is than the thread passed the hole the greater reciprocally is the velocity of the parts of the thread passed the hole than the volocity 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 thicknesse 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 Metal or Water hath to the thicknesse And therefore granting this discourse we may say that as often as two Taps with different velocity discharge equal quantities 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 velocity 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 demonstrated in our first Proposition and it being also true that in divers parts the same River may have various and different velocity 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 measure 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 established that the same Current of Water changeth measure according 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 particular 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 into the River they acquire or to say better keep the same velocity 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 River make lesse and lesse depths as the River grows more and more full since that also the Waters of the Torrent being entered 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 another 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 therefore 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 falleth 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 passing 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 measure 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 before 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 Torrent if it shall happen that the Torrent grow torbid and muddy and its streame be retarded in such a degree that it is not able to carry away those minute grains of Earth which compose 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 elegantly 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
the space of six hours in Ancona in * Ragusa in Corfu where the Tide is very small and happly unobservable Who will invent a way to pour new Water into an immoveable Vessel and to make that it rise onely in one determinate part of it and in other places not Will you say that this new Water is borrowed from the Ocean being brought in by the Straight of Gibraltar This will not remove the doubt aforesaid but will beget a greater And first tell me what ought to be the current of that Water that entering at the Straights mouth is carried in six hours to the remotest Creeks of the Mediterrane at a distance of two or three thousand Miles and that returneth the same space again in a like time at its going back What would Ships do that lye out at Sea What would become of those that should be in the Straights-mough in a continual precipice of a vast accumulation of Waters that entering in at a Channel but eight Miles broad is to give admittance to so much Water as in six hours over-floweth a tract of many hundred Miles broad thousands in length What Tygre what Falcon runneth or flyeth with so much swiftness With the swiftness I say of above 400 Miles an hour The currents run nor can it be denied the long-wayes of the Gulph but so slowly as that a Boat with Oars will out-go them though indeed not without defalking for their wanderings Moreover if this Water come in at the Straight the other doubt yet remaineth namely how it cometh to flow here so high in a place so remote without first rising a like or greater height in the parts more adjacent In a word I cannot think that either obstinacy or sharpness of wit can ever find an answer to these Objections nor consequently to maintain the stability of the Earth against them keeping within the bounds of Nature SAGR. I have all the while perfectly apprehended you in this and I stand greedily attending to hear in what manner these wonders may occur without obstruction from the motion already assigned to the Earth SALV These effects being to ensue in consequence of the motions that naturally agree with the Earth it is necessary that they not onely meet with no impediment or obstacle but that they do follow easily not onely that they follow with facility but with necessity so as that it is impossible that it should succeed otherwise for such is the property condition of things natural true Having therefore shewen the impossibility of rendring a reason of the motions discerned in the Waters at the same time to maintain the immobility of the vessel that containeth them we may proceed to enquire whether the mobility of the Container may produce the required effect in the manner that it is observed to evene Two kinds of motions may be conferred upon a Vessel whereby the Water therein contained may acquire a faculty of fluctuating in it one while towards one side and another while towards another and there one while to ebbe and another while to flow The first is when first one and then another of those sides is declined for then the Water running towards the inclining side will alternately be higher and lower sometimes on one side and sometimes on another But because that this rising and abating is no other than a recession and accession to the centre of the Earth such a motion cannot be ascribed to the Cavities of the said Earth that are the Vessels which contain the Waters the parts of which Vessel cannot by any whatsoever motion assigned to the Earth be made to approach or recede from the centre of the same The other sort of motion is when the Vessel moveth without inclining in the least with a progressive motion not uniform but that changeth velocity by sometimes accellerating and other times retarding from which disparity it would follow that the VVater contained in the Vessel its true but not fixed fast to it as its other solid parts but by reason of its fluidity as if it were separated and at liberty and not obliged to follow all the mutations of its Container in the retardation of the Vessel it keeping part of the impetus before conceived would run towards the the preceding part whereupon it would of necessity come to rise and on the contrary if new velocity should be added to the Vessel with retaining parts of its tardity staying somewhat behind before it could habituate it self to the new impetus it would hang back towards the following part where it would come to rise something The which effects we may plainly declare and make out to the Sense by the example of one of those same Barks yonder which continually come from Lizza-Fusina laden with fresh water for the service of the City Let us therefore fancy one of those Barks to come from thence with moderate velocity along the Lake carrying the water gently of which it is full and then either by running a ground or by some other impediment that it shall meet with let it be notably retarded The water therein contained shall not by that means lose as the Bark doth its pre-conceived impetus but retaining the same shall run forwards towards the prow where it shall rise notably falling as much a stern But if on the contrary the said Bark in the midst of its smooth course shall have a new velocity with notable augmentation added to it the water contained before it can habituate it self thereto continuing in its tardity shall stay behinde namely a stern where of consequence it shall mount and abate for the same at the prow This effect is undoubted and manifest and may hourly be experimented in which I desire that for the present three particulars may be noted The first is that to make the water to rise on one side of the vessel there is no need of new water nor that it run thither forsaking the other side The second is that the water in the middle doth not rise or fall notably unlesse the course of the Bark were not before that very swift and the shock or other arrest that held it exceeding strong and sudden in which case its possible that not only all the water might run forwards but that the greater part thereof might issue forth of the Bark and the same also would ensue whilst that being under sail in a smooth course a most violent impetus should upon an instant overtake it But when to its calme motion there is added a moderate retardation or incitation the middle parts as I said unobservedly rise and fall and the other parts according as they are neerer to the middle rise the lesse and the more remote more The third is that whereas the parts about the midst do make little alteration in rising and falling in respect of the waters of the sides on the contrary they run forwards and backwards very much in comparison of
in those that distend themselves for a great length from VVest to East namely according to the course of the motions of the Terrestrial Globe and as it is in a certain manner unthought of and without a president among the motions possible to be made by us so it is not hard for me to believe that effects may be derived from the same which are not to be imitated by our artificial experiments SALV These things being declared it is time that we proceed to examine the particular accidents which together with their diversities are observed by experience in the ebbing and flowing of the waters And first we need not think it hard to guesse whence it happeneth that in Lakes Pooles and also in the lesser Seas there is no notable flux and reflux the which hath two very solid reasons The one is that by reason of the shortnesse of the Vessel in its acquiring in several hours of the day several degrees of velocity they are with very little difference acquired by all its parts for as well the precedent as the subsequent that is to say both the Eastern and VVestern parts do accelerate and retard almost in the same manner and withal making that alteration by little and little and not by giving the motion of the conteining Vessel a sudden check and retardment or a sudden and great impulse or acceleration both it and all its parts come to be gently and equally impressed with the same degrees of velocity from which uniformity it followeth that also the conteined water with but small resistance and opposition receiveth the same impressions and by consequence doth give but very obscure signes of its rising or falling or of its running towards one part or another The which effect is likewise manifestly to be seen in the little artificial Vessels wherein the contained water doth receive the self same impressions of velocity when ever the acceleration and retardation is made by gentle and uniform proportion But in the Straights and Bays that for a great length distend themselves from East to West the acceleration and retardation is more notable and more uneven for that one of its extreams shall be much retarded in motion and the other shall at the same time move very swiftly The reciprocal libration or levelling of the water proceeding from the impetus that it had conceived from the motion of its container The which libration as hath been noted hath its undulations very frequent in small Vessels from whence ensues that though there do reside in the Terrestrial motions the cause of conferring on the waters a motion onely from twelve hours to twelve hours for that the motion of the conteining Vessels do extreamly accelerate and extreamly retard but once every day and no more yet neverthelesse this same second cause depending on the gravity of the water which striveth to reduce it self to equilibration and that according to the shortnesse of the Vessel hath its reciprocations of one two three or more hours this intermixing with the first which also it self in small Vessels is very little it becommeth upon the whole altogether insensible For the primary cause which hath the periods of twelve hours having not made and end of imprinting the precedent commotion it is overtaken and opposed by the other second dependant on the waters own weight which according to the brevity and profundity of the Vessel hath the time of its undulations of one two three four or more hours and this contending with the other former one disturbeth and removeth it not permitting it to come to the height no nor to the half of its motion and by this contestation the evidence of the ebbing and flowing is wholly annihilated or at least very much obscured I passe by the continual alteration of the air which disquieting the water permits us not to come to a certainty whether any though but small encrease or abatement of half an inch or losse do reside in the Straights or receptacles of water not above a degree or two in length I come in the second place to resolve the question why there not residing any vertue in the primary principle of commoving the waters save onely every twelve hours that is to say once by the greatest velocity and once by the greatest tardity of motion the ebbings and flowings should yet neverthelesse appear to be every six hours To which is answered that this determination cannot any wayes be taken from the primary cause onely but there is a necessity of introducing the secondary causes as namely the greater or lesse length of the Vessels and the greater or lesse depth of the waters in them conteined Which causes although they have not any operation in the motions of the waters those operations belonging to the sole primary cause without which no ebbing or flowing would happen yet neverthelesse they have a principal share in determining the times or periods of the reciprocations and herein their influence is so powerful that the primary cause must of force give way unto them The period of six hours therefore is no more proper or natural than those of other intervals of times though indeed its the most observed as agreeing with our Mediterrane which was the onely Sea that for many Ages was navigated though neither is that period observed in all its parts for that in some more angust places such as are the Hellespont and the Aegean Sea the periods are much shorter and also very divers amongst themselves for which diversities and their causes incomprehensible to Aristotle some say that after he had a long time observed it upon some cliffes of Negropont being brought to desperation he threw himself into the adjoyning Euripus and voluntarily drowned himself In the third place we have the reason ready at hand whence it commeth to passe that some Seas although very long as is the Red Sea are almost altogether exempt from Tides which happeneth because their length extendeth not from East to West but rather transversly from the Southeast to the Northwest but the motions of the Earth going from West to East the impulses of the water by that means alwayes happen to fall in the Meridians and do not move from parallel to parallel insomuch that in the Seas that extend themselves athwart towards the Poles and that the contrary way are narrow there is no cause of ebbing and flowing save onely by the participation of another Sea wherewith it hath communication that is subject to great commotions In the fourth place we shall very easily find out the reason why the fluxes and refluxes are greatest as to the waters rising and falling in the utmost extremities of Gulphs and least in the intermediate parts as daily experience sheweth here in Venice lying in the farther end of the Adriatick Sea where that difference commonly amounts to five or six feet but in the places of the Mediterrane far distant from the extreams that mutation is very small as in
distend for to this instance we answer with that which we have given notice of in the First Consideration touching the Lake of Venice treating of the abatement that is caused by the Brent let into the Lake And moreover if I shall adde thereto that which I write in the Second Consideration it will be very apparent how greatly harmfull and prejudicial these excursions of Waters from Fiume Sisto may be which are not kept under and confined within the River Therefore proceeding to the provisions and operations 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 bottome of the River those Weeds and Plants that grow and increase 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 mischief 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 become 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 Fiume 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 bear the Mouth della Torre may be opened and kept open into the Sea And it would last of all be of admirable benefit to cleanse Fiume Sisto from many Trees and Bushes wherewith 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 Pontine Fens 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 Honourable and Noble Monsignore Corsini who was heretofore Deputed Commissary General and Visitor of those Waters I am not able to make such another Discourse upon the same Subject but will only say somewhat for farther confirmation of that which I have said in this Book upon the Lake of Venice upon the Pontine Fens and upon the Draining of those Plains of Pisa lying between the Rivers Arno and Serchio whereby it is manifest that in all the aforementioned Cases and in the present one that we are in hand with there have in times past very grosse Errours been committed 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 iâ— 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 Valleys of Bologna and Ferrara might cause in the said Valleys is the certain cause that so many rich and fertile Fields are drowned 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 indeed 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 demonstrated 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 VVaters 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 introduced or that happen to be diverted shall be able with punctuality 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 much as it ran before so that when the water shall be quadruple 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 diverted 19 1â—â— the height of the River diminisheth onely 1 10
shall forbear to exasperate and attempt to reconcile such persons to this Hypothesis as devout esteem for Holy Scripture and dutifull Respect to Canonical Injunctions hath made to stand off from this Opinion and therefore for their sakes I have at the end of the Dialogues by way of supplement added an Epistle of Galileo to Her Most Serene Highness Christina Lotharinga the Grand Dutchesse Mother of Tuscany as also certain Abstracts of John Kepler Mathematician to two Emperours and Didacus à Stunica a famous Divine of Salamanca with an Epistle of Paulo Antonio Foscarini a learned Carmelite of Naples that shew the Authority of Sacred Scripture in determining of Philosophical and Natural Controversies hoping that the ingenious impartial Reader will meet with full satisfaction in the same And least what I have spoken of the prohibiting of these Pieces by the Inquisition may deterre any scrupulous person from reading of them I have purposely inserted the Imprimatur by which that Office licenced them And for a larger account of the Book or Author I refer you to the Relation of his Life which shall bring up the Reare in the Second Tome What remains of this is that Excellent Discourse of D. Benedetto Castelli Abbate di San Benedetto Aloysio concerning the Mensuration of Running Waters with other Treatises of that Learned Prelate of the Superintendent Corsini Some may alledge and I doe confess that I promised to publish the Life of Galileo in this place But the great miscarriages of Letters from some Friends in Italy and else where to whom I am a Debtor for several Remarques from whom I daily expect yet greater Helps concerning the History of that famous Personage these disappointments I say joyned with the undeniable Request of some Friends who were impatient to see Castelli in English together with a consideration of the disproportionate Bulk that would otherwise have bin betwixt the two Volumes perswaded me to this exchange This deviation from my Promise I hope is Venial and for the expiating of it I plead Supererrogation having in each Tome made so large Aditions though to my great expense that they make neer a third part more than I stood by promise bound to Publish That this is so will appear by comparing the Contents I here prefix with the Advertisment I formerly Printed For not to mention those Epitomes of Kepler and à Stunica the whole second and following Books of Castelli were not come to my hands at the time of my penning that Paper yet knowing how imperfect the Volume would be without them they being partly a supplement to the Theoremes and Problemes which the Abbot had formerly Printed and partly experiments that had procured him and his Doctrine a very great Reputation knowing this I say I apprehended a necessity of publishing them with the rest and hope that if you think not the service I have done therein worth your acknowledgement you will yet at least account the encrease of my expence a sufficient extenuation of the Trespass that those Additions have forced me to commit upon your Patience in point of Time As for the second Tome I have only this to assure the Generous Readers 1 that I am very confident I shall be much more punctual in publishing that than for the reasons above related I was able to be in setting forth this 2 that they shall not be abused in advancing of their moneys as hath bin used in the like case by selling the remaining Copyes at an under rate and 3 that I have a very great care that no disesteem may by my means arise unto this way of publishing Books for that it is of excellent use in ushering Great and Costly Volumes into the World To say nothing of the disadvantages of Translations in general this of mine doubtless is not without it's Errours and oversights but those of the Printer discounted I hope the rest may be allowed me upon the score of Human Imbecilitie The truth is I have assumed the Liberty to note the Mistakes in the Florid Version of Berneggerus in the Margent not so much to reproach him as to convince those who told me that they accounted my pains needless having his Latine Translation by them The like they said of the whole two Tomes but they thereby caused me to question their Understanding or Veracity For some of the Books were yet never extant As for instance the Mechanicks of Monsieur Des Cartes a Manuscript which I found amongst the many other Rarities that enrich the well-chosen Library of my Learned and Worthy Friend Dr. Charles Scarburgh the Experiments of Gravity and the Life of Galileo both my own Others were included in Volumes of great price or so dispersed that they were not to be purchased for any money as those of Kepler à Stunica Archimedes Tartaglia and the Mechanicks of Galileo And the remainder though easyer to procure were harder to be understood as Tartaglia his notes on Archimedes Torricellio his Doctrine of Projects Galileo his Epistle to the Dutchesse of Tuscany and above all his Dialogues de Motu never till now done into any Language which were so intermixt of Latine and Italian that the difficulty of the Stile joyned with the intricatnesse of the Subject rendered them Unpleasant if not wholly Vnintelligible to such as were not absolute Masters of both the Tongues To conclude according to the entertainment that you please to afford these Collections I shall be encouraged to proceed with the Publication of a large Body of Hydrography declaring the History Art Lawes and Apendages of that Princely Study of Navigation wherein I have omitted nothing of note that can be found either in Dudley Fournier Aurigarius Nonius Snellus Marsennus Baysius Morisetus Blondus Wagoner abroad or learnt amongst our Mariners at home touching the Office of an Admiral Commander Pilot Modellist Shipwright Gunner c. But order requiring that I should discharge my first Obligation before I contract a second I shall detein you no longer in the Portall but put you into possession of the Premises Novemb. 20. 1661. T. S. THE AUTHOR'S INTRODUCTION Judicious Reader THere was published some years since in Rome a salutiferous Edict that for the obviating of the dangerous Scandals of the present Age imposed a seasonable Silence upon the Pythagorean Opinion of the Mobility of the Earth There want not such as unadvisedly affirm that that Decree was not the production of a sober Scrutiny but of an illinformed Passion one may hear some mutter that Consultors altogether ignorant of Astronomical Observations ought not to clipp the Wings of Speculative Wits with rash Prohibitions My zeale cannot keep silence when I hear these inconsiderate complaints I thought fit as being thoroughly acquainted with that prudent Determination to appear openly upon the Theatre of the World as a Witness of the naked Truth I was at that time in Rome and had not only the audiences but applauds of the most Eminent Prelates of
by SIGNORE BARTOLOTTI in that affair of the DIVERSION of FIUME MORTO IX HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALABRIA X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOGNA FERRARA and ROMAGNA XI HIS LETTER to D. FERRANTE CESARINI applying his DOCTRINE to the MENSURATION of the LENGTH and DISTRIBUTION of the QUANTITY of the WATERS of RIVERS SPRINGS AQUEDUCTS c. XII D. CORSINUS SUPERINTENDENT of the GENERAL DRAINS and PRESIDENT of ROMAGNA his RELATION of the state of the VVATERS in the TERRITORIES of BOLOGNA and FERRARA A Table of the most observable Persons and Matters mentioned in the Second Part. The CONTENTS of the SECOND TOME PART THE FIRST Treatise I. GALILEUS GALILEUS his MATHEMATICAL DISCOURSES and DEMONSTRATIOMS touching two NEVV SCIENCES pertaining to the MECHANICKS and LOCAL MOTION with an APPENDIX of the CENTRE of GRAVITY of some SOLIDS in Four DIALOGUES II. HIS MECHANICKS a New PEICE III. RHENATUS DES CARTES his MECHANICKS translated from his FRENCH MANUSCRIPT a New PEICE IV. ARCHIMEDES his Tract DE INSIDENTIBUS HUMIDO with the NOTES and DEMONSTRASIONS of NICOLAUS TARTALEUS in Two BOOKS V. GALILEUS his DISCOURSE of the things that move in or upon the WATER VI. NICOLAUS TARTALEUS his INVENTIONS for DIVING UNDER WATER RAISING OF SHIPS SUNK c. in Two BOOKS PART THE SECOND I. EVANGELISTA TORRICELLIUS his DOCTRINE OF PROJECTS and TABLES of the RANGES of GREAT GUNNS of all sorts wherein he detects sundry ERRORS in GUNNERY An EPITOME II. T. S. his EXPERIMENTS of the COMPARATIVE GRAVITY OF BODIES in the AIRE and WATER III. GALILEUS GALILEUS his LIFE in Five BOOKS BOOK I. Containing Five Chapters Chap. 1. His Country 2. His Parents and Extraction 3. His time of Birth 4. His first Education 5. His Masters II. Containing Three Chapters Chap. 1. His judgment in several Learnings 2. His Opinions and Doctrine 3. His Auditors and Scholars III. Containing Four Chapters Chap. 1. His behaviour in Civil Affairs 2. His manner of Living 3. His morall Virtues 4. His misfortunes and troubles IV. Containing Four Chapters Chap. 1. His person described 2. His Will and Death 3. His Inventions 4. His Writings 5. His Dialogues of the Systeme in particular containing Nine Sections Section 1. Of Astronomy in General its Definition Praise Original 2. Of Astronomers a Chronological Catalogue of the most famous of them 3. Of the Doctrine of the Earths Mobility c. its Antiquity and Progresse from Pythagoras to the time of Copernicus 4. Of the Followers of Copernicus unto the time of Galileus 5. Of the severall Systemes amongst Astronomers 6. Of the Allegations against the Copern Systeme in 77 Arguments taken out of Ricciolo with Answers to them 7. Of the Allegations for the Copern Systeme in 50 Arguments 8. Of the Scriptures Authorities produced against and for the Earths mobility 9. The Conclusion of the whole Chapter V. Containing Four Chapters Chap. 1. His Patrons Friends and Emulators 2. Authors judgments of him 3. Authors that have writ for or against him 4. A Conclusion in certain Reflections upon his whole Life A Table of the whole Second TOME GALILAEUS Galilaeus Lyncaeus HIS SYSTEME OF THE WORLD The First Dialogue INTERLOCVTORS SALVIATUS SAGREDUS and SIMPLICIUS SALVIATUS IT was our yesterdayes resolution and agreement that we should to day discourse the most distinctly and particularly we could possible of the natural reasons and their efficacy that have been hitherto alledged on the one or other part by the maintainers of the Positions Aristotelian and Ptolomaique and by the followers of the Copernican Systeme And because Copernicus placing the Earth among the moveable Bodies of Heaven comes to constitute a Globe for the fame like to a Planet it would be good that we began our disputation with the examination of what and how great the energy of the Peripateticks arguments is when they demonstrate that this Hypothesis is impossible Since that it is necessary to introduce in Nature substances different betwixt themselves that is the Coelestial and Elementary that impassible and immortal this alterable and corruptible Which argument Aristotle handleth in his book De Coelo insinuating it first by some discourses dependent on certain general assumptions and afterwards confirming it with experiments and perticular demonstrations following the same method I will propound and freely speak my judgement submitting my self to your censure and particularly to Simplicius a Stout Champion and contender for the Aristotelian Doctrine And the first Step of the Peripatetick arguments is that where Aristotle proveth the integrity and perfection of the World telling us that it is not a simple line nor a bare superficies but a body adorned with Longitude Latitude and Profundity and because there are no more dimensions but these three The World having them hath all and having all is to be concluded perfect And again that by simple length that magnitude is constituted which is called a Line to which adding breadth there is framed the Superficies and yet further adding the altitude or profoundity there results the Body and after these three dimensions there is no passing farther so that in these three the integrity and to so speak totality is terminated which I might but with justice have required Aristotle to have proved to me by necessary consequences the rather in regard he was able to do it very plainly and speedily SIMPL. What say you to the excellent demonstrations in the 2. 3. and 4. Texts after the definition of Continual have you it not first there proved that there is no more but three dimensions for that those three are all things and that they are every where And is not this confirmed by the Doctrine and Authority of the Pythagorians who say that all things are determined by three beginning middle and end which is the number of All And where leave you that reason namely that as it were by the law of Nature this number is used in the sacrifices of the Gods And why being so dictated by nature do we atribute to those things that are three and not to lesse the title of all why of two is it said both and not all unless they be three And all this Doctrine you have in the second Text. Afterwards in the third Ad pleniorem scientiam we read that All the Whole and Perfect are formally one and the same and that therefore onely the Body amongst magnitudes is perfect because it is determined by three which is All and being divisible three manner of waies it is every way divisible but of the others some are dividible in one manner and some in two because according to the number affixed they have their division and continuity and thus one magnitude is continuate one way another two a third namely the Body every way Moreover in the fourth Text doth he not after some other Doctrines prove it by another demonstration Scilicet That no transition is made but
sit ratio totius partium those Countreys being a part of the Earth as well as ours they must of necessity be alterable as these are SALV And why have you not without being put to believe other mens relations examined and observed those alterations with your own eyes SIMPL. Because those places besides that they are not exposed to our eyes are so remote that our sight cannot reach to comprehend therein such like mutations SALV See now how you have unawares discovered the fallacy of your Argument for if you say that the alterations that are seen on the Earth neer at hand cannot by reason of the too great distance be seen in America much lesse can you see them in the Moon which is so many hundred times more remote And if you believe the alterations in Mexico upon the report of those that come from thence what intelligence have you from the Moon to assure you that there is no such alterations in it Therefore from your not seeing any alterations in Heaven whereas if there were any such you could not see them by reason of their too great distance and from your not having intelligence thereof in regard that it cannot be had you ought not to argue that there are no such alterations howbeit from the seeing and observing of them on Earth you well argue that therein such there are SIMPL. I will shew so great mutations that have befaln on the Earth that if any such had happened in the Moon they might very well have been observed here below We find in very antient records that heretofore at the Streights of Gibraltar the two great Mountains Abila and Calpen were continued together by certain other lesse Mountains which there gave check to the Ocean but those Hills being by some cause or other separated and a way being opened for the Sea to break in it made such an inundation that it gave occasion to the calling of it since the Mid-land Sea the greatness whereof considered and the divers aspects the surfaces of the Water and Earth then made had it been beheld afar off there is no doubt but so great a change might have been discerned by one that was then in the Moon as also to us inhabitants of the Earth the like alterations would be perceived in the Moon but we find not in antiquity that ever there was such a thing seen therefore we have no cause to say that any of the Coelestial bodies are alterable c. SALV That so great alterations have hapned in the Moon I dare not say but for all that I am not yet certain but that such changes might occur and because such a mutation could onely represent unto us some kind of variation between the more clear and more obscure parts of the Moon I know not whether we have had on Earth observant Selenographers who have for any considerable number of years instructed us with so exact Selenography as that we should confidently conclude that there hath no such change hapned in the face of the Moon of the figuration of which I find no more particular description than the saying of some that it represents an humane face of others that it is like the muzle of a Lyon and of others that it is Cain with a bundle of thorns on his back therefore to say Heaven is unalterable because that in the Moon or other Coelestial bodies no such alterations are seen as discover themselves on Earth is a bad illation and concludeth nothing SAGR. And there is another odd kind of scruple in this Argument of Simplicius running in my mind which I would gladly have answered therefore I demand of him whether the Earth before the Mediterranian inundation was generable and corruptible or else began then so to be SIMPL. It was doubtless generable and corruptible also before that time but that was so vast a mutation that it might have been observed as far as the Moon SAGR. Go to if the Earth was generable and corruptible before that Inundation why may not the Moon be so likewise without such a change Or why should that be necessary in the Moon which importeth nothing on Earth SALV It is a shrewd question But I am doubtfull that Simplicius a little altereth the Text of Aristotle and the other Peripateticks who say they hold the Heavens unalterable for that they see therein no one star generate or corrupt which is probably a less part of Heaven than a City is of the Earth and yet innumerable of these have been destroyed so as that no mark of them hath remain'd SAGR. I verily believed otherwise and conceited that Simplicius dissembled this exposition of the Text that he might not charge his Master and Consectators with a notion more absurd than the former And what a folly it is to say the Coelestial part is unalterable because no stars do generate or corrupt therein What then hath any one seen a Terrestrial Globe corrupt and another regenerate in its place And yet is it not on all hands granted by Philosophers that there are very few stars in Heaven less than the Earth but very many that are much bigger So that for a star in Heaven to corrupt would be no less than if the whole Terrestrial Globe should be destroy'd Therefore if for the true proof of generation and corruption in the Universe it be necessary that so vast bodies as a star must corrupt and regenerate you may satisfie your self and cease your opinion for I assure you that you shall never see the Terrestrial Globe or any other integral body of the World to corrupt or decay so that having been beheld by us for so many years past they should so dissolve as not to leave any footsteps of them SALV But to give Simplicius yet fuller satisfaction and to reclaim him if possible from his error I affirm that we have in our age new accidents and observations and such that I question not in the least but if Aristotle were now alive they would make him change his opinion which may be easily collected from the very manner of his discoursing For when he writeth that he esteemeth the Heavens inalterable c. because no new thing was seen to be begot therein or any old to be dissolved he seems implicitely to hint unto us that when he should see any such accident he would hold the contrary and 〈◊〉 as indeed it is meet sensible experiments to natural reason for had he not made any reckoning of the senses he would not then from the not seeing of any sensible mutation have argued immutability SIMPL. Aristotle deduceth his principal Argument à priori shewing the necessity of the inalterability of Heaven by natural manifest and clear principles and then stablisheth the same à posteriori by sense and the traditions of the antients SALV This you speak of is the Method he hath observed in delivering his Doctrine but I do not bethink it yet to be that wherewith he
