# Mathematical Collections and Translations, in Two Tomes/System of the World in Four Dialogues/Dialogue 3

GALILÆUS
Galilæus Lyncæus,
HIS
SYSTEME
OF THE
WORLD.
The Third Dialogue.
INTERLOCUTORS.
Salviatus, Sagredus, and Simplicius.
Sagr.
THe great desire wherewith I have expected your coming, that I might hear the novel conceits touching the annual conversion of this our Globe, hath made me think the houres of the last night, and those of this morning very tedious, although I spent them not idly, but lying awake I imployed a good part thereof in ruminating upon our yesterdayes discourses, weighing the reasons alledged by both parties, in favour of the two contrary Hypotheses, that of Aristotle and Ptolomy, and this of Aristarchus, and Copernicus. And really methinks, that which ever of these parties have been deceived, they are worthy of excuse, so specious and valid in appearance are the reasons that may have perswaded them either way; though neverthelesse we ​do for the most part close with those produced by the grave Authours first above mentioned. But albeit that the Peripatetick Hypothesis, by reason of its antiquity, hath had many followers and fautors, and the other very few; first, for its obscurity, and next, for its novelty, yet methinks I discover amongst those many, and particularly amongst the modernes some, who for the support of the opinion by them esteemed true, have introduced other reasons sufficiently childish, I could say ridiculous.
Salv.I have met with the like, and so much worse than yours,Some in arguing first fix in their minds the conclusion beleeved by them, and then adapt their reasons to that. that I blush to rehearse them, not so much to spare the fame of their Authours, the names of whom might be perpetually concealed, as because I am ashamed so much to stain the honour of mankinde. In observing of these men, I have found that some there are who preposterously reasoning, first stablish the conclusion in their fancy, and (either because it is their own, or else belongs to a person whom they much confide in) so firmly imprint it in their opinions, that it is altogether impossible ever wholly to efface it: and those reasons which they themselves stumble upon, or which they hear others to alledge in confirmation of the conceit entertained, though never so simple and insipid, instantly find credit and applause with them: but on the contrary, those which are brought against their opinion, though ingenuous and concluding, they receive not only with nauseating, but with disdain and bitter indignation, yea, you shall have one of these so inraged, as that he will not be backward to try all wayes to suppress and silence their adversaries: and of this I my self have had some experience.
Sagr.Indeed these men deduce not the conclusion from the premises, nor confirme them with reasons, but accomodate, or to say better, discommodate and distort the premises and arguments to make them speak in favour of their pre-assumed and pertinacious conclusions. It is not good therefore to contract familiarity with these men; and the rather, for that their conversation is not only unpleasant, but also dangerous. Yet let us continue our conference with Simplicius however, whom I have known this long while for a man of great ingenuity; and altogether void of malice: besides he is well verst in the Peripatetick Doctrine; so that I may assure my self, that what shall not fall within the reach of his reason for the support of the Aristotelian Hypothesis, will not easily be found out by others. But see yonder he comes, quite out of winde, whose company we have so long desired: we were just now speaking against the small hast you made to come to us.
Simpl.You must not blame me, but Neptune, for this my long stay; which in the ebbe of this mornings tide hath in a manner drain'd away the waters, for the Gondola that brought me, being entered not far from hence into a certain Channel, wanting depth, ​where I was stranded, and forced to stay there more than a full hour, in expecting the return of the tide: and there waiting in this manner, without being able to get out of the boat, which on a sudden ran a ground,The motion of the water in ebbing and flowing not interrupted by rest. I observed a certain accident, which to me seemed very strange; and it was this, that in the waters ebbing I saw it retreat very fast by several small rivolets, the ouze being in many places discovered, and whilst I stood looking upon this effect, I saw this motion in an instant to cease, and without a minutes interval the same water to begin to return back again, and the tide from ebbing to become young flood, without standing still a moment: an effect that as long as I have dwelt in Venice, I never took notice of before.
Sagr.It is very much, that you should be left thus on ground, amongst small Channels; in which rivolets, as having very little declivity, the rising or falling of the main sea, the thickness onely of a paper is sufficient to make the water to ebbe and flow for good long spaces of time: like as in some creeks of the Sea, its flowing four or six * yards onely, maketh the water to overflow the adjacent Marshes for some hundreds and thousands of ** Pertiche venetiani. acres.
Simpl.This I know very well, but I should have thought, that between the ultimate terme of ebbing, and the first beginnng to flow, there should have interposed some considerable interval of rest.
Sagr.This will appear unto you, if you cast your eye upon the bank or piles, where these mutations are made perpendicularly, but not that there is any real time of cessation.
Simpl.I did think, that because these two motions were contrary, there ought to be in the midst between them some kind of rest; conformable to the Doctrine of Aristotle, which demonstrates that in puncto regressus mediat quies.
Sagr.I very well remember this place: but I bear in minde also, that when I read Philosophy, I was not thorowly satisfied with Aristotles demonstration; but that I had many experiments on the contrary, which I could still rehearse unto you, but I am unwilling to sally out into any other digressions, we being met here to discourse of the proposed mattes, if it be possible, without these excursions wherewith we have interrupted our disputes in those dayes that are past.
Simpl.And yet we may with convenience, if not-interrupt them, at least prolong them very much, for returning yesterday home, I set my self to read the Tractate of Conclusions, where I find Demonstrations against this annual motion ascribed to the Earth, very solid; and because I would not trust my memory with the punctual relation of them, I have brought back the Book along with me.
​Sagr.You have done very well; but if we would re-assume our Disputations according to yesterdayes appointment, it is requisite that we first hear what account Salviatus hath to give us of the Book, De stellis novis, and then without interruption we may proceed to the Annual motion. Now what say you, Salviatus touching those stars? Are they really pull'd down from Heaven to these lower regions, by vertue of that Authours calculations, whom Simplicius mentioneth?
Salv.I set my self last night to peruse his proceedings, and I have this morning had another view of him, to see whether that which he seemed over night to affirm, were really his sense, or my dreams and phantastical nocturnal imaginations; and in the close found to my great grief that those things were really written and printed, which for the reputation-sake of this Philosopher I was unwilling to believe. It is in my judgment impossible, but that he should perceive the vanity of his undertaking, aswell because it is too apert, as because I remember, that I have heard him mentioned with applause by the Academick our Friend: it seemeth to me also to be a thing very unlikely, that in complacency to others, he should be induced to set so low a value upon his reputation, as to give consent to the publication of a work, for which he could expect no other than the censure of the Learned.
Sagr.Yea, but you know, that those will be much fewer than one for an hundred, compared to those that shall celebrate and extoll him above the greatest wits that are, or ever have been in the world: He is one that hath mentioned the Peripatetick inalterability of Heaven against a troop of Astronomers, and that to their greater disgrace hath foiled them at their own weapons: and what do you think four or five in a Countrey that discern his triflings, can do against the innumerable multitude, that, not being able to discover or comprehend them, suffer themselves to be taken with words, and so much more applaud him, by how much the lesse they understand him? You may adde also, that those few who understand, scorn to give an answer to papers so trivial and unconcludent; and that upon very good reasons, because to the intelligent there is no need thereof, and to those that do not understand, it is but labour lost.
Salv.The most deserved punishment of their demerits would certainly be silence, if there were not other reasons, for which it is haply no lesse than necessary to resent their timerity: one of which is, that we Italians thereby incur the censure of Illiterates, and attract the laughter of Forreigners; and especially to such who are separated from our Religion; and I could shew you many of those of no small eminency, who scoff at our Academick, and the many Mathematicians that are in Italic, for suffering the ​follies of such a ** Lorenzini. Fabler against Astronomers to come into the light, and to be openly maintained without contradiction; but this also might be dispensed with, in respect of the other greater occasions of laughter, wherewith we may confront them depending on the dissimulation of the intelligent, touching the follies of these opponents of the Doctrines that they well enough understand.
Sagr.I desire not a greater proof of those mens petulancy, and the infelicity of a Copernican, subject to be opposed by such as understand not so much as the very first positions, upon which he undertakes the quarrel.
Salv.You will be no lesse astonished at their method in confuting the Astronomers, who affirm the new Stars to be superiour to the Orbs of the Planets; and peradventure in the †† He taketh the Firmament for the Starry Sphere, and as we vulgarly receive the word. Firmament it self.
Sagr.But how could you in so short a time examine all this Book, which is so great a Volume, and must needs contain very many demonstrations?
Salv.I have confined my self to these his first confutations, in which with twelve demonstrations founded upon the observations of twelve Astronomers, (who all held, that the Star, Anno 1572. which appeared in Cassiopeia, was in the Firmament) he proveth it on the contrary, to be beneath the Moon, conferring, two by two, the meridian altitudes, proceeding in the method that you shall understand by and by. And because, I think, that in the examination of this his first progression, I have discovered in this Authour a great unlikelihood of his ability to conclude any thing against the Astronomers, in favour of the Peripatetick Philosophers, and that their opinion is more and more concludently confirmed, I could not apply my self with the like patience in examining his other methods, but have given a very slight glance upon them, and am certain, that the defect that is in these first impugnations, is likewise in the rest. And as you shall see, by experience, very few words will suffice to confute this whole Book, though compiled with so great a number of laborious calculations,The method observed by Clar. in confuting the Astronomers, and by Salviatus in confuting him. as here you see. Therefore observe my proceedings. This Authour undertaketh, as I say, to wound his adversaries with their own weapons, i.e. a great number of observations made by themselves, to wit, by twelve or thirteen Authours in number, and upon part of them he makes his supputations, and concludeth those stars to have been below the Moon. Now because the proceeding by interrogatories very much pleaseth me, in regard the Authour himself is not here, let Simplicius answer me to the questions that I shall ask him, as he thinks he himself would, if he were present. And presupposing that we speak of the foresaid Star, of Anno 1572. ap​pearing in Cassiopeia, tell me, Simplicius, whether you believe that it might be in the same time placed in divers places, that is, amongst the Elements, aud also amongst the planetary Orbs, and also above these amongst the fixed Stars, and yet again infinitely more high.
Simpl.There is no doubt, but that it ought to be confessed that it is but in one only place, and at one sole and determinate distance from the Earth.
Salv.Therefore if the observations made by the Astronomers were exact, and the calculations made by this Author were not erroneous, it were easie from all those and all these to recollect the same distances alwayes to an hair, is not this true?
Simpl.My reason hitherto tells me that so it must needs be; nor do I believe that the Author would contradict it.
Salv.But when of many and many computations that have been made, there should not be so much as two onely that prove true, what would you think of them?
