Mathematical Collections and Translations, in Two Tomes/System of the World in Four Dialogues/Dialogue 4

by Galileo Galilei

GALILÆUS

Galilæus Lyncæus,

HIS

SYSTEME

OF THE

WORLD.

---

The Fourth Dialogue.

---

INTERLOCUTORS.

Salviatus, Sagredus, and Simplicius.

Sagr.

I know not whether your return to our accustomed conferences hath really been later than usual, or whether the desire of hearing the thoughts of Salviatus, touching a matter so curious, hath made me think it so: But I have tarried a long hour at this window, expecting every moment when the Gondola would appear that I sent to fetch you.

Salv.I verily believe that your imagination more than our tarriance hath prolonged the time:Nature in sport maketh the ebbing and flowing of the Sea, to approve the Earths mobility. and to make no longer demurre, it would be well, if without interposing more words, we came to the matter it self; and did shew, that nature hath permitted (whether the business in rei veritate be so, or else to play and sport with our Fancies) hath,The tide, and mobility of the Earth mutually confirm each other I say, hath permitted that the motions for every other respect, except to resolve the ebbing and flowing of the Sea, assigned long since to the earth, should be found now at last to answer exactly to the cause thereof; and, as it were,All terrene effects, indifferently confirm the motion or rest of the Earth, except the ebbing and flowing of the Sea. with mutual a emulation, the said ebbing and flowing to appear in confirmation of the Terrestrial motion: the judices whereof have hitherto been taken from the cœlestial Phænomena, in regard that of those things that happen on Earth, not any one was of force to prove one opinion more than another, as we already have at large proved, by shewing that all the terrene occurrences upon which the stability of the Earth and mobility of the Sun and Firmament is commonly inferred, are to seem to us performed in the same manner, though we supposed the mobility of the Earth, and the immobility of them. The Element of Water onely, as being most vast, and which is not annexed and concatenated to the Terrestrial Globe as all its other solid parts are; yea, rather which by reason of its fluidity remaineth apart sui juris, and free, is to be ranked amongst those sublunary things, from which we may collect some hinte and intimation of what the Earth doth in relation to motion and rest. After I had many and many a time examined with my self the effects and accidents, partly seen and partly understood from others, that are to be observed in the motions of waters: and moreover read and heard the great vanities produced by many, as the causes of those accidents, The first general conclusion of the impossibility of the ebbing and flowing the immobility of the terrestrial Globe being granted. I have been induced upon no slight reasons to omit these two conclusions (having made withal the necessary presupposals) that in case the terrestrial Globe be immoveable, the flux and reflux of the Sea cannot be natural; and that, in case those motions be conferred upon the said Globe, which have been long since assigned to it, it is necessary that the Sea be subject to ebbing and flowing, according to all that which we observe to happen in the same.

Sagr.The Proposition is very considerable, as well for it self as for what followeth upon the same by way of consequence, so that I shall the more intensly hearken to the explanation and confirmation of it.

Salv.Because in natural questions,The knowledge of the effests contributes to the investigation of the causes. of which number this which we have in hand is one, the knowledge of the effects is a means to guide us to the investigation and discovery of the causes, and without which we should walk in the dark, nay with more uncertainty, for that we know not whither we would go, whereas the blind, at least, know where they desire to arrive; therefore first of all it is necessary to know the effects whereof we enquire the causes: of which effects you, Sagredus, ought more abundantly and more certainly to be informed than I am, as one, that besides your being born, and having, for a long time, dwelt in Venice, where the Tides are very notable for their greatnesse, have also sailed into Syria, and, as an ingenuous and apprehensive wit, must needs have made many Observations upon this subject: whereas I, that could onely for a time, and that very short, observe what happened in these extream parts of the Adriatick Gulph, and in our Seas below about the Tyrrhene shores, must needs take many things upon the relation of others, who, for the most part, not very well agreeing, and consequently being very uncertain, contribute more of confusion than confirmation to our speculations. Neverthelesse, from those that we are sure of, and which are the principal, I think I am able to attain to the true and primary causes; not that I pretend to be able to produce all the proper and adequate reasons of those effects that are new unto me, and which consequently I could never have thought upon. And that which I have to say, I propose only, as a key that openeth the door to a path never yet trodden by any, in certain hope, that some wits more speculative than mine, will make a further progresse herin, and penetrate much farther than I shall have done in this my first Discovery: And although that in other Seas, remote from us, there may happen several accidents, which do not happen in our Mediterranean Sea, yet doth not this invalidate the reason and cause that I shall produce, if so be that it verifie and fully resolve the accidents which evene in our Sea: for that in conclusion there can be but one true and primary cause of the effects that are of the same kind. I will relate unto you, therefore, the effects that I know to be true, and assigne the causes thereof that I think to be true, and you also, Gentlemen, shall produce such others as are known to you, besides mine, and then we will try whether the cause, by me alledged, may satisfie them also.

Three Periods of ebbings and flowings, diurnal, monethly, and annual.I therefore affirm the periods that are observed in the fluxes and refluxes of the Sea-waters to be three: the first and principal is this great and most obvious one; namely, the diurnal, according to which the intervals of some hours with the waters flow and ebbe; and these intervals are, for the most part, in the Mediterrane from six hours to six hours, or thereabouts, that is, they for six hours flow, and for six hours ebbe. The second period is monethly, and it seemes to take its origen from the motion of the Moon, not that it introduceth other motions, but only altereth the greatnesse of those before mentioned, with a notable difference, according as it shall wax or wane, or come to the Quadrature with the Sun. The third Period is annual, and is seen to depend on the Sunne, and onely altereth the diurnal motions, by making them different in the times of the Solstices, as to greatnesse, from what they are in the Equinoxes.

We will speak (in the first place, of the diurnal motion, as being the principal, and upon which the Moon and Sun seem to exercise their power secondarily,Varieties that happen in the diurnal period. in their monethly and annual alterations. Three differences are observable in these horary mutations; for in some places the waters rise and fall, without making any progressive motion; in others, without rising or falling they run one while towards the East, and recur another while towards the West; and in others they vary the heights and course also, as happeneth here in Venice, where the Tides in coming in rise, and in going out fall; and this they do in the extermities of the lengths of Gulphs that distend from West to East, and terminate in open shores, up along which shores the Tide at time of flood hath room to extend it self: but if the course of the Tide were intercepted by Cliffes and Banks of great height and steepnesse, there it will flow and ebbe without any progressive motion. Again, it runs to and again, without changing height in the middle parts of the Mediterrane, as notably happeneth in the ** A Strait, so called.Faro de Messina, between Scylla and Carybdis, where the Currents, by reason of the narrownesse of the Channel, are very swift; but in the more open Seas, and about the Isles that stand farther into the Mediterranean Sea, as the Baleares, Corsica, Sardignia, ** Or Ilva.Elba, Sicily towards the Affrican Coasts, Malta, ** Or Creta.Candia, &c. the changes of watermark are very small; but the currents indeed are very notable, and especially when the Sea is pent between Islands, or between them and the Continent.

Now these onely true and certain effects, were there no more to be observed, do, in my judgment, very probably perswade any man, that will contain himself within the bounds of natural causes, to grant the mobility of the Earth: for to make the vessel (as it may be called) of the Mediterrane stand still, and to make the water contained therein to do, as it doth, exceeds my imagination, and perhaps every mans else, who will but pierce beyond the rinde in these kind of inquiries.

Simpl.These accidents, Salviatus, begin not now, they are most ancient, and have been observed by very many, and several have attempted to assigne, some one, some another cause for the same: and there dwelleth not many miles from hence a famous Peripatetick,The cause of the ebbing and flowing alledged by a certain modern Philosopher. that alledgeth a cause for the same newly fished out of a certain Text of Aristotle, not well understood by his Expositors, from which Text he collecteth, that the true cause of these motions doth only proceed from the different profundities of Seas: for that the waters of greatest depth being greater in abundance, and therefore more grave, drive back the Waters of lesse depth, which being afterwards raised, desire to descend, and from this continual colluctation or contest proceeds the ebbing and flowing.The cause of the ebbing and flowing ascribed to the Moon by a certain Prelate. Again those that referre the same to the Moon are many, saying that she hath particular Domination over the Water; and at last a certain Prelate hath published a little Treatise, wherein he saith that the Moon wandering too and fro in the Heavens attracteth and draweth towards it a Masse of Water, which goeth continually following it, so that it is full Sea alwayes in that part which lyeth under the Moon; and because, that though she be under the Horizon, yet neverthelesse the Tide returneth, he saith that no more can be said for the salving of that particular, save onely, that the Moon doth not onely naturally retain this faculty in her self; but in this case hath power to confer it upon that degree of the Zodiack that is opposite unto it. Others,Hieronymus Borrius and other Peripateticks refer it to the temperate heat of the Moon. as I believe you know, do say that the Moon is able with her temperate heat to rarefie the Water, which being rarefied, doth thereupon flow. Nor hath there been wanting some that—

Sagr.I pray you Simplicius let us hear no more of them, for I do not think it is worth the while to wast time in relating them, or to spend our breath in confuting them; and for your part, if you gave your assent to any of these or the like fooleries, you did a great injury to your judgment, which neverthelesse I acknowledg to be very piercing.

Salv.But I that am a little more flegmatick than you,Answers to the vanities alledged as causes of the ebbing and flowing.Sagredus, will spend a few words in favour of Simplicius, if haply he thinks that any probability is to be found in those things that he hath related. I say therefore: The Waters, Simplicius, that have their exteriour superficies higher, repel those that are inferiour to them, and lower; but so do not those Waters that are of greatest profundity; and the higher having once driven back the lower, they in a short time grow quiet and ** Or rather smooth. level. This your Peripatetick must needs be of an opinion, that all the Lakes in the World that are in a calme, and that all the Seas where the ebbing and flowing is insensible, are level in their bottoms; but I was so simple, that I perswaded my self that had we no other plummet to sound with,The Isles are tokens of the unevennesse of the bottomes of Seas. the Isles that advance so high above Water, had been a sufficient evidence of the unevennesse of their bottomes. To that Prelate I could say that the Moon runneth every day along the whole Mediterrane, and yet its Waters do not rise thereupon, save onely in the very extream bounds of it Eastward, and here to us at Venice. And for those that make the Moons temperate heat able to make the Water swell, bid them put fire under a Kettle full of Water, and hold their right hand therein till that the Water by reason of the heat do rise but one sole inch, and then let them take it out, and write off the tumefaction of the Sea. Or at least desire them to shew you how the Moon doth to rarefie a certain part of the Waters, and not the remainder; as for instance, these here of Venice, and not those of Ancona, Naples, Genova: the truth is Poetick Wits are of two kinds,Poetick wits of two kinds. some are ready and apt to invent Fables, and others disposed and inclined to believe them.

Simpl.I believe that no man believeth Fables, so long as he knows them to be so; and of the opinions concerning the causes of ebbing and flowing, which are many, because I know that of one single effect there is but one single cause that is true and primary, I understand very well, and am certain that but one alone at the most can be true, and for all the rest I am sure that they are fabulous, and false; and its possible that the true one may not be among those that have been hitherto produced; nay I verily believe that it is not, for it would be very strange that the truth should have so little light,Truth hath not so little light as not to be discovered amidst the umbrages of falshoods. as that it should not be visible amongst the umbrages of so many falshoods. But this I shall say with the liberty that is permitted amongst us, that the introduction of the Earths motion, and the making it the cause of the ebbing and flowing of Tides, seemeth to me as yet a conjecture no lesse fabulous than the rest of those that I have heard; and if there should not be proposed to me reasons more conformable to natural matters, I would without any more ado proceed to believe this to be a supernatural effect, and therefore miraculous, and unsearchable to the understandings of men, as infinite others there are, that immediately depend on the Omnipotent hand of God.