of popular discourses the more empty and simple I find them And what greater folly can there be imagined than to call Jems Silver and Gold pretious and Earth and dirt vile For do not these persons consider that if there should be as great a scarcity of Earth as there is of Jewels and pretious metals there would be no Prince but would gladly give a heap of Diamonds and Rubies and many Wedges of Gold to purchase onely so much Earth as should suffice to plant a Gessemine in a little pot or to set therein a China Orange that he might see it sprout grow up and bring forth so goodly leaves so odiriferous flowers and so delicate fruit It is therefore scarcity and plenty that make things esteemed and contemned by the vulgar who will say that same is a most beautiful Diamond for that it resembleth a cleer water and yet will not part with it for ten Tun of water These men that so extol incorruptibility inalterability c. speak thus I believe out of the great desire they have to live long and for fear of death not considering that if men had been immortal they should have had nothing to do in the World These deserve to meet with a Medusa's head that would transform them into Statues of Dimond and Jasper that so they might become more perfect than they are SALV And it may be such a Metamorphosis would not be altogether unprofitable to them for I am of opinion that it is better not to discourse at all than to argue erroniously SIMPL. There is not the least question to be made but that the Earth is much more perfect being as it is alterable mutable c. than if it had been a masse of stone yea although it were one entire Diamond most hard and impassile But look how much these qualifications enoble the Earth they render the Heavenly bodies again on the other side so much the more imperfect in which such conditions would be superfluous in regard that the Coelestial bodies namely the Sun Moon and the other Stars which are ordained for no other use but to serve the Earth need no other qualities for attaining of that end save onely those of light and motion SAGR. How Will you affirm that nature hath produced and designed so many vast perfect and noble Coelestial bodies impassible immortal and divine to no other use but to serve the passible frail and mortal Earth to serve that which you call the drosse of the World and sink of all uncleannesse To what purpose were the Coelestial bodies made immortal c. to serve a frail c. Take away this subserviency to the Earth and the innumerable multitude of Coelestial bodies become wholly unuseful and superfluous since they neither have nor can have any mutual operation betwixt themselves because they are all unalterable immutable impassible For if for Example the Moon be impassible what influence can the Sun or any other Star have upon her it would doubtlesse have far lesse effect upon her than that of one who would with his looks or imagination lignifie a piece of Gold Moreover it seemeth to me that whilst the Coelestial bodies concurre to the generation and alteration of the Earth they themselves are also of necessity alterable for otherwise I cannot understand how the application of the Sun or Moon to the Earth to effect production should be any other than to lay a marble Statue by a Womans side and from that conjunction to expect children SIMPL. Corruptibility alteration mutation c. are not in the whole Terrestrial Globe which as to its whole is no lesse eternal than the Sun or Moon but it is generable and corruptible as to its external parts but yet it is also true that likewise in them generation and corruption are perpetual and as such require the heavenly eternal operations and therefore it is necessary that the Coelestial bodies be eternal SAGR. All this is right but if the corruptibility of the superficial parts of the Earth be nowise prejudicial to the eternity of its whole Globe yea if their being generable corruptible alterable c. gain them great ornament and perfection why cannot and ought not you to admit alteration generation c. likewise in the external parts of the Coelestial Globes adding to them ornament without taking from them perfection or bereaving them of action yea rather encreasing their effects by granting not onely that they all operate on the Earth but that they mutually operate upon each other and the Earth also upon them all SIMPL. This cannot be because the generations mutations c. which we should suppose v. g. in the Moon would be vain and uselesse natura nihil frustra facit SAGR. And why should they be vain and uselesse SIMPL. Because we cleerly see and feel with our hands that all generations corruptions c. made in the Earth are all either mediately or immediately directed to the use convenience and benefit of man for the use of man are horses brought forth for the feeding of horses the Earth produceth grasse and the Clouds water it for the use and nourishment of man herbs corn fruits beasts birds fishes are brought forth and in sum if we should one by one dilligently examine and resolve all these things we should find the end to which they are all directed to be the necessity use convenience and delight of man Now of what use could the generations which we suppose to be made in the Moon or other Planets ever be to mankind unlesse you should say that there were also men in the Moon that might enjoy the benefit thereof a conceit either fabulous or impious SAGR. That in the Moon or other Planets there are generated either herbs or plants or animals like to ours or that there are rains winds or thunders there as about the Earth I neither know nor believe and much lesse that it is inhabited by men but yet I understand not because there are not generated things like to ours that therefore it necessarily followeth that no alteration is wrought therein or that there may not be other things that change generate and dissolve which are not onely different from ours but exceedingly beyond our imagination and in a word not to be thought of by us And if as I am certain that one born and brought up in a spatious Forrest amongst beasts and birds and that hath no knowledg at all of the Element of Water could never come to imagine another World to be in Nature different from the Eatth full of living creatures which without legs or wings swiftly move and not upon the surface onely as beasts do upon the Earth but in the very bowels thereof and not onely move but also stay themselves and cease to move at their pleasure which birds cannot do in the air and that moreover men live therein and build Palaces and Cities and have so
of our mountains in a thicknesse of one mile onely SALV The very mountains of the Moon themselves are a proof thereof which percussed on one side of the Sun do cast on the contrary side very dark shadows terminate and more distinct by much than the shadows of ours but had these mountains been diaphanous we could never have come to the knowledg of any unevennesse in the superficies of the Moon not have seen those luminous montuosities distinguished by the terms which separate the lucid parts from the dark much lesse should we see this same term so distinct if it were true that the Suns light did penetrate the whole thicknesse of the Moon yea rather according to the Authors own words we should of necessity discern the passage and confine between the part of the Sun seen and the part not seen to be very confused and mixt with light and darknesse for that that matter which admits the passage of the Suns rayes thorow a space of two thousand miles must needs be so transparent that it would very weakly resist them in a hundredth or lesser part of that thicknesse neverthelesse the term which separateth the part illuminated from the obscure is incident and as distinct as white is distinct from black and especially where the Section passeth through the part of the Moon that is naturally more clear and montanous but where the old spots do part which are certain plains that by means of their spherical inclination receive the rayes of the Sun obliquely there the term is not so distinct by reason of the more dimme illumination That lastly which he saith how that the secondary light doth not diminish and languish according as the Moon encreaseth but conserveth it self continually in the same efficacy is most false nay it is hardly seen in the quadrature when on the contrary it should appear more splendid and be visible after the crepusculum in the dark of night Let us conclude therefore that the Earths reflection is very strong upon the Moon and that which you ought more to esteem we may deduce from thence another admirable congruity between the Moon and Earth namely that if it be true the Planets operate upon the Earth by their motion and light the Earth may probably be no lesse potent in operating reciprocally upon them with the same light and peradventure motion also And though it should not move yet may it retain the same operation because as it hath been proved already the action of the light is the self same I mean of the light of the Sun reflected and motion doth nothing save only vary the aspects which fall out in the same manner whether we make the Earth move and the Sun stand still or the contrary SIMPL. None of the Philosophers are found to have said that these inferiour bodies operate on the Coelestial nay Aristotle affirmes the direct contrary SALV Aristotle and the rest who knew not that the Earth and Moon mutually illuminated each other are to be excused but they would justly deserve our censure if whilest they desire that we should grant and believe with them that the Moon operateth upon the Earth with light they should deny to us who have taught them that the Earth illuminates the Moon the operation the Earth hath on the Moon SIMPL. In short I find in my self a great unwillingnesse to admit this commerce which you would perswade me to be betwixt the Earth and Moon placing it as we say amongst the number of the Stars for if there were nothing else the great separation and distance between it and the Coelestial bodies doth in my opinion necessarily conclude a vast disparity between them SALV See Simplicius what an inveterate affection and radicated opinion can do since it is so powerful that it makes you think that those very things favour you which you produce against your self For if separation and distance are accidents sufficient to perswade with you a great diversity of natures it must follow that proximity and contiguity import similitude Now how much more neerer is the Moon to the Earth than to any other of the Coelestial Orbs You must acknowledg therefore according to your own concession and you shall have other Philosophers bear you company that there is a very great affinity betwixt the Earth and Moon Now let us proceed and see whether any thing remains to be considered touching those objections which you made against the resemblances that are between these two bodies SIMPL. It rests that we say something touching the solidity of the Moon which I argued from its being exquisite smooth and polite and you from its montuosity There is another scruple also comes into my mind from an opinion which I have that the Seas reflection ought by the equality of its surface to be rendered stronger than that of the Earth whose superficies is so rough and opacous SALV As to the first objection I say that like as among the parts of the Earth which all by their gravity strive to approach the nearest they can possible to the center some of them alwayes are more remote from it than the rest as the mountains more than the valleys and that by reason of their solidity and firmnesse for if they were of fluid they would be even so the seeing some parts of the Moon to be elevated above the sphericity of the lower parts argueth their hardnesse for it is probable that the matter of the Moon is reduced into a spherical form by the harmonious conspiration of all its parts to the same sentense Touching the second doubt my thinks that the particulars already observed to happen in the Looking-glasses may very well assure us that the reflection of light comming from the Sea is far weaker than that which cometh from Land understanding it alwayes of the universal reflection for as to that particular on which the water being calm casteth upon a determinate place there is no doubt but that he who shall stand in that place shall see a very great reflection in the water but every way else he shall see the surface of the Water more obscure than that of the Land and to prove it to your senses let us go into yonder Hall and power forth a little water upon the Pavement Tell me now doth not this wet brick shew more dull than the other dry ones Doubtlesse it doth and will so appear from what place soever you behold it except one onely and this is that way which the light cometh that entereth in at yonder window go backwards therefore by a little and a little SIMPL. Here I see the west part shine more than all the rest of the pavement and I see that it so hapneth because the reflection of the light which entereth in at the window cometh towards me SALV That moisture hath done no more but filled those little cavities which are in the brick with water and reduced its superficies to an exact evenesse
whereupon the reflex rayes issue unitedly towards one and the same place but the rest of the pavement which is dry hath its protuberances that is an innumerable variety of inclinations in its smallest particles whereupon the reflections of the light scatter towards all parts but more weakly than if they had gone all united together and therefore the same sheweth almost all alike beheld several wayes but far lesse clear than the moistned brick I conclude therefore that the surface of the Sea beheld from the Moon in like manner as it would appear most equal the Islands and Rocks deducted so it would shew lesse clear than that of the Earth which is montanous and uneven And but that I would not seem as the saying is to harp too much on one string I could tell you that I have observed in the Moon that secondary light which I told you came to her from the reflection of the Terrestrial Globe to be notably more clear two or three dayes before the conjunction than after that is when we see it before break of day in the East than when it is seen at night after Sun-set in the West of which difference the cause is that the Terrestrial Hemisphere which looks towards the Eastern Moon hath little Sea and much Land to wit all Asia whereas when it is in the West it beholds very great Seas that is the whole Atlantick Ocean as far as America An Argument sufficiently probable that the surface of the water appears lesse splendid than that of the Earth SIMPL. So that perhaps you believe those great spots discovered in the face of the Moon to be Seas and the other clearer parts to be Land or some such thing SALV This which you ask me is the beginning of those incongruities which I esteem to be between the Moon and the Earth out of which it is time to dis-ingage our selves for we have stayed too long in the Moon I say therefore that if there were in nature but one way onely to make two superficies illustrated by the Sun to appear one more clear than the other and that this were by the being of the one Earth and the other Water it would be necessary to say that the surface of the Moon were part earthy and part aquatick but because we know many wayes to produce the same effect and others there may be which we know not of therefore I dare not affirm the Moon to consist of one thing more than another It hath been seen already that a silver plate boiled being toucht with the Burnisher becometh of white obscure that the moist part of the Earth shews more obscure than the dry that in the tops of Hills the woody parts appear more gloomy than the naked and barren which hapneth because there falleth very much shadow among the Trees but the open places are illuminated all over by the Sun And this mixtion of shadow hath such operation that in tufted velvet the silk which is cut is of a far darker colour than that which is not cut by means of the shadows diffused betwixt thred and thred and a plain velvet shews much blacker than a Taffata made of the same silk So that if there were in the Moon things which should look like great Woods their aspect might represent unto us the spots which we discover alike difference would be occasioned if there were Seas in her and lastly nothing hindreth but that those spots may really be of an obscurer colour than the rest for thus the snow makes the mountains shew brighter That which is plainly observed in the Moon is that its most obscure parts are all plains with few rises and bancks in them though some there be the rest which is of a brighter colour is all full of rocks mountains hillocks of spherical and other figures and in particular round about the spots are very great ledges of mountains That the spots be plain superficies we have assured proof in that we see how that the term which distinguisheth the part illuminated from the obscure in crossing the spots makes the intersection even but in the clear parts it shews all craggy and shagged But I know not as yet whether this evennesse of superficies may be sufficient of it self alone to make the obscurity appear and I rather think not Besides I account the Moon exceeding different from the Earth for although I imagine to my self that those are not idle and dead Regions yet I affirm not that there are in them motion and life much less that there are bred plants animals or other things like to ours but if such there be they should nevertheless be very different and remote from our imagination And I am induced so to think because in the first place I esteem that the matter of the Lunar Globe consists not of Earth and Water and this alone sufficeth to take away the generations and alterations resembling ours but now supposing that there were in the Moon Water and Earth yet would they not produce plants and animals like to ours and this for two principal reasons The first is that unto our productions there are required so many variable aspects of the Sun that without them they would all miscarry now the habitudes of the Sun towards the Earth are far different from those towards the Moon We as to the diurnal illumination have in the greater part of the Earth every twenty four hours part day and part night which effect in the Moon is monethly and that annual declination and elevation of the Sun in the Zodiack by which it produceth diversity of Seasons and inequality of dayes and nights are finished in the Moon in a moneth and whereas the Sun to us riseth and declineth so much that from the greatest to the least altitude there is a difference of almost 47 degrees for so much is the distance from one to the other Tropick this is in the Moon but ten degrees only or little more namely as much as the greatest Latitudes of the Dragon on each side the Ecliptick Now consider what effect the Sun would have in the torrid Zone should it continually for fifteen dayes together beam forth its Rayes upon it which without all question would destroy plants herbs and living creatures and if it should chance that there were any production it would be of herbs plants and creatures very different from those which are now there Secondly I verily believe that in the Moon there are no rains for if Clouds should gather in any part thereof as they do about the Earth they would thereupon hide from our sight some of those things which we with the Telescope behold in the Moon and in a word would some way or other change its Phaenomenon an effect which I could never by long and diligent observations discover but alwayes beheld it in a even and pure serenity SAGR. To this may be answered either that there might be great
mean of their flight hath nothing to do with the universal motion to which it is neither an help nor an hinderance and that which maintaineth the said motion unaltered in the birds is the Air it self thorough which they flie which naturally follovving the Vertigo of the Earth like as it carrieth the clouds along with it so it transporteth birds and every thing else which is pendent in the same in so much that as to the businesse of keeping pace vvith the Earth the birds need take no care thereof but for that work might sleep perpetually SAGR. That the Air can carry the clouds along with it as being matters easie for their lightnesse to be moved and deprived of all other contrary inclination yea more as being matters that partake also of the conditions and properties of the Earth I comprehend without any difficulty but that birds which as having life may move with a motion quite contrary to the diurnal once having surceased the said motion the Air should restore them to it seems to me a little strange and the rather for that they are solid and weighty bodies and withal we see as hath been said stones and other grave bodies to lie unmoved against the impetus of the air and when they suffer themselves to be overcome thereby they never acquire so much velocity as the wind which carrieth them SALV We ascribe not so little force Sagredus to the moved Air which is able to move and bear before it ships full fraught to tear up trees by the roots and overthrow Towers when it moveth swiftly and yet we cannot say that the motion of the Air in these violent operations is neer so violent as that of the diurnal revolution SIMP You see then that the moved Air may also cotinue the motion of projects according to the Doctrine of Aristotle and it seemed to me very strange that he should have erred in this particular SALV It may without doubt in case it could continue it self but lik as when the wind ceasing neither ships go on nor trees are blown down so the motion in the Air not continuing after the stone is gone out of the hand and the Air ceasing to move it followeth that it must be something else besides the Air that maketh the projects to move SIMP But how upon the winds being laid doth the ship cease to move Nay you may see that when the wind is down and the sails furl'd the vessel continueth to run whole miles SALV But this maketh against your self Simplicius for that the wind being laid that filling the sails drove on the ship yet neverthelesse doth it without help of the medium continue its course SIMP It might be said that the water was the medium which carried forward the ship and maintain'd it in motion SALV It might indeed be so affirmed if you would speak quite contrary to truth for the truth is that the water by reason of its great resistance to the division made by the hull of the ship doth with great noise resist the same nor doth it permit it of a great while to acquire that velocity which the wind would confer upon it were the obstacle of the water removed Perhaps Simplicius you have never considered with what fury the water besets a bark whil'st it forceth its way through a standing water by help of Oars or Sails for if you had ever minded that effect you would not now have produced such an absurdity And I am thinking that you have hitherto been one of those who to find out how such things succeed and to come to the knowledg of natural effects do not betake themselves to a Ship a Crosse-bow or a piece of Ordinance but retire into their studies and turn over Indexes and Tables to see whether Aristotle hath spoken any thing thereof and being assured of the true sense of the Text neither desire nor care for knowing any more SAGR. This is a great felicity and they are to be much envied for it For if knowledg be desired by all and if to be wise be to think ones self so they enjoy a very great happinesse for that they may perswade themselves that they know and understand all things in soorn of those who knowing that they understand not what these think they understand and consequently seeking that they know not the very least particle of what is knowable kill themselves with waking and studying and consume their days in experiments and observations But pray you let us return to our birds touching which you have said that the Air being moved with great velocity might restore unto them that part of the diurnal motion which amongst the windings of their flight they might have lost to which I reply that the agitated Air seemeth unable to confer on a solid and grave body so great a velocity as its own And because that of the Air is as great as that of the Earth I cannot think that the Air is able to make good the losse of the birds retardation in flight SALV Your discourse hath in it much of probability and to stick at trivial doubts is not for an acute wit yet neverthelesse the probability being removed I believed that it hath not a jot more force than the others already considered and resolved SAGR. It is most certain that if it be not necessarily concludent its efficacy must needs be just nothing at all for it is onely when the conclusion is necessary that the opponent hath nothing to alledg on the contrary SALV Your making a greater scruple of this than of the other instances dependeth if I mistake not upon the birds being animated and thereby enabled to use their strength at pleasure against the primary motion in-bred in terrene bodies like as for example we see them whil'st they are alive to fly upwards a thing altogether impossible for them to do as they are grave bodies whereas being dead they can onely fall downwards and therefore you hold that the reasons that are of force in all the kinds of projects above named cannot take place in birds Now this is very true and because it is so Sagredus that doth not appear to be done in those projects which we see the birds to do For if from the top of a Tower you let fall a dead bird and a live one the dead bird shall do the same that a stone doth that is it shall first follow the general motion diurnal and then the motion of descent as grave but if the bird let fall be a live what shall hinder it there ever remaining in it the diurnal motion from soaring by help of its wings to what place of the Horizon it shall please and this new motion as being peculiar to the bird and not participated by us must of necessity be visible to us and if it be moved by help of its wings towards the West what shall hinder it from returning with a like help of its wings unto the Tower
else was the first hinter of its mobility said that it did move Now that such a foolish conceit I mean of thinking that those who admit the motion of the Earth have first thought it to stand still from its creation untill the time of Pythagoras and have onely made it moveable after that Pythagoras esteemed it so findeth a place in the mindes of the vulgar and men of shallow capacities I do not much wonder but that such persons as Aristotle and Ptolomy should also run into this childish mistake is to my thinking a more admirable and unpardonable folly SAGR. You believe then Salviatus that Ptolomy thought that in his Disputation he was to maintain the stability of the Earth against such persons as granting it to have been immoveable untill the time of Pythagoras did affirm it to have been but then made moveable when the said Pythagoras ascribed unto it motion SALV We can think no other if we do but consider the way he taketh to confute their assertion the confutation of which consists in the demolition of buildings and the tossing of stones living creatures and men themselves up into the Air. And because such overthrows and extrusions cannot be made upon buildings and men which were not before on the Earth nor can men be placed nor buildings erected upon the Earth unlesse when it standeth still hence therefore it is cleer that Ptolomy argueth against those who having granted the stability of the Earth for some time that is so long as living creatures stones and Masons were able to abide there and to build Palaces and Cities make it afterwards precipitately moveable to the overthrow and destructiof Edifices and living creatures c. For if he had undertook to dispute against such as had ascribed that revolution to the Earth from its first creation he would have confuted them by saying that if the Earth had alwayes moved there could never have been placed upon it either men or stones much less could buildings have been erected or Cities founded c. SIMP I do not well conceive these Aristotelick and Ptolomaick inconveniences SALV Ptolomey either argueth against those who have esteemed the Earth always moveable or against such as have held that it stood for some time still and hath since been set on moving If against the first he ought to say that the Earth did not always move for that then there would never have been men animals or edifices on the Earth its vertigo not permitting them to stay thereon But in that he arguing saith that the Earth doth not move because that beasts men and houses before plac'd on the Earth would precipitate he supposeth the Earth to have been once in such a state as that it did admit men and beasts to stay and build thereon the which draweth on the consequence that it did for some time stand still to wit was apt for the abode of animals and erection of buildings Do you now conceive what I would say SIMP I do and I do not but this little importeth to the merit of the cause nor can a small mistake of Ptolomey committed through inadvertencie be sufficient to move the Earth when it is immoveable But omitting cavils let us come to the substance of the argument which to me seems unanswerable SALV And I Simplicius will drive it home and re-inforce it by shewing yet more sensibly that it is true that grave bodies turn'd with velocity about a settled centre do acquire an impetus of moving and receding to a distance from that centre even then when they are in a state of having a propension of moving naturally to the same Tie a bottle that hath water in it to the end of a cord and holding the other end fast in your hand and making the cord and your arm the semi-diameter and the knitting of the shoulder the centre swing the bottle very fast about so as that it may describe the circumference of a circle which whether it be parallel to the Horizon or perpendicular to it or any way inclined it shall in all cases follow that the water will not fall out of the bottle nay he that shall swing it shall find the cord always draw and strive to go farther from the shoulder And if you bore a hole in the bottom of the bottle you shall see the water spout forth no less upwards into the skie than laterally and downwards to the Earth and if instead of water you shall put little pebble stones into the bottle and swing it in the same manner you shall find that they will strive in the like manner against the cord And lastly we see boys throw stones a great way by swinging round a piece of a stick at the end of which the stone is let into a slit which stick is called by them a sling all which are arguments of the truth of the conclusion to wit that the vertigo or swing conferreth upon the moveable a motion towards the circumference in case the motion be swift and therefore if the Earth revolve about its own centre the motion of the superficies and especially towards the great circle as being incomparably more swift than those before named ought to extrude all things up into the air SIMP The Argument seemeth to me very well proved and inforced and I believe it would be an hard matter to answer and overthrow it SALV It s solution dependeth upon certain notions no less known and believed by you than by my self but because they come not into your mind therefore it is that you perceive not the answer wherefore without telling you it for that you know the same already I shall with onely assisting your memory make you to refute this argument SIMP I have often thought of your way of arguing which hath made me almost think that you lean to that opinion of Plato Quòd nostrum scire sit quoddam reminisci therefore I intreat you to free me from this doubt by letting me know your judgment SALV What I think of the opinion of Plato you may gather from my words and actions I have already in the precedent conferences expresly declared my self more than once I will pursue the same style in the present case which may hereafter serve you for an example thereby the more easily to gather what my opinion is touching the attainment of knowledg when a time shall offer upon some other day but I would not have Sagredâ—s offended at this digression SAGR. I am rather very much pleased with it for that I remember that when I studied Logick I could never comprehend that so much cry'd up and most potent demonstration of Aristotle SALV Let us go on therefore and let Simplicius tell me what that motion is which the stone maketh that is held fast in the slit of the sling when the boy swings it about to throw it a great way SIMP The motion of the stone so long as it is in the slit is circular that is