Simpl.I would think that they were all false, either through the fault of the computist, or through the defect of the observators, and at the most that could be said, I would say, that but onely one of them and no more was true; but as yet I know not which to choose.
Salv.Would you then from false fundamentals deduce and establish a doubtful conclusion for true? Certainly no. Now the calculations of this Author are such, that no one of them agrees with another, you may see then what credit is to be given to them.
Simpl.Indeed, if it be so, this is a notable failing.
Sagr.But by the way I have a mind to help Simplicius, and the Author by telling Salviatus, that his arguments would hold good if the Author had undertook to go about to find out exactly the distance of the Star from the Earth, which I do not think to be his intention; but onely to demonstrate that from those observations he collected that the Star was sublunary. So that if from those observations, and from all the computations made thereon, the height of the Star be alwayes collected to be lesse than that of the Moon, it serves the Authors turn to convince all those Astronomers of most impardonable ignorance, that through the defect either of Geometry or Arithmetick, have not known how to draw true conclusions from their own observations themselves.
Salv.It will be convenient therefore that I turn my self to you, Sagredus, who so cunningly aphold the Doctrine of this Author. And to see whether I can make Simplicius, though not very expert in calculations, and demonstrations to apprehend the ​inconclusivenesse at least of the demonstrations of this Author, first proposed to consideration, and how both he, and all the Astronomers with whom he contendeth, do agree that the new Star had not any motion of its own, and onely went round with the diurnal motion of the primum mobile; but dissent about the placing of it, the one party putting it in the Celestial Region, that is above the Moon, and haply above the fixed Stars, and the other judging it to be neer to the Earth, that is, under the concave of the Lunar Orb. And because the situation of the new star, of which we speak, was towards the North, and at no very great distance from the Pole, so that to us Septentrionals, it did never set, it was an easie matter with Astronomical instruments to have taken its several meridian altitudes, as well its smallest under the Pole, as its greatest above the same; from the comparing of which altitudes, made in several places of the Earth, situate at different distances from the North, that is, different from one another in relation to polar altitudes, the stars distance might be inferred:The greatest and least elevations of the new star differ not from each other more than the polar altitudes, the said star being in the Firmnment. For if it was in the Firmament amongst the other fixed stars, its meridian altitudes taken in divers elevations of the pole, ought necessarily to differ from each other with the same variations that are found amongst those elevations themselves; that is, for example, if the elevation of the star above the horizon was 30 degrees, taken in the place where the polar altitude was v. gr. 45 degrees, the elevation of the same star ought to have been encreased 4 or 5 degrees in those more Northernly places where the pole was higher by the said 4 or 5 degrees. But if the stars distance from the Earth was but very little, in comparison of that of the Firmament; its meridian altitudes ought approaching to the North to encrease considerably more than the polar altitudes; and by that greater encrease, that is, by the excesse of the encrease of the stars elevation, above the encrease of the polar elevation (which is called the difference of Parallaxes) is readily calculated with a cleer and sure method, the stars distance from the centre of the Earth. Now this Author taketh the observations made by thirteen Astronomers in sundry elevations of the pole, and conferring a part of them at his pleasure, he computeth by twelve collations the new stars height to have been alwayes beneath the Moon; but this he adventures to do in hopes to find so grosse ignorance in all those, into whose hands his book might come, that to speak the truth, it hath turn'd my stomack; and I wait to see how those other Astronomers, and particularly Kepler, against whom this Author principally inveigheth, can contein themselves in silence, for he doth not use to hold his tongue on such occasions; unlesse he did possibly think the enterprize too much below him. Now to give you to ​understand the same, I have upon this paper transcribed the conclusions that he inferreth from his twelve indagations; the first of which is upon the two observations:
These are twelve indagations made by the Author at his election, amongst many which, as he saith, might be made by combining the observations of these thirteen observators. The which twelve we may believe to be the most favourable to prove his intention.
Sagr.I would know whether amongst the so many other indagations pretermitted by the Author, there were not some that made against him, that is, from which calculating one might find the new star to have been above the Moon, as at the very first sight I think we may reasonably question; in regard I see these already produced to be so different from one another, that some of them give me the distance of the said star from the Earth, 4, 6, 10, 100, a thousand, and an hundred thousand times bigger one than another; so that I may well suspect that amongst those that he did not calculate, there was some one in fauour of the adverse party. And I guesse this to be the more probable, for that I cannot conceive that those Astronomers the observators could want the knowledg and practice of rhese computations, which I think do not depend upon the abstrucest things in the World. And indeed it will seem to me a thing more than miraculous, if whilst in these twelve investigations onely, there are some that make the star to be distant from the Earth but a few miles, and others that make it to be but a very fmall matter below the Moon, there are none to be found that in favour of the contrary part do make it so much as twenty yards above the Lunar Orb. And that which shall be yet again more extravagant, that all those Astronomers should have been so blind as not to have discovered that their so apparent mistake.
Salv.Begin now to prepare your ears to hear with infinite admiration to what excesses of confidence of ones own authority and others folly, the desire of contradicting and shewing ones self wiser than others, transports a man. Amongst the indagations omitted by the Author, there are such to be found as make the new star not onely above the Moon, but above the fixed stars also. And these are not a few, but the greater part, as you shall see in this other paper, where I have set them down.
Sagr.But what saith the Author to these? It may be he did not think of them?
Salv.He hath thought of them but too much: but saith, that the observations upon which the calculations make the star to be infinitely remote, are erroneous, and that they cannot be combined to one another.
​Simpl.But this seemeth to me a very lame evasion; for the adverse party may with as much reason reply, that those are erroneous wherewith he collecteth the star to have been in the Elementary Region.
Salv.Oh Simplicius, if I could but make you comprehend the craft, though no great craftinesse of this Author, I should make you to wonder, and also to be angry to see how that he palliating his sagacity with the vail of the simplicity of your self; and the rest of meer Philosophers, would insinuate himself into your good opinion, by tickling your ears, and swelling your ambition, pretending to have convinced and silenced these petty Astronomers, who went about to assault the impregnable inalterability of the Peripatetick Heaven, and which is more, to have foild and conquered them with their own arms. I will try with all my ability to do the same; and in the mean time let Sagredus take it in good part, if Simplicius and I try his patience, perhaps a little too much, whilst that with a superfluous circumlocution (superfluous I say to his most nimble apprehension) I go about to make out a thing, which it is not convenient should be hid and unknown unto him.
Sagr.I shall not onely without wearinesse, but also with much delight hearken to your discourses; and so ought all Peripatetick Philosophers, to the end they may know how much they are oblieged to this their Protector.
Salv.Tell me, Simplicius, whether you do well comprehend, how, the new star being placed in the meridian circle yonder towards the North, the same to one that from the South should go towards the North, would seem to rise higher and higher above the Horizon, as much as the Pole, although it should have been scituate amongst the fixed stars; but, that in case it were considerably lower, that is nearer to the Earth, it would appear to ascend more than the said pole, and still more by how much its vicinity was greater?
Simpl.I think that I do very well conceive the same; in token whereof I will try if I can make a mathematical Scheme of it, and in this great circle [in Fig. 1. of this Dialogue.] I will marke the pole P; and in these two lower circles I will note two stars beheld from one place on the Earth, which let be A; and let the two stars be these B and C, beheld in the same line ABC, which line I prolong till it meet with a fixed star in D. And then walking along the Earth, till I come to the term E, the two stars will appear to me separated from the fixed star D, and advanced neerer to the pole P, and the lower star B more, which will appear to me in G, and the star C lesse, which will appear to me in F, but the fixed star D will have kept the same distance from the Pole.
​Salv.I see that you understand the businesse very well. I believe that you do likewise comprehend, that, in regard the star B is lower than C, the angle which is made by the rayes of the sight, which departing from the two places A and E, meet in C, to wit, this angle ACE, is more narrow, or if we will say more acute than the angle constituted in B, by the rayes AB and EB.
Simpl.This I likewise understand very well.
Salv.And also, the Earth beine very little and almost insensible, in respect of the Firmament (or Starry Sphere;) and consequently the space AE, paced on the Earth, being very small in comparison of the immense length of the lines EG and EF, passing from the Earth unto the Firmament, you thereby collect that the star C might rise and ascend so much and so much above the Earth, that the angle therein made by the rayes which depart from the said stationary points A and E, might become most acute, and as it were absolutely null and insensible.
Simpl.And this also is most manifest to sense.
Salv.Now you know Simplicius that Astronomers and Mathematicians have found infallible rules by way of Geometry and Arithmetick, to be able by help of the quantity of these angles B and C, and of their differences, with the additional knowledg of the distance of the two places A and E, to find to a foot the remotenesse of sublime bodies; provided alwayes that the aforesaid distance, and angles be exactly taken.
Simpl.So that if the Rules dependent on Geometry and Astronomy be true, all the fallacies and errours that might be met with in attempting to investigate those altitudes of new Stars or Comets, or other things must of necessity depend on the distance AE, and on the angles B and C, not well measured. And thus all those differences which are found in these twelve workings depend, not on the defects of the rules of the Calculations, but on the errours committed in finding out those angles, and those distances, by means of the Instrumental Observations.
Salv.True; and of this there is no doubt to be made. Now it is necessary that you observe intensely, how in removing the Star from B to C, whereupon the angle alwayes grows more acute, the ray EBG goeth farther and farther off from the ray ABD in the part beneath the angle, as you may see in the line ECF, whose inferiour part EC is more remote from the part AC, than is the part EB, but it can never happen, that by any whatsoever immense recession, the lines AD and EF should totally sever from each other, they being finally to go and conjoyn in the Star: and onely this may be said, that they would separate, and reduce themselves to parallels, if so be the recession should be infinite, which ​case is not to be supposed. But because (observe well) the distance of the Firmament, in relation to the smallnesse of the Earth, as hath been said, is to be accounted, as if it were infinite; therefore the angle conteined betwixt the two rayes, that being drawn from the points A and E, go to determine in a fixed Star, is esteemed nothing, and those rayes held to be two parallel lines; and therefore it is concluded, that then only may the New Star be affirmed to have been in the Firmament, when from the collating of the Observations made in divers places, the said angle is, by calculation, gathered to be insensible, and the lines, as it were, parallels. But if the angle be of a considerable quantity, the New Star must of necessity be lower than those fixed; and also than the Moon, in case the angle ABE should be greater than that which would be made in the Moons centre.
Simpl.Then the remotenesse of the Moon is not so great, that a like angle should be ** Imperceptible. insensible in her?
