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
line F to the line G and because the quantity of water which passeth through the Section A is to that which passeth through the Section B in a proportion composed of the proportions of the Section A to the Section B and of the velocity through A to the velocity through B therefore the line E shall be the line to F in a proportion compounded of the same proportions namely of the proportion of the Section A to the Section B and of the velocity through A to the velocity through B but the line E hath to the line G the proportion of the Section A to the Section B therefore the proportion remaining of the line G to the line F shall be the proportion of the velocity through A to the velocity through B therefore also the line G shall be to the line E as the velocity by A to the velocity by B And conversly the velocity through B shall be to the velocity through A as the line E to the line G that is to say as the Section A to the Section B and therefore in two Sections c. which was to be demonstrated COROLLARIE HEnce it is manifest that Sections of the same River which are no other than the vulgar measures of the River have betwixt themselves reciprocal proportions to their velocities for in the first Proposition we have demonstrated that the Sections of the same River discharge equal quantities of Water in equal times therefore by what hath now been demonstrated the Sections of the same River shall have reciprocal proportion to their velocities And therefore the same running water changeth measure when it changeth velocity namely increaseth the measure when it decreaseth the velocity and decreaseth the measure when it increaseth the velocity On which principally depends all that which hath been said above in the Discourse and observed in the Corollaries and Appendixes and therefore is worthy to be well understood and heeded PROPOSITION IV. If a River fall into another River the height of the first in its own Chanel shall be to the height that it shall make in the second Chanel in a proportion compounded of the proportions of the breadth of the Chanel of the second to the breadth of the Chanel of the first and of the velocitie acquired in the Chanel of the second to that which it had in its proper and first Chanel LEt the River AB whose height is AC and breadth CB that is whose Section is ACB let it enter I say into another River as broad as the line EF and let it therein make the rise or height DE that is to say let it have its Section in the River whereinto it falls DEF I say that the height AC hath to the height DE the proportion compounded of the proportions of the breadth EF to the breadth CB and of the velocity through DF to the velocity through AB Let us suppose the Section G equal in velocity to the Section AB and in breadth equal to EF which carrieth a quantity of Water equal to that which the Section AB carrieth in equal times and consequently equal to that which DF carrieth Moreover as the breadth EF is to the breadth CB so let the line H be to the line I and as the velocity of DF is to the velocity of AB so let the line I be to the Line L because therefore the two Sections AB and G are equally swift and discharge equal quantity of Water in equal times they shall be equal Sections and therefore the height of AB to the height of G shall be as the breadth of G to the breadth of AB that is as EF to CB that is as the line H to the line I but because the Water which passeth through G is equal to that which passeth through DEF therefore the Section G to the Section DEF shall have the reciprocal proportion of the velocity through DEF to the velocity through G but also the height of G is to the height DE as the Section G to the Section DEF Therefore the height of G is to the height DE as the velocity through DEF is to the velocity through G that is as the velocity through DEF is to the velocity through AB That is finally as the line I to the line L Therefore by equal proportion the height of AB that is AC shall be to the height DE as H to L that is compounded of the proportions of the breadth EF to the breadth CB and of the velocity through DF to the velocity through AB So that if a River fall into another River c. which was to be demonstrated PROPOSITION V. If a River discharge a certain quantitie of Water in a certain time and after that there come into it a Flood the quantity of Water which is discharged in as much time at the Flood is to that which was discharged before whilst the River was low in a proportion compounded of the proportions of the velocity of the Flood to the velocity of the first Water and of the height of the Flood to the height of the first Water SUppose a River which whilst it is low runs by the Section AF and after a Flood cometh into the same and runneth through the Section DF I say that the quantity of the Water which is discharged through DF is to that which is discharged through AF in a 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 to the line S and as the height DB is to the height AB so let the line S to the line T and let us suppose a Section LMN equal to DF in height and breadth that is LM equal to DB and MN equal to BF but let it be in velocity equal to the Section AF therefore the quantity of Water which runneth through DF shall be to that which runneth through LN as the velocity through DF is to the velocity through LN that is to the velocity through AF and the line R being to the line S as the velocity through DF to the velocity through AF therefore the quantity which runneth through DF to that which runneth through LN shall have the proportion of R to S but the quantity which runneth through LN to that which runneth through AF the Sections being equally swift shall be in proportion as the Section LN to the Section AF that is as DB to AB that is as the line S to the line T Therefore by equal proportion the quantity of the water which runneth through DF shall be in proportion to that which runneth through AF as R is to T that is 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 discharge a certain quantity c.
