the Isles of Corsica and Sardinnia and in the Strands of Rome and Ligorne where it exceeds not half a foot we shall understand also why on the contrary where the risings and fallings are small the courses and recourses are great I say it is an easie thing to understand the causes of these accidents seeing that we meet with many manifest occurrences of the same nature in every kind of Vessel by us artificially composed in which the same effects are observed naturally to follow upon our moving it unevenly that is one while faster and another while flower Moreover considering in the fifth place that the same quantity of Water being moved though but gently in a spatious Channel comming afterwards to go through a narrow passage will of necessity run with great violence we shall not finde it hard to comprehend the cause of the great Currents that are made in the narrow Channel that separateth Calabria from Sicilia for that all the Waters that by the spaciousnesse of the Isle and by the Ionick Gulph happens to be pent in the Eastern part of the Sea though it do in that by reason of its largeness gently descend towards the West yet neverthelesse in that it is pent up in the Bosphorus it floweth with great violence between Scilla and Caribdis and maketh a great agitation Like to which and much greater is said to be betwixt Africa and the great Isle of St. Lorenzo where the Waters of the two vast Seas Indian and Ethiopick that lie round it must needs be straightned into a lesse Channel between the said Isle and the Ethiopian Coast. And the Currents must needs be very great in the Straights of Megallanes which joyne together the vast Oceans of Ethiopia and Del Zur called also the Pacifick Sea It follows now in the sixth place that to render a reason of some more abstruse and incredible accidents which are observed upon this occasion we make a considerable reflection upon the two principal causes of ebbings and flowings afterwards compounding and mixing them together The first and simplest of which is as hath often been said the determinate acceleration and retardation of the parts of the Earth from whence the Waters have a determinate period put to their decursions towards the East and return towards the West in the time of twenty four hours The other is that which dependeth on the proper gravity of the Water which being once commoved by the primary cause seeketh in the next place to reduce it self to Aequilibrium with iterated reciprocations which are not determined by one sole and prefixed time but have as many varieties of times as are the different lengths and profundities of the receptacles and Straights of Seas and by what dependeth on this second principle they would ebbe and flow some in one hour others in two in four in six in eight in ten c. Now if we begin to put together the first cause which hath its set Period from twelve hours to twelve hours with some one of the secondary that hath its Period verb. grat from five hours to five hours it would come to passe that at sometimes the primary cause and secondary would accord to make impulses both one the same way and in this concurrency and as one may call it unanimous conspiration the flowings shall be great At other times it happening that the primary impulse doth in a certain manner oppose that which the secondary Period would make and in this contest one of the Principles being taken away that which the other would give will weaken the commotion of the Waters and the Sea will return to a very tranquil State and almost immoveable And at other times according as the two aforesaid Principles shall neither altogether contest nor altogether concur there shall be other kinds of alterations made in the increase and diminution of the ebbing and flowing It may likewise fall out that two Seas considerably great and which communicate by some narrow Channel may chance to have by reason of the mixtion of the two Principles of motion one cause to flow at the time that the other hath cause to move a contrary way in which case in the Channel whereby they disimbogue themselves into each other there do extraordinary conturbations insue with opposite and vortick motions and most dangerous boilings and breakings as frequent relations and experiences do assure us From such like discordant motions dependent not onely on the different positions and longitudes but very much also upon the different profundities of the Seas which have the said intercourse there do happen at sometimes different commotions in the Waters irregular and that can be reduced to no rules of observation the reasons of which have much troubled and alwayes do trouble Mariners for that they meet with them without seeing either impulse of winds or other eminent aereal alteration that might occasion the same of which disturbance of the Air we ought to make great account in other accidents and to take it for a third and accidental cause able to alter very much the observation of the effects depending on the secondary and more essential causes And it is not to be doubted but that impetuous windes continuing to blow for example from the East they shall retein the Waters and prohibit the reflux or ebbing whereupon the second and third reply of the flux or tide overtaking the former at the hours prefixed they will swell very high and being thus born up for some dayes by the strength of the Winds they shall rise more than usual making extraordinary inundations We ought also and this shall serve for a seventh Probleme to take notice of another cause of motion dependant on the great abundance of the Waters of great Rivers that discharge themselves into Seas of no great capacity whereupon in the Straits or Bosphori that communicate with those Seas the Waters are seen to run always one way as it happeneth in the Thracian Bosphorus below Constantinople where the water alwayes runneth from the Black-Sea towards the Propontis For in the said Black-Sea by reason of its shortnesse the principal causes of ebbing and flowing are but of small force But on the contrary very great Rivers falling into the same those huge defluxions of water being to passe and disgorge themselves by the the straight the course is there very notable and alwayes towards the South Where moreover we ought to take notice that the said Straight or Channel albeit very narrow is not subject to perturbations as the Straight of Scilla and Carybdis for that that hath the Black-Sea above towards the North and the Propontis the Aegean and the Mediterranean Seas joyned unto it though by a long tract towards the South but now as we have observed the Seas though of never so great length lying North and South are not much subject to ebbings and flowings but because the Sicilian Straight is situate between the parts of the Mediterrane distended
against themselves observations experiences and reasons of farre greater force than those alledged by Aristotle Ptolomy and other opposers of the same conclusions and by this means you shall come to ascertain your self that they were not induced through want of knowledge or expetience to follow that opinion SAGR. It is requisite that upon this occasion I relate unto you some accidents that befell me so soon as I first began to hear speak of this new doctrine Being very young and having scarcely finished my course of Philosophy which I left off as being set upon other employments there chanced to come into these parts a certain Foreigner of Rostock whose name as I remember was Christianus Vurstitius a follower of Copernicus who in an Academy made two or three Lectures upon this point to whom many flock't as Auditors but I thinking they went more for the novelty of the subject than otherwise did not go to hear him for I had concluded with my self that that opinion could be no other than a solemn madnesse And questioning some of those who had been there I perceived they all made a jest thereof execpt one who told me that the businesse was not altogether to be laugh't at and because this man was reputed by me to be very intelligent and wary I repented that I was not there and began from that time forward as oft as I met with any one of the Copernican perswasion to demand of them if they had been alwayes of the same judgment and of as many as I examined I found not so much as one who told me not that he had been a long time of the contrary opinion but to have changed it for this as convinced by the strength of the reasons proving the same and afterwards questioning them one by one to see whether they were well possest of the reasons of the other side I found them all to be very ready and perfect in them so that I could not truly say that they had took up this opinion out of ignorance vanity or to shew the acutenesse of their wits On the contrary of as many of the Peripateticks and Ptolomeans as I have asked and out of curiosity I have talked with many what pains they had taken in the Book of Copernicus I found very few that had so much as superficially perused it but of those whom I thought had understood the same not one and moreover I have enquired amongst the followers of the Peripatetick Doctrine if ever any of them had held the contrary opinion and likewise found none that had Whereupon considering that there was no man who followed the opinion of Copernicus that had not been first on the contrary side and that was not very well acquainted with the reasons of Aristotle and Ptolomy and on the contrary that there is not one of the followers of Ptolomy that had ever been of the judgment of Copernicus and had left that to imbrace this of Aristotle considering I say these things I began to think that one who leaveth an opinion imbued with his milk and followed by very many to take up another owned by very few and denied by all the Schools and that really seems a very great Paradox must needs have been moved not to say forced by more powerful reasons For this cause I am become very curious to dive as they say into the bottom of this businesse and account it my great good fortune that I have met you two from whom I may without any trouble hear all that hath been and haply can be said on this argument assuring my self that the strength of your reasons will resolve all scruples and bring me to a certainty in this subject SIMPL. But it s possible your opinion and hopes may be disappointed and that you may find your selves more at a losse in the end than you was at first SAGR. I am very confident that this can in no wise befal me SIMPL. And why not I have a manifest example in my self that the farther I go the more I am confounded SAGR. This is a sign that those reasons that hitherto seemed concluding unto you and assured you in the truth of your opinion begin to change countenance in your mind and to let you by degrees if not imbrace at least look towards the contrary tenent but I that have been hitherto indifferent do greatly hope to acquire rest and satisfaction by our future discourses and you will not deny but I may if you please but to hear what perswadeth me to this expectation SIMPL. I will gladly hearken to the same and should be no lesse glad that the like effect might be wrought in me SAGR. Favour me therefore with answering to what I shall ask you And first tell me Simplicius is not the conclusion which we seek the truth of Whether we ought to hold with Aristotle and Ptolomy that the Earth onely abiding without motion in the Centre of the Universe the Coelestial bodies all move or else Whether the Starry Sphere and the Sun standing still in the Centre the Earth is without the same and owner of all those motions that in our seeming belong to the Sun and fixed Stars SIMPL. These are the conclusions which are in dispute SAGR. And these two conclusions are they not of such a nature that one of them must necessarily be true and the other false SIMPL. They are so We are in a Dilemma one part of which must of necessity be true and the other untrue for between Motion and Rest which are contradictories there cannot be instanced a third so as that one cannot say the Earth moves not nor stands still the Sun and Stars do not move and yet stand not still SAGR. The Earth the Sun and Stars what things are they in nature are they petite things not worth our notice or grand and worthy of consideration SIMPL. They are principal noble integral bodies of the Universe most vast and considerable SAGR. And Motion and Rest what accidents are they in Nature SIMPL. So great and principal that Nature her self is defined by them SAGR. So that moving eternally and the being wholly immoveable are two conditions very considerable in Nature and indicate very great diversity and especially when ascribed to the principal bodies of the Universe from which can ensue none but very different events SIMPL. Yea doubtlesse SAGR. Now answer me to another point Do you believe that in Logick Rhethorick the Physicks Metaphysicks Mathematicks and finally in the universaâ—ity of Disputations there are arguments sufficient to perswade and demonstrate to a person the fallacious no lesse then the true conclusions SIMPL. No Sir rather I am very confident and certain that for the proving of a true and necessary conclusion there are in nature not onely one but many very powerfull demonstrations and that one may discusse and handle the same divers and sundry wayes without ever falling into any absurdity and that the more
worth than the wool of a goat and whereas our argumentations should continually be conversant about serious and weighty points we consume our time in frivolous and impertinent wranglings Let us call to minde I pray you that the search of the worlds constitution is one of the greatest and noblest Problems that are in nature and so much the greater inasmuch as it is directed to the resolving of that other to wit of the cause of the Seas ebbing and flowing enquired into by all the famous men that have hitherto been in the world and possibly found out by none of them Therefore if we have nothing more remaining for the full confutation of the argument taken from the Earths vertigo which was the last alledged to prove its immobility upon its own centre let us passe to the examination of those things that are alledged for and against the Annual Motion SAGR. I would not have you Salviatus measure our wits by the scale of yours you who use to be continually busied about the sublimest contemplations esteem those notions frivolous and below you which we think matters worthy of our profoundest thoughts yet sometimes for our satisfaction do not disdain to stoop so low as to give way a little to our curiosity As to the refutation of the last argument taken from the extrusions of the diurnal vertigo far less than what hath been said would have given me satisfaction and yet the things superfluously spoken seemed to me so ingenious that they have been so far from wearying my fancy as that they have by reason of their novelty entertained me all along with so great delight that I know not how to desire greater Therefore if you have any other speculation to add produce it for I as to my own particular shall gladly hearken to it SALV I have always taken great delight in those things which I have had the fortune to discover and next to that which is my chief content I find great pleasure in imparting them to some friends that apprehendeth and seemeth to like them Now in regard you are one of these slacking a little the reins of my ambition which is much pleased when I shew my self more perspicacious than some other that hath the reputation of a sharp sight I will for a full and true measure of the past dispute produce another fallacy of the Sectators of Ptolomey and Aristotle which I take from the argument alledged SAGR. See how greedily I wait to hear it SALV We have hitherto over-passed and granted to Ptolomey as an effect indubitable that the extrusion of the stone proceeding from the velocity of the wheel turn'd round upon its centre the cause of the said extrusion encreaseth in proportion as the velocity of the vertigo or whirling is augmented from whence it was inferred that the velocity of the Earth's vertigo being very much greater than that of any machin whatsoever that we can make to turn round artificially the extrusion of stones of animals c. would consequently be far more violent Now I observe that there is a great fallacy in this discourse in that we do compare these velocities indifferently and absolutely to one another It 's true that if I compare the velocities of the same wheel or of two wheels equal to each other that which shall be more swiftly turn'd round shall extrude the stone with greater violence and the velocity encreasing the cause of the projection shall likewise encrease but when the velocity is augmented not by encreasing the velocity in the same wheel which would be by causing it to make a greater number of revolutions in equal times but by encreasing the diameter and making the wheel greater so as that the conversion taking up the same time in the lesser wheel as in the greater the velocity is greater onely in the bigger wheel for that its circumference is bigger there is no man that thinketh that the cause of the extrusion in the great wheel will encrease according to the proportion of the velocity of its circumference to the velocity of the circumference of the other lesser wheel for that this is most false as by a most expeditious experiment I shall thus grosly declare We may sling a stone with a stick of a yard long farther than we can do with a stick six yards long though the motion of the end of the long stick that is of the stone placed in the slit thereof were more than double as swift as the motion of the end of the other shorter stick as it would be if the velocities were such that the lesser stick should turn thrice round in the time whilst the greater is making one onely conversion SAGR. This which you tell me Salviatus must I see needs succeed in this very manner but I do not so readily apprehend the cause why equal velocities should not operate equally in extruding projects but that of the lesser wheel much more than the other of the greater wheel therefore I intreat you to tell me how this cometh to pass SIMP Herein Sagredus you seem to differ much from your self for that you were wont to penetrate all things in an instant and now you have overlook'd a fallacy couched in the experiment of the stick which I my self have been able to discover and this is the different manner of operating in making the projection one while with the short sling and another while with the long one for if you will have the stone fly out of the slit you need not continue its motion uniformly but at such time as it is at the swiftest you are to stay your arm and stop the velocity of the stick whereupon the stone which was in its swiftest motion flyeth out and moveth with impetuosity but now that stop cannot be made in the great stick which by reason of its length and flexibility doth not entirely obey the check of the arm but continueth to accompany the stone for some space and holdeth it in with so much less force and not as if you had with a stiff sling sent it going with a jerk for if both the sticks or slings should be check'd by one and the same obstacle I do believe they would fly aswell out of the one as out of the other howbeit their motions were equally swift SAGR. With the permission of Salviatus I will answer something to Simplicius in regard he hath addressed himself to me and I say that in his discourse there is somewhat good and somewhat bad good because it is almost all true bad because it doth not agree with our case Truth is that when that which carrieth the stones with velocity shall meet with a check that is immoveable they shall fly out with great impetuosity the same effect following in that case which we see dayly to fall out in a boat that running a swift course runs a-ground or meets with some sudden stop for all those in the boat being surprized stumble forwards
