſel to the mea­
ſure of the ſection of the Emiſſary, which was to be demon­
ſtrated.
That which hath been demonſtrated in the Veſſel, falls out ex­
actly alſo in our Lake of Perugia, and its Emiſsary; and becauſe
the immenſity of the ſuperficies of the Lake is in proportion to
the ſuperficies of the Emiſsary or Sluice, as many millions to
one, as may be eaſily calculated; it is manifeſt, that ſuch abate­
ment ſhall be imperceptible, and almoſt nothing, in two dayes
ſpace, nay in four or ſix: and all this will be true, when we
ſuppoſe that for that time there entreth no other Water into the
Lake from Ditches or Rivolets, which falling into the Lake would
render ſuch abatement yet leſs.
Now we ſee, that it's neceſsary to examine ſuch abatements
and riſings, with excellent reaſons, or at leaſt, with accurate ex­
periments, before we reſolve and conclude any thing; and how
farre the vulgar are diſtant from a right judgment in ſuch
matters.
APPENDIX XIII.
For greater confirmation of all this which I have ſaid, I
will inſtance in another like caſe, which alſo I met with here­
tofore, wherein, for that the buſineſs was not rightly un­
derſtood, many diſorders, vaſt expences, and conſiderable miſ­
chiefs have followed. There was heretofore an Emiſsary or
Sluice made to drain the Waters, which from Rains, Springs, and
Rivolets fall into a Lake; to the end, the ſhores adjoyning on
the Lake, ſhould be free from the overflowing of the Waters;
but becauſe perhaps the enterprize was not well managed and
carried on, it fell out, that the Fields adjacent to the ſaid Chanel
could not drain, but continued under water; to which diſorders
a preſent remedy hath been uſed, namely, in a time convenient
to ſtop up the Sluice, by meanes of certain Floodgates kept on
purpoſe for that end; and thus abating the Level of the Water
1in the Emiſſary, in the ſpace of three or four dayes, the Fields
have been haply drained. But on the other part, the proprietors
bordering on the Lake oppoſed this, grievouſly complaining, that
whilſt the Floodgates are ſhut, and the courſe 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 ſo continuing their ſuits, they got more of vexation than ſa­
tisfaction. Now, being asked my opinion herein, I judged it
requiſite (ſince the point in controverſie was about the riſing
and falling of the Lake) that the ſaid abatement, when the
Floodgates are open, and increaſe when they are ſhut ſhould be
exactly meaſured, and told them, that it might be eaſily done at
a time when no extraordinary Waters fell into the Lake, neither
of Rain, or otherwiſe; and the Lake was undiſturbed by winds
that might drive the Water to any ſide, by planting neer to an
Iſlet, which is about the middle of the Lake, a thick poſt, on
which ſhould be made the marks of the Lakes riſing and falling
for two or three dayes. I would not, at that time, pawn, or re­
ſolutely declare, my judgment, in regard I might be, by divers
accidents miſled. But this I told them, that (by what I have
demonſtrated, and particularly that which I have ſaid above
touching the Lake of Perugia) I inclined greatly to think,
that theſe riſings and fallings would prove imperceptible, and
inconſiderable; and therefore, that in caſe experience ſhould
make good my reaſon, it would be to no purpoſe for them to
continue diſputing and wrangling, which cauſeth, (according
to the Proverb) A great deal of cry, but produceth not much
Wool.
Laſtly, it importing very much to know what a Rain conti­
nued for many dayes can do in raiſing theſe Lakes, I will here in­
ſert the Copy of a Letter, which I writ formerly to Signior Ga­
lilæo Galilæi, chief Philoſopher to the Grand Duke of Tuſcany,
wherein I have delivered one of my conceits in this buſineſſe, and
it may be, by this Letter, I may, more ſtrongly, confirm what I
have ſaid above.
1
The Copy of a Letter to Signore GALILÆO
GALILÆI, Chief Philoſopher to the moſt Serene
Great Duke of TVSCANY.
Worthy and moſt Excellent SIR,
In ſatisfaction of my promiſe, in my former Letters of
repreſenting unto you ſome of my Conſiderations
made upon the Lake Thraſimeno, I ſay, That in times
paſt, being in Perugia, where we held our General
Convention, having underſtood that the Lake Thraſimeno, by
the great drought of many Moneths was much abated, It came
into my head, to go privately and ſee this novelty, both for my
particular ſatisfaction, as alſo that might I be able to relate the
whole to my Patrons, upon the certitude of my own ſight of the
place. And ſo being come to the Emiſſary of the Lake, I found
that the Level of the Lakes ſurface was ebbed about five Ro­
man Palmes of its wonted watermark, inſomuch that it was lower
than the tranſome of the mouth of the Emiſſary, by the length
of ----------------------------this deſcribed line, and there­
fore no Water iſſued out of the Lake, to the great prejudice of
all the places and villages circumjacent, in regard that the Wa­
ter which uſed to run from the ſaid Lake turned 22 Mills, which
not going, neceſſitated the inhabitants of thoſe parts to go a
dayes journey and more, to grinde upon the Tiber. Being retur­
ned to Perugia, there followed a Rain, not very great, but con­
ſtant, and even, which laſted for the ſpace of eight hours, or
thereabouts; and it came into my thoughts to examine, being
in Perugia, how much the Lake was increaſed and railed by this
Rain, ſuppoſing (as it was probable enough) that the Rain had
been univerſal over all the Lake; and like to that which fell in
Perugia, and to this purpoſe I took a Glaſſe formed like a Cy­
linder, about a palme high, and half a palme broad; and having
put in water ſnfficient to cover the bottome of the Glaſſe, I no­
ted diligently the mark of the height of the Water in the Glaſſe,
and afterwards expoſed it to the open weather, to receive the
Raine-water, which fell into it; and I let it ſtand for the
ſpace of an hour; and having obſerved that in that time the Wa­
ter was riſen in the Veſſel the height of the following line---,
I conſidered that if I had expoſed to the ſame rain ſuch other veſ­
ſels equal to that, the Water would have riſen in them all accor­
ding to that meaſure: And thereupon concluded, that alſo in all
1the whole extent of the Lake, it was neceſſary the Water ſhould
be raiſed in the ſpace of an hour the ſame meaſure. Yet here I
conſidered two difficulties that might diſtutb and altar ſuch an
effect, or at leaſt render it inobſerveable, which afterwards well
weighed, and reſolved, left me (as I will tell you anon) in the
concluſion the more confirmed; that the Lake ought to be in­
creaſed in the ſpace of eight hours, that the rain laſted eight
times that meaſure. And whilſt I again expoſed the Glaſs to re­
peat the experiment, there came unto me an Ingeneer to talk
with me touching certain affairs of our Monaſtary of Perugia, and
diſcourſing with him, I ſhewed him the Glaſs out at my Cham­
ber-window, expoſed in a Court-yard; and communicated to
him my fancy, relacing unto him all that I had done. But I
ſoon perceived that this brave fellow conceited me to be but of
a dull brain, for he ſmilling ſaid unto me; Sir, you deceive
your ſelf: I am of opinion that the Lake will not be increaſ­
ed by this rain, ſo much as the thickneſſe of a ^{*} Julio.

Hearing him pronounce this his opinion with freeneſs and
confidence, I urged him to give me ſome reaſon for what he
ſaid, aſſuring him, that I would change my judgement, when I
ſaw the ſtrength of his Arguments: To which he anſwered, that
he had been very converſant about the Lake, and was every day
upon it, and was well aſſured that it was not at all increaſed. And
importuning him further, that he would give me ſome reaſon
for his ſo thinking, he propoſed to my conſideration the great
drought paſſed, and that that ſame rain was nothing for the
great parching: To which I anſwered, I believe Sir that the ſur­
face of the Lake, on which the rain had fallen was moiſtned; and
therefore ſaw not how its drought, which was nothing at all,
could have drunk up any part of the rain. For all this he per­
ſiſting in his conceit, without yielding in the leaſt to my allega­
tion; he granted in the end (I believe in civility to me) that
my reaſon was plauſible and good, but that in practiſe it could
not hold. At laſt to clear up all, I made one be called, and
ſent him to the mouth of the Emiſſary of the Lake, with order
to bring me an exact account, how he found the water of the
Lake, in reſpect of the Tranſome of the Sluice. Now here,
Signore Galilo, I would not have you think that I had brought
the matter in hand to concern me in my honour; but believe me
(and there are witneſſes of the ſame ſtill living) that my meſſen­
ger returning in the evening to Perugia, he brought me word,
that the water of the Lake began to run through the Cave; and
that it was riſen almoſt a fingers breadth above the Tranſome:
Inſomuch, that adding this meaſure, to that of the lowneſs of
the ſurface of the Lake, beneath the Tranſome before the rain,
1it was manifeſt that the riſing of the Lake cauſed by the rain, was
to a hair thoſe 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 buſineſs, to which he knew not what to
anſwer.
* A Coyn of Pope
Julius worth ſix
pence.
Now the two difficulties which I thought of, able to impede
my concluſion, were theſe following: Firſt, I conſidered that
it might be, that the Wind blowing from the ſide where the
Sluice ſtood, to the Lake-ward; the mole and maſs of the Wa­
ter of the Lake might be driven to the contrary ſhore; on which
the Water riſing, it might be fallen at the mouth of the Emiſſa­
ry, and ſo the obſervation might be much obſcured. But this
difficulty wholly vaniſhed by reaſon of the Aires great tranqui­
lity; which it kept at that time, for no Wind was ſtirring on any
ſide, neither whilſt it rained, nor afterwards.
The ſecond difficulty which put the riſing in doubt, was, That
having obſerved in Florence, and elſewhere, thoſe Ponds into
which the rain-water, falling from the houſe, is conveyed
through the Common-ſhores: And that they are not thereby
ever filled, but that they ſwallow all that abundance of water,
that runs into them by thoſe conveyances which ſerve them with
water; inſomuch that thoſe conveyances which in time of
drought maintain the Pond, when there comes new abundance
of water into the Pond, they drink it up, and ſwallow it: A like
effect might alſo fall out in the Lake, in which there being many
veins (as it is very likely) that maintain and feed the Lake; theſe
veins might imbibe the new addition of the Rain-water, and ſo
by that means annuall the riſing; or elſe diminiſh it in ſuch ſort, as
to render it inobſervable. But this difficulty was eaſily reſolved
by conſidering my Treatiſe of the meaſure of Running-Waters;
foraſmuch as having demonſtrated, that the abatement of a Lake
beareth the reciprocal proportion to the velocity of the Emiſſa­
ry, which the meaſure of the Section of the Emiſſary of the Lake,
hath to the meaſure of the ſurface of the Lake: making the
calculation and account, though in groſs; by ſuppoſing that its
veins were ſufficiently large, and that the velocity in them were
notable in drinking up the water of the Lake; yet I found never­
theleſs, that many weeks and moneths would be ſpent in drink­
ing up the new-come abundance of water by the rain, ſo that
I reſted ſure, that the riſing would enſue, as in effect it did.
And becauſe many of accurate judgement, have again cauſed
me to queſtion this riſing, ſetting before me, that the Earth be­
ing parched by the great drought, that had ſo 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
1from the increaſing Lake, would not ſuffer it to increaſe in
height: I ſay therefore, that if we would rightly conſider this
doubt here propoſed, we ſhould, in the very conſideration of it,
ſee it reſolved; for, it being ſuppoſed that that liſt or border of
Banks which was to be occupied by the increaſe of the Lake, be
a Brace in breadth quite round the Lake, and that by reaſon of
its dryneſs it ſucks in water, and that by that means this propor­
tion of water co-operates not in raiſing of the Lake: It is abſo­
lutely neceſſary on the other hand, that we conſider, That the
Circuit of the water of the Lake being thirty miles, as its com­
monly held, that is to ſay, Ninety thouſand Braces of Florence
in compaſs; and therefore admitting for true, that each Brace of
this Bank drink two quarts of water, and that for the ſpieading
it require three quarts more, we ſhall finde, that the whole agre­
gate of this portion of water, which is not imployed in the raiſing
of the Lake, will be four hundred and fifty thouſand Quarts of
water; and ſuppoſing that the Lake be ſixty ſquare miles, three
thouſand Braces long, we ſhall finde, that to diſpence the water
poſſeſt by the Bank about the Lake, above the total ſurface of
the Lake, it ought to be ſpread ſo thin, that one ſole quart of
water may over-ſpread ten thouſand ſquare Braces of ſurface:
ſuch a thinneſs, as muſt much exceed that of a leaf of beaten
Gold, and alſo leſs than that skin of water which covers the Bub­
bles of it: and ſuch would that be, which thoſe men would have
ſubſtracted from the riſing of the Lake: But again, in the ſpace
of a quarter of an hour at the beginning of the rain, all that
Bank is ſoaked by the ſaid rain, ſo that we need not for the
moiſtning of it, imploy a drop of that water which falleth into
the Lake. Beſides we have not brought to account that abun­
dance of water which runs in time of rain into the Lake, from
the ſteepneſs of the adjacent Hills and Mountains; which would
be enough to ſupply all our occaſions: So that, neither ought
we for this reaſon to queſtion our pretended riſing. And this
is what hath fallen in my way touching the conſideration of the
Thraſimenian Lake.
After which, perhaps ſomewhat raſhly, 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
theſe cautions requiſite in ſuch like affairs; wherein we ought
not too poſitively to affirm any thing of our own heads for cer­
tain, but ought to ſubmit all to the ſound and ſecure delibera­
tion of the Holy Mother-Church, as I do this of mine, and all
others; moſt ready to change my judgement, and conform my
ſelf alwaies to the deliberations of my Superiors. Continu­
1ing therefore my above-ſaid conceit about the riſing of the wa­
ter in the glaſs tried before, it came into my minde, that the
forementioned rain having been very gentle, it might well be,
that if there ſhould have faln a Rain fifty, an hundred, or a thou­
ſand times greater than this, and much more intenſe (which
would inſue as oft as thoſe falling drops were four, ſive or ten
times bigger than thoſe of the above-mentioned rain, keeping
the ſame number) in ſuch a caſe its manifeſt, that in the ſpace
of an hour the Water would riſe in our Glaſs, two, three, and
perhaps more Yards or Braces; and conſequently, if ſuch a
Raine ſhould fall upon a Lake, that the ſaid Lake would
riſe, according to the ſame rate: And likewiſe, if ſuch a
Rain were univerſall, over the whole Terreſtriall Globe, it
would neceſſarily, in the ſpace of an hour, make a ri­
ſing of two, or three braces round about the ſaid Globe,
And becauſe we have from Sacred Records, that in the
time of the Deluge, it rained fourty dayes and fourty nights;
namely, for the ſpace of 960 houres; its clear, that if the ſaid
Rain had been ten times bigger than ours at Perugia, the riſing
of the Waters above the Terreſtrial Globe would reach and paſs
a mile higher than the tops of the Hills and Mountains that are
upon the ſuperficies of the Earth; and they alſo would concur
to increaſe the riſe. And therefore I conclude, that the riſe of
the Waters of the Deluge have a rational congruity with natural
Diſcourſes, of which I know very well that the eternal truths of
the Divine leaves have no need; but however I think ſo clear an
agreement is worthy of our conſideration, which gives us occa­
ſion to adore and admire the greatneſſe of God in his mighty
Works, in that we are ſometimes able, in ſome ſort, to meaſure
them by the ſhort Standard of our Reaſon.
Many Leſſons alſo may be deduced from the ſame Doctrine,
which I paſſe by, for that every man of himſelf may eaſily know
them, having once ſtabliſhed this Maxime; That it is not poſſi­
ble to pronounce any thing, of a certainty, touching the quantity
of Running Waters, by conſidering only the ſingle vulgar mea­
ſure of the Water wichout the velocity; and ſo on the contrary,
he that computes only the velocity, without the meaſure, ſhall
commit very great errours; for treating of the meaſure of Run­
ning Waters, it is neceſſary, the water being a body, in handling
its quantity, to conſider in it all the three dimenſions of breadth,
depth, and length: the two firſt dimenſions are obſerved by all
in the common manner, and ordinary way of meaſuring Running
Waters; but the third dimenſion of length is omitted; and hap­
ly ſuch an overſight is committed, by reaſon the length of Run­
1ning Water is reputed in ſome ſenſe infinite, in that it never cea­
ſeth to move away, and as infinite is judged incomprehenſible;
and ſuch as that there is no exact knowledge to be had thereof;
& ſo there comes to be no account made thereof; but if we ſhould
make ſtrict reflection upon our conſideration of the velocity of
Water, we ſhould find, that keeping account of the ſame, there
is a reckoning alſo made of the length; foraſmuch as whilſt we
ſay, the Water of ſuch a Spring runs with the velocity of paſſing
a thouſand or two thouſand paces an hour: this in ſubſtance is
no other than if we had ſaid, ſuch a Fountain diſchargeth in an
hour a Water of a thouſand or two thouſand paces long. So
that, albeit the total length of Running water be incomprehen­
ſible, as being infinite, yet nevertheleſſe its rendered intelligible
by parts in its velocity. And ſo much ſufficeth to have hinted
about this matter, hoping to impart on ſome other occaſion other
more accurate Obſervations in this affair.
LAVS DEO.
5[Figure 5]
1
[Empty page]
1
GEOMETRICAL
DEMONSTRATIONS
OF THE
MEASURE
OF
Running Waters.
BY
D. BENEDETTO CASTELLI,
Abbot of CASSINA, and Mathematician to
P. VRBAN. VIII.
DEDICATED
To the moſt Illuſtrious, and moſt Excellent Prince
DON THADDEO BARBERINI,
PRINCE OF
PALESTRINA,
AND
GENERAL of the HOLY CHURCH.
LONDON,
Printed Anno Domini, MDCLXI.
1
[Empty page]
1
OF THE
MENSURATION
OF
Running Waters.
SUPPOSITION I.
Let it be ſuppoſed, that the banks of the Rivers of which
we ſpeak be erected perpendicular to the plane of the up­
per ſuperficies of the River.
SUPPOSITION II.
We ſuppoſe that the plane of the bottome of the River, of
which we ſpeak is at right angles with the banks.
SUPPOSITION III.
It is to be ſuppoſed, that we ſpeak of Rivers, when they are at
ebbe, in that ſtate of ſhallowneſſe, or at flowing in that ſtate
of deepneſſe, and not in their tranſition from the ebbe to the
flowing, or fr m the flowing to the ebbe.
Declaration of Termes.
FIRST.
If a River ſhall be cut by a Plane at right angles to the ſurface
of the water of the River, and to the banks of the River,
that ſame dividing Plane we call the Section of the River; and
this Section, by the Suppoſitions above, ſhall be a right angled
Parallelogram.
SECOND.
We call thoſe Sections equally Swift, by which the water runs
with equal velocity; and more ſwift and leſs ſwift that
Section of another, by which the water runs with greater or leſſe
velocity.
1
AXIOME I.
Sections equal, and equally ſwift, diſcharge equal quantities
of Water in equal times.
AXIOME II.
Sections equally ſwift, and that diſcharge equal quantity of
Water, in equal time, ſhall be equal.
AXIOME III.
Sections equal, and that diſcharge equal quantities of Water
in equal times, ſhall be equally ſwift.
AXIOME IV.
When Sections are unequal, but equally ſwift, the quanti­
ty of the Water that paſſeth through the firſt Section,
ſhall have the ſame proportion to the quantity that paſ­
ſeth through the Second, that the firſt Section hath to the ſecond
Section. Which is manifeſt, becauſe the velocity being the
ſame, the difference of the Water that paſſeth ſhall be according
to the difference of the Sections.
AXIOME V.
If the Sections ſhall be equal, and of unequal velocity, the
quantity of the Water that paſſeth through the firſt, ſhall
have the ſame proportion to that which paſſeth through the
ſecond, that the velocity of the firſt Section, ſhall have to the
velocity of the ſecond Section. Which alſo is manifeſt, becauſe
the Sections being equal, the difference of the Water which
paſſeth, dependeth on the velocity.
PETITION.
A Section of a River being given, we may ſuppoſe another
equal to the given, of different breadth, heigth, and ve­
locity.
1
PROPOSITION I.
The Sections of the ſame River diſcharge equal quan­
tities of Water in equal times, although the Secti­
ons themſelves he unequal.
Let the two Sections be A and B, in the River C, running
from A, towards B; I ſay, that they diſcharge equal quan­
tity of Water in equal times; for if greater quantity of Wa­
ter ſhould paſs through A, than paſſeth through B, it would
6[Figure 6]
follow that the Water in the intermediate ſpace of the River C,
would increaſe continually, which is manifeſtly falſe, but if
more Water ſhould iſſue through the Section B, than entreth at
the Section A, the Water in the intermediate ſpace C, would
grow continually leſs, and alwaies ebb, which is likewiſe falſe;
therefore the quantity of Water that paſſeth through the Secti­
on B, is equal to the quantity of Water which paſſeth through
the Section A, and therefore the Sections of the ſame River diſ­
charge, &c. Which w s to be demonſtrated.
PROPOSITION II.
In two Sections of Rivers, the quantity of the Water
which paſſeth by one Section, is to that which paſ­
ſeth by the ſecond, in a Proportion compounded of
the proportions of the firſt Section to the ſecond, and
of the velocitie through the first, to the velocitie
of the ſecond.
I Et A, and B be two Sections of a River; I ſay, that the
quantity of Water which paſſeth through A, is to that which
paſſeth through B, in a proportion compounded of the pro­
portions of the firſt Section A, to the Section B; and of the velo­
city through A, to the velocity through B: Let a Section be
1ſuppoſed equal to the Section A, in magnitude; but of velocity
equal to the Section B, and let it be G, and as the Section A is
7[Figure 7]
to the Section B, ſo let the line F be to the line D; and as the
velocity A, is to the velocity by B, ſo let the line D be to the
line R: Therefore the Water which paſſeth thorow A, ſhall be
to that which paſſeth through G (in regard the Sections A and
G are of equal bigneſs, 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, ſo 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 paſſe the
through A, ſhall be to the quantity which paſſeth through G, as
the line D is to the line R; but the quantity which paſſeth
through G, is to that which paſſeth through B, (in regard the
Sections G, and B, are equally ſwift) 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 paſſeth through
A, hath the ſame proportion to that which paſſeth 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 alſo the quantity of
Water which paſſeth through the Section A, ſhall have a propor­
tion to that which paſſeth 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
paſſeth by the firſt, &c. which was to be demonſtrated.
COROLLARIE.
The ſame followeth, though the quantity of the Water which
paſſeth through the Section A, be equal to the quantity of
Water which paſſeth through the Section B, as is manifeſt by the
ſame demonſtration.
1
PROPOSITION III.
In two Sections unequal, through which paſs equal
quantities of Water in equal times, the Sections
have to one another, reciprocal proportion to their
velocitie.
Let the two unequal Sections, by which paſs equal quantities
of Water in equal times be A, the greater; and B, the leſſer:
I ſay, that the Section A, ſhall have the ſame Proportion
to the Section B, that reciprocally the velocity through B, hath to
the velocity through A; for ſuppoſing that as the Water that
paſſeth through A, is to that which paſſeth through B, ſo is the
8[Figure 8]
line E to the line F: therefore the quantity of water which paſ­
ſeth through A, being equal to that which paſſeth through B,
the line E ſhall alſo be equal to the line F: Suppoſing moreover,
That as the Section A, is to the Section B, ſo is the line F, to the
line G; and becauſe the quantity of water which paſſeth
through the Section A, is to that which paſſeth through the
Section B, in a proportion compoſed 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, ſhall be the line to F, in
a proportion compounded of the ſame 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,
ſhall be the proportion of the velocity through A, to the velocity
through B; therefore alſo the line G, ſhall be to the line E, as
the velocity by A, to the velocity by B: And converſly, the ve­
locity through B, ſhall be to the velocity through A, as the line
E, to the line G; that is to ſay, as the Section A, to the Section B,
and therefore in two Sections, &c. which was to be demonſtrated.
1
COROLLARIE.
Hence it is manifeſt, that Sections of the ſame River (which
are no other than the vulgar meaſures of the River) have
betwixt themſelves reciprocal proportions to their veloci­
ties; for in the firſt Propoſition we have demonſtrated that the
Sections of the ſame River, diſcharge equal quantities of Water
in equal times; therefore, by what hath now been demonſtrated
the Sections of the ſame River ſhall have reciprocal proportion
to their velocities; And therefore the ſame running water chan­
geth meaſure, when it changeth velocity; namely, increaſeth the
meaſure, when it decreaſeth the velocity, and decreaſeth the
meaſure, when it increaſeth the velocity.
On which principally depends all that which hath been ſaid
above in the Diſcourſe, and obſerved in the Corollaries and Ap­
pendixes; and therefore is worthy to be well underſtood and
heeded.
PROPOSITION IV.
If a River fall into another River, the height of the
firſt in its own Chanel ſhall be to the height that it
ſhall make in the ſecond Chanel, in a proportion
compounded of the proportions of the breadth of
the Chanel of the ſecond, to the breadth of the
Chanel of the firſt, and of the velocitie acquired in
the Chanel of the ſecond, to that which it had in
its proper and first Chanel.
Let the River A B, whoſe height is A C, and breadth C B,
that is, whoſe Section is A C B; let it enter, I ſay, into a­
nother River as broad as the line E F, and let it therein make
the riſe or height D E, that is to ſay, let it have its Section in
the River whereinto it falls D E F; I ſay, 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 ſup­
poſe 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 conſequently, equal to that which D F carrieth. Moreover,
as the breadth E F is to the breadth C B, ſo let the line H be to
1the line I; and as the velocity of D F is to the velocity of A B,
ſo let the line I be to the line L; becauſe therefore the two
Sections A B and G are equally ſwift, and diſcharge equal quan­
tity of Water in equal times, they ſhall be equal Sections; and
9[Figure 9]
therefore the height of A B to the height of G, ſhall be as the
breadth of G, to the breadth of A B, that is, as E F to C B,
that is, as the line H to the line I: but becauſe the Water which
paſſeth through G, is equal to that which paſſeth through D E F,
therefore the Section G, to the Section D E F, ſhall have the re­
ciprocal proportion of the velocity through D E F, to the velo­
city through G; but alſo 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 B; That is, finally, as the line I, to the
line L; Therefore, by equal proportion, the height of A B, that
is, A C, ſhall 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 B, and of the velocity through D F, to the velocity through
A B: So that if a River fall into another River, &c. which was
to be demonſtrated.
1
PROPOSITION V.
If a River diſcharge a certain quantitie of Water
in a certain time; and after that there come into it
a Flood, the quantity of Water which is diſchar­
ged in as much time at the Flood, is to that which
was diſcharged before, whilſt 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.
Suppoſe a River, which whilſt it is low, runs by the Section
AF; and after a Flood cometh into the ſame, and runneth
through the Section D F, I ſay, that the quantity of the Wa­
ter which is diſcharged through D F, is to that which is diſcharged
10[Figure 10]
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 B, to the height A B; As the velocity through DF
is to the velocity through A F, ſo let the line R, to the line S;
and as the height D B is to the height A B, ſo let the line S, to
the line T; and let us ſuppoſe a Section L M N, equal to D F
in height and breadth; that is L M equal to D B, and M N equal
to B F; but let it be in velocity equal to the Section A F, there­
fore the quantity of Water which runneth through D F, ſhall 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
A F; and the line R being to the line S, as the velocity through
D F, to the velocity through A F; therefore the quantity which
runneth through D F, to that which runneth through L N, ſhall
have the proportion of R to S; but the quantity which runneth
through L N, to that which runneth through A F, (the Sections
1being equally ſwift) ſhall be in proportion as the Section L N, to
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, ſhall 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 D F, to the velocity through A F; and therefore
if a River diſcharge a certain quantity, &c. which was to be de­
monſtrated.
ANNOTATION.
The ſame might have been demonſtrated by the ſecond
Propoſition above demonſtrated, as is manifeſt.
PROPOSITION VI.
If two equal ſtreams of the ſame Torrent, fall into a
River at divers times, the heights made in the Ri­
ver by the Torrent, ſhall have between them­
ſelves the reciprocal proportion of the velocities
acquired in the River.
Let A and B, be two equal ſtreams of the ſame Torrent,
which falling into a River at divers times, make the heights
C D, and F G; that is the ſtream A, maketh the height
C D, and the ſtream 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 ſay, that the height C D, ſhall 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 paſſeth
through A, being equal to the quantity which paſſeth through B,
in equal times; alſo the quantity which paſſeth through C E, ſhall
11[Figure 11]
be equal to that which paſſeth through F H: And therefore the
proportion that the Section C E, hath to the Section F H; ſhall
be the ſame 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 reaſon they are of the ſame breadth: Therefore
C D, ſhall 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 ſtreams of the ſame Torrent, &c. which was to be de­
monſtrated.
1
[Empty page]
1
OF THE
MENSURATION
OF
Running Waters.
Lib. II.
Having, in the cloſe of my Treatiſe of the
Menſuration of Running Waters promiſed
to declare upon another occaſion other par­
ticulars more obſcure, and of very great
concern upon the ſame argumement: I now
do perform my promiſe on the occaſion
that I had the paſt year 1641. to propound
my thoughts touching the ſtate of the Lake
of Venice, a buſineſs certainly moſt important, as being the
concernment of that moſt noble and moſt admirable City; and
indeed of all Italy, yea of all Europe, Aſia, & Africa; & one may
truly ſay of all the whole World. And being to proceed according
to the method neceſſary in Sciences, I wil propoſe, in the firſt place
certain Definitions of thoſe Terms whereof we are to make uſe
in our Diſcourſe: and then, laying down certain Principles we
will demonſtrate ſome Problemes and Theoremes neceſſary for
the underſtanding of thoſe things which we are to deliver; and
moreover, recounting ſundry caſes that have happened, we will
prove by practice, of what utility this contemplation of the
Meaſure of Running Waters is in the more important affairs both
Publique and Private.
DEFINITION I.
Two Rivers are ſaid to move with equal velocity, when in e­
qual times they paſſe ſpaces of equal length.
DEFINITION II.
Rivers are ſaid 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; ſo that if the upper
part of one River ſhall be more ſwift than the upper part of ano­
ther; then alſo the lower part of the former ſhall be more ſwift
than the part correſpondent to it in the ſecond, proportionally.
1
DEFINITON III.
To meaſure a River, or running Water, is in our ſenſe to finde
out how many determinate meaſures, or weights of Water
in a given time paſſeth through the River, or Channel of the
Water that is to be meaſured.
DEFINITION IV.
If a Machine be made either of Brick, or of Stone, or of
Wood, ſo compoſed that two ſides of the ſaid Machine be
placed at right angles upon the ends of a third ſide, that is
ſuppoſed to be placed in the bottom of a River, parallel to the
Horizon, in ſuch a manner, that all the water which runneth
through the ſaid River, paſſeth thorow the ſaid Machine: And
if all the water coming to be diverted
12[Figure 12]
that runneth through the ſaid River, the
upper ſuperficies of that third ſide placed
in the bottom do remain uncovered
and dry, and that the dead water be not
above it; This ſame Machine ſhall be