Salv.No Sir; nay it is sensible, not onely in the Moon, but in the Sun also.
Simpl.But if this be so, it's possible that the said angle may be observed in the New Star, without necessitating it to be inferiour to the Sun, aswell as to the Moon.
Salv.This may very well be, yea, and is in the present case, as you shall see in due place; that is, when I shall have made plain the way, in such manner that you also, though not very perfect in Astronomical calculations, may clearly see, and, as it were, with your hands feel how that this Author had it more in his eye to write in complacency of the Peripateticks, by palliating and dissembling sundry things, than to establish the truth, by producing them with naked sincerity: therefore let us proceed forwards. By the things hitherto spoken, I suppose that you comprehend very well how that the distance of the new Star can never be made so immense, that the angle so often named shall wholly disappear, and that the two rayes of the Observators at the places A and E, shall become altogether parallels: and you may consequently comprehend to the full, that if the calculations should collect from the observations, that that angle was totally null, or that the lines were truly parallels, we should be certain that the observations were at least in some small particular erroneous: But, if the calculations should give us the said lines to be separated not only to equidistance, that is, so as to be parallel, but to have past beyond that terme, and to be dilated more above than below, then must it be resolutely concluded, that the observations were made with lesse accuratenesse, and in a word, to be erroneous; as leading us to a manifest impossibility. In the next place, you must believe me, and suppose it for true, that two right lines ​which depart from two points marked upon another right line, are then wider above than below, when the angles included between them upon that right line are greater than two right angles; and if these angles should be equal to two right angles, the lines would be parallels; but if they were less than two right angles, the lines would be concurrent, and being continued out would undoubtedly intersect the triangle.
Simpl.Without taking it upon trust from you, I know the same; and am not so very naked of Geometry, as not to know a Proposition, which I have had occasion of reading very often in Aristotle, that is, that the three angles of all triangles are equall to two right angles: so that if I take in my Figure the triangle ABE, it being supposed that the line EA is right; I very well conceive, that its three angles A, E, B, are equal to two right angles; and that consequently the two angles E and A are lesse than two right angles, so much as is the angle B. Whereupon widening the lines AB and EB (still keeping them from moving out of the points A and E) untill that the angle conteined by them towards the parts B, disappear, the two angles beneath shall be equal to two right angles, and those lines shall be reduced to parallels: and if one should proceed to enlarge them yet more, the angles at the points E and A would become greater than two right angles.
Salv.You are an Archimedes, and have freed me from the expence of more words in declaring to you, that whensoever the calculations make the two angles A and E to be greater than two right angles, the observations without more adoe will prove erroneous. This is that which I had a desire that you should perfectly understand, and which I doubted that I was not able so to make out, as that a meer Peripatetick Philosopher might attain to the certain knowledg thereof. Now let us go on to what remains. And re-assuming that which even now you granted me, namely, that the new star could not possibly be in many places, but in one alone, when ever the supputations made upon the observations of these Astronomers do not assign it the same place, its necessary that it be an errour in the observations, that is, either in taking the altitudes of the pole, or in taking the elevations of the star, or in the one or other working. Now for that in the many workings made with the combinations two by two, there are very few of the observations that do agree to place the star in the same situation; therefore these few onely may happily be the non-erroneous, but the others are all absolutely false.
Sagr.It will be necessary then to give more credit to these few alone, than to all the rest together, and because you say, that these which accord are very few, and I amongst these 12, do find two that so accord, which both make the distance of the ​star from the centre of the Earth 4 semidiameters, which are these, the fifth and sixth, therefore it is more probable that the new star was elementary, than celestial.
Salv.You mistake the point; for if you note well it was not written, that the distance was exactly 4 semidiameters, but about 4 semidiameters; and yet you shall see that those two distances differed from each other many hundreds of miles. Here they are; you see that this fifth, which is 13389 Italian miles, exceeds the sixth, which is 13100 miles, by almost 300 miles.
Sagr.Which then are those few that agree in placing the star in the same situation?
Salv.They are, to the disgrace of this Author five workings, which all place it in the firmament, as you shall see in this note, where I have set down many other combinations. But I will grant the Author more than peradventure he would demand of me, which is in sum, that in each combination of the observations there is some error; which I believe to be absolutely necessary; for the observations being four in number that serve for one working, that is, two different altitudes of the Pole, and two different elevations of the star, made by different observers, in different places, Astronomical Instruments are very subject to errour. with different instruments, who ever hath any small knowledg of this art, will say, that amongst all the four, it is impossible but there will be some error; and especially since we see that in taking but one onely altitude of the Pole, with the same instrument, in the same place, by the same observer, that hath repeated the observation a thousand times, there will still be a titubation of one, or sometimes of many minutes, as in this same book you may see in several places. These things presupposed, I ask you Simplicius whether you believe that this Authour held these thirteen observators for wise, understanding and expert men in using those instruments, or else for inexpert, and bunglers?
Simpl.It must needs be that he esteemed them very acute and intelligent; for if he had thought them unskilful in the businesse, he might have omitted his sixth book as inconclusive, as being founded upon suppositions very erroneous; and might take us for excessively simple, if he should think he could with their inexpertnesse perswade us to believe a false position of his for truth.
Salv.Therefore these observators being such, and that yet notwithstanding they did erre, and so consequently needed correction, that so one might from their observations infer the best hints that may be; it is convenient that we apply unto them the least and neerest emendations and corrections that may be; so that they do but suffice to reduce the observations from impossibility to possibility; so as v. gr. if one may but correct a manifest errour, and an apparent impossibility of one of their obser​vations by the addition or substraction of two or three minutes, and with that amendment to reduce it to possibility, a man ought not to essay to adjust it by the addition or substraction of fifteen, twenty, or fifty.
Simpl.I think the Author would not deny this: for granting that they are expert and judicious men, it ought to be thought that they did rather erre little than much.
Salv.Observe again; The places where the new Star is placed, are some of them manifestly impossible, and others possible. Absolutely impossible it is, that it should be an infinite space superiour to the fixed Stars, for there is no such place in the world; and if there were, the Star there scituate would have been imperceptible to us: it is also impossible that it should go creeping along the superficies of the Earth; and much lesse that it should be within the said Terrestrial Globe. Places possible are these that be in controversie, it not interferring with our understanding, that a visible object in the likenesse of a Star might be aswell above the Moon, as below it. Now whilst one goeth about to compute by the way of Observations and Calculations made with the utmost certainty that humane diligence can attain unto what its place was, it is found that the greatest part of those Calculations make it more than infinitely superiour to the Firmament, others make it very neer to the surface of the Earth, and some also under the same; and of the rest, which place it in situations not impossible, none of them agree with each other; insomuch that it must be confessed, hat all those observations are necessarily false; so that if we would nevertheless collect some fruit from so many laborious calculations, we must have recourse to the corrections, amending all the observations.
Simpl.But the Authour will say, that of the observations that assign to the Star impossible places, there ought no account to be made, as being extreamly erroneous and false; and those onely ought to be accepted, that constitute it in places not impossible: and amongst these a man ought to seek, by help of the most probable, and most numerous concurrences, not if the particular and exact situation, that is, its true distance from the centre of the Earth, at least, whether it was amongst the Elements, or else amongst the Cœlestial bodies.
Salv.The discourse which you now make, is the self same that the Author made, in favour of his cause, but with too unreasonable a disadvantage to his adversaries; and this is that principal point that hath made me excessively to wonder at the too great confidence that he expressed to have, no less of his own authority, than of the blindness and inadvertency of the Astronomers; in favour of whom I will speak, and you shall answer for the Author. ​And first, I ask you, whether the Astronomers, in observing with their Instruments, and seeking v. gr. how great the elevation of a Star is above the Horizon, may deviate from the truth, aswell in making it too great, as too little; that is, may erroneously compute, that it is sometime higher than the truth, and sometimes lower; or else whether the errour must needs be alwayes of one kinde, to wit, that erring they alwayes make it too much, and never too little, or alwayes too little, and never too much?
Simpl.I doubt not, but that it is as easie to commit an errour the one way, as the other.
Salv.I believe the Author would answer the same. Now of these two kinds of errours, which are contraries, and into which the observators of the new star may equally have fallen, applied to calculations, one sort will make the star higher, and the other lower than really it is. And because we have already agreed, that all the observations are false; upon what ground would this Author have us to accept those for most congruous with the truth, that shew the star to have been near at hand, than the others that shew it excessively remote?
Simpl.By what I have, as yet, collected of the Authors mind, I see not that he doth refuse those observations, and indagations that might make the star more remote than the Moon, and also than the Sun, but only those that make it remote (as you your self have said) more than an infinite distance; the which distance, because you also do refuse it as impossible, he also passeth over, as being convicted of infinite falshood; as also those observations are of impossibility. Methinks, therefore, that if you would convince the Author, you ought to produce supputations, more exact, or more in number, or of more diligent observers, which constitute the star in such and such a distance above the Moon, or above the Sun, and to be brief, in a place possible for it to be in, like as he produceth these twelve, which all place the star beneath the Moon in places that have a being in the world, and where it is possible for it to be.
Salv.But Simplicius yours and the Authors Equivocation lyeth in this, yours in one respect, and the Authors in another; I discover by your speech that you have formed a conceit to your self, that the exorbitancies that are commited in the establishing the distance of the Star do encrease successively, according to the proportion of the errors that are made by the Instrument, in taking the observations, and that by conversion, from the greatness of the exorbitancies, may be argued the greatnesse of the error; and that thereforefore hearing it to be infered from such an observation, that the distance of the star is infinite, it is necessary, that the errour in observing was infinite, and therefore not to be amend​ed, and as such to be refused; but the businesse doth not succeed in that manner, my Simplicius, and I excuse you for not having comprehended the matter as it is, in regard of your small experience in such affairs; but yet cannot I under that cloak palliate the error of the Author, who dissembling the knowledge of this which he did perswade himself that we in good earnest did not understand, hath hoped to make use of our ignorance, to gain the better credit to his Doctrine, among the multitude of illiterate men. Therefore for an advertisement to those who are more credulous then intelligent, and to recover you from error, know that its possible (and that for the most part it will come to passe) that an observation, that giveth you the star v. gr. at the distance of Saturn, by the adition or substraction of but one sole minute from the elevation taken with the instrument, shall make it to become infinitely distant; and therefore of possible, impossible, and by conversion, those calculations which being grounded upon those observations, make the star infinitely remote, may possibly oftentimes with the addition or subduction of one sole minute, reduce it to a possible scituation: and this which I say of a minute, may also happen in the correction of half a minute, a sixth part, and less. Now fix it well in your mind, that in the highest distances, that is v. g. the height of Saturn, or that of the fixed Stars, very small errors made by the Observator, with the instrument, render the scituation determinate and possible, infinite & impossible. This doth not so evene in the sublunary distances, and near the earth, where it may happen that the observation by which the Star is collected to be remote v. g. 4. Semidiameters terrestrial, may encrease or diminish, not onely one minute but ten, and an hundred, and many more, without being rendred by the calculation either infinitely remote, or so much as superior to the Moon. You may hence comprehend that the greatnesse of the error (to so speak) instrumental, are not to be valued by the event of the calculation, but by the quantity it self of degrees and minutes numbred upon the instrument, and these observations are to be called more just or less erroneous, which with the addition or substraction of fewer minutes, restore the star to a possible situation; and amongst the possible places, the true one may be believed to have been that, about which a greater number of distances concurre upon calculating the more exact observations.