is ceased but by vertue of its own gravity and natural inclination to level and grow even it shall speedily return backwards of its own accord and as being grave and fluid shall not only move towards Aequilibrium but being impelled by its own impetus shall go beyond it rising in the part where before it was lowest nor shall it stay here but returning backwards anew with more reiterated reciprocations of its undulations it shall give us to know that it will not from a velocity of motion once conceived reduce it self in an instant to the privation thereof and to the state of rest but will successively by decreasing a little and a little reduce it self unto the same just in the same manner as we see a weight hanging at a cord after it hath been once removed from its state of rest that is from its perpendicularity of its own accord to return thither and settle it self but not till such time as it shall have often past to one side and to the other with its reciprocall vibrations The second accident to be observed is that the before-declared reciprocations of motion come to be made and repeated with greater or lesser frequency that is under shorter or longer times according to the different lengths of the Vessels containing the waters so that in the shorter spaces the reciprocations are more frequent and in the longer more rare just as in the former example of pendent bodies the vibrations of those that are hanged to longer cords are seen to be lesse frequent than those of them that hang at shorter strings And here for a third observation it is to be noted that not onely the greater or lesser length of the Vessel is a cause that the water maketh its reciprocations under different times but the greater or lesser profundity worketh the same effect And it happeneth that of waters contained in receptacles of equall length but of unequal depth that which shall be the deepest maketh its undulations under shorter times and the reciprocations of the shallower waters are lesse frequent Fourthly there are two effects worthy to be noted and diligently observed which the water worketh in those its vibrations the one is its rising and falling alternately towards the one and other extremity the other is its moving and running to so speak Horizontally forwards and backwards Which two different motions differently reside in divers parts of the Water for its extream parts are those which most eminently rise and fall those in the middle never absolutely moving upwards and downwards of the rest successively those that are neerest to the extreams rise and fall proportionally more than the remote but on the contrary touching the other progressive motion forwards and backwards the middle parts move notably going and returning and the waters that are in the extream parts gain no ground at all save onely in case that in their rising they overflow their banks and break forth of their first channel and receptacle but where there is the obstacle of banks to keep them in they onely rise and fall which yet hindereth not the waters in the middle from fluctuating to and again which likewise the other parts do in proportion undulating more or lesse according as they are neerer or more remote from the middle The fifth particular accident ought the more attentively to be considered in that it is impossible to represent the effect thereof by an experiment or example and the accident is this In the vessels by us framed with art and moved as the above-named Bark one while more and another while lesse swiftly the acceleration and retardation is imparted in the same manner to all the vessel and to every part of it so that whilst v. g. the Bark forbeareth to move the parts precedent retard no more than the subsequent but all equally partake of the same retardment and the self-same holds true of the acceleration namely that conferring on the Bark a new cause of greater velocity the Prow and Poop both accelerate in one and the same manner But in huge great vessels such as are the very long bottomes of Seas albeit they also are no other than certain cavities made in the solidity of the Terrestrial Globe it alwayes admirably happeneth that their extreams do not unitedly equall and at the same moments of time increase and diminish their motion but it happeneth that when one of its extreames hath by vertue of the commixtion of the two Motions Diurnal and Annual greatly retarded its velocity the other extream is animated with an extream swift motion Which for the better understanding of it we will explain reassuming a Scheme like to the former in which if we do but suppose a tract of Sea to be long v. g. a fourth part as is the arch B C in Fig. 2. because the parts B are as hath been already declared very swift in motion by reason of the union of the two motions diurnal and annual towards one and the same way but the part C at the same time is retarded in its motion as being deprived of the progression dependant on the diurnal motion If we suppose I say a tract of Sea as long as the arch B C we have already seen that its extreams shall move in the same time with great inequality And extreamly different would the velocities of a tract of Sea be that is in length a semicircle and placed in the position B C D in regard that the extream B would be in a most accelerate motion and the other D in a most slow one and the intermediate parts towards C would be in a moderate motion And according as the said tracts of Sea shall be shorter they shall lesse participate of this extravagant accident of being in some hours of the day with their parts diversly affected by velocity and tardity of motion So that if as in the first case we see by experience that the acceleration and retardation though equally imparted to all the parts of the conteining Vessel is the cause that the water contained fluctuates too and again what may we think would happen in a Vessel so admirably disposed that retardation and acceleration of motion is very unequally contributed to its parts Certainly we must needs grant that greater and more wonderful causes of the commotions in the Water ought to be looked for And though it may seem impossible to some that in artificial Machines and Vessels we should be able to experiment the effects of such an accident yet neverthelesse it is not absolutely impossible to be done and I have by me the model of an Engine in which the effect of these admirable commixtions of motions may be particularly observed But as to what concerns our present purpose that which you may have hitherto comprehended with your imagination may suffice SAGR. I for my own particular very well conceive that this admirable accident ought necessarily to evene in the Straights of Seas and especially
of the ebbing and flowing you must finde and give us some reason why it doth in the self same place run one while one way and another while another Effects that being contrary irregular can never be deduced from any uniform and constant Cause And this Argument that overthrows the Hypothesis of the motion contributed to the Sea from the Heavens diurnal motion doth also confute that Position of those who would admit the sole diurnal motion of the Earth and believe that they are able with that alone to give a reason of the Flux and Reflux Of which effect since it is irregular the cause must of necessity be irregular and alterable SIMP I have nothing to reply neither of my own by reason of the weakness of my understanding nor of that of others for that the Opinion is so new But I could believe that if it were spread amongst the Schools there would not want Phylosophers able to oppose it SAGR. Expect such an occasion and we in the mean time if it seem good to Salviatus will proceed forward SALV All that which hath been said hitherto pertaineth to the diurnal period of the ebbing and flowing of which we have in the first place demonstrated in general the primary and universal Cause without which no such effect would follow Afterwâ—â—ds passing to the particular Accidents various and in a certain sort irregular that are observed therein We have handled the secondary and concommitant Causes upon which they depend Now follow the two other Periods Monethly and Annual which do not bring with them new and different Accidents other than those already considered in the diurnal Period but they operate on the same Accidents by rendring them greater and lesser in several parts of the Lunar Moneth and in several times of the Solar Year as if that the Moon and Sun did each conceive it self apart in operating and producing of those Effects a thing that totally clasheth with my understanding which seeing how that this of Seas is a local and sensible motion made in an immense mass of Water it cannot be brought to subscribe to Lights to temperate Heats to predominacies by occult Qualities and to such like vain Imaginations that are so far from being or being possible to be Causes of the Tide that on the contrary the Tide is the cause of them that is of bringing them into the brains more apt for loquacity and ostentation than for the speculation and discovering of the more abstruse secrets of Nature which kind of people before they can be brought to pronounce that wise ingenious and modest sentence I know it not suffer to escape from their mouths and pens all manner of extravagancies And the onely observing that the same Moon and the same Sun operate not with their light with their motion with great heat or with temperate on the lesser reeeptaclâ—s of Water but that to effect their flowing by heat they must be reduced to little lesse than boiling and in short we not being able artificially to imitate any way the motions of the Tide save only by the motion of the Vessel ought it not to satisfie every one that all the other things alledged as causes of those effects are vaine fancies and altogether estranged from the Truth I say therefore that if it be true that of one effect there is but one sole primary cause and that between the cause and effect there is a firm and constant connection it is necessary that whensoever there is seen a firm and constant alteration in the effect there be a firm and constant alteration in the cause And because the alterations that happen in the ebbing and flowing in several parts of the Year and Moneths have their periods firm and constant it is necessary to say that a regular alteration in those same times happeneth in the primary cause of the ebbings and flowings And as for the alteration that in those times happens in the ebbings and flowings consisteth onely in their greatness that is in the Waters rising and falling more or lesse and in running with greater or lesse impetus therefore it is necessary that that which is the primary cause of the ebbing and flowing doth in those same determinate times increase and diminish its force But we have already concluded upon the inequality and irregularity of the motion of the Vessels containing the Water to be the primary cause of the ebbings and flowings Therefore it is necessary that that irregularity from time to time correspondently grow more irregular that is grow greater and lesser Now it is requisite that we call to minde that the irregularity that is the different velocity of the motions of the Vessels to wit of the parts of the Terrestrial Superficies dependeth on their moving with a compound motion resulting from the commixtion of the two motions Annual and Diurnal proper to the whole Terrestrial Globe of which the Diurnal conversion by one while adding to and another while substracting from the Annual motion is that which produceth the irregularity in the compound motion so that in the additions and substractions that the Diurnal revolution maketh from the Annual motion consisteth the original cause of the irregular motion of the Vessels and consequently of the Ebbing and Flowing insomuch that if these additions and substractions should alwayes proceed in the same proportion in respect of the Annual motion the cause of the Ebbing and Flowing would indeed continue but yet so as that they would perpetually return in the self same manner But we are to finde out the cause of making the same Ebbings and Flowings in divers times greater and lesser Therefore we must if we will retain the identity of the cause find the alteration in these additions and substractions that make them more less potent in producing those effects which depend thereupon But I see not how that potency and impotence can be introduced unlesse by making the same additions and substractions one while greater and another while lesser so that the acceleration and the retardment of the compound motion may be made sometimes in greater and sometimes in lesser proportion SAGR. I feel my self very gently led as it were by the hand and though I finde no rubs in the way yet neverthelesse like a blind man I see not whether your Clue leadeth me nor can I imagine where such a Journey will end SALV Though there be a great difference between my slow pac't Philosophy and your more nimble Reason yet neverthelesse in this particular which we are now upon I do not much wonder if the apprehensivenesse of your wit be a little obscured by the dark and thick mist that hides the mark at which we aime and that which lesseneth my admiration is the remembrance of the many hours many dayes yea more many nights that I have consumed in this contemplation and of the many times that despairing to bring it to a period I have for an incouragement of my self
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 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 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 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 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 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
greater measure than in those parts in which it is more swift and therefore ordinarily shall be also more deep and dangerous for passengers whence it is well said Take heed of the still Waters and this saying hath been since applied to things moral COROLLARIE VII LIkewise from the things demonstrated may be concluded that the windes which stop a River and blowing against the Current retard its course and ordinary velocity shall necessarily amplifie the measure of the same River and consequently shall be in great part causes or we may say potent con-causes of making the extraordinary inundations which Rivers use to make And it s most certain that as often as a strong and continual wind shall blow against the Current of a River and shall reduce the water of the River to such tardity of motion that in the time wherein before it run five miles it now moveth but one such a River will increase to five times the measure though there should not be added any other quantity of water which thing indeed hath in it something of strange but it is most certain for that look what proportion the waters velocity before the winde hath to the velocity after the winde and sueh reciprocally is the measure of the same water after the winde to the measure before the winde and because it hath been supposed in our case that the velocity is diminished to a fifth part therefore the measure shall be increased five times more than that which it was before COROLLARIE VIII WE have also probable the cause of the inundations of Tyber which befel at Rome in the time of Alexander the Sixth of Clement the Seventh which innundations came in a serene time and without great thaws of the Snows which therefore much puzzled the wits of those times But we may with much probability affirm That the River rose to such a height and excrescence by the retardation of the Waters dependant on the boistrous and constant Winds that blew in those times as is noted in the memorials COROLLARIE IX IT being most manifest that by the great abundance of Water the Torrents may increase and of themselves alone exorbitantly swell the River and having demonstrated that also without new Water but onely by the notable retardment the River riseth and increaseth in measure in proportion as the velocity decreaseth hence it is apparent that each of these causes being able of it self and separate from the other to swell the River when it shall happen that both these two causes conspire the augmentation of the River in such a case there must follow very great and irrepable innundations COROLLARIE X. FRom what hath been demonstrated we may with facility resolve the doubt which hath troubled and still poseth the most diligent but incautelous observers of Rivers who measuring the Streams and Torrents which fall into another River as those for instance which enter into the Po or those which fall into Tiber and having summed the total of these measures and conferring the measures of the Rivers and Brooks which fall into Tiber with the measure of Tiber and the measures of those which disimbogue into Po with the measure of Po they find them not equal as it seems to them they ought to be and this is because they have not well noted the most important point of the variation of velocity and how that it is the most potent cause of wonderfully altering the measures of running Waters but we most facilly resolving the doubt may say that these Waters diminish the measure being once entered the principal Channel because they increase in velocity COROLLARIE XI THrough the ignorance of the force of the velocity of the Water in altering its measure augmenting it when the velocity diminisheth and diminishing it when the velocity augmenteth The Architect Giovanni Fontana endeavoured to measure and and to cause to be measured by his Nephew all the Brooks and Rivers which discharged their Waters into Tiber at the time of the Innundation which happened at Rome in the year 1598 and published a small Treatise thereof wherein he summeth up the measures of the extraordinary Water which fell into Tiber and made account that it was about five hundred Ells more than ordinary and in the end of that Treatise concludeth that to remove the Innundation wholly from Rome it would be necessary to make two other Channels equal to that at present and that lesse would not suffice and finding afterwards that the whole Stream passed under the Bridge Quattro-Capi the Arch whereof is of a far less measure then five hundred Ells concludeth that under the said Bridge past a hundred fifty one Ells of Water compressed I have set down the precise term of comprest Water written by Fontana wherein I finde many errors The first of which is to think that the measures of these Waters compressed in the Channels of those Brooks and Rivers should maintain themselves the same in Tiber which by his leave is most false when ever those waters reduced into Tiber retain not the same velocity which they had in the place in which Fontana and his Nephew measured them And all this is manifest from the things which we have above explained for if the Waters reduced into Tiber increase in velocity they decrease in measure and if they decrease in velocity they increase in measure Secondly I consider that the measures of those Brooks and Rivers which enter into Tiber at the time of Innundation are not between themselves really the same when their velocities are not equal though they have the same names of Ells and Feet for that its possible that a disinboguement of ten Ells requadrated to speak in the phrase of Fontana of one of those Brooks might discharge into Tiber at the time of Innundation four ten and twenty times less Water than another mouth equal to the first in greatness as would occur when the first mouth were four ten or twenty times less swift than the second Whereupon whilst Fontana summes up the Ells and Feet of the measures of those Brooks and Rivers into a total aggregate he commits the same error with him which would add into one summe diverse moneys of diverse values and diverse places but that had the same name as if one should say ten Crowns of Roman money four Crowns of Gold thirteen Crowns of Florence five Crowns of Venice and eight Crowns of Mantua should make the same summe with forty Crowns of Gold or forty Crowns of Mantua Thirdly It might happen that some River or Current in the parts nearer Rome in the time of its flowing did not send forth more Water than ordinary and however it s a thing very clear that whilst the stream came from the superior parts that same Brook or River would be augmented in measure as hath been noted in the fourth Corollary in such sort that Fontana might have inculcated and noted that same River or Current as concurring to the Innundation although it
the Sun it would never behold the Earth of which the dark part would be continually turn'd towards the Moon and therefore invisible But when the Moon is in Quadrature of the Sun that half of the Terrestrial Hemisphere exposed to the sight of the Moon which is towards the Sun is luminous and the other towards the contrary is obscure and therefore the illuminated part of the Earth would represent it self to the Moon in a semi-circular figure SAGR. I clearly perceive all this and understand very well that the Moon departing from its Opposition to the Sun where it saw no part of the illumination of the Terrestrial superficies and approaching day by day nearer the Sun she begins by little and little to discover some part of the face of the illuminated Earth and that which appeareth of it shall resemble a thin sickle in regard the figure of the Earth is round and the Moon thus acquiring by its motion day by day greater proximity to the Sun successively discovers more and more of the Terrestrial Hemisphere enlightned so that at the Quadrature there is just half of it visible insomuch that we may see the other part of her continuing next to proceed towards the Conjunction it successively discovers more and more of its surface to be illuminated and in fine at the time of Conjunction seeth the whole Hemisphere enlightned And in short I very well conceive that what befalls the Inhabitants of the Earth in beholding the changes of the Moon would happen to him that from the Moon should observe the Earth but in a contrary order namely that when the Moon is to us at her full and in Opposition to the Sun then the Earth would be in Conjunction with the Sun and wholly obscure and invisible on the contrary that position which is to us a Conjunction of the Moon with the Sun and for that cause a Moon silent and unseen would be there an Opposition of the Earth to the Sun and to so speak Full Earth to wit all enlightned And lastly look what part of the Lunar surface appears to us from time to time illuminated so much of the Earth in the same time shall you behold from the Moon to be obscured and look how much of the Moon is to us deprived of light so much of the Earth is to the Moon illuminated In one thing yet these mutual operations in my judgment seem to differ and it is that it being supposed and not granted that some one being placed in the Moon to observe the Earth he would every day see the whole Terrestrial superficies by means of the Moons going about the Earth in twenty four or twenty five hours but we never see but half of the Moon since it revolves not in it self as it must do to be seen in every part of it SALV So that this befals not contrarily namely that her revolving in her self is the cause that we see not the other half of her for so it would be necessary it should be if she had the Epicycle But what other difference have you behind to exchange for this which you have named SAGR. Let me see Well for the present I cannot think of any other SALV And what if the Earth as you have well noted seeth no more than half the Moon whereas from the Moon one may see all the Earth and on the contrary all the Earth seeth the Moon and but onely half of it seeth the Earth For the inhabitants to so speak of the superior Hemisphere of the Moon which is to us invisible are deprived of the sight of the Earth and these haply are the Antiâ—thones But here I remember a particular accident newly observed by our Academian in the Moon from whch are gathered two necessary consequences one is that we see somewhat more than half of the Moon and the other is that the motion of the Moon hath exact concentricity with the Earth and thus he finds the Phoenomenon and observation When the Moon hath a correspondence and natural sympathy with the Earth towards which it hath its aspect in such a determinate part it is necessary that the right line which conjoyns their centers do passe ever by the same point of the Moons superficies so that who so shall from the center of the Earth behold the same shall alwayes see the same Discus or Face of the Moon punctually determined by one and the same circumference But if a man be placed upon the Terrestrial surface the ray which from his eye passeth to the centre of the Lunar Globe will not pass by the same point of its superficies by which the line passeth that is drawn from the centre of the Earth to that of the Moon save onely when it is vertical to him but the Moon being placed in the East or in the West the point of incidence of the visual ray is higher than that of the line which conjoyns the centres and therefore the observer may discern some part of the Lunar Hemisphere towards the upper circumference and alike part of the other is invisible they are discernable and undiscernable in respect of the Hemisphere beheld from the true centre of the Earth and because the part of the Moons circumference which is superiour in its rising is nethermost in its setting therefore the difference of the said superiour and inferiour our parts must needs be very observable certain spots and other notable things in those parts being one while discernable and another while not A like variation may also be observed towards the North and South extremities of the same Discus or Surface according as the Moons position is in its greatest North or South Latitude For if it be North some of its parts towards the North are hid and some of those parts towards the South are discovered and so on the contrary Now that these consequences are really true is verified by the Telescope for there be in the Moon two remarkable spots one of which when the Moon is in the meridian is situate to the Northwest and the other is almost diametrically opposite unto it and the first of these is visible even without the Telescope but the other is not That towards the Northwest is a reasonable great spot of oval figure separated from the other great ones the opposite one is lesse and also severed from the biggest and situate in a very cleer field in both these we may manifestly discern the foresaid variations and see them one after another now neer the edge or limb of the Lunar Discus and anon remote with so great difference that the distance betwixt the Northwest and the circumference of the Discus is more than twice as great at one time as at the other and as to the second spot because it is neerer to the circumference such mutation importeth more than twice so much in the former Hence its manifest that the Moon as if it were drawn by a magnetick vertue constantly