called by us ^{*} REGULATOR: And that third ſide of the
Machine which ſtandeth Horizontally is called the bottom of
the Regulator; and the other two ſides, are called the banks of
the Regulator; as is ſeen in this firſt Figure: A B C D, ſhall be
the Regulator; B C the bottom; and the other two ſides A B,
and C D are its banks.
* Or Sluice.
DEFINITION V.
By the quick height, we mean the Perpendicular from the upper
ſuperficies of the River, unto the upper ſuperficies of the bot­
tom of the Regulator; as in the foregoing Figure the line. G H.
DEFINITION VI.
If the water of a River be ſuppoſed to be marked by three
ſides of a Regulator, that Rightangled Parallelogram compre­
hended between the banks of the Regulator, and the bottom,
and the ſuperficies of the Water is called a Section of the
River.
1
ANNOTATION.
Here it is to be noted, that the River it ſelf may have ſundry
and divers heights, in ſeveral parts of its Chanel, by reaſon of
the various velocities of the water, and its meaſures; as hath
been demonſtrated in the firſt book.
SUPPOSITION I.
It is ſuppoſed, that the Rivers equal in breadth, and quick
height, that have the ſame inclination of bed or bottom, ought
alſo to have equal velocities, the accidental impediments being
removed that are diſperſed throughout the courſe of the water,
and abſtracting alſo from the external windes, which may velo­
citate, and retard the courſe of the water of the River.
SUPPOSITION II.
Let us ſuppoſe alſo, that if there be two Rivers that are in
their beds of equal length, and of the ſame inclination, but of
quick heights unequal, they ought to move with like velocity,
according to the ſenſe explained in the ſecond definition.
SUPPOSITION III.
Becauſe it will often be requiſite to meaſure the time exactly
in the following Problems, we take that to be an excellent
way to meaſure the time, which was ſhewed me many years ſince
by Signore Galilæo Galilæi, which is as followeth.
A ſtring 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 leſs, and then
let go, which will make many ſwings to and again, paſſing and
repaſſing the Perpendicular, before that it ſtay in the ſame: Now
it being required to meaſure the time that is ſpent in any what­
ſoever operation, thoſe vibrations are to be numbred, that are
made whilſt the work laſteth; and they ſhall be ſo many ſecond
minutes of an hour, if ſo be, that the ſtring be three Roman feet
long, but in ſhorter ſtrings, the vibrations are more frequent, and
in longer, leſs frequent; and all this ſtill followeth, whether the
Plummet be little or much removed from its Perpendicularity, or
whether the weight of the Lead be greater or leſſer.
Theſe things being pre-ſuppoſed, we will lay down ſome fa­
1miliar Problems, from which we ſhall paſs to the Notions and
queſtions more ſubtil and curious; which will alſo prove profi­
table, and not to be ſleighted in this buſineſs of Waters.
PROPOSITION I. PROBLEME I.
Achanel of Running-Water being given, the breadth
of which paſsing through a Regulator, is three
Palms; and the height one Palm, little more or
leſs, to meaſure what water paſſeth through the
Regulator in a time given.
Firſt, we are to dam up the Chanel; ſo that there paſs not any
water below the Dam; then we muſt place in the ſide 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 ſuch ſort, as that they may
drink up, or draw out of the Chanel all the water that the Cha­
nel beareth (and then ſhall we know that the Syphons drink up
all the water, when we ſee that the water at the Dam doth nei­
ther riſe higher, nor abate, but alwaies keepeth in the ſame Le­
vel.) Theſe things being prepared, taking the Inſtrument to
meaſure the time, we will examine the quantity of the water that
iſſueth by one of thoſe Syphons in the ſpace of twenty vibrations,
and the like will we do one by one with the other Syphons; and
then collecting the whole ſumme, we will ſay, that ſo much is
the water that paſſeth and runneth thorow the Regulator or
Chanel (the Dam being taken away) in the ſpace of twenty ſe­
cond minutes of an hour; and calculating, we may eaſily reduce
it to hours, dayes, months, and years: And it hath fallen to my
turn to meaſure this way the waters of Mills and Fountains, and I
have been well aſſured of its exactneſs, by often repeating the
ſame work.
CONSIDERATION.
And this method muſt be made uſe of in meaſuring the waters,
that we are to bring into Conducts, and carry into Cities
and Caſtles, for Fountains; and that we may be able afterwards
to divide and ſhare them to particular perſons juſtly; which will
prevent infinite ſuits and controverſies that every day happen in
theſe matters..
1
PROPOSITION II. THEOREM I.
If a River moving with ſuch a certain velocitie
through its Regulator, ſhall have a given quick
height, and afterwards by new water ſhall increaſe
to be double, it ſhall alſo increaſe 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 ſuppoſed to be raiſ­
ed to G, ſo that G B may be double to E B. I ſay, that all the
water G C ſhall be double in velocity to
13[Figure 13]
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 ſame breadth
B C, it ſhall have of it ſelf a velocity e­
qual to the velocity of the firſt water
F C: but becauſe, beſides its own moti­
on, which is imparted to it by the motion of the water E C, it
hath alſo over and above its own motion, the motion of E C. And
becauſe the two waters G C, and E C, are alike in velocity, by
the third Suppoſition; therefore the whole water G C ſhall be
double in velocity to the water E C; which was that which we
were to demonſtrate.
This demonſtration is not here inſerted, as perfect, the Authour ha­
ving by ſeveral letters to his friends confeſſed himſelf unſatisfi­
ed therewith; and that he intended not to publiſh the Theorem
without a more ſolid demonſtration, which he was in hope to light
upon. But being overtaken by Death, he could not give the
finiſhing touch either to this, or to the rest of the ſecond Book. In
conſideration of which, it ſeemed good to the Publiſher of the
ſame, rather to omit it, than to do any thing contrary to the mind of
the Authour. And this he hints, by way of advertiſement, to
thoſe that have Manuſcript Copies of this Book, with the ſaid de­
monſtration. For this time let the Reader content himſelf with
the knowledge of ſo ingenious and profitable a Concluſion; of the
truth of which he may, with ſmall expence and much pleaſure, be
aſſured by means of the experiment to be made in the ſame man­
ner, with that which is laid down in the ſecond Corollary of
1the fourth Theorem of this, with its Table, and the uſe there­
of annexed.
COROLLARIE
Hence it followeth, that when a River increaſeth in quick
height by the addition of new water, it alſo increaſeth in ve­
locity; ſo that the velocity hath the ſame proportion to the velo­
city that the quick height hath to the quick height; as may be
demonſtrated in the ſame manner.
PROPOS. III. PROBLEME II.
Achanel of Water being given whoſe breadth exceeds not
twenty Palms, or thereabouts, and whoſe quick beight
is leſs than five Palms, to meaſure the quantity of the
Water that runneth thorow the Chanel in a time
given.
Place in the Chanel a Regulator, and obſerve the quick
height in the ſaid Regulator; then let the water be turned
away from the Chanel by a Chanellet of three or four Palms
in breadth, or thereabouts: And that being done, meaſure the
quantity of the water which paſſeth thorow the ſaid Chanellet,
as hath been taught in the ſecond Propoſition; and at the ſame
time obſerve exactly how much the quick height ſhall be abated
in the greater Chanel, by means of the diverſion of the Chancl­
let; and all theſe particulars being performed, multiply the quick
height of the greater Chanel into it ſelf, and likewiſe multiply
into it ſelf the leſſer height of the ſaid bigger Chanel, and the
leſſer ſquare being taken, from the greater, the remainder ſhall
have the ſame proportion to the whole greater ſquare, as the wa­
ter of the Chanellet diverted, hath to the water of the bigger
Chanel: And becauſe the water of the Chanellet is known by
the Method laid down in the firſt Theorem, and the terms of the
Theorem being alſo known, the quantity of the water which run­
neth thorow the bigger Chanel, ſhall be alſo known by the Gol­
den Rule, which was that that was deſired to be known. We
will explain the whole buſineſs by an example.
Let a Chanel be, for example, 15 Palms broad, its quick height
before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
inches; but after the diverſion, let the quick height of the Chanel
be onely 22 inches. Therefore the greater height to the leſſer,
is as the number 11. to 12. But the ſquare of 11. is 121, and the
ſquare of 12. is 144, the difference between the ſaid leſſer
1ſquare and the greater is 23. Therefore the diverted water, is
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 ſhall have, to all the water
that runneth thorow the great Chanel. Now if we ſhould finde
by the Rule mentioned above in the firſt Propoſition, that the
quantity of the water that runneth through the Chanellet, is
v. g. an hundred Barrels, in the ſpace of 15 ſecond minutes of
an hour, it is manifeſt, that the water which runneth through the
great Chanel in the ſaid time of 35 min. ſec. ſhall be about 600
Barrels.
The ſame operation performed another way.
And becauſe very often in applying the Theory to Practice
it happeneth, that all the neceſſary particulars in the The­
ory cannot ſo eaſily be put in execution; therefore we will
here add another way of performing the ſame Problem, if it ſhould
chance to happen that the Chanellet could not commodiouſly be
diverted from the great Chanel, but that it were eaſier for the
water of another ſmaller Chanel to be brought into the greater
Chanel; which water of the ſmaller Chanel might be eaſily mea­
ſured, as hath been ſhewen in the firſt Probleme; or in caſe that
there did fall into a greater Chanel, a leſſer Chanel that might
be diverted and meaſured. Therefore I ſay in the firſt caſe, If
we would meaſure the quantity of the water that runneth in a
certain time thorow the greater Chanel, into which another leſſer
Chanel that is meaſurable may be brought, we muſt firſt exactly
meaſure the Chanellet, and then obſerve the quick height of the
greater Chanel, before the introduction of the leſſer; and having
brought in the ſaid Chanellet, we muſt agnin find the propor­
tion that the water of the Chanellet hath to all the water of the
great Ghanel; for theſe terms of the proportion being known, as
alſo the quantity of the water of the Chanellet, we ſhall alſo
come to know the quantity of the water that runneth thorow
the great Chanel. It is likewiſe manifeſt, that we ſhall obtain
our intent, if the caſe were that there entered into the great
Chanel, another leſſer Chanel that was meaſurable, and that
might be diverted.
CONSIDERATION.
It would be neceſſary to make uſe of this Doctrine in the di­
ſtribution of the waters that are imploy'd to overflow the fields,
as is uſed in the Breſciau, Cremoneſe, Bergamaſe, Lodigian, Mila-
1neſe territories, and many other places, where very great ſuits
and differences ariſe, which not being to be determined with in­
telligible reaſons, come oftentimes to be decided, by force of
armes; and inſtead of flowing their Grounds with Waters, they
cruelly flow them with the ſhedding of humane blood, impiouſly
inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders
and feuds, as that they are ſometimes accompanied with the ru­
ine of whole Cities, or elſe unprofitably charge them with vain,
and ſometimes prejudicial expences.
PROPOS. IV. THEOR. II.
If a River increaſe in quick height, the quantitie of
Water which the River diſchargeth after the in­
creaſe, 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 whilſt 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 ſay, that the quantity of the Water that is diſcharged
through D F, to that which diſchargeth 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, ſo let the line R be to the line S; and as
the height D B is to the height A B; ſo let the line S be to the
14[Figure 14]
line T. And let a Section be ſuppoſed 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, ſhall be
1as the velocity through D F, to the velocity of L N, that is, to
the velocity through L N, that is, to the velocity through A F.
therefore the quantity of Water which runneth through D F,
to that which paſſeth through L N, ſhall have the proportion
that R hath to S; but the quantity of the Water that runneth
through L N, to that which runneth through A F; (the Sections
being equally ſwift) ſhall have the proportion that the Section
L N hath to the Section A F, that is, that the height B D hath to
the height B A, that is, that S hath to T. Therefore, by equal
proportion, the quantity of the Water which runneth by D F,
to that which runneth by A F, ſhall have the proportion of R to
T, that is, ſhall be compounded of the proportions of the height
D B, to the height A B; and of the velocity through D F, to
the velocity through A F. And therefore if a River increaſe in
quick height, the quantity of the Water that runneth after the
increaſe, to that which runneth before the increaſe, hath the
proportion compounded, &c. Which was to be demonſtrated.
COROLLARIE I.
Hence it followeth, that we having ſhewn, that the quantity of
the Water which runneth, whilſt the River is high, to that
which ran, whilſt it was low, hath the proportion compounded
of the velocity to the velocity, and of the height to the height.
And it having been demonſtrated, that the velocity to the velo­
city is as the height to the height; it followeth, I ſay, that the
quantity of the Water that runneth, whilſt the River is high, to
that which runneth, whilſt it is low, hath duplicate proportion of
the height to the height, that is, the proportion that the ſquares
of the heights have.
COROLLARIE II.
Vpon which things dependeth the reaſon of that which I have
ſaid, in my ſecond Conſideration, that if by the diverſion of
5/9 of the Water that entereth by the Rivers into the Moor or
Fen, the Water be abated ſuch a meaſure, that ſame ſhall be
only one third of its whole height; but moreover diverting the 4/9, it
ſhall abate two other thirds, a moſt principal point; and ſuch,
that its not having been well underſtood, hath cauſed very great
diſorders, and there would now, more than ever, follow extream
dammage, if one ſhould put in execution the diverſion of the Sile
and other Rivers; and it is manifeſt, that in the ſame manner,
wherewith it hath been demonſtrated, that the quantity of the
Water increaſing quadruple, the height would increaſe onely
1double, and the quantity increaſing nonuple, the height increa­
ſeth triple; ſo that, by adding to units all the odde numbers, ac­
cording to their Series, the heights increaſe according to the na­
tural progreſſion of all the numbers, from units. As for exam­
ple, there paſſing thorow a Regulator ſuch a certain quantity of
Water in one time; adding three of thoſe meaſures, the quick
height is two of thoſe parts, which at firſt was one; and con­
tinuing to adde five of thoſe ſaid meaſures, the height is three of
thoſe parts which at firſt were one; and thus adding ſeven, and
then nine, and then 11. and then 13, &c. the heights ſhall be 4.
then 5, then 6. then 7, &c. And for the greater facility of the
Work, we have deſcribed the following Table, of which we will
declare the uſe: The Table is divided into three Series or Pro­
greſſions of Numbers: the firſt Series containeth all the Num­
bers in the Natural Progreſſion, beginning at a Unit, and is called
the Series of the Heights; the ſecond containeth all the odde
numbers, beginning at an unit, and is called the Series of the
Additions: the third containeth all the ſquare numbers, begin­
ning at an unit, and is called the Series of Quantity.
Heights.1234567891011Additions.13579111315171921Quantities.149162536496481100121
The uſe of the afore-mentioned Table.
Firſt, if we ſuppoſe the whole quick height of a River of Run­
ning Water to be divided into any number of equal parts, at
pleaſure, and would abate the ſame one fift, by means of a divi­
ſron; 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 ſubſtracted from the
number 25. placed underneath the ſame in the row of Quanti­
ties, the remainder 16. ſignifieth that of the 25. parts of Water
that ran in the River, whilſt it was 5 meaſures high, there do
onely run 16. parts; ſo that to make it abate 1/5 it is neceſſary to
take 9/25 from the Water that the whole River did carry; ſo that
with ſubſtracting ſomewhat more than one third of the Water of
the River, it is abated but only one fift.
2. And thus, in the ſecond place, if on the contrary, one would
know how much water is to be added to the ſaid River to make
it increaſe one fift more in height, ſo as that it may run in the
1Regulator 6. of thoſe parts high; of which it ran before but 5. let
6 be found in the row of heights, and let the number 11. ſtand­
ing under the ſame 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 ſhall have 36; which is the quantity of the
water that runneth with the height of the River, when it is high
6 of thoſe parts, whereof it was before but 5.
3. But if it ſhould be deſired, to know how much water it is
requiſite to add to make the River riſe ſo, as that it may run in
height 8. of thoſe parts of which before it ran but 5; one
ought to take the ſum of the number of the Series of Additions
ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
and this ſhall be the ſumme that muſt be added to 25: So that
to make the River to run 8. of thoſe parts in height, of which it
before did run 5, it will be neceſſary to add 39. of thoſe parts,
of which the River before was 25.
4. Likewiſe the ſame Table giveth the quantity of water
that runneth from time to time through a River, that increaſeth
by the addition of new water to the ſame 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 diſchargeth 2500. of thoſe mea­
ſures of water, and runneth in height 5. parts in the Regulator, and
afterwards ſhould ſee that it runneth 8 Palms high, finding in the
row of quantity the number placed under 8. which is 64. we would
ſay that the River heightned, carrieth of water 64. of thoſe parts
whereof it carried before but 25; and becauſe before it carried
2500. meaſures, by the Golden Rule we will ſay, that the River
carrieth 6400. of thoſe meaſures, of which before it carried 2500.
In this progreſs of Nature, is one thing really curious, and that
at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro­
ceeding ordinately in the diverſions and additions, with additi­
ons and diverſions ſo unequal, the abatings do notwithſtanding
alwaies prove equal, and ſo do the riſings: And who would ever
think that a River in height, v. g. 10. Palms, running and carry­
ing an hundred meaſures in a minute of an hour, is to abate but
one Palm, onely by the diverſion of 19. of thoſe meaſures; and
then again, that the buiſineſs cometh to that paſs, that it abateth
likewiſe a Palm by the diverſion of three onely of thoſe meaſures,
nay, by the diverſion of but one meaſure? and yet it is moſt
certain: And this truth meets with ſo manifeſt proofs in experi­
ence, that it is very admirable! And for the full ſatisfaction of
thoſe, who not being able to comprehend ſubtil demonſtrati­
ons, desire to be clearly inform'd by the matters of fact, and to
ſee with their bobily eyes, and touch with their hands, what their
underſtanding and reaſon cannot reach unto: I will hear add
another very eaſie way to reduce all to an experiment, the
1which may be made in little, in great, or in very great; of
which I make uſe frequently, to the admiration of ſuch as ſee it.
I prepared an hundred Siphons, or, if you will, bowed Pipes,
all equal; and placed them at the brim of a Veſſel, wherein the
water is kept at one and the ſame level (whether all the Syphons
work, or but a certain number of them) the mouths by which
the water iſſueth being all placed in the ſame level, parallel to
the Horizon; but lower in level than the water in the Veſſel; and
gathered all the water falling from the Syphons into another
Veſſel ſtanding lower than the former, I made it to run away
thorow a Chanel, in ſuch manner inclined, that wanting water
from the Syphons, the ſaid Chanel remained quite dry.
And this done, I meaſured the quick height of the Chanel
with care, and afterwards divided it exactly into 10 equal parts,
and cauſing 19. of thoſe Syphons to be taken away, ſo that the
Chanel did not run water, ſave onely with 81 of thoſe Syphons,
I again obſerved the quick height of the water in the ſame ſite
obſerved before, and found that its height was diminiſhed pre­
ciſely the tenth part of all its firſt height; and thus continuing to
take away 17. other Syphons, the height was likewiſe diminiſh­
ed 1/1. of all its firſt quick height; and trying to take away 15.
Syphons, then 13, then 11, then 9, then 7, then 5, and then 3.
alwaies in theſe diverſions, made in order as hath been ſaid, there
enſued ſtill an abatement of 1/1. of the whole height.
And here was one thing worthy of obſervation, that the water
encreaſing in [or through] the Chanel, its quick height was diffe­
rent in different ſites of the Chanel, that is ſtill leſſer, the more
one approached to the Out-let; notwithſtanding which the abate­
ment followed in all places proportionably, that is in all its ſites
the firſt part of the height of that ſite diminiſhed: And more­
over the water iſſued from the Chanel, and dilated into a broader
courſe, from which likewiſe having divers Out-lets and Mouths;
yet nevertheleſs in that breadth alſo the quick heights ſucceſſive­
ly varied and altered in the ſame proportions. Nor did I here
deſiſt my obſervation, but the water being diminiſhed, that iſſu­
ed from the Syphons, and there being but one of them left that
diſcharged water; I obſerved the quick height that it made in the
above-ſaid ſites, (the which was likewiſe 1/1. of all the firſt height)
there being added to the water of that Syphon, the water of
three other Syphons; ſo that all the water was of 4 Syphons,
and conſequently quadruple to the firſt Syphon; but the quick
height was onely double, and adding five Siphons, the quick
height became triple, and with adding ſeven Syphons, the height
increaſed quadruple; and ſo by adding of 9. it increaſed quin­
tuple, and by adding of 11. it increaſed ſextuple, and by ad­
1ding of 13. it increaſed ſeptuple, and by adding of 15. octuple,
and by adding of 17. nonuple, and laſtly by adding 19. Syphons;
ſo that all the water was centuple to the water of one Syphon,
yet nevertheleſs the quick height of all this water was onely de­
cuple to the firſt height conjoyned by the water that iſſued from
one onely Syphon.
For the more clear underſtanding of all which, I have made
the following Figure; in which we have the mouth A, that
maintaineth the water of the Veſſel B C in the ſame level; though
it continually run; to the brim of the Veſſel are put 25. Sy­
phons (and there may be many more) divided into 5 Claſſes,
D E F G H, and the firſt D, are of one onely Syphon; the ſecond
E, of three Syphons; the third F, of five; the fourth G, of 7; the
fifth H, of 9; and one may ſuppoſe the ſixth of 11, the ſeventh
of 13 Syphons, and ſo of the other Claſſes, all containing in con­
ſequent odd numbers ſucceſſively (we are content to repreſent in
the Figure no more but the five forenamed Claſſes to avoid con­
fuſion) 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 ſo
much ſufficeth for the explanation of this experiment.
15[Figure 15]
1
PROPOS. V. PROB. III.
Any River of any bigneſs, if being given to examine the
quantity of the Water that runneth thorow the River
in a time aſſigned.
By what we have ſaid already in the two preceding Pro­
blems, we may alſo reſolve this that we have now before
us; and it is done, by diverting in the firſt place from the
great River a good big meaſurable Chanel, as is taught in the
ſecond Probleme, and obſerving the abatement of the River,
cauſed by the diverſion 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 meaſured by the ſecond Pro­
bleme, and work as above, and you ſhall have your deſire.
CONSIDERATION. I.
And although it ſeemeth as if it might prove difficult, and
almoſt impoſſible to make uſe of the Regulator number, if
one be about to meaſure the water of ſome great River,
and conſequently would be impoſſible, or at leaſt very difficult
to reduce the Theory of the firſt Probleme into practice: Yet ne­
vertheleſs, I could ſay that ſuch great conceits of meaſuring the
water of a great River, are not to come into the minds of any
but great Perſonages, and potent Princes; of whom it is expected
for their extraordinary concerns, that they will make theſe kinde
of enquiries; as if here in Italy it ſhould be of the Rivers Tyber,
Velino, Chiana, Arno, Serchio, Adice, in which it ſeemeth real­
ly difficult to apply the Regulator, to finde exactly the quick
height of the River: But becauſe in ſuch like caſes ſometimes
it would turn to account to be at ſome charge, to come to the
exact and true knowledge of the quantity of water which that
River carrieth, by knowledge whereof, other greater diſ­
burſments might afterwards be avoided, that would oft times be
made in vain; and prevent the diſguſts, which ſometimes happen
amongſt Princes: Upon this ground I think it will be well to
ſhew alſo the way how to make uſe of the Regulator in theſe
great Rivers; in which if we will but open our eyes, we ſhall meet
with good ones, and thoſe made without great coſt or labour,
which will ſerve our turn.
For upon ſuch like Rivers there are Wears, or Lockes made,
1to cauſe the Waters to riſe, and to turn them for the ſervice of
Mills, or the like. Now in theſe Caſes it is ſufficient, that one
erect upon the two extreames of the Weare two Pilaſters either
of Wood or Brick, which with the bottome of the Weare do
compoſe our Regulator, wherewith we may make our deſired
operation, yea the Chanel it ſelf diverted ſhall ſerve, without
making any other diverſion or union. And in brief, if the bu­
fineſſes be but managed by a judicious perſon, there may wayes
and helps be made uſe of, according to occaſion, of which it
would be too tedious to ſpeak, and therefore this little that hath
been hinted ſhall ſuſſice.
CONSIDERATION II.
From what hath been declared, if it ſhall be well under­
ſtood, may be deduced many benefits and conveniences,
not onely in dividing of Running Waters for infinite uſes
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 ſuch other Machines; but alſo in ordering Navigable Cha­
nels, diverting Rivers and Chanels of Waters, or terminating
and limiting the ſizes of Pipes for Fountains: In all which af­
fairs there are great errours committed, to the loſſe of much
expence, the Chanels and Pipes that are made, ſometimes not
being ſufficient to carry the deſigned Waters, and ſometimes they
are made bigger than is neceſſary; which diſorders ſhall be
avoided, if the Engineer be adviſed of the things aboveſaid: and
in caſe that to theſe Notions there be added the knowledge of
Philoſophy and Mathematicks, agreeable to the ſublime Diſco­
veries of Signore Galilæo, and the further improvement thereof
by Signore Evangeliſta Torricelli, Mathematician to the Grand
Duke of Tuſcany, who hath ſubtilly and admirably handled this
whole buſineſſe of Motion, one ſhall then come to the know­
ledge of particular notions of great curioſity in the Theoricks,
and of extraordinary benefit in the Practicks that daily occur in
theſe buſineſſes.
And to ſhew, in effect, of what utility theſe Notions are, I
have thought fit to inſert, in this place, the Conſiderations by
me made upon the Lake of Venice, and to repreſent,
at large, by the experience of the laſt year 1641. the moſt Se­
rene Erizzo, then Duke of the ſaid Republique. Being
therefore at Venice, in the year aforeſaid, I was requeſted by the
moſt Illuſtrious and moſt Excellent Signore Giovanni Baſa-
1donna, a Senatour of great worth and merit, that I would inge­
nuouſly deliver my opinion touching the ſtate of the Lake
of Venice; and after I had diſcourſed with his Honour ſeve­
ral times, in the end I had order to ſet down the whole
buſineſſe in writing, who having afterwards read it privately,
the ſaid Signore imparted the ſame, with like privacy, to the
moſt Serene PRINCE, and I received order to repreſent the
ſame to the full Colledge, as accordingly I did in the Moneth
of May, the ſame year, and it was as followeth.
16[Figure 16]
1
CONSIDER ATIONS
Concerning the
LAKE
OF
VENICE.
BY
D. BENEDETTO CASTELLI,
Abbot of S. Benedetto Aloyſio, Mathematician to
Pope VR BAN VIII. and Profeſſor in
ROME.
CONSIDERATION I.
Though the principal cauſe be but one
onely, that in my judgment threatneth
irreparable ruine to the Lake of
Venice, in the preſent ſtate in which it
now ſtands; Yet nevertheleſſe, I think
that two Heads may be conſidered.
And this Conſideration may peradven­
ture ſerve us for to facilitate and explain
the opportune remedies, though not to
render the ſtate of things abſolutely unchangeable and eternal:
an enterprize impoſſible, and eſpecially in that which having had
ſome beginning, ought likewiſe neceſſarily to have its end; or
at leaſt to prevent the danger for many hundreds of years; and
poſſibly it may, in the mean time, by the mutation it ſelf be
brought into a better condition.
I ſay therefore, that the preſent diſorder may be conſidered
under two Heads; One is the very notable diſcovery of Land
that is obſerved at the time of low Water, the which, beſides
the obſtructing of Navigation in the Lake and alſo in the
Chanels, doth likewiſe threaten another miſchief and diſorder
1worthy of very particular conſideration, which is, That the Sun
drying up that mudde, eſpecially in the times of hot Summers,
doth raiſe thence the putrified and pernicious vapours, fogs, and
exhalations that infect the Air, and may render the City unha­
bitable.
The ſecond Head is the great Stoppage that daily is grow­
ing in the Ports, eſpecially of Venice, at Malamoco; concerning
which matters I will hint certain general points, and then
will proceed to the more particular and important affairs.
And firſt, I ſay, that I hold it altogether impoſſible to effect
any thing, though never ſo profitable, which doth not bring with
it ſome miſchief; and therefore the good and the hurt ought to
be very well weighed, and then the leſſe harmful part to be im­
braced.
Secondly, I propoſe to conſideration, that the ſo notable diſ­
covery of Earth & Mud, hath not been long obſerved, as I under­
ſtand, from old perſons that can remember paſſages for fifty
years paſt; which thing being true, as to me it ſeemeth moſt
true, it ſhould appear that it could not but be good to reduce
matters to that paſſe that they were at formerly, (laying aſide
all affection or paſſion that ſelf-flattering minds have entertained
for their own conceits) or at leaſt it ſhall be neceſſary ſpeedily to
conſult the whole.
Thirdly, I hold that it is neceſſary to weigh, whether from the
foreſaid diſcovery of Land, it followeth, that onely the Earth ri­
ſeth, as it is commonly thought by all, without diſpute; or whe­
ther the Waters are abated and faln away; or elſe whether it
proceedeth from both the one and other cauſe. And here it would
be ſeaſonable to enquire, what ſhare the ſaid cauſes may have,
each conſidered apart in the foreſaid effect. For, in the firſt
caſe, if the Earth have been raiſed, it would be neceſſary to
conſider of taking it down, and removing it: But if the Wa­
ters have failed or abated, I believe that it would be extreamly ne­
ceſſary to reſtore and raiſe them: And if both theſe reaſons have
conſpired in this effect, it will be neceſſary to remedy them each
apart. And I do, for my part, think, that the ſo notable appea­
rance of Shelves at the time of low Water, proceeds principally
from the decreaſe and abatement of the Waters, which may
confidently be affirmed to need no other proof, in regard that the
Brent hath been actually diverted which did formerly diſcharge
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
ſometimes diſturbed by windes, eſpecially at the time of the wa­
ters flowing, doth continually raiſe from its bottome immenſe
1heaps of ſand, carrying them by the tide; and force of the waves
into the Lake; it not having on its part any ſttength of current
that may raiſe and carry them away, they ſink to the bottom, and
ſo they choke up the Ports. And that this effect happeneth in
this manner, we have moſt frequent experiences thereof along the
Sea-coaſts: And I have obſerved in Tuſcany on the Roman­
ſhores, and in the Kingdom of of Naples, that when a river fal­
leth into the Sea, there is alwaies ſeen in the Sea it ſelf, at the place
of the rivets out-let, the reſemblance, as it were, of an half-Moon,
or a great ſhelf of ſettled ſand under water, much higher then the
reſt of the ſhore, and it is called in Tuſcany, il Cavallo; and here
in Venice, lo Scanto: the which cometh to be cut by the current
of the river, one while on the right ſide, another while on the
left, and ſometimes in the midſt, according as the Wind fits. And
a like effect I have obſerved in certain little Rillets of water,
along the Lake of Bolſena; with no other difference, ſave that of
ſmall and great.
Now whoſo well conſidereth this effect, plainly ſeeth that it
proceeds from no other, than from the contrariety of the ſtream
of the River, to the impetus of the Sea waves; ſeeing that
great abundance of ſand which the Sea continually throws upon
the ſhore, cometh to be driven into the Sea by the ſtream of the
river; and in that place where thoſe two impediments meet
with equal force, the ſand ſetleth under water, and thereupon is
made that ſame Shelf or Cavallo; the which if the river carry
water, and that any conſiderable ſtore, it ſhall be thereby cut
and broken; one while in one place, and another while in ano­
ther; as hath been ſaid, according as the Wind blows: And
through that Chanel it is that Veſſels fall down into the Sea, and
again make to the river, as into a Port. But if the Water of
the river ſhall not be continual or ſhall be weak, in that caſe the
force of the Sea-Wind ſhall drive ſuch a quantity of ſand into
the mouth of the Port, and of the river, as ſhall wholly choak it
up. And hereupon there are ſeen along the Sea-ſide, very many
Lakes and Meers, which at certain times of the year abound with
waters, and the Lakes bear down that encloſure, and run into
the Sea.
Now it is neceſſary to make the like reflections on our Ports
of Venice, Malamocco, Bondolo, and Chiozza; which in a certain
ſenſe are no other than Creeks, mouths, and openings of the ſhore
that parts the Lake from the main Sea; and therefore I hold that
if the Waters in the Lake were plentiful, they would have
ſtrength to ſcowr the mouths of the Ports thorowly, & with great
force; but the Water in the Lake failing, the Sea will with­
out any oppoſal, bring ſuch a drift of ſand into the Ports; that if
1it doth not wholly choke them up, it ſhall render them at leaſt
unprofitable, and impoſſible for Barks and great Veſſels.
Many other conſiderations might be propounded concerning
theſe two heads of the ſtoppage of the Ports, and of the appea­
rance of the Ouze and Mud in the Lakes, but ſo much ſhall ſuf­
fice us to have hinted, to make way for diſcourſing of the opera­
tions about the oportune remedies.
Yet before that I propound my opinion, I ſay, That I know
very well that my propoſal, at firſt ſight, will ſeem abſurd and in­
convenient; and therefore, as ſuch, will perhaps be rejected by
the moſt: and ſo 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 ſo wedded to my opinions, but that I
do conſider what others may judge thereof: But be it as it will,
I am obliged to ſpeak my thoughts freely, and that being done,
I will leawe it to wiſer men than my ſelf; when they ſhall have
well conſidered my reaſons, to judge and deliberate of the quid
agendum: And if the ſentence ſhall go againſt me, I appeal to the
moſt equitable and inexorable Tribunal of Nature, who not
caring in the leaſt to pleaſe either one party or another, will be
alwaies a punctual and inviolable executrix of her eternal De­
crees, againſt which neither humane deliberations, nor our vain
deſires; ſhall ever have power to rebell. I added by word of
mouth that which followeth.
Though your Highneſs intereſt your ſelf in this Noble Col­
ledge, and cauſe it to be confirmed in the ^{*} Senate by univerſal