downwards is no less natural and intrinsecal than that principle of light bodies vvhich moveth them upwards so that I propose to your consideration a ball of lead vvhich descending through the Air from a great altitude and so moving by an intern principle and comming to a depth of vvater continueth its descent and without any other externe mover submergeth a great vvay and yet the motion of descent in the vvater is preternatural unto it but yet nevertheless dependeth on a principle that is internal and not external to the ball You see it demonstrated then that a moveable may be moved by one and the same internal principle with contrary motions SIMP I believe there are solutions to all these objections though for the present I do not remember them but however it be the Author continueth to demand on what principle this circular motion of grave and light bodies dependeth that is whether on a principle internal or external and proceeding forvvards sheweth that it can be neither on the one nor on the other saying Si ab externo Deusne illum excitat per continuum miraculum an verò Angelus an aër Et hunc quidem multi assignant Sed contra In English thus If from an externe principle Whether God doth not excite it by a continued Miracle or an Angel or the Air And indeed many do assign this But on the contrary SALV Trouble not your self to read his argument for I am none of those who ascribe that principle to the ambient air As to the Miracle or an Angel I should rather incline to this side for that which taketh beginning from a Divine Miracle or from an Angelical operation as for instance the transportation of a Cannon ball or bullet into the concave of the Moon doth in all probability depend on the vertue of the same principle for performing the rest But as to the Air it serveth my turn that it doth not hinder the circular motion of the moveables which we did suppose to move thorow it And to prove that it sufficeth nor is more required that it moveth with the same motion and finisheth its circulations with the same velocity that the Terrestrial Globe doth SIMP And he likewise makes his opposition to this also demanding who carrieth the air about Nature or Violence And proveth that it cannot be Nature alledging that that is contrary to truth experience and to Copernicus himself SALV It is not contrary to Copernicus in the least who writeth no such thing and this Author ascribes these things to him with two excessive courtesie It 's true he saith and for my part I think he saith well that the part of the air neer to the Earth being rather a terrestrial evaporation may have the same nature and naturally follow its motion or as being contiguous to it may follow it in the same manner as the Peripateticks say that the superiour part of it and the Element of fire follow the motion of the Lunar Concave so that it lyeth upon them to declare whether that motion be natural or violent SIMP The Author will reply that if Copernicus maketh only the inferiour part of the Air to move and supposeth the upper part thereof to want the said motion he cannot give a reason how that quiet air can be able to carry those grave bodies along with it and make them keep pace with the motion of the Earth SALV Copernicus will say that this natural propension of the elementary bodies to follow the motion of the Earth hath a limited Sphere out of which such a natural inclination would cease besides that as I have said the Air is not that which carrieth the moveables along with it which being separated from the Earth do follow its motion so that all the objections come to nothing which this Author produceth to prove that the Air cannot cause such effects SIMP To shew therefore that that cannot be it will be necessary to say that such like effects depend on an interne principle against which position oboriuntur difficillimae immò inextricabiles quaestiones secundae of which sort are these that follow Principium illud internum vel est accidens vel substantia Si primum quale nam illud nam qualitas locomotiva circum hactenus nulla videtur agniâ—a In English thus Contrary to which position there do arise most difficult yea inextricable second questions such as these That intern principle is either an accident or a substance If the first what manner of accident is it For a locomotive quality about the centre seemeth to be hitherto acknowledged by none SALV How is there no such thing acknowledged Is it not known to us that all these elementary matters move round together with the Earth You see how this Author supposeth for true that which is in question SIMP He saith that we do not see the same and me thinks he hath therein reason on his side SALV We see it not because we turn round together with them SIMP Hear his other Argument Quae etiam si esset quomodò tamen inveniretur in rebus tam contrariis in igne ut in aquâ in aëre ut in terra in viventibus ut in animà carentibus in English thus Which although it were yet how could it be found in things so contrary in the fire as in the water in the air as in the earth in living creatures as in things wanting life SALV Supposing for this time that water and fire are contraries as also the air and earth of which yet much may be said the most that could follow from thence would be that those motions cannot be common to them that are contrary to one another so that v. g. the motion upwards which naturally agreeth to fire cannot agree to water but that like as it is by nature contrary to fire so to it that motion suiteth which is contrary to the motion of fire which shall be the motion deorsum but the circular motion which is not contrary either to the motion sursum or to the motion deorsum but may mix with both as Aristotle himself affirmeth why may it not equally suit with grave bodies and with light The motions in the next place which cannot be common to things alive and dead are those which depend on the soul but those which belong to the body in as much as it is elementary and consequently participateth of the qualities of the elements why may not they be common as well to the dead corps as to the living body And therefore if the circular motion be proper to the elements it ought to be common to the mixt bodies also SAGR. It must needs be that this Author holdeth that a dead cat falling from a window it is not possible that a live cat also could fall it not being a thing convenient that a carcase should partake of the qualities which suit with things alive SALV Therefore the discourse of this Author concludeth nothing against one
Aequinoctial doth move in lesser circles SALV Because so would nay according to the doctrine of Ptolomey so have some fixed stars done which once were very near the Aequinoctial and described very vast circles and now that they are farther off describe lesser SAGR. If I could now but keep in mind all these fine notions I should think that I had made a great purchase I must needs intreat you Simplicius to lend me this Book for there cannot chuse but be a sea of rare and ingenious matters contained in it SIMP I will present you with it SAGR. Not so Sir I would not deprive you of it but are the Queries yet at an end SIMP No Sir hearken therefore Si latio circularis gravibus levibus est naturalis qualis est ea quae fit secundùm lineam rectam Nam si naturalis quomodo is motus qui circum est naturalis est cùm specie differat à recto Si violentus quî fit ut missile ignitum sursum evolans scintillosum caput sursùm à terrâ non autem circum volvatur c. Which take in our idiom If a circular lation is natural to heavy and light things what is that which is made according to a right line For if it be natural how then is that motion which is about the centre natural seeing it differs in species from a right motion If it be violent how is it that a fiery dart flying upwards sparkling over our heads at a distance from the Earth but not turning about c. SALV It hath been said already very often that the circular motion is natural to the whole and to its parts whilst they are in perfect disposure and the right is to reduce to order the parts disordered though indeed it is better to say that neither the parts ordered or disordered ever move with a right motion but with one mixed which might as well be averred meerly circular but to us but one part onely of this motion is visible and observable that is the part of the right the other part of the circular being imperceptible to us because we partake thereof And this answers to the rays which move upwards and round about but we cannot distinguish their circular motion for that with that we our selves move also But I believe that this Author never thought of this mixture for you may see that he resolutely saith that the rays go directly upwards and not at all in gyration SIMP Quare centrum sphaere delapsae sub Aequatore spiram describit in ejus plano sub aliis parallelis spiram describit in cono sub Polo descendit in axe lineam gyralem decurrens in superficie cylindricâ consignatam In English to this purpose Why doth the centre of a falling Globe under the Aequinoctial describe a spiral line in the plane of the Aequator and in other parallels a spiral about a Cone and under the Pole descend in the axis describing a gyral line running in a Cylindrical Superficie SALV Because of the lines drawn from the Centre to the circumference of the sphere which are those by which graves descend that which terminates in the Aequinoctial designeth a circle and those that terminate in other parallels describe conical superficies now the axis describeth nothing at all but continueth in its own being And if I may give you my judgment freely I will say that I cannot draw from all these Queries any sense that interfereth with the motion of the Earth for if I demand of this Author granting him that the Earth doth not move what would follow in all these particulars supposing that it do move as Copernicus will have it I am very confident that he would say that all these effects would happen that he hath objected as inconveniences to disprove its mobility so that in this mans opinion necessary consequences are accounted absurdities but I beseech you if there be any more dispatch them and free us speedily from this wearisom task SIMP In this which follows he opposes Copernicus his Sectators who affirm that the motion of the parts separated from their whole is onely to unite themselves to their whole but that the moving circularly along with the vertigenous diurnal revolution is absolutely natural against which he objecteth saying that according to these mens opinion Si tota terra unà cum aquà in nihilum redigeretur nulla grando aut pluvia è nube decideret sed naturalater tantùm circumferetur neque ignis ullus aut igneum ascenderet cùm illorum non improbabili sententià ignis nullus sit suprà Which I translate to this sense If the whole Earth together with the Water were reduced into nothing no hail or rain would fall from the clouds but would be onely naturally carried round neither any fire or fiery thing would ascend seeing to these that men it is no improbable opinion that there is no fire above SALV The providence of this Philosopher is admirable and worthy of great applause for he is not content to provide for things that might happen the course of Nature continuing but will shew hic care in what may follow from those things that he very well knows shall never come to pass I will grant him therefore that I may get som pretty passages out of him that if the Earth and Water should be reduced to nothing there would be no more hails or rains nor would igneal matters ascend any longer upwards but would continually turn round what will follow what will the Philosopher say then SIMP The objection is in the words which immediately follow here they are Quibus tamen experientia ratio adversatur Which nevertheless saith he is contrary to experience and reason SALV Now I must yield seeing he hath so great an advantage of me as experience of which I am unprovided For as yet I never had the fortune to see the Terrestrial Globe and the element of Water turn'd to nothing so as to have been able to observe what the hail and water did in that little Chaos But he perhaps tells us for our instruction what they did SIMP No he doth not SALV I would give any thing to change a word or two with this person to ask him whether when this Globe vanished it carried away with it the common centre of gravity as I believe it did in which case I think that the hail and water would remain insensate and stupid amongst the clouds without knowing what to do with themselves It might be also that attracted by that great void Vacuum left by the Earths absenting all the ambients would be rarified and particularly the air which is extreme easily drawn and would run thither with very great haste to fill it up And perhaps the more solid and material bodies as birds for there would in all probability be many of them scattered up and down in the air would retire more towards the centre of the great vacant sphere for it
much trouble or difficulty master the roughnesses of these novel and fantastical opinions SALV If that which Gilbert writeth be true then is it no opinion but the subject of Science nor is it new but as antient as the Earth it self nor can it being true be rugged or difficult but plain and easie and when you please I shall make you feel the same in your hand for that you of your self fancy it to be a Ghost and stand in fear of that which hath nothing in it of dreadfull like as a little child doth fear the Hobgoblin without knowing any more of it save the name as that which besides the name is nothing SIMP I should be glad to be informed and reclaimed from an errour SALV Answer me then to the questions that I shall ask you And first of all Tell me whether you believe that this our Globe which we inhabit and call Earth consisteth of one sole and simple matter or else that it is an aggregate of matters different from each other SIMP I see it to be composed of substances and bodies very different and first for the greatest parts of the composition I see the Water and the Earth which extreamly differ from one another SALV Let us for this once lay aside the Seas and other Waters and let us consider the solid parts and tell me if you think them one and the same thing or else different SIMP As to appearance I see that they are different things there being very great heaps of unfruitful sands and others of fruitful soiles There are infinite sharp and steril mountains full of hard stones and quarries of several kinds as Porphyre Alablaster Jasper and a thousand other kinds of Marbles There are vast Minerals of so many kinds of metals and in a word such varieties of matters that a whole day would not suffice only to enumerate them SALV Now of all these different matters do you think that in the composition of this grand masse there do concur portions or else that amongst them all there is one part that far exceeds the rest and is as it were the matter and substance of the immense lump SIMP I believe that the Stones Marbles Metals Gems and the so many other several matters are as it were Jewels and exteriour and superficial Ornaments of the primary Globe which in grosse as I believe doth without compare exceed all these things put together SALV And this principal and vast masse of which those things above named are as it were excressences and ornaments of what matter do you think that it is composed SIMP I think that it is the simple or lesse impure element of Earth SALV But what do you understand by Earth Is it haply that which is dispersed all over the fields which is broke up with Mattocks and Ploughs wherein we sowe corne and plant fruits and in which great boscages grow up without the help of culture and which is in a word the habitation of all animals and the womb of all vegetables SIMP T is this that I would affirm to be the substance of this our Globe SALV But in this you do in my judgment affirm that which is not right for this Earth which is broke up is sowed and is fertile is but one part and that very small of the surface of the Globe which doth not go very deep yea its depth is very small in comparison of the distance to the centre and experience sheweth us that one shall not dig very low but one shall finde matters very different from this exteriour scurf more solid and not good for the production of vegetables Besides the interne parts as being compressed by very huge weights that lie upon them are in all probability slived and made as hard as any hard rock One may adde to this that fecundity would be in vain conferred upon those matters which never were designed to bear fruit but to rest eternally buried in the profound and dark abysses of the Earth SIMP But who shall assure us that the parts more inward and near to the centre are unfruitful They also may perhaps have their productions of things unknown to us SALV You may aswell be assured thereof as any man else as being very capable to comprehend that if the integral bodies of the Universe be produced onely for the benefit of Mankind this above all the rest ought to be destin'd to the sole conveniences of us its inhabitants But what benefit can we draw from matters so hid and remote from us as that we shall never be able to make use of them Therefore the interne substance of this our Globe cannot be a matter frangible dissipable and non-coherent like this superficial part which we call EARTH but it must of necessity be a most dense and solid body and in a word a most hard stone And if it ought to be so what reason is there that should make you more scrupulous to believe that it is a Loadstone than a Porphiry a Jasper or other hard Marble Happily if Gilbert had written that this Globe is all compounded within of Pietra Serena or of Chalcedon the paradox woulâ— have seemed to you lesse exorbitant SIMP That the parts of this Globe more intern are more compressed and so more slived together and solid and more and more so according as they lie lower I do grant and so likewise doth Aristotle but that they degenerate and become other than Earth of the same sort with this of the superficial parts I see nothing that obliegeth me to believe SALV I undertook not this discourse with an intent to prove demonstratively that the primary and real substance of this our Globe is Load-stone but onely to shew that no reason could be given why one should be more unwilling to grant that it is of Load-stone than of some other matter And if you will but seriously consider you shall find that it is not improbable that one sole pure and arbitrary name hath moved men to think that it consists of Earth and that is their having made use commonly from the beginning of this word Earth as well to signifie that matter which is plowed and sowed as to name this our Globe The denomination of which if it had been taken from stone as that it might as well have been taken from that as from the Earth the saying that its primary substance was stone would doubtlesse have found no scruple or opposition in any man And is so much the more probable in that I verily believe that if one could but pare off the scurf of this great Globe taking away but one full thousand or two thousand yards and afterwards seperate the Stones from the Earth the accumulation of the stones would be very much biger than that of the fertile Mould But as for the reasons which concludently prove de facto that is our Globe is a Magnet I have mentioned none of them nor is this a time to alledg
them and the rather for that to your benefit you may read them in Gilbert onely to encourage you to the perusal of them I will set before you in a similitude of my own the method that he observed in his Philosophy I know you understand very well how much the knowledg of the accidents is subservient to the investigation of the substance and essence of things therefore I desire that you would take pains to informe your self well of many accidents and properties that are found in the Magnet and in no other stone or body as for instance of attracting Iron of conferring upon it by its sole presence the same virtue of communicating likewise to it the property of looking towards the Poles as it also doth it self and moreover endeavour to know by trial that it containeth in it a virtue of conferring upon the magnetick needle not onely the direction under a Meridian towards the Poles with an Horizontal motion a property a long time ago known but a new found accident of declining being ballanced under the Meridian before marked upon a little spherical Magnet of declining I say to determinate marks more or lesse according as that needle is held nearer or farther from the Pole till that upon the Pole it self it erecteth perpendicularly whereas in the middle parts it is parallel to the Axis Furthermore procure a proof to be made whether the virtue of attracting Iron residing much more vigorously about the Poles than about the middle parts this force be not notably more vigorous in one Pole than in the other and that in all pieces of Magnet the stronger of which Poles is that which looketh towards the South Observe in the next place that in a little Magnet this South and more vigorous Pole becometh weaker when ever it is to take up an iron in presence of the North Pole of another much bigger Magnet and not to make any tedious discourse of it assertain your self by experience of these and many other properties described by Gilbert which are all so peculiar to the Magnet as that none of them agree with any other matter Tell me now Simplicius if there were laid before you a thousand pieces of several matters but all covered and concealed in a cloth under which it is hid and you were required without uncovering them 〈…〉 a guesse by external signes at the matter of each of them and that in making trial you should hit upon one that should openly shew it self to have all the properties by you already acknowledged to reside onely in the Magnet and in no other matter what judgment would you make of the essence of such a body Would you say that it might be a piece of Ebony or Alablaster o◠Tin SIMP I would say without the least haesitation that it was a piece of Load-stone SALV If it be so say resolutely that under this cover and scurf of Earth stones metals water c. there is hid a great Magnet forasmuch as about the same there may be seen by any one that will heedfully observe the same all those very accidents that agree with a true and visible Globe of Magnet but if no more were to be seen than that of the Declinatory Needle which being carried about the Earth more and more inclineth as it approacheth to the North Pole and declineth lesse towards the Equinoctial under which it finally is brought to an Aequilibrium it might serve to perswade even the most scrupulous judgment I forbear to mention that other admirable effect which is sensibly observed in every piece of Magnet of which to us inhabitants of the Northern Hemisphere the Meridional Pole of the said Magnet is more vigorous than the other and the difference is found greater by how much one recedeth from the Equinoctial and under the Equinoctial both the parts are of equal strength but notably weaker But in the Meridional Regions far distant from the Equinoctial it changeth nature and that part which to us was more weak acquireth more strength than the other and all this I confer with that which we see to be done by a small piece of Magnet in the presence of a great one the vertue of which superating the lesser maketh it to become obedient to it and according as it is held either on this or on that side the Equinoctial of the great one maketh the self same mutations which I have said are made by every Magnet carried on this side or that side of the Equinoctiall of the Earth SAGR. I was perswaded at the very first reading of the Book of Gilbertus and having met with a most excellent piece of Magnet I for a long time made many Observations and all worthy of extream wonder but above all that seemeth to me very stupendious of increasing the faculty of taking up Iron so much by arming it like as the said Authour teacheth and with arming that piece of mine I multiplied its force in octuple proportion and whereas unarmed it scarce took up nine ounces of Iron it being armed did take up above six pounds And it may be you have seen this Loadstone in the Gallery of your Most Serene Grand Duke to whom I presented it upholding two little Anchors of Iron SALV I saw it many times and with great admiration till that a little piece of the like stone gave me greater cause of wonder that is in the keeping of our Academick which being no more than of six ounces weight and sustaining when unarmed hardly two ounces doth when armed take up 160. ounces so as that it is of 80. times more force armed than unarmed and takes up a weight 26. times greater than its own a much greater wonder than Gilbert could ever meet with who writeth that he could never get any Loadstone that could reach to take up four times its own weight SAGR. In my opinion this Stone offers to the wit of man a large Field to Phylosophate in and I have many times thought with my self how it can be that it conferreth on that Iron which armeth it a strength so superiour to its own and finally I finde nothing that giveth me satisfaction herein nor do I find any thing extraordinary in that which Gilbert writes about this particular I know not whether the same may have befallen you SALV I extreamly praise admire and envy this Authour for that a conceit so stupendious should come into his minde touching a thing handled by infinite sublime wits and hit upon by none of them I think him moreover worthy of extraordinary applause for the many new and true Observations that he made to the disgrace of so many fabulous Authours that write not only what they do not know but what ever they hear spoken by the foolish vulgar never seeking to assure themselves of the same by experience perhaps because they are unwilling to diminish the bulk of their Books That which I could have desired in Gilbert is that he had
so between them both compose this our Globe writeth that the seeing the small * particles of water shape themselves into rotundity as in the drops and in the dew daily apparent upon the leaves of several herbs is a strong argument and because according to the trite Axiome there is the same reason for the whole as for the parts the parts affecting that same figure it is necessary that the same is proper to the whole Element and truth is methinks it is a great oversight that these men should not perceive so apparent a vanity and consider that if their argument had run right it would have followed that not only the small drops but that any whatsoever greater quantity of water separated from the whole Element should be reduced into a Globe Which is not seen to happen though indeed the Senses may see and the Understanding perceive that the Element of Water loving to form it self into a Spherical Figure about the common centre of gravity to which all grave bodies tend that is the centre of the Terrestrial Globe it therein is followed by all its parts according to the Axiome so that all the surfaces of Seas Lakes Pools and in a word of all the parts of Waters conteined in vessels distend themselves into a Spherical Figure but that Figure is an arch of that Sphere that hath for its centre the centre of the Terrestrial Globe and do not make particular Spheres of themselves SALV The errour indeed is childish and if it had been onely the single mistake of Sacrobosco I would easily have allowed him in it but to pardon it also to his Commentators and to other famous men and even to Ptolomy himselfe this I cannot do without blushing for their reputation But it is high time to take leave it now being very late and we being to meet again to morrow at the usual hour to bring all the foregoing Discourses to a final conclusion Place this Plate at the end of the third Dialogue GALILAEUS Gailaeus Lyncaeus HIS SYSTEME OF THE WORLD The Fourth Dialogue INTERLOCVTORS SALVIATUS SAGREDUS SIMPLICIUS SAGR. I know not whether your return to our accustomed conferences hath really been later than usual or whether the desire of hearing the thoughts of Salviatus touching a matter so curious hath made me think it so But I have tarried a long hour at this window expecting every moment when the Gondola would appear that I sent to fetch you SALV I verily believe that your imagination more than our tarriance hath prolonged the time and to make no longer demurre it would be well if without interposing more words we came to the matter it self and did shew that nature hath permitted whether the business in rei veritate be so or else to play and sport with our Fancies hath I say hath permitted that the motions for every other respect except to resolve the ebbing and flowing of the Sea assigned long since to the earth should be found now at last to answer exactly to the cause thereof and as it were with mutual a emulation the said ebbing and flowing to appear in confirmation of the Terrestrial motion the judices whereof have hitherto been taken from the coelestial Phaenomena in regard that of those things that happen on Earth not any one was of force to prove one opinion more than another as we already have at large proved by shewing that all the terrene occurrences upon which the stability of the Earth and mobility of the Sun and Firmament is commonly inferred are to seem to us performed in the same manner though we supposed the mobility of the Earth and the immobility of them The Element of Water onely as being most vast and which is not annexed and concatenated to the Terrestrial Globe as all its other solid parts are yea rather which by reason of its fluidity remaineth apart sui juris and free is to be ranked amongst those sublunary things from which we may collect some hinte and intimation of what the Earth doth in relation to motion and rest After I had many and many a time examined with my self the effects and accidents partly seen and partly understood from others that are to be observed in the motions of waters and moreover read and heard the great vanities produced by many as the causes of those accidents I have been induced upon no slight reasons to omit these two conclusions having made withal the necessary presupposals that in case the terrestrial Globe be immoveable the flux and reflux of the Sea cannot be natural and that in case those motions be conferred upon the said Globe which have been long since assigned to it it is necessary that the Sea be subject to ebbing and flowing according to all that which we observe to happen in the same SAGR. The Proposition is very considerable as well for it self as for what followeth upon the same by way of consequence so that I shall the more intensly hearken to the explanation and confirmation of it SALV Because in natural questions of which number this which we have in hand is one the knowledge of the effects is a means to guide us to the investigation and discovery of the causes and without which we should walk in the dark nay with more uncertainty for that we know not whither we would go whereas the blind at least know where they desire to arrive therefore first of all it is necessary to know the effects whereof we enquire the causes of which effects you Sagredus ought more abundantly and more certainly to be informed than I am as one that besides your being born and having for a long time dwelt in Venice where the Tides are very notable for their greatnesse have also sailed into Syria and as an ingenuous and apprehensive wit must needs have made many Observations upon this subject whereas I that could onely for a time and that very short observe what happened in these extream parts of the Adriatick Gulph and in our Seas below about the Tyrrhene shores must needs take many things upon the relation of others who for the most part not very well agreeing and consequently being very uncertain contribute more of confusion than confirmation to our speculations Neverthelesse from those that we are sure of and which are the principal I think I am able to attain to the true and primary causes not that I pretend to be able to produce all the proper and adequate reasons of those effects that are new unto me and which consequently I could never have thought upon And that which I have to say I propose only as a key that openeth the door to a path never yet trodden by any in certain hope that some wits more speculative than mine will make a further progresse herin and penetrate much farther than I shall have done in this my first Discovery And although that in other Seas remote from us there may â—appen several accidents which