Sagr.You argue very prudently,Aristotle holdeth those effects to be miraculous, of which the causes are unknown. and according to the Doctrine of Aristotle, who you know in the beginning of his mechanical questions referreth those things to a Miracle, the causes whereof are occult. But that the cause of the ebbing and flowing is one of those that are not to be found out, I believe you have no greater proof than onely that you see, that amongst all those that have hitherto been produced for true causes thereof, there is not one wherewith, working by what artifice you will, we are able to represent such an effect; in regard that neither with the light of the Moon nor of the Sun, nor with temperate heats, nor with different profundities, shall one ever artificially make the Water conteined in an immoveable Vessel to run one way or another, and to ebbe and flow in one place, and not in another. But if without any other artifice, but with the onely moving of the Vessel, I am able punctually to represent all those mutations that are observed in the Sea Water, why will you refuse this reason and run to a Miracle?

Simpl.I will run to a Miracle still, if you do not with some other natural causes, besides that of the motion of the Vessels of the Sea-water disswade me from it; for I know that those Vessels move not, in regard that all the entire Terrestrial Globe is naturally immoveable.

Salv.But do not you think, that the Terrestrial Globe might supernaturally, that is, by the absolute power of God, be made moveable?

Simpl.Who doubts it?

Salv.Then Simplicius, seeing that to make the flux and reflux of the Sea, it is necessary to introduce a Miracle, let us suppose the Earth to move miraculously, upon the motion of which the Sea moveth naturally: and this effect shall be also the more simple, and I may say natural, amongst the miraculous operations, in that the making a Globe to move round, of which kind we see many others to move, is lesse difficult than to make an immense masse of water go forwards and backwards, in one place more swiftly, and in another lesse, and to rise and fall in some places more; in some lesse, and in some not at all: and to work all these different effects in one and the same Vessel that containeth it: besides, that these are several Miracles, and that is but one onely. And here it may be added, that the Miracle of making the water to move is accompanied with another, namely, the holding of the Earth stedfast against impetuosities of the water, able to make it swage sometimes one way, and sometimes another, if it were not miraculously kept to rights.

Sagr.God Simplicius, let us for the present suspend our judgement about sentencing the new opinion to be vain that Salviatus is about to explicate unto us, nor let us so hastily flye out into passion like the scolding overgrown Haggs: and as for the Miracle, we may as well recurre to it when we have done hearing the Discourses contained within the bounds of natural causes: though to speak freely, all the Works of nature, or rather of God, are in my judgement miraculous.

Salv.And I am of the same opinion; nor doth my saying, that the motion of the Earth is the Natural cause of the ebbing and flowing, hinder, but that the said motion of the Earth may be miraculous. Now reassuming our Argument, I apply, and once again affirm, that it hath been hitherto unknown how it might be that the Waters contained in our Mediterranean Straights should make those motions, as we see it doth, if so be the said Straight, or containing Vessel were immoveable. And that which makes the difficulty, and rendreth this matter inextricable, are the things which I am about to speak of, and which are daily observed. Therefore lend me your attention.

We are here in Venice, where at this time the Waters are low, the Sea calm,It is proved impossible that there should naturally be any ebbing and flowing, the Earth being immoveable. the Air tranquil; suppose it to be young flood, and that in the term of five or six hours the water do rise ten ** Palms. hand breadths and more; that rise is not made by the first water, which was said to be rarefied, but it is done by the accession of new Water: Water of the same sort with the former, of the same brackishness, of the same density, of the same weight: Ships, Simplicius, float therein as in the former, without drawing an hairs breadth more water; a Barrel of this second doth not weigh one single grain more or less than such another quantity of the other, and retaineth the same coldness without the least alteration: And it is, in a word, Water newly and visibly entred by the Channels and Mouth of the † † Lio is a fair Port in the Venetian Gulph, lying N. E. from the City.Lio. Consider now, how and from whence it came thither. Are there happly hereabouts any Gulphs or Whirle-pools in the bottom of the Sea, by which the Earth drinketh in and spueth out the Water, breathing as it were a great and monstruous Whale? But if this be so, how comes it that the Water doth not flow in 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-mouth 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,True and natural effects follow without difficulty. & 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,Two sorts of motions of the containing Vessel, may make the contained water to rise and fall. 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,The Cavities of the Earth cannot approach or go farther from the centre of the same. 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,The progressive and uneven motion may make the water contained in a Vessel to run to and fro. that the Water 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 † A Town lying S. E. of Venice* 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 the extreams. Now, my Masters, that which the Bark doth, in respect of the water by it contained, and that which the water contained doth, in respect of the Bark its container, is the self-same, to an hair, with that which the Mediterranean Vessel doth, in respect of the waters in it contained, and that which the waters contained do, in respect of the Mediterranean Vessel their container.The parts of the terrestrial Globe accelerate and retard in their motion. It followeth now that we demonstrate how, and in what manner it is true, that the Mediterrane, and all the other Straits; and in a word, all the parts of the Earth do all move, with a motion notably uneven, though no motion that is not regular and uniforme, is thereby assigned to all the said Globe taken collectively.

Simpl.This Proposition, at first sight to me, that am neither Geometrician nor Astronomer, hath the appearance of a very great Paradox; and if it should be true, that the motion of the whole, being regular, that of the parts, which are all united to their whole, may be irregular, the Paradox will overthrow the Axiome that affirmeth, Eandem esse rationem totius & partium.

Salv.I will demonstrate my Paradox, and leave it to your care, Simplicius, to defend the Axiome from it, or else to reconcile them; and my demonstration shall be short and familiar, depending on the things largely handled in our precedent conferences, without introducing the least syllable, in favour of the flux and reflux.

We have said,Demonstrations how the parts of the terrestriall Globe accelerate and retard. that the motions assigned to the Terrestrial Globe are two, the first Annual, made by its centre about the circumference of the Grand Orb, under the Ecliptick, according to the order of the Signes, that is, from West to East; the other made by the said Globe revolving about its own centre in twenty four hours; and this likewise from West to East: though about an Axis somewhat inclined, and not equidistant from that of the Annual conversion. From the mixture of these two motions, each of it self uniform, I say, that there doth result an uneven and deformed motion in the parts of the Earth. Which, that it may the more easily be understood, I will explain, by drawing a Scheme thereof. And first, about the centre A [in Fig. 1. of this Dialogue] I will describe the circumference of the Grand Orb B C,The parts of a Circle regularly moved about its own centre move in divers times with contrary motions. in which any point being taken, as B, about it as a centre we will describe this lesser circle D E F G, representing the Terrestrial Globe; the which we will suppose to run thorow the whole circumference of the Grand Orb, with its centre B, from the West towards the East, that is, from the part B towards C; and moreover we will suppose the Terrestrial Globe to turn about its own centre B likewise from West to East, that is, according to the succession of the points D E F G, in the space of twenty four hours. But here we ought carefully to note, that a circle turning round upon its own centre, each part of it must, at different times, move with contrary motions: the which is manifest, considering that whilst the parts of the circumference, about the point D move to the left hand, that is, towards E, the opposite parts that are about F, approach to the right hand, that is, towards G; so that when the parts D shall be in F, their motion shall be contrary to what it was before. when it was in D. Furthermore, the same time that the parts E descend, if I may so speak, towards F, those in G ascend towards D. It being therefore presupposed, that there are such contrarieties of motions in the parts of the Terrestrial Surface,The mixture of the two motions annnal and diurnal, causeth the inequality in the motion of the parts of the terrestrial Globe. whilst it turneth round upon its own centre, it is necessary, that in conjoyning this Diurnal Motion, with the other Annual, there do result an absolute motion for the parts of the said Terrestrial Superficies, one while very accelerate, and another while as slow again. The which is manifest, considering first the parts about D, the absolute motion of which shall be extream swift, as that which proceedeth from two motions made both one way, namely, towards the left hand; the first of which is part of the Annual Motion, common to all the parts of the Globe, the other is that of the said point D., carried likewise to the left, by the Diurnal Revolution; so that, in this case, the Diurnal motion increaseth and accelerateth the Annual. The contrary to which happeneth in the opposite part F, which, whilst it is by the common annual motion carried, together with the whole Globe, towards the left, it happeneth to be carried by the Diurnal conversion also towards the right: so that the Diurnal motion by that means detracteth from the Annual, whereupon the absolute motion, resulting from the composition of both the other, is much retarded. Again, about the points E and G, the absolute motion becometh in a manner equal to the simple Annual one, in regard that little or nothing increaseth or diminisheth it, as not tending either to the left hand, or to the right, but downwards and upwards. We will conclude therefore, that like as it is true, that the motion of the whole Globe, and of each of its parts, would be equal and uniforme, in case they did move with one single motion, whether it were the meer Annual, or the single Diurnal Revolution, so it is requisite, that mixing those two motions together, there do result thence for the parts of the said Globe irregular motions, one while accelerated, and another while retarded, by means of the additions or substractions of the Diurnal conversion from the annual circulation. So that, if it be true (and most true it is, as experience proves) that the acceleration and retardation of the motion of the Vessel, makes water contained therein to run to and again the long wayes of it, and to rise and fall in its extreames, who will make scruple of granting, that the said effect may, nay ought to succeed in the Sea-waters, contained within their Vessels, subject to such like alterations, and especially in those that distend themselves long-wayes from West to East, which is the course that the motion of those same Vessels steereth?The most potent and primary cause of the ebbing and flowing. Now this is the most potent and primary cause of the ebbing and flowing, without the which no such effect would ensue. But because the particular accidents are many and various, that in several places and times are observed, which must of necessity have dependance on other different concomitant causes, although they ought all to have connexion with the primary; therefore it is convenient that we propound and examine the several accidents that may be the causes of such different effects.

Sundry accidents that happen in the ebbings & flowingsThe first of which is, that when ever the water, by means of a notable retardation or acceleration of the motion of the Vessel, its container, shall have acquired a cause of running towards this or that extream,The first accident. and shall be raised in the one, and abated in the other, it shall not neverthelesse continue, for any time in that state, when once the primary cause 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, The Water raised in one end of the Vessel returneth of its self to Æquilibrium.and, as being grave and fluid, shall not only move towards Æquilibrium; 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.

In the shorter Vessels the undulations of waters are more frequent.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.

The greater profundity maketh the undulations of waters more frequent.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;Water riseth & falleth in the extream parts of the Vessel, and runneth to and fro in the midst. 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,An accident of the Earths motions impossible to be reduced to practice by art. 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 abovenamed 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 in those that distend themselves for a great length from West to East; namely according to the course of the motions of the Terrestrial Globe; and as it is in a certain manner unthought of, and without a president among the motions possible to be made by us, so it is not hard for me to believe, that effects may be derived from the same, which are not to be imitated by our artificial experiments.