Vote, that the Winds do not blow, that the Sea doth not fluctuate,
that the Rivers do not run; yet ſhall the Winds be alwaies deaf,
the Sea ſhall be conſtant in its inconſtancy, and the Rivers moſt
obſtinate: And theſe ſhall be my Judges, and to their determi­
nation I refer my ſelf.
* In Pregadi, a
particular Coun­
cil, the Senators of
which have great
Authority.
By what hath been ſaid, in my opinion, that is made very clear
and manifeſt, which in the beginning of this diſcourſe I glanced
at; namely, That the whole diſorder, although it be divided into
two heads, into the diſcovery of the Mud, and of the ſtoppage
Ports, yet nevertheleſs, by the application of one onely remedy,
and that in my eſteem very eaſie, the whole ſhall be removed:
And this it is; That there be reſtored into the Lake as much
Water as can be poſſible, and in particular from the upper parts
of Venice, taking care that the Water be as free from Mud as is
poſſible. And that this is the true and real remedy of the prece­
dent diſorders, is manifeſt: For in the paſſage that this Water
ſhall make thorow the Lakes, it ſhall of it ſelf by degrees clear
the Chanels in ſundry parts of them, according to the currents
that it ſhall ſucceſſively acquire, and in this manner being diſ­
1perſed thorow the Lake, it ſhall maintain the waters in the ſame,
and in the Chanels much higher, as I ſhall prove hereafter; a
thing that will make Navigation commodious; and that, which
moreover is of great moment in our buſineſſe; thoſe Shelves
of Mud which now diſcover themſelves at the time of Low­
Waters ſhall be alwayes covered, ſo that the putrefaction of
the Air ſhall alſo be remedied.
And laſtly, this abundance of Water being alwayes to diſ­
charge it ſelf into the Sea by the Ports, I do not doubt, but that
their bottomes will be ſcoured. And that theſe effects muſt fol­
low, Nature her ſelf ſeemeth to perſwade, there remaining onely
one great doubt, whether that abundance of Water that ſhall be
brought into the Lake may be really ſufficient to make the Wa­
ters riſe ſo much as to keep the Shelves covered, and to facilitate
Navigation, which ought to be at leaſt half a ^{*} Brace, or there­

abouts. And indeed it ſeemeth at firſt ſight to be impoſſible,
that the ſole Water of the ^{*} Brent let into the Lake, and diſ­

perſed over the ſame, can occaſion ſo notable an height of water;
and the more to confirm the difficulties, one might ſay, reducing
the reaſon to calculation, that in caſe the Brent were 40. Bra­
ces broad, and two and an half high, and the breadth of the
Lake were 20000. Braces, it would ſeem neceſſary that the
height of the water of the Brent dilated and diſtended thorow
the Lake would be but onely 1/200 of a Brace in height, which is
imperceptible, and would be of no avail to our purpoſe; nay
more, it being very certain that the Brent runneth very muddy
and foul, this would occaſion very great miſchief, filling and
contracting the Lake, and for that reaſon this remedy ought, as
pernicious, to be totally excluded and condemned.
* A Venice Brace
is 11/16 of our yard.
* A River of
that name.
I here confeſſe that I am ſurprized at the forme of the Argu­
ment, as if I were in a certain manner convinced, that I dare not
adventure to ſay more, or open my mouth in this matter; but
the ſtrength it ſelf of the Argument, as being founded upon
the means of Geometrical and Arithmetical Calculation, hath
opened me the way to diſcover a very crafty fraud that is couch­
ed in the ſame Argument, which fraud I will make out to any
one that hath but any inſight in Geometry and Arithmetick.
And as it is impoſſible, that ſuch an argument ſhould be produced
by any but ſuch as have taſted of theſe, in ſuch affairs, moſt pro­
fitable, and moſt neceſſary Sciences; ſo do not I pretend to make
my ſelf underſtood, ſave onely by ſuch, to whom I will evince
ſo clearly, as that more it cannot be deſired, the errour and fraud
wherein thoſe Ancients and Moderns have been, and alwayes
are intangled, that have in any way yet handled this matter of
conſidering the Meaſure and Quantity of the Waters that move.
1And ſo great is the eſteem that I have for that which I am now
about to ſay touching this particular, that I am content that all
the reſt of my Diſcourſe be rejected; provided, that that be per­
fectly underſtood, which I am hereafter to propoſe, I holding
and knowing it to be a main Principle, upon which all that is
founded that can be ſaid either well or handſomely on this parti­
cular. The other Diſcourſes may have an appearance of being
probable, but this hits the mark as full as can be deſired, arriving
at the higheſt degree of certainty.
I have, ſeventeen years ſince, as I repreſented to the moſt Se­
rene Prince, and to the Right Honourable the Preſident of the
Lords the Commiſſioners of the ^{*}Sewers, written a Treatiſe of the