do not happen in our Mediterranean Sea yet doth not this invalidate the reason and cause that I shall produce if so be that it verifie and fully resolve the accidents which evene in our Sea for that in conclusion there can be but one true and primary cause of the effects that are of the same kind I will relate unto you therefore the effects that I know to be true and assigne the causes thereof that I think to be true and you also Gentlemen shall produce such others as are known to you besides mine and then we will try whether the cause by me alledged may satisfie them also I therefore affirm the periods that are observed in the fluxes and refluxes of the sea-Sea-waters to be three the first and principal is this great and most obvious one namely the diurnal according to which the intervals of some hours with the waters flow and ebbe and these intervals are for the most part in the Mediterrane from six hours to six hours or thereabouts that is they for six hours flow and for six hours ebbe The second period is monethly and it seemes to take its origen from the motion of the Moon not that it introduceth other motions but only altereth the greatnesse of those before mentioned with a notable difference according as it shall wax or wane or come to the Quadrature with the Sun The third Period is annual and is seen to depend on the Sunne and onely altereth the diurnal motions by making them different in the times of the Solstices as to greatnesse from what they are in the Equinoxes We will speak in the first place of the diurnal motion as being the principal and upon which the Moon and Sun seem to exercise their power secondarily in their monethly and annual alterations Three differences are observable in these horary mutations for in some places the waters rise and fall without making any progressive motion in others without rising or falling they run one while towards the East and recur another while towards the West and in others they vary the heights and course also as happeneth here in Venice where the Tides in coming in rise and in going out fall and this they do in the extermities of the lengths of Gulphs that distend from West to East and terminate in open shores up along which shores the Tide at time of flood hath room to extend it self but if the course of the Tide were intercepted by Cliffes and Banks of great height and steepnesse there it will flow and ebbe without any progressive motion Again it runs to and again without changing height in the middle parts of the Mediterrane as notably happeneth in the Faro de Messina between Scylla and Carybdis where the Currents by reason of the narrownesse of the Channel are very swift but in the more open Seas and about the Isles that stand farther into the Mediterranean Sea as the Baleares Corsica Sardignia Elba Sicily towards the Affrican Coasts Malta Candia c. the changes of watermark are very small but the currents indeed are very notable and especially when the Sea is pent between Islands or between them and the Continent Now these onely true and certain effects were there no more to be observed do in my judgment very probably perswade any man that will contain himself within the bounds of natural causes to grant the mobility of the Earth for to make the vessel as it may be called of the Mediterrane stand still and to make the water contained therein to do as it doth exceeds my imagination and perhaps every mans else who will but pierce beyond the rinde in these kind of inquiries SIMP These accidents Salviatus begin not now they are most ancient and have been observed by very many and several have attempted to assigne some one some another cause for the same and there dwelleth not many miles from hence a famous Peripatetick that alledgeth a cause for the same newly fished out of a certain Text of Aristotle not well understood by his Expositors from which Text he collecteth that the true cause of these motions doth only proceed from the different profundities of Seas 〈…〉 waters of greatest depth being greater in abundance and therefore more grave drive back the Waters of lesse depth which being afterwards raised desire to descend and from this continual colluctation or contest proceeds the ebbing and flowing Again those that referre the same to the Moon are many saying that she hath particular Domination over the Water and at last a certain Prelate hath published a little Treatise wherâ—in he saith that the Moon wandering too and fro in the Heavens attracteth and draweth towards it a Masse of Water which goeth continually following it so that it is full Sea alwayes in that part which lyeth under the Moon and because that though she be under the Horizon yet neverthelesse the Tide returneth he saith that no more can be said for the salving of that particular save onely that the Moon doth not onely naturally retain this faculty in her self but in this case hath power to confer it upon that degree of the Zodiack that is opposite unto it Others as I believe you know do say that the Moon is able with her temperate heat to rarefie the Water which being rarefied doth thereupon flow Nor hath there been wanting some that SAGR. I pray you Simplicius let us hear no more of them for I do not think it is worth the while to wast time in relating them or to spend our breath in confuting them and for your part if you gave your assent to any of these or the like fooleâ—ies you did a great injury to your judgment which neverthelesse I acknowledg to be very piercing SALV But I that am a little more flegmatick than you Sagredus will spend a few words in favour of Simplicius if haply he thinks that any probability is to be found in those things that he hath related I say therefore The Waters Simplicius that have their exteriour superficies higher repel those that are inferiour to them and lower but so do not those Waters that are of greatest profundity and the higher having once driven back the lower they in a short time grow quiet and level This your Peripatetick must needs be of an opinion that all the Lakes in the World that are in a calme and that all the Seas where the ebbing and flowing is insensible are level in their bottoms but I was so simple that I perswaded my self that had we no other plummet to sound with the Isles that advance so high above Water had been a sufficient evidence of the unevennesse of their bottomes To that Prelate I could say that the Moon runneth every day along the whole Mediterrane and yet its Waters do not rise thereupon save onely in the very extream bounds of it Eastward and here to us at Venice And for those that make the Moons
temperate heat able to make the Water swell bid them put fire under a Kettle full of Water and hold their right hand therein till that the Water by reason of the heat do rise but one sole inch and then let them take it out and write off the tumefaction of the Sea Or at least desire them to shew you how the Moon doth to rarefie a certain part of the Waters and not the remainder as for instance these here of Venice and not those of Ancona Naples Genova the truth is Poetick Wits are of two kinds some are ready and apt to invent Fables and others disposed and inclined to believe them SIMP I believe that no man believeth Fables so long as he knows them to be so and of the opinions concerning the causes of ebbing and flowing which are many because I know that of one single effect there is but one single cause that is true and primary I understand very well and am certain that but one alone at the most can be true and for all the rest I am sure that they are fabulous and false and its possible that the true one may not be among those that have been hitherto produced nay I verily believe that it is not for it would be very strange that the truth should have so little light as that it should not be visible amongst the umbrages of so many falshoods But this I shall say with the liberty that is permitted amongst us that the introduction of the Earths motion and the making it the cause of the ebbing and flowing of Tides seemeth to me as yet a conjecture no lesse fabulous than the rest of those that I have heard and if there should not be proposed to me reasons more conformable to natural matters I would without any more ado proceed to believe this to be a supernatural effect and therefore miraculous and unsearchable to the understandings of men as infinite others there are that immediately depend on the Omnipotent hand of God SAGR. You argue very prudently and according to the Doctrine of Aristotle who you know in the beginning of his mechanical questions referreth those things to a Miracle the causes whereof are occult But that the cause of the ebbing and flowing is one of those that are not to be found out I believe you have no greater proof than onely that you see that amongst all those that have hitherto been produced for true causes thereof there is not one wherewith working by what artifice you will we are able to represent such an effect in regard that neither with the light of the Moon nor of the Sun nor with temperate heats nor with different profundities shall one ever artificially make the Water conteined in an immoveable Vessel to run one way or another and to ebbe and flow in one place and not in another But if without any other artifice but with the onely moving of the Vessel I am able punctually to represent all those mutations that are observed in the Sea Water why will you refuse this reason and run to a Miracle SIMP I will run to a Miracle still if you do not with some other natural causes besides that of the motion of the Vessels of the Sea-water disswade me from it for I know that those Vessels move not in regard that all the entire Terrestrial Globe is naturally immoveable SALV But do not you think that the Terrestrial Globe might supernaturally that is by the absolute power of God be made moveable SIMP Who doubts it SALV Then Simplicius seeing that to make the flux and reflux of the Sea it is necessary to introduce a Miracle let us suppose the Earth to move miraculously upon the motion of which the Sea moveth naturally and this effect shall be also the more simple and I may say natural amongst the miraculous operations in that the making a Globe to move round of which kind we see many others to move is lesse difficult than to make an immense masse of water go forwards and backwards in one place more swiftly and in another lesse and to rise and fall in some places more in some lesse and in some not at all and to work all these different effects in one and the same Vessel that containeth it besides that these are several Miracles and that is but one onely And here it may be added that the Miracle of making the water to move is accompanied with another namely the holding of the Earth stedfast against impetuosities of the water able to make it swage sometimes one way and sometimes another if it were not miraculously kept to rights SAGR. God Simplicius let us for the present suspend our judgement about sentencing the new opinion to be vain that Salviatus is about to explicate unto us nor let us so hastily flye out into passion like the scolding overgrown Haggs and as for the Miracle we may as well recurre to it when we have done hearing the Discourses contained within the bounds of natural causes though to speak freely all the Works of nature or rather of God are in my judgement miraculous SALV And I am of the same opinion nor doth my saying that the motion of the Earth is the Natural cause of the ebbing and flowing hinder but that the said motion of the Earth may be miraculous Now reassuming our Argument I apply and once again affirm that it hath been hitherto unknown how it might be that the Waters contained in our Mediterranean Straights should make those motions as we see it doth if so be the said Straight or containing Vessel were immoveable And that which makes the difficulty and rendreth this matter inextricable are the things which I am about to speak of and which are daily observed Therefore lend me your attention We are here in Venice where at this time the Waters are low the Sea calm the Air tranquil suppose it to be young flood and that in the term of five or six hours the water do rise ten hand breadths and more that rise is not made by the first water which was said to be rarefied but it is done by the accession of new Water Water of the same sort with the former of the same brackishness of the same density of the same weight Ships Simplicius float therein as in the former without drawing an hairs breadth more water a Barrel of this second doth not weigh one single grain more or less than such another quantity of the other and retaineth the same coldness without the least alteration And it is in a word Water newly and visibly entred by the Channels and Mouth of the Lio. Consider now how and from whence it came thither Are there happly hereabouts any Gulphs or Whirle-pools in the bottom of the Sea by which the Earth drinketh in and spueth out the Water breathing as it were a great and monstruous Whale But if this be so how comes it that the Water doth not flow in
is ceased but by vertue of its own gravity and natural inclination to level and grow even it shall speedily return backwards of its own accord and as being grave and fluid shall not only move towards Aequilibrium but being impelled by its own impetus shall go beyond it rising in the part where before it was lowest nor shall it stay here but returning backwards anew with more reiterated reciprocations of its undulations it shall give us to know that it will not from a velocity of motion once conceived reduce it self in an instant to the privation thereof and to the state of rest but will successively by decreasing a little and a little reduce it self unto the same just in the same manner as we see a weight hanging at a cord after it hath been once removed from its state of rest that is from its perpendicularity of its own accord to return thither and settle it self but not till such time as it shall have often past to one side and to the other with its reciprocall vibrations The second accident to be observed is that the before-declared reciprocations of motion come to be made and repeated with greater or lesser frequency that is under shorter or longer times according to the different lengths of the Vessels containing the waters so that in the shorter spaces the reciprocations are more frequent and in the longer more rare just as in the former example of pendent bodies the vibrations of those that are hanged to longer cords are seen to be lesse frequent than those of them that hang at shorter strings And here for a third observation it is to be noted that not onely the greater or lesser length of the Vessel is a cause that the water maketh its reciprocations under different times but the greater or lesser profundity worketh the same effect And it happeneth that of waters contained in receptacles of equall length but of unequal depth that which shall be the deepest maketh its undulations under shorter times and the reciprocations of the shallower waters are lesse frequent Fourthly there are two effects worthy to be noted and diligently observed which the water worketh in those its vibrations the one is its rising and falling alternately towards the one and other extremity the other is its moving and running to so speak Horizontally forwards and backwards Which two different motions differently reside in divers parts of the Water for its extream parts are those which most eminently rise and fall those in the middle never absolutely moving upwards and downwards of the rest successively those that are neerest to the extreams rise and fall proportionally more than the remote but on the contrary touching the other progressive motion forwards and backwards the middle parts move notably going and returning and the waters that are in the extream parts gain no ground at all save onely in case that in their rising they overflow their banks and break forth of their first channel and receptacle but where there is the obstacle of banks to keep them in they onely rise and fall which yet hindereth not the waters in the middle from fluctuating to and again which likewise the other parts do in proportion undulating more or lesse according as they are neerer or more remote from the middle The fifth particular accident ought the more attentively to be considered in that it is impossible to represent the effect thereof by an experiment or example and the accident is this In the vessels by us framed with art and moved as the above-named Bark one while more and another while lesse swiftly the acceleration and retardation is imparted in the same manner to all the vessel and to every part of it so that whilst v. g. the Bark forbeareth to move the parts precedent retard no more than the subsequent but all equally partake of the same retardment and the self-same holds true of the acceleration namely that conferring on the Bark a new cause of greater velocity the Prow and Poop both accelerate in one and the same manner But in huge great vessels such as are the very long bottomes of Seas albeit they also are no other than certain cavities made in the solidity of the Terrestrial Globe it alwayes admirably happeneth that their extreams do not unitedly equall and at the same moments of time increase and diminish their motion but it happeneth that when one of its extreames hath by vertue of the commixtion of the two Motions Diurnal and Annual greatly retarded its velocity the other extream is animated with an extream swift motion Which for the better understanding of it we will explain reassuming a Scheme like to the former in which if we do but suppose a tract of Sea to be long v. g. a fourth part as is the arch B C in Fig. 2. because the parts B are as hath been already declared very swift in motion by reason of the union of the two motions diurnal and annual towards one and the same way but the part C at the same time is retarded in its motion as being deprived of the progression dependant on the diurnal motion If we suppose I say a tract of Sea as long as the arch B C we have already seen that its extreams shall move in the same time with great inequality And extreamly different would the velocities of a tract of Sea be that is in length a semicircle and placed in the position B C D in regard that the extream B would be in a most accelerate motion and the other D in a most slow one and the intermediate parts towards C would be in a moderate motion And according as the said tracts of Sea shall be shorter they shall lesse participate of this extravagant accident of being in some hours of the day with their parts diversly affected by velocity and tardity of motion So that if as in the first case we see by experience that the acceleration and retardation though equally imparted to all the parts of the conteining Vessel is the cause that the water contained fluctuates too and again what may we think would happen in a Vessel so admirably disposed that retardation and acceleration of motion is very unequally contributed to its parts Certainly we must needs grant that greater and more wonderful causes of the commotions in the Water ought to be looked for And though it may seem impossible to some that in artificial Machines and Vessels we should be able to experiment the effects of such an accident yet neverthelesse it is not absolutely impossible to be done and I have by me the model of an Engine in which the effect of these admirable commixtions of motions may be particularly observed But as to what concerns our present purpose that which you may have hitherto comprehended with your imagination may suffice SAGR. I for my own particular very well conceive that this admirable accident ought necessarily to evene in the Straights of Seas and especially
the Isles of Corsica and Sardinnia and in the Strands of Rome and Ligorne where it exceeds not half a foot we shall understand also why on the contrary where the risings and fallings are small the courses and recourses are great I say it is an easie thing to understand the causes of these accidents seeing that we meet with many manifest occurrences of the same nature in every kind of Vessel by us artificially composed in which the same effects are observed naturally to follow upon our moving it unevenly that is one while faster and another while flower Moreover considering in the fifth place that the same quantity of Water being moved though but gently in a spatious Channel comming afterwards to go through a narrow passage will of necessity run with great violence we shall not finde it hard to comprehend the cause of the great Currents that are made in the narrow Channel that separateth Calabria from Sicilia for that all the Waters that by the spaciousnesse of the Isle and by the Ionick Gulph happens to be pent in the Eastern part of the Sea though it do in that by reason of its largeness gently descend towards the West yet neverthelesse in that it is pent up in the Bosphorus it floweth with great violence between Scilla and Caribdis and maketh a great agitation Like to which and much greater is said to be betwixt Africa and the great Isle of St. Lorenzo where the Waters of the two vast Seas Indian and Ethiopick that lie round it must needs be straightned into a lesse Channel between the said Isle and the Ethiopian Coast. And the Currents must needs be very great in the Straights of Megallanes which joyne together the vast Oceans of Ethiopia and Del Zur called also the Pacifick Sea It follows now in the sixth place that to render a reason of some more abstruse and incredible accidents which are observed upon this occasion we make a considerable reflection upon the two principal causes of ebbings and flowings afterwards compounding and mixing them together The first and simplest of which is as hath often been said the determinate acceleration and retardation of the parts of the Earth from whence the Waters have a determinate period put to their decursions towards the East and return towards the West in the time of twenty four hours The other is that which dependeth on the proper gravity of the Water which being once commoved by the primary cause seeketh in the next place to reduce it self to Aequilibrium with iterated reciprocations which are not determined by one sole and prefixed time but have as many varieties of times as are the different lengths and profundities of the receptacles and Straights of Seas and by what dependeth on this second principle they would ebbe and flow some in one hour others in two in four in six in eight in ten c. Now if we begin to put together the first cause which hath its set Period from twelve hours to twelve hours with some one of the secondary that hath its Period verb. grat from five hours to five hours it would come to passe that at sometimes the primary cause and secondary would accord to make impulses both one the same way and in this concurrency and as one may call it unanimous conspiration the flowings shall be great At other times it happening that the primary impulse doth in a certain manner oppose that which the secondary Period would make and in this contest one of the Principles being taken away that which the other would give will weaken the commotion of the Waters and the Sea will return to a very tranquil State and almost immoveable And at other times according as the two aforesaid Principles shall neither altogether contest nor altogether concur there shall be other kinds of alterations made in the increase and diminution of the ebbing and flowing It may likewise fall out that two Seas considerably great and which communicate by some narrow Channel may chance to have by reason of the mixtion of the two Principles of motion one cause to flow at the time that the other hath cause to move a contrary way in which case in the Channel whereby they disimbogue themselves into each other there do extraordinary conturbations insue with opposite and vortick motions and most dangerous boilings and breakings as frequent relations and experiences do assure us From such like discordant motions dependent not onely on the different positions and longitudes but very much also upon the different profundities of the Seas which have the said intercourse there do happen at sometimes different commotions in the Waters irregular and that can be reduced to no rules of observation the reasons of which have much troubled and alwayes do trouble Mariners for that they meet with them without seeing either impulse of winds or other eminent aereal alteration that might occasion the same of which disturbance of the Air we ought to make great account in other accidents and to take it for a third and accidental cause able to alter very much the observation of the effects depending on the secondary and more essential causes And it is not to be doubted but that impetuous windes continuing to blow for example from the East they shall retein the Waters and prohibit the reflux or ebbing whereupon the second and third reply of the flux or tide overtaking the former at the hours prefixed they will swell very high and being thus born up for some dayes by the strength of the Winds they shall rise more than usual making extraordinary inundations We ought also and this shall serve for a seventh Probleme to take notice of another cause of motion dependant on the great abundance of the Waters of great Rivers that discharge themselves into Seas of no great capacity whereupon in the Straits or Bosphori that communicate with those Seas the Waters are seen to run always one way as it happeneth in the Thracian Bosphorus below Constantinople where the water alwayes runneth from the Black-Sea towards the Propontis For in the said Black-Sea by reason of its shortnesse the principal causes of ebbing and flowing are but of small force But on the contrary very great Rivers falling into the same those huge defluxions of water being to passe and disgorge themselves by the the straight the course is there very notable and alwayes towards the South Where moreover we ought to take notice that the said Straight or Channel albeit very narrow is not subject to perturbations as the Straight of Scilla and Carybdis for that that hath the Black-Sea above towards the North and the Propontis the Aegean and the Mediterranean Seas joyned unto it though by a long tract towards the South but now as we have observed the Seas though of never so great length lying North and South are not much subject to ebbings and flowings but because the Sicilian Straight is situate between the parts of the Mediterrane distended
for a long tract or distance from West to East that is according to the course of the fluxes and refluxes therefore in this the agitations are very great and would be much more violent between Hercules Pillars in case the Straight of Gibraltar did open lesse and those of the Straight of Magellanes are reported to be extraordinary violent This is what for the present cometh into my mind to say unto you about the causes of this first period diurnal of the Tide and its various accidents touching which if you have any thing to offer you may let us hear it that so we may afterwards proceed to the other two periods monethly and annual SIMP In my opinion it cannot be denied but that your discourse carrieth with it much of probability arguing as we say ex suppositione namely granting that the Earth moveth with the two motions assigned it by Copernicus but if that motion be disproved all that you have said is vain and insignificant and for the disproval of that Hypothesis it is very manifestly hinted by your Discourse it self You with the supposition of the two Terrestrial motions give a reason of the ebbing and flowing and then again arguing circularly from the ebbing and flowing draw the reason and confirmation of those very motions and so proceeding to a more specious Discourse you say that the Water as being a fluid body and not tenaciously annexed to the Earth is not constrained punctually to obey every of its motions from which you afterwards infer its ebbing and flowing Now I according to your own method argue the quite contrary and say the Air is much more tenuous and fluid than the Water and lesse annexed to the Earths superficies to which the Water if it be for nothing else yet by reason of its gravity that presseth down upon the same more than the light Air adhereth therefore the Air is much obliged to follow the motions of the Earth and therefore were it so that the Earth did move in that manner we the inhabitants of it and carried round with like velocity by it ought perpetually to feel a Winde from the East that beateth upon us with intolerable force And that so it ought to fall out quotidian experience assureth us for if with onely riding post at the speed of eight or ten miles an hour in the tranquil Air the incountering of it with our face seemeth to us a Winde that doth not lightly blow upon us what should we expect from our rapid course of 800. or a thousand miles an hour against the Air that is free from that motion And yet notwithstanding we cannot perceive any thing of that nature SALV To this objection that hath much of likelihood in it I reply that its true the Air is of greater tenuity and levity and by reason of its levity lesse adherent to the Earth than Water so much more grave and bulky but yet the consequence is false that you infer from these qualities namely that upon account of that its levity tenuity and lesse adherence to the Earth it should be more exempt than the Water from following the Terrestrial Motions so as that to us who absolutely pertake of of them the said exemption should be sensible and manifest nay it happeneth quite contrary for if you well remember the cause of the ebbing and flowing of the Water assigned by us consisteth in the Waters not following the unevennesse of the motion of its Vessel but retaining the impetus conceived before without diminishing or increasing it according to the precise rate of its diminishing or increasing in its Vessel Because therefore that in the conservation and retention of the impetus before conceived the disobedience to a new augmentation or diminution of motion consisteth that moveable that shall be most apt for such a retention shall be also most commodious to demonstrate the effect that followeth in consequence of that retention Now how much the Water is disposed to maintain such a conceived agitation though the causes cease that impress the same the experience of the Seas extreamly disturbed by impetuous Winds sheweth us the Billows of which though the Air be grown calm and the Wind laid for a long time after continue in motion As the Sacred Poet pleasantly sings Qual l'alto Egeo c. And that long continuing rough after a storm dependeth on the gravity of the water For as I have elsewhere said light bodies are much easier to be moved than the more grave but yet are so much the less apt to conserve the motion imparted when once the moving cause ceaseth Whence it comes that the Aire as being of it self very light and thin is easily mov'd by any very small force yet it is withall very unable to hold on its motion the Mover once ceasing Therefore as to the Aire which environs the Terrestrial Globe I would fay that by reason of its adherence it is no lesse carried about therewith then the Water and especially that part which is contained in its vessels which vessels are the valleys enclosed with Mountains And we may with much more reason affirm that this same part of the Air is carried round and born forwards by the rugged parts of the Earth than that the higher is whirl'd about by the motion of the Heavens as ye Peripateticks maintain What hath been hitherto spoken seems to me a sufficient answer to the allegation of Simplitius yet nevertheless with a new instance and solution founded upon an admirable experiment I will superabundantly satisfie him and confirm to Sagredus the mobility of the Earth I have told you that the Air and in particular that part of it which ascendeth not above the tops of the highest Mountains is carried round by the uneven parts of the Earths surface from whence it should seem that it must of consequence come to passe that in case the superficies of the Earth were not uneven but smooth and plain no cause would remain for drawing the Air along with it or at least for revolving it with so much uniformity Now the surface of this our Globe is not all craggy and rugged but there are exceeding great tracts very even to wit the surfaces of very vast Seas which being also far remote from the continuate ledges of Mountains which environ it seem to have no faculty of carrying the super-ambient Air along therewith and not carrying it about we may perceive what will of consequence ensue in those places SIMP I was about to propose the very same difficulty which I think is of great validity SALV You say very well Simplicius for from the not finding in the Air that which of consequence would follow did this our Globe move round you argue its immoveablenesse But in case that this which you think ought of necessary consequence to be found be indeed by experience proved to be so will you accept it for a sufficient testimony and an argument for the mobility of
the said Globe SIMP In this case it is not requisite to argue with me alone for if it should so fall out and that I could not comprehend the cause thereof yet haply it might be known by others SALV So that by playing with you a man shall never get but be alwayes on the losing hand and therefore it would be better to give over Nevertheless that we may not cheat our third man we will play on We said even now and with some addition we reitterate it that the Ayr as if it were a thin and fluid body and not solidly conjoyned with the Earth seem'd not to be necessitated to obey its motion unlesse so far as the cragginess of the terrestrial superficies transports and carries with it a part thereof contigious thereunto which doth not by any great space exceed the greatest altitude of Mountains the which portion of Air ought to be so much less repugnant to the terrestrial conversion by how much it is repleat with vapours fumes and exhalations matters all participating of terrene qualities and consequently apt of their own nature to the same motions But where there are wanting the causes of motion that is where the surface of the Globe hath great levels and where there is less mixture of the terrene vapours there the cause whereby the ambient Air is constrained to give entire obedience to the terrestrial conversion will cease in part so that in such places whilst the Earth revolveth towards the East there will be continually a wind perceived which will beat upon us blowing from the East towards the West and such gales will be the more sensible where the revolution of the Globe is most swift which will be in places more remote from the Poles and approaching to the greatest Circle of the diurnal conversion But now de facto experience much confirmeth this Phylosophical argumentation for in the spatious Seas and in their parts most remote from Land and situate under the Torrid Zone that is bounded by the Tropicks where there are none of those same terrestrial evaporations we finde a perpetual gale move from the East with so constant a blast that ships by favour thereof sail prosperously to the West-India's And from the same coasting along the Mexican shore they with the same felicity pass the Pacifick Ocean towards the India's which to us are East but to them are West Whereas on the contrary the Course from thence towards the East is difficult and uncertain and not to be made by the same Rhumb but must vere more to Land-ward to recover other Winds which we may call accidentary and tumultuary produced from other Principles as those that inhabit the continent find by experience Of which productions of Winds the Causes are many and different which shall not at this time be mentioned And these accidentary Winds are those which blow indifferently from all parts of the Earth and make rough the Seas remote from the Equinoctial and environed by the rugged Surface of the Earth which is as much as to say environ'd with those perturbations of Air that confound that primary Gale The which in case these accidental impediments were removed would be continually felt and especially upon the Sea Now see how the effect of the Water and Air seem wonderfully to accord with the Celestial observations to confirm the mobility of our Terrestrial Globe SAGR. I also for a final close will relate to you one particular which as I believe is unknown unto you and which likewise may serve to confirm the same conclusion You Salviatus alledged That Accident which Sailers meet with between the Tropicks I mean that perpetual Gale of Winde that beats upon them from the East of which I have an account from those that have many times made the Voyage And moreover which is very observable I understand that the Mariners do not call it a Wind but by another name which I do not now remember taken haply from its so fixed and constant Tenor which when they have met with they tie up their shrouds and other cordage belonging to the Sails and without any more need of touching them though they be in a sleep they can continue their course Now this constant Trade-wind was known to be such by its continual blowing without interruptions for if it were interrupted by other Windes it would not have been acknowledged for a singular Effect and different from the rest from which I will infer That it may be that also our Mediterranean Sea doth partake of the like accident but it is not observed as being frequently altered by the confluence of other windes And this I say not without good grounds yea upon very probable conjectures whch came unto my knowledge from that which tendred it self to my notice on occasion of the voyage that I made into Syria going Consul for this Nation to Aleppo and this it is That keeping a particular account and memorial of the dayes of the departure and arrival of the Ships in the Ports of Alexandria of Alexandretta and this of Venice in comparing sundry of them which I did for my curiosity I found that in exactness of account the returns hither that is the voiages from East to West along the Mediterrane are made in less time then the contrary courses by 25. in the Hundred So that we see that one with another the Eastern windes are stronger then the Western SALV I am very glad I know this particular which doth not a little make for the confirmation of the Earths mobility And although it may be alledged That all the Water of the Mediterrane runs perpetually towards the Straits-mouth as being to disimbogue into the Ocean the waters of as many Rivers as do discharge themselves into the same I do not think that that current can be so great as to be able of it self alone to make so notable a difference which is also manifest by observing that the water in the Pharo of Sicily runneth back again no less towards the East than it runneth forwards towards the West SAGR. I that have not as Simplicius an inclination to satisfie any one besides my self am satisfied with what hath been said as to this first particular Therefore Salviatus when you think it sit to proceed forward I am prepared to hear you SALV I shall do as you command me but yet I would fain hear the opinion also of Simplicius from whose judgement I can argue how much I may promise to my self touching these discourses from the Peripatetick Schools if ever they should come to their ears SIMP I desire not that my opinion should serve or stand for a measure whereby you should judge of others thoughts for as I have often said I am inconsiderable in these kinde of studies and such things may come into the mindes of those that are entered into the deepest passages of Philosophy as I could never think of as having according to the Proverb