beholds the Terrestrial Globe with one and the same aspect never deviating from the same SAGR. Oh! when will there be an end put to the new observations and discoveries of this admirable Instrument SALV If this succeed according to the progresse of other great inventions it is to be hoped that in processe of time one may arrive to the sight of things to us at present not to be imagined But returning to our first discourse I say for the sixth resemblance betwixt the Moon and Earth that as the Moon for a great part of time supplies the want of the Suns light and makes the nights by the reflection of its own reasonable clear so the Earth in recompence affordeth it when it stands in most need by reflecting the Solar rayes a very cleer illumination and so much in my opinion greater than that which cometh from her to us by how much the superficies of the Earth is greater than that of the Moon SAGR. Hold there Salviatus hold there and permit me the pleasure of relating to you how at this first hint I have penetrated the cause of an accident which I have a thousand times thought upon but could never find out You would say that the imperfect light which is seen in the Moon especially when it is horned comes from the reflection of the light of the Sun on the Supersicies of the Earth and Sea and that light is more clear by how much the horns are lesse for then the luminous part of the Earth beheld by the Moon is greater according to that which was a little before proved to wit that the luminous part of the Earth exposed to the Moon is alway as great as the obscure part of the Moon that is visible to the Earth whereupon at such time as the Moon is sharp-forked and consequently its tenebrous part great great also is the illuminated part of the Earth beheld from the Moon and its reflection of light so much the more potent SALV This is exactly the same with what I was about to say In a word it is a great pleasure to speak with persons judicious and apprehensive and the rather to me for that whilest others converse and discourse touching Axiomatical truths I have many times creeping into my brain such arduous Paradoxes that though I have a thousand times rehearsed this which you at the very first have of your self apprehended yet could I never beat it into mens brains SIMPL. If you mean by your not being able to perswade them to it that you could not make them understand the same I much wonder thereat and am very confident that if they did not understand it by your demonstration your way of expression being in my judgment very plain they would very hardly have apprehended it upon the explication of any other man but if you mean you have not perswaded them so as to make them believe it I wonder not in the least at this for I confesse my self to be one of those who understand your discourses but am not satisfied therewith for there are in this and some of the other six congruities or resemblances many difficulties which I shall instance in when you have gone through them all SALV The desire I have to find out any truth in the acquist whereof the objections of intelligent persons such as your self may much assist me will cause me to be very brief in dispatching that which remains For a seventh conformity take their reciprocal responsion as well to injuries as favours whereby the Moon which very often in the height of its illumination by the interposure of the Earth betwixt it and the Sun is deprived of light and eclipsed doth by way of revenge in like manner interpose it self between the Earth and the Sun and with its shadow obscureth the Earth and although the revenge be not answerable to the injury for that the Moon often continueth and that for a reasonable long time wholly immersed in the Earths shadow but never was the Earth wholly nor for any long time eclipsed by the Moon yet neverthelesse having respect to the smalnesse of the body of this in comparision to the magnitude of the other it cannot be denied but that the will and as it were valour of this is very great Thus much for their congruities or resemblances It should next follow that we discourse touching their disparity but because Simplicius will favour us with his objections against the former its necessary that we hear and examine them before we proceed any farther SAGR. And the rather because it is to be supposed that Simplicius will not any wayes oppose the disparities and incongruities betwixt the Earth and Moon since that he accounts their substances extremely different SIMPL. Amongst the resemblances by you recited in the parallel you make betwixt the Earth and Moon I find that I can admit none confidently save onely the first and two others I grant the first namely the spherical figure howbeit even in this there is some kind of difference for that I hold that of the Moon to be very smooth and even as a looking-glasse whereas we find and feel this of the Earth to be extraordinary montuous and rugged but this belonging to the inequality of superficies it shall be anon considered in another of those Resemblances by you alledged I shall therefore reserve what I have to say thereof till I come to the consideration of that Of what you affirm next that the Moon seemeth as you say in your second Resemblance opacous and obscure in its self like the Earth I admit not any more than the first attribute of opacity of which the Eclipses of the Sun assure me For were the Moon transparent the air in the total obscuration of the Sun would not become so duskish as at such a time it is but by means of the transparency of the body of the Moon a refracted light would passe through it as we see it doth through the thickest clouds But as to the obscurity I believe not that the Moon is wholly deprived of light as the Earth nay that clarity which is seen in the remainder ot its Discus over and the above the small crescent enlightened by the Sun I repute to be its proper and natural light and not a reflection of the Earth which I esteem unable by reason of its asperity cragginesse and obscurity to reflect the raies of the Sun In the third Parallel I assent unto you in one part and dissent in another I agree in judging the body of the Moon to be most solid and hard like the Earth yea much more for if from Aristotle we receive that the Heavens are impenetrable and the Stars the most dense parts of Heaven it must necessarily follow that they are most solid and most impenetrable SAGR. What excellent matter would the Heavens afford us for to make Pallaces of if we could procure a substance so hard and so
would acquiese in granting that the Moon Venus and the other Planets were not of so bright and smooth a surface as a Looking-glass but wanted some small matter of it namely were as a silver plate onely boyled white but not burnished would this yet suffice to the making of it visible and apt for darting forth the light of the Sun SALV It would suffice in part but would not give a light so strong as it doth being mountainous and in sum full of eminencies and great cavities But these Philosophers will never yield it to be lesse polite than a glasse but far more if more it can be imagined for they esteeming that to perfect bodies perfect figures are most sutable it is necessary that the sphericity of those Coelestial Globes be most exact besides that if they should grant me some inequality though never so small I would not scruple to take any other greater for that such perfection consisting in indivisibles an hair doth as much detract from its perfection as a mountain SAGR. Here I meet with two difficulties one is to know the reason why the greater inequality of superficies maketh the stronger reflection of light the other is why these Peripatetick Gentlemen are for this exact figure SALV I will answer to the first and leave to Simplicius the care of making reply to the second You must know therefore that the same superficies happen to be by the same light more or less illuminated according as the rayes of illumination fall upon them more or lesse obliquely so that the greatest illumination is where the rayes are perpendicular And see how I will prove it to your sense I bend this paper so that one part of it makes an angle upon the other and exposing both these parts to the reflection of the light of that opposite Wall you see how this side which receiveth the rayes obliquely is lesse shining than this other where the reflection fals at right angles and observe that as I by degrees receive the illumination more obliquely it groweth weaker SAGR. I see the effect but comprehend not the cause SALV If you thought upon it but a minute of an hour you would find it but that I may not waste the time see a kind of demonstration thereof in Fig. 7. SAGR. The bare sight of this Figure hath fully satisfied me therefore proceed SIMPL. Pray you let me hear you out for I am not of so quick an apprehension SALV Fancie to your self that all the paralel lines which you see to depart from the terms A. B. are the rays which fall upon the line C. D. at right angles then incline the said C. D. till it hang as D. O. now do not you see that a great part of those rays which peirce C. D. pass by without touching D. O? If therefore D. O. be illuminated by fewer rays it is very reasonable that the light received by it be more weak Let us return now to the Moon which being of a spherical figure if its superficies were smooth as this paper the parts of its hemisphere illuminated by the Sun which are towards its extremity would receive much less light than the middle parts the rays falling upon them most obliquely and upon these at right angles whereupon at the time of full Moon when we see almost its whole Hemisphere illuminated the parts towards the midst would shew themselves to us with more splendor than those others towards the circumference which is not so in effect Now the face of the Moon being represented to me full of indifferent high mountains do not you see how their tops and continuate ridges being elevated above the convexity of the perfect spherical superficies come to be exposed to the view of the Sun and accommodated to receive its rays much less obliquely and consequently to appear as luminous as the rest SAGR. All this I well perceive and if there are such mountains its true the Sun will dart upon them much more directly than it would do upon the inclination of a polite superficies but it is also true that betwixt those mountains all the valleys would become obscure by reason of the vast shadows which in that time would be cast from the mountains whereas the parts towards the middle though full of valleys and hills by reason they have the Sun elevated would appear without shadow and therefore more lucid by far than the extreme parts which are no less diffused with shadow than light and yet we can perceive no such difference SIMPL. I was ruminating upon the like difficulty SALV How much readier is Simplicius to apprehend the objections which favour the opinions of Aristotle than their solutions I have a kind of suspition that he strives also sometimes to dissemble them and in the present case he being of himself able to hit upon the doubt which yet is very ingenious I cannot believe but that he also was advis'd of the answer wherefore I will attempt to wrest the same as they say out of his mouth Therefore tell me Simplicius do you think there can be any shadow where the rays of the Sun do shine SIMPL. I believe nay I am certain that there cannot for that it being the grand luminary which with its rays driveth away darkness it is impossible any tenebrosity should remain where it cometh moreover we have the definition that Tenebrae sunt privatio luminis SALV Therefore the Sun beholding the Earth Moon or other opacous body never seeth any of its shady parts it not having any other eyes to see with save its rays the conveyers of light and consequently one standing in the Sun would never see any thing of umbrage forasmuch as his visive rays would ever go accompanied with those illuminating beams of the Sun SIMPL. This is true without any contradiction SALV But when the Moon is opposite to the Sun what difference is there between the tract of the rayes of your sight and that motion which the Suns rayes make SIMPL. Now I understand you for you would say that the rayes of the sight and those of the Sun moving by the same lines we cannot perceive any of the obscure valleys of the Moon Be pleased to change this your opinion that I have either simulation or dissimulation in me for I protest unto you as I am a Gentleman that I did not guesse at this solution nor should I have thought upon it without your help or without long study SAGR. The resolutions which between you two have been alledged touching this last doubt hath to speak the truth satisfied me also But at the same time this consideration of the visible rayes accompanying the rayes of the Sun hath begotten in me another scruple about the other part but I know not whether I can expresse it right or no for it but just now comming into my mind I have not yet methodized it to my mind but let us see if we can all together make it
Moon shews it self more bright by night than by day in respect of the obscurity of the space of the ambient and confequently do you not know in genere that every bright body shews the clearer by how much the ambient is obscurer SIMPL. This I know very well SALV When the Moon is horned and that secondary light seemeth to you very bright is it not ever nigh the Sun and consequently in the light of the crepusculum twilight SIMPL. It is so and I have oftentimes wish'd that the Air would grow thicker that I might be able to see that same light more plainly but it ever disappeared before dark night SALV You know then very certainly that in the depth of night that light would be more conspicuous SIMPL. I do so and also more than that if one could but take away the great light of the crescent illuminated by the Sun the presence of which much obscureth the other lesser SALV Why doth it not sometimes come to pass that one may in a very dark night see the whole face of the Moon without being at all illuminated by the Sun SIMPL. I know not whether this ever happeneth save onely in the total Ecclipses of the Moon SALV Why at that time this its light would appear very clear being in a most obscure medium and not darkned by the clarity of the luminous crescents but in that position how light did it appear to you SIMPL. I have sometimes seen it of the colour of brass and a little whitish but at other times it hath been so obscure that I have wholly lost the sight of it SALV How then can that light be so natural which you see so cleer in the close of the twilight notwithstanding the impediment of the great and contiguous splendor of the crescents and which again in the more obscure time of night all other light removed appears not at all SIMPL. I have heard of some that believed that same light to be participated to these crescents from the other Stars and in particular from Venus the Moons neighbour SALV And this likewise is a vanity because in the time of its total obscuration it ought to appear more shining than ever for you cannot say that the shadow of the Earth intercepts the sight of Venus or the other Stars But to say true it is not at that instant wholly deprived thereof for that the Terrestrial Hemisphere which in that time looketh towards the Moon is that where it is night that is an intire privation of the light of the Sun And if you but diligently observe you will very sensibly perceive that like as the Moon when it is sharp-horned doth give very little light to the Earth and according as in her the parts illuminated by the Suns light do encrease so likewise the splendor to our seeming encreaseth which from her is reflected towards us thus the Moon whilst it is sharp-forked and that by being between the Sun and the Earth it discovereth a very great part of the Terrestrial Hemisphere illuminated appeareth very clear and departing from the Sun and passing towards the Quadrature you may see the said light by degrees to grow dim and after the Quadrature the same appears very weak because it continually loseth more and more of the view of the luminous part of the Earth and yet it should succeed quite contrary if that light were its own or communicated to it from the Stars for then we should see it in the depth of night and in so very dark an ambient SIMPL. Stay a little for I just now remember that I have read in a little modern tract full of many novelties That this secondary light is not derived from the Stars nor innate in the Moon and least of all communicated by the Earth but that it is received from the same illumination of the Sun which the substance of the Lunar Globe being somewhat transparent penetrateth thorow all its body but more livelily illuminateth the superficies of the Hemisphere exposed to the rays of the Sun and its profundity imbuing and as I may say swallowing that light after the manner of a cloud or chrystal transmits it and renders it visibly lucid And this if I remember aright he proveth by Authority Experience and Reason citing Cleomedes Vitellion Macrobius and a certain other modern Author and adding That it is seen by experience to shine most in the days nearest the Conjunction that is when it is horned and is chiefly bright about its limb And he farther writes That in the Solar Ecclipses when it is under the Discus of the Sun it may be seen translucid and more especially towards its utmost Circle And in the next place for Arguments as I think he saith That it not being able to derive that light either from the Earth or from the Stars or from it self it necessarily follows that it cometh from the Sun Besides that if you do but grant this supposition one may easily give convenient reasons for all the particulars that occur For the reason why that secundary light shews more lively towards the outmost limb is the shortness of the space that the Suns rays hath to penetrate in regard that of the lines which pass through a circle the greatest is that which passeth through the centre and of the rest those which are farthest from it are always less than those that are nearer From the same principle he saith may be shewn why the said light doth not much diminish And lastly by this way the cause is assigned whence it comes that that same more shining circle about the utmost edge of the Moon is seen at the time of the Solar Ecclipse in that part which lyeth just under the Discus of the Sun but not in that which is beside the Discus which happeneth because the rays of the Sun pass directly to our eye through the parts of the Moon underneath but as for the parts which are besides it they fall besides the eye SALV If this Philosopher had been the first Author of this opinion I would not wonder that he should be so affectionate to it as to have received it for truth but borrowing it from others I cannot find any reason sufficient to excuse him for not perceiving itâ— fallacies and especially after he had heard the true cause of that effect and had it in his power to satisfie himself by a thousand experiments and manifest circumstances that the same proceeded from the reflection of the Earth and from nothing else and the more this speculation makes something to be desired in the judgment of this Author and of all those who give no credit to it so much the more doth their not having understood and remembred it excuse those more recess Antients who I am very certain did they now understand it would without the least repugnance admit thereof And if I may freely tell you what I think I cannot believe but that this Modern doth in his