Meaſure of the waters that move, in which I Geometrically de­
monſtrate and declare this buſineſſe, and they who ſhall have
well underſtood the ground of my Diſcourſe, will reſt fully ſa­
tisfied with that which I am now about to propoſe: But that all
may become rhe more eaſie, I will more briefly explicate and
declare ſo much thereof as I have demonſtrated in the Diſcourſe,
which will ſuffice for our purpoſe: And if that ſhould not be
enough, we have alwayes the experiment of a very eaſie and
cheap way to clear up the whole buſineſſe. And moreover I
will take the boldneſſe to affirm, that in caſe there ſhould not for
the preſent any deliberation be made concerning this affair, ac­
cording to my opinion; yet nevertheleſſe it will be, at ſome
time or other; or if it be not, things will grow worſe and
worſe.
* I. Savii dell'
Acque, a particu­
lar Council that
take care of the
Lakes and other
Aquatick affairs.
For more clear underſtanding, therefore, it ought to be known,
that it being required, as it is generally uſed, to meaſure the wa­
ters of a River, its breadth and its depth is taken, and theſe two
dimenſions being multiplied together, the product is affirmed to
be the quantity of that River: As for example, if a River ſhall
be 100. feet broad, and 20. feet high, it will be ſaid, that that
River is 2000 feet of Water, and ſo if a Ditch ſhall be 15. feet
broad, and 5. feet high, this ſame Ditch will be affirmed to be
75. feet of Water: And this manner of meaſuring Running
Water hath been uſed by the Ancients, and by Moderns, with
no other difference, ſave onely that ſome have made uſe of the
Foot, others of the Palme, others of the Brace, and others of
other meaſures.
Now becauſe that in obſerving theſe Waters that move, I fre­
quently found, that the ſame Water of the ſame River was in
ſome ſites of its Chanel pretty big, and in others much leſſe,
not arriving in ſome places to the twentieth, nor to the hundreth
part of that which it is ſeen to be in other places; therefore this
vulgar way of meaſuring the Waters that move, for that they did
1not give me a certain and ſtable meaſure and quantity of Water,
began deſervedly to be ſuſpected by me, as difficult and defective,
being alwayes various, and the meaſure, on the contrary, being
to be alwayes determinate, and the ſame; it is therefore written,
that Pondus & Pondus, Menſura & Menſura, utrumque abomi­
nabile eſt apud Deum, Exod. I conſidered that in the Terri­
tory of Breſcia, my native Countrey, and in other places, where
Waters are divided to overflow the Grounds, by the like way of
meaſuring them, there were committed grievous and moſt impor­
tant errours, to the great prejudice of the Publique and of Pri­
vate perſons, neither they that ſell, nor they that buy under­
ſtanding the true quantity of that which is ſold and bought: In
regard that the ſame ſquare meaſure, as is accuſtomed in thoſe
parts, aſſigned one particular perſon, carried to ſometimes above
twice or thrice as much water, as did the ſame ſquare meaſure aſ­
ſigned to another. Which thing proveth to be the ſame incon­
venience, as if the meaſure wherewith Wine and Oil is bought
and ſold, ſhould hold twice or thrice as much Wine or Oil at one
time as at another. Now this Conſideration invited my minde
and curioſity to the finding out of the true meaſure of Running
Waters. And in the end, by occaſion of a moſt important bu­
ſineſſe that I was imployed in ſome years ſince, with great in­
tenſeneſſe of minde, and with the ſure direction of Geometry, I
have diſcovered the miſtake, which was, that we being upon the
buſineſſe of taking the meaſure of the Waters that move, do make
uſe of two dimenſions onely, namely, breadth and depth, keep­
ing no account of the length. And yet the Water being, though
running, a Body, it is neceſſary in forming a conceit of its quan­
tity, in relation to another, to keep account of all the three Di­
menſions, that is of length, breadth, and depth.
Here an objection hath been put to me, in behalf of the ordi­
nary way of meaſuring Running Waters, in oppoſition to what
I have above conſidered and propoſed: and I was told, Its true,
that in meaſuring a Body that ſtands ſtill, one ought to take all
the three Dimenſions; but in meaſuring a Body that continually
moveth, as the Water, the caſe is not the ſame: For the length
is not to be had, the length of the water that moveth being infi­
nite, as never finiſhing its running; and conſequently is incom­
prehenſible by humane underſtanding, and therefore with reaſon,
nay upon neceſſity it cometh to be omitted.
In anſwer to this, I ſay, that in the aboveſaid Diſcourſe, two
things are to be conſidered diſtinctly; Firſt, whether it be poſſible
to frame any conceit of the quantity of the Body of the Water
with two Dimenſions onely. And ſecondly, whether this length
be to be found. As to the firſt, I am very certain that no man, let
1him be never ſo great a Wit, can never promiſe to frame a con­
ceit of the quantity of the Body of Water, without the third
Dimenſion of length: and hereupon I return to affirm, that the
vulgar Rule of meaſuring Running water is vain and erroneous.
This point being agreed on, I come to the ſecond, which is, Whe­
ther the third Dimenſion of length may be meaſured. And I ſay,
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 impoſſible enterprize, nay the
knowing of it would not be uſeful. 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 ſay, that it is a very
poſſible and profitable enquiry, by reaſon 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
demonſtrated the ſame above in the beginning of this Book; and
of this we ſtand in need in the buſineſſe of the Lake, that ſo we
may be able to determine how much ſhall be the height of the
Brent, when it is ſpread all over the Lake: For the three dimen­
ſions of a Body being given, the Body is known; and the quan­
tity of a Body being given, if you have but two dimenſions, the
third ſhall be known. And thus diving farther and farther into
this Conſideration, I found that the Velocity of the courſe of the
water may be an hundred times greater or leſſer in one part of
its Chanel than in another. And therefore although there ſhould
be two mouths of Waters equal in bigneſſe; yet nevertheleſs it
might come to paſſe, that one might diſcharge an hundred or a
thouſand times more water than another: and this would be, if
the water in one of the mouths ſhould run with an hundred or a
thouſand times greater velocity, than the other; for that it
would be the ſame as to ſay, that the ſwifter was an hundred or
a thouſand times longer, than the ſlower: and in this manner I
diſcovered that to keep account of the velocity, was the keeping
account of the Length.
And therefore it is manifeſt, that when two Mouths diſcharge
the ſame quantity of Wa r in an equal velocity, it is neceſſary
that the leſs ſwift Mouth be ſo much bigger than the more ſwift;
as the more ſwift exceedeth in velocity the leſs ſwift; as for
example.
In caſe two Rivers ſhould carry equal quantity of water in
equal times, but that one of them ſhould be four times more
ſwift than the other, the more ſlow ſhould of neceſſity be four
times more large. And becauſe the ſame River in any part
thereof alwaies diſchargeth the ſame quantity of Water in equal
times (as is demonſtrated in the firſt Propoſition of the firſt
1
Book^{*} of the meaſure of Running Watets;) but yet doth not
run thorowout with the ſame velocity: Hence it is, that the vul­
gar meaſures of the ſaid River, in divers parts of its Chanel, are
alwaies divers; inſomuch, that if a River paſſing through its cha­
nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour­
and afterwards the ſaid River ſhould be reduced to ſo much tardi,
ty of motion, as that in the ſame time it ſhould not run more than
one Brace, it would be neceſſary that that ſame River ſhould 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
ſwifter. And let it be kept well in mind, that this point rightly
underſtood, will clear the underſtanding to diſcover very many
accidents worthy to be known. But for this time let it ſuffice,
that we have onely declared that which makes for our purpoſe,
referring apprehenſive and ſtudious Wits to the peruſal of my
aforenamed Treatiſe; for therein he ſhall finde profit and delight
both together.
* He here intends
the Demonſtrati­
ons following, at
the end of the firſt
Book
Now applying all to our principal intent, I ſay, That by what
hath been declared it is manifeſt, that if the Brent were 40. Bra­
ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after­
wards the ſame Water of the Brent falling into the Lake, andpaſ­
ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve­
locity, that it ſhould run but one Brace, in the time wherein
whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra­
ces. It would be abſolutely neceſſary, that increaſing in mea­
ſure, it ſhould become an hundred times ^{*} thicker; and therefore