Simpl.I do not very well apprehend this which you say: nor can I of my self conceive how it can be, that in greater distances, greater exorbitancies can arise from the errour of one minute only, than in the smaller from ten or an hundred; and therefore would gladly understand the same.
Salv.You shall see it, if not Theorically, yet at least Practi​cally, by this short assumption, that I have made of all the combinations, and of part of the workings pretermitted by the Author, which I have calculated upon this same paper.
Sagr.You must then from yesterday, till now, which yet is not above eighteen hours, have done nothing but compute, without taking either food or sleep.
Salv.I have refreshed my self both those wayes; but truth is, make these supputations with great brevity; and, if I may speak the truth, I have much admired, that this Author goeth so farre about, and introduceth so many computations no wise necessary to the question in dispute. And for a full knowledge of this, and also to the end it may soon be seen, how that from the observations of the Astronomers, whereof this Author makes use, it is more probably gathered, that the new star might have been above the Moon, and also above all the Planets, yea amongst the fixed stars, and yet higher still than they, I have transcribed upon this paper all the observations set down by the said Authour, which were made by thirteen Astronomers, wherein are noted the Polar altitude, and the altitudes of the star in the meridian, aswell the lesser under the Pole, as the greater and higher, and they are these.
Tycho. gr. m.
Altitude of the Pole 55 58
Altitude of the Star 84 00 the greatest.
27 57 the least.
And these are, according to the first paper: but according to the second, the greatest is— 27 45
gr. m. sec.
Altitude of the Pole 48 22
Altitude of the Star 76 34
76 33 45
76 35
20 09 40
20 09 30
20 09 20
​Peucerus and Sculerus. Landgravius.
gr. m. gr. m.
Altitude of the pole 51 54 Altitude of the pole 51 18
Altitude of the Star 79 56 Altitude of the Star 79 30
23 33
Camerarius.
gr. m.
Altitude of the pole 52 24
Altitude of the Star 80 30
80 27
80 26
24 28
24 20
24 17
Hagecius Maurolycus.
gr. m. gr. m.
Altitude of the pole 48 22 Altitude of the pole 38 30
Altitude of the Star 20 15 Altitude of the Star 62 00
gr. m. gr. m.
Altitude of the pole 39 30 Altitude of the pole 49 24
Altitude of the star 67 30 Altitude of the star 79 00
11 30 22 00
Reinholdus. Buchius.
gr. m. gr. m.
Altitude of the pole 51 18 Altitude of the pole 51 10
Altitude of the star 79 30 Altitude of the star 79 20
23 02 22 40
Gemma.
gr. m.
Altitude of the pole 50 50
Altitude of the star 79 45
Simpl.Perhaps he doth this to finde with such small measures, and with their fractions the distance of the Star terminated to three or four inches; for we that do not understand your rules of Arithmetick, are stupified in hearing your conclusions; as for instance, whilst we read; Therefore the new Star or Comet was distant from the Earths centre three hundred seventy and three thousand eight hundred and seven miles; and moreover, two hundred and eleven, four thousand ninety sevenths 373807 ⁠211/4097⁠, and upon these precise punctualities, wherein you take notice of such small matters, we do conceive it to be impossible, that you, who in our calculations keep an account of an inch, can at the close deceive us so much as an hundred miles.
Salv.This your reason and excuse would passe for currant, if in a distance of thousands of miles, a yard over or under were of any great moment, and if the suppositions that we take for true, were so certain, as that they could assure us of producing an indubitable truth in the conclusion; but here you see in the twelve workings of the Author, the distances of the Star, which from them one may conclude to have been different from each other, (and therefore wide of the truth) for many hundreds and thousands of miles: now whilst that I am more than certain, that that which I seek must needs differ from the truth by hundreds of miles, to what purppse is it to be so curious in our calculations, for fear of missing the quantity of an inch? But let us proceed, at last, to the working, which I resolve in this manner. Tycho, as may be ​seen in that same note observed the star in the polar altitude of 55 degrees and 58 mi. pri. And the polar altitude of the Landgrave was 51 degrees and 18 mi. pri. The altitude of the star in the Meridian taken by Tycho was 27 degrees 45 mi. pri. The Landgrave found its altitude 23 degrees 3 mi. pri. The which altitudes are these noted here, as you see.
gr. m. gr. m. Tycho. Pole 55 58 * 27 45 Landgr. Pole 51 18 * 23 3
This done, substract the lesse from the greater, and there remains these differences here underneath.
gr. m.
4 40
4 42 Parall. 2
Where the difference of the poles altitudes 4 gr. 4 mi. pr. is lesse than the difference of the altitudes of the Star 4 gr. 42 mi. pr. and therefore we have the difference of parallaxes, 0 gr. 2 mi. pri. These things being found, take the Authours own figure [Fig. 2.] in which the point B is the station of the Landgrave, D the station of Tycho, C the place of the star, A the centre of the Earth, ABE the vertical line of the Landgrave, ADF
of Tycho, and the angle BCD the difference of Parallaxes. And ​because the angle BAD, conteined between the vertical lines, is equal to the difference of the Polar altitudes, it shall be 4gr. 40m. which I note here apart; and I finde the chord of it by the Table of Arches and Chords, and set it down neer unto it, which is 8142 parts, of which the semidiameter AB is 100000. Next, I finde the angle BDC with ease, for the half of the angle BAD, which is 2gr. 20 m. added to a right angle, giveth the angle BDF 92gr. 20 m. to which adding the angle CDF, which is the distance from the vertical point of the greatest altitude of the Star, which here is 62 gr. 15 m. it giveth us the quantity of the angle BDC, 154 grad. 45 min. the which I set down together with its Sine, taken out of the Table, which is 42657, and under this I note the angle of the Parallax BCD 0 gr. 2 m. with its Sine 58. And because in the Triangle BCD, the side DB is to the side BC; as the sine of the opposite angle BCD, to the sine of the opposite angle BDC: therefore, if the line BD were 58. BC would be 42657. And because the Chord DB is 8142. of those parts whereof the semidiameter BA is 100000. and we seek to know how many of those parts is BC; therefore we will say, by the Golden Rule, if when BD is 58. BG is 42657. in case the said DB were 8142. how much would BC be? I multiply the second term by the third, and the product is 347313294. which ought to be divided by the first, namely, by 58. and the quotient shall be the number of the parts of the line BC, whereof the semidiameter AB is 100000. And to know how many semidiameters BA, the said line BC doth contein, it will be necessary anew to divide the said quotient so found by 100000. and we shall have the number of semidiameters conteined in BC. Now the number 347313294. divided by 58. giveth 5988160⁠1/4⁠. as here you may see.
And this divided by 100000. the product is 59 ⁠88160/100000⁠
1|00000|59|88160.
And this way also there will come forth 59 ⁠5113294/5800000⁠
And so many semidiameters are contained in the line BC, to which one being added for the line AB, we shall have little lesse than 61. semidiameters for the two lines ABC; and therefore the right distance from the centre A, to the Star C, shall be more than 60. semidiameters, and therefore it is superiour to the Moon, according to Ptolomy, more than 27. semidiameters, and according to Copernicus, more than 8. supposing that the distance of the Moon from the centre of the Earth by Copernicus his account is what the Author maketh it, 52 semidiameters. With this same working, I find by the observations of Camerarius, and of Munosius, that the Star was situate in that same distance, to wit, somewhat more than 60. semidiameters. These are the observations, and these following next after them the calculations.
​The next working is made upon two observations of Tycho, and of Munosius, from which the Star is calculated to be distant from the Centre of the Earth 478 Semidiameters and more.
The Golden Rule.
These workings following make the Star remote from the Centre, more than 358 Semidiameters.
The Golden Rule.
From this other working the star is found to be distant from the centre more than 716. semidiameters.
The Golden Rule.
These as you see are five workings which place the star very much above the Moon. And here I desire you to consider upon that particular, which even now I told you, namely, that in great ​distances, the mutations, or if you please corrections, of a very few minutes, removeth the star a very great way farther off. As for example, in the first of these workings, where the calculation made the star 60. semidiameters remote from the centre, with the Parallax of 2. minutes; he that would maintain that it was in the Firmament, is to correct in the observations but onely two minutes, nay lesse, for then the Parallax ceaseth, or becommeth so small, that it removeth the star to an immense distance, which by all is received to be the Firmament. In the second indagation, or working, the correction of lesse than 4 m. prim. doth the same. In the third, and fourth, like as in the first, two minutes onely mount the star even above the Firmament. In the last preceding, a quarter of a minute, that is 15. seconds, gives us the same. But it doth not so occur in the sublunary altitudes; for if you fancy to your self what distance you most like, and go about to correct the workings made by the Authour, and adjust them so as that they all answer in the same determinate distance, you will find how much greater corrections they do require.
Sagr.It cannot but help us in our fuller understanding of things, to see some examples of this which you speak of.
Salv.Do you assign any whatsoever determinate sublunary distance at pleasure in which to constitute the star, for with small ado we may assertain our selves whether corrections like to these, which we see do suffice to reduce it amongst the fixed stars, will reduce it to the place by you assigned.
Sagr.To take a distance that may favour the Authour, we will suppose it to be that which is the greatest of all those found by him in his 12 workings; for whilst it is in controversie between him and Astronomers, and that they affirm the star to have been superiour to the Moon, and he that it was inferiour, very small space that he proveth it to have been lower, giveth him the victory.