of the ebbing and flowing you must finde and give us some reason why it doth in the self same place run one while one way and another while another Effects that being contrary irregular can never be deduced from any uniform and constant Cause And this Argument that overthrows the Hypothesis of the motion contributed to the Sea from the Heavens diurnal motion doth also confute that Position of those who would admit the sole diurnal motion of the Earth and believe that they are able with that alone to give a reason of the Flux and Reflux Of which effect since it is irregular the cause must of necessity be irregular and alterable SIMP I have nothing to reply neither of my own by reason of the weakness of my understanding nor of that of others for that the Opinion is so new But I could believe that if it were spread amongst the Schools there would not want Phylosophers able to oppose it SAGR. Expect such an occasion and we in the mean time if it seem good to Salviatus will proceed forward SALV All that which hath been said hitherto pertaineth to the diurnal period of the ebbing and flowing of which we have in the first place demonstrated in general the primary and universal Cause without which no such effect would follow Afterwâ—â—ds passing to the particular Accidents various and in a certain sort irregular that are observed therein We have handled the secondary and concommitant Causes upon which they depend Now follow the two other Periods Monethly and Annual which do not bring with them new and different Accidents other than those already considered in the diurnal Period but they operate on the same Accidents by rendring them greater and lesser in several parts of the Lunar Moneth and in several times of the Solar Year as if that the Moon and Sun did each conceive it self apart in operating and producing of those Effects a thing that totally clasheth with my understanding which seeing how that this of Seas is a local and sensible motion made in an immense mass of Water it cannot be brought to subscribe to Lights to temperate Heats to predominacies by occult Qualities and to such like vain Imaginations that are so far from being or being possible to be Causes of the Tide that on the contrary the Tide is the cause of them that is of bringing them into the brains more apt for loquacity and ostentation than for the speculation and discovering of the more abstruse secrets of Nature which kind of people before they can be brought to pronounce that wise ingenious and modest sentence I know it not suffer to escape from their mouths and pens all manner of extravagancies And the onely observing that the same Moon and the same Sun operate not with their light with their motion with great heat or with temperate on the lesser reeeptaclâ—s of Water but that to effect their flowing by heat they must be reduced to little lesse than boiling and in short we not being able artificially to imitate any way the motions of the Tide save only by the motion of the Vessel ought it not to satisfie every one that all the other things alledged as causes of those effects are vaine fancies and altogether estranged from the Truth I say therefore that if it be true that of one effect there is but one sole primary cause and that between the cause and effect there is a firm and constant connection it is necessary that whensoever there is seen a firm and constant alteration in the effect there be a firm and constant alteration in the cause And because the alterations that happen in the ebbing and flowing in several parts of the Year and Moneths have their periods firm and constant it is necessary to say that a regular alteration in those same times happeneth in the primary cause of the ebbings and flowings And as for the alteration that in those times happens in the ebbings and flowings consisteth onely in their greatness that is in the Waters rising and falling more or lesse and in running with greater or lesse impetus therefore it is necessary that that which is the primary cause of the ebbing and flowing doth in those same determinate times increase and diminish its force But we have already concluded upon the inequality and irregularity of the motion of the Vessels containing the Water to be the primary cause of the ebbings and flowings Therefore it is necessary that that irregularity from time to time correspondently grow more irregular that is grow greater and lesser Now it is requisite that we call to minde that the irregularity that is the different velocity of the motions of the Vessels to wit of the parts of the Terrestrial Superficies dependeth on their moving with a compound motion resulting from the commixtion of the two motions Annual and Diurnal proper to the whole Terrestrial Globe of which the Diurnal conversion by one while adding to and another while substracting from the Annual motion is that which produceth the irregularity in the compound motion so that in the additions and substractions that the Diurnal revolution maketh from the Annual motion consisteth the original cause of the irregular motion of the Vessels and consequently of the Ebbing and Flowing insomuch that if these additions and substractions should alwayes proceed in the same proportion in respect of the Annual motion the cause of the Ebbing and Flowing would indeed continue but yet so as that they would perpetually return in the self same manner But we are to finde out the cause of making the same Ebbings and Flowings in divers times greater and lesser Therefore we must if we will retain the identity of the cause find the alteration in these additions and substractions that make them more less potent in producing those effects which depend thereupon But I see not how that potency and impotence can be introduced unlesse by making the same additions and substractions one while greater and another while lesser so that the acceleration and the retardment of the compound motion may be made sometimes in greater and sometimes in lesser proportion SAGR. I feel my self very gently led as it were by the hand and though I finde no rubs in the way yet neverthelesse like a blind man I see not whether your Clue leadeth me nor can I imagine where such a Journey will end SALV Though there be a great difference between my slow pac't Philosophy and your more nimble Reason yet neverthelesse in this particular which we are now upon I do not much wonder if the apprehensivenesse of your wit be a little obscured by the dark and thick mist that hides the mark at which we aime and that which lesseneth my admiration is the remembrance of the many hours many dayes yea more many nights that I have consumed in this contemplation and of the many times that despairing to bring it to a period I have for an incouragement of my self
haply many others also undiscovered It is to be supposed that the first observers of Heaven knew no more but one motion common to all the Stars as is this diurnal one yet I believe that in few dayes they perceived that the Moon was inconstant in keeping company with the other Stars but yet withal that many years past before that they distinguished all the Planets And in particular I conceit that Saturn by its slowness and Mercury by reason of its seldom appearing were the last that were observed to be wandring and errant It is to be thought that many more years run out before the statioâ—s and retrogradations of the three superiour Planets were known as also their approximations and recessions from the Earth necessary occasions of introducing the Eccentrix and Epicicles things unknown even to Aristotle for that he makes no mention thereof Mercury and Venus with their admirable apparitions how long did they keep Astronomers in suspence before that they could resolve not to speak of any other of their qualities upon their situation Insomuch that the very order onely of the Mundane bodies and the integral structure of the parts of the Universe by us known hath been doubted of untill the time of Copernicus who hath at last given us notice of the true constitution and real systeme according to which those parts are disposed so that at length we are certain that Mercury Venus and the other Planets do revolve about the Sun and that the Moon revolveth about the Earth But how each Planet governeth it self in its particular revolution and how precisely the structure of its Orb is framed which is that which is vulgarly called the Theory of the Planets we cannot as yet undoubtedly resolve Mars that hath so much puzled our Modern Astronomers is a proof of this And to the Moon her self there have been assigned several Theories after that the said Copernicus had much altered it from that of Ptolomy And to descend to our particular case that is to say to the apparent motion of the Sun and Moon touching the former there hath been observed a certain great irregularity whereby it passeth the two semicircles of the Ecliptick divided by the points of the Equinoxes in very different times in passing one of which it spendeth about nine dayes more than in passing the other a difference as you see very great and notable But if in passing small arches such for example as are the twelve Signs he maintain a most regular motion or else proceed with paces one while a little more swift and another more slow as it is necessary that it do in case the annual motion belong to the Sun onely in appearance but in reality to the Earth in company with the Moon it is what hath not hitherto been observed nor it may be sought Touching the Moon in the next place whose restitutions have been principally lookt into an account of the Eclipses for which it is sufficient to have an exact knowledge of its motion about the Earth it hath not been likewise with a perfect curiosity inquired what itâ— course is thorow the particular arches of the Zodiack That therefore the Earth and Moon in running through the Zodiack that is round the Grand Orb do somewhat accellerate at the Moons change and retard at its full ought not to be doubted for that the said difference is not manifest which cometh to be unobserved upon two accounts First Because it hath not been lookt for Secondly Because that its possible it may not be very great Nor is there any need that it should be great for the producing the effect that we see in the alteration of the greatness of ebbings and flowings For not onely those alterations but the Tides themselves are but small matters in respect of the grandure of the subjects on which they work albeit that to us and to our littleness they seem great For the addition or subduction of one degree of velocity where there are naturally 700 or 1000 can be called no great alteration either in that which conferreth it or in that Which receiveth it the Water of our Mediterrane carried about by the diurnal revolution maketh about 700 miles an hour which is the motion common to the Earth and to it and therefore not perceptible to us that which we sensibly discern to be made in the streams or currents is not at the rate of full one mile an hour I speak of the main Seas and not of the Straights and this is that which altereth the first naturall and grand motion and this motion is very great in respect of us and of Ships for a Vessel that in a standing Water by the help of Oares can make v. g. three miles an hour in that same current will row twice as far with the stream as against it A notable difference in the motion of the Boat though but very small in the motion of the Sea which is altered but its seven hundredth part The like I say of its rising and falling one two or three feet and scarcely four or five in the utmost bounds of a streight two thousand or more miles long and where there are depths of hundreds of feet this alteration is much less than if in one of the Boats that bring us fresh Water the said Water upon the arrest of the Boat should rise at the Prow the thickness of a leaf I conclude therefore that very small alterations in respect of the immense greatness and extraordinary velocity of the Seas is sufficient to make therein great mutations in relation to our smallness and to our accidents SAGR. I am fully satisfied as to this particular it remains to declare unto us how those additions and substractions derived from the diurnal Vertigo are made one while greater and another while lesser from which alterations you hinted that the annual period of the augmentations and diminutions of the ebbings and flowings did depend SALV I will use my utmost endeavours to render my self intelligible but the difficulty of the accident it self and the great attention of mind requisite for the comprehending of it constrains me to be obscure The unequalities of the additions and substractions that the diurnal motion maketh to or from the annual dependeth upon the inclination of the Axis of the diurnal motion upon the plane of the Grand Orb or if you please of the Ecliptick by means of which inclination the Equinoctial intersecteth the said Ecliptick remaining inclined and oblique upon the same according to the said inclination of Axis And the quantity of the additions importeth as much as the whole diameter of the said Equinoctial the Earths centre being at the same time in the Solstitial points but being out of them it importeth lesse and lesse according as the said centre successively approacheth to the points of the Equinoxes where those additions are lesser than in any other places This is the whole businesse but wrapt up in the
many alterations for the more minute observations I remit them to be made by those that frequent several Seas and onely by way of a conclusion to this our conference I will propose to be considered how that the precise times of the fluxes and refluxes do not onely happen to be altered by the length of Straights and by the difference of depths but I believe that a notable alteration may also proceed from the comparing together of sundry tarcts of Sea different in greatness and in position or if you will inclination which difference happeneth exactly here in the Adriatick Gulph lesse by far than the rest of the Mediterrane and placed in so different an inclination that whereas that hath its bounds that incloseth it on the Eastern part as are the Coasts of Syria this is shut up in its more Westerly part and because the ebbings and flowings are much greater towards the extremities yea because the Seas risings and fallings are there onely greatest it may probably happen that the times of Flood at Venice may be the time of low Water in the other Sea which as being much greater and distended more directly from West to East cometh in a certain sort to have dominion over the Adriatick and therefore it would be no wonder in case the effects depending on the primary causes should not hold true in the times that they ought and that correspond to the periods in the Adriatick as it doth in the rest of the Mediterrane But these Particularities require long Observations which I neither have made as yet nor shall I ever be able to make the same for the future SAGR. You have in my opinion done enough in opening us the way to so lofty a speculation of which if you had given us no more than that first general Proposition that seemeth to me to admit of no reply where you declare very rationally that the Vessels containing the Sea-waters continuing stedfast it would be impossible according to the common course of Nature that those motions should follow in them which we see do follow and that on the other side granting the motions ascribed for other respects by Copernicus to the Terrestrial Globe these same alterations ought to ensue in the Seas if I say you had told us no more this alone in my judgment so far exceeds the vanities introduced by so many others that my meer looking on them makes me nauseate them and I very much admire that among men of sublime wit of which nevertheless there are not a few not one hath ever considered the incompatibility that is between the reciprocal motion of the Water contained and the immobility of the Vessel containing which contradiction seemeth to me now so manifest SALV It is more to be admired that it having come into the thoughts of some to refer the cause of the Tide to the motion of the Earth therein shewing a more than common apprehension they should in afterwards driving home the motion close with no side and all because they did not see that one simple and uniform motion as v. gr the sole diurnal motion of the Terrestrial Globe doth not suffice but that there is required an uneven motion one while accelerated and another while retarded for when the motion of the Vessels are uniforme the waters contained will habituate themselves thereto without ever making any alteration To say also as it is related of an ancient Mathematician that the motion of the Earth meeting with the motion of the Lunar Orb the concurrence of them occasioneth the Ebbing and Flowing is an absolute vanity not onely because it is not exprest nor seen how it should so happen but the falsity is obvious for that the Revolution of the Earth is not contrary to the motion of the Moon but is towards the same way So that all that hath been hitherto said and imagined by others is in my judgment altogether invalid But amongst all the famous men that have philosophated upon this admirable effect of Nature I more wonder at Kepler than any of the rest who being of a free and piercing wit and having the motion ascribed to the Earth before him hath for all that given his ear and assent to the Moons predominancy over the Water and to occult properties and such like trifles SAGR. I am of opinion that to these more spaculative persons the same happened that at present befalls me namely the not understanding the intricate commixtion of the three Periods Annual Monethly and Diurnal And how their causes should seem to depend on the Sun and on the Moon without the Suns or Moons having any thing to do with the Water a businesse for the full understanding of which I stand in need of a little longer time to consider thereof which the novelty and difficulty of it hath hitherto hindred me from doing but I despair not but that when I return in my solitude and silence to ruminate that which remaineth in my fancy not very well digested I shall make it my own We have now from these four dayes Discourse great attestations in favour of the Copernican Systeme amongst which these three taken the first from the Stations and Retrogradations of the Planets and from their approaches and recessions from the Earth the second from the Suns revolving in it self and from what is observed in its spots the third from the Ebbing and Flowing of the Sea do shew very rational and concluding SALV To which also haply in short one might adde a fourth and peradventure a fifth a fourth I say taken from the fixed stars seeing that in them upon exact observations those minute mutations appear that Copernicus thought to have been insensible There starts up at this instant a fifth novelty from which one may argue mobility in the Terrestrial Globe by means of that which the most Illustrious Signore Caesare of the noble Family of the Marsilii of Bologna and a Lyncean Academick discovereth with much ingenuity who in a very learned Tract of his sheweth very particularly how that he had observed a continual mutation though very slow in the Meridian line of which Treatise at length with amazement perused by me I hope he will communicate Copies to all those that are Students of Natures Wonders SAGR. This is not the first time that I have heard speak of the exquisite Learning of this Gentleman and of his shewing himself a zealous Patron of all the Learned and if this or any other of his Works shall come to appear in publique we may be aforehand assured that they will be received as things of great value SALV Now because it is time to put an end to our Discourses it remaineth that I intreat you that if at more leasure going over the things again that have been alledged you meet with any doubts or scruples not well resolved you will excuse my oversight as well for the novelty of the Notion as for the weaknesse of my wit as also
Earth answered by Examples of the like Motions in other Celestial Bodies 236 A fourth Argument of Claramontius against the Copernican Hypothesis of the Earths Mobility 239 From the Earths obscurity and the splendor of the fixed Stars it is argued that it is moveable and they immoveable 239 A fifth Argument of Claramontius against the Copernican Hypothesis of the Earths Mobility 240 Another difference between the Earth and Celestial Bodies taken from Purity and impurity 240 It seems a Solecisme to affirme that the Earth is not in Heaven 241 Granting to the Earth the Annual it must of necessity also have the Diurnal Motion assigned to it 300 Discourses more than childish that serve to keep Fools in the Opinion of the Earths Stability 301 The Difficulties removed that arise from the Earths moving about the Sun not solitarily but in consort with the Moon 307 The Axis of the Earth continueth alwayes parallel to it self and describeth a Cylindraical Superficies inclining to the Orb. 344 The Orb of the Earth never inclineth but is immutably the same 345 The Earth approacheth or recedeth from the fixed Stars of the Ecliptick the quantity of the Grand Orb. 349 If in the fixed Stars one should discover any Mutation the Motion of the Earth would be undeniable 351 Necessary Propositions for the better conceiving of the Consequences of the Earths Motion 354 An admirable Accident depending on the not-inclining of the Earths Axis 358 Four several Motions assigned to the Earth 362 The third Motion ascribed to the Earth is rather a resting immoveable 363 An admirable interne vertue or faculty of the Earths Globe to behold alwayes the same part of Heaven 363 Nature as iâ— sport maketh the Ebbing and Flowing of the Sea to prove the Earths Mobility 379 All Terrene Effects indifferently confirm the Motion or Rest of the Earth except the Ebbing and Flowing of the Sea 380 The Cavities of the Earth cannot approach or recede from the Centre of the same 387 The Hypothesis of the Earths Mobility taken in favour of the Ebbing and Flowing opposed 399 The Answers to those Objections made against the Earths Motion 399 The Revolution of the Earth confirmed by a new Argument taken from the Aire 400 The vaporous parts of the Earth partake of its Motions 400 Another observation taken from the Ayr in confirmation of the motion of the Earth 402 A Reason of the continual Motion of the Air and Water may be given by making the Earth moveable rather then by making it immoveable 405 The Earths Mobility held by sundry great Philosophers amongst the Antients 437 468 The Fathers agree not in expounding the Texts of Scripture that are alledged against the Earths Mobility 450 The Earth Mobility defended by many amongst the Modern Writers 478 The Earth shall stand still after the Day of Judgement 480 The Earth is another Moon or Star 486 The Earths several Motions according to Copernicus 491 The Earth secundum totum is Immutable though not Immoveable 491 The Earths Natural Place 492 The Earths Centre keepeth her in her Natural Place 493 The Earth in what Sense it may absolutely be said to be in the lowest part of the World 496 EBBING and Ebbings The first general Conclusion of the impossibility of Ebbing and Flowing the Immobility of the Terrestrial Globe being granted 380 The Periods of Ebbings and Flowings Diurnal Monethly and Annual 381 Varieties that happen in the Diurnal Period of the Ebbings and Flowings 382 The Causes of Ebbings and Flowings alledged by a Modern Phylosopher 382 The Cause of the Ebbing and Flowing ascribed to the Moon by a certain Prelate 383 The Cause of the Ebbing c. referred by Hyeronimus Borrius and other Peripateticks to the temperate heat of the Moon 383 Answers to the Vanities alledged as Causes of the Ebbing and Flowing 383 It s proved impossible that there should naturally be any Ebbing and Flowing the Earth being immoveable 386 The most potent and primary Cause of the Ebbing and Flowing 390 Sundry accidents that happen in the Ebbings and Flowings 391 Reasons renewed of the particular Accidents observed in the Ebbings and Flowings 393 Second Causes why in several Seas and Lakes there are no Ebbings and Flowings 394 The Reason why the Ebbings and Flowings for the most part are every Six Hours 395 The Cause why some Seas though very long suffer no Ebbing and Flowing 395 Ebbings and Flowings why greatest in the Extremities of Gulphs and least in the middle parts 396 A Discussion of some more Abstruce Accidents observed in the Ebbing and Flowing 396 The Ebbing and Flowing may depend on the Diurnal Motion of Heaven 404 The Ebbing and Flowing cannot depend on the Motion of Heaven 405 The Causes of the Periods of the Ebbings and Flowings Monethly and Annual at large assigned 407 The Monethly and Annual alterations of the Ebbings and Flowings can depend on nothing save on the alteration of the Additions and Subtractions of the Diurnal Period from the Annual 408 Three wayes of altering the proportion of the Additions of the Diurnal Revolution to the Annual Motion of the Ebbing and Flowing 409 Ebbings and Flowings are petty things in comparison of the vastnesse of the Seas and the Velocity of the Motion of the Terrestrial Globe 417 EFFECT and Effects Of a new Effect its necessary that the Cause be likewise new 370 The Knowledge of the Effects contribute to the investigation of the Causes 380 True and Natural Effects follow without difficulty 387 Alterations in the Effects argue alteration in the Cause 407 ELEMENTS and their Motions Vide MOTION ENCYCLOPEDIA Subtilties sufficiently insipid ironically spoken and taken from a certain Encyclopedia 153 EXPERIMENTS Sensible Experiments are to be preferred before Humane Argumentations 21 33 42. It is good to be very cautious in admitting Experiments for true to those that never tryed them 162 Experiments and Arguments against the Earths Motion seem so far concluding as they lye under Equivokes 162 The Authority of Sensible Experiments and necessary Demonstrations in deciding of Physical Controversies 436 EYE The Circle of the Pupil of the Eye contracteth and enlargeth 329 How to finde the distance of the Rays Concourse from the Pupil of the Eye 329 F FAITH Faith more infallible than either Sense or Reason 475 FIRE Fire moveth directly upwards by Nature and round about by Participation according to Aristotle 122 It is improbable that the Element of Fire should be carried round by the Concave of the Moon 405 FIGURE and Figures Figure is not the Cause of Incorruptibility but of Longer Duration 66 The perfection of Figure appeareth in Corruptible Bodies but not in the Eternal 69 If the Spherical Figure conferred Eternity all things would be Eternal 69 It is more difficult to finde Figures that touch in a part of their Surface then in one sole point 185 The Circular Figure placed amongst the Postulata of Mathematicians 186 Irregular Figures and Formes difficult to be introduced 187 Superficial figures increase in proportion
the Sun from the Summer Solstice 352 The Sun passeth one half of the Zodiack nine dayes sooner than the other 416 The Miracle in Joshuah of the Suns standing still answers not to the intent of lengthening the day but on the contrary excellently agreeth with the Copernican Systeme 456 The Sun without change of place revolveth upon its own Centre in the space of a Moneth 457 The Nobility of the Sun as being the Fountain of Light Heart of the World and Principle of Motion 457 The Suns standing still in Joshuah explained by Kepler 462 The Sun found to be neerer to us than in times past by five thousand Miles 469 The Sun Moon and Stars are one and the same thing 485 Why the Sun to our thinking moveth and not the Earth 486 How the Sun is said to rise and set by extrinsick denomination 489 The Sun is the King Heart and Lamp of the World 497 SYMPATHY Sympathy and Antipathy terms introduced by Phylosophers the more easily to give a reason of many Natural Effects 373 SYSTEM of Copernicus The Copernican System once admitted for true Expositions might be found out for all those Scriptures than that seem to make against it 459 Didacus à Stunica held that the Scripture may be best expounded by the Copernican System 468 SYSTEM of Vniverse The System of the Universe designed from the Appearances 296 The System of the Universe might probably have been intended to have been represented by the Golden Candlestick 500 The System represented likewise by the Apple in Paradice 501 T TELESCOPE The Telescope enableth us to discourse better of Celestial Matters than Aristotle himself 42 Invention of the Telescope taken from Aristotle 92 An ingenious Consideration about using of the Telescope with as much facility on the Round-top of the Mast of a Ship as on the Deck 225 The Mutations made in the Telescope depending on the Agitation of the Ship 226 The Operations of the Telescope accounted Fallacies by the Peripateticks 304 319 The Telescope is the best means to take away the Irradiations of the Stars 306 The Telescope hath much contributed to the Restauration of Astronomy 476 THEOLOGY Theology the Queen of the Sciences and wherein her Prerogative consists 44 THINGS Some Things are of that nature that their parts may seperate from one another and from their whole others not 492 Things are simply denominated in comparison of all or the greatest number of things of that kinde 496 THREE The Number Three celebrated amongst the Pythagoreans 2 TIDE The Tide and the Mobility of the Earth mutually confirm each other 380 Tyde Vide Ebbing and Flowing TRUE True and Fair are one and the same as also False and Deformed 115 For proof of True Conclusions many solid Arguments may be produced but to prove a false one none 112. 245 TRUTH and Truths Untruths cannot be Demonstrated as Truths are 112 The Truth sometimes gains strength by Contradiction 181 Truth hath not so little light as not to be discovered amongst the Umbrages of Falshoods 384 TYCHO The Argument of Tycho grounded upon a false Hypothesis 324 Tycho and his Followers never attempted to see whether there were any Phaenomena in the Firmament for or against the Annual Motion 337 Tycho and others argue against the Annual Motion from the invariable Elevation of the Pole 338 V VELOCITY Vniform Velocity sutable with Circular Motion 12 Nature doth not immediately conferre a determinate degree of Velocity although She could 12 The Velocity by the inclining plane equal to the Velocity by the Perpendicular and the Motion by the Perpendicular swifter than by the inclining plane 14 Velocities are said to be equal when the Spaces passed are proportionate to their times 15 The greater Velocity exactly compensates the greater Gravity 192 VENUS The Mutation of Figure in Venus argueth its Motion to be about the Sun 295 Venus very great towards the Vespertine Conjunction and very small towards the Matutine 297 Venus necessarily proved to move about the Sun 298 The Phaenomena of Venus appear contrary to the System of Copernicus 302 Another Difficulty raised by Venus against Copernicus 302 Venus according to Copernicus either lucid in it self or a transparent substance 302 The Reason why Venus and Mars do not appear to vary Magnitude so much as is requisite 303 A second Reason of the small apparent encrease of Venus 306 Venus renders the Errour of Astronomers in determining the Magnitude of Stars inexcuseable 327 VESSEL Of the Motion of Water in a Vessel Vide Water UNDERSTAND c. Man Understandeth very much intensive but little extensive 86 Humane Uuderstanding operates by Ratiocination 87 UNIVERSE The Constitution of the Uuiverse is one of the Noblest Problems a Man can study 187 The Centre of the Universe according to Aristotle is that Polnt about which the Celestial Spheres do revolve 294 Which ought to be accounted the Sphere of the Universe 299 It is a great rashnesse to censure that to be superfluous in the Universe which we do not perceive to be made for us 334 VURSTITIUS Christianus Vurstitius read certain Lectures touching the Opinion of Copernicus and what happened thereupon 110 W WATER He that had not heard of the Element of Water could never fancie to himself Ships and Fishes 47 An Experiment to prove the Reflection of Water less bright than that of the Land 81 The Motion of the Water in Ebbing and Flowing not interrupted by Rest. 251 The vain Argumentation of some to prove the Element of Water to be of a Spherical Superficies 377 The Progressive and uneven Motion makes the Water in a Vessel to run to and fro 387 The Several Motions in the conteining Vessel may make the conteined Water to rise and fall 387 The Water raised in one end of the Vessel returneth it self to Aequilibrium 391 In the shorter Vessels the Undulations of Waters are more frequent 391 The greater profundity maketh the Undulations of Water the more frequent 391 Why in narrow places the Course of the Waters is swifter than in larger 396 The cause why in some narrow Chanels we see the Sea Waters run alwayes one way 398 The Water more apt to conserve an Impetus conceived than the Air. 400 The Motion of the Water dependeth on the Motion of Heaven 404 WEIGHTS It s questionable whether Descending Weights move in a Right Line 21 WEST The Course to the West India's easie the return difficult 402 WINDE Constant Gales of Winde within the Tropicks blow towards the West 402 Windes from the Land make rough the Seas 402 WISDOME Divine Divine Wisdome infinitely infinite 85 The Discourses which Humane Reason makes in time the Divine Wisdom resolveth in a Moment that is hath them alwayes present 87 WIT. The Wit of Man admirably acute 87 The Pusilanimity of Popular Wits 364 Poetick Wits of two kinds 384 WORLD World Vide Universe The Worlds parts are according to Aristotle two Celestial and Elementary contrary to each other 6 The World