from each other of which the gravity attends only to the drawing of the moveable towards the centre and the vertue impress't to the conducting it about the centre there remaineth no occasion of impediment SIMPL. Your argumentation to give you your due is very probable but in reality it is invelloped with certain intricacies that are not easie to be extricated You have all along built upon a supposition which the Peripatetick Schools will not easily grant you as being directly contrary to Aristotle and it is to take for known and manifest That the project separated from the projicient continueth the motion by vertue impressed on it by the said projicient which vertue impressed is a thing as much detested in Peripatetick Philosophy as the passage of any accident from one subject into another Which doctrine doth hold as I believe it is well known unto you that the project is carried by the medium which in our case happeneth to be the Air. And therefore if that stone let fall from the round top ought to follow the motion of the ship that effect should be ascribed to the Air and not to the vertue impressed But you presuppose that the Air doth not follow the motion of the ship but is tranquil Moreover he that letteth it fall is not to throw it or to give it impetus with his arm but ought barely to open his hand and let it go and by this means the stone neither through the vertue impressed by the projicient nor through the help of the Air shall be able to follow the ships motion and therefore shall be left behind SALV I think then that you would say that if the stone be not thrown by the arm of that person it is no longer a projection SIMPL. It cannot be properly called a motion of projection SALV So then that which Aristotle speaks of the motion the moveable and the mover of the projects hath nothing to do with the businesse in hand and if it concern not our purpose why do you alledg the same SIMP I produce it on the oceasion of that impressed vertue named and introduced by you which having no being in the World can be of no force for non-entium nullae sunt operationes and therefore not onely of projected but of all other preternatural motions the moving cause ought to be ascribed to the medium of which there hath been no due consideration had and therefore all that hath been said hitherto is to no purpose SALV Go to now in good time But tell me seeing that your instance is wholly grounded upon the nullity of the vertue impressed if I shall demonstrate to you that the medium hath nothing to do in the continuation of projects after they are separated from the projicient will you admit of the impressed vertue or will you make another attempt to overthrow it SIMP The operation of the medium being removed I see not how one can have recourse to any thing else save the faculty impressed by the mover SALV It would be well for the removing as much as is possible the occasions of multiplying contentions that you would explain with as much distinctnesse as may be what is that operation of the medium in continuing the motion of the project SIMP The projicient hath the stone in his hand and with force and violence throws his arm with which jactation the stone doth not move so much as the circumambient Air so that when the stone at its being forsaken by the hand findeth it self in the Air which at the same time moveth with impetousity it is thereby born away for if the air did not operate the stone would fall at the foot of the projicient or thrower SALV And was you so credulous as to suffer your self to be perswaded to believe these fopperies so long as you had your senses about you to confute them and to understand the truth thereof Therefore tell me that great stone and that Canon bullet which but onely laid upon a table did continue immoveable against the most impetuous winds according as you a little before did affirm if it had been a ball of cork or other light stuffe think you that the wind would have removed it from its place SIMP Yes and I am assured that it would have blown it quite away and with so much more velocity by how much the matter was lighter for upon this reason we see the clouds to be transported with a velocity equal to that of the wind that drives them SALV And what is the Wind SIMP The Wind is defined to be nothing else but air moved SALV Then the moved air doth carry light things more swiftly and to a greater distance then it doth heavy SIMP Yes certainly SALV But if you were to throw with your arm a stone and a lock of cotton wool which would move swiftest and farthest SIMP The stone by much nay the wool would fall at my feet SALV But if that which moveth the projected substance after it is delivered from the hand be no other than the air moved by the arm and the moved air do more easily bear away light than grave matters how cometh it that the project of wool flieth not farther and swifter than that of stone Certainly it argueth that the stone hath some other impulse besides the motion of the air Furthermore if two strings of equal length did hang at yonder beam and at the end of one there was fastened a bullet of lead and a ball of cotton wool at the other and both were carried to an equal distance from the perpendicular and then let go it is not to be doubted but that both the one and the other would move towards the perpendicular and that being carried by their own impetus they would go a certain space beyond it and afterwards return thither again But which of these two pendent Globes do you think would continue longest in motion before that it would come to rest in its perpendicularity SIMP The ball of lead would swing to and again many times and that of wool but two or three at the most SALV So that the impetus and that mobility whatsoever is the cause thereof would conserve its self longer in grave substances than light I proceed now to another particular and demand of you why the air doth not carry away that Lemon which is upon that same Table SIMP Because that the air it self is not moved SALV It is requisite then that the projicient do confer motion on the Air with which it afterward moveth the project But if such a motion cannot be impressed i. e. imparted it being impossible to make an accident passe out of one subject into another how can it passe from the arm into the Air Will you say that the Air is not a subject different from the arm SIMP To this it is answered that the Air in regard it is neither heavy nor light in its own Region is disposed with facility
contemplations like as Lions are not much moved at the barking of little Dogs We will therefore reserve the instance of birds to the last place and for the present see if we can give Simplicius satisfaction in the others by shewing him in our wonted manner that he himself hath their answers at hand though upon first thoughts he doth not discover them And to begin with the shots made at randome with the self same piece powder and ball the one towards the East the other towards the West if the diurnal conversion belonged to the Earth ought to be much longer than that towards the East SIMP I am moved so to think because in the shot made towards the East the ball whil'st it is out of the piece is followed by the said piece the which being carried round by the Earth runneth also with much velocity towards the same part whereupon the fall of the ball to the ground cometh to be but little distant from the piece On the contrary in the shot towards the West before that the ball falleth to the ground the piece is retired very far towards the East by which means the space between the ball and the piece that is Range will appear longer than the other by how much the piece that is the Earth had run in the time that both the bals were in the air SALV I could wish that we did know some way to make an experiment corresponding to the motion of these projects as that of the ship doth to the motion of things perpendicularly falling from on high and I am thinking how it may be done SAGR. I believe that it would be a very opposite proof to take an open Chariot and to accomodate therein a Stock-bow at half elevation to the end the flight may prove the greatest that my be and whil'st the horses shall run to shoot first towards the part whither you drive and then another backwards towards the contrary part causing some one to mark diligently where the Chariot was in that moment â—f time when the shaft came to the ground as well in the one shot as in the other for thus you may see exactly how much one shaft flew farther than the other SIMP In my thoughts this experiment is very proper and I do not doubt but that the flight that is the space between the shaft and the place where the chariot was at the shafts fall will be less by much when one shooteth towards the chariots course than when one shooteth the contrary way For an example let the flight of it self be three hundred yards and the course of the chariot in the time whilst the shaft stayeth in the air an hundred yards therefore shooting towards the course of the three hundred yards of the flight the chariot will have gone one hundred so then at the shafts coming to the ground the space between it and the chariot shall be but two hundred yards onely but on the contrary in the other shoot the chariot running contrary to the shaft when the shaft shall have passed its three hundred yards and the chariot it s other hundred the contrary way the distance interposing shall be found to be four hundred yards SALV Is there any way to shoot so that these flights may be equal SIMP I know no other way unless by making the chariot to stand still SALV This we know but I mean when the chariot runneth in full carreer SIMP In that case you are to draw the Bow higher in shooting forwards and to slack it in shooting the contrary way SALV Then you see that there is one way more But how much is the bow to be drawn and how much slackened SIMP In our case where we have supposed that the bow carried three hundred yards it would be requisite to draw it so as that it might carry four hundred and in the other to slacken it so as that it might carry no more than two hundred For so each of the flights would be but three hundred in relation to the chariot the which with its course of an hundred yards which it substracts from the shoot of four hundred and addeth to that of two hundred would reduce them both to three hundred SALV But what effect hath the greater or less intensness of the bow upon the shaft SIMP The stiffer bow carrieth it with greater velocity and the weaker with less and the same shaft flieth so much farther at one time than another with how much greater velocity it goeth out of the tiller at one time than another SALV So that to make the shaft shot either way to flie at equal distance from the running chariot it is requisite that if in the first shoot of the precedent example it goeth out of the tiller with v. g. four degrees of velocity that then in the other shoot it depart but with two onely but if the same bow be used it always receiveth thence three degrees SIMP It doth so and for this reason shooting with the same bow in the chariots course the shoots cannot be equal SALV I had forgot to ask with what velocity it is supposed in this particular experiment that the chariot runneth SIMP The velocity of the chariot must be supposed to be one degree in comparison to that of the bow which is three SALV Very right for so computation gives it But tell me when the chariot moveth doth not all things in the same move with the same velocity SIMP Yes doubtless SALV Then so doth the shaft also and the bow and the string upon which the shaft is nock't SIMP They do so SALV Why then in discharging the shaft towards the course of the chariot the bow impresseth its three degrees of velocity on a shaft that had one degree of velocity before by means of the chariot which transported it so fast towards that part so that in its going off it hath four degrees of velocity On the contrary in the other shoot the same bow conferreth its same three degrees of velocity on a shaft that moveth the contrary way with one degree so that in its departing from the bow-string it hath no more left but onely two degrees of velocity But you your self have already said that the way to make the shoots equal is to cause that the shaft be let flie the first time with four degrees of velocity and the second time with two Therefore without changing the bow the very course of the chariot is that which adjusteth the flights and the experiment doth so represent them to any one who is not either wilfully or naturally incapable of reason Now apply this discourse to Gunnery and you shall find that whether the Earth move or stand still the shots made with the same force will always curry equal ranges to what part soever aimed The error of Aristotle Ptolomey Tycho your self and all the rest is grounded upon that fixed and strong persuasion that the Earth standeth still which you
and fall towards the part whither the boat steered And in case the Earth should meet with such a check as should be able to resist and arrest its vertigo then indeed I do believe that not onely beasts buildings and cities but mountains lakes and seas would overturn and the globe it self would go near to shake in pieces but nothing of all this concerns our present purpose for we speak of what may follow to the motion of the Earth it being turn'd round uniformly and quietly about its own centre howbeit with a great velocity That likewise which you say of the slings is true in part but was not alledged by Salviatus as a thing that punctually agreed with the matter whereof we treat but onely as an example for so in gross it may prompt us in the more accurate consideration of that point whether the velocity increasing at any rate the cause of the projection doth increase at the same rate so that v. g. if a wheel of ten yards diameter moving in such a manner that a point of its circumference will pass an hundred yards in a minute of an hour and so hath an impetus able to extrude a stone that same impetus shall be increased an hundred thousand times in a wheel of a million of yards diameter the which Salviatus denieth and I incline to his opinion but not knowing the reason thereof I have requested it of him and stand impatiently expecting it SALV I am ready to give you the best satisfaction that my abilities will give leave And though in my first discourse you thought that I had enquired into things estranged from our purpose yet neverthelesse I believe that in the sequel of the dispute you will find that they do not prove so Therefore let Sagredus tell me wherein he hath observed that the resistance of any moveable to motion doth consist SAGR. I see not for the present that the moveable hath any internal resistance to motion unlesse it be its natural inclination and propension to the contrary motion as in grave bodies that have a propension to the motion downwards the resistance is to the motion upwards and I said an internal resistance because of this I think it is you intend to speak and not of the external resistances which are many and accidental SALV It is that indeed I mean and your nimblenesse of wit hath been too hard for my craftinesse but if I have been too short in asking the question I doubt whether Sagredus hath been full enough in his answer to satisfie the demand and whether there be not in the moveable besides the natural inclination to the contrary term another intrinsick and natural quality which maketh it averse to motion Therefore tell me again do you not think that the inclination v. g. of grave bodies to move downwards is equal to the resistance of the same to the motion of projection upwards SAGR. I believe that it is exactly the same And for this reason I see that two equal weights being put into a ballance they do stand still in equilibrium the gravity of the one resisting its being raised by the gravity wherewith the other pressing downwards would raise it SALV Very well so that if you would have one raise up the other you must encrease the weight of that which depresseth or lessen the weight of the other But if the resistance to ascending motion cunsist onely in gravity how cometh it to passe that in ballances of unequal arms to wit in the Stiliard a weight sometimes of an hundred pounds with its pression downwards doth not suffice to raise up on of four pounds that shall counterpoise with it nay this of four descending shall raise up that of an hundred for such is the effect of the pendant weight upon the weight which vve vvould vveigh If the resistance to motion resideth onely in the gravity hovv can the arm with its vveight of four pounds onely resist the vveight of a sack of wool or bale of silk vvhich shall be eight hundred or a thousand vveight yea more hovv can it overcome the sack vvith its moment and raise it up It must therefore be confest Sagredus that here it maketh use of some other resistance and other force besides that of simple gravity SAGR. It must needs be so therefore tell me vvhat this second virtue should be SALV It is that vvhich vvas not in the ballance of equal arms you see then vvhat variety there is in the Stiliard and upon this doubtlesse dependeth the cause of the nevv effect SAGR. I think that your putting me to it a second time hath made me remember something that may be to the purpose In both these beams the business is done by the weight and by the motion in the ballance the motions are equal and therefore the one weight must exceed it in gravity before it can move it in the stiliard the lesser weight will not move the greater unless when this latter moveth little as being hung at a lesser distance and the other much as hanging at a greater distance from the lacquet or cock It is necessary therefore to conclude that the lesser weight overcometh the resistance of the greater by moving much whilst the other is moved but little SALV Which is as much as to say that the velocity of the moveable less grave compensateth the gravity of the moveable more grave and less swift SAGR. But do you think that the velocity doth fully make good the gravity that is that the moment and force of a moveable of v. g. four pounds weight is as great as that of one of an hundred weight whensoever that the first hath an hundred degrees of velocity and the later but four onely SALV Yes doubtless as I am able by many experiments to demonstrate but for the present let this onely of the stiliard suffice in which you see that the light end of the beam is then able to sustain and equilibrate the great Wool-sack when its distance from the centre upon which the stiliard resteth and turneth shall so much exceed the lesser distance by how much the absolute gravity of the Wool-sack exceedeth that of the pendent weight And we see nothing that can cause this insufficiencie in the great sack of Wool to raise with its weight the pendent weight so much less grave save the disparity of the motions which the one and the other should make whilst that the Wool-sack by descending but one inch onely will raise the pendent weight an hundred inches supposing that the sack did weigh an hundred times as much and that the distance of the small weight from the centre of the beam were an hundred times greater than the distance between the said centre and the point of the sacks suspension And again the pendent weight its moving the space of an hundred inches in the time that the sack moveth but one inch onely is the same as to say that the velocity
should toss you up towards the Stars It 's true that by the other senses but yet assisted by Reason you may perceive the motion of the boat that is with the sight in that you see the trees and buildings placed on the shoar which being separated from the boat seem to move the contrary way But if you would by such an experiment receive intire satisfaction in this business of the Terrestrial motion look on the stars which upon this reason seem to move the contrary way As to the wondering that we should not feel such a principle supposing it to be internal is a less reasonable conceit for if we do not feel such a one that cometh to us from without and that frequently goeth away with what reason can we expect to feel it if it immutably and continually resides in us Now let us see what you have farther to allege on this argument SIMP Take this short exclamation Ex hac itaque opinione necesse est diffidere nostris sensibus ut penitùs fallacibus vel stupidis in sensilibus etiam conjunctissimis dijudicandis Quam ergò veritatem sperare possumus à facultate adeò fallaci ortum trahentem Which I render thus From this opinion likewise we must of necessity suspect our own senses as wholly fallible or stupid in judging of sensible things even very near at hand What truth therefore can we hope for to be derived from so deceiveable a faculty SALV But I desire not to deduce precepts more profitable or more certain learning to be more circumspect and less confident about that which at first blush is represented to us by the senses which may easily deceive us And I would not have this Author trouble himself in attempting to make us comprehend by sense that this motion of descending Graves is simply right and of no other kind nor let him exclaim that a thing so clear manifest and obvious should be brought in question for in so doing he maketh others believe that he thinketh those that deny that motion to be absolutely streight but rather circular the stone did sensibly see it to move in an arch seeing that he inviteth their senses more than their Reason to judg of that effect which is not true Simplicius for like as I that am indifferent in all these opinions and onely in the manner of a Comedian personate Copernicus in these our representations have never seen nor thought that I have seen that stone fall otherwise than perpendicularly so I believe that to the eyes of all others it seemed to do the same Better it is therefore that deposing that appearance in which all agree we make use of our Reason either to confirm the reality of that or to discover its fallacy SAGR. If I could any time meet with this Philosopher who yet me thinks is more sublime than the rest of the followers of the same doctrines I would in token of my affection put him in mind of an accident which he hath doubtless very often beheld from which with great conformity to that which we now discourse of it may be collected how easily one may be deceived by the bare appearance or if you will representation of the sense And the accident is the Moons seeming to follow those that walk the streets in the night with a pace equal to theirs whilst they see it go gliding along the Roofs of houses upon which it sheweth just like a cat that really running along the ridges of houses leaveth them behind An appearance that did not reason interpose would but too manifestly delude the sight SIMP Indeed there want not experiments that render us certain of the fallacy of the meer senses therefore suspending such sensations for the present let us hear the Arguments that follow which are taken as he saith ex rerum natura The first of which is that the Earth cannot of its own nature move with three motions very different or otherwise we must deny many manifest Axioms The first whereof is that Omnis effectus dependeat ab aliquâ causà i. e. that every effect dependeth on some cause The second that Nulla res seipsam producat i. e. that nothing produceth it self from whence it follows that it is not possible that the move and moved should be totally the same thing And this is manifest not onely in things that are moved by an extrinsick mover but it is gathered also from the principles propounded that the same holdeth true in the natural motion dependent on an intrinsick principle otherwise being that the mover as a mover is the cause and the thing moved as moved is the effect the same thing would totally be both the cause and effect Therefore a body doth not move its whole self that is so as that all moveth and all is moved but its necessary in the thing moved to distinguish in some manner the efficient principle of the motion and that which with that motion is moved The third Axiom is that in rebus quae sensui subjiciuntur unum quatenus unum unam solam rem producat i. e. That in things subject to the senses one as it is one produceth but onely one thing That is the soul in animals produceth its true divers operations as the sight the hearing the smell generation c. but all these with several instruments And in short in things sensible the diversity of operations is observed to derive it self from the diversity that is in the cause Now if we put all these Axioms together it will be a thing very manifest that one simple body as is the Earth cannot of its own nature move at the same time with three motions very divers For by the foregoing suppositions all moveth not its self all it is necessary therefore to distinguish in it three principles of its three motions otherwise one and the same principle would produce many motions but if it contein in it three principles of natural motions besides the part moved it shall not be a simple body but compounded of three principle movers and of the part moved If therefore the Earth be a simple body it shall not move with three motions nay more it will not move with any of those which Copernicus ascribeth to it it being to move but with one alone for that it is manifest by the reasons of Aristotle that it moveth to its centre as its parts do shew which descend at right angles to the Earths Spherical Surface SALV Many things might be said and considered touching the connection of this argument but in regard that we can resolve it in few words I will not at this time without need inlarge upon it and so much the rather because the same Author hath furnished me with an answer when he saith that from one sole prinple in animals there are produced divers operations so that for the present my answer shall be that in the same manner the Earth from one onely