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
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
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
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
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
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
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
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
answer proportionably as if descended from the same place 19 Immense Magnitudes and Numbers are incomprehensible by our Vnderstandings 332 MARS Mars necessarily includeth within its Orb the Earth and also the Sun 298 Mars at its Opposition to the Sun seems sixty times bigger than towards the Conjunction 298 Mars makes an hot assault upon the Copernican Systeme 302 MARSILIUS Signor Caesar Marsilius observeth the Meridian to be moveable 422 MEDICEAN The time of the Medicean Planets conversions 101 The Medicean Planets are as it were four Moons about Jupiter 307 MEDITERRAN Mediterranean Sea made by the Seperation of Abila and Calpen 35 The Voyages in the Mediterran from East to West are made in shorter times than from West to East 403 MERCURY The Revolution of Mercury concluded to be about the Sun within the Orb of Venus 298 Mercury admitteth not of clear Observations 307 MOON The Moon hath no Generation of things like as we have nor is it inhabited by Men. 47 In the Moon may be a Generation of things different from ours 47 There may be Substances in the Moon very different from ours 48 The first resemblance between the Moon and Earth which is that of Figure is proved by their manner of being illuminated by the Sun 48 The second resemblance is the Moons being Opacous as the Earth 48 The third resemblance is the Moons being Dense and Mountainous as the Earth 49 The fourth resemblance is the Moons being distinguished into two different parts for Clarity and Obscurity as the Terrestrial Globe into Sea and Land 49 The fifth resemblance is Mutation of Figures in the Earth like those of the Moon and made with the same Periods 49 All the Earth seeth halfe onely of the Moon and halfe onely of the Moon seeth all the Earth 51 Two Spots in the Moon by which it is perceived that She hath respect to the Centre of the Earth in her Motion 52 Light reflected from the Earth into the Moon 52 The sixth resemblance is that the Earth and Moon interchangeably illuminate 53 The seventh resemblance is that the Earth and Moon interchangeably Ecclipse 53 The Secondary Clarity of the Moon esteemed to be its Native Light 54 The Surface of the Moon more sleek then any Looking-Glasse 55 The eminencies and Cavities in the Moon are illusions of its Opacous and Perspicuous parts 55 The Moons Surface is sharp as is largely proved 57 The Moon if it it were sleek like a Spherical Looking-Glasse would be invisible 60 62 The apparent Vnevennesses of the Moons Surface aptly represented by Mother of Pearl 70 The apparent Vnevennesses of the Moon cannot be imitated by way of more and lesse Opacity and Perspicuity 71 The various Aspects of the Moon imitable by any Opacous matter 71 Sundry Phaenomena from whence the Moons Montuosity is argued 71 The Moon appears brighter by night than by day 72 The Moon beheld in the day time is like to a little Cloud 72 Clouds are no lesse apt than the Moon to be illuminated by the Sun 73 A Wall illuminated by the Sun compared to the Moon shines no lesse than it 73 The third reflection of a Wall illuminates more than the first of the Moon 74 The Light of the Moon weaker than that of the Twy-light 74 The secondary Light of the Moon caused by the Sun according to some 76 The secondary Light of the Moon appears in form of a Ring i. e. bright in the extreme Circumference and not in the midst and why 77 The secondary Light of the Moon how it is to be observed 78 The Moons Discus in a Solar Eclipse can be seen onely by Privation 78 Solidity of the Moons Globe argued from its being Mountainous 81 The secondary Light of the Moon clearer before the Conjunction than after 82 The obscurer parts of the Moon are Plains and the more bright Mountains 83 Long Ledges of Mountains about the Spots of the Moon 83 There are not generated in the Moon things like to ours but if there be any Productions they are very different 83 The Moon not composed of Water and Earth 83 Those Aspects of the Sun necessary for our Productions are not so in the Moon 83 Natural Dayes in the Moon are of a Moneth long 84 To the Moon the Sun declineth with a difference of ten Degrees and to the Earth of Forty seven Degrees 84 There are no Rains in the Moon 84 The Moon cannot