if we ſhould ſuppoſe that the Lake were 20000. Braces, the
Brent that already hath been ſuppoſed in its Chanel 100. Braces,
being brought into the Lake, ſhould be 100. times 100. Brates;
that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall
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.
* Deeper.
Now one may ſee into what a groſs errour of 99. in 100. one
may fall through the not well underſtanding the true quantity
of Running Water, which being well underſtood, doth open a
direct way to our judging aright in this moſt conſiderable affair.
And therefore admitting that wich hath been demonſtrated,
I fay, that I would (if it did concern me) greatly encline to con­
ſult upon the returning of the Brent again into the Lake: For it
being moſt evident, that the Brent in the Chanel of its mouth, is
much ſwifter than the Brent being brought into the Lake, it will
certainly follow thereupon, that the thickneſs of the Water of
Brent in the Lake, ſhall be ſo much greater than that of Brent in
Brent, by how much the Bront in Brent is ſwifter than thh Brent
in the Lake.
1
1. From which operation doth follow in the firſt place, that
the Lake being filled and increaſed by tbeſe Waters, ſhall be
more Navigable, and paſſible, than at preſent we ſee it to be.
2. By the current of theſe Waters, the Chanels will be ſcour­
ed, and will be kept clean from time to time.
3. There will not appear at the times of low-waters ſo many
Shelves, and ſuch heaps of Mud, as do now appear.
4. The Ayr will become more wholeſom, for that it ſhall not
be ſo infected by putrid vapours exhaled by the Sun, ſo long as
the Miery Ouze ſhall be covered by the Waters.
5. Laſtly, in the current of theſe advantagious Waters,, which
muſt iſſue out of the Lake into the Sea, beſides thoſe of the Tyde,
the Ports will be kept ſcoured, and clear: And this is as much as
I ſhall offer for the preſent, touching this weighty buiſineſs; al­
waies ſubmitting my ſelf to ſounder judgements.
Of the above-ſaid Writing I preſented a Copy at Venice, at a
full Colledge, in which I read it all, and it was hearkned to with
very great attention; and at laſt I preſented it to the Duke, and
left ſome Copies thereof with ſundry Senators, and went my way,
promiſing with all intenſeneſs to apply my pains with reiterated
ſtudies in the publick ſervice; and if any other things ſhould come
into my minde, I promiſed to declare them ſincerely, and ſo took
leave of His ſerenity, and that Noble Council. When I was
returned to Rome, this buſineſs night and day continually run­
ning in my mind, I hapned to think of another admirable and
moſt important conceit, which with effectual reaſons, confirmed
by exact operations, I with the Divine aſſiſtance, made clear and
manifeſt; and though the thing at firſt ſight ſeemed to me a moſt
extravagant Paradox, yet notwithſtanding, having ſatisfied my
ſelf of the whole buſineſs, I ſent it in writing to the moſt Illuſtri­
ous and moſt Noble Signore Gio. Baſadonna; who after he had
well conſidered my Paper, carried it to the Council; and after
that thoſe Lords had for many months maturely conſidered
thereon, they in the end reſolved to ſuſpend the execution of the
diverſion which they had before conſulted to make of the River
Sile, and of four other Rivers, which alſo fall into the Lake; a
thing by me blamed in this ſecond Paper, as moſt prejudicial,
and harmful. The writing ſpake as followeth.
1
CONSIDERATIONS
Concerning the
LAKE
OF
VENICE.
CONSIDERATION II.
If the diſcourſing well about the truth of
things, Moſt Serene Prince, were as the
carrying of Burdens, in which we ſee
that an hundred Horſes carry a greater
weight than one Horſe onely; it would
ſeem that one might make more account
of the opinion of many men, than of
one alone; But becauſe that diſcourſing
more reſembleth running, than carrying
Burdens, in which we ſee that one Barb alone runneth faſter
than an hundred heavy-heel'd Jades; therefore I have ever more
eſteemed one Concluſion well managed, and well conſidered by
one underſtanding man, although alone, than the common and
Vulgar opinions; eſpecially, when they concern abſtruce and
arduous points: Nay in ſuch caſes the opinions moulded and
framed by the moſt ignorant and ſtupid Vulgar, have been ever
ſuſpected by me as falſe, for that it would be a great wonder if
in difficult matters a common capacity ſhould hit upon that
which is handſom, good, and true. Hence I have, and do hold
in very great veneration the ſumme of the Government of the
moſt Serene, and eternal Republick of Venice; which although,
as being in nature a Common-wealth, it ought to be governed by
the greater part; yet nevertheleſs, in arduous affairs, it is alwaies
directed by the Grave Judgement of few, and not judged blindly
1by the Plebeian Rout. Tis true, that he that propoundeth Pro­
poſitions far above the reach of common capacity, runneth a
great hazard of being very often condemned without further Pro­
ceſs, or knowledge of the Cauſe; but yet for all that, the truth
is not to be deſerted in moſt weighty affairs, but ought rather to
be explained in due place and time with all poſſible perſpicuity;
that ſo being well underſtood, and conſidered, it may come after­
wards for the Common good to be embraced.
This which I ſpeak in general, hath often been my fortune in
very many particulars, not onely when I have kept within the
bounds of meer ſpeculation, but alſo when I have chanced to de­
ſcend to Practice, and to Operations: and your Highneſs know­
eth very well what befel me the laſt Summer 1641. when in obe­
dience to your Soveraign Command, I did in full Colledge repre­
ſent my thoughts touching the ſtate of the Lake of Venice; for
there not being ſuch wanting, who without ſo much as vouch­
ſafing to underſtand me, but having onely had an inkling, and
bad apprehenſion of my opinion, fell furiouſly upon me, and by
violent means both with the Pen and Preſs, full of Gall, did abuſe
me in reward of the readineſs that I had expreſt to obey and
ſerve them: But I was above meaſure encouraged and pleaſed, to
ſee that thoſe few who vouchſafed to hear me, were all either
thorowly perſwaded that my opinion was well grounded, or at
leaſt ſuſpended their prudent verdict to more mature deliberati­
on. And though at the firſt bout I chanced to propoſe a thing
that was totally contrary to the moſt received and antiquated
opinion, and to the reſolutions and conſultations taken above an
hundred years ago: Moved by theſe things, and to ſatisfie alſo
to the promiſe that I had made of tendering unto them what
ſhould farther offer it ſelf unto me touching the ſame buſineſs; I
have reſolved to preſent to the Throne of your Highneſs, another
Conſideration of no leſs importance, which perhaps at firſt ſight
will appear a ſtranger Paradox; but yet brought to the Teſt and
Touch-ſtone of experience, it ſhall prove moſt clear and evident.
If it ſhall be accounted of, ſo that it ſucceedeth to the benefit of
your Highneſs, I ſhall have obtained my defire and intent: And
if not, I ſhall have ſatisfied my ſelf, and ſhall not have been
wanting to the Obligation of your moſt faithful Servant, and na­
tive ſubject.
That which I propounded in the Mouths paſs, touching the
moſt important buſineſs of the Lake, though it did onely expreſ­
ly concern the point of the diverſion of the Mouth of the Lake,
already made and put in execution; yet it may be underſtood
and applyed alſo to the diverſion under debate, to be made of
the other five Rivers, and of the Sile in particular.
1
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 Ve­
nice.
I ſay therefore, that by diverting theſe five Rivers that re­
main, although their water that they diſcharge for the preſent in­
to the Lake is not all taken together 4/5 parts of what the Brent
alone did carry, yet nevertheleſſe the abatement of the water of
the Lake which ſhall enſue upon this laſt diverſion of four parts,
which was the whole water, ſhall prove double to that which hath
happened by the diverſion of Brent onely, although that the
Brent alone carried five parts of that water, of which the Rivers
that are to be diverted carry four: A wonder really great, and
altogether unlikely; for the reducing all this Propoſition to be
underſtood, is as if we ſhould ſay, that there being given us
three Rivers, of which the firſt diſchargeth five parts, the ſecond
three, and the third one, and that from the diverſion of the
firſt, there did follow ſuch a certain abatement or fall; from
the taking away of the ſecond there ought to follow alſo ſo
much more abatement; And laſtly, from the withdrawing of
the third the water ought to fall ſo much more, which is wholly
impoſſible: And yet it is moſt certain, and beſides the demon­
ſtration that perſwades me to it, which I ſhall explain in due
time, I can ſet before your eyes ſuch an experiment as is not to
be denied by any one, although obſtinate: and I will make it
plainly ſeen and felt, that by taking away only four parts of the
five, which ſhall have been taken away, the abatement proveth
double to the abatement enſuing upon the diverting firſt of the
five onely; which thing being true, as moſt certainly it is, it
will give us to underſtand how pernicious this diverſion of five
Rivers is like to prove, if it ſhall be put in execution.
By this little that I have hinted, and the much that I could
ſay, let your Highneſſe gather with what circumſpection this bu­
ſineſſe ought to be managed, and with how great skill he ought
to be furniſhed who would behave himſelf well in theſe difficult
affairs.
I have not at this time explained the demonſtration, nor have
I ſo much as propounded the way to make the Experiment, that
I am able to make in confirmation of what I have ſaid, that ſo
by ſome one or others miſ-apprehending the Demonſtration,
and maiming the Experiment, the truth may not happen to ſhine
with leſſe clarity than it doth, when all miſts of difficulty are re­
moved: and if ſo be, no account ſhould be made of the Reaſons
by me alledged, and that men ſhould ſhut their eyes againſt the
Experiments that without coſt or charge may be made, I do de­
1clare and proteſt that there ſhall follow very great dammages
to the Fields of the main Land, and extraordinary ſummes
ſhall be expended to no purpoſe. The Lake undoubtedly will
become almoſt dry, and will prove impaſſible for Navigation,
with a manifeſt danger of corrupting the Air: And in the laſt
place there will unavoidably enſue the choaking and ſtoppage of
the Ports of Venice.
Upon the 20th. of December, 1641. I imparted this my ſecond
Conſideration to the moſt Excellent Signore Baſadonna, preſen­
ting him with a Copy thereof amongſt other Writings, which I
have thought good to inſert, although they ſeem not to belong
directly to our buſineſſe of the Lake.
The way to examine the MUD and SAND
that entereth and remaineth in the
LAKE of VENICE.
To the moſt Excellent
SIGNORE GIO. BASADONNA.
Two very conſiderable Objections have been made a­
gainſt my opinion concerning the Lake of Venice: One
was that, of which I have ſpoken at large in my firſt
Conſideration, namely, that the Brents having been taken out of
the Lake, cannot have been the occaſion of the notable fall of
the Waters in the Lake, as I pretend, and conſequently, that
the turning Brent into the Lake would be no conſiderable reme­
dy, in regard that the water of Brent, and the great expanſion
of the Lake over which the water of Brent is to diffuſe and
ſpread being conſidered, it is found that the riſe proveth in­
ſenſible.
The ſecond Objection was, that the Brent is very muddy, and
therefore if it ſhould fall muddy into the Lake, the Sand would
ſink and fill up the ſame.
Touching the firſt Query, enough hath been ſaid in my firſt
Conſideration, where I have plainly diſcovered the deceipt of the
Argument, and ſhewn its fallacy; It remaineth now to examine
1the ſecond: to which in the firſt place I ſay, that one of the firſt
things that I propoſed in this affair was, that I held it impoſſible
to do any act, though never ſo beneficial, that was not alſo ac­
companied by ſome inconvenience and miſchief; and therefore
we are to conſider well the profit, and the loſſe and prejudice;
and they both being weighed, we ſhall be able to chooſe the leſ­
ſer evil: Secondly, I admit it to be moſt true, that Brent is at ſome
times muddy, but it is alſo true, that for the greater part of the
year it is not muddy. Thirdly, I do not ſee nor underſtand
what ſtrength this objection hath, being taken ſo at large, and in
general; and methinks that it is not enough to ſay, that the
Brent runneth muddy, and to aſſert that it depoſeth its Muddi­
neſſe in the Lake, but we ought moreover to proceed to particu­
lars, and ſhew how much this Mud is, and in what time this
choaking up of the Ports may be effected. For the Reaſons are
but too apparent and particular, that conclude the ruine of the
Lake, and that in a very ſhort time, (for mention is made of
dayes) the Waters diverſion being made, and moreover we
have the circumſtance of an Experiment, the ſtate of things be­
ing obſerved to have grown worſe ſince the ſaid diverſion. And
I have demonſtrated, that in caſe the Diverſion of the Sile and
the other Rivers ſhould be put in execution, the Lake would in a
few dayes become almoſt dry; and the Ports would be loſt, with
other miſchievous conſequences. But on the other ſide, al­
though that we did grant the choaking of them, we may very
probably ſay, that it will not happen, ſave onely in the ſucceſſion
of many and many Centuries of years. Nor can I think it pru­
dent counſel to take a reſolution and imbrace a Deſigne now, to
obtain a benefit very uncertain, and more than that, which only
ſhall concern thoſe who are to come very many Ages after us,
and thereby bring a certain inconvenience upon our ſelves, and
upon our children that are now alive and preſent.
Let it be alledged therefore, (although I hold it falſe) that by
the diverſions of the Rivers the Lake may be kept in good con­
dition for ſeveral years to come.
But I ſay confidently, and hope to demonſtrate it; That the
Diverſions will bring the Lake, even in our dayes, to be almoſt
dry, and at leaſt will leave ſo little water in it, that it ſhall ceaſe
to be Navigable, and the Ports ſhall moſt infallibly be choaked
up. I will therefore ſay upon experience, in anſwer to this Ob­
jection, that it is very neceſſary firſt well to diſcourſe, and ratio­
nally to particularize and aſcertain the beſt that may be this
point of the quantity of this ſinking Mud or Sand.
Now I fear I ſhall make my ſelf ridiculous to thoſe, who mea­
ſuring the things of Nature with the ſhallowneſſe of their brains
1do think that it is abſolutely impoſſible to make this enquiry, and
will ſay unto me, Quis menſus eſt pugillo aquas, & terram palmo
ponderavit? Yet nevertheleſs I will propound a way whereby,
at leaſt in groſs, one may find out the ſame.
Take a Veſſel of Cylindrical Figure, holding two barrels of
water, or thereabouts; and then fill it with the water of Brent,
at its Mouth or Fall into the Lake; but in the Lake at the time
that the Brent runneth muddy, and after it hath begun to run
muddy for eight or ten hours, to give the mud time to go as far
as S. Nicolo, to iſſue into the Sea; and at the ſame time take
another Veſſel, like, and equal to the firſt, and fill it with the wa­
ter of the Lake towards S. Nicolo, (but take notice that this ope­
ration ought to be made at the time when the waters go out,
and when the Sea is calm) and then, when the waters ſhall have
ſetled in the aforeſaid Veſſels, take out the clear water, and con­
ſider the quantity of Sand that remains behind, and let it be ſet
down, or kept in mind: And I am eaſily induced to think, that
that ſhall be a greater quantity of Sand which ſhall be left in the
firſt Veſſel, than that left in the ſecond Veſſel. Afterwards
when the Brent ſhall come to be clear, let both the operations be
repeated, and obſerve the quantity of Sand in the aforeſaid Veſ­
ſels; for if the Sand in the firſt Veſſel ſhould be moſt, it would
be a ſign, that in the revolution of a year the Brent would depoſe
Sand in the Lake: And in this manner one may calculate to a
ſmall 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 ſhall be for publick benefit. And if at
ſeveral times of the year you carefully repeat the ſame operati­
ons, or rather obſervations, you would come to a more exact
knowledge in this buſineſs: And it would be good to make the
ſaid operations at thoſe times, when the Lake is diſturbed by
ſtrong high Winds, and made muddy by its own Mud, raiſed by
the commotion of the Waters.
This notion would give us great light, if the ſame obſervations
ſhould be made towards the Mouth of Lio, at ſuch time as the
waters flow and ebb, in calm ſeaſons; for ſo one ſhould 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 meaſuring Sands and Mud, to ſhew that we are not ſo
generally, and inconſiderately to pronounce any ſentence, but
proceed to ſtricter inquiries, and then deliberate what ſhall be
moſt expedient to be done. Others may propoſe more exqui­
ſite examinations, but this ſhall ſerve me for the preſent.
I will add onely, that if any one had greater curioſity (it would
be profitable to have it) in inveſtigating more exactly the quan­
1tity of the Water that entereth into the Lake, by the means that
I have ſhewen in the beginning of this Book: When he ſhall
have found the proportion of the quantity of water to the quan­
tity of Sand or Mud, he ſhall come to know how much Sand the
Brent ſhall leave in the Lake in the ſpace of a year. But to
perform theſe things, there are required perſons of diſcretion, and
fidelity, and that are imployed by publick Order; for there
would thence reſult eminent benefit and profit.
Here are wanting LETTERS from ſeveral perſons.
To the Reverend Father, Franceſco di
S. GIUSEPPE.
In execution of the command that you laid upon me in your
former Letters, by order from the moſt Serene, my Lord,
Prince Leopold; that I ſhould ſpeak my judgment concern­
ing the diſimboguement of the River called Fiume morto, whe­
ther it ought to be let into the Sea, or into Serchio; I ſay, that
I chanced 18. years ſince to be preſent, when the ſaid Mouth was
opened into the Sea, and that of Serchio ſtopt; which work was
done to remedy the great Innundation that was made in all that
Country, and Plain of Piſa, that lyeth between the River Arno,
and the Mountains of S. Giuliano, and the River Serchio; which
Plain continued long under water, inſomuch that not onely in the
Winter, but alſo for a great part of the Summer, thoſe fields
were overflowed; and when that the Mouth of Fiume morto was
effectually opened into the Sea, the place was preſently freed from
the waters. and drained, to the great ſatisfaction of the Owners
of thoſe Grounds. And here I judge it worth your notice, that
for the generality of thoſe that poſſeſs eſtates in thoſe parts, they
deſired that the Mouth of Fiume morto might ſtand open to the
Sea, and thoſe who would have it open into Serchio, are perſons
that have no other concernment there, ſave the hopes of gaining
by having the diſpoſe of Commiſſions, and the like, &c,
But for the more plain underſtanding of that which is to be
ſaid, it muſt be known, That the reſolution of opening the ſaid
Mouth into Serchio, was taken in the time of the Great Duke
Ferdinando the firſt, upon the ſame motives that are at this time
again propoſed, as your Letters tell me, Since that, it manifeſt­
ly appearing, that Fiume morto had, and hath its Mouth open to
the Sea, the Plain hathbeen kept dry; and it being alſo true, that
1the fury of the South, and South-Weſt-Winds carryed ſuch
abundance of ſand into the Mouth, or Out-let of Fiume morto,
that it wholly ſtopt it up: eſpecially when the waters on Piſa
ſide were low and ſhallow, And they think, that turning the
Lake of Fiume morto into Serchio, and the Serchio maintaining
continually its own Mouth with the force of its waters open to the
Sea, and conſequently alſo Fiume morto, they would have had the
Out-let clear and open; and in this manner they think, that the
Plain of Piſa would have been freed from the waters. The bu­
ſineſs paſſeth for current, at firſt ſight; but experience proveth
the contrary, and Reaſon confirmeth the ſame: For the height
of the water of thoſe Plains, was regulated by the height of the
waters in the Mouth of Fiume morto; that is, The waters at the
Mouth being high, the waters alſo do riſe in the fields; and when
the waters at the Mouth are low, the waters of the fields do like­
wiſe abate: Nor is it enough to ſay, That the Out-let or Vent
of Fiume morto is continual, but it muſt be very low: Now if
Fiume morto did determine in Serchio, it is manifeſt that it
would determine high; for Serchio terminating in the Sea, when
ever it more and more aboundeth with water, and riſeth, it is ne­
ceſlary that alſo Fiume morto hath its level higher, and conſe­
quently ſhall keep the waters in the Plains higher. Nay, it hath
happened ſometimes (and I ſpeak it upon my own ſight) that
Fiume morto hath reverſed its courſe upwards towards Piſa;
which caſe will ever happen, whenſoever the Piſan waters chance
to be lower than the level of thoſe of Serchio; for in that caſe
the waters of Serchio return back upon the Plains thorow Fiume
morto in ſuch ſort, that the Muddineſſes, and the Serchio have
been obſerved to be carried by this return as farr as the Walls of
Piſa; and then before ſuch time as ſo great waters can be aſ­
ſwaged, which come in with great fury, and go out by little and
little, there do paſs very many days, and moneths, nay ſome­
times one being never able to find the waters of Serchio,
when at the ſhalloweſt, ſo low as the Sea in level; (which is the
loweſt place of the waters) it thence doth follow, that the wa­
ters of Fiume morto ſhould never at any time of the year, ſo long
as they determine in Serchio, be ſo low, as they come to be when
the ſame Fiume morto determineth in the Sea. Tis true indeed,
that the Mouth of Fiume morto, opened into the Sea, is ſubject to
the inconvenience of being ſtopt up by the force of Winds: But
in this caſe, it is neceſſary to take ſome pains in opening it; which
may eaſily be done, by cutting that Sand a little which ſtayeth
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
1that Sand away with it, and there will enſue a deep and broad
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
Weſt-Wind, into the Mouth of Fiume morto, I having cauſed the
little gutter to be made in the Morning, ſomewhat before Noon,
a Mouth hath been opened of 40. Braces wide, and notably deep,
inſomuch that the water, which before had incommoded all the
Champian ran away in leſs than three dayes, and left the Coun­
try free and dry, to the admiration of all men. There was pre­
ſent upon the place, at this buſineſs, on the ſame day that I
opened the Mouth, the moſt Serene great Duke, the moſt Serene
Arch-Dutcheſs Mother, all the Commiſſioners of Sewers, with
many other Perſons and Peaſants of thoſe parts; and they all ſaw
very well, that it was never poſſible that a little Bark of eight
Oars, which was come from Legorn to wait upon the great
Duke, ſhould ever be able to maſter the Current, and to make
up into Fiume morto; and his Highneſs, who came with an intent
to cauſe the ſaid Mouth towards the Sea to be ſtopt; and that
into Serchio to be opened, changed his judgement, giving order
that it ſhould be left open towards the Sea, as it was done. And
if at this day it ſhall return into Serchio, I am very certain that it
will be neceſſary to open it again into the Sea. And there was
alſo charge and order given to a perſon appointed for the pur­
poſe, that he ſhould take care to open the ſaid Mouth, as hath
been ſaid upon occaſion. And thus things have ſucceeded very
well unto this very time. But from the middle of October, until
this firſt of February, there having continued high South, and
South-Weſt-Winds, with frequent and abundant Rains; it is no
wonder that ſome innundation hath happened; but yet I will
affirm, that greater miſchiefs would have followed, if the Mouth
had been opened into Serchio. This which I have hitherto ſaid,
is very clear and intelligible to all ſuch as have but competent in­
ſight, and indifferent skill in theſe affairs. But that which I am
now about to propoſe farther, will, I am very certain, be under­
ſtood by your ſelf, but it will ſeem ſtrange and unlikely to many
others. The point is, that I ſay, That by raiſing the level of
Fiume morto, one half Brace, onely at its Mouth, (it will peni­
penitrate into Serchio farther than it would into the Sea) it ſhall
cauſe the waters to riſe three, or perhaps more Braces upon the
fields towards Piſa, and ſtill more by degrees as they ſhall recede
farther from the Sea-ſide; and thus there will follow very great
Innundations, and conſiderable miſchiefs. And to know that
this is true, you are to take notice of an accident, which I give
warning of in my diſcourſe of the Meaſure of Running Waters:
1where alſo I give the reaſon thereof, ^{*} Coroll. 14. The ac­
cident is this, That there coming a Land-Flood, for example,
into Arno, which maketh it to riſe above its ordinary Mouth
wthin Piſa, or a little above or below the City ſix or ſeven Bra­
ces; this ſame height becometh alwaies leſſer and leſſer, the more
we approach towards the Sea-ſide; inſomuch, that near to the
Sea the ſaid River ſhall be raiſed hardly half a Brace: Whence
it followeth of neceſſary conſequence, that ſhould I again be at
the Sea-ſide, and knowing nothing of what hapneth, ſhould ſee
the River Arno raiſed by the acceſſion of a Land-flood, one third
of a Brace; I could certainly infer, that the ſame River was raiſed
in Piſa thoſe ſame ſix or ſeven Braces. And that which I ſay of
Arno, is true of all Rivers that fall into the Sea. Which thing
being true, it is neceſſary to make great account of every ſmall
riſing, that Fiume morto maketh towards the Sea-ſide by fal­
ling into Serchio. For although the riſing of Fiume morto, by
being to diſgorge its Waters into Serchio, towards the Sea, were
onely a quarter of a Brace; we might very well be ſure, that fart
from the Sea, about Piſa, and upon thoſe fields the riſe ſhall be
much greater, and ſhall become two or three Braces: And be­
cauſe the Countrey lyeth low, that ſame riſe will cauſe a conti­
nual Innundation of the Plains, like as it did before; I cauſed the
Mouth to be opened into the Sea. And therefore I conclude
that the Mouth of Fiume morto, ought by no means to be opened
into Serchio; but ought to be continued into the Sea, uſing all
diligence to keep it open after the manner aforeſaid, ſo ſoon as
ever the Wind ſhall be laid. And if they ſhall do otherwiſe, I
confidently affirm, that there will daily follow greater damages;
not onely in the Plains, but alſo in the wholeſomneſs of the
Air; as hath been ſeen in times paſt. And again, It ought with
all care to be procured, that no waters do by any means run or
fall from the Trench of Libra, into the Plain of Piſa, for theſe
Waters being to diſcharge into Fiume morto, they maintain it
much higher than is imagined, according to that which I have de­
monſtrated in my conſideration upon the ſtate of the Lake of
Venice. I have ſaid but little, but I ſpeak to you, who under­
ſtandeth much, and I ſubmit all to the moſt refined judgment of
our moſt Serene Prince Leopold, whoſe hands I beſeech you in all
humility to kiſs in my name, and implore the continuance of his
Princely favour to me; and ſo deſiring your prayers to God for
me, I take my leave.
Rome 1. Feb.
1642.
Your moſt affectionate Servant,
D. BENEDETTO CASTELLI.
1
The anſwer to a Letter written by BAR­
TOLOTTI, touching the
difficultyes obſerved.
The former part of the Letter is omitted, and the diſcourſe
beginneth at the firſt Head.
And firſt I ſay, Whereas I ſuppoſe that the level of the Ser­
chio is higher than that of Fiume morto; this is moſt true,
at ſuch time as the waters of Fiume morto are diſcharged in­
to the Sea; but I did never ſay that things could never be brought
to that paſs, as that the level of Fiume morto ſhould be higher than
Serchio: and ſo I grant that it will follow, that the waters of
Fiume morto ſhall go into Serchio, and its very poſſible, that the
Drain of Fiume morto into Serchio may be continuate; and I far­
ther grant, that its poſſible, that the Serchio doth never diſgorge
thorow Fiume morto towards Piſa; Nay, I will yet farther grant
that it might have happened, that Fiume morto might have had
ſuch a fall into Serchio, as would have ſufficed to have turned
Mills: But then I add withall, that the Plains of Piſa, and the
City it ſelf muſt be a meer Lake.
2. Signore Bartololti ſaith confidently, that when the Sea ſwel­
leth by the South-Weſt, or other Winds, the level of Serchio in
the place marked A in the Platt, diſtant about 200. Braces, riſeth
very little: But that Fiume morto in D, and in E, many miles
more up into Land riſeth very much, and that certain Fiſhermen
confirm this, and ſhew him the ſignes of the riſing of the Water.
I grant it to be very true, and I have ſeen it with my own eyes:
But this cometh to paſs, when the Mouth of Fiume morto is ſtopt
up by the Sea; as I ſhall ſhew by and by. And this riſing near
the Sea-ſide, is of no conſiderable prejudice to the fields. And
this is as much as I find to be true in the aſſertion of Signore Bar­
tolotti, (without his confirming it by any other proof; as indeed
it needs none) That the level of Fiume morto riſeth in E, and ma­
ny miles farther upwards it riſeth much; nor did I ever affirm the
contrary.
3. Concerning the difficulty of opening the Mouth of Fiume
morto into the Sea, that which Il Caſtellano ſaith is moſt certain;
namely, That at the entrance upon the opening of the Mouth, it
is neceſſary to make a deep Trench: But I ſay, that at that time
it is difficult to open it, unleſs upon great occaſions; for that the
1difficulty proceedeth from the waters of Fiume morto being low,
and the fields drained.
4. As to the particular of the Cauſes that you tell me men
preſs ſo much unto the moſt Serene Grand Duke, and to the
Prince, I have not much to ſay, becauſe it is not my profeſſion;
nor have I conſidered of the ſame: Yet I believe, that when the
Prince and his Highneſſe ſee the benefit of his People and Sub­
jects in one ſcale of the Ballance, and the accomodation of
Huntſmen in the other, his Highneſſe will incline to the profit
of his ſubjects; ſuch have I alwayes found his Clemency and
Nobleneſſe of minde. But if I were to put in my vote upon
this buſineſſe, I would ſay, that the points of Spears, and the
mouths of Guns, the yelping of Dogs, the wilyneſſe of Huntſ­
men, who run thorow and narrowly ſearch all thoſe Woods,
Thickets and Heathes, are the true deſtroyers of Bucks and
Boares, and not a little Salt-water, which ſetleth at laſt in ſome
low places, and ſpreadeth not very far. Yet nevertheleſſe, I will
not enter upon any ſuch point, but confine my ſelf ſolely to the
buſineſſe before me.
5. That Experiment of joyning together the water of Fiume
morto, and that of Serchio by a little trench to ſee what advan­
tage the Level E hath upon the Level I, doth not give me full
ſatisfaction, taken ſo particularly, for it may come to paſſe, that
ſometimes E may be higher, and ſometimes A lower, and I do
not queſtion but that when Serchio is low, and Fiume morto full
of Water, the level of Fiume morto will be higher than that of
Serchio. But Serchio being full, and Fiume morto ſcant of Wa­
ter, the contrary will follow, if the Mouth ſhall be opened to
the Sea. And here it ſhould ſeem to me, that it ought to be
conſidered, that there is as much advantage from E to the Sea
through the little Trench opened anew into Serchio, as from E to
the Sea by the Mouth of Fiume morto. But the difficulty (which
is that we are to regard in our caſe) is, that the courſe of the
Waters thorow the Trench is three times longer than the courſe
of the Mouth of Fiums morto, as appeareth by the Draught or
Plat which you ſent me, which I know to be very exactly drawn,
for that the ſituation of thoſe places are freſh in my memory.
Here I muſt give notice, that the waters of Fiume morto determi­
ning thorow the Trench in Serchio (the waters of which Fiume
morto are, for certain, never ſo low as the Sea) their pendency or
declivity ſhall, for two cauſes, be leſſe than the pendency of thoſe
waters through the Mouth towards the Sea, that is, becauſe of
the length of the line through the Trench, and becauſe of the
height of their entrance into Serchio, a thing which is of very
great import in diſcharging the waters which come ſuddenly, as
1he ſhall plainly ſee, who ſhall have underſtood my Book of the
Meaſure of Running Waters And this was the Reaſon why all
the Countrey did grow dry upon the opening of the Mouth into
the Sea. And here I propoſe to conſideration that which the Pea­
ſants about Piſa relate, namely, That the Water in the Fields
doth no conſiderable harm by continuing there five or ſix, yea, or
eight dayes. And therefore the work of the Countrey is to o­
pen the Mouth of Fiume morto, in ſuch manner, that the Water
being come, they may have the Trench free and ready, when that
the Water cometh it may have a free drain, and may not ſtay
there above eight or nine dayes, for then the overflowings be­
come hurtful. It is to be deſired alſo, that if any Propoſition is
produced touching theſe affairs, it might be propounded the moſt
diſtinctly that may be poſſible, and not conſiſt in generals, eſpe­
cially when the Diſpute is of the riſings, of velocity, of tardity,
of much and little water; things that are all to be ſpecified by
meaſures.
6. Your Letter ſaith, in the next place, that Signore Barto­
lotti confeſſeth, that if the Mouth of the Fiume morto might al­
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 courteſie, I confeſſe,
for the keeping it ſtopt on all ſides would be a thing moſt per­
nicious. But admitting of his confeſſion I again reply, that Fi­
ume morto ought not to be let into Serchio, but immediately in­
to the Sea; becauſe although ſometimes the Mouth to Sea­
wards be ſtopt up, yet for all that, the raiſing of the Bank above
the Plains (which is all the buſineſſe of importance) ſhall be ever
leſſer, if we make uſe of the Mouth leading to the Sea, than u­
ſing that of Serchio.
7. I will not omit to mention a kinde of ſcruple that I have
concerning the poſition of Sign. Bartolotti, that is, where he ſaith
that the two Mouths A and D are equal to the like Mouths into
the Sea; Now it ſeems to me, that the Mouth A of Fiume morto
into Serchio is abſolutely within Serchio, nor can it be made low­
er, and is regulated by the height of Serchio: But the Mouth
of Fiume morto terminates, and ought to be underſtood to ter­
minate in the Sea it ſelf, the loweſt place. And this I believe
was very well peroeived by Sig. Bartolotti, but I cannot tell why
he paſt it over without declaring it: and we ſee not that the
Mouth D falleth far from the Sea, which Mouth ought to be let
into the Sea it ſelf, and ſo the advantage of the Mouth into the
Sea more clearly appeareth.
8. That which Sig. Bartolotti addeth, that when it is high
Waters, at ſuch time as the Waters are out, and when Winds
choak up Fiume morto, they not only retard it, but return the
1courſe of the Waters upwards very leaſurely, perſwadeth me
more readily to believe that Sig. Bartolotti knoweth very well,
that the Mouth of Fiume morto let into Serchio is hurtful: for
by this he acknowledgeth that the Mouth towards the Sea doth
in ſuch ſort drain the Countrey of the Waters, as that they be­
come very low; and therefore upon every little impetus the wa­
ters turn their courſe: And from the motions, being exceeding
ſlow, is inferred, that the abundance of Sea-water that com­
eth into Fiume morto, is ſo much as is believed, and as Sig. Bat­
tolotti affirmeth.
9. After that Sig. Bartolotti hath ſaid what he promiſeth a­
bove, namely, that when the Windes blowing ſtrongly do ſtop
up Fiume morto, and not onely retard but turn the courſe up­
wards, the time being Rainy, and the Mouth of Fiume morto ſhut
up, the Waves of the Sea paſſe over the Bank of Fiume morto; at
that time, ſaith Signore Bartolotti, the Champain ſhall know the
benefit of Fiume morto diſcharged into Serchio, and the mouth A
ſhall ſtand alwayes open; and Fiume morto may alwayes con­
ſtantly run out, as alſo the Rains and Rain-waters, although the
hurtful Tempeſt ſhould laſt many dayes, &c. And I reply, that
all the Art conſiſts in this; for the benefit of thoſe Fields doth
not depend on, or conſiſt in ſaying, that Fiume morto is alwayes
open, and Fiume morto draineth continually; But all the buſi­
neſſe of profit lyeth and conſiſteth in maintaining the Waters
low in thoſe Plaines, and thoſe Ditches, which ſhall never be ef­
fected whilſt the World ſtands, if you let Fiume morto into Ser­
chio; but yet it may, by opening the mouth into the Sea: and
ſo much reaſon and nature proveth, and (which importeth) Ex­
perience confirmeth.
10. In the tenth place I come to conſider the anſwer that
was made to another Propoſition in the Letter which I writ to
Father Franceſco, which prudently of it ſelf alone might ſerve
to clear this whole buſineſſe. I ſaid in my Letter, That great
account is to be made of every ſmall riſing and ebbing of the
Waters neer to the Sea in Fiume morto, for that theſe riſings and
fallings, although that they be ſmall neer to the Sea-ſide, yet ne­
vertheleſſe, they operate and are accompanied by notable riſings
and fallings within Land, and far from the Sea-ſide, and I have
declared by an example of Arno, in which a Land-flood falling,
that made it increaſe above its ordinary height within Piſa ſix or
ſeven Braces, that this height of the ſame Flood becometh ſtill
leſſer, the neerer we approach to the Sea-coaſts. Nor ſhall the
ſaid River be raiſed hardly half a Brace; whereupon it neceſſ­
rily followeth, that if I ſhould return to the Sea-ſide, and not
knowing any think of that which happeneth at Piſa, and ſeeing
1the River Arno raiſed by a Land-flood half a Brace, I might con­
fidently affirm the ſaid River to be raiſed in Piſa thoſe ſix or ſe­
ven Braces, &c. From ſuch like accidents I conclude in the ſame
Letter, that it is neceſſary to make great account of every little
riſe that Fiume morto ſhall make towards the Sea. Now cometh
Bartolotti (and perhaps becauſe I knew not how to expreſs my
ſelf better, underſtandeth not my Propoſition) and ſpeaketh that
which indeed is true, but yet beſides our caſe: Nor have I ever
ſaid the contrary; and withall doth not apply it to his purpoſe.
Nay I ſay, that if he had well applyed it, this alone had been a­
ble to have made him change his opinion. And becauſe he ſaith,
that I ſaid, that it is true, when the abatement proceedeth from
ſome cauſe above, as namely by Rain, or opening of Lakes;
But when the cauſe is from below, that is, by ſome ſtop, as for
inſtance ſome Fiſhers Wears or Locks, or ſome impediment re­
mote from the Sea, although at the Level it ſhall riſe ſome Braces
where the impediment is, yet that riſing ſhall go upwards; and
here he finiſheth his Diſcourſe, and concludeth not any thing
more. To which I ſay firſt, that I have alſo ſaid the ſame in the
Propoſition, namely, that a Flood coming (which maketh Arno
to riſe in Piſa ſix or ſeven Braces (which I take to be a ſuperiour
cauſe whether it be Rain or the opening of Lakes, as beſt plea­
ſeth Bartolotti) in ſuch a caſe I ſay, and in no other (for towards
the Sea-coaſts it ſhall not cauſe a riſing of full half a Brace; and
therefore ſeeing Arno at the Sea-ſide to be raiſed by a Flood, whe­
ther of Rain, or of opening of Lakes half a Brace) it may be
inferred, that at Piſa it ſhall be raiſed thoſe ſix or ſeven Braces;
which variety, well conſidered, explaineth all this affair in favour
of my opinion: For the riſing that is made by the impediment
placed below, of Fiſhing Weares and Locks, operateth at the be­
ginning, raiſing the Waters that are neer to the impediment;
and afterwards leſs and leſs, as we retire upwards from the im­
pediment: provided yet that we ſpeak not of a Flood that com­
meth by acceſſion, but onely of the ordinary Water impeded.
But there being a new acceſſion, as in our caſe, then the Water
of the Flood, I ſay, ſhall make a greater riſing in the parts ſuperi­
our, far from the impediment; and theſe impediments ſhall
come to be thoſe that ſhall overflow the Plains, as happened
eighteen or nineteen years ago, before the opening of Fiume
morto into the Sea, The ſame will certainly follow, if Fiume
morto be let into Serchio. Here I could alledge a very pretty
caſe that befell me in la ^{*} Campagna di Roma, neer to the Sea­