Salv.These things being declared, it is time that we proceed to examine the particular accidents, which, together with their diversities, are observed by experience in the ebbing and flowing of the waters.Reasons renewed of the particular accidents observed in the ebbings and flowings. And first we need not think it hard to guesse whence it happeneth, that in Lakes, Pooles, and also in the lesser Seas there is no notable flux and reflux; the which hath two very solid reasons. The one is, that by reason of the shortnesse of the Vessel,Second causes why in small Seas and in Lakes there are no ebbings and flowings. in its acquiring in several hours of the day several degrees of velocity, they are with very little difference acquired by all its parts; for as well the precedent as the subsequent, that is to say, both the Eastern and Western parts, do accelerate and retard almost in the same manner; and withal making that alteration by little and little, and not by giving the motion of the conteining Vessel a sudden check, and retardment, or a sudden and great impulse or acceleration; both it and all its parts, come to be gently and equally impressed with the same degrees of velocity; from which uniformity it followeth, that also the conteined water with but small resistance and opposition, receiveth the same impressions, and by consequence doth give but very obscure signes of its rising or falling, or of its running towards one part or another. The which effect is likewise manifestly to be seen in the little artificial Vessels, wherein the contained water doth receive the self same impressions of velocity; when ever the acceleration and retardation is made by gentle and uniform proportion. But in the Straights and Bays that for a great length distend themselves from East to West, the acceleration and retardation is more notable and more uneven, for that one of its extreams shall be much retarded in motion, and the other shall at the same time move very swiftly: The reciprocal libration or levelling of the water proceeding from the impetus that it had conceived from the motion of its container. The which libration, as hath been noted, hath its undulations very frequent in small Vessels; from whence ensues, that though there do reside in the Terrestrial motions the cause of conferring on the waters a motion onely from twelve hours to twelve hours, for that the motion of the conteining Vessels do extreamly accelerate and extreamly retard but once every day, and no more; yet neverthelesse this same second cause depending on the gravity of the water which striveth to reduce it self to equilibration, and that according to the shortnesse of the Vessel hath its reciprocations of one, two, three, or more hours, this intermixing with the first, which also it self in small Vessels is very little, it becommeth upon the whole altogether insensible. For the primary cause, which hath the periods of twelve hours, having not made and end of imprinting the precedent commotion, it is overtaken and opposed by the other second, dependant on the waters own weight, which according to the brevity and profundity of the Vessel, hath the time of its undulations of one, two, three, four, or more hours; and this contending with the other former one, disturbeth and removeth it, not permitting it to come to the height, no nor to the half of its motion; and by this contestation the evidence of the ebbing and flowing is wholly annihilated, or at least very much obscured. I passe by the continual alteration of the air, which disquieting the water, permits us not to come to a certainty, whether any, though but small, encrease or abatement of half an inch, or losse, do reside in the Straights, or receptacles of water not above a degree or two in length.

I come in the second place to resolve the question,The reason given, why the ebbings and flowings, for the most part, are every six hours. why, there not residing any vertue in the primary principle of commoving the waters, save onely every twelve hours, that is to say, once by the greatest velocity, and once by the greatest tardity of motion; the ebbings and flowings should yet neverthelesse appear to be every six hours. To which is answered, that this determination cannot any wayes be taken from the primary cause onely; but there is a necessity of introducing the secondary causes, as namely the greater or lesse length of the Vessels, and the greater or lesse depth of the waters in them conteined. Which causes although they have not any operation in the motions of the waters, those operations belonging to the sole primary cause, without which no ebbing or flowing would happen, yet neverthelesse they have a principal share in determining the times or periods of the reciprocations, and herein their influence is so powerful, that the primary cause must of force give way unto them. The period of six hours therefore is no more proper or natural than those of other intervals of times, though indeed its the most observed, as agreeing with our Mediterrane, which was the onely Sea that for many Ages was navigated: though neither is that period observed in all its parts; for that in some more angust places, such as are the Hellespont, and the Ægean Sea, the periods are much shorter, and also very divers amongst themselves; for which diversities, and their causes incomprehensible to Aristotle, some say, that after he had a long time observed it upon some cliffes of Negropont, being brought to desperation, he threw himself into the adjoyning Euripus, and voluntarily drowned himself.

The cause why some Seas, though very long, suffer no ebbing and flowing. In the third place we have the reason ready at hand, whence it commeth to passe, that some Seas, although very long, as is the Red Sea, are almost altogether exempt from Tides, which happeneth because their length extendeth not from East to West, but rather transversly from the Southeast to the Northwest; but the motions of the Earth going from West to East; the impulses of the water, by that means, alwayes happen to fall in the Meridians, and do not move from parallel to parallel; insomuch that in the Seas that extend themselves athwart towards the Poles, and that the contrary way are narrow, there is no cause of ebbing and flowing, save onely by the participation of another Sea, wherewith it hath communication, that is subject to great commotions.

Ebbings and flowings why greatest in the extremities of Gulphs, and least in the middle parts.In the fourth place we shall very easily find out the reason why the fluxes and refluxes are greatest, as to the waters rising and falling in the utmost extremities of Gulphs, and least in the intermediate parts; as daily experience sheweth here in Venice, lying in the farther end of the Adriatick Sea, where that difference commonly amounts to five or six feet; but in the places of the Mediterrane, far distant from the extreams, that mutation is very small, as in the Isles of Corsica and Sardinnia, and in the Strands of Rome and Ligorne, where it exceeds not half a foot; we shall understand also, why on the contrary, where the risings and fallings are small, the courses and recourses are great: I say it is an easie thing to understand the causes of these accidents, seeing that we meet with many manifest occurrences of the same nature in every kind of Vessel by us artificially composed, in which the same effects are observed naturally to follow upon our moving it unevenly, that is, one while faster, and another while flower.

Why in narrow places the course of the waters is more swift than in larger.Moreover, considering in the fifth place, that the same quantity of Water being moved, though but gently, in a spatious Channel, comming afterwards to go through a narrow passage, will of necessity run, with great violence, we shall not finde it hard to comprehend the cause of the great Currents that are made in the narrow Channel that separateth Calabria from Sicilia: for that all the Waters that, by the spaciousnesse of the Isle, and by the Ionick Gulph, happens to be pent in the Eastern part of the Sea, though it do in that, by reason of its largeness, gently descend towards the West, yet neverthelesse, in that it is pent up in the Bosphorus, it floweth with great violence between Scilla and Caribdis, and maketh a great agitation. Like to which, and much greater, is said to be betwixt Africa and the great Isle of St. Lorenzo, where the Waters of the two vast Seas, Indian and Ethiopick, that lie round it, must needs be straightned into a lesse Channel between the said Isle and the Ethiopian Coast. And the Currents must needs be very great in the Straights of Magellanes, which joyne together the vast Oceans of Ethiopia, and Del Zur, called also the Pacifick Sea.

A discussion of some more abstruse accidents observed in the ebbing and flowing.It follows now, in the sixth place, that to render a reason of some more abstruse and incredible accidents, which are observed upon this occasion, we make a considerable reflection upon the two principal causes of ebbings and flowings, afterwards compounding and mixing them together. The first and simplest of which is (as hath often been said) the determinate acceleration and retardation of the parts of the Earth, from whence the Waters have a determinate period put to their decursions towards the East, and return towards the West, in the time of twenty four hours. The other is that which dependeth on the proper gravity of the Water, which being once commoved by the primary cause, seeketh, in the next place, to reduce it self to Æquilibrium, with iterated reciprocations; which are not determined by one sole and prefixed time; but have as many varieties of times as are the different lengths and profundities of the receptacles, and Straights of Seas; and by what dependeth on this second principle, they would ebbe and flow, some in one hour, others in two, in four, in six, in eight, in ten, &c. Now if we begin to put together the first cause, which hath its set Period from twelve hours to twelve hours, with some one of the secondary, that hath its Period verb. grat. from five hours to five hours, it would come to passe, that at sometimes the primary cause and secondary would accord to make impulses both one the same way; and in this concurrency, and (as one may call it) unanimous conspiration the flowings shall be great. At other times it happening that the primary impulse doth, in a certain manner, oppose that which the secondary Period would make, and in this contest one of the Principles being taken away, that which the other would give, will weaken the commotion of the Waters, and the Sea will return to a very tranquil State, and almost immoveable. And at other times, according as the two aforesaid Principles shall neither altogether contest, nor altogether concur, there shall be other kinds of alterations made in the increase and diminution of the ebbing and flowing. It may likewise fall out that two Seas, considerably great and which communicate by some narrow Channel, may chance to have, by reason of the mixtion of the two Principles of motion, one cause to flow at the time that the other hath cause to move a contrary way; in which case in the Channel, whereby they disimbogue themselves into each other, there do extraordinary conturbations insue, with opposite and vortick motions, and most dangerous boilings and breakings, as frequent relations and experiences do assure us. From such like discordant motions, dependent not onely on the different positions and longitudes, but very much also upon the different profundities of the Seas, which have the said intercourse there do happen at sometimes different commotions in the Waters, irregular, and that can be reduced to no rules of observation, the reasons of which have much troubled, and alwayes do trouble Mariners, for that they meet with them without seeing either impulse of winds, or other eminent aereal alteration that might occasion the same; of which disturbance of the Air we ought to make great account in other accidents, and to take it for a third and accidental cause, able to alter very much the observation of the effects depending on the secondary and more essential causes. And it is not to be doubted, but that impetuous windes, continuing to blow, for example, from the East, they shall retein the Waters and prohibit the reflux or ebbing; whereupon the second and third reply of the flux or tide overtaking the former, at the hours prefixed, they will swell very high; and being thus born up for some dayes, by the strength of the Winds, they shall rise more than usual, making extraordinary inundations.

We ought also, (and this shall serve for a seventh Probleme) to take notice of another cause of motion dependant on the great abundance of the Waters of great Rivers that discharge themselves into Seas of no great capacity,The cause why, in some narrow Channels, we see the Sea-waters run alwayes one way. whereupon in the Straits or Bosphori that communicate with those Seas, the Waters are seen to run always one way: as it happeneth in the Thracian Bosphorus below Constantinople, where the water alwayes runneth from the Black-Sea, towards the Propontis: For in the said Black-Sea by reason of its shortnesse, the principal causes of ebbing and flowing are but of small force. But, on the contrary, very great Rivers falling into the same, those huge defluxions of water being to passe and disgorge themselves by the the straight, the ** Or current. course is there very notable and alwayes towards the South. Where moreover we ought to take notice, that the said Straight or Channel, albeit very narrow, is not subject to perturbations, as the Straight of Scilla and Carybdis; for that that hath the Black-Sea above towards the North, and the Propontis, the Ægean, and the Mediterranean Seas joyned unto it, though by a long tract towards the South; but now, as we have observed, the Seas, though of never so great length, lying North and South, are not much subject to ebbings and flowings; but because the Sicilian Straight is situate between the parts of the Mediterrane distended for a long tract or distance from West to East, that is, according to the course of the fluxes and refluxes; therefore in this the agitations are very great; and would be much more violent between Hercules Pillars, in case the Straight of Gibraltar did open lesse; and those of the Straight of Magellanes are reported to be extraordinary violent.

This is what, for the present, cometh into my mind to say unto you about the causes of this first period diurnal of the Tide, and its various accidents, touching which, if you have any thing to offer, you may let us hear it, that so we may afterwards proceed to the other two periods, monethly and annual.