those Channels for iustance which formerly were Navigable unto the very Walls of York 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 Reputation 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 Mathematical 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 Conclusion § The other particular that I am to offer is that out of my desire to contribute what lyeth in me to the compleating of this Piece for English Practice I have exeeded my promise not onely in giving you the Second and following Books which were not extant at the time of tendring my Overtures but also in that I have added â— 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. ERRATA of the second PART of the first TOME In PREFACE read 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 Giulto 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. Soâ— 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 Breâ—t 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. Discourses 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 OF THE MENSURATION OF Running Waters LIB I. WHat and of how great moment the consideration of Motion is in natural things is so manifest that the Prince of Peripateticks pronounced that in his Schools now much used Sentence Ignorato motu 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 sublimity of understanding Under the same Science of Motion is comprehended all that which is written by Mechanitians concerning Engines moving of themselves Machins moving by the force of Air and those which serve to move weights and immense 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 dilated that there are few things which fall under mans notice which are not conjoyned with Motion or at least depending 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 And 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 exquisitness 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 suppositions and cognitions sufficiently clear from which I will afterwards 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 understood 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 demonstrations placed towards the end and return afterwards to the consideration 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 followeth I say therefore that having in times past on divers occasions 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 remained still infolded in such an obscurity that I well knew I understood 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 determinate and the same And here I freely confesse that I had singular 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 â—or 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 from 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 Superficies 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 neverthelesse there issueth from them in equal times unequal quantities of water And if we should more attentively consider this businesse we should find that the water by the lower Tap runneth 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 beneath 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 fromthâ—e neather part I will declare my self by another example If we should imagine 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 maintaining 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 thickness 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 codâ—s 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 velocity 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 understood 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 wound about a Rocket or Barrel the thread of the Metal they place the Rocket 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 passing 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 thicknesse 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 matter we should finde that the thicker the thread before the hole
greater measure than in those parts in which it is more swift and therefore ordinarily 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 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 it s 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 sueh reciprocally is the measure 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 probability affirm That the River rose to such a height and excrescence by the retardation of the Waters dependant on the boistrous and constant Winds that blew in those times as is noted 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 the River in such a case there must follow very great and irrepable innundations COROLLARIE X. FRom what hath been demonstrated we may with facility resolve 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 Tiber and having summed the total of these measures and conferring 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 variation of velocity and how that it is the most potent cause of wonderfully 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 Water 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 remove 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 whereof 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 Water written by Fontana wherein I finde many errors The first of which is to think that the measures of these Waters compressed in the Channels of those Brooks and Rivers should 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 Fontana and his Nephew measured them And all this is manifest from the things which we have above explained for if the Waters reduced into Tiber increase in velocity they decrease in measure and if they decrease in velocity they increase in measure 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 Crowns 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 it s 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 concurring 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 Innundation by augmenting in the measure of its own Channel which matter is sufficiently evident for if it be supposed that the River in the time of flood had not had of it self and from its proper springs more Water than ordinary it s a thing certain that the Water of Tiber rising and increasing also that River to level it self with the Water of Tiber would have retained some of its Waters in its own Chanel without discharging them into Tyber 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 Inundation 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 only 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 Currents 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 water 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 experimentally seen in the Wind-Gun invented in our dayes by M. Vincenzo Vincenti of Vrbin which property of the Air of admitting 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 violence 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 occupy a less place it would thence follow that two Vessels of equal measure but of unequal height should be of unequal capacity 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 erected the water put therein would be more pressed and crowded 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 easily resolveth all difficulties COROLLARIE XII THrough the same inadvertency of not regarding the variation of velocity in the same Current there are committed by Ingineers 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 hundred feet which thing doth not indeed so fall out and the reason is plain for that the Chanel being derived the rest of the main River diminisheth in velocity and therefore retains a greater measure than it had at first before the derivation of the Chanel and moreover if the Chanel being derived it shall not conserve the same velocity which it had at first in the main River but shall diminish it it will be necessary that it hath a greater 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 quantity 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 water of Ferara when I was in those parts in service of the most Reverend and Illustrious Monsignor Corsini the sublime wit of whom hath been a very great help to me in these contemplations it s 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 moreover 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 consequences most important nor doth it seem to me requisite in difficult matters such as these we have in hand to resigne 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 particular 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 heretofore 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 restrained 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 disgorgeth 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 experiment 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 Ferara 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 the 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 it s 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 superior 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 diligently 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 the 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 overflowings 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 remaineth 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 experience 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 is 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 maintaining this diversion I should think it were more sound advice to keep that Bank alwaies whole at Bondeno or in any other convenient place and not to permit that the Water of the Grand Po should ever come near to Ferara COROLLARIE XIV 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 it s 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 place 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 approacheth the Sea and therefore decreaseth in measure and consequently 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 reason 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 familiar 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 decreaseth 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 in the beginning they are small and afterwards become greater and bigge and the reason is most manifest because in the beginning 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 afterwards 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 Commentariis 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 beginning of the Aqueducts finding it neer 10000. Quinaries bigger than it was in Commentariis 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 measured it might be different from those velocities which are found in other places before measured by others and therefore the measures of the waters might yea ought necessarily to be different it having been by us demonstrated that the measures of the same running water have reciprocal proportion to their velocities Which Frontino not well considering and finding the water in Commentariis 12755. Quinaries in erogatione 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 APPENDIX II. A Like 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 so 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 discontents 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. A Like errour in my judgement hath been 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 intolerable 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 demonstrared 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 Proposition 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 considered 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 VVaters for the watering of fields as is done in the Territories of Brescia Bergama 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 VVater but onely to the bare Vulgar measure there will alwaies very great disorders and prejudices ensue to the persons concerned APPENDIX VII IT seemeth that one may observe that whilst the Water runneth 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 VVater 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 discovering a very nice mistake into which those commonly fall who divide the VVaters of Fountains VVhich 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 Circles 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 afterwards adjust the Cocks to dispence the VVaters The other manner of dividing the VVaters 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 being most exactly made the VVater 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 VVater than the just quantity in comparison of the lesser that is to speak more properly The VVater which passeth through the greater Cock hath alwaies a greater proportion to that which passeth through the lesser than the greater Cock hath to the lesser All which I will declare by an example The like errour occurreth also in the other manner of measuring the VVater 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 the 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 depend 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 satisfactory is nevertheless insufficient to give the total reason of that notable abatement which hath been spoken of But it is necessary to have recourse to our consideration of the velocity in the course of the water the chiefest and true cause of the variation of the measure of the same Running-Waterâ— for that multitudes of reeds weeds and plants dispersed through the current 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 cleansing that the velocity after the cleansing hath to the velocity before the cleansing And be cause those weeds being cleansed away 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 committed 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 divisions 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 determinate time as for instance ow many Barrels or Tuns it carrieth in a set time and in case you are afterwards to distribute the water distribute it at the rate of so many 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 Modern 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 onely 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 evacuate 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 discharge for example four inches and having the former sole measure 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 proportion 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 discharge 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 accomodate 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 to adjust the Cistern so that the excess above the ordinary water 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 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 unequal and it may be also that the bigger doth discharge a greater quantity of Water And lastly it may be that the less mouth dischargeth more Water than the greater and all this is manifest by the things noted in the beginning of this discourse and by the said second Proposition Now to examine the proportion of the Water that passeth by one Ditch to that which passeth by another that this being known the same Waters and mouths of Ditches may be then adjusted we are to keep account not onely of the greatness of the mouths or passages of the Water but of the velocity also which we will do by first finding two numbers that have the same proportion between themselves as have the mouths which are the numbers 32 and 8 in our example Then this being done let the velocity of the Water by the passages 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 demonstrated 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 proportion being composed of the proportions of 32 to 8 and of 8 to 4 namely to the 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 dischargeth 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 sundry occasions observed are involved in so many difficulties and such a multiplicity of most extravagant accidents that it is no marvel if continually many and very important errours 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 precipitious Torrents and vast Fennes And in particular I had occasion some years past to go see the Cave 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 industry truly heroicall and admirable by Monsignor Maffei Barherino 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 appearance 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 Rabble 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 Perugia standing in the same manner 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 That which hath been demonstrated in the Vessel falls out exactly 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 abatement 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 experiments before we resolve and conclude any thing and how farre the vulgar are distant from a right judgement 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 heretofore wherein for that the business was not rightly understood many disorders vast expences and considerable mischiefs 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 in 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 satisfaction 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 resolutely 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 continued for many dayes can do in raising these Lakes I will here insert the Copy of a Letter which I writ formerly to Signior Galilaeo Galilaei 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 The Copy of a Letter to Signore GALILAEO GALILAEI 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 I might 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 Roman 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 therefore no Water issued out of the Lake to the great
prejudice of all the places and villages circumjacent in regard that the Water 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 returned to Perugia there followed a Rain not very great but constant 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 raised 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 Cylinder about a palme high and half a palme broad and having put in water sufficient to cover the bottome of the Glasse I noted 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 Water was risen in the Vessel the height of the following line I considered that if I had exposed to the same rain such other vessels equal to that the Water would have risen in them all according to that measure And thereupon concluded that also in all the 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 disturb 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 increased in the space of eight hours that the rain lasted eight times that measure And whilst I again exposed the Glass to repeat 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 Chamber-window exposed in a Court-yard and communicated to him my fancy relating 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 smiling said unto me Sir you deceive your self I am of opinion that the Lake will not be increased by this rain so much as the thicknesse of 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 surface 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 persisting in his conceit without yielding in the least to my allegation 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 Galilaeo 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 messenger 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 it 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 related to him the whole business to which he knew not what to answer 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 Water of the Lake might be driven to the contrary shore on which the Water rising it might be fallen at the mouth of the Emissary and so the observation might be much obscured But this difficulty wholly vanished by reason of the Aires great tranquility 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 come 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 annull 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 Emissary 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 nevertheless that many weeks and moneths would be spent in drinking 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 being 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 from 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 proportion of water co-operates not in raising of the Lake It is absolutely necessary on the other hand that we consider That the Circuit of the water of the Lake being thirty miles as it s commonly 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 spreading it require three quarts more we shall finde that the whole agregate 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 Bubbles 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 abundance 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 relate 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 certain but ought to submit all to the sound and secure deliberation 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 Continuing therefore my above-said conceit about the rising of the water 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 thousand times greater than this and much more intense which would insue as oft as those falling drops were four five 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 rising 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 occasion 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 possible to pronounce any thing of a certainty touching the quantity of Running Waters by considering only the single vulgar measure of the Water without 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 Running 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 haply such an oversight is committed by reason the length of Running Water is reputed in some sense infinite in that it never ceaseth 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 incomprehensible as being infinite yet neverthelesse it s 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 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 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 upper 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 from 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 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 quantity of the Water that passeth through the first Section shall have the same proportion to the quantity that passeth 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 height and velocity PROPOSITION I. The Sections of the same River discharge equal quantities of Water in equal times although the Sections 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 quantity of Water in equal times for if greater quantity of Water should pass through A than passeth through B it would 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 Section B is equal to the quantity of Water which passeth through the Section A and therefore the Sections of the same River discharge c. Which was to be demonstrated PROPOSITION II. In two Sections of Rivers the quantity of the Water which passeth by one Section is to that which passeth 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 LEt 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 proportions of the first Section A to the Section B and of the velocity through A to the velocity through B Let a Section be supposed 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 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 C and B are equally swift as the Section G to the Section 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 proportion 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 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 line E to the line F therefore the quantity of water which passeth 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
which was to be demonstrated 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 River by the Torrent shall have between themselves the reciprocal proportion of the velocities acquired in the River LEt A and B be was equal streams of the same Torrent which falling into a River at divers times make the heights CD and FG that is the stream A maketh the height CD and the stream B maketh the height FG that is Let their Sections in the River into which they are fallen be CE and FH I say that the height CD shall be to the height FG in reciprocal proportion as the velocity through FH to the velocity through CE 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 CE shall be equal to that which passeth through FH And therefore the proportion that the Section CE hath to the Section FH shall be the same that the velocity through FH hath to the velocity through CE But the Section CE is to the Section FH as CD to FG by reason they are of the same breadth Therefore CD shall be to FG in reciprocal proportion as the velocity through FH is to the velocity through CE and therefore if two equal streams of the same Torrent c. which was to be demonstrated 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 particulars more obscure and of very great concern upon the same argument 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 equal times they passe spaces of equal length DEFINITION II. RIvers are said to move with like velocity when their proportional 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 another then also the lower part of the former shall be more swift than the part correspondent to it in the second proportionally DEFINITION 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 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 ABCD shall be the Regulator BC the bottom and the other two sides AB and CD are its banks DEFINITION V. BY the quick height we mean the Perpendicular from the upper superficie of the River unto the upper superficies of the bottom of the Regulator as in the foregoing Figure the line GH DEFINITION VI. IF the water of a River be supposed to be marked by three sides of a Regulator that Rightangled Parallelogram comprehended between the banks of the Regulator and the bottom and the superficies of the Water is called a Section of the River 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 velocitate 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 Galilaeo Galilaei 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 whatsoever 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 familiar Problems from which we shall pass to the Notions and questions more subtil and curious which will also prove profitable and not to be sleighted in this business of Waters PROPOSITION I. PROBLEME I. A Chanel 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 Chanel beareth and then shall we know that the Syphons drink up all the water when we see that the water at the Dam doth neither rise higher nor abate but alwaies keepeth in the same Level 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 second 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 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 velocitie LEt the quick height of a River in the Regulator ABCD be the perpendicular FB and afterwards by new water that is added to the River let the water be supposed to be raised to G so that GB may be double to EB I say that all the water GC shall be double in velocity to that of EC For the water GF having for its bed the bottom EF equally inclined as the bed BC and its quick height GE being equal to the quick height EC and having the same breadth BC it shall have of it self a velocity equal to the velocity of the first water FC but because besides its own motion which is imparted to it by the motion of the water EC it hath also over and above its own motion the motion of EC And because the two waters GC and EC are alike in velocity by the third Supposition therefore the whole water GC shall be double in velocity to the water EC which was that which we were to demonstrate This demonstration is not here inserted as perfect the Authour having by several letters to his friends confessed himself unsatisfied 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 demonstration 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 manner with that which is laid down in the second Corollary of the fourth Theorem of this with its Table and the use thereof annexed COROLLARIE HEnce it followeth that when a River increaseth in quick height by the addition of new water it also increaseth in velocity so that the velocity hath the same proportion to the velocity that the quick height hath to the quick height as may be demonstrated in the same manner PROPOS III. PROBLEME II. A Chanel of Water being given whose breadth exceeds not twenty Palms or thereabouts and whose quick height 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 Chanellet 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 water of the Chanellet diverted hath to the water of the bigger Chanel And because the water of the Chanellet is known by the Method said down in the first Theorem and the terms of the Theorem being also known the quantity of the water which runneth thorow the bigger Chanel shall be also known by the Golden 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 square 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 6â— 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 Theory 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 measured 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 proportion that the water of the Chanellet hath to all the water of the great Chanel 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 distribution of the waters that are imploy'd to overflow the fields as is used in the Brescian Cremonese Bergamase Lodigian Milanese territories and many other places where very great suits and differences arise which not being to be determined with intelligible 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 ruine 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 increase 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 DF with the Quick height AB and afterwards let a Flood come and then let it run with the height DB I say that the quantity of the Water that is discharged through DF to that which dischargeth through AF hath the proportion compounded of the proportions of the velocity through DF to the velocity through AF and of the height DB to the height AB As the velocity through DF is to the velocity through AF so let the line R be to the line S and as the height DB is to the height AB so let the line S be to the line T. And let a Section be supposed LMN equal to the Section DF in height and length but let it be in velocity equal to the Section AF. Therefore the quantity of the Water that runneth through DF to that which runneth through LN shall be as the velocity through DF to the velocity of LN that is to the velocity through LN that is to the velocity through AF. therefore the quantity of Water which runneth through DF to that which passeth through LN shall have the proportion that R hath to S but the quantity of the Water that runneth through LN to that which runneth through AF the Sections being equally swift shall have the proportion that the Section LN hath to the Section AF that is that the height BD hath to the height BA that is that S hath to T. Therefore by equal proportion the quantity of the Water which runneth by DF to that which runneth by AF shall have the proportion of R to T that is shall be compounded of the proportions of the height DB to the height AB and of the velocity through DF to the velocity through AF. 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 velocity 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 of59. 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 49 it shall abate two other thirds a most principal point and such that it s 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 double and the quantity increasing nonuple the height increaseth triple so that by adding to units all the odde numbers according to their Series the heights increase according to the natural progression of all the numbers from units As for example 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 continuing 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