ſide. where I drained a Bog or Fen, of the nature of the Wa­
ters of Piſa, and I ſucceeded in the enterprize, the Waters in their
ſite towards the Sea abating only three Palmes, and yet in the
1Fen they fell more than fifteen Palmes. But the buſineſſe
would be long, and not ſo eaſily to be declared, and I am cer­
tain that Sig. Bartolotti having conſidered this, would alter his
judgment, and withall would know that remitting that impedi­
ment anew, which I had left for leſſe than three Palmes towards
the Sea, the Waters in the Fen would return with the firſt Floods
and Raines to the ſame height as before, as likewiſe Fiume morto
will do if it ſhall be let again into Serchio.
* The Countrey
or Province lying
round the City,
heretofore called
Latium
Here I intreat your Honour to do me the favour to importune
P. Franceſco in my behalf, that he would be pleaſed to deelare
my meaning in the aforeſaid Letter to Sig. Bartolotti, for I hope
that if he will underſtand this point, he will be no longer ſo te­
nacious in his opinion.
Next that theſe Lords in the Commiſſion of Sewers, with the
Right Honourable the Marqueſſe of S. Angelo, and your Honour
do approve of my judgment, doth very much rejoyce me; but
becauſe that I know that they do it not in deſign to complement
me, but onely to ſerve his Highneſs our Grand Duke, I freely
profeſs that I will pretend no farther obligations from them there­
in, than I account my ſelf to owe to thoſe whoſe opinions are
contrary to mine, for that I know that they have the ſame end.
The definitive ſentence of this whole buſineſs is, that they give
theſe Plains, theſe Draines, and theſe Waters farre fetcht ap­
pellations.
11. As to the quantity of the Water that Fiume morto diſ­
chargeth into the Sea, there are very great diſputes about it, and
I have been preſent at ſome of them. But let your Honour be­
lieve me, that as this is not continual, but only during a few
dayes, ſo it will never be of any great prejudice to theſe Fields;
and if your Lordſhip would be aſcertained thereof, you may
pleaſe to go to Fiume morto at about a mile's diſtance from the
Sea, in the time of theſe ſtrong Windes, and obſerve the cur­
rent from thence upwards, for you ſhall finde it extream ſlow,
and conſequently will know that the quantity of the Water that
is repuls'd is very ſmall. And this ſeems to be contradicted by the
rule of Riſings proceeding from cauſes below, which occaſion no
conſiderable alteration far from the Sea.
I am neceſſitated to go to morrow out of Rome with his Emi­
nence Cardinal Gaetano about certain affairs touching Waters,
therefore I ſhall not farther inlarge, but for a cloſe to this tedious
Diſcourſe, I conclude in few words, that Fiume morto is by no
means to be let into Serchio, nor are there any means intermedi­
ate courſes to be taken, for they will alwayes be prejudicial; but
Fiume morto is to be diſcharged immediately into the Sea. When
it is ſtopt up by the fury of the Sea waves, I affirm that it is a
1ſign that there is no need of opening it; and if there be any oc­
caſion to open it, it is eaſily done. As for the reſt your Lordſhip
may pleaſe to keep account of all the particulars that occur, for
the memory of things paſt is our Tutreſſe in thoſe that are to
come. If occaſion ſhall offer, I intreat you to bow humbly in
my name to His Highneſs the Grand Duke, and the moſt Serene
Prince Leopold; and to attend the ſervice of Their Highneſſes, for
you ſerve I rinces of extraordinary merit; And to whom I my
ſelf am alſo exceedingly obliged. In the controverſies that ariſe
reſpect the pious end of ſpeaking the Truth, for then every
thing will ſucceed happily. I kiſs the hands of Padre Franceſco,
of Sig. Bartolotti, and of your Lordſhip.
Rome, 14. March 1642.
Your Honours
most Obliged Servant
D. BENEDETTO CASTELLI.
Vpon this occaſion I will here inſert a Diſcourſe that I made
upon the Draining and improvement of the Pontine Fens,
for that I think that whatſoever may be done well and to pur­
poſe in this matter hath abſolute dependance on the perfect know­
ledge of that ſo important Propoſition, by me demonſtrated and
explained in my Treatiſe of the Menſuration of Running Wa­
ters, namely, That the ſame water of a River doth continually
change Meaſures, according as it altereth and changeth the ve­
locity of its courſe; ſo that the meaſure of the thickneſſe of a
River in one Site, to the meaſure of the ſame River in another
Site, hath the ſame proportion reciprocally that the velocity in
this ſite hath to the velocity in the firſt ſite. And this is a Truth
ſo conſtant and unchangeable, that it altereth not in the leaſt
point on any occurrences of the Waters that change: and
being well underſtood, it openeth the way to the knowledge of
ſundry advertiſements in theſe matters, which are all reſolved by
this ſole Principle; and from it are derived very conſiderable be­
nefits; and without theſe it is impoſſible to do any thing with
abſolute perfection
1
[Empty page]
1
A
CONSIDERATION
Upon the
DRAINING
OF THE
Pontine Fenns.
BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO, and Profeſſor
of the Mathematicks to P. Urban VIII. in the
Univerſity of ROME.
CONSIDERATION III.
Amongſt the enterprizes by me eſteemed, if not ab­
ſolutely impoſſible, , at leaſt exceeding difficult,
one was that famous one of Draining the Pontine
Fenns; and therefore I was thorowly reſolved
never to apply my minde thereunto, although
by my Patrons I ſhould be commanded to the
ſame: accounting that it was an occaſion rather of loſing repu­
tation by the miſcarriage of the attempt, than of gaining fame by
reducing things to a better paſs then they now are at. Yet never­
theleſs, having of late years obſerved the place, and ſailed through
thoſe Chanels, and thoſe Waters; after I had made ſome reflection
thereupon, I thought that the enterprize was not ſo difficult as
I had at firſt conceited it to be; and I am the more confirmed in
this opinion, upon the inducement of that which I have written
1Geometrically in my Treatiſe of the Menſuration of Running
Waters; ſo that talking with ſeveral perſons, I adventured to
affirm, in diſcoures, that this improvement might poſſibly be
brought into a good eſtate.
Now I have reſolved to ſet down my thoughts in writing, and
to honour this my Paper with the Noble Name of your Lordſhip,
to render it the more credible and conſpicuous at the firſt view,
if it ſhould chance that the Subject I treat of, were not of ſuch
moment, as that it did deſerve to be valued for any other reaſon.
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 Pontine Fenns, hath been undertaken both in the time of
the antient Romans, and laſt of all, in our days; yea in the late
times by Sixtus V. I do not doubt in the leaſt, but that it will
be poſſible yet to reduce things to a very good paſs; and if I be not
miſtaken, with a very ſmall charge in compariſon of the profit that
would be received from thoſe rich Grounds. This improvement
was of great expence in the time of Sixtus Quintus, but by rea­
ſon the thing was not rightly underſtood, there were made many
Drains; a great part of which were unprofitable and vain: and
amongſt ſo many operations, there hapned ſome to be made that
ſucceeded, as was deſired; but not being underſtood, they were
held in no account; and thus the buſineſs being neglected, the
waters are returned into the ſame ſtate as they were at firſt, be­
fore the improvement. Here I have by familiar diſcourſes
with my friends, explained this enterprize undertaken by Six­
tus V. and haply alſo by ſome more antient, with the example of
the Fable of Orilo, in Arioſto. This Monſter was made up with
ſuch enchantment, that men fought with him alwayes in vain;
for though in the Combate he were cut in pieces, thoſe divided
Members preſently re-united, and returned to the fight more
fierce then ever. But the Paladine Aſtolfo coming to undertake
him, after a long diſpute, at the end he cut his head ſheer off
from the ſhoulders at one blow; and nimbly alighting from his
Horſe, took the Monſtrous head, and mounting again, as he rid
away he fell to ſhave the Pole of that Monſter, and ſo he loſt
the Lock of Hair, in which alone the enchantment lay; and then
the horrible Head in an inſtant manifeſted ſigns of death, and the
trunk which ran, ſeeking to reunite to it anew, gave the laſt gaſp,
and in this manner the enchantment ended. The Book of Fate
ſerved admirably to the Paladine, whereby he came to under­
ſtand that Charm; for by ſhaving his whole head, the enchanted
hairs came to be cut off amongſt the reſt: In the ſame manner, I
ſay, that it hath ſometimes happened in Draining thoſe Fields;
1for that amongſt ſo many tryals as have been made, that alſo
was light upon, on which the improvement and remedy to the
diſorder did depend. And to us my fore-named Treatiſe ſhall
ſerve for a Rule, which being well underſtood, ſhall make us to
know wherein conſiſteth, and whereon dependeth this miſcarri­
age, and conſequently it will be eaſie to apply thereunto a ſeaſo­
nable remedy.
And firſt I ſay, That there is no doubt but that the waters
continue ſo high on thoſe Plains becauſe they are ſo high in the
principal River, which ought to receive them, and carry them
into the Sea. Now the Cauſes of the height of the River, may
in my judgement be reduced to one alone; which is that by me
ſo often mentioned for the moſt Potent one, and declared in my
afore-named Tractate; to wit, The tardity of the motion of the
waters, which doth alwayes infallibly, and preciſely cauſe the
ſelf ſame Running Water to change the meaſure of its thickneſs
at ſuch a rate, that the more it encreaſeth in velocity, the more
it decreaſeth in meaſure; and the more it decreaſeth in velocity,
the more it encreaſeth in meaſure: As for example; If a River
run in ſuch a place with the velocity of moving a mile in the
ſpace of an hour, and afterwards the ſame River in another place
doth encreaſe in velocity, ſo as to make three miles an hour;
that ſame River ſhall diminiſh in thickneſs two thirds: And on
the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth
but half a mile in the ſame time, it ſhall encreaſe the double in
thickneſs and meaſure. And in a word, look what proportion
the velocity in the firſt place, hath to the velocity in the ſecond,
and ſuch hath reciprocally the meaſure of the thickneſs in the
ſecond place, to the meaſure in the firſt; as I have clearly demon­
ſtrated in my Treatiſe: Which I repeat ſo frequently, that I
fear the Profeſſors of Polite Learning will charge me with Tua­
tologie, and vain Repetition. But I am ſo deſirous in this moſt
important point to be well underſtood, becauſe it will then be
eaſie to comprehend all the reſt; and without this it is impoſſible
(I will not ſay difficult, but abſolutely impoſſible) to underſtand,
or ever to effect any thing to purpoſe. And the better to ex­
plain the example, let it be ſuppoſed,
17[Figure 17]
That the water of a River A D,
runneth high at the level of A F,
with ſuch a certain velocity; and let
it, by the ſame water, be velocitated
three times more; I ſay, that it will
abate 1/3, and ſhall ſtand at the level
in B E; and if it ſhall more veloci­
tate, it will abate the more at the Sea; But if it ſhould retard
1more than it did at the level AF, it would riſe yet more above
the ſaid level A F; although that the ſelf ſame quantity of water
runneth all the while. By the above-named ſolid Principle I
reſolve extravagant Problems in my Treatiſe, and aſſign the Rea­
ſons of admirable effects of Running Waters: But as for what
concerneth our purpoſe of the Pontine Fenns, we have the Cau­
ſes very plain and clear; for which, by the trampling of Cattle
which paſs thorow the Draining River, the waters abate ſo nota­
bly, that it is as it were a miracle for thoſe Reeds, Flags, and
Weeds that ſpring up, encreaſe, and ſpread all over the River,
ſtop and impede that velocity of the waters which they would
have by means of their declivity. But that paſſage of thoſe Beaſts,
treading down thoſe Weeds unto the bottom of the River, in ſuch
ſort, as that they no longer hinder the Current of the Water;
and the ſame Waters increaſing in their courſe, they do dimi­
niſh in meaſure and height; and by this meanes the Ditches of the
Plains empty into the ſame ſucceſsfully, and leave them free
from Waters, and Drained. But theſe Weeds in a ſhort
time ſprouting up anew, and raiſing their ſtalkes thorow the
body of the Waters, they reduce things to the ſame evil
ſtate, as before, retarding the velocity of the Water, ma­
king it to increaſe in height, and perhaps do occaſion grea­
ter miſchiefs; ſeeing that thoſe many knots which each plant
ſhoots 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 conſequently make the height
of the waters to encreaſe ſo much the more, and do more miſchief
than before.
Another head to which theſe harms may be reduced, but pro­
ceeding from the ſame Root, which hath a great part in this
diſorder, is the impediment of thoſe Wears in the River which
are made by heightning the bed of the ſame, for placing of fiſh­
ing-nets; of which Piſcaries I reckoned above ten, when I made
a voyage thorow thoſe waters to Sandolo. And theſe Fiſhing­
Wears are ſuch impediments, that ſome one of them makes the
water of the River in the upper part to riſe half a Palm, and
ſometimes a whole Palm, and more; ſo that when they are all
gathered together, theſe impediments amount to more than ſeven,
or poſſibly than eight Palms.
There concurreth for a third moſt Potent Cauſe of the waters
continuing high in the evacuating, or Draining Chanel, and con­
ſequently on the Plains; The great abundance of water that iſſu­
eth from Fiume Siſto, the waters of which do not keep within its
Banks when they are abundant; but encreaſing above its Chanel,
they unite with thoſe of the Evacuator, and diſperſing thorow
1the Fens are raiſed with great prejudice, and much grea­
ter than is conceived, according to what hath been demon­
ſtrated in the Second Conſideration upon the Lake of Venice.
Nor is it to any purpoſe to ſay, that if we ſhould meaſure
all the Waters that disimbogue from Fiume Siſto, and gather
them into one ſumme, we ſhould not finde them to be ſuch,
as that they ſhall be able to make the Waters of the Fens
to increaſe, by reaſon of the great expanſion of them, over
which that body of water is to diſtend: for to this inſtance we
anſwer wich that which we have given notice of in the Firſt Con­
ſideration touching the Lake of Venice, treating of the abate­
ment that is cauſed by the Brent let into the Lake. And more­
over, if I ſhall adde thereto that which I write in the Second
Conſideration, it will be very apparent how greatly harmfull
and prejudicial theſe excurfions of Waters from Fiume Siſto
may be, which are not kept under, and confined within the
River: Therefore, proceeding to the proviſions, and ope­
rations that are to be accounted Principall, I reduce them to
three Heads.
In the firſt place it is neceſſary to throw down thoſe Weares,
and to take the Piſciaries quite away, obſerving a Maxime, in
my judgment, infallible, that Fiſhing and Sowing are two things
that can never conſiſt together; Fiſhing being on the Water, and
Sowing on land.
Secondly, it will be neceſſary to cut under Water in the bot­
tome of the River thoſe Weeds and Plants that grow and in­
creaſe in the River, and leave them to be carried into the Sea by
the Stream; for by this means theſe Reeds ſhall not ſpring up
and diſtend along the bottome of the River, by means of the
Beaſts treading upon them; And the ſame ought to be done
often, and with care, and muſt not be delaied till the miſ­
chief increaſe, and the Champain Grounds be drowned, but
one ought to order matters ſo, as that they may not drown.
And I will affirm, that otherwiſe this principal point would be­
come a moſt conſiderable inconvenience.
Thirdly, it is neceſſary to make good the Banks of Fiume Siſto
on the left hand, and to procure that thoſe 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 thoſe things, but we are to
put them all in execution; for omitting any thing, the whole
machine will be out of tune, and ſpoiled. But proceeding with
due care, you ſhall not only Drain the Pontine Fens, but by
means of this laſt particular the Current of Fiums Sisto ſhall
ſcowr its own Chanel of its ſelf, even to the carrying part of it
away: and haply with this abundance of water that it ſhall
1bear, the Mouth della Torre may be opened, and kept open
into the Sea. And it would, laſt of all, be of admirable bene­
fit to cleanſe Fiume Sisto from many Trees and Buſhes where­
with it is overgrown.
And with this I conclude, that the Improvement or Drain
poſſible to be made conſiſteth in theſe three particulars. Firſt,
in taking away the Fiſhing Weares, leaving the Courſe
of the Waters free. Secondly, in keeping the Principal
Rivers clear from Weeds and Plants. Thirdly, in keeping
the water of Fiume Sisto in its own Chanel. All which are
things that may be done with very little charge, and to the
manifeſt benefit of the whole Country, and to the rendering
the Air wholſomer in all thoſe Places adjoyning to the Pon­
tine Fens.
18[Figure 18]
1
A
CONSIDERATION
Upon the
DRAINING
Of the Territories of
Bologna, Ferrara,
AND
Romagna.
BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO, Mathematician
to P. Vrban VIII. and Profeſſor in the
Univerſity of ROME.
The weghty buſineſſe of the Draining of
the Territories of Bologna, Ferrara,
and Romagna having been punctually
handled and declared in writing from
the excellent memory of the Right Ho­
nourable and Noble Monſignore Corſini,
who was heretofore Deputed Commiſ­
ſary General, and Viſitor of thoſe Wa­
ters; I am not able to make ſuch ano­
ther Diſcourſe upon the ſame Subject, but will only ſay ſome­
what for farther confirmation of that which I have ſaid in this
Book upon the Lake of Venice, upon the Pontine Fens, and up­
on the Draining of thoſe Plains of Piſa, lying between the Ri­
vers Arno and Serchio; whereby it is manifeſt, that in all the
1aforementioned Caſes, and in the preſent one that we are in hand
with, there have, in times paſt, very groſſe Errours been com­
mitted, through the not having ever well underſtood the true
meaſure of Running waters; and here it is to be noted, that the
buſineſſe is, that in Venice, the diverſion of the waters of the
Lake, by diverting the Brent was debated, and in part executed,
without conſideration had how great abatement of water might
follow in the Lake, if the Brent were diverted, as I have ſhewn
in the firſt Conſideration upon this particular, from which act
there hath inſued very bad conſequences, not only the difficulty
of Navigation, but it hath infected the wholſomneſſe of the Air,
and cauſed the ſtoppage of the Ports of Venice. And on the
contrary, the ſame inadvertency of not conſidering what riſing of
the Water the Reno, and other Rivers being opened into the Val­
leys of Bologna and Ferrara, might cauſe in the ſaid Valleys, is
the certain cauſe that ſo many rich and fertile Fields are drown­
ed under water, converting the happy habitations and dwellings
of men into miſerable receptacles for Fiſhes: Things which
doubtleſſe would never have happened, if thoſe Rivers had been
kept at their height, and Reno had been turn'd into Main-Po,
and the other Rivers into that of Argenta, and of Volano. Now
there having ſufficient been ſpoken by the above-named Monſig.
Corſini in his Relation, I will only adde one conceit of my own,
which after the Rivers ſhould be regulated, as hath been ſaid, I
verily believe would be of extraordinary profit, I much doubt in­
deed that I ſhall finde it a hard matter to perſwade men to be of
my mind, but yet nevertheleſs I will not queſtion, but that thoſe,
at leaſt, who ſhall have underſtood what I have ſaid and demon­
ſtrated concerning the manners and proportions, according to
which the abatements and riſings of Running waters proceed,
that are made by the Diverſions and Introductions of Waters,
will apprehend that my conjecture is grounded upon Reaſon.
And although I deſcend not to the exactneſſe of particulars, I
will open the way to others, who having obſerved the requiſite
Rules of conſidering the quantity of the waters that are intro­
duced, or that happen to be diverted, ſhall be able with punctu­
ality to examine the whole buſineſſe, and then reſolve on that
which ſhall be expedient to be done.
Reflecting therefore upon the firſt Propoſition, that the
Riſings of a Running Water made by the acceſſion of new water
into the River, are to one another, as the Square-Roots of the
quantity of the water that runneth; and conſequently, that the
ſame cometh to paſs in the Diverſions: Inſomuch, that a River
running in height one ſuch a certain meaſure, to make it encreaſe
double in height, the water is to be encreaſed to three times as
1much as it ran before; ſo that when the water ſhall be quadru­
ple, the height ſhall be double; and if the water were centuple,
the height would be decuple onely, and ſo from one quantity
to another: And on the contrary, in the Diverſions; If of the
100. parts of water that run thorow a River, there ſhall be di­
verted 19/160, the height of the River diminiſheth onely 1/10, and con­
tinuing to divert 17/100, the height of the River abateth likewiſe 1/10,
and ſo 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 theſe diverſions, the height of the Running Water di­
miniſheth the tenth part: although that the diverſions be ſo une.
qual. Reflecting I ſay upon this infallible Truth, I have had a
conceit, that though the Reno and other Rivers were diverted
from the Valleyes, and there was onely left the Chanel of Navi­
gation, which was onely the 1/20 part of the whole water that fal­
leth into the Valleys; yet nevertheleſs, the water in thoſe ſame
Valleyes would retain a tenth part of that height that became
conjoyned by the concourſe of all the Rivers: And therefore I
ſhould think that it were the beſt reſolution to maintain the Gha­
nel of Navigation (if it were poſſible) continuate unto the Po of
Ferrara, and from thence to carry it into the Po of Volano; for
beſides that it would be of very great eaſe in the Navigation of
Bologna, and Ferrara, the ſaid water would render the Po oſ
Volano navigable as far as to the very Walls of Ferrara, and con­
ſequently the Navigation would be continuate from Bologna to
the Sea-ſide.
But to manage this enterprize well, it is neceſſary to meaſure
the quantity of the Water that the Rivers diſcharge into the Val­
leys, and that which the Chanel of Navigation carryeth, in man­
ner as I have demonſtrated at the beginning of this Book; for this
once known, we ſhall alſo come to know, how profitable this di­
verſion of the Chanel of Navigation from the Valleys is like to
prove; which yet would ſtill be unprofitable, if ſo be that all
the Rivers that diſcharge their waters into the Valleys, ſhould
not ſirſt be Drained, according to what hath been above ad­
vertiſed.
Abbot CASTELLI, in the preſent conſideration referring
himfelf to the Relation of Monſig. Corſini, grounded upon the Ob­
ſervations and Precepts of the ſaid Abbot; as is ſeen in the pre­
ſent Diſcourſe. I thought it convenient for the compleating of the
Work of our Aulhour, upon theſe ſubjects, to inſert it in this
place.
1
A
Relation of the Waters in the Territories
of Bologna and Ferrara.
BY
The Right Honourable and Illuſtrious, Monſig­
nore CORSINI, a Native of Juſcany, Su­
perintendent of the general DRAINS,
and Preſident of Romagna-
The Rheno, and other Brooks of Romagna, were by the
advice of P. Agoſtino Spernazzati the Jeſuite, towards
the latter end of the time of Pope Clement VIII. notwith­
ſtanding the oppoſition of the Bologneſi, and others concerned
therein, diverted from their Chanels, for the more commodious
cleanſing of the Po of Ferrara, and of its two Branches of Prima­
ro, and Volano; in order to the introducing the water of the
Main-Po into them, to the end that their wonted Torrents being
reſtored, they might carry the Muddy-water thence into the Sea,
and reſtore to the City the Navigation which was laſt, as is ma­
nifeſt by the Brief of the ſaid Pope Clement, directed to the Car­
dinal San Clemence, bearing date the 22. of Auguſt, 1604.
The work of the ſaid cleanſing, and introducing of the ſaid
Po, either as being ſuch in it ſelf, or by the contention of the
Cardinal Legates then in theſe parts; and the jarrings that hap­
ned betwixt them, proved ſo difficult, that after the expence of
vaſt ſumms in the ſpace of 21. years, there hath been nothing
done, ſave 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
Po of Argenta, and the Rheno thoſe on its Banks; of which I
will ſpeak in the firſt place, as of that which is of greater impor­
tance, and from which the principal cauſe of the miſchiefs that
reſult from the reſt doth proceed.
* Or Lordſhip.
This Rbeno having overflowed the ^{*} Tennency of Sanmartina,
in circumference about fourteen miles given it before, and part
of that of Cominale given it afterwards, as it were, for a recepta­
cle; from whence, having depoſed the matter of its muddineſs,
it iſſued clear by the Mouths of Maſi, and of Lievaloro, into
the Po of Primaro, and of Volano; did break down the encom­
1paſſing Bank or Dam towards S. Martino, and that of its new
Chanel on the right hand neer to Torre del Fondo.
By the breaches on this ſide it ſtreamed out in great abun­
dance from the upper part of Cominale, and in the parts about
Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Agoſtino, San
Proſpero, San Vincenzo, and others, and made them to become
incultivable: it made alſo thoſe places above but little fruitful,
by reaſon of the impediments that their Draines received, finding
the Conveyances called Riolo and Scorſuro, not only filled by la
Motta and la Belletta, but that they turned backwards of them­
ſelves.
But by the Mouths in the incloſing Bank or Dam at Borgo di
S. Martino iſſuing with violence, it firſt gave obſtruction to the
ancient Navigation of la Torre del la Foſſa, and afterwards to
the moderne of the mouth of Maſi, ſo that at preſent the Com­
merce between Bologna and Ferrara is loſt, nor can it ever be
in any durable way renewed, whilſt that this exceeds its due
bounds, and what ever moneys ſhall be imployed about the ſame
ſhall be without any equivalent benefit, and to the manifeſt

and notable prejudice of the ^{*} Apoſtolick Chamber.
* The Popes
Exchequer.
Thence paſſing into the Valley of Marzara, it ſwelleth high­
er, not only by the riſing of the water, but by the raiſing of the
bottome, by reaſon of the matter ſunk thither after Land­
floods, and dilateth ſo, 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 paſſage for Rain-waters that ſettle, become
either altogether unproſitable or little better.
From this Valley, by the Trench or Ditch of Marzara, or of
la Duca by la Buova, or mouth of Caſtaldo de Roſſi, and by the
new paſſage it falleth into the Po of Argenta, which being to re­
ceive it clear, that ſo it may ſink farther therein, and receiving
it muddy, becauſe it hath acquired a quicker courſe, there will
ariſe a very contrary effect.
Here therefore the ſuperficies of the water keeping high, until
it come to the Sea, hindereth the Valleys of Ravenna, where
the River Senio, thoſe of San Bernardino where Santerno was
turned, thoſe of Buon' acquiſto, and thoſe of Marmorto, where
the Idice, Quaderna, Sellero ſall in, from ſwallowing and taking
in their Waters by their uſual In-lets, yet many times, as I my
ſelf have ſeen in the Viſitation, they drink them up plentifully,
whereupon, being conjoyned with the muddineſſe of thoſe Ri­
vers that fall into the ſame, they ſwell, and dilate, and overflow
ſome grounds, and deprive others of their Drains in like manner
1as hath been ſaid of that of Marrara, inſomuch that from the
Point of S. Giorgio, as far as S. Alberto all thoſe that are between
the Valleys and Po are ſpoiled, of thoſe that are between Valley
and Valley many are in a very bad condition, and thoſe that are
ſome conſiderable ſpace above not a little damnified.
In fine, by raiſing the bottom or ſand of the Valleys, and the
bed of Reno, and the too great repletion of the Po of Primaro
with waters, the Valleys of Comacchio (on which ſide the Banks
are very bad) and ^{*} Poleſine di S. Giorgio are threatned with a

danger, that may in time, if it be not remedied, become irrepa­
rable, and at preſent feeleth the incommodity of the Waters,
which penetrating thorow the pores of the Earth do ſpring up in
the ſame, which they call Purlings, which is all likely to redound
to the prejudice of Ferrara, ſo noble a City of Italy, and ſo im­
portant to the Eccleſtaſtick State.
+ Poleſine is a
plat of Ground al­
moſt ſurrounded
with Bogs or wa­
ters, like an Iſland
Which particulars all appear to be atteſted under the hand of
a Notary in the Viſitation which I made upon the command of
His Holineſſe, and are withall known to be true by the ^{*}Ferrareſt

themſelves, of whom (beſides the requeſt of the Bologneſi) the
greater part beg compaſſion with ſundry Memorials, and reme­
dies, aſwell for the miſchiefs paſt, as alſo for thoſe in time to
come, from which I hold it a duty of Conſcience, and of Cha­
rity to deliver them.
* People of Fer­
rara.
Pope Clement judged, that the ſufficient means to effect this
was the ſaid Introduction of the Main Po into the Chancl of
Ferrara; a reſolution truly Heroical, and of no leſſe beauty
than benefit to that City, of which I ſpeak not at preſent, be­
cauſe I think that there is need of a readier and more acco­
modate remedy.
So that I ſee not how any other thing can be ſo much conſide­
rable as the removal of Reno, omitting for this time to ſpeak of