therefore be 25. times so much and lastly the four inches of hair or fringe added to a small circle of an inch in diameter the same would be increased 81. times and so continually the augmentations are made with a proportion greater and greater according as the real objects that increase are lesser and lesser SAGR. The doubt which puzzled Simplicius never troubled me but certain other things indeed there are of which I desire a more distinct understanding and in particular I would know upon what ground you affirm that the said agrandizement is alwayes equal in all visible objects SALV I have already declared the same in part when I said that onely lucid objects so increased and not the obscure now I adde what remaines that of the resplendent objects those that are of a more bright light make the reflection greater and more resplendent upon our pupil whereupon they seem to augment much more than the lesse lucid and that I may no more inlarge my self upon this particular come we to that which the true Mistris of Astronomy Experience teacheth us Let us this evening when the air is very obscure observe the star of Jupiter we shall see it very glittering and very great let us afterwards look through a tube or else through a small trunk which clutching the hand close and accosting it to the eye we lean between the palm of the hands and the fingers or else by an hole made with a small needle in a paper and we shall see the said star divested of its beams but so small that we shall judge it lesse even than a sixtieth part of its great glittering light seen with the eye at liberty we may afterwards behold the Dog-stars beautiful and bigger than any of the other fixed stars which seemeth to the bare eye no great matter lesse than Jupiter but taking from it as before the irradiation its Discus will shew so little that it will not be thought the twentieth part of that of Jupiter nay he that hath not very good eyes will very hardly discern it from whence it may be rationally inferred that the said star as having a much more lively light than Jupiter maketh its irradiation greater than Jupiter doth his In the next place as to the irradiation of the Sun and Moon it is as nothing by means of their magnitude which possesseth of it self alone so great a space in our eye that it leaveth no place for the adventitious rayes so that their faces seem close clipt and terminate We may assure our selves of the same truth by another experiment which I have often made triall of we may assure ourselves I say that bodies shining with most lively light do irradiate or beam forth rayes more by far than those that are of a more languishing light I have many times seen Jupiter and Venus together twenty or thirty degrees distant from the Sun and the air being very dark Venus appeared eight or ten times bigger than Jupiter being both beheld by the eye at liberty but being beheld afterwards with the Telescope the Discus of Jupiter discovered it self to be four or more times greater than that of Venus but the vivacity of the splendour of Venus was incomparably bigger than the languishing light of Jupiter which was only because of Jupiters being far from the Sun and from us and Venus neer to us and to the Sun These things premised it will not be difficult to comprehend how Mars when it is in opposition to the Sun and therefore neerer to the Earth by seven times and more than it is towards the conjunction cometh to appear scarce four or five times bigger in that state than in this when as it should appear more than fifty times so much of which the only irradiation is the cause for if we divest it of the adventitious rayes we shall find it exactly augmented with the due proportion but to take away the capillitious border the Telescope is the best and only means which inlarging its Discus nine hundred or a thousand times makes it to be seen naked and terminate as that of the Moon and different from it self in the two positions according to its due proportions to an hair Again as to Venus that in its vespertine conjunction when it is below the Sun ought to shew almost fourty times bigger than in the other matutine conjunction and yet doth not appear so much as doubled it happeneth besides the effect of the irradiation that it is horned and its crescents besides that they are sharp they do receive the Suns light obliquely and therefore emit but a faint splendour so that as being little and weak its irradiation becometh the lesse ample and vivacious than when it appeareth to us with its Hemisphere all shining but now the Telescope manifestly shews its hornes to have been as terminate and distinct as those of the Moon and appear as it were with a great circle and in a proportion those well neer fourty times greater than its same Discus at such time as it is superiour to the Sun in its ultimate matutine apparition SAGR. Oh Nicholas Copernicus how great would have been thy joy to have seen this part of thy Systeme confirmed with so manifest experiments SALV T is true But how much lesse the fame of his sublime wit amongst the intelligent when as it is seen as I also said before that he did constantly continue to affirm being perswaded thereto by reason that which sensible experiments seemed to contradict for I cannot cease to wonder that he should constantly persist in saying that Venus revolveth about the Sun and is more than six times farther from us at one time than at another and also seemeth to be alwayes of an equal bigness although it ought to shew forty times bigger when nearest to us than when farthest off SAGR. But in Jupiter Saturn and Mercury I believe that the differences of their apparent magnitudes should seem punctually to answer to their different distances SALV In the two Superiour ones I have made precise observation yearly for this twenty two years last past In Mercury there can be no observation of moment made by reason it suffers not it self to be seen save onely in its greatest digâ—ssieons from the Sun in which its distances from the earth are insensibly unequal and those differences consequently not to be observed as also its mutations of figures which must absolutely happen in it as in Venus And if we do see it it must of necessity appear in form of a Semicircle as Venus likewise doth in her greatest digressions but its discns is so very small and its splendor so very great by reason of its vicinity to the Sun that the virtue of the Telescope doth not suffice to clip its tresses or adventitious rayes so as to make them appear shaved round about It remains that we remove that which seemed a great inconvenience in the
a very exact observation and of great consequence we are advertized to make the observation of that concourse in the act of the same or just such another operation but in this our case wherein we are to shew the errour of Astronomers this accuratenesse is not necessary for though we should in favour of the contrary party suppose the said concourse to be made upon the pupil it self it would import little their mistake being so great I am not certain Sagredus that this would have been your objection SAGR. It is the very same and I am glad that it was not altogether without reason as your concurrence in the same assureth me but yet upon this occasion I would willingly hear what way may be taken to finde out the distance of the concourse of the visual rayes SALV The method is very easie and this it is I take two long labels of paper one black and the other white and make the black half as broad as the white then I stick up the white against a wall and far from that I place the other upon a stick or other support at a distance of fifteen or twenty yards and receding from this second another such a space in the same right line it is very manifest that at the said distance the right lines will concur that departing from the termes of the breadth of the white piece shall passe close by the edges of the other label placed in the mid-way whence it followeth that in case the eye were placed in the point of the said concourse or intersection the black slip of paper in the midst would precisely hide the opposite blank if the sight were made in one onely point but if we should find that the edges of the white cartel appear discovered it shall be a necessary argument that the visual rayes do not issue from one sole point And to make the white label to be hid by the black it will be requisite to draw neerer with the eye Therefore having approached so neer that the intermediate label covereth the other and noted how much the required approximation was the quantity of that approach shall be the certain measure how much the true concourse of the visive rayes is remote from the eye in the said operation and we shall moreover have the diameter of the pupil or of that circlet from whence the visive rayes proceed for it shall be to the breadth of the black paper as is the distance from the concourse of the lines that are produced by the edges of the papers to the place where the eye standeth when it first seeth the remote paper to be hid by the intermediate one as that distance is I say to the distance that is between those two papers And therefore when we would with exactnesse measure the apparent diameter of a Star having made the observation in manner as aforesaid it would be necessary to compare the diameter of the rope to the diameter of the pupil and having found v. g. the diameter of the rope to be quadruple to that of the pupil and the distance of the eye from the rope to be for example thirty yards we would say that the true concourse of the lines produced from the ends or extremities of the diameter of the star by the extremities of the diameter of the rope doth fall out to be fourty yards remote from the said rope for so we shall have observed as we ought the proportion between the distance of the rope from the concourse of the said lines and the distance from the said concourse to the place of the eye which ought to be the same that is between the diameter of the rope and diameter of the pupil SAGR. I have perfectly understood the whole businesse and therefore let us hear what Simplicius hath to alledge in defence of the Anti-Copernicans SIMP Albeit that grand and altogether incredible inconvenience insisted upon by these adversaries of Copernicus be much moderated and abated by the discourse of Salviatus yet do I not think it weakened so as that it hath not strength enough left to foil this same opinion For if I have rightly apprehended the chief and ultimate conclusion in case the stars of the sixth magnitude were supposed to be as big as the Sun which yet I can hardly think yet it would still be true that the grand Orb or Ecliptick would occasion a mutation and variation in the starry Sphere like to that which the semidiameter of the Earth produceth in the Sun which yet is observable so that neither that no nor a lesse mutation being discerned in the fixed Stars methinks that by this means the annual motion of the Earth is destroyed and overthrown SALV You might very well so conclude Simplicius if we had nothing else to say in behalf of Copernicus but we have many things to alledge that yet have not been mentioned and as to that your reply nothing hindereth but that we may suppose the distance of the fixed Stars to be yet much greater than that which hath been allowed them and you your self and whoever else will not derogate from the propositions admitted by Piolomy's sectators must needs grant it as a thing most requisite to suppose the Starry Sphere to be very much bigger yet than that which even now we said that it ought to be esteemed For all Astronomers agreeing in this that the cause of the greater tardity of the Revolutions of the Planets is the majority of their Spheres and that therefore Saturn is more slow than Jupiter and Jupiter than the Sun for that the first is to describe a greater circle than the second and that than this later c. confidering that Saturn v. g. the altitude of whose Orb is nine times higher than that of the Sun and that for that cause the time of one Revolution of Saturn is thirty times longer than that of a conversion of the Sun in regard that according to the Doctrine of Ptolomy one conversion of the starry Sphere is finished in 36000. years whereas that of Saturn is consummate in thirty and that of the Sun in one arguing with a like proportion and saying if the Orb of Saturn by reason it is nine times bigger than that of the Sun revolves in a time thirty times longer by conversion how great ought that Orb to be which revolves 36000. times more slowly it shall be found that the distance of the starry Sphere ought to be 10800 semidiameters of the grand Orb which should be full five times bigger than that which even now we computed it to be in case that a fixed Star of the sixth magnitude were equal to the Sun Now see how much lesser yet upon this account the variation occasioned in the said Stars by the annual motion of the Earth ought to appear And if at the same rate we would argue the distance of the starry Sphere from Jupiter and from Mars that would give it us
them and the rather for that to your benefit you may read them in Gilbert onely to encourage you to the perusal of them I will set before you in a similitude of my own the method that he observed in his Philosophy I know you understand very well how much the knowledg of the accidents is subservient to the investigation of the substance and essence of things therefore I desire that you would take pains to informe your self well of many accidents and properties that are found in the Magnet and in no other stone or body as for instance of attracting Iron of conferring upon it by its sole presence the same virtue of communicating likewise to it the property of looking towards the Poles as it also doth it self and moreover endeavour to know by trial that it containeth in it a virtue of conferring upon the magnetick needle not onely the direction under a Meridian towards the Poles with an Horizontal motion a property a long time ago known but a new found accident of declining being ballanced under the Meridian before marked upon a little spherical Magnet of declining I say to determinate marks more or lesse according as that needle is held nearer or farther from the Pole till that upon the Pole it self it erecteth perpendicularly whereas in the middle parts it is parallel to the Axis Furthermore procure a proof to be made whether the virtue of attracting Iron residing much more vigorously about the Poles than about the middle parts this force be not notably more vigorous in one Pole than in the other and that in all pieces of Magnet the stronger of which Poles is that which looketh towards the South Observe in the next place that in a little Magnet this South and more vigorous Pole becometh weaker when ever it is to take up an iron in presence of the North Pole of another much bigger Magnet and not to make any tedious discourse of it assertain your self by experience of these and many other properties described by Gilbert which are all so peculiar to the Magnet as that none of them agree with any other matter Tell me now Simplicius if there were laid before you a thousand pieces of several matters but all covered and concealed in a cloth under which it is hid and you were required without uncovering them 〈…〉 a guesse by external signes at the matter of each of them and that in making trial you should hit upon one that should openly shew it self to have all the properties by you already acknowledged to reside onely in the Magnet and in no other matter what judgment would you make of the essence of such a body Would you say that it might be a piece of Ebony or Alablaster o◠Tin SIMP I would say without the least haesitation that it was a piece of Load-stone SALV If it be so say resolutely that under this cover and scurf of Earth stones metals water c. there is hid a great Magnet forasmuch as about the same there may be seen by any one that will heedfully observe the same all those very accidents that agree with a true and visible Globe of Magnet but if no more were to be seen than that of the Declinatory Needle which being carried about the Earth more and more inclineth as it approacheth to the North Pole and declineth lesse towards the Equinoctial under which it finally is brought to an Aequilibrium it might serve to perswade even the most scrupulous judgment I forbear to mention that other admirable effect which is sensibly observed in every piece of Magnet of which to us inhabitants of the Northern Hemisphere the Meridional Pole of the said Magnet is more vigorous than the other and the difference is found greater by how much one recedeth from the Equinoctial and under the Equinoctial both the parts are of equal strength but notably weaker But in the Meridional Regions far distant from the Equinoctial it changeth nature and that part which to us was more weak acquireth more strength than the other and all this I confer with that which we see to be done by a small piece of Magnet in the presence of a great one the vertue of which superating the lesser maketh it to become obedient to it and according as it is held either on this or on that side the Equinoctial of the great one maketh the self same mutations which I have said are made by every Magnet carried on this side or that side of the Equinoctiall of the Earth SAGR. I was perswaded at the very first reading of the Book of Gilbertus and having met with a most excellent piece of Magnet I for a long time made many Observations and all worthy of extream wonder but above all that seemeth to me very stupendious of increasing the faculty of taking up Iron so much by arming it like as the said Authour teacheth and with arming that piece of mine I multiplied its force in octuple proportion and whereas unarmed it scarce took up nine ounces of Iron it being armed did take up above six pounds And it may be you have seen this Loadstone in the Gallery of your Most Serene Grand Duke to whom I presented it upholding two little Anchors of Iron SALV I saw it many times and with great admiration till that a little piece of the like stone gave me greater cause of wonder that is in the keeping of our Academick which being no more than of six ounces weight and sustaining when unarmed hardly two ounces doth when armed take up 160. ounces so as that it is of 80. times more force armed than unarmed and takes up a weight 26. times greater than its own a much greater wonder than Gilbert could ever meet with who writeth that he could never get any Loadstone that could reach to take up four times its own weight SAGR. In my opinion this Stone offers to the wit of man a large Field to Phylosophate in and I have many times thought with my self how it can be that it conferreth on that Iron which armeth it a strength so superiour to its own and finally I finde nothing that giveth me satisfaction herein nor do I find any thing extraordinary in that which Gilbert writes about this particular I know not whether the same may have befallen you SALV I extreamly praise admire and envy this Authour for that a conceit so stupendious should come into his minde touching a thing handled by infinite sublime wits and hit upon by none of them I think him moreover worthy of extraordinary applause for the many new and true Observations that he made to the disgrace of so many fabulous Authours that write not only what they do not know but what ever they hear spoken by the foolish vulgar never seeking to assure themselves of the same by experience perhaps because they are unwilling to diminish the bulk of their Books That which I could have desired in Gilbert is that he had
been a little greater Mathematician and particularly well grounded in Geometry the practice whereof would have rendered him less resolute in accepting those reasons for true Demonstrations which he produceth for true causes of the true conclusions observed by himself Which reasons freely speaking do not knit and bind so fast as those undoubtedly ought to do in that of natural necessary and lasting conclusions may be alledged And I doubt not but that in processe of time this new Science will be perfected with new observations and which is more with true and necessary Demonstrations Nor ought the glory of the first Inventor to be thereby diminished nor do I lesse esteem but rather more admire the Inventor of the Harp although it may be supposed that the Instrument at first was but rudely framed and more rudely fingered than an hundred other Artists that in the insuing Ages reduced that profession to great perfection And methinks that Antiquity had very good reason to enumerate the first Inventors of the Noble Arts amongst the Gods seeing that the common wits have so little curiosity and are so little regardful of rare and elegant things that though they see and hear them exercitated by the exquisite professors of them yet are they not thereby perswaded to a desire of learning them Now judge whether Capacities of this kind would ever have attempted to have found out the making of the Harp or the invention of Musick upon the hint of the whistling noise of the dry sinews of a Tortois or from the striking of four Hammers The application to great inventions moved by small hints and the thinking that under a primary and childish appearance admirable Arts may lie hid is not the part of a trivial but of a super-humane spirit Now answering to your demands I say that I also have long thought upon what might possibly be the cause of this so tenacious and potent union that we see to be made between the one Iron that armeth the Magnet and the other that conjoyns it self unto it And first we are certain that the vertue and strength of the stone doth not augment by being armed for it neither attracts at greater distance nor doth it hold an Iron the faster if between it and the arming or cap a very fine paper or a leaf of beaten gold be interposed nay with that interposition the naked stone takes up more Iron than the armed There is therefore no alteration in the vertue and yet there is an innovation in the effect And because its necessary that a new effect have a new cause if it be inquired what novelty is introduced in the act of taking up with the cap or arming there is no mutation to be discovered but in the different contact for whereas before Iron toucht Loadstone now Iron toucheth Iron Therefore it is necessary to conclude that the diversity of contacts is the cause of the diversity of effects And for the difference of contacts it cannot as I see be derived from any thing else save from that the substance of the Iron is of parts more subtil more pure and more compacted than those of the Magnet which are more grosse impure and rare From whence it followeth that the superficies of two Irons that are to touch by being exquisitely plained filed and burnished do so exactly conjoyn that all the infinite points of the one meet with the infinite points of the other so that the filaments if I may so say that collegate the two Irons are many more than those that collegate the Magnet to the Iron by reason that the substance of the Magnet is more porous and lesse compact which maketh that all the points and filaments of the Loadstone do not close with that which it unites unto In the next place that the substance of Iron especially the well refined as namely the purest steel is of parts much more dense subtil and pure than the matter of the Loadstone is seen in that one may bring its edge to an extraordinary sharpnesse such as is that of the Rasor which can never be in any great measure effected in a piece of Magnet Then as for the impurity of the Magnet and its being mixed with other qualities of stone it is first sensibly discovered by the colour of some little spots for the most part white and next by presenting a needle to it hanging in a thread which upon those stonynesses cannot find repose but being attracted by the parts circumfused seemeth to fly from those and to leap upon the Magnet contiguous to them and as some of those Heterogeneal parts are for their magnitude very visible so we may believe that there are others in great abundance which for their smallnesse are imperceptible that are disseminated throughout the whole masse That which I say namely that the multitude of contacts that are made between Iron and Iron is the cause of the so solid conjunction is confirmed by an experiment which is this that if we present the sharpned point of a needle to the cap of a Magnet it will stick no faster to it than to the same stone unarmed which can proceed from no other cause than from the equality of the contacts that are both of one sole point But what then Let a Needle be taken and placed upon a Magnet so that one of its extremities hang somewhat over and to that present a Nail to which the Needle will instantly cleave insomuch that withdrawing the Nail the Needle will stand in suspense and with its two ends touching the Magnet and the Iron and withdrawing the Nail yet a little further the Needle will forsake the Magnet provided that the eye of the Needle be towards the Nail and the point towards the Magnet but if the eye be towards the Loadstone in withdrawing the Nail the Needle will cleave to the Magnet and this in my judgment for no other reason save onely that the Needle by reason it is bigger towards the eye toucheth in much more points than its sharp point doth SAGR. Your whole discourse hath been in my judgment very concluding and this experiment of the Needle hath made me think it little inferiour to a Mathematical Demonstration and I ingenuously confesse that in all the Magnetick Philosophy I never heard or read any thing that with such strong reasons gave account of its so many admirable accidents of which if the causes were with the same perspicuity laid open I know not what sweeter food our Intellects could desire SALV In seeking the reasons of conclusions unknown unto us it is requisite to have the good fortune to direct the discourse from the very beginning towards the way of truth in which if any one walk it will easily happen that one shall meet with several other Propositions known to be true either by disputes or experiments from the certainty of which the truth of ours acquireth strength and evidence as it did in every respect