Simpl.In my opinion, it cannot be denied, but that your discourse carrieth with it much of probability, arguing, as we say, ex suppositione, namely, granting that the Earth moveth with the two motions assigned it by Copernicus:The Hypothesis of the Earths mobility taken in favour of the Tide, opposed. but if that motion be disproved, all that you have said is vain, and insignificant: and for the disproval of that Hypothesis, it is very manifestly hinted by your Discourse it self. You, with the supposition of the two Terrestrial motions, give a reason of the ebbing and flowing; and then again, arguing circularly, from the ebbing and flowing, draw the reason and confirmation of those very motions; and so proceeding to a more specious Discourse, you say that the Water, as being a fluid body, and not tenaciously annexed to the Earth, is not constrained punctually to obey every of its motions, from which you afterwards infer its ebbing and flowing, Now I, according to your own method, argue the quite contrary, and say; the Air is much more tenuous, and fluid than the Water, and lesse annexed to the Earths superficies, to which the Water, if it be for nothing else, yet by reason of its gravity that presseth down upon the same more than the light Air, adhereth; therefore the Air is much obliged to follow the motions of the Earth: and therefore were it so, that the Earth did move in that manner, we the inhabitants of it, and carried round with like velocity by it, ought perpetually to feel a Winde from the East that beateth upon us with intolerable force. And that so it ought to fall out, quotidian experience assureth us: for if with onely riding post, at the speed of eight or ten miles an hour in the tranquil Air, the incountering of it with our face seemeth to us a Winde that doth not lightly blow upon us, what should we expect from our rapid course of 800. or a thousand miles an hour, against the Air, that is, free from that motion? And yet, notwithstanding we cannot perceive any thing of that nature.

Salv.To this objection that hath much of likelihood in it,The answer to the objections made against the motion of the Terrestrial Globe. I reply, that its true, the Air is of greater tenuity and levity; and, by reason of its levity, lesse adherent to the Earth than Water so much more grave and †† Corpulenta. bulky; but yet the consequence is false that you infer from these qualities; namely, that upon account of that its levity, tenuity, and lesse adherence to the Earth, it should be more exempt than the Water from following the Terrestrial Motions; so as that to us, who absolutely pertake of of them, the said exemption should be sensible and manifest; nay, it happeneth quite contrary; for, if you well remember, the cause of the ebbing and flowing of the Water assigned by us, consisteth in the Waters not following the unevennesse of the motion of its Vessel, but retaining the impetus conceived before, without diminishing or increasing it according to the precise rate of its diminishing or increasing in its Vessel. Because therefore that in the conservation and retention of the impetus before conceived, The Water more apt to conserve an impetus conceived, then the Air. the disobedience to a new augmentation or diminution of motion consisteth, that moveable that shall be most apt for such a retention, shall be also most commodious to demonstrate the effect that followeth in consequence of that retention. Now how much the Water is disposed to maintain such a conceived agitation; though the causes cease that impress the same, the experience of the Seas extreamly disturbed by impetuous Winds sheweth us; the Billows of which, though the Air be grown calm, and the Wind laid, for a long time after continue in motion: As the Sacred Poet pleasantly sings,

Qual l'alto Egeo, &c.————

Light bodies easier to be moved than heavy, but less apt to conserve the motion.And that long continuing rough after a storm, dependeth on the gravity of the water: For, as I have elsewhere said, light bodies are much easier to be moved than the more grave, but yet are so much the less apt to conserve the motion imparted, when once the moving cause ceaseth. Whence it comes that the Aire, as being of it self very light and thin, is easily mov'd by any very small force, yet it is withall very unable to hold on its motion, the Mover once ceasing. Therefore, as to the Aire which environs the Terrestrial Globe, I would fay, that by reason of its adherence, it is no lesse carried about therewith then the Water; and especially that part which is contained in its vessels; which vessels are the valleys enclosed with Mountains.Its more rational that the Air be commoved by the rugged surface of the Earth, than by the Celestial motion. And we may with much more reason affirm that this same part of the Air is carried round, and born forwards by the rugged parts of the Earth, than that the higher is whirl'd about by the motion of the Heavens, as ye Peripateticks maintain.

The revolution of the Earth confirmed by a new argument taken from the Air.What hath been hitherto spoken, seems to me a sufficient answer to the allegation of Simplitius; yet nevertheless with a new instance and solution, founded upon an admirable experiment, I will superabundantly satisfie him, and confirm to Sagredus the mobility of the Earth. I have told you that the Air, and in particular that part of it which ascendeth not above the tops of the highest Mountains, is carried round by the uneven parts of the Earths surface: from whence it should seem, that it must of consequence come to passe, that in case the superficies of the Earth were not uneven, but smooth and plain, no cause would remain for drawing the Air along with it, or at least for revolving it with so much uniformity. Now the surface of this our Globe, is not all craggy and rugged, but there are exceeding great tracts very even, to wit, the surfaces of very vast Seas, which being also far remote from the continuate ledges of Mountains which environ it, seem to have no faculty of carrying the super-ambient Air along therewith: and not carrying it about, we may perceive what will of consequence ensue in those places.

Simpl.I was about to propose the very same difficulty, which I think is of great validity.

Salv.You say very well Simplicius, for from the not finding in the Air that which of consequence would follow, did this our Globe move round; you argue its immoveablenesse. But in case that this which you think ought of necessary consequence to be found, be indeed by experience proved to be so; will you accept it for a sufficient testimony and an argument for the mobility of the said Globe?

Simpl.In this case it is not requisite to argue with me alone, for if it should so fall out, and that I could not comprehend the cause thereof, yet haply it might be known by others.

Salv.So that by playing with you, a man shall never get, but be alwayes on the losing hand; and therefore it would be better to give over: Nevertheless, that we may not cheat our third man we will play on. We said even now, and with some addition we reitterate it, that the Ayr as if it were a thin and fluid body, and not solidly conjoyned with the Earth, seem'd not to be necessitated to obey its motion; unlesse so far as the cragginess of the terrestrial superficies, transports and carries with it a part thereof contigious thereunto; which doth not by any great space exceed the greatest altitude of Mountains: the which portion of Air ought to be so much less repugnant to the terrestrial conversion, by how much it is repleat with vapours,The vaporous parts of the earth, partake of its motions. fumes, and exhalations, matters all participating of terrene qualities, and consequently apt of their own nature to the same motions. But where there are wanting the causes of motion, that is, where the surface of the Globe hath great levels, and where there is less mixture of the terrene vapours, there the cause whereby the ambient Air is constrained to give entire obedience to the terrestrial conversion will cease in part; so that in such places, whilst the Earth revolveth towards the East, there will be continually a wind perceived which will beat upon us, blowing from the East towards the West: and such gales will be the more sensible, where the revolution of the Globe is most swift; which will be in places more remote from the Poles, and approaching to the greatest Circle of the diurnal conversion. But now de facto experience much confirmeth this Phylosophical argumentation; for in the spatious Seas, and in their parts most remote from Land, and situate under the Torrid Zone, that is bounded by the Tropicks, where there are none of those same terrestrial evaporations,Constant gales within the Tropicks blow towards the West. we finde a perpetual gale move from the East with so constant a blast, that ships by favour thereof sail prosperously to the West-India's. And from the same coasting along the Mexican shore, they with the same felicity pass the Pacifick Ocean towards the India's; which to us are East, but to them are West.The course to the West-India's easie, the return difficult. Whereas on the contrary the Course from thence towards the East is difficult and uncertain, and not to be made by the same Rhumb, but must vere more to Land-ward, to recover other Winds, which we may call accidentary and tumultuary, produced from other Principles, as those that inhabit the continent find by experience. Of which productions of Winds, the Causes are many and different, which shall not at this time be mentioned.Winds from Land make rough the Seas. And these accidentary Winds are those which blow indifferently from all parts of the Earth, and make rough the Seas remote from the Equinoctial, and environed by the rugged Surface of the Earth; which is as much as to say environ'd with those perturbations of Air, that confound that primary Gale. The which, in case these accidental impediments were removed, would be continually felt, and especially upon the Sea. Now see how the effect of the Water and Air seem wonderfully to accord with the Celestial observations, to confirm the mobility of our Terrestrial Globe.

Sagr.I also for a final close will relate to you one particular,Another observation taken from the Air in confirmation of the motion of the Earth. which as I believe is unknown unto you, and which likewise may serve to confirm the same conclusion: You Salviatus alledged, That Accident which Sailers meet with between the Tropicks; I mean that perpetual Gale of Winde that beats upon them from the East, of which I have an account from those that have many times made the Voyage: And moreover (which is very observable) I understand that the Mariners do not call it a Wind, but by another ** Which Wind with our English Mariners is called the Trade-wind. name, which I do not now remember, taken haply from its so fixed and constant Tenor; which when they have met with, they tie up their shrouds and other cordage belonging to the Sails, and without any more need of touching them, though they be in a sleep, they can continue their course. Now this constant Trade-wind was known to be such by its continual blowing without interruptions; for if it were interrupted by other Windes, it would not have been acknowledged for a singular Effect, and different from the rest: from which I will infer, That it may be that also our Mediterranean Sea doth partake of the like accident; but it is not observed, as being frequently altered by the confluence of other windes. And this I say, not without good grounds, yea upon very probable conjectures whch came unto my knowledge, from that which tendred it self to my notice on occasion of the voyage that I made into Syria, going Consul for this Nation to Aleppo,The voiages in the Mediterrane from East to West are made in shorter times than from West to East. and this it is: That keeping a particular account and memorial of the dayes of the departure and arrival of the Ships in the Ports of Alexandria, of Alexandretta, and this of Venice; in comparing sundry of them, which I did for my curiosity, I found that in exactness of account the returns hither, that is the voiages from East to West along the Mediterrane, are made in less time then the contrary courses by 25. in the Hundred: So that we see that one with another, the Eastern windes are stronger then the Western.

Salv.I am very glad I know this particular, which doth not a little make for the confirmation of the Earths mobility. And although it may be alledged, That all the Water of the Mediterrane runs perpetually towards the Straits-mouth, as being to disimbogue into the Ocean, the waters of as many Rivers, as do discharge themselves into the same; I do not think that that current can be so great, as to be able of it self alone to make so notable a difference: which is also manifest by observing that the water in the Pharo of Sicily runneth back again no less towards the East, than it runneth forwards towards the West.

Sagr.I, that have not as Simplicius, an inclination to satisfie any one besides my self, am satisfied with what hath been said as to this first particular: Therefore Salviatus, when you think it sit to proceed forward, I am prepared to hear you.

Salv.I shall do as you command me, but yet I would fain hear the opinion also of Simplicius, from whose judgement I can argue how much I may promise to my self touching these discourses from the Peripatetick Schools, if ever they should come to their ears.