Salv.Let us therefore take the seventh working wrought upon the observations of Tycho and Thaddæus Hagecius, by which the Authour found the star to have been distant from the centre 32. semidiameters, which situation is most favourable to his purpose; and to give him all advantages, let us moreover place it in the distance most disfavouring the Astronomers, which is to situate it above the Firmament. That therefore being supposed, let us seek in the next place what corrections it would be necessary to apply to his other 11 workings. And let us begin at the first calculated upon the observations of Hainzelius and Mauroice; in which the Authour findeth the distance from the centre about 3. semidiameters with the Parallax of 4 gr. 42 m. 30. sec. Let ​us see whether by withdrawing it 20. minutes onely, it will rise to the height of 32. semidiameters: See the short and true operation. Multiply the sine of the angle BDC, by the sine of the
chord BD, and divide the product, the five last figures being cut off by the sine of the Parallax, and the quotient will be 28. semidiameters, and an half, so that though you make a correction of 4 gr. 22 min. 30 sec. taken from 4 gr. 42 min. 30 sec. it shall not elevate the star to the altitude of 32. semidiameters, which correction for Simplicius his understanding it, is of 262. minutes, and an half.
In the second operation made upon the observations of Hainzelius, and Sculerus, with the Parallax of 0 gr. 8 min. 30 sec. the star is found in the height of 25. semidiameters or thereabouts, as may be seen in the subsequent working.
* 979870
* 61660
* 5879220
* 58792200
* 97987000
* 5879220000
* 24000000
* 247|6041|87842
* 1103000000
* 110000000
And bringing back the Parallax 0 gr. 8 m. 30 sec. to 7 gr. 7 m. whose sine is 204, the star elevateth to 30 semidiameters or thereabouts; therefore the correction of 0 gr. 1 mi. 30 sec. doth not suffice.
* 20000000
* 204|6041|87342
* 1965000000
* 12000000
Now let us see what correction is requisite for the third working made upon the observations of Hainzelius and Tycho, which rendereth the star about 19 semidiameters high, with the Parallax of 10 m. pri. The usual angles and their sines, and chord found by the Authour, are these next following; and they remove the star (as also in the Authours working) 19 semidiameters from the centre of the Earth. It is necessary therefore for the raising of it, to diminish the Parallax according to the Rule which he likewise observeth in the ninth working. Let us therefore suppose the Parallax to be 6 m. prim. whose sine is 175, and the division being made, there is found likewise lesse than 31 semidiameters for the stars distance. And therefore the correction of 4 min. prim. is too little to serve the Authours purpose.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BAD | 007036 | Chord | 132540 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | 195052 | Sine | 40886 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD | 000010 | Sine | 291 |
* 1325400000000
* 4088600000000
* —————000000
* 7952400000000
* 106032000000000
* 106032000000000
* 530160000000000
* ———————000000
* 1800000000030
* 291|5419|03044|175|5419
* 25000000000016
* 1810000000000
Let us come to the fourth working, and the rest with the same rule, and with the chords and sines found out by the Authour himself; in this the Parallax is 14 m. prim. and the height found lesse than 10 semidiameters, and diminishing the Parallax from 14 min. to 4 min. yet neverthelesse you see that the star doth not elevate full 31 semidiameters. Therefore 10 min. in 14 min. doth not suffice.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BAD | Chord | 8142 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | Sine | 43235 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD | | 407 |
* 43235000
* 8142000
* —————00
* 86470000
* 1729400000
* 4323500000
* 345880000000
* ———————00
* 3000000
* 116|3520|19370
* 4000000
In the fifth operation of the Authour we have the sines and the chord as you see, and the Parallax is 0 gr. 42 m. 30 sec. which rendereth the height of the star about 4 semidiameters, and correcting the Parallax, with reducing it from 0 gr. 42 m. 30 sec. to 0 gr. 5 m. onely, doth not suffice to raise it to so much as 28 semidiameters, the correction therefore of 0 gr. 37 m. 30 sec. is too little.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BAD | Chord | 4034 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | Sine | 97998 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD | | 1236 |
* 9799800
* 403400
* 39199200
* 293994000
* 39199200000
* 27|000000
* 145|3953|239320
* 1058|000000
* 3|0000000
In the sixth operation the chord, the sines and Parallax are as followeth, and the star is found to be about 4. semidiameters; let us see whether it will be reduced, abating the Parallax from 8 m. to 1 m. onely; Here is the operation, and the star raised but to 27. semidiameters or thereabout; therefore the correction of 7 m. in 8 m. doth not suffice.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BD | Chord | 1920 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | Sine | 40248 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD 8gr. | Sine | 233 |
* 40248|00
* 1920|00
* 804960|00
* 362232|0000
* 40248|00000
* 26|0000000
* 29|772|7616000
* 198|0000000
* 1|00000000
In the eighth operation the chord, the sines, and the Parallax, as you see, are these ensuing, and hence the Authour calculates the height of the star to be 1. semidiameter and an half, with the Parallax of 43. min. which reduced to 1 min. yet notwithstanding giveth the star lesse remote than 24. semidiameters, the correction therefore of 42. min. is not enough.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BD | Chord | 1804 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | Sine | 36643 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD | Sine | 29 |
Let us now see the ninth. Here is the chord, the sines and the Parallax which is 15 m. From whence the Authour calculates the distance of the star from the superficies of the Earth to be lesse than a ** Here the Latine version is erroneous, making it a fortieth part of, &c. seven and fortieth part of a semidiameter, but this is an errour in the calculation, for it cometh forth truly, as we shall see here below, more than a fifth: See here the quotient is ⁠20/436⁠, which is more than one fifth.
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BD | Chord | 232 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BDC | Sine | 39046 |
| Angles | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$ | BCD | Sine | 436 |
That which the Authour presently after subjoyns in way of amending the observations, that is, that it sufficeth not to reduce the difference of Parallax, neither to a minute, nor yet to the eighth part of a minute is true. But I say, that neither will the tenth part of a minute reduce the height of the star to 32. semidiameters; for the sine of the tenth part of a minute, that is of six seconds, is 3; by which if we according to our Rule should divide 90. or we may say, if we should divide 9058672. by 300000. the quotient will be 30 ⁠58672/100000⁠, that is little more than 30. semidiameters and an half.
The tenth giveth the altitude of the star one fifth of a semidiameter, with these angles, sines, and Parallax, that is, 4 gr. ​30 m. which I see that being reduced from 4 gr. 30 min. to 2 min. yet neverthelesse it elevates not the star to 29. semidiameters.
| BD | | Chord | 1746 |
| BDC | | Sine | 92050 |
| BCD | 4 gr. 30 m. | Sine | 7846 |
The eleventh rendereth the star to the Authour remote about 13. semidiameters, with the Parallax of 55. min. let us see, reducing it to 20 min. whether it will exalt the star: See here the calculation elevates it to little lesse than 33. semidiameters, the correction therefore is little lesse than 35. min. in 55. min.
| BD | | Chord | 19748 |
| BDC | | Sine | 96166 |
| BCD | 0 gr. 55 m. | Sine | 1600 |
The twelfth with the Parallax of 1. gr. 36. min. maketh the star lesse high than 6. semidiameters, reducing the Parallax to 20 min. it carrieth the star to lesse than 30. semidiameters distance, therefore the correction of 1 gr. 16. min. sufficeth not.
| BD | | Chord | 17258 |
| BDC | | Sine | 96150 |
| BCD | 1 gr. 36 m. | Sine | 2792 |
These are the Corrections of the Parallaxes of the ten workings of the Author, to reduce the Star to the altitude of 32 Semidiameters. gr. m. sec. gr. m. sec. 04 22 30 in 04 42 30 00 04 00 in 00 10 00 00 10 00 in 00 14 00 00 37 00 in 00 42 30 00 07 00 in 00 18 00 00 42 00 in 00 43 00 00 14 50 in 00 15 00 04 28 00 in 04 30 00 00 35 00 in 00 55 00 01 16 00 in 01 36 00
From hence we see, that to reduce the Star to 32. Semidiameters in altitude, it is requisite from the sum of the Parallaxes 836. to subtract 756. and to reduce them to 80. nor yet doth that correction suffice.
​Here we see also, (as I have noted even now) that should the Authour consent to assign the distance of 32. Semidiameters for the true height of the Star, the correction of those his 10. workings, (I say 10. because the second being very high, is reduced to the height of 32. Semidiameters, with 2. minutes correction) to make them all to restore the said Star to that distance, would require such a reduction of Parallaxes, that amongst the whole number of substractions they should make more than 756 m. pr. whereas in the 5. calculated by me, which do place the Star above the Moon, to correct them in such sort, as to constitute it in the Firmament, the correction onely of 10. minutes, and one fourth sufficeth.
Now adde to these, other 5. workings, that place the Star precisely in the Firmament, without need of any correction at all, and we shall have ten workings or indagations that agree to place it in the Firmament, with the correction onely of 5. of them (as hath been seen) but 10. m. and 15 sec. Whereas for the correction of those 10. of the Authour, to reduce them to the altitude of 32. semidiameters, there will need the emendations of 756 minutes in 836. that is, there must from the summe 836 be substracted 756. if you would have the Star elevated to the altitude of 32. semidiameters, and yet that correction doth not fully serve.
The workings that immediately without any correction free the Star from Parallaxes, and therefore place it in the Firmament, and that also in the remotest parts of it, and in a word, as high as the Pole it self, are these 5. noted here.
Of the remaining combinations that might be made of the Observations of all these Astronomers, those that make the Stars sublime to an infinite distance, are many in number, namely, about 30. more than those who give the Star, by calculation, to be below the Moon; and because (as it was agreed upon between us) it is to be believed that the Observators have erred rather little than much, it is a manifest thing that the corrections to be applied to the Observaations, which make the star of an infinite altitude, to reduce it lower, do sooner, and with lesser amendment place it in the Firmament, than beneath the Moon; so that all these applaud the opinion of those who put it amongst the fixed Stars. You may adde, that the corrections required for those emendations, are much lesser than those, by which the Star from an unlikely proximity may be removed to the height more favourable for this Authour, as by the foregoing examples hath been seen; amongst which impossible proximities, there are three that seem to remove the Star from the Earths centre, a lesse distance than one Semidiameter, making it, as it were, to turn round under ground, and these are those combinations, wherein the Polar altitude of one of the Observators being greater than the Polar altitude of the other, the elevation of the Star taken by the first, is lesser than the elation of the Star taken by the latter.
The first of these is this of the Landgrave with Gemma, where the Polar altitude of the Landgrave 51 gr. 18 min. is greater than the Polar altitude of Gemma, which is 50 gr. 50 m. But the altitude of the Star of the Landgrave 79 gr. 30 min. is lesser than that of the Star, of Gemma 79 gr. 45 min.