all external and accidental impediments were removed and this opinion Gilbert himself seemeth also to applaud So that Simplicius you see how tottering the Axiome of Aristotle is SIMP This doth â—ot only not make against the Maxime but not so much as look towards it for that he speaketh of a simple body and of that which may naturally consist therewith but you propose that which befalleth a mixt body nor do you tell us of any thing that is new to the doctrine of Aristotle for that he likewise granteth to mixt bodies compound motions by SAGR. Stay a little Simplicius answer me to the questions I shall ask you You say that the Load-stone is no simple body now I desire you to tell me what those simple bodies are that mingle in composing the Load-stone SIMP I know not how to tell you th' ingredients nor simples precisely but it sufficeth that they are things elementary SALV So much sufficeth me also And of these simple elementary bodies what are the natural motions SIMP They are the two right and simple motions sursum and deorsum SAGR. Tell me in the next place Do you believe that the motion that shall remain natural to that same mixed body should be one that may result from the composition of the two simple natural motions of the simple bodies compounding or that it may be a motion impossible to be composed of them SIMP I believe that it shall move with the motion resulting from the composition of the motions of the simple bodies compounding and that with a motion impossible to be composed of these it is impossible that it should move SAGR. But Simplicius with two right and simple motions you shall never be able to compose a circular motion such as are the two or three circular motions that the magnet hath you see then into what absurdities evil grounded Principles or to say better the ill-inferred consequences of good Principles carry a man for you are now forced to say that the Magnet is a mixture compounded of substances elementary and coelestial if you will maintain that the straight motion is a peculiar to the Elements and the circular to the coelestial bodies Therefore if you will more safely argue you must say that of the integral bodies of the Universe those that are by nature moveable do all move circularly and that therefore the Magnet as a part of the true primary and integral substance of our Globe pertaketh of the same qualities with it And take notice of this your fallacy in calling the Magnet a mixt body and the Terrestrial Globe a simple body which is sensibly perceived to be a thousand times more compound for besides that it containeth an hundred an hundred matters exceeding different from one another it containeth great abundance of this which you call mixt I mean of the Load-stone This seems to me just as if one should call bread a mixt body and Pannada a simple body in which there is put no small quantity of bread besides many other things edible This seemeth to me a very admirable thing amongst others of the Peripateticks who grant nor can it be denied that our Terrestrial Globe is de facto a compound of infinite different matters and grant farther that of compound bodies the motion ought to be compound now the motions that admit of composition are the right and circular For the two right motions as being contrary are incompatible together they affirm that the pure Element of Earth is no where to be found they confesse that it never hath been moved with a local motion and yet they will introduce in Nature that body which is not to be found and make it move with that motion which it never exercised nor never shall do and to that body which hath and ever had a being they deny that motion which before they granted ought naturally to agree therewith SALV I beseech you Sagredus let us not weary our selves any more about these particulars and the rather because you know that our purpose was not to determine resolutely or to accept for true this or that opinion but only to propose for our divertisement such reasons and answers as may be alledged on the one side or on the other and Simplicius maketh this answer in defence of his Peripateticks therefore let us leave the judgment in suspense and remit the determination into the hands of such as are more known than we And because I think that we have with sufficient prolixity in these three dayes discoursed upon the Systeme of the Universe it will now be seasonable that we proceed to the grand accident from whence our Disputations took beginning I mean of the ebbing and flowing of the Sea the cause whereof may in all probability be referred to the motion of the Earth But that if you so please we will reserve till to morrow In the mean time that I may not forget it I will speak to one particular to which I could have wished that Gilbert had not lent an ear I mean that of admitting that in case a little Sphere of Loadstone might be exactly librated it would revolve in it self because there is no reason why it should do so For if the whole Terrestrial Globe hath a natural faculty of revolving about its own centre in twenty four hours and that all its parts ought to have the same I mean that faculty of turning round together with their whole about its centre in twenty four hours they already have the same in effect whilst that being upon the Earth they turn round along with it And the assigning them a revolution about their particular centres would be to ascribe unto them a second motion much different from the first for so they would have two namely the revolving in twenty four hours about the centre of their whole and the turning about their own now this second is arbitrary nor is there any reason for the introducing of it If by plucking away a piece of Loadstone from the whole natural masse it were deprived of the faculty of following it as it did whilst it was united thereto so that it is thereby deprived of the revolution about the universal centre of the Terrestrial Globe it might haply with somewhat greater probability be thought by some that the said Magnet was to appropriate to it self a new conversion about its particular centre but if it do no lesse when separated than when conjoyned continue always to pursue its first eternal and natural course to what purpose should we go about to obtrude upon it another new one SAGR. I understand you very well and this puts me in mind of a Discourse very like to this for the vanity of it falling from certain Writers upon the Sphere and I think if I well remember amongst others from Sacrobosco who to shew how the Element of Water doth together with the Earth make a compleat Spherical Figure and
so between them both compose this our Globe writeth that the seeing the small * particles of water shape themselves into rotundity as in the drops and in the dew daily apparent upon the leaves of several herbs is a strong argument and because according to the trite Axiome there is the same reason for the whole as for the parts the parts affecting that same figure it is necessary that the same is proper to the whole Element and truth is methinks it is a great oversight that these men should not perceive so apparent a vanity and consider that if their argument had run right it would have followed that not only the small drops but that any whatsoever greater quantity of water separated from the whole Element should be reduced into a Globe Which is not seen to happen though indeed the Senses may see and the Understanding perceive that the Element of Water loving to form it self into a Spherical Figure about the common centre of gravity to which all grave bodies tend that is the centre of the Terrestrial Globe it therein is followed by all its parts according to the Axiome so that all the surfaces of Seas Lakes Pools and in a word of all the parts of Waters conteined in vessels distend themselves into a Spherical Figure but that Figure is an arch of that Sphere that hath for its centre the centre of the Terrestrial Globe and do not make particular Spheres of themselves SALV The errour indeed is childish and if it had been onely the single mistake of Sacrobosco I would easily have allowed him in it but to pardon it also to his Commentators and to other famous men and even to Ptolomy himselfe this I cannot do without blushing for their reputation But it is high time to take leave it now being very late and we being to meet again to morrow at the usual hour to bring all the foregoing Discourses to a final conclusion Place this Plate at the end of the third Dialogue GALILAEUS Gailaeus Lyncaeus HIS SYSTEME OF THE WORLD The Fourth Dialogue INTERLOCVTORS SALVIATUS SAGREDUS SIMPLICIUS SAGR. I know not whether your return to our accustomed conferences hath really been later than usual or whether the desire of hearing the thoughts of Salviatus touching a matter so curious hath made me think it so But I have tarried a long hour at this window expecting every moment when the Gondola would appear that I sent to fetch you SALV I verily believe that your imagination more than our tarriance hath prolonged the time and to make no longer demurre it would be well if without interposing more words we came to the matter it self and did shew that nature hath permitted whether the business in rei veritate be so or else to play and sport with our Fancies hath I say hath permitted that the motions for every other respect except to resolve the ebbing and flowing of the Sea assigned long since to the earth should be found now at last to answer exactly to the cause thereof and as it were with mutual a emulation the said ebbing and flowing to appear in confirmation of the Terrestrial motion the judices whereof have hitherto been taken from the coelestial Phaenomena in regard that of those things that happen on Earth not any one was of force to prove one opinion more than another as we already have at large proved by shewing that all the terrene occurrences upon which the stability of the Earth and mobility of the Sun and Firmament is commonly inferred are to seem to us performed in the same manner though we supposed the mobility of the Earth and the immobility of them The Element of Water onely as being most vast and which is not annexed and concatenated to the Terrestrial Globe as all its other solid parts are yea rather which by reason of its fluidity remaineth apart sui juris and free is to be ranked amongst those sublunary things from which we may collect some hinte and intimation of what the Earth doth in relation to motion and rest After I had many and many a time examined with my self the effects and accidents partly seen and partly understood from others that are to be observed in the motions of waters and moreover read and heard the great vanities produced by many as the causes of those accidents I have been induced upon no slight reasons to omit these two conclusions having made withal the necessary presupposals that in case the terrestrial Globe be immoveable the flux and reflux of the Sea cannot be natural and that in case those motions be conferred upon the said Globe which have been long since assigned to it it is necessary that the Sea be subject to ebbing and flowing according to all that which we observe to happen in the same SAGR. The Proposition is very considerable as well for it self as for what followeth upon the same by way of consequence so that I shall the more intensly hearken to the explanation and confirmation of it SALV Because in natural questions of which number this which we have in hand is one the knowledge of the effects is a means to guide us to the investigation and discovery of the causes and without which we should walk in the dark nay with more uncertainty for that we know not whither we would go whereas the blind at least know where they desire to arrive therefore first of all it is necessary to know the effects whereof we enquire the causes of which effects you Sagredus ought more abundantly and more certainly to be informed than I am as one that besides your being born and having for a long time dwelt in Venice where the Tides are very notable for their greatnesse have also sailed into Syria and as an ingenuous and apprehensive wit must needs have made many Observations upon this subject whereas I that could onely for a time and that very short observe what happened in these extream parts of the Adriatick Gulph and in our Seas below about the Tyrrhene shores must needs take many things upon the relation of others who for the most part not very well agreeing and consequently being very uncertain contribute more of confusion than confirmation to our speculations Neverthelesse from those that we are sure of and which are the principal I think I am able to attain to the true and primary causes not that I pretend to be able to produce all the proper and adequate reasons of those effects that are new unto me and which consequently I could never have thought upon And that which I have to say I propose only as a key that openeth the door to a path never yet trodden by any in certain hope that some wits more speculative than mine will make a further progresse herin and penetrate much farther than I shall have done in this my first Discovery And although that in other Seas remote from us there may â—appen several accidents which
do not happen in our Mediterranean Sea yet doth not this invalidate the reason and cause that I shall produce if so be that it verifie and fully resolve the accidents which evene in our Sea for that in conclusion there can be but one true and primary cause of the effects that are of the same kind I will relate unto you therefore the effects that I know to be true and assigne the causes thereof that I think to be true and you also Gentlemen shall produce such others as are known to you besides mine and then we will try whether the cause by me alledged may satisfie them also I therefore affirm the periods that are observed in the fluxes and refluxes of the Sea-waters to be three the first and principal is this great and most obvious one namely the diurnal according to which the intervals of some hours with the waters flow and ebbe and these intervals are for the most part in the Mediterrane from six hours to six hours or thereabouts that is they for six hours flow and for six hours ebbe The second period is monethly and it seemes to take its origen from the motion of the Moon not that it introduceth other motions but only altereth the greatnesse of those before mentioned with a notable difference according as it shall wax or wane or come to the Quadrature with the Sun The third Period is annual and is seen to depend on the Sunne and onely altereth the diurnal motions by making them different in the times of the Solstices as to greatnesse from what they are in the Equinoxes We will speak in the first place of the diurnal motion as being the principal and upon which the Moon and Sun seem to exercise their power secondarily in their monethly and annual alterations Three differences are observable in these horary mutations for in some places the waters rise and fall without making any progressive motion in others without rising or falling they run one while towards the East and recur another while towards the West and in others they vary the heights and course also as happeneth here in Venice where the Tides in coming in rise and in going out fall and this they do in the extermities of the lengths of Gulphs that distend from West to East and terminate in open shores up along which shores the Tide at time of flood hath room to extend it self but if the course of the Tide were intercepted by Cliffes and Banks of great height and steepnesse there it will flow and ebbe without any progressive motion Again it runs to and again without changing height in the middle parts of the Mediterrane as notably happeneth in the Faro de Messina between Scylla and Carybdis where the Currents by reason of the narrownesse of the Channel are very swift but in the more open Seas and about the Isles that stand farther into the Mediterranean Sea as the Baleares Corsica Sardignia Elba Sicily towards the Affrican Coasts Malta Candia c. the changes of watermark are very small but the currents indeed are very notable and especially when the Sea is pent between Islands or between them and the Continent Now these onely true and certain effects were there no more to be observed do in my judgment very probably perswade any man that will contain himself within the bounds of natural causes to grant the mobility of the Earth for to make the vessel as it may be called of the Mediterrane stand still and to make the water contained therein to do as it doth exceeds my imagination and perhaps every mans else who will but pierce beyond the rinde in these kind of inquiries SIMP These accidents Salviatus begin not now they are most ancient and have been observed by very many and several have attempted to assigne some one some another cause for the same and there dwelleth not many miles from hence a famous Peripatetick that alledgeth a cause for the same newly fished out of a certain Text of Aristotle not well understood by his Expositors from which Text he collecteth that the true cause of these motions doth only proceed from the different profundities of Seas 〈…〉 waters of greatest depth being greater in abundance and therefore more grave drive back the Waters of lesse depth which being afterwards raised desire to descend and from this continual colluctation or contest proceeds the ebbing and flowing Again those that referre the same to the Moon are many saying that she hath particular Domination over the Water and at last a certain Prelate hath published a little Treatise wherâ—in he saith that the Moon wandering too and fro in the Heavens attracteth and draweth towards it a Masse of Water which goeth continually following it so that it is full Sea alwayes in that part which lyeth under the Moon and because that though she be under the Horizon yet neverthelesse the Tide returneth he saith that no more can be said for the salving of that particular save onely that the Moon doth not onely naturally retain this faculty in her self but in this case hath power to confer it upon that degree of the Zodiack that is opposite unto it Others as I believe you know do say that the Moon is able with her temperate heat to rarefie the Water which being rarefied doth thereupon flow Nor hath there been wanting some that SAGR. I pray you Simplicius let us hear no more of them for I do not think it is worth the while to wast time in relating them or to spend our breath in confuting them and for your part if you gave your assent to any of these or the like fooleâ—ies you did a great injury to your judgment which neverthelesse I acknowledg to be very piercing SALV But I that am a little more flegmatick than you Sagredus will spend a few words in favour of Simplicius if haply he thinks that any probability is to be found in those things that he hath related I say therefore The Waters Simplicius that have their exteriour superficies higher repel those that are inferiour to them and lower but so do not those Waters that are of greatest profundity and the higher having once driven back the lower they in a short time grow quiet and level This your Peripatetick must needs be of an opinion that all the Lakes in the World that are in a calme and that all the Seas where the ebbing and flowing is insensible are level in their bottoms but I was so simple that I perswaded my self that had we no other plummet to sound with the Isles that advance so high above Water had been a sufficient evidence of the unevennesse of their bottomes To that Prelate I could say that the Moon runneth every day along the whole Mediterrane and yet its Waters do not rise thereupon save onely in the very extream bounds of it Eastward and here to us at Venice And for those that make the Moons
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 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 SIMP 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 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 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 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 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 The 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 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