Simp.I desire not that my opinion should serve or stand for a measure, whereby you should judge of others thoughts; for as I have often said, I am inconsiderable in these kinde of studies, and such things may come into the mindes of those that are entered into the deepest passages of Philosophy, as I could never think of; as having (according to the Proverb) scarce kist her Maid: yet nevertheless, to give you my sudden thoughts, I shall tell you, That of those effects by you recounted, and particularly the last, there may in my judgement very sufficient Reasons be given without the Earths mobility, by the mobility of the Heavens onely; It is demonstrated inverting the argument, that the perpetual motion of the Air from East to West cometh from the motion of Heaven.never introducing any novelty more, than the inversion of that which you your self propose unto us. It hath been received by the Peripatetick Schools, that the Element of Fire, and also a great part of the Aire is carried about according to the Diurnal conversion from East to West, by the contact of the Concave of the Lunar Orb, as by the Vessel their container. Now without going out of your track, I will that we determine the Quantity of the Aire which partaketh of that motion to distend so low as to the Tops of the highest Hills,It is demonstrated inverting the argument, that the perpetual motion of the Air from East to West, cometh from the motion of Heaven. and that likewise they would reach to the Earth, if those Mountains did not impede them, which agreeth with what you say: For as you affirm, the Air, which is invironed by ledges of Mountains, to be carried about by the asperity of the moveable Earth; we on the contrary say, That the whole Element of Air is carried about by the motion of Heaven, that part only excepted which lyeth below those bodies, which is hindred by the asperity of the immoveable Earth. And whereas you said, That in case that asperity should be removed, the Air would also cease to be whirld about; we may say, That the said asperity being removed, the whole Aire would continue its motion. Whereupon, because the surfaces of spacious Seas are smooth, and even; the Airs motion shall continue upon those, alwaies blowing from the East: And this is more sensibly perceived in Climates lying under the Line, and within the Tropicks, where the motion of Heaven is swifter; and like as that Celestial motion is able to bear before it all the Air that is at liberty, so we may very rationally affirm that it contributeth the same motion to the Water moveable, as being fluid and not connected to the immobility of the Earth:The motion of the Water dependeth on the motion of Heaven. And with so much the more confidence may we affirm the same, in that by your confession, that motion ought to be very small in resect of the efficient Cause; which begirting in a natural day the whole Terrestrial Globe, passeth many hundreds of miles an hour, and especially towards the Equinoctial; whereas in the currents of the open Sea, it moveth but very few miles an hour. And thus the voiages towards the West shall come to be commodious and expeditious, not onely by reason of the perpetual Eastern Gale, but of the course also of the Waters; from which course also perhaps the Ebbing and Flowing may come, by reason of the different scituation of the Terrestrial Shores:The flux and reflux may depend on the diurual motion of Heaven. against which the Water coming to beat, may also return backwards with a contrary motion, like as experience sheweth us in the course of Rivers; for according as the Water in the unevenness of the Banks, meeteth with some parts that stand out, or make with their Meanders some Reach or Bay, here the Water turneth again, and is seen to retreat back a considerable space. Upon this I hold, That of those effects from which you argue the Earths mobility, and alledge it as a cause of them, there may be assigned a cause sufficiently valid, retaining the Earth stedfast, and restoring the mobility of Heaven.

Salv.It cannot be denied, but that your discourse is ingenious, & hath much of probability, I mean probability in appearance, but not in reality & existence: It consisteth of two parts: In the first it assignes a reason of the continual motion of the Eastern Winde, and also of a like motion in the Water. In the second, It would draw from the same Sourse the cause of the Ebbing and Flowing. The first part hath (as I have said) some appearance of probability, but yet extreamly less then that which we take from the Terrestrial motion. The second is not onely wholly improbable, but altogether impossible and false.A reason of the continual motion of the Air and Water may be given, making the Earth moveable, then by making it immoveable. And coming to the first, whereas it is said that the Concave of the Moon carrieth about the element of Fire, and the whole Air, even to the tops of the higher Mountains. I answer first, that it is dubious whether there be any element of Fire: But suppose there be, it is much doubted of the Orbe of the Moon, as also of all the rest; that is, Whether there be any such solid bodies and vast, or elss, Whether beyond the Air there be extended a continuate expansion of a substance of much more tenuity and purity than our Air, up and down which the Planets go wandring, as now at last a good part of those very Phylosophers begin to think:Its improbable that the element of Fire should be carried round by the Concave of the Moon. But be it in this or in that manner, there is no reason for which the Fire, by a simple contract to a superficies, which you your self grant to be smooth and terse, should be according to its whole depth carried round in a motion different from its natural inclination; as hath been defusely proved, and with sensible reasons demonstrated by †† A Treatise of our Author formerly cited. Il Saggiatore: Besides the other improbability of the said motions transfusing it self from the subtilest Fire throughout the Air, much more dense; and from that also again to the Water. But that a body of rugged and mountainous surface, by revolving in it self, should carry with it the Air contiguous to it, and against which its promontaries beat, is not onely probable but necessary, and experience thereof may be daily seen; though without seeing it, I believe that there is no judgement that doubts thereof. As to the other part, supposing that the motion of Heaven did carry round the Air, and also the Water; yet would that motion for all that have nothing to do with the Ebbing and Flowing. For being that from one onely and uniform cause, there can follow but one sole and uniform effect; that which should be discovered in the Water, would be a continuate and uniform course from East to West; and in that a Sea onely, which running compass environeth the whole Globe. But in determinate Seas, such as is the Mediterrane shut up in the East, there could be no such motion. For if its Water might be driven by the course of Heaven towards the West, it would have been dry many ages since: Besides that our Water runneth not onely towards the West, But returneth backwards towards the East, and that in ordinal Periods: And whereas you say by the example of Rivers, that though the course of the Sea were Originally that onely from East to West, yet nevertheless the different Position of the Shores may make part of the Water regurgitate, and return backwards: I grant it you, but it is necessary that you take notice my Simplicius, that where the Water upon that account returneth backwards, it doth so there perpetually; and where it runneth straight forwards, it runneth there alwayes in the same manner; for so the example of the Rivers shewes you. But in the case of the ebbing and flowing, you must finde and give us some reason why it doth in the self same place run one while one way, and another while another; Effects that being contrary & irregular, can never be deduced from any uniform and constant Cause: And this Argument, that overthrows the Hypothesis of the motion contributed to the Sea from the Heavens diurnal motion, doth also confute that Position of those who would admit the sole diurnal motion of the Earth, and believe that they are able with that alone to give a reason of the Flux and Reflux: Of which effect since it is irregular, the cause must of necessity be irregular and alterable.

Simp.I have nothing to reply, neither of my own, by reason of the weakness of my understanding; nor of that of others, for that the Opinion is so new: But I could believe that if it were spread amongst the Schools, there would not want Phylosophers able to oppose it.

Sagr.Expect such an occasion; and we in the mean time if it seem good to Salviatus, will proceed forward.

Salv.All that which hath been said hitherto, pertaineth to the diurnal period of the ebbing and flowing; of which we have in the first place demonstrated in general the primary and universal Cause, without which, no such effect would follow: ⟨Afterwards⟩ passing to the particular Accidents, various, and in a certain sort irregular, that are observed therein: We have handled the secondary and concommitant Causes upon which they depend. Now follow the two other Periods, Monethly, and Annual, which do not bring with them new and different Accidents, other than those already considered in the diurnal Period; but they operate on the same Accidents, by rendring them greater and lesser in several parts of the Lunar Moneth, and in several times of the Solar Year; as if that the Moon and Sun did each conceive it self apart in operating and producing of those Effects; a thing that totally clasheth with my understanding, which seeing how that this of Seas is a local and sensible motion, made in an immense mass of Water, it cannot be brought to subscribe to Lights, to temperate Heats, to predominacies by occult Qualities, and to such like vain Imaginations, that are so far from being, or being possible to be Causes of the Tide; that on the contrary, the Tide is the cause of them, that is, of bringing them into the brains more apt for loquacity and ostentation, than for the speculation and discovering of the more abstruse secrets of Nature; which kind of people, before they can be brought to pronounce that wise, ingenious, and modest sentence, I know it not, suffer to escape from their mouths and pens all manner of extravagancies. And the onely observing, that the same Moon, and the same Sun operate not with their light with their motion, with great heat, or with temperate, on the lesser reeeptacles of Water, but that to effect their flowing by heat, they must be reduced to little lesse than boiling, and in short, we not being able artificially to imitate any way the motions of the Tide, save only by the motion of the Vessel, ought it not to satisfie every one, that all the other things alledged, as causes of those effects, are vaine fancies, and altogether estranged from the Truth. I say,The alterations in the effects argue alteration in the cause. therefore, that if it be true, that of one effect there is but one sole primary cause, and that between the cause and effect, there is a firm and constant connection; it is necessary that whensoever there is seen a firm and constant alteration in the effect, there be a firm and constant alteration in the cause. And because the alterations that happen in the ebbing and flowing in several parts of the Year and Moneths, have their periods firm and constant, it is necessary to say, that a regular alteration in those same times happeneth in the primary cause of the ebbings and flowings.The causes at large assigned of the Periods Monethly and Annual of the ebbing and flowing. And as for the alteration that in those times happens in the ebbings and flowings consisteth onely in their greatness; that is, in the Waters rising and falling more or lesse, and in running with greater or lesse impetus; therefore it is necessary, that that which is the primary cause of the ebbing and flowing, doth in those same determinate times increase and diminish its force. But we have already concluded upon the inequality and irregularity of the motion of the Vessels containing the Water to be the primary cause of the ebbings and flowings. Therefore it is necessary, that that irregularity, from time to time, correspondently grow more irregular, that is, grow greater and lesser. Now it is requisite, that we call to minde, that the irregularity, that is, the different velocity of the motions of the Vessels, to wit, of the parts of the Terrestrial Superficies, dependeth on their moving with a compound motion, resulting from the commixtion of the two motions, Annual and Diurnal, proper to the whole Terrestrial Globe; of which the Diurnal conversion, by one while adding to, and another while substracting from, the Annual motion, is that which produceth the irregularity in the compound motion; so that, in the additions and substractions, that the Diurnal revolution maketh from the Annual motion, consisteth the original cause of the irregular motion of the Vessels, The monethly and annual alterations of the tide can depend upon nothing, save on the alteration of the additions & substractions of the diurnal period from the annual. and consequently of the Ebbing and Flowing: insomuch that if these additions and substractions should alwayes proceed in the same proportion, in respect of the Annual motion, the cause of the Ebbing and Flowing would indeed continue, but yet so as that they would perpetually return in the self same manner: But we are to finde out the cause of making the same Ebbings and Flowings in divers times greater and lesser: Therefore we must (if we will retain the identity of the cause) find the alteration in these additions and substractions, that make them more & less potent, in producing those effects which depend thereupon. But I see not how that potency and impotence can be introduced, unlesse by making the same additions and substractions, one while greater, and another while lesser; so that the acceleration and the retardment of the compound motion, may be made, sometimes in greater, and sometimes in lesser proportion.

Sagr.I feel my self very gently led, as it were, by the hand, and though I finde no rubs in the way, yet neverthelesse, like a blind man, I see not whether your Clue leadeth me, nor can I imagine where such a Journey will end.

Salv.Though there be a great difference between my slow pac't Philosophy, and your more nimble Reason, yet neverthelesse, in this particular which we are now upon, I do not much wonder, if the apprehensivenesse of your wit be a little obscured by the dark and thick mist that hides the mark, at which we aime: and that which lesseneth my admiration is, the remembrance of the many hours, many dayes, yea more, many nights that I have consumed in this contemplation, and of the many times that, despairing to bring it to a period, I have, for an incouragement of my self, indeavoured to believe, by the example of the unfortunate Orlando, that that might not possibly be true, which yet the testimony of so many credible men set before my eyes: wonder not, therefore, if this once, contrary to your custome, you do not foresee what I intend: and if you will needs admire, I believe that the event, as far as I can judge unexpected, will make you cease your wonderment.

Sagr.I thank God, that he did not permit that desperation of yours to end in the Exit that is fabled of the miserable Orlando, nor in that which haply is no lesse fabulously related of Aristotle, that so neither my self nor others should be deprived of the discovery of a thing, as abstruse as it was desirable: I beseech you, therefore, to satisfie my eager appetite as soon as you can.