seperate from the Earth 295 The Moons Orbe environeth the Earth but not the Sun 299 The Moon much disturbeth the Order of the other Planets 362 The Moons Motion principally sought in the Account of Eclipses 416 The Moon is an Aethereal Earth 492 MOTION and Motions Motion of Projects Vide Projects The Conditions and Attributes which differ the Celestial and Elementary Bodies depend on the Motions assigned them by Aristotle 25 Peripateticks improperly assign those Motions to the Elements for Natural with which they never were moved and those for Preternatural with which they alwayes move 33 Motion as to the things that move thereby is as if it never were and so farre operates as it relates to things deprâ—ved of Motion 98 Motion cannot be made without its moveable Subject 104 Motion and Rest principal Accidents in Nature 112 Two things necessary for the perpetuating of a Motion an unlimited Space and an incorruptible Moveable 117 Disparity in the Motions of a Stone falling from the Round Top of a Ship and from the Top of a Tower 123 The Motion of grave Pendula might be perpetuated impediments being removed 203 Whence the Motion of a Cadent Body is collected 224 The Motion of the Eye argueth the Motion of the Body looked on 224 Different Motions depending on the Fluctuation of the Ship 226 Our Motion may be either interne or externe and yet we never perceive or feel it 229 The Motion of a Boat insensible to those that are within it as to the Sense of Feeling 229 The Motion of a Boat sensible to Sight joyned with Reason 229 A simple Body as the Earth cannot move with three several Motions 231 Motion and Rest are more different than Right Motion and Circular 237 One may more rationally ascribe to the Earth two intern Principles to the Right and Circular Motion than two to Motion and Rest. 237 The diversity of Motions helpeth us to know the Diversity of Natures 237 Bodies of the same kind have Motions that agree in kinde 239 The greatnesse and smallnesse of the Body make a difference in Motion and not in Rest. 243 Every pensile and librated Body carried round in the Circumference of a Circle acquireth of it self a Motion in it self equal to the same 362 Two sorts of Motion in the containing Vessel may make the containing Water to rise and fall 387 An Accident in the Earths Motion impossible to be imitated 392 ABSOLUTE MOTION Things said to move according to certain of their parts and not according to their whole may not be said to
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
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
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
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
c. And for the greater facility of the Work we have described the following Table of which we will declare the use The Table is divided into three Series or Progressions of Numbers the first Series containeth all the Numbers in the Natural Progression beginning at a Unit and is called the Series of the Heights the second containeth all the odde numbers beginning at an unit and is called the Series of the Additions the third containeth all the square numbers beginning at an unit and is called the Series of Quantity Heights 1 2 3 4 5 6 7 8 9 10 11 Additions 1 3 5 7 9 11 13 15 17 19 21 Quantities 1 4 9 16 25 36 49 64 81 100 121 The use of the afore-mentioned Table FIrst if we suppose the whole quick height of a River of Running Water to be divided into any number of equal parts at pleasure and would abate the same one fift by means of a division let there be found in the Table in the Series of heights the number 5. the denominator of the part which the River is to abate and take the number that is immediately under it in the row of Additions which is 9. which let be substracted from the number 25. placed underneath the same in the row of Quantities the remainder 16. signifieth that of the 25. parts of Water that ran in the River whilst it was 5 measures high there do onely run 16. parts so that to make it abate â…• it is necessary to take 925 from the Water that the whole River did carry so that with substracting somewhat more than one third of the Water of the River it is abated but only one fift 2. And thus in the second place if on the contrary one would know how much water is to be added to the said River to make it increase one fift more in height so as that it may run in the Regulator 6. of those parts high of which it ran before but 5. let 6 be found in the row of heights and let the number 11. standing under the same be taken and added to the number 25. that is placed under the number 9. in the Additions and 5. in the heights and you shall have 36 which is the quantity of the water that runneth with the height of the River when it is high 6 of those parts whereof it was before but 5. 