in those that distend themselves for a great length from VVest to East namely according to the course of the motions of the Terrestrial Globe and as it is in a certain manner unthought of and without a president among the motions possible to be made by us so it is not hard for me to believe that effects may be derived from the same which are not to be imitated by our artificial experiments SALV These things being declared it is time that we proceed to examine the particular accidents which together with their diversities are observed by experience in the ebbing and flowing of the waters And first we need not think it hard to guesse whence it happeneth that in Lakes Pooles and also in the lesser Seas there is no notable flux and reflux the which hath two very solid reasons The one is that by reason of the shortnesse of the Vessel in its acquiring in several hours of the day several degrees of velocity they are with very little difference acquired by all its parts for as well the precedent as the subsequent that is to say both the Eastern and VVestern parts do accelerate and retard almost in the same manner and withal making that alteration by little and little and not by giving the motion of the conteining Vessel a sudden check and retardment or a sudden and great impulse or acceleration both it and all its parts come to be gently and equally impressed with the same degrees of velocity from which uniformity it followeth that also the conteined water with but small resistance and opposition receiveth the same impressions and by consequence doth give but very obscure signes of its rising or falling or of its running towards one part or another The which effect is likewise manifestly to be seen in the little artificial Vessels wherein the contained water doth receive the self same impressions of velocity when ever the acceleration and retardation is made by gentle and uniform proportion But in the Straights and Bays that for a great length distend themselves from East to West the acceleration and retardation is more notable and more uneven for that one of its extreams shall be much retarded in motion and the other shall at the same time move very swiftly The reciprocal libration or levelling of the water proceeding from the impetus that it had conceived from the motion of its container The which libration as hath been noted hath its undulations very frequent in small Vessels from whence ensues that though there do reside in the Terrestrial motions the cause of conferring on the waters a motion onely from twelve hours to twelve hours for that the motion of the conteining Vessels do extreamly accelerate and extreamly retard but once every day and no more yet neverthelesse this same second cause depending on the gravity of the water which striveth to reduce it self to equilibration and that according to the shortnesse of the Vessel hath its reciprocations of one two three or more hours this intermixing with the first which also it self in small Vessels is very little it becommeth upon the whole altogether insensible For the primary cause which hath the periods of twelve hours having not made and end of imprinting the precedent commotion it is overtaken and opposed by the other second dependant on the waters own weight which according to the brevity and profundity of the Vessel hath the time of its undulations of one two three four or more hours and this contending with the other former one disturbeth and removeth it not permitting it to come to the height no nor to the half of its motion and by this contestation the evidence of the ebbing and flowing is wholly annihilated or at least very much obscured I passe by the continual alteration of the air which disquieting the water permits us not to come to a certainty whether any though but small encrease or abatement of half an inch or losse do reside in the Straights or receptacles of water not above a degree or two in length I come in the second place to resolve the question why there not residing any vertue in the primary principle of commoving the waters save onely every twelve hours that is to say once by the greatest velocity and once by the greatest tardity of motion the ebbings and flowings should yet neverthelesse appear to be every six hours To which is answered that this determination cannot any wayes be taken from the primary cause onely but there is a necessity of introducing the secondary causes as namely the greater or lesse length of the Vessels and the greater or lesse depth of the waters in them conteined Which causes although they have not any operation in the motions of the waters those operations belonging to the sole primary cause without which no ebbing or flowing would happen yet neverthelesse they have a principal share in determining the times or periods of the reciprocations and herein their influence is so powerful that the primary cause must of force give way unto them The period of six hours therefore is no more proper or natural than those of other intervals of times though indeed its the most observed as agreeing with our Mediterrane which was the onely Sea that for many Ages was navigated though neither is that period observed in all its parts for that in some more angust places such as are the Hellespont and the Aegean Sea the periods are much shorter and also very divers amongst themselves for which diversities and their causes incomprehensible to Aristotle some say that after he had a long time observed it upon some cliffes of Negropont being brought to desperation he threw himself into the adjoyning Euripus and voluntarily drowned himself In the third place we have the reason ready at hand whence it commeth to passe that some Seas although very long as is the Red Sea are almost altogether exempt from Tides which happeneth because their length extendeth not from East to West but rather transversly from the Southeast to the Northwest but the motions of the Earth going from West to East the impulses of the water by that means alwayes happen to fall in the Meridians and do not move from parallel to parallel insomuch that in the Seas that extend themselves athwart towards the Poles and that the contrary way are narrow there is no cause of ebbing and flowing save onely by the participation of another Sea wherewith it hath communication that is subject to great commotions In the fourth place we shall very easily find out the reason why the fluxes and refluxes are greatest as to the waters rising and falling in the utmost extremities of Gulphs and least in the intermediate parts as daily experience sheweth here in Venice lying in the farther end of the Adriatick Sea where that difference commonly amounts to five or six feet but in the places of the Mediterrane far distant from the extreams that mutation is very small as in
for a long tract or distance from West to East that is according to the course of the fluxes and refluxes therefore in this the agitations are very great and would be much more violent between Hercules Pillars in case the Straight of Gibraltar did open lesse and those of the Straight of Magellanes are reported to be extraordinary violent This is what for the present cometh into my mind to say unto you about the causes of this first period diurnal of the Tide and its various accidents touching which if you have any thing to offer you may let us hear it that so we may afterwards proceed to the other two periods monethly and annual SIMP In my opinion it cannot be denied but that your discourse carrieth with it much of probability arguing as we say ex suppositione namely granting that the Earth moveth with the two motions assigned it by Copernicus but if that motion be disproved all that you have said is vain and insignificant and for the disproval of that Hypothesis it is very manifestly hinted by your Discourse it self You with the supposition of the two Terrestrial motions give a reason of the ebbing and flowing and then again arguing circularly from the ebbing and flowing draw the reason and confirmation of those very motions and so proceeding to a more specious Discourse you say that the Water as being a fluid body and not tenaciously annexed to the Earth is not constrained punctually to obey every of its motions from which you afterwards infer its ebbing and flowing Now I according to your own method argue the quite contrary and say the Air is much more tenuous and fluid than the Water and lesse annexed to the Earths superficies to which the Water if it be for nothing else yet by reason of its gravity that presseth down upon the same more than the light Air adhereth therefore the Air is much obliged to follow the motions of the Earth and therefore were it so that the Earth did move in that manner we the inhabitants of it and carried round with like velocity by it ought perpetually to feel a Winde from the East that beateth upon us with intolerable force And that so it ought to fall out quotidian experience assureth us for if with onely riding post at the speed of eight or ten miles an hour in the tranquil Air the incountering of it with our face seemeth to us a Winde that doth not lightly blow upon us what should we expect from our rapid course of 800. or a thousand miles an hour against the Air that is free from that motion And yet notwithstanding we cannot perceive any thing of that nature SALV To this objection that hath much of likelihood in it I reply that its true the Air is of greater tenuity and levity and by reason of its levity lesse adherent to the Earth than Water so much more grave and bulky but yet the consequence is false that you infer from these qualities namely that upon account of that its levity tenuity and lesse adherence to the Earth it should be more exempt than the Water from following the Terrestrial Motions so as that to us who absolutely pertake of of them the said exemption should be sensible and manifest nay it happeneth quite contrary for if you well remember the cause of the ebbing and flowing of the Water assigned by us consisteth in the Waters not following the unevennesse of the motion of its Vessel but retaining the impetus conceived before without diminishing or increasing it according to the precise rate of its diminishing or increasing in its Vessel Because therefore that in the conservation and retention of the impetus before conceived the disobedience to a new augmentation or diminution of motion consisteth that moveable that shall be most apt for such a retention shall be also most commodious to demonstrate the effect that followeth in consequence of that retention Now how much the Water is disposed to maintain such a conceived agitation though the causes cease that impress the same the experience of the Seas extreamly disturbed by impetuous Winds sheweth us the Billows of which though the Air be grown calm and the Wind laid for a long time after continue in motion As the Sacred Poet pleasantly sings Qual l'alto Egeo c. And that long continuing rough after a storm dependeth on the gravity of the water For as I have elsewhere said light bodies are much easier to be moved than the more grave but yet are so much the less apt to conserve the motion imparted when once the moving cause ceaseth Whence it comes that the Aire as being of it self very light and thin is easily mov'd by any very small force yet it is withall very unable to hold on its motion the Mover once ceasing Therefore as to the Aire which environs the Terrestrial Globe I would fay that by reason of its adherence it is no lesse carried about therewith then the Water and especially that part which is contained in its vessels which vessels are the valleys enclosed with Mountains And we may with much more reason affirm that this same part of the Air is carried round and born forwards by the rugged parts of the Earth than that the higher is whirl'd about by the motion of the Heavens as ye Peripateticks maintain What hath been hitherto spoken seems to me a sufficient answer to the allegation of Simplitius yet nevertheless with a new instance and solution founded upon an admirable experiment I will superabundantly satisfie him and confirm to Sagredus the mobility of the Earth I have told you that the Air and in particular that part of it which ascendeth not above the tops of the highest Mountains is carried round by the uneven parts of the Earths surface from whence it should seem that it must of consequence come to passe that in case the superficies of the Earth were not uneven but smooth and plain no cause would remain for drawing the Air along with it or at least for revolving it with so much uniformity Now the surface of this our Globe is not all craggy and rugged but there are exceeding great tracts very even to wit the surfaces of very vast Seas which being also far remote from the continuate ledges of Mountains which environ it seem to have no faculty of carrying the super-ambient Air along therewith and not carrying it about we may perceive what will of consequence ensue in those places SIMP I was about to propose the very same difficulty which I think is of great validity SALV You say very well Simplicius for from the not finding in the Air that which of consequence would follow did this our Globe move round you argue its immoveablenesse But in case that this which you think ought of necessary consequence to be found be indeed by experience proved to be so will you accept it for a sufficient testimony and an argument for the mobility of
the said Globe SIMP In this case it is not requisite to argue with me alone for if it should so fall out and that I could not comprehend the cause thereof yet haply it might be known by others SALV So that by playing with you a man shall never get but be alwayes on the losing hand and therefore it would be better to give over Nevertheless that we may not cheat our third man we will play on We said even now and with some addition we reitterate it that the Ayr as if it were a thin and fluid body and not solidly conjoyned with the Earth seem'd not to be necessitated to obey its motion unlesse so far as the cragginess of the terrestrial superficies transports and carries with it a part thereof contigious thereunto which doth not by any great space exceed the greatest altitude of Mountains the which portion of Air ought to be so much less repugnant to the terrestrial conversion by how much it is repleat with vapours fumes and exhalations matters all participating of terrene qualities and consequently apt of their own nature to the same motions But where there are wanting the causes of motion that is where the surface of the Globe hath great levels and where there is less mixture of the terrene vapours there the cause whereby the ambient Air is constrained to give entire obedience to the terrestrial conversion will cease in part so that in such places whilst the Earth revolveth towards the East there will be continually a wind perceived which will beat upon us blowing from the East towards the West and such gales will be the more sensible where the revolution of the Globe is most swift which will be in places more remote from the Poles and approaching to the greatest Circle of the diurnal conversion But now de facto experience much confirmeth this Phylosophical argumentation for in the spatious Seas and in their parts most remote from Land and situate under the Torrid Zone that is bounded by the Tropicks where there are none of those same terrestrial evaporations we finde a perpetual gale move from the East with so constant a blast that ships by favour thereof sail prosperously to the West-India's And from the same coasting along the Mexican shore they with the same felicity pass the Pacifick Ocean towards the India's which to us are East but to them are West Whereas on the contrary the Course from thence towards the East is difficult and uncertain and not to be made by the same Rhumb but must vere more to Land-ward to recover other Winds which we may call accidentary and tumultuary produced from other Principles as those that inhabit the continent find by experience Of which productions of Winds the Causes are many and different which shall not at this time be mentioned And these accidentary Winds are those which blow indifferently from all parts of the Earth and make rough the Seas remote from the Equinoctial and environed by the rugged Surface of the Earth which is as much as to say environ'd with those perturbations of Air that confound that primary Gale The which in case these accidental impediments were removed would be continually felt and especially upon the Sea Now see how the effect of the Water and Air seem wonderfully to accord with the Celestial observations to confirm the mobility of our Terrestrial Globe SAGR. I also for a final close will relate to you one particular which as I believe is unknown unto you and which likewise may serve to confirm the same conclusion You Salviatus alledged That Accident which Sailers meet with between the Tropicks I mean that perpetual Gale of Winde that beats upon them from the East of which I have an account from those that have many times made the Voyage And moreover which is very observable I understand that the Mariners do not call it a Wind but by another name which I do not now remember taken haply from its so fixed and constant Tenor which when they have met with they tie up their shrouds and other cordage belonging to the Sails and without any more need of touching them though they be in a sleep they can continue their course Now this constant Trade-wind was known to be such by its continual blowing without interruptions for if it were interrupted by other Windes it would not have been acknowledged for a singular Effect and different from the rest from which I will infer That it may be that also our Mediterranean Sea doth partake of the like accident but it is not observed as being frequently altered by the confluence of other windes And this I say not without good grounds yea upon very probable conjectures whch came unto my knowledge from that which tendred it self to my notice on occasion of the voyage that I made into Syria going Consul for this Nation to Aleppo and this it is That keeping a particular account and memorial of the dayes of the departure and arrival of the Ships in the Ports of Alexandria of Alexandretta and this of Venice in comparing sundry of them which I did for my curiosity I found that in exactness of account the returns hither that is the voiages from East to West along the Mediterrane are made in less time then the contrary courses by 25. in the Hundred So that we see that one with another the Eastern windes are stronger then the Western SALV I am very glad I know this particular which doth not a little make for the confirmation of the Earths mobility And although it may be alledged That all the Water of the Mediterrane runs perpetually towards the Straits-mouth as being to disimbogue into the Ocean the waters of as many Rivers as do discharge themselves into the same I do not think that that current can be so great as to be able of it self alone to make so notable a difference which is also manifest by observing that the water in the Pharo of Sicily runneth back again no less towards the East than it runneth forwards towards the West SAGR. I that have not as Simplicius an inclination to satisfie any one besides my self am satisfied with what hath been said as to this first particular Therefore Salviatus when you think it sit to proceed forward I am prepared to hear you SALV I shall do as you command me but yet I would fain hear the opinion also of Simplicius from whose judgement I can argue how much I may promise to my self touching these discourses from the Peripatetick Schools if ever they should come to their ears SIMP I desire not that my opinion should serve or stand for a measure whereby you should judge of others thoughts for as I have often said I am inconsiderable in these kinde of studies and such things may come into the mindes of those that are entered into the deepest passages of Philosophy as I could never think of as having according to the Proverb
many alterations for the more minute observations I remit them to be made by those that frequent several Seas and onely by way of a conclusion to this our conference I will propose to be considered how that the precise times of the fluxes and refluxes do not onely happen to be altered by the length of Straights and by the difference of depths but I believe that a notable alteration may also proceed from the comparing together of sundry tarcts of Sea different in greatness and in position or if you will inclination which difference happeneth exactly here in the Adriatick Gulph lesse by far than the rest of the Mediterrane and placed in so different an inclination that whereas that hath its bounds that incloseth it on the Eastern part as are the Coasts of Syria this is shut up in its more Westerly part and because the ebbings and flowings are much greater towards the extremities yea because the Seas risings and fallings are there onely greatest it may probably happen that the times of Flood at Venice may be the time of low Water in the other Sea which as being much greater and distended more directly from West to East cometh in a certain sort to have dominion over the Adriatick and therefore it would be no wonder in case the effects depending on the primary causes should not hold true in the times that they ought and that correspond to the periods in the Adriatick as it doth in the rest of the Mediterrane But these Particularities require long Observations which I neither have made as yet nor shall I ever be able to make the same for the future SAGR. You have in my opinion done enough in opening us the way to so lofty a speculation of which if you had given us no more than that first general Proposition that seemeth to me to admit of no reply where you declare very rationally that the Vessels containing the Sea-waters continuing stedfast it would be impossible according to the common course of Nature that those motions should follow in them which we see do follow and that on the other side granting the motions ascribed for other respects by Copernicus to the Terrestrial Globe these same alterations ought to ensue in the Seas if I say you had told us no more this alone in my judgment so far exceeds the vanities introduced by so many others that my meer looking on them makes me nauseate them and I very much admire that among men of sublime wit of which nevertheless there are not a few not one hath ever considered the incompatibility that is between the reciprocal motion of the Water contained and the immobility of the Vessel containing which contradiction seemeth to me now so manifest SALV It is more to be admired that it having come into the thoughts of some to refer the cause of the Tide to the motion of the Earth therein shewing a more than common apprehension they should in afterwards driving home the motion close with no side and all because they did not see that one simple and uniform motion as v. gr the sole diurnal motion of the Terrestrial Globe doth not suffice but that there is required an uneven motion one while accelerated and another while retarded for when the motion of the Vessels are uniforme the waters contained will habituate themselves thereto without ever making any alteration To say also as it is related of an ancient Mathematician that the motion of the Earth meeting with the motion of the Lunar Orb the concurrence of them occasioneth the Ebbing and Flowing is an absolute vanity not onely because it is not exprest nor seen how it should so happen but the falsity is obvious for that the Revolution of the Earth is not contrary to the motion of the Moon but is towards the same way So that all that hath been hitherto said and imagined by others is in my judgment altogether invalid But amongst all the famous men that have philosophated upon this admirable effect of Nature I more wonder at Kepler than any of the rest who being of a free and piercing wit and having the motion ascribed to the Earth before him hath for all that given his ear and assent to the Moons predominancy over the Water and to occult properties and such like trifles SAGR. I am of opinion that to these more spaculative persons the same happened that at present befalls me namely the not understanding the intricate commixtion of the three Periods Annual Monethly and Diurnal And how their causes should seem to depend on the Sun and on the Moon without the Suns or Moons having any thing to do with the Water a businesse for the full understanding of which I stand in need of a little longer time to consider thereof which the novelty and difficulty of it hath hitherto hindred me from doing but I despair not but that when I return in my solitude and silence to ruminate that which remaineth in my fancy not very well digested I shall make it my own We have now from these four dayes Discourse great attestations in favour of the Copernican Systeme amongst which these three taken the first from the Stations and Retrogradations of the Planets and from their approaches and recessions from the Earth the second from the Suns revolving in it self and from what is observed in its spots the third from the Ebbing and Flowing of the Sea do shew very rational and concluding SALV To which also haply in short one might adde a fourth and peradventure a fifth a fourth I say taken from the fixed stars seeing that in them upon exact observations those minute mutations appear that Copernicus thought to have been insensible There starts up at this instant a fifth novelty from which one may argue mobility in the Terrestrial Globe by means of that which the most Illustrious Signore Caesare of the noble Family of the Marsilii of Bologna and a Lyncean Academick discovereth with much ingenuity who in a very learned Tract of his sheweth very particularly how that he had observed a continual mutation though very slow in the Meridian line of which Treatise at length with amazement perused by me I hope he will communicate Copies to all those that are Students of Natures Wonders SAGR. This is not the first time that I have heard speak of the exquisite Learning of this Gentleman and of his shewing himself a zealous Patron of all the Learned and if this or any other of his Works shall come to appear in publique we may be aforehand assured that they will be received as things of great value SALV Now because it is time to put an end to our Discourses it remaineth that I intreat you that if at more leasure going over the things again that have been alledged you meet with any doubts or scruples not well resolved you will excuse my oversight as well for the novelty of the Notion as for the weaknesse of my wit as also