The other two are these below. gr. m. gr. m. Buschius. Polar Altitude 51 10 Altit. of the Star 79 20 Gemma. 50 50 79 45 Reinholdus. Polar Altitude 51 18 Altit. of the Star 79 30 Gemma. 50 50 79 45
From what I have hitherto demonstrated, you may guesse how much this first way of finding out the distance of the Star, and proving it sublunary introduced by the Authour, maketh against himself, and how much more probably and clearly the distance thereof is collected to have been amongst the more remote fixed Stars.
Simpl.As to this particular, I think that the inefficacy of the Authors demonstrations is very plainly discovered; But I see that all this was comprised in but a few leaves of his Book, and it may be, that some other of his Arguments are more conclusive then these first.
Salv.Rather they must needs be lesse valid, if we will take those that lead the way for a proof of the rest: For (as it is clear) the uncertainty and inconclusivenesse of those, is manifestly observed to derive it self from the errours committed in the instrumental observations, upon which the Polar Altitude, and height of the Star was thought to have been justly taken, all in effect having easily erred; And yet to find the Altitude of the Pole, Astronomers have had Ages of time to apply themselves to it, at their leasure: and the Meridian Altitudes of the Star are easier to be observed, as being most terminate, and yielding the Observator some time to continue the same, in regard they change not sensibly, in a short time, as those do that are remote from the Meridian. And if this be so, as it is most certain, what credit shall we give to Calculations founded upon Observations more numerous, more difficult to be wrought, more momentary in variation, and we may add, with Instruments more incommodious and erroneous? Upon a slight perusal of the ensuing demonstrations, I see that the Computations are made upon Altitudes of the Star taken in different Vertical Circles, which are called by the Arabick name, Azimuths; in which observations moveable instruments are made use of, not only in the Vertical Circles, but in the Horizon also, at the same time; insomuch that it is requisite in the same moment that the altitude is taken, to have observed, in the Horizon, the distance of the Vir​tical point in which the Star is, from the Meridian; Moreover, after a considerable interval of time, the operation must be repeated, and exact account kept of the time that passed, trusting either to Dials, or to other observations of the Stars. Such an Olio of Observations doth he set before you, comparing them with such another made by another observer in another place with another different instrument, and at another time; and from this the Authour seeks to collect what would have been, the Elevations of the Star, and Horizontal Latitudes happened in the time and hour of the other first observations, and upon such a coæquation he in the end grounds his account. Now I refer it to you, what credit is to be given to that which is deduced from such like workings. Moreover, I doubt not in the least, but that if any one would torture himself with such tedious computations, he would find, as in those aforegoing, that there were more that would favour the adverse party, than the Authour: But I think it not worth the while to take so much pains in a thing, which is not, amongst those primary ones, by us understood.
Sagr.I am of your Opinion in this particular: But this businesse being environed with so many intricacies, uncertainties, and errours, upon what confidence have so many Astronomers positively pronounced the new Star to have been so high?
Salv.Upon two sorts of observations most plain, most easie, and most certain; one only of which is more than sufficient to assure us, that it was scituate in the Firmament, or at least by a great distance superiour to the Moon. One of which is taken from the equality, or little differing inequality of its distances from the Pole, aswell whilst it was in the lowest part of the Meridian, as when it was in the uppermost: The other is its having perpetually kept the same distances from certain of the fixed Stars, adjacent to it, and particularly from the eleventh of Cassiopea, no more remote from it than one degree and an half; from which two particulars is undoubtedly inferred, either the absolute want of Parallax, or such a smalnesse thereof, that it doth assure us with very expeditious Calculations of its great distance from the Earth.
Sagr.But these things, were they not known to this Author? and if he saw them, what doth he say unto them?
Salv.We are wont to say, of one that having no reply that is able to cover his fault, produceth frivolous excuses, cerca di attaccarsi alle funi del cielo, [He strives to take hold of the Cords of Heaven;] but this Authour runs, not to the Cords, but to the Spiders Web of Heaven; as you shall plainly see in our examination of these two particulars even now hinted. And first, that which sheweth us the Polar distances of the Observators one by one, I have noted down in these brief Calculations; For a full under​standing of which, I ought first to advertise you, that when ever the new Star, or other Phænomenon is near to the earth, turning with a Diurnal motion about the Pole, it will seem to be farther off from the said Pole, whilst it is in the lower part of the Meridian, then whilst it is above, as in this Figure [being fig. third of this Dial.] may be seen. In which the point T. denotes the centre of the Earth; O. the place of the Observator; the Arch VPC the Firmament; P. the Pole. The Phænomenon, [or appearance] moving along the Circle FS. is seen one while under the Pole by the Ray OFC. and another while above, according to the Ray OSD. so that the places seen in the Firmament are D. and C. but the true places in respect of the Centre T, are B, and A, equidistant from the Pole. Where it is manifest that the apparent place of the Phænomenon S, that is the point D, is nearer to the Pole than the other apparent place C, seen along the Line or Ray OFC, which is the first thing to be noted. In the second place you must note that the exces of the apparent inferiour distance from the Pole, over and above the apparent superiour distance from the said Pole, is greater than the Inferiour Parallax of the Phænomenon, that is, I say, that the excesse of the Arch CP, (the apparent inferior distance) over and above the Arch PD, (the apparent superior distance) is greater then the Arch CA, (that is the inferiour Paralax.) Which is easily proved; for the Arch CP. more exceedeth PD, then PB; PB, being bigger than PD, but PB. is equal to PA, and the excesse of CP, above PA, is the arch, CA, therefore the excesse of the arch CP above the arch PD, is greater than the arch CA, which is the parallax of the Phænomenon placed in F, which was to be demonstrated. And to give all advantages to the Author, let us suppose that the parallax of the star in F, is the whole excesse of the arch CP (that is of the inferiour distance from the pole) above the arch PD (the inferiour distance.) I proceed in the next place to examine that which the observations of all Astronomers cited by the Authour giveth us, amongst which, there is not one that maketh not against himself and his purpose. And let us begin with these of Buschius, who findeth the stars distance from the pole, when it was superiour, to be 28 gr. 10 m. and the inferiour to be 28 gr. 30 m. so that the excesse is 0 gr. 20 m. which let us take (in favour of the Author) as if it all were the parallax of the star in F, that is the angle TFO. Then the distance from the Vertex [or Zenith] that is the arch CV, is 67 gr. 20 m. These two things being found, prolong the line CO, and from it let fall the perpendicular TI, and let us consider the triangle TOI, of which the angle I is right angle, and the angle IOT known, as being vertical to the angle VOC, the distance of the star from the Vertex, Moreover in the triangle ​TIF, which is also rectangular, there is known the angle F, taken by the parallax. Then note in some place apart the two angles IOT and IFT, and of them take the sines, which are here set down to them, as you seen. And because in the triangle IOT, the sine TI is 92276. of those parts, whereof the whole sine TO is 100000; and moreover in the triangle IFT, the sine TI is 582. of those parts, whereof the whole sine TF is 100000, to find how many TF is of those parts, whereof TO is 100000; we will say by the Rule of three: If TI be 582. TF is an 100000. but if T I were 92276. how much would T F be. Let us multiply 92276. by 100000. and the product will be 9227600000. and this must be divided by 582. and the quotient will be 15854982. and so many shall there be in TF of those parts, of which there are in TO an 100000. So that if it were required to know how many lines TO, are in TF, we would divide 15854982 by 100000. and there will come forth 158. and very near an half; and so many diameters shall be the distance of the star F, from the centre T, and to abreviate the operation, we seeing, that the product of the multiplication of 92276. by 100000, ought to be divided first by 582, and then the quotient of that division by 100000. we may without multiplying 92276. by 100000. and with one onely division of the sine 92276. by the sine 582. soon obtain the same solution, as may be seen there below; where 92276. divided by 582. giveth us the said 158 1/2, or thereabouts. Let us bear in mind therefore, that the onely division of the sine TI, as the sine of the angle TOI by the sine TI, as the sine of the angle IFT, giveth us the distance sought TF, in so many diameters TO.
​See next that which the observations of Peucerus giveth us, in which the inferiour distance from the Pole is 28 gr. 21 m. and the superiour 28 gr. 2 m. the difference 0 gr. 19 m. and the distance from the vertical point 66 gr. 27 m. from which particulars is gathered the stars distance from the centre almost 166 semediameters.
Here take what Tycho his observation holdeth forth to us, interpreted with greatest favour to the adversary; to wit, the inferiour distance from the pole is 28 gr. 13 m. and the superiour 28 gr. 2 m. omitting the difference which is 0 gr. 11 m. as if all were one Parallax; the distance from the vertical point 62 gr. 15 m. Behold here below the operation, and the distance of the star from the centre found to be 976 ⁠9/16⁠ semidiameters.
The observation of Reinholdus, which is the next ensuing, giveth us the distance of the Star from the Centre 793. Semidiameters.
​From the following observation of the Landgrave, the distance of the Star from the Centre is made to be 1057, Semidiameters.
Two of the most favourable observations for the Authour being taken from Camerarius, the distance of the Star from the Centre is found to be 3143 Semidiameters.
The Observation of Munosius giveth no Parallax, and therefore rendreth the new Star amongst the highest of the fixed. That of Hainzelius makes it infinitely remote, but with the correction of an half min. prim. placeth it amongst the fixed Stars. And the same is collected from Vrsinus, with the correction of 12. min. prim. The other Astronomers have not give us the distance above and below the Pole, so that nothing can be concluded from them. By this time you see, that all the observations of all these men conspire against the Author, in placing the Star in the Heavenly and highest Regions.
Sagr.But what defence hath he for himself against so manifest contradictions?