3. But if it should be desired to know how much water it is requisite to add to make the River rise so as that it may run in height 8. of those parts of which before it ran but 5 one ought to take the sum of the number of the Series of Additions standing under 8. 7. and 6 which are 15. 13. and 11. that is 39. and this shall be the summe that must be added to 25 So that to make the River to run 8. of those parts in height of which it before did run 5 it will be necessary to add 39. of those parts of which the River before was 25. 4. Likewise the same Table giveth the quantity of water that runneth from time to time through a River that increaseth by the addition of new water to the same in one of its heights the quantity of its water be known As for example If we knew that the River in one minute of an hour dischargeth 2500. of those measures of water and runneth in height 5. parts in the Regulator and afterwards should see that it runneth 8 Palms high finding in the row of quantity the number placed under 8. which is 64. we would say that the River heightned carrieth of water 64. of those parts whereof it carried before but 25 and because before it carried 2500. measures by the Golden Rule we will say that the River carrieth 6400. of those measures of which before it carried 2500. In this progress of Nature is one thing really curious and that at first sight seemeth to be somewhat Paradoxal that we proceeding ordinately in the diversions and additions with additions and diversions so unequal the abatings do notwithstanding alwaies prove equal and so do the risings And who would ever think that a River in height v. g. 10. Palms running and carrying an hundred measures in a minute of an hour is to abate but one Palm onely by the diversion of 19. of those measures and then again that the business cometh to that pass that it abateth likewise a Palm by the diversion of three onely of those measures nay by the diversion of but one measure and yet it is most certain And this truth meets with so manifest proofs in experience that it is very admirable And for the full satisfaction of those who not being able to comprehend subtil demonstrations desire to be clearly inform'd by the matters of fact and to see with their bobily eyes and touch with their hands what their understanding and reason cannot reach unto I will hear add another very easie way to reduce all to an experiment the which may be made in little in great or in very great of which I make use frequently to the admiration of such as see it I prepared an hundred Siphons or if you will bowed Pipes all equal and placed them at the brim of a Vessel wherein the water is kept at one and the same level whether all the Syphons work or but a certain number of them the mouths by which the water issueth being all placed in the same level parallel to the Horizon but lower in level than the water in the Vessel and gathered all the water falling from the Syphons into another Vessel standing lower than the former I made it to run away thorow a Chanel in such manner inclined that wanting water from the Syphons the said Chanel remained quite dry And this done I measured the quick height of the Chanel with care and afterwards divided it exactly into 10 equal parts and causing 19. of those Syphons to be taken away so that the Chanel did not run water save onely with 81 of those Syphons I again observed the quick height of the water in the same site observed before and found that its height was diminished precisely the tenth part of all its first height and thus continuing to take away 17. other Syphons the height was likewise diminished 1 10 of all its first quick height and trying to take away 15. Syphons then 13 then 11 then 9 then 7 then 5 and then 3. alwaies in these diversions made in order as hath been said there ensued still an abatement of 1 10 of the whole height And here was one thing worthy of observation that the water encreasing in or through the Chanel its quick height was different in different sites of the Chanel that is still lesser the more one approached to the Out-let notwithstanding which the abatement followed in all places proportionably that is in all its sites the first part of the height of that site diminished And moreover the water issued
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
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
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