think a greater part should rather be imployed than a lesser 105 PRINCIPLES By denying Principles in Sciences any Paradox may be maintained 28 Contrary Principles cannot naturally reside in the same Subject 211 PROJECT c. The Project according to Aristotle is not moved by virtue impressed but by the Medium 130 Operation of the Medium in continuing the Motion of the Project 131 Many Experiments and Reasons against the Motions of Projects assigned by Aristotle 132 The Medium doth impede and not conferre the Motion of Projects 134 An admirable accident in the Motion of Projects 135 Sundry curious Problems touching the Motion of Projects 137 Projects continue their Motion by a Right Line that follows the direction of the Motion made together with the Projicient whilst they were conjoyned therewith 154 The Motion impressed by the Projicient is onely in a Right Line 170 The Project moveth by the Tangent of the Circle of the Motion preceeding in the instant of Seperation 172 A Grave Project assoon as it is seperated from the Projicient beginneth to decline 173 The Cause of the Projection encreaseth not according to the Proportion of Velocity encreased by making the Wheel bigger 189 The Virtue which carrieth Grave Projects upwards is no lesse Natural to them than the Gravity which moveth them downwards 211 PTOLOMY c. Inconveniences that are in the System of Ptolomy 309 Ptolomies System full of defects 476 The Learned both of elder and later times dissatisfied with the Ptolomaick System 477 PYTHAGORAS c. Pythagorick Mistery of Numbers fabulous 3 Pythagoras offered an Hecatombe for a Geometrical Demonstration which he found 38 Pythagoras and many other Ancients enumerated that held the Earths Mobility 437 468 R RAYS Shining Objects seem fringed and environed with adventitious Rays 304 REST. Rest. Vide Motion Rest the Infinite degree of Tardity 11 RETROGRADATIONS Retrogradations more frequent in Saturn lesse frequent in Jupiter and yet lesse in Mars and why 311 The Retrogradations of Venus and Mercury demonstrated by Apollonius and Copernicus 311 S SATURN Saturn for its slownesse and Mercury for its late appearing were amongst those that were last observed 416 SCARCITY Scarcity and Plenty enhanse and debase the price of all things 43 SCHEINER Christopher Scheiner the Jesuit his Book of Conclusions confuted 78 195 seq 323 A Canon Bullet would spend more than six dayes in falling from the Concave of the Moon to the Center of the Earth according to Scheiner 195 Christopher Scheiner his Book entituled Apelles post Tabulam censured and disproved 313 The Objections of Scheiner by way of Interrogation 336 Answers to the Interrogations of Scheiner 336 Questions put to Scheiner by which the weaknesse of his is made appear 336 SCIENCES In Natural Sciences the Art of Oratory is of no use 40 In Natural Sciences it is not necessary to seek Mathematical evidence 206 SCRIPTURE c. The Caution we are to use in determining the Sense of Scripture in difficult points of Phylosophy 427 Scripture studiously condescendeth to the apprehension of the Vulgar 432 In dicussing of Natural Questions we ought not to begin at Scripture but at Sensible Experiments and Necessary Demonstrations 433 The intent of Scripture is by its Authority to recommend those Truths to our beliefe which being un-intelligible could no other wayes be rendered credible 434 Scripture Authority to be preferred even in Natural Controversies to such Sciences as are not confined to a Demonstrative Method 434 The Pen-men of Scripture though read in Astronomy intentionally forbear to teach us any thing of the Nature of the Stars 435 The Spirit had no intent at the Writing of the Scripture to teach us whether the Earth moveth or standeth still as nothing concerning our Salvation 436 Inconveniencies that arise from licentious usurping of Scripture to stuffe out Books that treat of Nat. Arguments 438 The Literal Sense of Scripture joyned with the universal consent of the Fathers is to be received without farther dispute 444 A Text of Scripture ought no lesse diligently to be reconciled with a Demonstrated Proposition in Philosophy than with another Text of Scripture sounding to a contrary Sense 446 Demonstrated Truth ought to assist the Commentator in finding the true Sense of Scripture 446 It was necessary by way of condescension to Vulgar Capacities that the Scripture should speak of the Rest and Motion of the Sun and Earth in the same manner that it doth 447 Not onely the Incapacity of the Vulgar but the Current Opinion of those times made the Sacred Writers of the Scripture to accommodate themselves to Popular Esteem more than Truth 447 The Scripture had much more reason to affirm the Sun Moveable and the Earth Immoveable than otherwise 448 Circumspection of the Fathers about imposing positive Senses on Doubtful Texts of Scripture 451 T is Cowardice makes the Anti-Copernican fly to Scripture Authorities thinking thereby to affright their Adversaries 455 Scripture speaks in Vulgar and Common Points after the manner of Men. 462 The intent of Scripture is to be observed in Places that seem to affirme the Earths Stability 464 Scripture Authorities that seem to affirm the Motion of the Sun and Stability of the Earth divided into six Classes 478 Six Maximes to be observed in Expounding Dark Texts of Scripture 481 Scripture Texts speaking of things inconvenient to be understood in their Literal Sense are to be interpreted one of the four wayes named 81 Why the Sacred Scripture accommodates it self to the Sense of the Vulgar 487 SEA The Seas Surface would shew at a distance more obscure than the Land 49 The Seas Reflection of Light much weaker than that of the Earth 81 The Isles are tokens of the unevennesse of the Bottoms of Seas 383 SELEUCUS Opinion of Seleucus the Mathematician censured 422 SENSE He who denieth Sense deserves to be deprived of it 21 Sense sheweth that things Grave move ad Medium and the Light to the Concave 21 It is not probable that God who gave us our Senses would have us lay them aside and look for other Proofs for such Natural Points as Sense sets before our Eyes 434 Sense and Reason lesse certain than Faith 475 SILVER Silver burnished appears much more obscure than the unburnished and why 64 SIMPLICIUS Simplicius his Declamation 43 SOCRATES The Answer of the Oracle true in judging Socrates the Wisest of his time 85 SORITES The Forked Sylogisme called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 29 SPEAKING We cannot abstract our manner of Speaking from our Sense of Seeing 461 SPHERE The Motion of 24 hours ascribed to the Highest Sphere disorders the Period of the Inferiour 102 The Sphere although Material toucheth the Material Plane but in one point onely 182 The Definition of the Sphere 182 A Demonstration that the Sphere toucheth the Plane but in one point 183 Why the Sphere in abstract toucheth the Plane onely in one point and not the Material in Concrete 184 Contact in a Single Point is not
another conceipt thereof they would meet peradventure as many others that accord with it and haply would judge that the Holy Church doth very appositly teach That God placed the Sun in the Centre of Heaven and that thereupon by revolving it in it self after the manner of a Wheel He contributed the ordinary Courses to the Moon and other Erratick Stars whilst that she Sings Coeli Deus sanctissime Qui lucidum Centrum Poli Candore pingis igneo Augens decoro lumine Quarto die qui flammeam Solis rotam constituens Lunae ministras ordinem Vagosque cursus Syderum They might say that the Name of Firmament very well agreeth ad literam to the Starry Sphere and to all that which is above the Planetary Conversions which according to this Hypothesis is altogether firme and immoveable Ad litteram the Earth moving circularly they might understand its Poles where it 's said Nec dum Terram fecerat flumina Cardines Orbis Terrae Which Cardines or Hinges seem to be ascribed to the Earth in vain if it be not to turn upon them FINIS AN ABSTRACT OF THE Learned Treatise OF JOHANNIS KEPLERUS The Emperours Mathematician ENTITULED His Introduction upon MARS IT must be confessed that there are very many who are devoted to Holinesse that dissent from the Judgment of Copernicus fearing to give the Lye to the Holy Ghost speaking in the Scriptures if they should say that the Earth moveth and the Sun stands still But let such consider that since we judge of very many and those the most principal things by the Sense of Seeing it is impossible that we should alienate our Speech from this Sense of our Eyes Therefore many things daily occur of which we speak according to the Sense of Sight when as we certainly know that the things themselves are otherwise An Example whereof we have in that Verse of Virgil Provehimur portu Terraeque urbesque recedunt So when we come forth of the narrow straight of some Valley we say that a large Field discovereth it self So Christ to Peter Duc in altum Lanch forth into the Deep or on high as if the Sea were higher than its Shores For so it seemeth to the Eye but the Opticks shew the cause of this fallacy Yet Christ useth the most received Speech although it proceed from this delusion of the Eyes Thus we conceive of the Rising and Setting of the Stars that is to say of their Ascension and Descension when at the same time that we affirm the Sun riseth others say that it goeth down See my Optices Astronomiae cap. 10. fol. 327. So in like manner the Ptolomaicks affirm that the Planets stand still when for some dayes together they seem to be fixed although they believe them at that very time to be moved in a direct line either downwards to or upwards from the Earth Thus the Writers of all Nations use the word Solstitium and yet they deny that the Sun doth really stand still Likewise there will never any man be so devoted to Copernicus but he will say the Sun entereth into Cancer and Leo although he granteth that the Earth enters Capricorn or Aquarius And so in other cases of the like nature But now the Sacred Scriptures speaking to men of vulgar matters in which they were not intended to instruct men after the manner of men that so they might be understood by men do use such Expressions as are granted by all thereby to insinuate other things more Mysterious and Divine What wonder is it then if the Scripture speaks according to mans apprehension at such time when the Truth of things doth dissent from the Conception that all men whether Learned or Unlearned have of them Who knows not that it is a Poetical allusion Psal. 19. where whilst under the similitude of the Sun the Course of the Gospel as also the Peregrination of our Lord Christ in this World undertaken for our sakes is described The Sun is said to come forth of his Tabernacle of the Horizon as a Bridegroom out of his Chamber rejoycing as a Giant to run a Race Which Virgil thus imitates Tithono croceum linquens Aurora cubile For the first Poets were amongst the Jews The Psalmist knew that the Sun went not forth of the Horizon as out of its Tabernacle yet it seemeth to the Eye so to do Nor did he believe that the Sun moved for that it appeared to his sight so to do And yet he saith both for that both were so to his seeming Neither is it to be adjudged false in either Sense for the perception of the Eyes hath its verity fit for the more secret purpose of the Psalmist in shadowing forth the current passage of the Gospel as also the Peregrination of the Son of God Joshua likewise mentioneth the Vallies on or in which the Sun and Moon moved for that they appeared to him at Jordan so to do And yet both these Pen-men may obtain their ends David and with him Syracides the magnificence of God being made known which caused these things to be in this manner represented to sight or otherwise the mystical meaning by means of these Visibles being discerned And Joshua in that the Sun as to his Sense of Seeing staid a whole day in the midst of Heaven whereas at the same time to others it lay hid under the Earth But incogitant persons onely look upon the contrariety of the words The Sun stood still that is The Earth stood still not considering that this contradiction is confined within the limits of the Opticks and Astronomy For which cause it is not outwardly exposed to the notice and use of men Nor will they understand that the onely thing Joshuah prayed for was that the Mountains might not intercept the Sun from him which request he expressed in words that suited with his Ocular Sense Besides it had been very unseasonable at that time to think of Astronomy or the Errours in Sight for if any one should have told him that the Sun could not really move upon the Valley of Ajalon but onely in relation to Sense would not Joshuah have replyed that his desire was that the day might be prolonged so it were by any means whatsoever In like manner would he have answered if any one had started a question about the Suns Mobility and the Earths Motion But God easily understood by Joshuahs words what he asked for and by arresting the Earths Motion made the Sun in his apprehension seem to stand still For the summ of Joshuahs Prayer amounts to no more but this that it might thus appear to him let it in the mean time be what it would of it self For that it s so seeming was not in vain and ridiculous but accompanied with the desired effect But read the tenth Chap. of my Book that treats of the Optick part of Astronomy where thou shalt finde the Reasons why the Sun doth in this manner seem to all mens thinking to
Propositions far above the reach of common capacity runneth a great hazard of being very often condemned without further Process or knowledge of the Cause but yet for all that the truth is not to be deserted in most weighty affairs but ought rather to be explained in due place and time with all possible perspicuity that so being well understood and considered it may come afterwards for the Common good to be embraced This which I speak in general hath often been my fortune in very many particulars not onely when I have kept within the bounds of meer speculation but also when I have chanced to descend to Practice and to Operations and your Highness knoweth very well what befel me the last Summer 1641. when in obedience to your Soveraign Command I did in full Colledge represent my thoughts touching the state of the Lake of Venice for there not being such wanting who without so much as vouchsafing to understand me but having onely had an inkling and bad apprehension of my opinion fell furiously upon me and by violent means both with the Pen and Press full of Gall did abuse me in reward of the readiness that I had exprest to obey and serve them But I was above measure encouraged and pleased to see that those few who vouchsafed to hear me were all either thorowly perswaded that my opinion was well grounded or at least suspended their prudent verdict to more mature deliberation And though at the first bout I chanced to propose a thing that was totally contrary to the most received and antiquated opinion and to the resolutions and consulations taken above an hundred years ago Moved by these things and to satisfie also to the promise that I had made of tendering unto them what should farther offer it self unto me touching the same business I have resolved to present to the Throne of your Highness another Consideration of no less importance which perhaps at first sight will appear a stranger Paradox but yet brought to the Test and Touch-stone of experience it shall prove most clear and evident If it shall be accounted of so that it succeedeth to the benefit of your Highness I shall have obtained my desire and intent And if not I shall have satisfied my self and shall not have been wanting to the Obligation of your most faithful Servant and native subject That which I propounded in the Mouths pass touching the most important business of the Lake though it did onely expresly concern the point of the diversion of the Mouth of the Lake already made and put in execution yet it may be understood and applyed also to the diversion under debate to be made of the other five Rivers and of the Sile in particular Now touching this I had the fortune to offer an admirable accident that we meet with when we come to the effect which I verily believe will be an utter ruine to the Lake of Venice I say therefore that by diverting these five Rivers that remain although their water that they discharge for the present into the Lake is not all taken together 4 5 parts of what the Brent alone did carry yet neverthelesse the abatement of the water of the Lake which shall ensue upon this last diversion of four parts which was the whole water shall prove double to that which hath happened by the diversion of Brent onely although that the Brent alone carried five parts of that water of which the Rivers that are to be diverted carry four A wonder really great and altogether unlikely for the reducing all this Proposition to be understood is as if we should say that there being given us three Rivers of which the first dischargeth five parts the second three and the third one and that from the diversion of the first there did follow such a certain abatement or fall from the taking away of the second there ought to follow also so much more abatement And lastly from the withdrawing of the third the water ought to fall so much more which is wholly impossible And yet it is most certain and besides the demonstration that perswades me to it which I shall explain in due time I can set before your eyes such an experiment as is not to be denied by any one although obstinate and I will make it plainly seen and felt that by taking away only four parts of the five which shall have been taken away the abatement proveth double to the abatement ensuing upon the diverting first of the five onely which thing being true as most certainly it is it will give us to understand how pernicious this diversion of five Rivers is like to prove if it shall be put in execution By this little that I have hinted and the much that I could say let your Highnesse gather with what circumspection this businesse ought to be managed and with how great skill he ought to be furnished who would behave himself well in these difficult affairs I have not at this time explained the demonstration nor have I so much as propounded the way to make the Experiment that I am able to make in confirmation of what I have said that so by some one or others mis-apprehending the Demonstration and maiming the Experiment the truth may not happen to shine with lesse clarity than it doth when all mists of difficulty are removed and if so be no account should be made of the Reasons by me alledged and that men should shut their eyes against the Experiments that without cost or charge may be made I do declare and protest that there shall follow very great dammages to the Fields of the main Land and extraordinary summes shall be expended to no purpose The Lake undoubtedly will become almost dry and will prove impassible for Navigation with a manifest danger of corrupting the Air And in the last place there will unavoidably ensue the choaking and stoppage of the Ports of Venice Upon the 20th of December 1641. I imparted this my second Confideration to the most Excellent Signore Basadonna presenting him with a Copy thereof amongst other Writings which I have thought good to insert although they seem not to belong directly to our businesse of the Lake The way to examine the MUD and SAND that entereth and remaineth in the LAKE of VENICE To the most Excellent SIGNORE GIO. BASADONNA TWo very considerable Objections have been made against my opinion concerning the Lake of Venice One was that of which I have spoken at large in my first Consideration namely that the Brents having been taken out of the Lake cannot have been the occasion of the notable fall of the Waters in the Lake as I pretend and consequently that the turning Brent into the Lake would be no considerable remedy in regard that the water of Brent and the great expansion of the Lake over which the water of Brent is to diffuse and spread being considered it is found that the rise proveth insensible The second Objection was that the
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 invariablâ— 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