Salv.I am ready to serve you: We were upon an inquiry in what manner the additions and substractions of the Terrestriall conversion from the Annual motion, could be made, one while in a greater, and another while in a lesser proportion; which diversity, and no other thing, could be assigned for the cause of the alterations, Monethly and Annual, that are seen in the greatnesse of the Ebbings and Flowings. I will now consider how this proportion of the additions and substractions of the Diurnal Revolution,Three wayes of altering the proportion of the additions of the diurnal Revolution to the annual motion. and Annual motion may grow greater and lesser three several wayes. One is by increasing and diminishing the velocity of the Annual motion, retaining the additions and substractions made by the Diurnal conversion in the same greatnesse, because the Annual motion being about three times greater, that is, more velocious than the Diurnal motion (considered likewise in the Grand Circle) if we increase it anew, the additions and substractions of the Diurnal motion will occasion lesse alteration therein: but, on the other side, making it more slow, it will be altered in greater proportion, by that same diurnal motion, just as the adding or substracting four degrees of velocity from one that moveth with twenty degrees, altereth his course lesse, than those very four degrees would do, added or substracted from one that should move onely with ten degrees. The second way would be, by making the additions and substractions greater and lesser, retaining the annual motion in the same velocity; which is as easie to be understood, as it is manifest, that a velocity v. gr. of 20 degr. is more altered by the addition or substraction of 10. deg. than by the addition or substraction of 4. The third way would be, in case these two were joyned together, diminishing the annual motion, & increasing the diurnal additions and substractions. Hitherto, as you see, it was no hard matter to attain, but yet it proved to me very hard to find by what means this might be effected in Nature.That which to us is hard to be understood, is with Nature easie to be effected. Yet in the end, I finde that she doth admirably make use thereof, and in wayes almost incredible: I mean, admirable and incredible to us, but not to her, who worketh even those very things, which, to our capacity, are of infinite wonder, with extraordinary facility and simplicity: and that which it is hard for us to understand, is easie for her to effect. Now to proceed, having shewn that the proportion between the additions and substractions of the Diurnal conversion and Annual motion may be made greater and lesser, two wayes, (and I say two, because the third is comprized in the two first) I adde, that Nature maketh use of them both: and farthermore, I subjoyn, that if she did make use but of one alone, it would be necessary to take away one of the two Periodical alterations.If the Diurnal motion should not alter, the annual Period would cease That of the Monethly Period would cease, if the annual motion should not alter. And in case the additions and substractions of the diurnal revolution should continually be equal, the alterations of the annual Period would fail.

Sagr.It seems then, that the Monethly alteration of ebbings and flowings dependeth on the alteration of the annual motion of the Earth? And the annual alteration of those ebbings and flowings do, it seems, depend on the additions and substractions of the diurnal conversion? And here now I finde my self worse puzzled than before, and more out of hope of being able to comprehend how this intricacy may be, which is more inextricable, in my judgment, than the Gordian knot. And I envy Simplicius, from whose silence I argue that he doth apprehend the whole businesse, and is acquit of that confusion which greatly puzzleth my brains.

Simp.I believe verily, Sagredus, that you are put to a a stand; and I believe that I know also the cause of your confusion, which, if I mistake not, riseth from your understanding part of those particulars but even now alledged by Salviatus, and but a part. It is true likewise that I find my self free from the like confusion; but not for that cause as you think, to wit, because I apprehend the whole, nay it happens upon the quite contrary account; namely, from my not comprehending any thing, and confusion is in the plurality of things, and not in nothing.

Sagr.You see Salviatus, how a few checks given to Simplicius in the dayes preceding, have rendered him gentle, and brought him from the capriol to the amble. But I beseech you without farther delay, put us both out of suspence.

Salv.I will endeavour it to the utmost of my harsh way of expressing my self, the obtusenesse of which, the acutenesse of your wit shall supply. The accidents of which we are to enquire the causes are two: The first respecteth the varieties that happen in the ebbings and flowings in the Monethly Period; and the othr relateth to the Annual. We will first speak of the Monethly, and then treat of the Annual; and it is convenient that we resolve them all according to the Fundamentals and Hypothesis already laid down, without introducing any novelty either in Astronomy, or in the Universe, in favour of the ebbings and flowings; therefore let us demonstrate that of all the several accidents in them observed, the causes reside in the things already known,The true Hypothesis may dispatch its revolutions in a shorter time, in lesser circles than in greater; the which is proved by two examples. and received for true and undoubted. I say therefore, that it is a truly natural, yea necessary thing, that one and the same moveable made to move round by the same moving virtue in a longer time, do make its course by a greater circle, rather than by a lesser; and this is a truth received by all, and confirmed by all experiments,The first example. of which we will produce a few. In the wheel-clocks, and particularly in the great ones, to moderate the time, the Artificers that make them accomodate a certain voluble staffe horozontally, and at each end of it they fasten two Weights of Lead, and when the time goeth too slow, by the onely removing those Leads a little nearer to the centre of the staffe, they render its vibrations more frequent; and on the contrary to retard it, it is but drawing those Weights more towards the ends; for so the vibrations are made more seldome, and consequently the intervals of the hours are prolonged.

The second example.Here the movent vertue is the same, namely the counterpoise, the moveables are those same Weights of lead, and their vibrations are more frequent when they are neerer to the centre, that is, when they move by lesser circles. Hanging equal Weights at unequal cords, and being removed from their perpendicularity, letting them go; we shall see those that are pendent at the shorter cords, to make their vibrations under shorter times, as those that move by lesser circles. Again, let such a kind of Weight be fastened to a cord, which cord let play upon a staple fastened in the Seeling, and do you hold the other end of the cord in your hand, and having given the motion to the pendent Weight, whilst it is making its vibrations, pull the end of the cord that you hold in your hand, so that the Weight may rise higher and higher: In its rising you shall see the frequency of its vibrations encrease, in regard that they are made successively by lesser and lesser circies.Two particular notable accidents in the penduli and their vibrations. And here I desire you to take notice of two particulars worthy to be observed. One is that the vibrations of one of those plummets are made with such a necessity under such determinate times, that it is altogether impossible to cause them to be made under other times, unlesse it be by prolonging, or abreviating the cord; of which you may also at this very instant ascertain your selves by experience, tying a stone to a pack-threed, and holding the other end in your hand, trying whether you can ever by any artifice be able to swing it this way and that way in other than one determinate time, unlesse by lengthening of shortening the string, which you will find to be absolutely impossible. The other particular truly admirable is, that the self same pendulum makes its vibrations with one and the same frequency, or very little, and as it were insensibly different, whether they be made by very great, or very small arches of the self-same circumference. I mean that whether we remove the pendulum from perpendicularity one, two, or three degrees onely, or whether we remove it 70. 80. nay to an entire quadrant, it being let go, will in the one case and in the other make its vibrations with the same frequency, as well the former where it is to move by an arch of but four or six degrees, as the second, where it is to passe arches of 160. or more degrees. Which may the better be seen, by hanging two weights at two strings of equal length, and then removing them from perpendicularity, one a little way, and the other very far; the which being set at liberty, will go & return under the same times, the one by arches very small, & the other by very great ones, from whence followeth the conclusion of an admirable Problem;Admirable Problems of moveables descending by the Quadrant of a Circle, and of those descending by all the cords of the whole Circle. which is, That a Quadrant of a Circle being given (take a little diagram of the same, [in Fig. 3.]) as for instance: AB erect to the Horizon, so as that it rest upon the plain touching in the point B. and an Arch being made with a Hoop well plained and smoothed in the concave part, bending it according to the curvity of the Circumference ADB. So that a Bullet very round and smooth may freely run to and again within it (the rim of a Sieve is very proper for the experiment) I say, that the Bullet being put in any what ever place, neer or far from the lowest term B. As for instance, putting it in the point C, or here in D, or in E; and then let go, it will in equal times, or insensibly different arrive at the term B, departing from C, or from D, or from E, or from whatever other place; an accident truly wonderfull. We may add another accident no less strange than this, which is, That moreover by all the cords drawn from the point B to the points C, D, E; and to any other whatsoever, taken not onely in the Quadrant BA, but in all the whole circumference of the Circle the said moveable shall descend in times absolutely equal; insomuch that it shall be no longer in descending by the whole Diameter erect perpendicularly upon the point B, then it shall in descending by B. C. although it do sublend but one sole degree, or a lesser Arch. Let us add the other wonder, which is, That the motions of the falling bodies made by the Arches of the Quadrant AB; are made in shorter times than those that are made by the cords of those same Arches; so that the swiftest motion, and made by a moveable in the shortest time, to arrive from the point A, to the term B, shall be that which is made, not by the right line A, B, (although it be the shortest of all those that can de drawn between the points A. B.) but by the circumference ADB. And any point being taken in the said Arch; as for example: The point D. and two cords drawn A D, and D. B. the moveable departing from the qoint A, shall in a less time come to B, moving by the two cords A D and D B. than by the sole cord A, B. But the shortest of all the times shall be that of the fall by the Arch A D B. And the self same accidents are to be understood of all the other lesser Arches taken from the lowermost term B. upwards.

Sagr.No more, no more; for you so confund and fill me with Wonders, and distract my thoughts so many several wayes, that I fear I shall have but a small part of it left free and disingaged, to apply to the principal matter that is treated of, and which of it self is but even too obscure and intricate: So that I intreat you to vouchsafe me, having once dispatcht the business of the ebbings and flowings, to do this honour to my house (and yours) some other dayes, and to discourse upon the so many other Problems that we have left in suspence; and which perhaps are no less curious and admirable, than this that hath been discussed these dayes past, and that now ought to draw to a conclusion.

Salv.I shall be ready to serve you, but we must make more than one or two Sessions; if besides the other questions reserved to be handled apart, we would discusse those many that pertain to the local motion, as well of natural moveables, as of the rejected: an Argument largely treated of by our Lyncean Accademick. But turning to our first purpose, where we were about to declare, That the bodies moving circularly by a movent virtue, which continually remaineth the same, the times of the circulation were prefixt and determined, and impossible to be made longer or shorter, having given examples, and produced experiments thereof, sensible, and feasible, we may confirm the same truth by the experiences of the Celestial motions of the Planets; in which we see the same rule observed; for those that move by greater Circles, confirm longer times in passing them. A most pertinent observation of this we have from the Medicæan Planets, which in short times make their revolutions about Jupiter: Insomuch that it is not to be questioned, nay we may hold it for sure and certain, that if for example, the Moon continuing to be moved by the same movent faculty, should retire by little and little in lesser Circles, it would acquire a power of abreviating the times of its Periods, according to that Pendulum, of which in the course of its vibrations, we by degrees shortned the cord, that is contracted the Semidiameter of the circumferences by it passed. Know now that this that I have alledged an example of it in the Moon, is seen and verified essentially in fact. Let us call to mind, that it hath been already concluded by us, together with Copernicus,The Earths annual motion by the Ecliptick, unequal by means of the Moons motion. That it is not possible to separate the Moon from the Earth, about which it without dispute revolveth in a Moneth: Let us remember also that the Terrestrial Globe, accompanyed alwayes by the Moon, goeth along the circumference of the Grand Orb about the Sun in a year, in which time the Moon revolveth about the Earth almost thirteen times; from which revolution it followeth, that the said Moon sometimes is found near the Sun; that is, when it is between the Sun and the Earth, and sometimes much more remote, that is, when the Earth is situate between the Moon and Sun; neer, in a word, at the time of its conjun¦ction and change; remote, in its Full and Opposition; and the greatest vicinity differ the quantity of the Diameter of the Lunar Orb. Now if it be true that the virtue which moveth the Earth and Moon, about the Sun, be alwayes maintained in the same vigour; and if it be true that the same moveable moved by the same virtue, but in circles unequal, do in shorter times passe like arches of lesser circles, it must needs be granted, that the Moon when it is at a lesse distance from the Sun, that is in the time of conjunction, passeth greater arches of the Grand Orb, than when it is at a greater distance, that is in its Opppsition and Full. And this Lunar inequality must of necessity be imparted to the Earth also; for if we shall suppose a right line produced from the centre of the Sun by the centre of the Terrestrial Globe, and prolonged as far as the Orb of the Moon, this shall be the semidiameter of the Grand Orb, in which the Earth, in case it were alone, would move uniformly, but if in the same semidiameter we should place another body to be carried about, placing it one while between the Earth and Sun, and another while beyond the Earth, at a greater distance from the Sun, it is necessary, that in this second case the motion common to both, according to the circumference of the great Orb by means of the distance of the Moon, do prove a little slower than in the other case, when the Moon is between the Earth and Sun, that is at a lesser distance. So that in this businesse the very same happeneth that befals in the time of the clock; that lead which is placed one while farther from the centre, to make the vibrations of the staffe or ballance lesse frequent, and another while nearer, to make them thicker, representing the Moon. Hence it may be manifest, that the annual motion of the Earth in the Grand Orb, and under the Ecliptick, is not uniform, and that its irregularity proceedeth from the Moon, and hath its Monethly Periods and Returns. And because it hath been concluded, that the Monethly and Annual Periodick alterations of the ebbings and flowings, cannot be deduced from any other cause than from the altered proportion between the annual motion and the additions and substractions of the diurnal conversion; and that those alterations might be made two wayes, that is by altering the annual motion, keeping the quantity of the additions unaltered, or by changing of the bignesse of these, reteining the uniformity of annual motion. We have already found the first of these, depending on the irregularity of the annual motion occasioned by the Moon, and which hath its Monethly Periods. It is therefore necessary, that upon that account the ebbings and flowings have a Monethly Period in which they do grow greater and lesser. Now you see that the cause of the Monethly Period resideth in the annual motion; and withal you see how much the Moon is concerned in this business, and how it is therewith interrupted apart, without having any thing to do with either, with Seas or Waters.