^{*} incloſing it from Valley to Valley untill it come to the Sea, as
the Dukes of Ferrara did deſign, foraſmuch as all thoſe Ferra­
reſi that have intereſt in the Poleſine di S. Giorgio, and on the
right hand of the Po of Argenta do not deſire it, and do, but too
openly, proteſt againſt it; and becauſe that before the Chanel
were made as far as the Sea, many hundreds of years would be
ſpent, and yet would not remedy the dammages of thoſe who
now are agrieved, but would much increaſe them, in regard the
Valleys would continue ſubmerged, the Drains ſtopped, and the
other Brooks obſtructed, which would of neceſſity drown not a
few Lands that lie between Valley and Valley; and in fine, in
regard it hath not from San Martina to the Sea for a ſpace of ſif­
ty miles a greater fall then 19, 8, 6, feet, it would want that force
which they themſelves who propound this project do require it to
1have, that ſo it may not depoſe the matter of the muddineſs when
it is intended to be let into Volana.
* In Chanels
made by hand.
So that making the Line of the bottome neer to Vigarano, it
would riſe to thoſe prodigious termes that they do make bigger,
and they may thence expect thoſe miſchiefs, for which they
will not admit of introducing it into the ſaid Po of Volana.
Amongſt the wayes therefore that I have thought of for effect­
ing that ſame remotion, and which I have cauſed to be viewed by
skilful men that have taken a level thereof, (with the aſſiſtance of
the venerable Father, D. Benedetto Caſtelli of Caſina, a man of
much fidelity and honeſty, and no leſs expert in ſuch like affairs
touching waters, than perfect in the Mathematick Diſciplines) two
onely, the reſt being either too tedious, or too dangerous to the
City, have ſeemed to me worthy, and one of them alſo more than
the other, to offer to your Lordſhip.
The one is to remit it into the Chanel of Volana, thorow which
it goeth of its own accord to the Sea.
The other is to turn it into Main-Po at Stellata, for, as at other
times it hath done, it will carry it to the Sea happily.
As to what concerns the making choice of the firſt way, that
which ſeemeth to perſwade us to it is, that we therein do nothing
that is new, in that it is but reſtored to the place whence it was
removed in the year 1522. in the time of Pope Adrian, by an
agreement made in way of contract, between Alfonſo, Duke of
Ferrara, and the Bologneſi; and that it was diverted for reaſons,
that are either out of date, or elſe have been too long time
deferred.
In like manner the facility wherewith it may be effected, let­
ting it run into the divided Po, whereby it will be turned to Fer­
rara, or elſe carrying it by Torre del Fondo, to the mouth of Maſi,
and from thence thorow the Trench made by the Ferrareſi,
along by Panaro, where alſo finding an ample Bed, and high and
thick Banks, that will ſerve at other times for it, and for the wa­
ters of Po, there may a great expence be ſpared.
That what ever its Fall be, it would maintain the ſame, not
having other Rivers, which with their Floods can hinder it; and
that running confined between good Banks, without doubt it
would not leave la Motto by the way; but eſpecially, that it
would be ſufficient if it came to Codigoro, where being aſſiſted by
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 alſo no mean Navigation
might be expected.
On the contrary it is objected, That it is not convenient to
1think of returning this Torrent into the divided Po, by reaſon of
the peril that would thence redound to this City.
And that going by Torre del Fondo, through Sanmartina to
the Mouth de Maſi by the Chappel of Vigarano unto the Sea, it is
by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, ſo
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 depoſe their ſand that they bring
with them in Land-Floods) requireth the twenty fourth part of
the hundredth part of their whole length, which in our caſe,
accounting according to the meaſure of theſe places, is 16. inches

a ^{*} mile; whereupon the ſinking of the Mud and Sand would
moſt certainly follow, and ſo an immenſe heightning of the Line
of the Bottom, and conſequently a neceſſity of raiſing the Banks,
the impoſſibility of maintaining them, the danger of breaches
and decayes, things very prejudicial to the Iſlets of this City, and
of San Giorgio, the obſtruction of the Drains, which from the
Tower of Tienne downwards, fall into the ſaid Chanel; to wit,
thoſe of the Sluices of Goro, and the Drains, of the Meadows of
Ferrara: And moreover, the damages that would ariſe unto the
ſaid Iſlet of S. Giorgio, and the Valleys of Comachio, by the wa­
ters that ſhould enter into the Goro or Dam of the Mills of Belri­
guardo, thorow the Trenches of Quadrea, which cannot be ſtopt,
becauſe they belong to the Duke of Modena, who hath right of
diverting the waters of that place at his pleaſure to the work of
turning Mills.
* The inch of
theſe places is
ſomewhat bigger
than ours.
The greater part of which Objections, others pretend to prove
frivolous, by ſaying, that its running there till at the laſt it was
turned another way, is a ſign that it had made ſuch an elevation
of the Line, of its Bed as it required; denying that it needeth
ſo great a declivity as is mentioned above; and that for the fu­
ture it would riſe no more.
That the ſaid Dra ns and Ditches did empty into the ſame,
whilſt Po was there; ſo that they muſt needs be more able to do
ſo when onely Reno runs that way.
That there would no Breaches follow, or if they did, they
would be onely of the water of Reno, which in few hours might
be taken away (in thoſe parts they call damming up of Breaches,
and mending the Bank, taking away the Breaches) and its a que­
ſtion whether they would procure more inconvenience than bene­
fit, for that its Mud and Sand might in many places, by filling
them up, occaſion a ſeaſonable improvement.
Now omitting to diſcourſe of the ſolidity of the reaſons on the
oneſide, or on the other, I will produce thoſe that move me to
ſuſpend my allowance of this deſign.
1
The firſt is, that although I dare not ſubſcribe to the opinion
of thoſe that require 16. inches Declivity in a mile to Reno, to
prevent its depoſing of Mud; yet would I not be the Author that
ſhould make a trial of it with ſo much hazard, for having to ſa­
tisfie my ſelf in ſome particulars cauſed a Level to be taken of
the Rivers L'amone, Senio, and Santerno, by Bernardino Aleotti,
we found that they have more Declivity by much than Artiſts re­
quire, as alſo the Reno hath from la Botta de Ghiſlieri to the
Chappel of Vigarano, for in the ſpace of four miles its Bottom­
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, eſpecially ſince, that the effects cauſed by Reno
it ſelf do confirm me in the ſame, for when it was forſaken by
the Po, after a few years, either becauſe it had choaked up its
Chanel with Sand, or becauſe its too long journey did increaſe
it, it alſo naturally turned aſide, and took the way of the ſaid
Po towards Stellata. Nay, in thoſe very years that it did run that
way, it only began (as relations ſay) to make Breaches, an evi­
dent ſign that it doth depoſe Sand, and raiſe its Bed; which a­
greeth with the teſtimony of ſome that were examined in the
Viſitation of the Publique Notary, who found great benefit by
having Running Water, and ſome kind of paſſage for Boats,
and yet nevertheleſs affirm that it for want of Running Water
had made too high Stoppages and Shelfes of Sand; ſo that if
it ſhould be reſtored to the Courſe that it forſook, I much fear
that after a ſhort time, if not ſuddenly, it would leave it a­
again.
The ſecond I take from the obſervation of what happened to
Panaro, when with ſo great applauſe of the Ferareſi, it was
brought by Cardinal Serra into the ſaid Chanel of Volana; for
that notwithſtanding that it had Running Waters in much grea­
ter abundance than Reno; yet in the time that it continued in
that Chanel it raiſed its Bed well neer five feet, as is to be ſeen
below the Sluice made by Cardinal Capponi to his new Chanel;
yea, the ſaid Cardinal Serra who deſired that this his under taking
ſhould appear to have been of no danger nor damage, was con­
ſtrained at its Overflowings, to give it Vent into Sanmartina, that
it might not break in upon, and prejudice the City; which dan­
ger I ſhould more fear from Reno, in regard it carrieth a greater
abundance of Water and Sand
Thirdly, I am much troubled (in the uncertainty of the ſuc­
ceſs of the affair) at the great expence thereto required; For in
regard I do not approve of letting it in, neer to the Fortreſſe,
for many reſpects, and carrying it by la Torre del Fondo to the
Month de Maſt, it will take up eight miles of double Banks, a
1thing not eaſie to be procured, by reaſon that the Grounds lie
under Water; but from the Mouth de Maſi unto Codigoro, it
would alſo be neceſſary to make new Scowrings of the Chanel;
to the end, that the Water approaching (by wearing and carry­
ing away the Earth on both ſhores, might make a Bed ſufficient
for its Body, the depth made for Panaro not ſerving the turn, as
I conceive; and if it ſhould ſuffice, when could the people of
Ferrara hope to be re-imburſed and ſatisfied for the charge
thereof?
Fourthly, it ſerves as an Argument with me, to ſee that the
very individual perſons concerned in the Remotion or Diverſion
of the ſaid Torrent, namely, the Bologneſi do not incline unto it,
and that the whole City of Ferrara, even thoſe very perſons who
at preſent receive damage by it, cannot indure to hear thereof.
The reaſon that induceth theſe laſt named to be ſo averſe thereto,
is, either becauſe that this undertaking will render the introducti­
on of the Water of Main-Po more difficult; or becauſe they fear
the danger thereof; The others decline the Project, either for
that they know that Reno cannot long continue in that Courſe,
or becauſe they fear that it is too much expoſed to thoſe mens re­
vengeful Cutting of it who do not deſire it ſhould; and if a
man have any other wayes, he ought, in my opinion, to forbear
that, which to ſuch as ſtand in need of its Removal, is leſſe ſatiſ­
factory, and to ſuch as oppoſe it, more prejudicial.
To conclude, I exceedingly honour the judgment of Cardinal
Capponi, who having to his Natural Ability and Prudence added
a particular Study, Obſervation, and Experience of theſe Wa­
ters for the ſpace of three years together, doth not think that
Reno can go by Volana; to which agreeth the opinion of Car­
dinal S. Marcello, Legate of this City, of whom, for his exqui­
ſite underſtanding, we ought to make great account. But if e­
ver this ſhould be reſolved on, it would be materially neceſſary
to unite the Quick and Running Waters of the little Chanel of
Cento, of the Chanel Navilio, of Guazzaloca, and at its very
beginning thoſe of Dardagna, which at preſent, is one of the
Springs or Heads of Panaro, that ſo they might aſſiſt it in carry­
ing its Sand, and the matter of its Muddineſs into the Sea; and
then there would not fail to be a greater evacuation and ſcowr­
ing; but withall the Proprietors in the Iſlet of San Giorgio and
of Ferrara muſt prepare themſelves to indure the inconveniences
of Purlings or Sewings of the Water from the River thorow
the Boggy Ground thereabouts.
I ſhould more eaſily incline therefore to carry it into Main-Po
at Stellata, for the Reaſons that Cardinal Capponi moſt ingeni­
ouſly enumerates in a ſhort, but well-grounded Tract of his: not
1becauſe that indeed it would not both by Purlings and by Brea­
ches occaſion ſome inconvenience; eſpecially, in the beginning:
but becauſe I hold this for the incomodities of it, to be a far leſs
evil than any of the reſt; and becauſe that by this means there is
no occaſion given to them of Ferrara, to explain that they are
deprived of the hope of ever ſeeing the Po again under the Walls
of their City: To whom, where it may be done, it is but reaſon
that ſatisfaction ſhould be given.
It is certain that Po was placed by Nature in the midſt of this
great Valley made by the Appennine Hills, and by the Alps, to
carry, as the Maſter-Drain to the Sea, that is the grand receptacle
of all Waters; thoſe particular ſtreams which deſcend from
them.
That the Reno by all Geographers, Strabo, Pliuy, Solimas,
Mella, and others is enumerated among the Rivers that fall into
the ſaid Po.
That although Po ſhould of it ſelf change its courſe, yet would
Reno go to look it out, if the works erected by humane ind uſtry
did not obſtruct its paſſage; ſo that it neither is, nor ought to
ſeem ſtrange, if one for the greater common good ſhould turn it
into the ſame.
Now at Stellata it may go ſeveral waies into Po, as appeareth
by the levels that were taken by my Order; of all which I ſhould
beſt like the turning of it to la Botta de' Ghiſlieri, carrying it
above Bondeno to the Church of Gambarone, or a little higher or
lower, as ſhall be judged leaſt prejudicial, when it cometh to the
execution, and this for two principal reaſons: The one becauſe
that then it will run along by the confines of the Church P tri­
mony, without ſeparating Ferrara from the reſt of it; The other
is, Becauſe the Line is ſhorter, and conſequently the fall greater;
for that in a ſpace of ten miles and one third, it falleth twenty ſix
feet, more by much than is required by Artiſts; and would go
by places where it could do but little hurt, notwithſtanding that
the perſons interreſſed ſtudy 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. Bianca, of the Chanel of Cento, and of Burana, and all thoſe
others that enter into Po, do hinder this diverſion of Reno, by the
encreaſing of the waters in the Po. The other is that Po riſing
about the Tranſom of the Pilaſter-Sluice, very near 20 feet, the
Reno would have no fall into the ſame; whereupon it would riſe
to a terrible height, at which it would not be poſſible to make, or
keep the Banks made, ſo that it would break out and drown
the Meadowes, and cauſe miſchiefs, and damages unſpeakable
and irreparable; as is evident by the experiment made upon
1Panaro, which being confined between Banks, that it might go
into Po, this not being neither in its greateſt excreſcenſe, it broke
out into the territories of Final, and of Ferrara. And though
that might be done, it would thereupon enſue, that there being
let into the Chanel of Po, 2800, ſquare feet of water (for ſo much
we account thoſe of Reno and Panaro, taken together in their
greateſt heights) the ſuperficies of it would riſe at leaſt four feet,
inſomuch that either it would be requiſite to raiſe its Banks all the
way unto the Sea, to the ſame height, which the treaſures of the
Indies would not ſuffice to effect; or elſe there would be a neceſ­
ſity of enduring exceſſive Breaches. To theſe two Heads are the
Arguments reduced, which are largely amplified againſt our opi­
nion; and I ſhall anſwer firſt to the laſt, as moſt material.
I ſay therefore, that there are three caſes to be conſidered:
Firſt, Po high, and Reno low. Secondly, Reno high, and Po
low. Thirdly, Reno and Po both high together.
As to the firſt and ſecond, there is no difficulty in them; for if
Po ſhall not be at its greateſt height, Reno ſhall ever have a fall
into it, and there ſhall need no humane Artifice about the Banks:
And if Reno ſhall be low, Po ſhall regurgitate and flow up into
the Chanel of it; and alſo from thence no inconvenience ſhall
follow. The third remains, from which there are expected ma­
ny miſchiefs; but it is a moſt undoubted truth, that the excreſcen­
cies of Reno, as coming from the adjacent Appennines and Rains,
are to continue but ſeven, or eight hours at moſt, and ſo would
never, or very rarely happen to be at the ſame time with thoſe of
Po, cauſed by the melting of the ſnowes of the Alps, at leaſt 400.
miles diſtance from thence. But becauſe it ſometimes may hap­
pen, I reply, that when it cometh to paſs, Reno ſhall not go into
Po, but it ſhall have allowed it one or two Vents; namely, into
the Chanel of Ferrara, as it hath ever had; and into Sanmartina,
where it runneth at preſent, and wherewith there is no doubt, but
that the perſons concerned will be well pleaſed, it being a great
benefit to them, to have the water over-flow their grounds once
every four or five years, inſtead of ſeeing it anoy them continu­
ally. Yea, the Vent may be regulated, reſerving for it the Cha­
nel in which Reno at preſent runneth; and inſtead of turning it
by a Dam at la Betta de Chiſlieri, perhaps, to turn it by help of
ſtrong Sluices, that may upon all occaſions be opened and ſhut.
And for my part, I do not queſtion but that the Proprietors
themſelves in Sanmartina would make a Chanel for it; which
receiving, and confining it in the time of the Vents, might carry
the Sand into the Po of Primaro: Nor need there thence be fear­
ed any ſtoppage by Mud and Sand, ſince that it is ſuppoſed that
there will but very ſeldom be any neceſſity of uſing it; ſo that
1time would be allowed, upon occaſion, to ſcowr and cleanſe
it.
And in this manner all thoſe Prodigies vaniſh that are raiſed
with ſo much fear from the enterance of the Water of Reno
ſwelled into Po, when it is high, to which there needeth no other
anſwer; yet nevertheleſſe we do not take that quantity of Wa­
ter, that is carried by Reno, and by Panaro, to be ſo great as is affir­
med: For that P. D. Benedetto Caſtelli hath no leſſe accutely
than accurately obſerved the meaſures of this kind, noting that
the breadth and depth of a River is not enough to reſolve the
queſtion truly, but that there is reſpect to be had to the velocity
of the Waters, and the term of time, things hitherto not conſi­
dered by the Skilful in theſe affairs; and therefore they are not
able to ſay what quantity of Waters the ſaid Rivers carry, nor
to conclude of the riſings that will follow thereupon. Nay, it
is moſt certain, that if all the Rivers that fall into Po, which are
above thirty, ſhould riſe at the rate that theſe compute Reno to
do, an hundred feet of Banks would not ſuffice, and yet they
have far fewer: So that this confirmes the Rule of R. P. D. Bene­
detto, namely, that the proportion of the height of the Water
of Reno in Reno to the height of the Water of Reno in Po, is
compounded of the proportion of the breadth of the Chanel of
Po to that of Reno, and of the velocity of the Water of Reno
in Po to the velccity of the Water of Reno in Reno; a manifeſt
argument that there cannot in it, by this new augmentation of
Waters follow any alteration that neceſſitates the raiſing of its
Banks, as appeareth by the example of Panaro, which hath been
ſo far from ſwelling Po, that it hath rather aſſwaged it, for it hath
carried away many Shelfs and many Iſlets that had grown in its
Bed, for want of Waters ſufficient to bear away the matter of
Land-floods in ſo broad a Chanel; and as is learnt by the trial
made by us in Panaro with the Water of Burana; for erecting
in the River ſtanding marks, and ſhutting the ſaid Sluice, we could
ſee no ſenſible abatement, nor much leſs after we had opened it
ſenſible increaſment; by which we judge that the ſame is to ſuc­
ceed to Po, by letting in of Reno, Burana having greater pro­
portion to Panaro than Reno to Po, conſidering the ſtate of thoſe
Rivers in which the Obſervation was made. So that there is no
longer any occaſion for thoſe great raiſings of Banks, and the
danger of the ruptures as well of Reno as of Po do vaniſh, as al­
ſo the fear leſt that the Sluices which empty into Po ſhould re­
ceive obſtruction: which if they ſhould, yet it would be over in
a few hours. And as to the Breaches of Panaro which happened
in 1623. I know not why, ſeeing that it is confeſſed that the Po
was not, at that time, at its height, one ſhould rather charge it
1with the crime, than quit it thereof. The truth is, that the
Bank was not made of proof, ſince that the ſame now continu­
eth whole and good, and Panaro doth not break out; nay, there
was, when it brake more than a foot and half of its Banks above
the Water, and to ſpare; but it broke thorow by a Moles wor­
king, or by the hole of a Water-Rat, or ſome ſuch vermine;
and by occaſion of the badneſs of the ſaid Banks, as I finde by
the teſtimony of ſome witneſſes examined by my command, that
I might know the truth thereof. Nor can I here forbear to ſay,
that it would be better, if in ſuch matters men were more candid
and ſincere. But to ſecure our ſelves nevertheleſſe, to the ut­
moſt of our power, from ſuch like Breaches which may happen
at the firſt, by reaſon of the newneſſe of the Banks, I preſuppoſe
that from Po unto the place whence Reno is cut, there ought to
be a high and thick Fence made with its Banks, ſo that there
would be no cauſe to fear any whatſoever acceſſions of Water,
although that concurrence of three Rivers, which was by ſome
more ingeniouſly aggravated than faithfully ſtated by that which
was ſaid above were true; to whom I think not my ſelf bound
to make any farther reply, neither to thoſe who ſay that Po will
aſcend upwards into Reno, ſince that theſe are the ſame perſons
who would introduce a ſmall branch of the ſaid Po into the
Chanel of Ferrara, that ſo it may conveigh to the Sea, not Reno
onely, but alſo all the other Brooks of which we complained;
and becauſe that withal it is impoſſible, that a River ſo capacious
as Po ſhould be incommoded by a Torrent, that, as I may ſay,
hath no proportion to it.
I come now to the buſineſſe of the Ditches and Draines; and
as to the Conveyance of Burana, it hath heretofore been deba­
ted to turn it into Main-Po, ſo that in this caſe it will receive no
harm, and though it were not removed, yet would it by a Trench
under ground purſue the courſe that it now holdeth, and alſo
would be able to diſ-imbogue again into the ſaid new Chanel of
Reno, which conforming to the ſuperficies of the Water of Po,
would continue at a lower level than that which Panara had
when it came to Ferrara, into which Burana did nevertheleſſe
empty it ſelf for ſome time.
The Conveyance or Drain of Santa Bianca, and the little
Chanel of Cento may alſo empty themſelves by two ſubterranean
Trenches, without any prejudice where they run at preſent, or
without any more works of that nature, they may be turned into
the ſaid new Chanel, although with ſomewhat more of incon­
venience; and withall, the Chanel of Ferrara, left dry, would
be a ſufficient receptacle for any other Sewer or Drain whatſoe­
ver, that ſhould remain there.
1
All which Operations might be brought to perfection with
150. thouſand Crowns, well and faithfully laid out; which ſumm
the Bologneſi will not be unwilling to provide; beſides that thoſe
Ferrareſi ought to contribute to it, who ſhall partake of the
benefit.
Let me be permitted in this place to propoſe a thing which I
have thought of, and which peradventure might occaſion two
benefits at once, although it be not wholly new. It was in the
time of Pope Paul V. propounded by one Creſcenzio an Ingi­
neer, to cut the Main-Po, above le Papozze; and having made a
ſufficient evacuation to derive the water thereof into the Po of
Adriano, and ſo to procure it to be Navigable, which was not at
that time effected, either by reaſon of the oppoſitions of thoſe,
whoſe poſſeſſions were to be cut thorow, or by reaſon of the
great ſum of money that was neceſſary for the effecting of it: But
in viewing thoſe Rivers, we have obſerved, that the ſedge cutting
might eaſily be made below le Papozze, in digging thorow the
Bank called Santa Maria, & drawing a Trench of the bigneſs that
skilful Artiſts ſhall judge meet unto the Po ^{*} of Ariano, below the

