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A31214 Of the mensuration of running waters an excellent piece written in Italian by Don Benedetto Castelli ... ; Englished from the third and best edition ; with the addition of a second book not before extant / by Thomas Salusbury.; Della misura dell'acque correnti. English Castelli, Benedetto, 1577 or 8-1643.; Salusbury, Thomas. Mathematical collections. 1661 (1661) Wing C1222; ESTC R19153 102,705 134

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thence redound to this City And that going by Torre del Fondo through Sanmartina to the Mouth de Masi by the Chappel of Vigarano unto the Sea it is by this way 70. miles nor is the Fall greater than 26. 5. 6. Feet so that it would come to fall but 4. inches an half or thereabouts in a mile whereas the common opinion of the skilfull to the end that the Torrents may not depose their sand that they bring with them in Land-Floods requireth the twenty fourth part of the hundredth part of their whole length which in our case accounting according to the measure of these places is 16. inches a mile whereupon the sinking of the Mud and Sand would most certainly follow and so an immense heightning of the Line of the Bottom and consequently a necessity of raising the Banks the impossibility of maintaining them the danger of breaches and decayes things very prejudicial to the Islets of this City and of San Giorgio the obstruction of the Drains which from the Tower of Tienne downwards fall into the said Chanel to wit those of the Sluices of Goro and the Drains of the Meadows of Ferrara And moreover the damages that would arise unto the said Islet of S. Giorgio and the Valleys of Comachio by the waters that should enter into the Goro or Dam of the Mills of Belriguardo thorow the Trenches of Quadrea which cannot be stopt because they belong to the Duke of Modena who hath right of diverting the waters of that place at his pleasure to the work of turning Mills The greater part of which Objections others pretend to prove frivolous by saying that its running there till at the last it was turned another way is a sign that it had made such an elevation of the Line of its Bed as it required denying that it needeth so great a declivity as is mentioned above and that for the future it would rise no more That the said Dra●ns and Ditches did empty into the same whilst Po was there so that they must needs be more able to do so when onely Reno runs that way That there would no Breaches follow or if they did they would be onely of the water of Reno which in few hours might be taken away in those parts they call damming up of Breaches and mending the Bank taking away the Breaches and it s a question whether they would procure more inconvenience than benefit for that its Mud and Sand might in many places by filling them up occasion a seasonable improvement Now omitting to discourse of the solidity of the reasons on the oneside or on the other I will produce those that move me to suspend my allowance of this design The first is that although I dare not subscribe to the opinion of those that require 16. inches Declivity in a mile to Reno to prevent its deposing of Mud yet would I not be the Author that should make a trial of it with so much hazard for having to satisfie my self in some particulars caused a Level to be taken of the Rivers L'amone Senio and Santerno by Bernardino Aleotti we found that they have more Declivity by much than Artists require as also the Reno hath from la Botta de Ghislieri to the Chappel of Vigarano for in the space of four miles its Bottom-Line falleth five feet and five inches So that I hold it greater prudence to depend upon that example than to go contrary to a common opinion especially since that the effects caused by Reno it self do confirm me in the same for when it was forsaken by the Po after a few years either because it had choaked up its Chanel with Sand or because it s too long journey did increase it it also naturally turned aside and took the way of the said Po towards Stellata Nay in those very years that it did run that way it only began as relations say to make Breaches an evident sign that it doth depose Sand and raise its Bed which agreeth with the testimony of some that were examined in the Visitation of the Publique Notary who found great benefit by having Running Water and some kind of passage for Boats and yet nevertheless affirm that it for want of Running Water had made too high Stoppages and Shelfes of Sand so that if it should be restored to the Course that it forsook I much fear that after a short time if not suddenly it would leave it a-again The second I take from the observation of what happened to Panaro when with so great applause of the Feraresi it was brought by Cardinal Serra into the said Chanel of Volana for that notwithstanding that it had Running Waters in much greater abundance than Reno yet in the time that it continued in that Chanel it raised its Bed well neer five feet as is to be seen below the Sluice made by Cardinal Capponi to his new Chanel yea the said Cardinal Serra who desired that this his undertaking should appear to have been of no danger nor damage was constrained at its Overflowings to give it Vent into Sanmartina that it might not break in upon and prejudice the City which danger I should more fear from Reno in regard it carrieth a greater abundance of Water and Sand. Thirdly I am much troubled in the uncertainty of the success of the affair at the great expence thereto required For in regard I do not approve of letting it in neer to the Fortresse for many respects and carrying it by la Torre del Fondo to the Mouth de Masi it will take up eight miles of double Banks a thing not easie to be procured by reason that the Grounds lie under Water but from the Mouth de Masi unto Codigoro it would also be necessary to make new Scowrings of the Chanel to the end that the Water approaching by wearing and carrying away the Earth on both shores might make a Bed sufficient for its Body the depth made for Panaro not serving the turn as I conceive and if it should suffice when could the people of Ferrara hope to be re-imbursed and satisfied for the charge thereof Fourthly it serves as an Argument with me to see that the very individual persons concerned in the Remotion or Diversion of the said Torrent namely the Bolognesi do not incline unto it and that the whole City of Ferrara even those very persons who at present receive damage by it cannot indure to hear thereof The reason that induceth these last named to be so averse thereto is either because that this undertaking will render the introduction of the Water of Main-Po more difficult or because they fear the danger thereof The others decline the Project either for that they know that Reno cannot long continue in that Course or because they fear that it is too much exposed to those mens revengeful Cutting of it who do not desire it should and if a man have any other wayes he ought in my opinion to forbear that
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