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 successively varied and altered in the same proportions Nor did I here desist my observation but the water being diminished that issued 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 10 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 quintuple and by adding of 11. it increased sextuple and by adding 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 decuple 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 BC in the same level though it continually run to the brim of the Vessel are put 25. Syphons and there may be many more divided into 5 Classes DEFGH 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 consequent odd numbers successively we are content to represent in the Figure no more but the five forenamed Classes to avoid confusion the gathered water DEFGH which runneth thorow the Chanel IKL and falleth into the out-let MNOP and so much sufficeth for the explanation of this experiment 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 Problems 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 proportion that the Water of the Chanel hath to that of the River then let the Water of the Chanel be measured by the second Probleme 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 nevertheless 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 really 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 disbursments 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 to 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 businesses 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 suffice CONSIDERATION II. FRom what hath been declared if it shall be well understood 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 Sawing-Mills Mirtle-Mills Felling-Mills Fulling-Mills Silk-Mills and such other Machines but also in ordering Navigable Chanels diverting Rivers and Chanels of Waters or terminating and limiting the sizes of Pipes for Fountains In all which affairs there are great errours coâ—â—â—â—â—ed 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 Discoveries of Signore Galilaeo 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 knowledge 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 Serene 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 Basadonna a Senatour of great worth and merit that I would ingenuously deliver my opinion touching the state of the Lake of Venice and after I had discoursed with his Honour several 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 CONSIDERATIONS Concerning the LAKE OF VENICE BY D. BENEDETTO CASTELLI Abbot of S. Benedetto Aloysio Mathematician to Pope VRBAN 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 peradventure 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 worthy 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 unhabitable The second Head is the great Stoppage that daily is growing 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 imbraced Secondly I propose to consideration that the so notable discovery of Earth Mud hath not been long observed as I understand 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 riseth as it is commonly thought by all without dispute or whether 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 Waters have failed or abated I believe that it would be extreamly necessary 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 appearance 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 waters flowing doth continually raise from its bottome immense heaps 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 falleth into the Sea there is alwaies seen in the Sea it self at the place of the rivers 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 sits 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 who so 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 another 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 without any opposal
bring such a drift of sand into the Ports that if it 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 appearance of the Ouze and Mud in the Lakes but so much shall suffice us to have hinted to make way for discoursing of the operations 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 inconvenient 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 leave it to wiser men than my sâ—lf 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 Decrees 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 Colledge 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 determination I refer my self 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 precedent 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 dispersed 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 discharge it self into the Sea by the Ports I do not doubt but that their bottomes will be scoured And that these effects must follow 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 Waters rise so much as to keep the Shelves covered and to facilitate Navigation which ought to be at least half a Brace or thereabouts And indeed it seemeth at first sight to be impossible that the sole Water of the Brent let into the Lake and dispersed 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. Braces 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 1 100 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 I here confesse that I am surprized at the forme of the Argument 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 couched 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 profitable 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 And 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 perfectly 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 particular 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 Serene 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 demonstrate and declare this businesse and they who shall have well understood the ground of my Discourse will rest fully satisfied 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 according to my opinion yet neverthelesse it will be at some time or other or if it be not things will grow worse and worse For more clear understanding therefore it ought to be known that it being required as it is generally used to measure the waters 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 frequently 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 not 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 abominabile est apud Deum Exod. I considered that in the Territory 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 important errours to the great prejudice of the Publique and of Private persons neither they that sell nor they that buy understanding 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 assigned to another Which thing proveth to be the same inconvenience 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 businesse that I was imployed in some years since with great intensenesse 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 keeping no account of the length And yet the Water being though running a Body it is necessary in forming a conceit of its quantity in relation to another to keep account of all the three Dimensions that is of length breadth and depth Here an objection hath been put to me in behalf of the ordinary way of measuring Running Waters in opposition to what I have above considered and proposed and I was told It s 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 infinite as never finishing its running and consequently is incomprehensible 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 him be never so great a Wit can never promise to frame a conceit 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 Whether 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 dimensions of a Body being given the Body is known and the quantity 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 Water 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 Book of the measure of Running Waters but yet doth not run thorowout with the same velocity Hence it is that the vulgar measures of the said River in divers parts of its Chanel are alwaies divers insomuch that if a River passing through its chanel had such velocity that it ran 100 Braces in the 1 1 60 of an hour-and afterwards the said River should be reduced to so much tardity 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 become 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 Now applying all to our principal intent I say That by what hath been declared it is manifest that if the Brent were 40. Braces broad and 2 1 2 high in some one part of its Chanel that afterwards the same Water of the Brent falling into the Lake and passing thorow the same to the Sea it should lose so much of its velocity that it should run but one Brace in the time wherein whilst it was in its Chanel at the place aforesaid it ran 100. Braces It would be absolutely necessary that increasing in measure 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 1â—â— 200 of a Brace as was concluded in the Argument 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 say that I would if it did concern me greatly encline to consult 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. From which operation doth follow in the first place that the Lake being filled and increased by these 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 scoured 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 alwaies 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 running 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 Illustrious 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 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 by the Plebeian Rout. T is true that he that propoundeth
Propositions far above the reach of common capacity runneth a great hazard of being very often condemned without further Process 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 afterwards 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 descend to Practice and to Operations and your Highness knoweth very well what befel me the last Summer 1641. when in obedience to your Soveraign Command I did in full Colledge represent my thoughts touching the state of the Lake of Venice for there not being such wanting who without so much as vouchsafing 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 deliberation 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 consulations 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 desire 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 native subject That which I propounded in the Mouths pass touching the most important business of the Lake though it did onely expresly 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 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 Venice I say therefore that by diverting these five Rivers that remain although their water that they discharge for the present into 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 demonstration 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 businesse 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 removed 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 declare 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 Confideration to the most Excellent Signore Basadonna presenting 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 against 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 remedy 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 insensible 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 the 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 accompanied 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 lesser 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 Muddinesse in the Lake but we ought moreover to proceed to particulars 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 being 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 although 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 prudent 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 condition 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 Objection that it is very necessary first well to discourse and rationally 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 measuring the things of Nature with the shallownesse of their brains do 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 water of the Lake towards S. Nicolo but take notice that this operation 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 consider 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 Vessels 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 operations 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 exquisite 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 quantity 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 quantity 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 judgement concerning the disimboguement of
the River called Fiume morto whether 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 manifestly appearing that Fiume morto had and hath its Mouth open to the Sea the Plain hath been kept dry and it being also true that the 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 business 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 likewise 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 necessary that also Fiume morto hath its level higher and consequently 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 asswaged which come in with great fury and go out by little and little there do pass very many days and moneths nay sometimes 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 waters 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 T is 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 that 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 little 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 Country free and dry to the admiration of all men There was present 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 purpose 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 insight and indifferent skill in these affairs But that which I am now about to propose farther will I am very certain be understood 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 penipenitrate 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 where also I give the reason thereof Coroll 14. The accident is this That there coming a Land-Flood for example into Arno which maketh it to rise above its ordinary Mouth within Pisa or a little above or below the City six or seven Braces 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 falling 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 farr from the Sea about Pisa and upon those fields the rise shall be much greater and shall become two or three Braces And because the Countrey lyeth low that same â—ise will cause a continual 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 demonstrated in my consideration upon the state of the Lake of Venice I have said but little but I speak to you who understandeth 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 The answer to a Letter written by BARTOLOTTI 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 Serchio is higher than that of Fiume morto this is most true at such time as the waters of Fiume morto are discharged into 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 it s very possible that the Drain of Fiume morto into Serchio may be continuate and I farther 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 Bartolotti saith confidently that when the Sea swelleth 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 Bartolotti without his confirming it by any other proof as indeed it needs none That the level of Fiume morto riseth in E and many 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 difficulty 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 Subjects 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 Huntsmen 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 advantage 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 Water 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 Fiume 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 determining 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 he 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 Peasants 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 open 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 become 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 especially 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 Bartolotti confesseth that if the Mouth of the Fiume morto might alwayes 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 pernicious But admitting of his confession I again reply that Fiume morto ought not to be let into Serchio but immediately into the Sea because although sometimes the Mouth to seawards 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 using 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 lower and is regulated by the height of Serchio But the Mouth of Fiume morto terminates and ought to be understood to terminate in the Sea it self the lowest place And this I believe was very well perceived 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 course 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 become very low and therefore upon every little impetus the waters turn their course And from the motions being exceeding slow is inferred that the abundance of Sea-water that cometh into Fiume morto is so much as is believed and as Sig. Bartolotti affirmeth 9. After that Sig. Bartolotti hath said what he promiseth above namely that when the Windes blowing strongly do stop up Fiume morto and not onely retard but turn the course upwards 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 constantly 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 businesse of profit lyeth and consisteth in maintaining the Waters low in those Plaines and those Ditches which shall never be effected whilst the World stands if you let Fiume morto into Serchio but yet it may by opening the mouth into the Sea and so much reason and nature proveth and which importeth Experience 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 neverthelesse 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 necessrily followeth that if I should return to the Sea-side and not knowing any think of that which happeneth at Pisa and seeing the River Arno raised by a Land-flood half a Brace I might confidently affirm the said River to be raised in Pisa those six or seven 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 able 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 remote 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 pleaseth 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 whether 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 beginning raising the Waters that are neer to the impediment and afterwards less and less as we retire upwards from the impediment provided yet that we speak not of a Flood that commeth 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 superiour 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 Waters of Pisa and I succeeded in the enterprize the Waters in their site towards the Sea abating only three Palmes and yet in the Fen they fell more than fifteen Palmes But the businesse would be long and not so easily to be declared and I am certain that Sig. Bartolotti having considered this would alter his judgment and withall would know that remitting that impediment anew which I had left for lesse than three â—almes 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 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 tenacious 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 therein 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 appellations 11. As to the quantity of the Water that Fiume morto dischargeth into the Sea there are very great disputes about it and I have been present at some of them But let your Honour believe 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 current 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 Eminence 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 intermediate 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 sign that there is no need of opening it and if there be any occasion 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 â—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 purpose in this matter hath absolute dependance on the perfect knowledge of that so important Proposition by me demonstrated and explained in my Treatise of the Mensuration of Running Waters namely That the same water of a River doth continually change Measures according as it altereth and changeth the velocity 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 Water 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 benefits and without these it is impossible to do any thing with absolute perfection 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. Vrban VIII in the University of ROME CONSIDERATION III. AMongst the enterprizes by me esteemed if not absolutely 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 reputation by the miscarriage of the attempt than of gaining fame by reducing things to a better pass then they now are at Yet nevertheless 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 Geometrically 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 conspiâ—uous 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 reason 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 before the improvement Here I have by familiar discourses with my friends explained this enterprize undertaken by Sixtus 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 understand 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 for 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 miscarriage and consequently it will be easie to apply thereunto a seasonable remedy Another head to which these harms may be reduced but proceeding 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 fishing-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 consequently on the Plains The great abundance of water that issueth 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 the Fens are raised with great prejudice and much greater than is conceived according to what hath been demonstrated 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
and continuing 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 diminisheth the tenth part although that the diversions be so unequal 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 Navigation which was onely the 1 20 part of the whole water that falleth 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 Chanel 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 of Volano navigable as far as to the very Walls of Ferrara and consequently 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 Valleys and that which the Chanel of Navigation carryeth in manner as I have demonstrated at the beginning of this Book for this once known we shall also come to know how profitable this diversion 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 first be Drained according to what hath been above advertised Abbot CASTELLI in the present consideration referring himself to the Relation of Monsig Corsini grounded upon the Observations and Precepts of the said Abbot as is seen in the present Discourse I thought it convenient for the compleating of the Work of our Authour upon these subjects to insert it in this place A Relation of the Waters in the Territories of Bologna and Ferrara BY The Right Honourable and Illustrious Monsignore CORSINI a Native of Tuscany Superintendent 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 notwithstanding 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 Primaro 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 manifest by the Brief of the said Pope Clement directed to the Cardinal 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 hapned 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 importance and from which the principal cause of the mischiefs that result from the rest doth proceed This Rheno 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 receptacle 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 encompassing 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 abundance from the upper part of Cominale and in the parts about Raveda Pioggio Caprara Ghiare 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 themselves 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 della Fossa and afterwards to the moderne of the mouth of Masi so that at present the Commerce 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 Thence passing into the Valley of Marzara it swelleth higher 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 thereabouts nor doth it receive with the wonted facility the Drains of the upper Grounds of which the next unto it lying under the waters that return upwards by the Conveyances and the more remote not finding a passage for Rain-waters that settle become either altogether unprofitable 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 receive 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 fall 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 Rivers that fall into the same they swell and dilate and overflow some grounds and deprive others of their Drains in like manner
as 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. Grorgio are threatned with a danger that may in time if it be not remedied become irreparable 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 important to the Ecclesiastick State 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 Ferraresi themselves of whom besides the request of the Bolognesi the greater part beg compassion with sundry Memorials and remedies aswell for the mischiefs past as also for those in time to come from which I hold it a duty of Conscience and of Charity to deliver them Pope Clement judged that the sufficient means to effect this was the said Introduction of the Main Po into the Chanel of Ferrara a resolution truly Heroical and of no lesse beauty than benefit to that City of which I speak not at present because I think that there is need of a readier and more accomodate remedy So that I see not how any other thing can be so much considerable 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 Ferraresi 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 fifty 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 have that so it may not depose the matter of the muddiness when it is intended to be let into Volana 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 effecting 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 letting it run into the divided Po whereby it will be turned to Ferrara 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 waters 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 think 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 waters that should enter into the Goro or Dam of the Mills of Belriguardo 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 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 future it would rise no more That the said Draâ—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 it s a question whether they would procure more inconvenience than benefit 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 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 satisfie 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 require 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 it s 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 evident sign that it doth depose Sand and raise its Bed which agreeth 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 greater 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 undertaking should appear to have been of no danger nor damage was constrained at its Overflowings to give it Vent into Sanmartina that it might not break in upon and prejudice the City which danger 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 success 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 Mouth de Masi it will take up eight miles of double Banks a thing 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 carrying 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 introduction 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 revengeful 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 satisfactory 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 Waters for the space of three years together doth not think that Reno can go by Volana to which agreeth the opinion of Cardinal S. Marcello Legate of this City of whom for his exquisite understanding we ought to make great account But if ever 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 carrying its Sand and the matter of its Muddiness into the Sea and then there would not fail to be a greater evacuation and scowring 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 ingeniously enumerates in a short but well-grounded Tract of his not because that indeed it would not both by Purlings and by Breaches 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 Pliny 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 industry 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 Pâ—trimony 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 Panaro 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 necessity of enduring excessive Breaches To these two Heads are the Arguments reduced which are largely amplified against our opinion 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 many mischiefs but it is a most undoubted truth that the excrescencies 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 happen 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 continually Yea the Vent may be regulated reserving for it the Chanel in which Reno at present runneth and instead of turning it by a Dam at la Betta de Ghislieri 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 feared 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 time 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 Water that is carried by Reno and by Panaro to be so great as is affirmed 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 considered 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 and hundred feet of Banks would not suffice and yet they have far fewer So that this confirmes the Rule of R. P. D. Benedetto 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 velâ—city 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 Pavaro 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 succeed to Po by letting in of Reno Burana having greater proportion 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 also the fear lest that the Sluices which empty into Po should receive 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 with the crime than quit it thereof The truth is that the Bank was not made of proof since that the same now continueth 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 working 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 utmost 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 debated 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 inconvenience and withall the Chanel of Ferrara left dry would be a sufficient receptacle for any other Sewer or Drain whatsoever that should remain there 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 Ingineer 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 First it is to be believed that the waters running that way would nor fail to open that Mouth into the Sea which at present 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 Gero 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