Salv.He betakes himself to one of those weak threads which I speak of; saying that the Parallaxes come to be lessened by means of the refractions, which opperating contrarily sublimate the Phænomenon, whereas the Parallaxes abase it. Now of what little stead this lamentable refuge is, judge by this, that in case that effect of the refractions were of such an efficacy, as that which not long time since some Astronomers have introduced, the most that they could work touching the elevating a Phæuomenon above the Horizon ​more than truth, when it is before hand 23. or 24. Degrees high, would be the lessening its Parallax about 3. minutes, the which abatement is too small to pull down the Star below the Moon, and in some cases is lesse than the advantage given him by us in admitting that the excesse of the inferiour distance from the Pole above the Superiour, is all Parallax, the which advantage is far more clear and palpable than the effect of Refracton, of the greatnesse of which I stand in doubt, and not without reason. But besides, I demand of the Author, whether he thinks that those Astronomers, of whose observations he maketh use, had knowledge of these effects of Refractions, and considered the same, or no; if they did know and consider them, it is reasonable to think that the, kept account of them in assigning the true Elevation of the Star, making in those degrees of Attitude discovered with the Instruments, such abatements as were convenient on the account of the alterations made by the Refractions; insomuch that the distances by them delivered, were in the end those corrected and exact, and not the apparent and false ones. But if he think that those Authors made no reflection upon the said Refractions, it must be confessed, that they had in like manner erred in determining all those things which cannot be perfectly adjusted without allowance for the Refractions; amongst which things one is the precise investigation of the Polar Altitudes, which are commonly taken from the two Meridian Altitudes of some of the fixed Stars that are constantly visible, which Altitudes will come to be altered by Refraction in the same manner, just as those of the new Star; so that the Polar Altitude that is deduced from them, will prove to be defective, and to partake of the self same want which this Author assigns to the Altitudes ascribed to the new Star, to wit, both that and these will be with equal falshood placed higher than really they are. But any such errour, as far as concerns our present businesse, doth no prejudce at all: For we not needing to know any more, but onely the difference between the two distances of the new Star from the Pole at such time as it was inferiour and superiour, it is evident that such distances would be the same, taking the alteration of Refraction commonly for the Star and for the Pole, or for them when commonly amended. The Authors Argument would indeed have had some strength, though very small, if he had assured us that the Altitude of the Pole had been once precisely assigned, and corrected from the errour depending on refraction, from which again the Astronomers had not kept themselves in assigning the altitudes of the new Star; but he hath not ascertained us of that, nor perhaps could he have done, nor haply, (and this is more probable) was that caution wanting in the Observators.
Sagr.This argument is in my judgment sufficiently answer​ed; therefore tell me how he dis-ingageth himself in the next place from that particular of the Stars having constantly kept the same distance from the fixed Stars circumjacent to it.
Salv.He betakes himself, in like manner, to two threads, yet more unable to uphold him than the former: one of which is likewise fastened to refraction, but so much less firmly, in that he saith, that refraction operating upon the new Star, and sublimating it higher than its true situation, maketh the seeming distances untain to be distinguished from the true, when compared to the circumposed fixed Stars that environ it. Nor can I sufficiently admire how he can dissemble his knowing how that the same refraction will work alike upon the new Star, as upon the antient one its neighbour, elevating both equally, so as that such a like accident altereth not the space betwixt them. His other subterfuge is yet more unhappy, and carryeth with it much of ridiculous, it being founded upon the errour that may arise in the instrumental operation it self; whilst that the Observator not being able to constitute the centre of the eyes pupil in the centre of the Sextant (an Instrument imployed in observing the distance between two Stars) but holding it elevated above that centre, as much as the said pupil is distant from I know not what bone of the cheek, against which the end of the Instrument resteth, there is formed in the eye an angle more acute than that which is made by the sides of the Instrument; which angle of rayes differeth also from it self, at such time as a man looketh upon Stars, not much elevated above the Horizon, and the same being afterwards placed at a great height; that angle, saith he, is made different, while the Instrument goeth ascending, the head standing still: but if in mounting the Instrument, the neck should bend backwards, and the head go rising, together with the Instrument, the angle would then continue the same. So that the Authours answer supposeth that the Observators in using the Instrument have not raised the head, as they ought to have done; a thing which hath nothing of likelihood in it. But granting that so it had been, I leave you to judge what difference can be between two acute angles of two equicrural triangles, the sides of one of which triangles are each four [Italian] Braces [i.e. about three English yards] and those of the other, four braces within the quantity of the diameter of a Pea; for the differences cannot be absolutely greater between the length of the two visive rayes, whilst the line is drawn perpendicularly from the centre of the pupil, upon the plain of the Rule of the Sextant (which line is no bigger than the breath of the thumb) and the length of the same rayes, whilst elevating the Sextant, without raising the head together with it, that same line no longer falleth perpendicularly upon the said plane, but inclineth, making ​the angle towards the circumference something acute. But wholly to free this Authour from these unhappy lies, let him know, (in regard it appears that he is not very skilful in the use of Astronomicall Instruments) that in the sides of the Sextant or Quadrant there are placed two ** Traguardi. Sights, one in the centre, and the other at the other at the opposite end, which are raised an inch or more above the plane of the Rule; and through the tops of those sights the ray of the eye is made to passe, which eye likewise is held an hands breadth or two, or it may be more, from the Instrument; so that neither the pupil, nor any bone of the cheek, nor of the whole body toucheth or stayeth it self upon the Instrument, nor much lesse is the Instrument upheld or mounted in the armes, especially if it be one of those great ones, as is usual, which weighing tens, hundreds, and also thousands of pounds, are placed upon very strong feet or frames: so that the whole objection vanisheth. These are the subterfuges of this Authour, which, though they were all of steel, would not secure him the hundredth part of a minute; and with these he conceits to make us believe, that he hath compensated that difference, which importeth more than an hundred minutes; I mean, that of the not observing a notable difference in the distances between one of the fixed stars, and the new star in in any of their circulations; which, had it been neer to the Moon, it ought to have been very conspicuous to the meer sight, without any Instrument, especially comparing it with the eleventh of Cassiopeia, its neighbour, within 1 gr. 30 m. which ought to have varied from it more than two diameters of the moon, as the more intelligent Astronomers of those times do well note.
Sagr.Methinks I see that unfortunate Husbandman, who after all his expected crops, have been beaten down and destroyed by a storm, goeth up and down with a languishing and down-cast look, gleaning up every small ear that would not suffice to keep a chicken alive one sole day.
Salv.Truly, this Authour came out too slenderly provided with armes against the assailants of the Heavens inalterability, and with too brittle a chain attempted to pull down the new star of Cassiopeia from the highest Regions, to these so low and elementary. And for that I think that we have sufficiently demonstrated the vast difference that is between the arguments of those Astronomers, and of this their Antagonist, it will be convenient that we leave this particular, and return to our principal matter; in which there presents it self to our consideration the annual motion commonly ascribed to the Sun, but by Aristarchus Samius first of all, and after by Copernicus taken from the Sun, and transferred upon the Earth; against which Hypothesis, methinks I see Simplicius to come strongly provided, and particularly with the sword and ​buckler of the little Treatise of Conclusions, or Disquisitions Mathematical, the oppugnations of which it would be good to begin to produce.
Simpl.I will, if you so please, reserve them to the last, as those that are of latest invention.
Salv.It will therefore be necessary, that in conformity to the method hitherto observed, you do orderly, one by one, propound the arguments, on the contrary, aswell of Aristotle, as of the other ancients, which shall be my task also, that so nothing may escape our strict consideration and examination; and likewise Sagredus, with the vivacity of his wit, shall interpose his thoughts, as he shall finde himself inclined.
Sagr.I will do it with my wonted freedome; and your commands shall oblige you to excuse me in so doing.
Salv.The favour will challenge thanks, and not an excuse. But now let Simplicius begin to propose those doubts which disswade him from believing that the Earth, in like manner, as the other planets, may move round about a fixed centre.
Simpl.The first and greatest difficulty is the repugnance and incompatibility that is between being in the centre, and being far from it; for if the Terrestrial Globe were to move in a year by the circumference of a circle, that is, under the Zodiack, it is impossible that it should, at the same time, be in the centre of the Zodiack; but that the Earth is in the said centre Aristotle, Ptolomy, and others have many wayes proved.
Salv.You very well argue, and there is no question but that one that would make the Earth to move in the circumference of a circle, must first of necessity prove, that it is not in the centre of that same circle; it now followeth, that we enquire, whether the Earth be, or be not in that centre, about which, I say, that it turneth, and you say that it is fixed; and before we speak of this, it is likewise necessary that we declare our selves, whether you and I have both the same conceit of this centre, or no. Therefore tell me, what and where is this your intended centre?
Simpl.When I speak of the centre, I mean that of the Universe, that of the World, that of the Starry Sphere.
Salv.Although I might very rationally put it in dispute, whether there be any such centre in nature,It hath not been hitherto proved by any, whether the World be finite or infinite. or no; being that neither you nor any one else hath ever proved, whether the World be finite and figurate, or else infinite and interminate; yet nevertheless granting you, for the present, that it is finite, and of a terminate Spherical Figure, and that thereupon it hath its centre; it will be requisite to see how credible it is that the Earth, and not rather some other body, doth possesse the said centre.
Simpl.That the world is finite, terminate, and spherical, Ari​stotle proveth with an hundred demonstrations.
Salv.All which in the end are reduced to one alone,The Demonstrations of Aristotle to prove that the Universe is finite, are all nullified by denying it to be moveable. and that one to none at all; for if I deny his assumption, to wit, that the Universe is moveable, all his demonstrations come to nothing, for he onely proveth the Universe to be finite and terminate, for that it is moveable. But that we may not multiply disputes, let it be granted for once, that the World is finite, spherical, and hath its centre. And seeing that that centre and figure is argued from its mobility, it will, without doubt, be very reasonable, if from the circular motions of mundane bodies we proceed to the particular investigation of that centres proper place:Aristotle makes that point to be the centre of the Universe about which all the Celestial Spheres do revolve. Nay Aristotle himself hath argued and determined in the same manner, making that same to be the centre of the Universe about which all the Cœlelestial Spheres revolve, and in which he beleived the Terrestrial Globe to have been placed.A question is put, in case that if Aristotle were forced to receive one of two propositions that make against his doctrine, which he would admit. Now tell me Simplicius, if Aristotle should be constrained by evident experience to alter in part this his disposure and order of the Universe, and confesse himself to have been deceived in one of these two propositions, namely, either in placing the Earth in the centre, or in saying, that the Cœlestial Spheres do move about that centre, which of the two confessions think you would he choose?
Simpl.I believe, that if it should so fall out, the Peripateticks.
Salv.I do not ask the Peripateticks, I demand of Aristotle, for as to those, I know very well what they would reply; they, as observant and humble vassals of Aristotle, would deny all the experiments and all the observations in the World, nay, would also refuse to see them, that they might not be forced to acknowledg them, and would say that the World stands as Aristotle writeth, and not as nature will have it, for depriving them of the shield of his Authority, with what do you think they would appear in the field? Tell me therefore what you are perswaded Aristotle himself would do in the case.
Simpl.To tell you the truth, I know not how to resolve which of the two inconveniences is to be esteemed the lesser.