Sagr.If one that never had seen any kinde of Stairs or Lader, were shewed a very high Tower, and asked if ever he hoped to climb to the top of it, I verily believe that he would answer he did not, not conceiving how one should come thither any way except by flying; but shewing him a stone of but a foot high, and asking him whether he thought he could get to the top of that, I am certain that he would answer he could; and farther, that he would not deny, but that it was not onely one, but ten, twenty, and an hundred times easier to climb that: But now if he should be shewed the Stairs, by means whereof, with the facility by him granted, it is possible to get thither, whither he a little before had affirmed it was impossible to ascend, I do think that laughing at himself he would confess his dulness of apprehension. Thus, Salviatus, have you step by step so gently lead me, that, not without wonder, I finde that I am got with small pains to that height which I despaired of arriving at. 'Tis true; that the Staircase having been dark, I did not perceive that I was got nearer to, or arrived at the top, till that coming into the open Air I discovered a great Sea, and spacious Country: And as in ascending one step, there is no labour; so each of your propositions by it self seemed to me so plain, that thinking I heard but little or nothing that was new unto me, I conceived that my benefit thereby had been little or none at all: Whereupon I was the more amazed at the unexpected exit of this discourse, that hath guided me to the knowledge of a thing which I held impossible to be demonstrated. One doubt onely remains, from which I desire to be freed, and this it is; Whether that if the motion of the Earth together with that of the Moon under the Zodiack are irregular motions, those irregularities ought to have been observed and taken notice of by Astronomers, which I do not know that they are: Therefore I pray you, who are better acquainted with these things than I, to free me from this doubt, and tell me how the case stands.

Salv.You ask a rational question, and answering to the Objection, Many things may remain as yet unobserved in Astronomy.I say; That although Astronomy in the courses of many ages hath made a great progress in discovering the constitution and motions of the Celestial bodies, yet is it not hitherto arrived at that height, but that very many things remain undecided, and haply many others also undiscovered. It is to be supposed that the first observers of Heaven knew no more but one motion common to all the Stars, as is this diurnal one: yet I believe that in few dayes they perceived that the Moon was inconstant in keeping company with the other Stars; but yet withal, that many years past, before that they distinguished all the Planets: And in particular, Saturn for its slowness, and Mercury for its rareness of appearing were amongst those that were last observed. I conceit that Saturn by its slowness, and Mercury by reason of its seldom appearing, were the last that were observed to be wandring and errant. It is to be thought that many more years run out before the stations and retrogradations of the three superiour Planets were known, as also their approximations and recessions from the Earth, necessary occasions of introducing the Eccentrix and Epicicles, things unknown even to Aristotle, for that he makes no mention thereof. Mercury, and Venus, with their admirable apparitions; how long did they keep Astronomers in suspence, before that they could resolve (not to speak of any other of their qualities) upon their situation? Insomuch that the very order onely of the Mundane bodies, and the integral structure of the parts of the Universe by us known, hath been doubted of untill the time of Copernicus, who hath at last given us notice of the true constitution, and real systeme, according to which those parts are disposed; so that at length we are certain that Mercury, Venus, and the other Planets do revolve about the Sun; and that the Moon revolveth about the Earth. But how each Planet governeth it self in its particular revolution,Particular structures of the Orbs of the Planets not yet well resolved. and how precisely the structure of its Orb is framed; which is that which is vulgarly called the Theory of the Planets, we cannot as yet undoubtedly resolve. Mars, that hath so much puzled our Modern Astronomers, is a proof of this: And to the Moon her self there have been assigned several Theories, after that the said Copernicus had much altered it from that of Ptolomy. And to descend to our particular case, that is to say, to the apparent motion of the Sun and Moon; touching the former, there hath been observed a certain great irregularity, whereby it passeth the two semicircles of the Ecliptick,The Sun passeth one half of the Zodiack nine days sooner than the other. divided by the points of the Equinoxes in very different times; in passing one of which, it spendeth about nine dayes more than in passing the other; a difference, as you see, very great and notable. But if in passing small arches, such for example as are the twelve Signs, he maintain a most regular motion, or else proceed with paces, one while a little more swift, and another more slow, as it is necessary that it do, in case the annual motion belong to the Sun onely in appearance, but in reality to the Earth in company with the Moon, it is what hath not hitherto been observed,The Moons motion principally sought in the account of Eclipses. nor it may be, sought. Touching the Moon in the next place, whose restitutions have been principally lookt into an account of the Eclipses, for which it is sufficient to have an exact knowledge of its motion about the Earth, it hath not been likewise with a perfect curiosity inquired, what its course is thorow the particular arches of the Zodiack. That therefore the Earth and Moon in running through the Zodiack, that is round the Grand Orb, do somewhat accellerate at the Moons change, and retard at its full, ought not to be doubted; for that the said difference is not manifest, which cometh to be unobserved upon two accounts; First, Because it hath not been lookt for. Secondly, Because that its possible it may not be very great. Nor is there any need that it should be great, for the producing the effect that we see in the alteration of the greatness of ebbings and flowings.Ebbings and flowings are petty things in comparison of the vastness of Seas, and of the velocity of the motion of the Terrestrial Globe. For not onely those alterations, but the Tides themselves are but small matters in respect of the grandure of the subjects on which they work; albeit that to us, and to our littleness they seem great. For the addition or subduction of one degree of velocity where there are naturally 700, or 1000, can be called no great alteration, either in that which conferreth it, or in that Which receiveth it: the Water of our Mediterrane carried about by the diurnal revolution, maketh about 700 miles an hour, (which is the motion common to the Earth and to it, and therefore not perceptible to us) & that which we sensibly discern to be made in the streams or currents, is not at the rate of full one mile an hour, (I speak of the main Seas, and not of the Straights) and this is that which altereth the first, naturall, and grand motion; and this motion is very great in respect of us, and of Ships: for a Vessel that in a standing Water by the help of Oares can make v. g. three miles an hour, in that same current will row twice as far with the stream as against it: A notable difference in the motion of the Boat, though but very small in the motion of the Sea, which is altered but its seven hundredth part. The like I say of its rising, and falling one, two, or three feet; and scarcely four or five in the utmost bounds of a streight, two thousand, or more miles long, and where there are depths of hundreds of feet; this alteration is much less than if in one of the Boats that bring us fresh Water, the said Water upon the arrest of the Boat should rise at the Prow the thickness of a leaf. I conclude therefore that very small alterations in respect of the immense greatness, and extraordinary velocity of the Seas, is sufficient to make therein great mutations in relation to our smallness, and to our accidents.

Sagr.I am fully satisfied as to this particular; it remains to declare unto us how those additions and substractions derived from the diurnal Vertigo are made one while greater, and another while lesser; from which alterations you hinted that the annual period of the augmentations and diminutions of the ebbings and flowings did depend.

Salv.I will use my utmost endeavours to render my self intelligible,The causes of the inequality of the additions and substractions of the diurnal conversion from the annual motion. but the difficulty of the accident it self, and the great attention of mind requisite for the comprehending of it, constrains me to be obscure. The unequalities of the additions and substractions, that the diurnal motion maketh to or from the annual dependeth upon the inclination of the Axis of the diurnal motion upon the plane of the Grand Orb, or, if you please, of the Ecliptick; by means of which inclination the Equinoctial intersecteth the said Ecliptick, remaining inclined and oblique upon the same according to the said inclination of Axis. And the quantity of the additions importeth as much as the whole diameter of the said Equinoctial, the Earths centre being at the same time in the Solstitial points; but being out of them it importeth lesse and lesse, according as the said centre successively approacheth to the points of the Equinoxes, where those additions are lesser than in any other places. This is the whole businesse, but wrapt up in the obscurity that you see.

Sagr.Rather in that which I do no not see; for hitherto I comprehend nothing at all.

Salv.I have already foretold it. Neverthelesse we will try whether by drawing a Diagram thereof, we can give some small light to the same; though indeed it might better be set forth by solid bodies than by bare Schemes; yet we will help our selves with Perspective and fore-shortning. Let us draw therefore, as before, the circumference of the Grand Orb, [as in Fig. 4.] in which the point A is understood to be one of the Solstitials, and the diameter AP the common Section of the Solstitial Colure, and of the plane of the Grand Orb or Ecliptick; and in that same point A let us suppose the centre of the Terrestrial Globe to be placed, the Axis of which CAB, inclined upon the Plane of the Grand Orb, falleth on the plane of the said Colure that passeth thorow both the Axis of the Equinoctial, and of the Ecliptick. And for to prevent confusion, let us only draw the Equinoctial circle, marking it with these characters DGEF, the common section of which, with the plane of the grand Orb, let be the line DE, so that half of the said Equinoctial DFE will remain inclined below the plane of the Grand Orb, and the other half DGE elevated above. Let now the Revolution of the said Equinoctial be made, according to the order of the points DGEF, and the motion of the centre from A towards E. And because the centre of the Earth being in A, the Axis CB (which is erect upon the diameter of the Equinoctial DE) falleth, as hath been said, in the Solstitial Colure, the common Section of which and of the Grand Orb, is the diameter PA, the said line PA shall be perpendicular to the same DE, by reason that the Colure is erect upon the grand Orb; and therefore the said DE, shall be the Tangent of the grand Orb in the point A. So that in this Position the motion of the Centre by the arch AE; that is, of one degree every day differeth very little; yea, is as if it were made by the Tangent DAE. And because by means of the diurnal motion the point D, carried about by G, unto E, encreaseth the motion of the Centre moved almost in the same line DE, as much as the whole diameter DE amounts unto; and on the other side diminisheth as much, moving about the other semicircle EFD. The additions and subductions in this place therefore, that is in the time of the solstice, shall be measured by the whole diameter DE.