judgements are approved in these affairs I return now from where I degrest and affirm it as indubitable 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 which 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 manner that the Valleys would have a greater Fall into the same and consequently it would take in and swallow greater abundance of water and by this means the Ditches and Draines of the Up-Lands would likewise more easily Fall into them especially 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 quantity 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 carrying 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 TO The Right Honourable MONSIGNORE D. Ferrante Cesarini MY Treatise of the MENSURATION of RUNNING WATERS Right Honourable and most Noble Sir hath not a greater Prerogative than its having been the production of the command of Pope Vrban VIII when His Holiness 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 themselves 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 Honour most refined judgement As to that Point which I touch upon in the Conclusion namely That the consideration of the Velocity of Running Water supplyeth the consideration of the Length omitted in the common way of measuring Running Waters Your Lordship having commanded me that in favour of Practise and for the perfect discovery of the disorder that commonly happeneth now adayes in the distribution of the Waters of Fountains I should demonstrate 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 those who finde therein some kinde of obscurity In the dayes of yore before that the admirable Art of Weaving was in use there was found in Persia a vast and unvaluable Treasure which consisted in an huge multitude of pieces of Ermesin 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 difficulty 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 inestimable Treasure selling the propriety in those pieces to divers Merchants 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 havâ— 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 Thickness bargained for and that of the Length which was infinite there 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 stuffe was retarded as it issued out of the Cave and although the total length of the Piece was infinite for that it never ceased coming forth and so was not to be computed yet nevertheless 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 velocity 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 Water and to remedy such an inconvenience it is necessary to determine the length in the velocity for never shall we be able to make a guesse at the quantity of the Body of Running VVater 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 exact and constant First the quantity of the Water ought diligently to be examined 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 dischargeth 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 determinate 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 without the least errour which Rule was taught me by my Master Sign Galilaeo Galilaei Chief Philosopher to the most Serene 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 Aqueduct 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 Aqueducts do not maintain them alwayes equally high and full of Water but that sometimes they increase and sometimes decrease which accident might possibly procure some difficulty in our distribution Therefore to the end that all manner of scruple 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 benefit as being in my judgment the most enormous and intolerable The first inconvenience is that in the common way of measuring 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 many a day so many in a year c. The second disorder that happeneth at present in the distribution 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 belongeth to them of right And I have seen it done of my own experience But in our way of measuring and distributing Waters there can no fraud be committed and putting the case that they should be committed it s an easie matter to know it and amend it by repairing to the Tribunal appointed Thirdly it happens very often and we have examples thereof both antient and modern that in dispensing the Water after the common and vulgar way there is sometimes more Water dispended than there is in the Register in which there will be registred 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 Frontano writes in his 2. Book De Aquaductibus Vrbis Romae where he observeth that they had in Commentariis 12755. Quinaries of Water and found that they dispensed 14018. Quinaries 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 Pondus pondus Mensura mensura as the Holy Ghost speaketh 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 VVaters 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 likewise 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 Mensura 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 necessary 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 A TABLE Of the most observable matters in this Treatise of the MENSURATION of RUNNING WATERS A ABatements of a River in different and unequal Diversions is alwaies equal which is proved with 100. Syphons Page 75 Arno River when it riseth upon a Land-Flood near the Sea one third of a Brace it riseth about Pisa 6. or 7. Braces 82 B Banks near to the Sea lower than far from thence Corollary XIV 16 Brent River diverted from the Lake of Venice and its effects 64 Brent supposed insufficient to remedy the inconveniences of the Lake and the falsity of that supposition 67 Brent and its benefits in the Lake 70 Its Deposition of Sand in the Lake how great it is 78 79 Bridges over Rivers and how they are to be made Appendix VIII 20 Burana River its rising and falling in Panaro 110 C Castelli applyed himself to this Study by Order of Urban VIII 2 Chanel of Navigation in the Valleys of Bologna and its inconveniences 99 Carried into the Po of Ferrara and its benefits ibid. Ciampoli a lover of these Observations of Waters 3 D Difficulty of this business of Measuring Waters 2 Disorders that happen in the distribution of the Waters of Aqueducts and their remedies 113 Distribution of the Waters of Fountains and Aqueducts Appendix X. 22 Distribution of Water to over-flow Grounds Appendix XI 23 69 70 Diversion of Reno and other Brooks of Romagna advised by P. Spernazzati to what end it was 100 Drains and Ditches the benefit they receive by cutting away the Weeds and Reeds Appendix IX 21 Drains and Sewers obstructed in the Diversion of Reno into Main Po and a remedy for the same 110 E Engineers unvers'd in the matter of Waters 2 Erour found in the common way of Measuring Running Waters 68 69 Errour inderiving the Water of Acqua Paola Appendix II. 17 18 Errour of Bartolotti 86 87 Errours of Engineers in the Derivation of Chenels Corollary XII 12 Errour 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 9 Errour of Giulio Frontino in Measuring the Waters of Aqueducts Appendix I. 17 Errours committed in cutting the Bank at Bondeno in the swellings of Po Corollary XIII 81 F Fenns Pontine Drained by Pope Sixtus Quintus with vast expence 92 The ruine and miscarriage thereof 93 Tardity of the principal Chanel that Drains them cause of the Drowning ibid. They are obstructed by the Fishing-Wears which swell the River 94 Waters of Fiume Sisto which flow in great abundance into the Evacuator of the said Fenns 94 95 Remedies to the disorders of those Fenns 95 96 Fontana Giovanni his errours in Measuring Waters Corollary XI 9 Fiume Morto whether it ought to fall into the Sea or into Serchio 79 Let into Serchio and its inconveniences 79 80 The dangerous rising of its Waters when to be expected 81 Its inconveniences when it is higher in level than Serchio and why it riseth most On the Sea-coasts at such time at the Winds make the Sea to swell 83 G Galilaeo Galilaei honourably mentioned Page 2 28 His Rules for measuring the time 49 H Height vide Quick Heights different made by the same stream of a Brook or Torrent according to the divers Velocities in the entrance of the River Corollary I. 6 Heights different made by the Torrent in the River according to the different heights of the River Corollary II. ibid. K Knowledge of Motion how much it importeth 1 L Lake of Perugia and he Observation made on it Appendix XII 42 Lake of Thrasimenus and Considerations upon it a Letter written to Sig. Galilaeo Galilaei 28 Lake of Venice and Considerations upon it 63 73 Low Waters which let the bottom of it be discovered 64 The 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 66 Lakes and Meers along the Sea-ccosts and the causes thereof 65 Length of Waters how it is to be Measured 70 M Measure and Distributions of Waters Appendix V. 18 Measure of Rivers that fall into others difficult Coroll X. 9 Measure of the Running Water of a Chanel of an height known by a Regulator of a Measure given in a time assigned Proposition I. Problem I. 50 Measure of the Water of any River of any greatness in a time given Proposition V. Problem III. 60 Measure that shewes how much Water a River dischargeth in a time given 48 Mole-holes Motion the principal subject of Philosophy 1 Mud. Vide Sand. N Navigation from Bologna to Ferrara is become impossible till such time as Reno be diverted 101 Navigation in the Lake of Venice endangered and how restored 65 70 P Perpendicularity of the Banks of the River to the upper superficies of it 37 Perpendicularity of the Banks to the bottom 37 Perugia Vide Lake Pontine Vide Fenns Ports of Venice Malamocco Bondolo and Chiozza choaked up for wâ—nt of Water in the Lake 65 Proportions of unequal Sections of equal Velocity and of equal Sections of unequal Velocity Axiome IV. and V. 38 Proportions of equal and unequal quantities of Water which pass by the Sections of different Rivers Proposition II. 39 Proportions of unequal Sections that in equal times discharge equal quantities of Water Proposition III. 41 Proportion wherewith one River falling into another varieth in height Proposition IV. 44 Proportion 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. 44 Proportion of the Heights made by two equal Brooks or Streams falling into the same River Proposition VI. 45 Proportion of the Water which a River dischargeth encreasing in Quick-height
by the addition of new Water to that which it dischargeth after the encrease is made Proposition IV. Theor. II. 54 Proportion of a River when highâ—â— to it self when low Coroll I. 55 Q Quantity of Running Waters is never certain if with the Vulgar way of Measuring them their Velocities be not considered 32 Quantities 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. 38 Quick-Height of a River what it is Definition V. 48 R Reason of the Proverb Take heed of the still Waters Coroll VI. 7 Reasons of Monsignore Corsini against the diversion of Reno into the Po of Volano 105 Reasons of Cardinal Capponi and Monsig Corsini for the turning of Reno into Main Po. 106 Two objections on the contrary and answers to them 104 105 What ought to be the proportion of the Heights of Reno in Reno and of Reno in Po. 110 Regulator what it is Definition IV. 48 Relation of the Waters of Bologna and Ferrara by Monsignore Corsini 100 Reno in the Valleys and its bad effects 100 101 Two wayes to divert it 103 The facility and utility of those wayes Ibid. The difficulties objected 104 Reply to Bartolotti touching the dangers of turning Eiume Morto into Serchio 83 Retardment of the course of a River caused by its Banks Appendix VII 19 Risings made by Flood-Gates but small Appendix XIII 26 Rivers that are shallow swell much upon small showers such as are deep rise but little upon great Floods Corollary III. 6 Rivers the higher they are the swifter Ibid. Rivers the higher they are the lesse they encrease upon Floods 49 Rivers when they are to have equal and when like Velocity Ibid. Rivers in falling into the Sea form a Shelf of Sand called Cavallo 65 Five Rivers to be diverted from the Lake of Venice and the inconveniences that would ensue thereupon 74 75 A 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. Theorem I. 51 Keepeth the proportion of the heights to the Velocities Corollary 52 S Sand and Mud that entereth into the Lake of Venice and the way to examine it 76 Seas agitated and driven by the Winds stop up the Ports 64 65 Sections of a River what they are Definition I. 37 Sections 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 38 Sections of the same River and their Proportions to their Velocities Coroll I. 42 Sections of a River discharge in any whatsoever place of the said River equal quantities of Water in equal times Proposition I. 39 Sile River what mischiefes it threatneth diverted from the Lake 74 Spirtings of Waters grow bigger the higher they go Coroll XVI 16 Streams of Rivers how they encrease and vary Coroll I. 6 Streams retarded and the effects thereof Coroll IX 8 T Table of the Heights Additions and Quantities of Waters and its use 56 Thrasimenus Vide Lake Time how it s measured in these Operations of the Waters 49 Torrents encrease at the encreasing of a River though they carry no more Water than before Coroll IV. 6 Torrents when they depose and carry away the Sand. Coroll V. 7 Torrents and their effects in a River 6 7 Torrents that fall into the Valleys or into Po of Valano and their mischiefs prevented by the diverting of Reno into Main Po. 100 Tyber and the causes of its inundations Coroll VIII 8 V Valleys of Bologna and Ferrara their inundations and disorders whence they proceed 97 Velocity of the Water shewn by several Examples 3 Its proportion to the Measure 5 Velocities equal what they are 47 Velocities like what they are 47 48 Velocities of Water known how they help us in finding the Lengths 113 A Fable to explain the truth thereof Ibid. Venice Vide Lake Vse of the Regulator in measuring great Rivers Consideration I. 60 W Waters falling why they disgross Coroll XVI 16 Waters how the Length of them is Measured 70 Waters that are imployed to flow Grounds how they are to be distributed 19 53 54 Waters to be carryed in Pipes to serve Aquaducts and Conduits how they are to be Measured 15 116 Way to know the rising of Lakes by Raines 28 Way of the Vulgar to Measure the VVaters of Rivers 68 Wind Gun and Portable Fountain of Vincenzo Vincenti of Urbin 11 Windes contrary retard and make Rivers encrease Coroll VII 8 The END of the TABLE of the Second Part of the First TOME Copernicus reputeth the Earth a Globe like to a Planet Coelestial substances that are in alterable and Elementary that be alterable art necessary in the opinion of Aristotle Aristotle maketh the World perfect because it hath the threefold demension Aristotles demonstrations to prove the dimensions to be three and no more The number three celebrated amongst the Pythagorians Omne Totum Perfectum Or Solid Plato held that humane understanding partook of divinity because it understood numbers The Mystery of Pythagorick numbers fabulous De Papyrio pâ—aetextato Gellius 1. 2. 3. A Geometrical demonstration of the triple dimension In physical proofs â—eâ—metrical exactness is not necessary Parts of the world are two according to Aristotle Coelestial and Elementary contrary to one another Local motion of three kinds right circular mixt Circular and streight motions are simple as proceeding by simple lines Ad medium à 〈◊〉 circa medium The definition of Nature either imperfect or unseasonable produced by Aristotle The Helix about the Cylinder may be said to be a simple line Aristotle accommodates the rules of Architecture to the frame of the World and not the frame to the rules Right motion sometimes simple and sometimes mixt according to Arist. The circular line perfect according to Aristotle and but the right imperfect and why The world is supposed by the Author to be perfectly ordinate Streight motion impossible in the world exactly ordinate Right motion nature infinite Motion by a right line naturally impossible Nature attempts not things impossible to be effected Right motion might perhaps be in thâ— first Chaos Right motion is commodious to range in order things out of order Mundane bodies moved in the beginning in a right line and afterwards circularly according to Plato * Thus doth he coverâ—ly and modestly stile himselfe throughout this work A moveable being in a state of rest shall not move unless it have an inclination to some particular place The moveable accelerates its motion going towards the place whither it hath an inclination The moveable passing from rest goeth thorow all the degrees of tardity Rest the infinite degree of tardity The moveable doth not accelerate save only as it approacheth nearer to us term Nature to introduce in the moveable a certain degree of velocity made it move in a right line Vniform
Fiorentini Weariness more to be feared in the starry Sphere than in the terrestriall Globe Some in arguing first fix in their minds the conclusion beleeved by them and then adapt their reasons to that The motion of the water in ebbing and flowing not interrupted by rest * Pertiche venetiani * Pertiche venetiani * 〈◊〉 †He taketh 〈◊〉 Firmament 〈◊〉 the Sâ—arry Sphere and not as we vulgâ—â—ly receive the word The method observed by Clar. in confuting the Astronomers and by Salviatus in confuting him The greatest and least elevations of the new star differ not from each other more than the polar altitudes the said star being in the Firmnment * 〈◊〉 Astronomical Instruments are very subject to errour * Here the Latine version is erroneous making it a fortieth part of c. * Traguardi In hath not been hitherto proved by any whether the World be finite or infinite The Demonstrations of Aristotle to pâ—ove that the Vniverse is finite are all nullified by denying it to be moveable Aristotle makes that point to be the centre of the Universe about which all the Celestial Spheres do revolve A question is put in case that if Aristotle were forced to receive one of two propositions that make against his doctrine which he would admit It s more rational that the Orb containing and the parts contained do move all about one centre than uâ—on divers If the centre of the World be the 〈…〉 that about which the planets move the Sun and not the Earth is placed in it Observations from whence it is collected that the Sun and not the Earth is in the centre of the Celestial revolutions The mutation of figure in Venus argueth its motion to be about the Sun The Moon cannot seperate from the Earth The annual motion of the Earth mixing with the motions of the other Planets produce extravagant appearances The Systeme of the Universe designed from the appearances Venus very great towards the respective conjunction and very small towards the maintine Venus necessarily proved to move about the Sun The revolution of Mercury concluded to be about the Sun within the Orb of Venus Mars necessarily includeth within its Orb the Earth and also the Sun Mars at its opposition to the Sun shews to be sixty times bigger than towards the conjunction Jupiter and Saturn do likewise encompasse the Earth and the Sun The approximation and recession of the three superiour Planets importeth double the Suns distance The difference of the apparent magnitude lesse in Saturn than in Jupiter andâ— Jupiter than in Mars and why The Moons Orb invironeth the Earth but not the Sun The probable situation of the fixed stars Which ought to be accounted the sphere of the Vniverse Rest the annual motion and the diurnal ought to be distributed betwixt the Sun Earth and Firmament In a moveable sphere it seemeth more reasonable that its centre be stable than any other of its parts Granting to the Earth the annual it must of necessity also have the diurnal motion assigned to it Discourses more than childish serve to keep fools in the opinion of the Earths stability A declaration of the improbability of Copernicus his opinion Reasons and discourse in Aristarcus and Copernicus prevailed over manifest sence Mars makes an hot assaults upon the Coperâ—â—can Systeme The Phaenomena of Venus appear contrary to the Systeme of Copernicus Another difficulty raised by Venus against Copernicus Venus according to Copernicus either lucid in it self or else of a transparent substance Copernicus speaketh nothing of the small variation of bigness in Venus and in Mars The moon much disturbeth the order of the other Planets Answers to the three first objections against the Copernican Systeme The reason whence it happens that Venus and Mars do not appear to vary magnitude so much as is requisite The operations of the Telescope accounted fallacies by the Peripateticks Shining objects seem environed with adventitious rayes The reason why luminous bodies appear enlarged much the more by how much they are lesser Superficial figures encreasing proportion double to their lines Objects the more vigorous they are in light the more they do seem to increase An easie experiment that sheweth the increase in the stars by means of the adventitious rays Jupiter augments lesse than the Dog-star The Sun and Moon increase little It is seen by manifest experience that the more splendid bodies do much more irradiate than the lesse lucid The Telescope is the best means to take away the irradiations of the Stars Another second reason of the small apparent increase of Venus Copernicus perswaded by reasons contrary to sensible experiments Mercury admitteth not of clear observations The difficulties removed that arise from the Earths moving about the Sun not solitarily but in consort with the Moon The Medicean Stars areas it were four Moons about Jupiter The Principal scope of Astronomers is to give a reason of appearances Copernicus restored Astronomy upon the suppositions of Ptolomy What moved Copernicus to establish his Systeme Inconveniencies that are in the Systeme of Ptolomy The annual motion of the Earth most apt to render a reason of the exorbitances of the five Planets The Sun it self testifieth the annual motion to belong to the Earth The Lyncaean Academick the first discoverer of the Solar spots and all the other celestial novelties The history of the proceedings of the Academian for a long time about the observation of the Solar spots * Duumviro * This Authors true name is Christopher Scheinerus a Jesuit and his Book here meant is intituled Apelles post tabulam * La mia villa delle Sâ—lue A conceipt that came suddenly into the minde of the Academian Lyncaeus concerning the great consequence that followed upon the motion of the Solar spots Extravagant mutations to be observed in the motions of the spots foreseen by the Academick in case the Earth had the annual motion The first Accident to be observed in the motion of the Solar spots and consequently all the rest explained The events being observed were answerable to the predictions Though the annual motion assigned to the Earth answerth to the Phaenomena of the solar spots yet doth it not follow by conversion that from the Phaenomena of the spots one may infâ—r the annual motion to belong to the Earth The Pure Peripatetick Philosophers will laugh at the spots and their Phaenomena as illusions of the Chrystals in the Telescope If the Earth be immoveable in the centre of the Zodiack there must be ascribed to the Sun four several motions as is declared at length * I should have told you that the true name of this concealed Authour is Christopher Scheinerus and its title Disquisitiones Mathematica * i. e. the Ecliptick Instances of a certain Book Ironically propounded against Copernicus Supposing the annual motion to belong to the Earth it followeth that one fixed Star is bigger than the whole grand Orb. Tycho his Argument grounded upon a false Hypothesis
of Tycho made with great expence What Instruments are apt for most exact observation * Italian braces An exquisite observation of the approach and departure of the Sun from the Summer Solstice A place accommodated for the observation of the fixed stars as to what concers the annual motion of the Earth The Copernican Systeme difficult to be understood but easie to be effected Necessary prepositions for the better conceiving of the consequences of the Earths motion A plain Scheme representing the Copernican Hypothesis and its consequences Axiomes commonly admitted by all Philosophers Aristotle taxeth Plato for being too studious of Geometry Peripatetick Philosophers condemn the Study of Geometry and why Four several motions assigned to the Earth The motion of descent belongs not to the terrestrial Globe but to its parts The annual and diurnal motion are compatible in the Earth Every pensil and librated body carryed round in the circumference of a circle acquireth of it self a motion in it self contrary to that An Experiment which sensibly shews that two contrary motions may naturally agree in the same moveable The third motion ascribed to the Earth is rather a resting immoveable An admirable intern vertue of the terrestrial Globe of alwayes beholding the same part of Heaven The terrestrial Globe made of Loade-stone * An eminent Doctor of Physick our Countreyman born at Colchester and famous for this his learned Treatise published about 60 years since at London The Magnetick Philosophy of William Gilbert The Pusillanimity of Popular Wits The Terrestrial Globe composed of sundry matters The interne parts of the terrestrial Globe must of necessity be solid * Or MOULD * Of which with the Latin translatour I must once more professe my self ignorant Our Globe would have been called stone in stead of Earth of that name had been giuen it in the beginning The method of Gilbert in his Philosophy Many properties in the Magnet 〈…〉 The Magnet armed takes up much more Iron than when armed * Or Closet of rarities The first observers and inventers of things ought to be admired The true cause of the multiplication of vertue in the Magnet by means of the arming Of a new effect its necessary that the cause be likewise new It is proved that Iron consists of parts more subtil pure and compact than the magnet A sensible proof of the impurity of the Magnet * The Author hereby meaneth that the stone doth not all consist of magnetick matter but that the whiter specks being weak those other parts of the Loadstone of a more dark constant colour contain all that vertue wherewith bodies are attracted * A common sewing needle Sympathy and Antipathy terms used by Philosophers to give a reason easily of many natural effests A pleasant example declaring the invalidity of some Phylosophical argumentations The several natural motions of the Magnet Aristole grants a compound motion to mixt bodies The motion of mixt bodies ought to be such as may result from the composition of the motions of the simple bodies compounding With two right motions one cannot compose circular motions Philosophers are forced to confesse that the Magnet is compounded of coelestial substances and of elementary The errour of those who call the Magnet a mixt body and the terrestrial Globe a simble body * Ogliopotrida a Spanish dish of many ingredients boild together The Discourses of Peripateticks full of errours and contradictions An improbable effect admired by Gilbertus in the Loadstone The vain argumentation of some to prove the Element of Water to be of a Spherical superficies Nature in sport maketh the ebbing and flowing of the Sea to approve the Earthâ— mobility The tide and mobility of the Earth mutually confirm each other All terrene effects indifferently confirm the motion or rest of the Earth except the ebbing and flowing of the Sea The first general conclusion of the impossibility of the ebbing and flowing the immobility of the terrestrial Globe being granted The knowledge of the effests contributes to the investigation of the causes Three Periods of ebbings and flowings diurnal monethly and annual Varieties that â—appen in the diurâ—â—â— period * A Strair so called * Or Ilva * Or Crets The cause of the ebbing and flowing alledged by a certain modern Philosopher The cause of the ebbing and flowing ascribed to the Moon by a certain Prelate Hieronymus Borrius and other Peripateticks refer it to the temperate heat of the Moon Answers to the vanities alledged as causes of the ebbing and flowing * Or rather smooth The Isles are tokens of the unevennesse of the bottomes of Seas Poetick wits of two kinds Truth hath not so little light as not to be discovered amidst the umbrages of falshoods Aristotle holdeth those effects to be miraculous of which the causes are unknown It is proved impossible that there should naturally be any ebbing and flowing the Earth being immoveable * Palms †Lio is a fair Port in the Venetian Gulph lying N. E. from the City True and natural effects follow without difficulty Two sorts of motions of the containing Vessel may make the contained water to rise and fall The Cavities of the Earth cannot approach or go farther from the centre of the same The progpessive and uneven motion may make the water contained in a Vessel to run to and fro * A Town lying S. E. of Venice The parts of the terrestrial Globe accelerate and regard in their motion Demonstrations how the parts of the terrestriall Globe accelerate and retard The parts of a Circle regularly moved about its own centre move in divers times with contrary motions The mixture of the two motions annnal and diurnal causeth the inequality in the motion of the parts of the terrestrial Globe The most potent and primary cause of the ebbing and flowing Sundry accidents that happen in the ebbings flowings The first accident The Water raised in one end of the Vessel returneth of its self to Aequilibrium In the shorter Vessels the undulations of waters are more frequent The greater profundity maketh the undulations of waters more frequent Water riseth falleth in the extream parts of the Vessel and runneth to and fro in the midst An accident of the Earths motions impossible to be reduced to practice by art Reasons renewed of the particnlar accidents observed in the ebbings and flowings Second causes why in small Seas and in Lakes there are no ebbings and flowings The reason given why the ebbings and flowings for the most part are every six hours The cause why some Seas though very long suffer no ebbing and flowing Ebbings and flowings why greatest in the extremities of Gulphs and least in the middle parts Why in narrow places the course of the waters is more swift than in larger A discussion of 〈…〉 â—abstruce 〈…〉 obseâ—ved 〈…〉 ebbing and â—â—â—wing The cause why in some narrow Channels we see the Sea-waters run alwayes one way * Or current The Hypothesis of the Earths mobility taken in favour of the
Christianus ita noverit ut cirtissima ratione vel experientiâ teneat Turpe autem est nimis perniciosum ac maxime cavendum ut Christianum de his rebus quasi secundum Christianas litteras loquentem ita delirare quilibet infidelis audiat ut quem admodum dicitur toto Caelo errare conspiciens risuÌ„tenere vix possit non tam molestum est quod errans homo derideretur sed quod auctores nostri ab tis qui foris sunt talia sensisse creduntur cum magno exitio corim de quorum salute satagimus tanquam indocti reprehenduntur atque respuuntur Cum enim quemquam de numero Christianorum eaiâ—re quam ipsi optime norunt deprehenderint vanam sententiam suam de nostris libris asserent quo pacto illis Libris credituri sunt de Resurrectione Mortuorum de spe vitae eternae Regnoque Celorum quando de his rebus quas jam experiri vel indubitatis rationibus percipere potuerunt fallaciter putaverint esse conscriptos y Quid enim molestiae tristiaeque ingerant prudentibus fratribus tenerarâ—j praesumpiores satis dici non potest cum si quando de falsa prava opinione sua reprehendi convinci caeperint ab iis qui nostrorum librorum auctoritate apertissima falsitate dixerunt eosdnm libros Sanctos unde id probent proferre conantur vel etiam memoriter quae ad testimonium vâ—lere arbitrantur multa inde verba pronunciant non intelligentes neque quae loquuntur neque de quibus affirmant If this passage seem harsh the Reader must remember that I do but Translate * 〈…〉 On it s own Axis * Lux ejus colligit convertitque ad se omnia quae videntur quae moventur quae illustrantur quae calescunt uno nomine ea quae ab ejus splendore continentur Itaque Sol 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 dicitur quod omnia congreget colligatque dispersa * Si enim Sol hic quem videmus eorum quae sub sensum cadunt essentias qualitates quaeque multa sint ac dissimiles tamen ipse qui unus est aequaliterque lumen fundit renovat alit tuetur perficit dividit conjungit fovet faecunda reddit auget mutat firmat edit movet vitaliaque facit omnia unaquaque res hujus universitatis pro captu suo unius atque ejusdem Solis est particeps causasque multorum quae participent in se aequabiliter anticipatas habet certe majori raticne c. Solem stetisse dum adhuc in Hemisphaerio nostro supra scilicet Horizontem existeret Cajetan in loco * Or Poles * Gen. Chp. 〈◊〉 v. 1. * Psal. 24. 2. * Psal. 137. 1. * Chap. 1. v. 4 to 9. Psal. 104. v. 5. * Shelter * Officium * In vita ejus * Followers of that Learned Kings Hypothesis * That is 5000 miles eight of these making an Italian or English mile of a 1000. paces every pacâ— containing 5. Feet * Chap. 1. v. 4. The Motion of the Earth not against Scripture Faith is more certain than either Sense or Reason * 2 Pet. 1. 19. * Or Primum Mobile * Cardan de rerum vaâ—iet Lib. 1. Cap. 1. * P. Clavius in ultima suor Operum editione The Author first Theologically dâ—fendeâ—h the â—arths Mâ—bility approved by â—ary of the Moderns b Or In Sole posuit tabernaculum suum according to the Translation our Author followeth In Sphericall Bodies Deorsum is the Centre and Sursum the Circumference Hell is in the centre of the Earth not of the World Heaven and Eartâ— are always 〈◊〉 opposed to each other After the day of Judgment the Earth shall stand immoveable * Circa Cardines Coeli Luke 16. Alia sunt notiora nobis alia notiora natura vel secundum se Arist lib. 1. Phys. * Aut ad Umbram Which are really the great Lights in Heaven The Sun Moon and Stars are one the same thing The Earth is another Moon or Star Why the Sunne seemeth to us to move not the Earth Aeneid 3. a Eccles. c. 1. v. ult b Chap. 3. v. 11. c 1 Cor. c. 4. v. 5. d 1 Cor. c. 13. v. 12. e 1 John c. 3. v. 2. f 1 Cor. c. 13. v. 12. g Ecclesiast 15. 3. h 1 Cor. c. 2. v. 2. i Isa. c. 48. v. 17. 1 Thess. 4. Joshua c. 10. ver 12. * expected Isa. c. 38. v. 8. â— Several Motions of the Earth according to Copernicus The Earth Secundum Totum is Immutable though not Immovable The Earth cannot Secundum Totum remove out of its Natural Place The Natural Place of the Earth The Moon is an Aetherial Body The Earths Centre keepeth it in its Natural Place Gravity and Levity of Bodies what it is All Coelestial Bodies have Gravity and Levity Compressive Motion proper to Gravity the Extensive to Levity Heaven is not composed of a fift Essence differing from the matter of inferior Bodies Nor yet a Solid or dense Body but Rare * Delle Macchie solarj * Vnius Corporis simplicis unus est motus simplex et huic dua species Rectus Circularis Rectus duplex à medio ad medium primus levium ut Aeris Ignis secundus gravium ut Aquae Terra Circularis quiest circa medium competit Coelo quod neque est grave neque leve Arist. de Coelo Lib. 1. * Vide Copernicum de Revolutionibus Coelest Simple Motion peculiar to only Simple Bodies Right Motion belongeth to Imperfect Bodies and that are out of their natural Places Right Motion cannot be Simple Right Motion is ever mixt with the Circular * aequabilis * Even Circular Motion is truly Simple and Perpetual Circular Motion belongeth to the Whole Body and the Right to its parts Circular and Right Motion coincedent and may consist together in the same Body The Earth in 〈◊〉 sense it may 〈…〉 be said 〈…〉 the lowest 〈◊〉 of the World Christ in his Incarnation truly descended from Heaven and in his Asceâ—sion truly ascended into Heaven 2 Cor. c. 12. v. 3. Whether in the body or out of the body I cannot tell The Sun is King Heart and Lamp of the World himself being 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 absolutely independent The Aenigma of Plato a Circa omniâ—m Regem sunt omnia Secunda circa Secundum et Tertia circa Tertium Vide Theodo de Graec. affect curat lib. 2. Sâ—euch lib. de Parennj Philoso Eccles. c. 1. 2. 3. and almost thoout * Quod fiunt vel sunt sub sole Heaven according to Copernicus is the same with the most tenuous Aether but different from Paradice which surpasseth all the Heavens a Exod. 25. 31. b My Authour following the vulgar Translation which hath an Eligance in some things beyond ours cites the words thus Facies Candelabrum ductile de auro mundissimo Hastile ejus Calamos Sphaerulas ac Lilia ex ipso procedentia c verse 12. d or Spheres e Though our Authour speaketh here positively of nine Months c. Fathers are not agreed about the period of this planet nor that of Mercury as you may see at large in Ricciolus Almagest nov Tom. 1. part 1. l. 7. sect 3. cha 11. num 11. page 627. where he maketh Venus to consummate her Revolution in neer 225 dayes or 7 12 Mon. and Mercury in about 88 dayes or 3 Months in which he followeth Kepl. in Epitome Astronom p. 760. f vers 33 34. g 1 Kings c. 7. v. 49. 2 Chron. c. 4. vers 7. h Exod. 28. 33 34 39. v. 24 25 26. i Sap. c. 18. v. 24. k Exod. c. 28. v. 6 9 17 36. l Or totus Orbis Terrarum as the vulgar Translation hath it m Numb c. 20. v. 5. n Joel c. 1. v. 12. o Hagg. c. 2. v. 19. p Deut. c. 8. v. 8. q 1 Kings c 7. v. 20. 2 Kings c. 25. v. 17. 2 Chro. c. 3. v. 15 16. c. 4. v. 12. 13. Jerem. c. 52. v. 21 22. r Gen. c. 1. v. 1. s Psal. 67. v. 6 7. * Psal. 9 v. 5 6. * Institutionum omnium Doctrâ—narum * De Oraculis * De Divinatiâ—-ne artificiosa * De Divinatiâ—-ne Naturali Cosmologica a Nella continuatione dell Nuntio siderio b Lâ—ttera al P. Abbaâ—â— D. B. Castelli D'Aâ—cetro li. 3. Decemb. 16 9. c De Motu Aquanâ— â—ib 2. Prop. 37. p. 191. * And as is at large demonstrated by that most excellent and Honourable personage Mr. Boile in the industrious experiment of his Pneumatical Engine * Artesia * Commentarius beareth many senses but in this place signifieth a certain Register of the quantities of the Waters in the several publique Aquiducts of Rome which word I find frequently used in the Law-books of antient Civilians And by errogation we are to understand the distribution or delivering out of those stores of Water * A Coyn of Pope Julius worth six pence * Or Sluice * In Pregadi a particular Council the Senators of which have great Authority * A Venice Brace is 11 16 of our yard * A River of that name * I. Savii dell ' Acque a particular Council that take care of the Lakes and other Aquatick affairs * He here intends the Demonstrations following at the end of the first Book * Deeper * Lib. 1. * The Countrey or Province lying round the City heretofore called Latium * Or Lordship * The Popes Exchequer * Polesine is a plat of Ground almost surrounded with Bogs or waters like an Island * People of Ferrara * In Chanels made by hand * The inch of these places is somewhat bigger than ours * Of Adriano * Larghezza but misprinted