Secche of the ſaid S. Maria; which as being a work of not
above 160. Perches in length, would be finiſhed with onely
12000. Crowns.
* Of Adriano.
Firſt; it is to be believed, that the waters running that way,
would not fail to open that Mouth into the Sea, which at pre­
ſent is almoſt choakt up by the Shelf of Sand, which the new
Mouth of Ponto Virro hath brought thither; and that it would
again bring into uſe the Port Goro, and its Navigation.
And haply experience might teach us, that the ſuperficies of
Po might come to fall by this aſſwagement of Water, ſo that the
acceſſion of Reno would queſtionleſs make no riſing in it:
Whereupon, if it ſhould ſo fall out, thoſe Princes would have
no reaſon to complain; who ſeem to queſtion, leſt by this new
acceſſion of water into Po, the Sluices might be endangered.
Which I thought not fit to omit to repreſent to your Lordſhip;
not, that I propoſe it to you as a thing abſolutely certain, but that
you might, if you ſo pleaſed, lay it before perſons whoſe judge­
ments are approved in theſe affairs.
I return now from where I degreſt, and affirm it as indubita­
ble, that Reno neither can, nor ought to continue longer where
it at this day is; and that it cannot go into any other place but
that, whither Cardinal Capponi deſigned to carry it, and which
at preſent pleaſeth me better than any other; or into Volana,
whence it was taken away; the vigilance of Men being able to
obviate part of thoſe miſchiefs, which it may do there.
But from its Removal, beſides the alleviation of the harm
1which by it ſelf is cauſed, there would alſo reſult the diminution
of that which is occaſioned by the other Brooks, to the right hand
of the Po of Argenta; foraſmuch as the ſaid Po wanting all the
water of Reno, it would of neceſſity come to ebb in ſuch man­
ner, that the Valleys would have a greater Fall into the ſame,
and conſequently it would take in, and ſwallow greater abun­
dance of water; and by this means the Ditches and Draines
of the Up-Lands would likewiſe more eaſily Fall into them; eſ­
pecially if the ſcouring of Zenzalino were brought to perfection,
by which the waters of Marrara would fall into Marmorta: And
if alſo that of Baſtia were enlarged, and finiſhed, by which there
might enter as much water into the ſaid Po of Argenta, as is taken
from it by the removal of Reno; although that by that meanes
the water of the Valleys would aſſwage double: Nor would the
people of Argenta, the Iſles of S. Giorgio, and Comacchio have any
cauſe to complain; for that there would not be given to them
more water than was taken away: Nay ſometimes whereas they
had Muddy waters, they would have clear; nor need they to fear
any riſing: And furthermore, by this means a very great quan­
tity of ground would be reſtored to culture; For the effecting of
all which, the ſumm of 50. thouſand Crowns would go very far,
and would ſerve the turn at preſent touching thoſe 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 vaſter
and harder work, that would bring with it the difficulties of other
operations, and ſo would hinder the benefit which theſe people
expect from the paternal charity of His Holineſs.
1
TO
The Right Honourable,
MONSIGNORE
D. Ferrante Ceſarini.
My Treatiſe of the MENSURATION of RUN­
NING WATERS, Right Honourable, and
moſt Noble Sir, hath not a greater Preroga­
tive than its having been the production of the
command of Pope Vrban VIII. when His Ho­
lineſs was pleaſed to enjoyn me to go with
Monſignore Corſini, in the Viſitation that was
impoſed upon him in the year 1625. of the Waters of Ferrara,
Bologna, Romagna, and Romagnola; for that, on that occaſion
applying my whole Study to my ſervice and duty, I publiſhed in
that Treatiſe ſome particulars till then not rightly underſtood and
conſidered (that I knew) by any one; although they be in them­
ſelves moſt important, and of extraordinary conſequence. Yet
I muſt render thanks to Your Lordſhip for the honour you have
done to that my Tract; but wiſh withal, that your Eſteem of it
may not prejudice the univerſal Eſteem that the World hath of
Your Honours moſt refined judgement.
As to that Point which I touch upon in the Concluſion, name­
ly, That the conſideration of the Velocity of Running Water ſup­
plyeth the conſideration of the ^{*} Length omitted in the common

way of meaſuring Running Waters; Your Lordſhip having com­
manded me that in favour of Practiſe, and for the perfect diſco­
very of the diſorder that commonly happeneth now adayes in
the diſtribution of the Waters of Fountains, I ſhould demon­
ſtrate that the knowledge of the Velocity ſerveth for the finding
of the Length: I have thought fit to ſatisfie your Command by
relating a Fable; which, if I do not deceive my ſelf, will make
out to us the truth thereof; inſomuch that the reſt of my Treatiſe
ſhall thereby alſo become more manifeſt and intelligible, even to
1thoſe who finde therein ſome kinde of obſcurity.
* Larghezza, but
miſprinted.
In the dayes of yore, before that the admirable Art of Wea­
ving was in uſe, there was found in Perſia a vaſtand unvaluable
Treaſure, which conſiſted in an huge multitude of pieces of Er­
meſin, or Damask, I know not whether; which, as I take it,
amounted to near two thouſand pieces; which were of ſuch a
nature, that though their Breadth and Thickneſs were finite and
determinate, as they uſe to be at this day; yet nevertheleſs, their
Length was in a certain ſenſe infinite, for that thoſe two thouſand
pieces, day and night without ceaſing, iſſued out with their ends
at ſuch a rate, that of each piece there iſſued 100. Ells a day, from
a deep and dark Cave, conſecrated by the Superſtition of thoſe
people, to the fabulous Arachne. In thoſe innocent and early
times (I take it to have been, in that ſo much applauded and
deſired Golden age) it was left to the liberty of any one, to cut
off of thoſe pieces what quantity they pleaſed without any diffi­
culty: But that felicity decaying and degenerating, which was
altogether ignorant of Meum and Tuum; terms certainly moſt
pernicious, the Original of all evils, and cauſe of all diſcords;
there were by thoſe people ſtrong and vigilant Guards placed
upon the Cave, who reſolved to make merchandize of the Stuffes;
and in this manner they began to ſet a price upon that ineſtima­
ble Treaſure, ſelling the propriety in thoſe pieces to divers Mer­
chants; to ſome they ſold a right in one, to ſome in two, and to
ſome in more. But that which was the worſt of all, There was
found out by the inſatiable avarice of theſe men crafty inventions
to deceive the Merchants alſo; who came to buy the aforeſaid
commodity, and to make themſelves Maſters, ſome of one
ſome of two, and ſome of more ends of thoſe pieces of ſtuff;
and in particular, there were certain ingenuous Machines placed
in the more ſecret places of the Cave, with which at the pleaſure
of the Guards, they did retard the velocity of thoſe Stuffs, in
their iſſuing out of the Cave; inſomuch, that he who ought to have
had 100. Ells of Stuff in a day, had not above 50, and he who
ſhould have had 400, enjoyed the benefit of 50. onely; and ſo all
the reſt were defrauded of their Rights, the ſurpluſage being ſold,
appropriated, and ſhared at the will of the corrupt Officers: So
that the buſineſs was without all order or juſtice, inſomuch that
the Goddeſs Arachne being diſpleaſed at thoſe people, deprived
every one of their benefit, and with a dreadful Earthquake for
ever cloſing the mouth of the Cave, in puniſhment of ſo much
impiety and malice: Nor did it avail them to excuſe themſelves,
by ſaying that they allowed the Buyer the Breadth and Thick­
neſs bargained for; and that of the Length, which was infinite,
1there could no account be kept: For the wiſe and prudent
Prieſt of the Sacred Grotto anſwered, That the deceit lay in the
length, which they were defrauded of, in that the velocity of the
ftuffe was retarded, as it iſſued out of the Cave: and although
the total length of the Piece was infinite, for that it never cea­
ſed coming forth, and ſo was not to be computed; yet never­
theleſs its length conſidered, part by part, as it came out of the
Cave, and was bargained for, continued ſtill finite, and might
be one while greater, and another while leſſer, according as the
Piece was conſtituted in greater or leſſer velocity; and he added
withall, that exact Juſtice required, that when they ſold a piece
of ſtuff, and the propriety or dominion therein, they ought not
only to have aſcertained the breadth and thickneſſe of the Piece,
but alſo to have determined the length, determining its ve­
locity.
The ſame diſorder and confuſion, that was repreſented in the
Fable, doth come to paſſe in the Hiſtory of the Diſtribution of
the Waters of Conduits and Fountains, ſeeing that they are ſold
and bought, having regard only to the two Dimenſions, I mean
of Breadth and Height of the Mouth that diſchargeth the Wa­
ter; and to remedy ſuch an inconvenience, it is neceſſary to de­
termine the length in the velocity; for never ſhall we be able to
make a gueſſe at the quantity of the Body of Running Water,
with the two Dimenſions only of Breadth and Height, without
Length.
And to the end, that the whole buſineſs may be reduced
to a moſt eaſie practice, by which the waters of Aqueducts
may be bought and ſold juſtly, and with meaſures alwayes ex­
act and conſtant.
Firſt, the quantity of the Water ought diligently to be exa­
mined, which the whole principal ^{*} Pipe diſchargeth in a time
certain, as for inſtance, in an hour, in half an hour, or in a leſſe
interval of time, (for knowing which I have a moſt exact and
eaſie Rule) and finding that the whole principal pipe diſchar­
geth v. g. a thouſand Tuns of Water in the ſpace of one or
more hours, in ſelling of this water, it ought not to be uttered by
the ordinary and falſe meaſure, but the diſtribution 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 ſhall be
made, in the ſpace of an hour, or of ſome other ſet and deter­
minate time. And here I adde, that if I were to undertake to
make ſuch an adjuſtment, I would make uſe of a way to divide
and meaſure the time with ſuch accurateneſſe, that the ſpace of
an hour ſhould be divided into four, ſix, or eight thouſand parts
1without the leaſt errour; which Rule was taught me by my
Maſter Sign. Galilæo Galilæi, Chief Philoſopher to the moſt Se­
rene Grand Duke of Tuſcany. And this way will ſerve eaſily and
admirably to our purpoſe and occaſion; ſo that we ſhall
thereby be able to know how many Quarts of Water an A­
queduct will diſcharge in a given time of hours, moneths, or
years. And in this manner we may conſtitute a Cock that ſhall
diſcharge a certain and determinate quantity of water in a time
given.
And becauſe daily experience ſhews us, that the Springs of A­
queducts do not maintain them alwayes equally high, and full
of Water, but that ſometimes they increaſe, and ſometimes de­
creaſe, which accident might poſſibly procure ſome difficulty in
our diſtribution: Therefore, to the end that all manner of ſcru­
ple may be removed, I conceive that it would be convenient to
provide a Ciſtern, according to the occaſion, into which there
might alwayes fall one certain quantity of water, which ſhould
not be greater than that which the principal pipe diſchargeth in
times of drought, when the Springs are bare of water, that ſo in
this Ciſtern the water might alwayes keep at one conſtant height.
Then to the Ciſtern ſo prepared we are to faſten the Cocks of
particular perſons, to whom the Water is ſold by the Reverend
Apoſtolique Chamber, according to what hath been obſerved
before; and that quantity of Water which remaineth over and
above, is to be diſcharged into another Ciſtern, in which the
Cocks of the Waters for publick ſervices, and of thoſe which
people buy upon particular occaſions are to be placed. And
when the buſineſſe ſhall have been brought to this paſſe, there
will likewiſe a remedy be found to the ſo many diſorders that
continually happen; of which, for brevity ſake, I will inſtance
in but four only, which concern both publique and private bene­
fit, as being, in my judgment, the moſt enormous and intole­
rable.
The firſt inconvenience is, that in the common way of meaſu­
ring, diſpenſing, and ſelling the Waters of Aqueducts, it is not
underſtood, neither by the Buyer nor Seller, what the quantity
truly is that is bought and ſold; nor could I ever meet with any
either Engineer or Architect, or Artiſt, 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 diſpenſing the Waters of
Aqueducts we may very eaſily know the true quantity of Water
that is bought or ſold, as that it is ſo many Tuns an hour, ſo ma­
ny a day, ſo many in a year, &c.
The ſecond diſorder that happeneth, at preſent, in the diſtri­
1bution of Aqueducts is, that as the buſineſſe is now governed, it
lieth in the power of a ſordid Maſon to take unjuſtly from one,
and give undeſervedly to another more or leſſe Water than be­
longeth to them of right: And I have ſeen it done, of my
own experience. But in our way of meaſuring and diſtri­
buting Waters, there can no fraud be committed; and put­
ting the caſe that they ſhould be committed, its an eaſie 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 diſpenſing the Water after
the common and vulgar way; there is ſometimes more Water diſ­
pended than there is in the Regiſter, in which there will be regi­
ſtred, as they ſay, two hundred inches (for example) and there
will be diſpenſed two hundred and fifty inches, or more. Which
paſſage happened in the time of Nerva the Emperour, as Giulio
Frontino writes, in his 2. Book, De Aquaductibus Vrbis Romæ,
where he obſerveth that they had in Commentariis 12755. Qui­
naries of Water; and found that they diſpenſed 14018. Qui­
naries. And the like Errour hath continued, and is in uſe alſo
modernly until our times. But if our Rule ſhall be obſerved,
we ſhall incur no ſuch diſorder, nay there will alwayes be given
to every one his ſhare, according to the holy end of exact juſtice,
which dat unicuique quod ſuum eſt. As on the contrary, it is
manifeſt, that His Divine Majeſty hateth and abominateth Pon­
dus & pondus, Menſura & menſura, as the Holy Ghoſt ſpeak­
eth by the mouth of Solomon in the Proverbs, Chap. 20. Pondus
& Pondus, Menſura & Menſura, utrumque abominabile eſt apud
Deum. And therefore who is it that ſeeth not that the way of
dividing and meaſuring of Waters, commonly uſed, is expreſly
againſt the Law of God. Since that thereby the ſame meaſure
is made ſometimes greater, and ſometimes leſſer; A diſorder ſo
enormous and execrable, that I ſhall take the boldneſs to ſay, that
for this ſole reſpect it ought to be condemned and prohibited like­
wiſe by human Law, which ſhould Enact that in this buſineſs there
ſhould be imployed either this our Rule, or ſome other that
is more exquiſite and practicable, whereby the meaſure
might keep one conſtant and determinate tenor, as we make it,
and not, as it is now, to make Pondus & Pondus, Menſur a &
Menſura.
And this is all that I had to offer to Your moſt Illuſtrious
Lordſhip, in obedience to your commands, reſerving to my ſelf
the giving of a more exact account of this my invention, when
the occaſion ſhall offer, of reducing to practice ſo holy, juſt, and
1neceſſary a reformation of the Meaſure of Running Waters and
of Aqueducts in particular: which Rule may alſo be of great
benefit in the diviſion of the greater Waters to over-flow
Grounds, and for other uſes: I humbly bow,
Your Most Devoted,
and
Moſt Obliged Servant,
D. Benedetto Caſtelli, Abb. Caſin.
FINIS.
1
A TABLE
Of the moſt obſervable matters in this Treatiſe of the
MENSURATION of RUNNING
WATERS.
AAbatements of a River in different and unequal Diverſions, is alwaies equal, which is proved with 100. Syphons.Page 75Arno River when it riſeth upon a Land-Flood near the Sea one third of a Brace, it riſeth about Piſa 6. or 7. Braces.82BBanks near to the Sea lower, than far from thence. Corollary XIV.16Brent River diverted from the Lake of Venice, and its effects.64Brent ſuppoſed inſufficient to remedy the inconveniences of the Lake, and the falſity of that ſuppoſition.67Brent, and its benefits in the Lake.70Its Depoſition of Sand in the Lake, bow great it is.78, 79Bridges over Rivers, and how they are to be made. Appendix VIII.20Burana River, its riſing, and falling in Panaro.110CCaſtelli applyed himſelf to this Study by Order of Urban VIII.2Chanel of Navigation in the Valleys of Bologna, and its inconveniences.99Carried into the Po of Ferrara, and its benefitsibid.Ciampoli alover of theſe Obſervations of Waters.3DDifficulty of this buſineſs of Meaſuring Waters.2Diſorders that happen in the diſtribution of the Waters of Aqueducts, and their re-medies.113Diſtribution of the Waters of Fountains, and Aqueducts. Appendix X.22Diſtribution of Water to over-flow Grounds. Appendix XI.23, 69, 70Diverſion of Reno and other Brooks of Romagna, adviſed by P. Spernazzati to what end it was.100Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix IX.21Drains and Sewers obſtructed, in the Diverſion of Reno into Main Po, and a remedy for the ſame.110EEngineers unverſ'd in the matters of Waters.2Erour found in the common way of Meaſuring Running Waters.68, 69Errour in deriving the Water of Acqua Paola. Appendix II.17, 18
1Errour of Bartolotti.86, 87Errours of Engineers in the Derivation of Chenels. Corollary XII.12Errour of Engineers in Meaſuring of Reno in Po. Appendix III.ibid.Errour of other Engineers, contrary to the precedent. Appendix IV.Ibid.Errour of Giovanni Fontana in Meaſuring Waters, Corollary XI.9Errour of Giulio Frontino in Meaſuring the Waters of Aqueducts. Appen-dix I.17Errours committed in cutting the Bank at Bondeno, in the ſwellings of Po: CorollaryXIII.81FFenns Pontine, Drained by Pope Sixtus Quintus, with vaſt expence.92The ruine and miſcarriage thereof.93Tardity of the principal Chanel that Drains them, cauſe of the Drowning.ibid.They are obſtructed by the Fiſhing-Wears, which ſuell the River.94Waters of Fiume Siſto, which flow in great abundance into the Evacuator of the ſaid Fenns.94, 95Remedies to the diſorders of thoſe Fenns.95, 96Fontana Giovanni, his errours in Meaſuring Waters. Corollary XI.9Fiume Morto, whether it ought to fall into the Sea, or into Serchio,79Let into Serchio and its inconveniences.79, 80The dangerous riſing of its Waters, when to be expected.81Its inconveniences when it is higher in level than Serchio, and why it riſeth moſt On the Sea-coaſts, at ſuch time as the Winds make the Sea to ſuell.83GGalilæo Galilæi. hoxourably mentioned.Page 2, 28His Rule for meaſuring the time.49HHeight, vide QuickHeights different, made by the ſame ſtream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary I.6Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary II.ibid.KKnowledge of Motion how much it importeth.1LtLake of Perugia, and, he Obſervation made on it. Appendix XII.42Lake of Thraſimenus and Conſiderations upon it, a Letter written to Sig. Galilæo Galilæi.28Lake of Venice, and Conſiderations upon it.63, 73Low Waters which let the bottom of it be diſcovered.64The ſtoppage and choaking of the Ports, a main cauſe of the diſorders of the Lake, and the grand remedy to thoſe diſorders what it is.66Lakes and Metrs along the Sea-coaſts, and the cauſes thereof.65Length of Waters, how it is to be Meaſured.70MMeaſure and Diſtributions of Waters. Appendix V.18
1Meaſure of Rivers that fall into others difficult. Coroll. X:9Meaſure of the Running Water of a Chanel of an height known by a Regulator of a Mea-ſure given, in a time aſſigned. Propoſition I. Problem I.50Meaſure of the Water of any River, of any greatneſs, in a time given. Propoſition V. Problem III.60Meaſure that ſhewes how much Water a River diſchargeth in a time given.48Mole-holes,Motion the principal ſubject of Philoſophy.1Mud. Vide Sand.NNavigation from Bologna to Ferrara, is become impoſſible, till ſuch time as Reno be diverted.101Navigation in the Lake of Venice endangered, and how restored.65, 70PPerpendicularity of the Banks of the River, to the upper ſuperficies of it.37Perpendicularity of the Banks to the bottom.37Perugia. Vide Lake.Pontine. Vide Fenns.Ports of Venice, Malamocco, Bondolo, and Chiozza, choaked up for want of Water in the Lake.65Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome IV. and V.38Proportions of equal and unequal quantities of Water, which paſs by the Sections of dif-ferent Rivers. Propoſition II.39Proportions of unequal Sections that in equal times diſcharge equal quantities of Water. Propoſition III.41Proportion wherewith one River falling into another, varieth in height. Propo-ſition IV.44Proportion of the Water diſcharged by a River in the time of Flood, to the Water diſcharged in an equal time by the ſaid River, before or after the Flood. Propoſition V.44Proportion of the Heights made by two equal Brooks or Streams falling into the ſame River. Propoſition VI.45Proportion of the Water which a River diſchargeth encreaſing in Quick-height by the ad-dition of new Water, to that which it diſchargeth after the encreaſe is made. Propo-ſition IV. Theor. II.54Proportion of a River when high, to it ſelf when low. Coroll. I.55QQuantity of Running Waters is never certain, if with the Vulgar way of Meaſuring them, their Velocities be not conſidered.32Quantities of Waters which are diſcharged by a River, anſwer in equality to the Velocities and times in which they are diſcharged. Axiome I, II, III.38Quick-Height of a River, what it is. Definition V.48RReaſon of the Proverb, Take heed of the ſtill Waters. Coroll. VI.7Reaſons of Monſignore Corſini againſt the diverſion of Reno into the Po ofVolano.105Reaſons of Cardinal Capponi and Monſig. Corſini, for the turning of Reno into Main Po.106
1Two objections on the contrary, and anſwers to them.104 & 105What ought to be the proportion of the Heights of Reno in Reno, and of Reno inPo.110Regulator what it is. Definition IV.48Relation of the Waters of Bologna and Ferrara, by Monſignore Corſini100Reno in the Valleys, and its bad effects.100, 101Two wayes to divert it.103The facility and utility of thoſe wayes.Ibid.The difficulties objected.104Reply to Bartolotti touching the dangers of turning Fiume Morto into Serchio.83Retardment of the courſe of a River cauſed by its Banks. Appendix VII.19Riſings made by Flood-Gates but ſmall. Appendix XIII.26Rivers that are ſhallow ſwell much upon ſmall ſhowers, ſuch as are deep riſe but little upon great Floods. Corollary III.6Rivers the higher they are, the ſwifter.Ibid.Rivers the higher they are, theleſſe they encreaſe upon Floods.49Rivers when they are to have equal and when like Velocity.Ibid.Rivers in falling into the Sea, form a Shelf of Sand called Cavallo.65Five Rivers to be diverted from the Lake of Venice, and the inconveniences that would enſue thereupon.74, 75A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth alſo in Velocity. Propoſition II. The-orem I.51Keepeth the proportion of the heights, to the Velocities. Corollary52SSand and Mud that entereth into the Lake of Venice, and the way to examine it.76Seas agitated and driven by the Winds ſtop up the Ports.64, 65Sections of a River what they are. Definition I.37Sections equally ſwift what they are. Definition II.Ibid.Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.38Sections of the ſame River, and their Proportions to their Velocities. Coroll. I.42Sections of a River diſcharge in any whatſoever place of the ſaid River, equal quantities of Water in equal times. Propoſition I.39Sile River what miſchiefes it threatneth, diverted from the Lake.74Spirtings of Waters grow bigger the higher they go. Coroll. XVI.16Sreams of Rivers how they encreaſe and vary. Coroll. I.6Streams retarded, and the effects thereof. Coroll. IX.8TTable of the Heights, Additions, and Quantities of Waters, and its uſe.56Thraſimenus. Vide Lake.Time how its meaſured in theſe Operations of the Waters.49Torrents encreaſe at the encreaſing of a River, though they carry no more Water than before: Coroll. IV.6Torrents when they depoſe and carry away the Sand. Coroll. V.7Torrents and their effects in a River.6, 7Torrents that fall into the Valleys, or into Po of Volano, and their miſchiefs prevent-ed, by the diverting of Reno into Main Po.100Tyber and the cauſes of its inundations. Coroll. VIII.8
1VValleys of Bologna and Ferrara, their inundations and diſorders, whence they pro-ceed.97Velocity of the Water ſhewn by ſeveral Examples.3Its proportion to the Meaſure.5Velocities equal, what they are.47Velocities like, what they are.47, 48Velocities of Water known, how they help us in finding the Lengths.113A Fable to explain the truth thereof.Ibid.Venice. Vide Lake.Vſe of the Regulator in meaſuring great Rivers. Conſideration I.60WWaters falling, why they diſgroß. Coroll. XVI.16Waters, how the Length of them is Meaſured.70Waters that are imployed to flow Grounds, how they are to be diſtributed.19, 53, 54Waters to be carryed in Pipes, to ſerve Aquaducts and Conduits, how they are to be Mea-ſured.115, 116Way to know the riſing of Lakes by Raines.28Way of the Vulgar to Meaſure the Waters of Rivers.68Wind Gun, and Tortable Fountain of Vincenzo Vincenti of Urbin.11Windes contrary, retard, and make Rivers encreaſe. Coroll. VII.8
The END of the TABLE of the Second Part
of the Firſt TOME.