Let us in the next place enquire, Whether they be of the same bigness in the times of the Equinoxes; and transporting the Centre of the Earth to the point I, distant a Quadrant of a Circle from the point A. Let us suppose the said Equinoctial to be GEFD, its common section with the grand Orb DE, the Axis with the same inclination CB; but the Tangent of the grand Orb in the point I shall be no longer DE, but another which shall cut that at right Angles; and let it be this marked HIL, according to which the motion of the Centre I, shall make its progress, proceeding along the circumference of this grand Orb. Now in this state the Additions and Substractions are no longer measured by the diameter DE, as before was done; because that diameter not distending it self according to the line of the annual motion HL, rather cutting it at right angles, those terms DE, do neither add nor substract any thing; but the Additions and Substractons are to be taken from that diameter that falleth in the plane that is errect upon the plane of the grand Orb, and that intersects it according to the line HL; which diameter in this case shall be this GF and the Adjective, if I may so say, shall be that made by the point G, about the semicircle GEF, and the Ablative shall be the rest made by the other semicircle FDG. Now this diameter, as not being in the same line HL of the annual motion, but rather cutting it, as we see in the point I, the term G being elevated above, and E depressed below the plane of the grand Orb, doth not determine the Additions and Substractions according to its whole length, but the quantity of those first ought to be taken from the part of the line HL, that is intercepted between the perpendiculars drawn upon it from the terms GF; namely, these two GS, and FV: So that the measure of the additions is the line SV lesser then GF, or then DE; which was the measure of the additions in the Solstice A. And so successively, according as the centre of the Earth shall be constituted in other points of the Quadrant AI, drawing the Tangents in the said points, and the perpendiculars upon the same falling from the terms of the diameters of the Equinoctial drawn from the errect planes by the said Tangents to the plane of the grand Orb; the parts of the said Tangents (which shall continually be lesser towards the Equinoctials, and greater towards the Solstices) shall give us the quantities of the additions and substractions. How much in the next place the least additions differ from the greatest, is easie to be known, because there is the same difference betwixt them, as between the whole Axis or Diameter of the Sphere, and the part thereof that lyeth between the Polar-Circles; the which is less than the whole diameter by very near a twelfth part, supposing yet that we speak of the additions and substractions made in the Equinoctial; but in the other Parallels they are lesser, according as their diameters do diminish.

This is all that I have to say upon this Argument, and all perhaps that can fall under the comprehension of our knowledge, which, as you well know, may not entertain any conclusions, save onely those that are firm and constant, such as are the three kinds of Periods of the ebbings and flowings; for that they depend on causes that are invariable, simple, and eternal. But because that secondary and particular causes, able to make many alterations, intermix with these that are the primary and universal; and these secondary causes being part of them inconstant, and not to be observed; as for example, The alteration of Winds, and part (though terminate and fixed) unobserved for their multiplicity, as are the lengths of the Straights, their various inclinations towards this or that part, the so many and so different depths of the Waters, who shall be able, unless after very long observations, and very certain relations, to frame so expeditious Histories thereof, as that they may serve for Hypotheses, and certain suppositions to such as will by their combinations give adequate reasons of all the appearances, and as I may say, Anomalie, and particular irregularities that may be discovered in the motions of the Waters? I will content my self with advertising you, that the accidental causes are in nature, and are able to produce many alterations; for the more minute observations, I remit them to be made by those that frequent several Seas: and onely by way of a conclusion to this our conference, I will propose to be considered, how that the precise times of the fluxes and refluxes do not onely happen to be altered by the length of Straights, and by the difference of depths; but I believe that a notable alteration may also proceed from the comparing together of sundry tarcts of Sea, different in greatness; and in position, or, if you will, inclination; which difference happeneth exactly here in the Adriatick Gulph, lesse by far than the rest of the Mediterrane, and placed in so different an inclination, that whereas that hath its bounds that incloseth it on the Eastern part, as are the Coasts of Syria, this is shut up in its more Westerly part: and because the ebbings and flowings are much greater towards the extremities, yea, because the Seas risings and fallings are there onely greatest, it may probably happen that the times of Flood at Venice may be the time of low Water in the other Sea, which, as being much greater, and distended more directly from West to East, cometh in a certain sort to have dominion over the Adriatick: and therefore it would be no wonder, in case the effects depending on the primary causes, should not hold true in the times that they ought, and that correspond to the periods in the Adriatick, as it doth in the rest of the Mediterrane. But these Particularities require long Observations, which I neither have made as yet, nor shall I ever be able to make the same for the future.

Sagr.You have, in my opinion, done enough in opening us the way to so lofty a speculation, of which, if you had given us no more than that first general Proposition that seemeth to me to admit of no reply, where you declare very rationally, that the Vessels containing the Sea-waters continuing stedfast, it would be impossible, according to the common course of Nature, that those motions should follow in them which we see do follow; and that, on the other side, granting the motions ascribed, for other respects, by Copernicus to the Terrestrial Globe, these same alterations ought to ensue in the Seas, if I say you had told us no more, this alone in my judgment, so far exceeds the vanities introduced by so many others, that my meer looking on them makes me nauseate them, and I very much admire, that among men of sublime wit, of which nevertheless there are not a few, not one hath ever considered the incompatibility that is between the reciprocal motion of the Water contained, and the immobility of the Vessel containing, which contradiction seemeth to me now so manifest.

Salv.It is more to be admired,One single motion of the terrestrial Globe sufficeth not to produce the Ebbing & Flowing that it having come into the thoughts of some to refer the cause of the Tide to the motion of the Earth, therein shewing a more than common apprehension, they should, in afterwards driving home the motion close with no side; and all, because they did not see that one simple and uniform motion, as v. gr. the sole diurnal motion of the Terrestrial Globe, doth not suffice, but that there is required an uneven motion, one while accelerated, and another while retarded: for when the motion of the Vessels are uniforme, the waters contained will habituate themselves thereto, without ever making any alteration. To say also (as it is related of an ancient The opinion of Seleucus the Mathematician censured.Mathematician) that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing, is an absolute vanity, not onely because it is not exprest, nor seen how it should so happen, but the falsity is obvious, for that the Revolution of the Earth is not contrary to the motion of the Moon, but is towards the same way. So that all that hath been hitherto said, and imagined by others, is, in my judgment, altogether invalid. But amongst all the famous men that have philosophated upon this admirable effect of Nature,Kepler is with respect blamed. I more wonder at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascribed to the Earth, before him, hath for all that given his ear and assent to the Moons predominancy over the Water, and to occult properties, and such like trifles.

Sagr.I am of opinion, that to these more spaculative persons the same happened, that at present befalls me, namely, the not understanding the intricate commixtion of the three Periods Annual, Monethly, and Diurnal; And how their causes should seem to depend on the Sun, and on the Moon, without the Suns or Moons having any thing to do with the Water; a businesse, for the full understanding of which I stand in need of a little longer time to consider thereof, which the novelty and difficulty of it hath hitherto hindred me from doing: but I despair not, but that when I return in my solitude and silence to ruminate that which remaineth in my fancy, not very well digested, I shall make it my own. We have now, from these four dayes Discourse, great attestations, in favour of the Copernican Systeme, amongst which these three taken: the first, from the Stations and Retrogradations of the Planets, and from their approaches, and recessions from the Earth; the second, from the Suns revolving in it self, and from what is observed in its spots; the third, from the Ebbing and Flowing of the Sea do shew very rational and concluding.

Salv.To which also haply, in short, one might adde a fourth, and peradventure a fifth; a fourth, I say, taken from the fixed stars, seeing that in them, upon exact observations, those minute mutations appear, that Copernicus thought to have been insensible. There starts up, at this instant, a fifth novelty, from which one may argue mobility in the Terrestrial Globe, by means of that which the most Illustrious Signore Cæsare,Sig. Cæsare Marsilius observeth the Meridian to be moveable. of the noble Family of the Marsilii of Bologna, and a Lyncean Academick, discovereth with much ingenuity, who in a very learned Tract of his, sheweth very particularly how that he had observed a continual mutation, though very slow in the Meridian line, of which Treatise, at length, with amazement, perused by me, I hope he will communicate Copies to all those that are Students of Natures Wonders.

Sagr.This is not the first time that I have heard speak of the exquisite Learning of this Gentleman, and of his shewing himself a zealous Patron of all the Learned, and if this, or any other of his Works shall come to appear in publique, we may be aforehand assured, that they will be received, as things of great value.

Salv.Now because it is time to put an end to our Discourses, it remaineth, that I intreat you, that if, at more leasure going over the things again that have been alledged you meet with any doubts, or scruples not well resolved, you will excuse my oversight, as well for the novelty of the Notion, as for the weaknesse of my wit, as also for the grandure of the Subject, as also finally, because I do not, nor have pretended to that assent from others, which I my self do not give to this conceit, which I could very easily grant to be a Chymæra, and a meer paradox; and you Sagredus, although in the Discourses past you have many times, with great applause, declared, that you were pleased with some of my conjectures, yet do I believe, that that was in part more occasioned by the novelty than by the certainty of them, but much more by your courtesie, which did think and desire, by its assent, to procure me that content which we naturally use to take in the approbation and applause of our own matters: and as your civility hath obliged me to you; so am I also pleased with the ingenuity of Simplicius. Nay, his constancy in maintaining the Doctrine of his Master, with so much strength & undauntedness, hath made me much to love him. And as I am to give you thanks, Sagredus, for your courteous affection; so of Simplicius, I ask pardon, if I have sometimes moved him with my too bold and resolute speaking: and let him be assured that I have not done the same out of any inducement of sinister affection, but onely to give him occasion to set before us more lofty fancies that might make me the more knowing.

Simp.There is no reason why you should make all these excuses, that are needlesse, and especially to me, that being accustomed to be at Conferences and publique Disputes, have an hundred times seen the Disputants not onely to grow hot and angry at one another, but likewise to break forth into injurious words, and sometimes to come very neer to blows. As for the past Discourses, and particulatly in this last, of the reason of the Ebbing and Flowing of the Sea, I do not, to speak the truth, very well apprehend the same, but by that slight Idea, what ever it be, that I have formed thereof to my self, I confesse that your conceit seemeth to me far more ingenuous than any of all those that I ever heard besides, but yet neverthelesse I esteem it not true and concluding: but keeping alwayes before the eyes of my mind a solid Doctrine that I have learn't from a most learned and ingenuous person, and with which it is necessary to sit down; I know that both you being asked, Whether God, by his infinite Power and Wisdome might confer upon the Element of Water the reciprocal motion which we observe in the same in any other way, than by making the containing Vessel to move; I know, I say, that you will answer, that he might, and knew how to have done the same many wayes, and those unimaginable to our shallow understanding: upon which I forthwith conclude, that this being granted, it would be an extravagant boldnesse for any one to goe about to limit and confine the Divine Power and Wisdome to some one particular conjecture of his own.

Salv.This of yours is admirable, and truly Angelical Doctrine, to which very exactly that other accords, in like manner divine, which whilst it giveth us leave to dispute, touching the constitution of the World, addeth withall (perhaps to the end, that the exercise of the minds of men might neither be discouraged, nor made bold) that we cannot find out the works made by his hands. Let therefore the Disquisition permitted and ordain'd us by God, assist us in the knowing, and so much more admiring his greatnesse, by how much lesse we finde our selves too dull to penetrate the profound Abysses of his infinite Wisdome.

Sagr.And this may serve for a final close of our four dayes Disputations, after which, if it seem good to Salviatus, to take some time to rest himself, our curiosity must, of necessity, grant him the same, yet upon condition, that when it is lesse incommodious for him, he will return and satisfie my desire in particular concerning the Problemes that remain to be discust, and that I have set down to be propounded at one or two other Conferences, according to our agreement: and above all, I shall very impatiently wait to hear the Elements of the new Science of our Academick about the natural and violent local Motions. And in the mean time, we may, according to our custome, spend an hour in taking the Air in the Gondola that waiteth for us.

 

FINIS.