Salv.Apply not I pray you this term of inconvenience to a thing which possibly may of necessity be so. It was an inconvenience to place the Earth in the centre of the Cœlestial revolutions; but seeing you know not to which part he would incline, I esteeming him to be a man of great judgment, let us examine which of the two choices is the more rational, and that we will hold that Aristotle would have received. Reassuming therefore our discourse from the beginning, we suppose with the good liking of Aristotle, that the World (of the magnitude of which we have no sensible notice beyond the fixed stars) as being of a spherical ​figure; and moveth circularly, hath necessarily, and in respect of its figure a centre; and we being moreover certain, that within the starry Sphere there are many Orbs, the one within another, with their stars, which likewise do move circulary, it is in dispute whether it is most reasonable to believe and to say that these conteined Orbs do move round the said centre of the World, or else about some other centre far remote from that? Tell me now Simplicius what you think concerning this particular.
Its more rational that the Orb conteining, and the parts conteined, do move all about one centre, than upon divers.Simpl.If we could stay upon this onely supposition, and that we were sure that we might encounter nothing else that might disturb us, I would say that it were much more reasonable to affirm that the Orb containing, and the parts contained, do all move about one common centre, than about divers.
If the centre of the World be the same with that about which the planets move, the Sun and not the Earth is placed in it.Salv.Now if it were true that the centre of the World is the same about which the Orbs of mundane bodies, that is to say, of the Planets, move, it is most certain that it is not the Earth, but the Sun rather that is fixed in the centre of the World. So that as to this first simple and general apprehension, the middle place belongeth to the Sun, and the Earth is as far remote from the centre, as it is from that same Sun.
Simpl.But from whence do you argue that not the Earth, but the Sun is in the centre of the Planetary revolutions?
Salv.I infer the same from most evident, and therefore necessarily concludent observations, of which the most palpable to exclude the Earth from the said centre,Observations from whence it is collected that the Sun and not the Earth is in the centre of the Celestial revolutions. and to place the Sun therein, are, the seeing all the Planets one while neerer and another while farther off from the Earth with so great differences, that for example, Venus when it is at the farthest, is six times more remote from us, than when it is neerest, and Mars riseth almost eight times as high at one time as at another. See therefore whether Aristotle was not somewhat mistaken in thinking that it was at all times equidistant from us.
Simpl.What in the next place are the tokens that their motions are about the Sun?
Salv.It is argued in the three superiour planets Mars, Jupiter, and Saturn, in that we find them alwayes neerest to the Earth when they are in opposition to the Sun, and farthest off when they are towards the conjunction, and this approximatian and recession importeth thus much that Mars neer at hand, appeareth very neer 60 times greater than when it is remote.The mutation of figure in Venus argueth its motion to be about the Sun. As to Venus in the next place, and to Mercury, we are certain that they revolve about the Sun, in that they never move far from him, and in that we see them one while above and another while below it,The Moon cannot seperate from the Earth. as the mutations of figure in Venus necessarily argueth. Tonching the Moon it is certain, that she cannot in any way ​seperate from the Earth, for the reasons that shall be more distinctly alledged hereafter.
Sagr.I expect that I shall hear more admirable things that depend upon this annual motion of the Earth, than were those dependant upon the diurnal revolution.
Salv.You do not therein erre:The annual motion of the Earth mixing with the motions of the other Planets produce extravagant appearances. For as to the operation of the diurnal motion upon the Celestial bodies, it neither was, nor can be other, than to make the Universe seem to run precipitately the contrary way; but this annual motion intermixing with the particular motions of all the planets, produceth very many extravagancies, which have disarmed and non-plust all the greatest Scholars in the World. But returning to our first general apprehensions, I reply that the centre of the Celestial conversions of the five planets Saturn, Jupiter, Mars, Venus and Mercury, is the Sun; and shall be likewise the centre of the motion of the Earth, if we do but succeed in our attempt of placing it in Heaven. And as for the Moon, this hath a circular motion about the Earth, from which (as I said before) it can by no means alienate it self, but yet doth it not cease to go about the Sun together with the Earth in an annual motion.
Simpl.I do not as yet very well apprehend this structure, but it may be, that with making a few draughts thereof, one may better and more easily discourse concerning the same.
Salv.Tis very true: yea for your greater satisfaction and admiration together, I desire you, that you would take the pains to draw the same; and to see that although you think you do not apprehend it, yet you very perfectly understand it; And onely by answering to my interrogations you shall designe it punctually. Take therefore a sheet of paper and Compasses;The Systeme of the Universe designed from the appearances. And let this white paper be the immense expansion of the Universe; in which you are to distribute and dispose its parts in order, according as reason shall direct you. And first, in regard that without my instruction you verily believe that the Earth is placed in this Universe, therefore note a point at pleasure, about which you intend it to to be placed, and mark it with some characters.
Simpl.Let this mark A be the place of the Terrestrial Globe.
Salv.Very well. I know secondly, that you understand perfectly that the said Earth is not within the body of the Sun, nor so much as contiguous to it, but distant for some space from the same, and therefore assign to the Sun what other place you best like, as remote from the Earth as you please, and mark this in like manner.
Simpl.Here it is done: Let the place of the Solar body be O.
Salv.These two being constituted, I desire that we may ​think of accomodating the body of Venus in such a manner that its state and motion may agree with what sensible experiments do shew us; and therefore recall to mind that which either by the past discourses, or your own observations you have learnt to befal that star, and afterwards assign unto it that state which you think agreeth with the same.
Simpl.Supposing those Phænomena expressed by you, and which I have likewise read in the little treatise of Conclusions, to [illustration] be true, namely, that that star never recedes from the Sun beyond such a determinate space of 40 degrees or thereabouts, so as that it never cometh either to apposition with the Sun, or so much as to quadrature, or yet to the sextile aspect; and more than that,Venus very great towards the respective conjunction and very small towards the matutine. supposing that it sheweth at one time almost 40 times greater than at another; namely, very great, when being retrograde, it goeth to the vespertine conjnnction of the Sun, and very small when with a ​motion straight forwards, it goeth to the matutine conjunction; and moreover it being true, that when it appeareth bigge it shews with a corniculate figure, and when it appeareth little, it seems perfectly round, these appearances, I say, being true, I do not see how one can choose but affirm the said star to revolve in a circle about the Sun,Venus necessarily proved to move about the Sun. for that the said circle cannot in any wise be said to encompasse or to contain the Earth within it, nor to be inferiour to the Sun, that is between it and the Earth, nor yet superiour to the Sun. That circle cannot incompasse the Earth, because Venus would then sometimes come to opposition with the Sun; it cannot be inferiour, for then Venus in both its conjunctions with the Sun would seem horned; nor can it be superiour, for then it would alwayes appear round, and never cornicular; and therefore for receit of it I will draw the circle CH, about the Sun, without encompassing the Earth.
Salv.Having placed Venus, it is requisite that you think of Mercury, which, as you know, alwayes keeping about the Sun, doth recede lesse distance from it than Venus; therefore consider with your self, what place is most convenient to assign it.
Simpl.It is not to be questioned,The revolution of Mercury concluded to be about the Sun, within the Orb of Venus. but that this Planet imitating Venus, the most commodious place for it will be, a lesser circle within this of Venus, in like manner about the Sun, being that of its greatest vicinity to the Sun, an argument, an evidence sufficiently proving the vigour of its illumination, above that of Venus, and of the other Planets, we may therefore upon these considerations draw its Circle, marking it with the Characters BG.
Salv.But Mars,Mars necessarily includeth within its Orb the Earth, and also the Sun. Where shall we place it?
Simpl.Mars, Because it comes to an opposition with the Sun, its Circle must of necessity encompass the Earth; But I see that it must necessarily encompass the Sun also, for coming to conjunction with the Sun, if it did not move over it, but were below it, it would appear horned, as Venus and the Moon; but it shews alwayes round, and therefore it is necessary, that it no less includeth the Sun within its circle than the Earth.Mars at its opposition to the Sun shews to be sixty times bigger than towards the conjunction. And because I remember that you did say, that when it is in opposition with the Sun, it seems 60 times bigger than when it is in the conjunction, me thinks that a Circle about the Centre of the Sun, and that taketh in the earth, will very well agree with these Phænomena, which I do note and mark DI, where Mars in the point D, is near to the earth, and opposite to the Sun; but when it is in the point I, it is at Conjuction with the Sun, but very far from the Earth. And because the same appearances are observed in Jupiter and Saturn,Jupiter and Saturn do likewise encompasse the Earth, and the Sun. although with much lesser difference in Jupiter than in Mars, and with yet lesse in Saturn than in Jupiter; me thinks I ​understand that we should very commodiously salve all the Phænomena of these two Planets, with two Circles, in like manner, drawn about the Sun, and this first for Jupiter, marking it EL, and another above that for Saturn marked FM.
Salv.You have behaved your self bravely hitherto.The approximation and recession of the three superiour Planets, importeth double the Suns distance. And because (as you see) the approach and recession of the three Superiour Planets is measured with double the distance between the Earth and Sun, this maketh greater difference in Mars than in Jupiter, the Circle DI,The difference of the apparent magnitude lesse in Saturn, than in Jupiter, an dn Jupiter than in Mars, and why. of Mars, being lesser than the Circle EL, of Jupiter, and likewise because this EL, is lesse than this Circle FM, of Saturn, the said difference is also yet lesser in Saturn than in Jupiter, and that punctually answereth the Phænomena. It remains now that you assign a place to the Moon.
Simpl.Following the same Method (which seems to me very conclusive) in regard we see that the Moon cometh to conjunction and opposition with the Sun,The Moons Orb invironeth the Earth, but not the Sun. it is necessary to say, that its circle encompasseth the Earth, but yet doth it not follow, that it must environ the Sun, for then at that time towards its conjunction, it would not seem horned, but alwayes round and full of Light. Moreover it could never make, as it often doth, the Eclipse of the Sun, by interposing betwixt it and us; It is necessary therefore to assign it a circle about the Earth, which should be this NP, so that being constituted in P, it will appear from the Earth A, to be in conjunction with the Sun, and placed in N, it appeareth opposite to the Sun, and in that position it may fall under the Earths shadow, and be obscured.
Salv.Now, Simplicius, what shall we do with the fixed stars? Shall we suppose them scattered through the immense abisses of the Universe, at different distances, from any one determinate point; or else placed in a superficies spherically distended about a centre of its own, so that each of them may be equidistant from the said centre?
Simpl.I would rather take a middle way;The probable situation of the fixed stars. and would assign them an Orb described about a determinate centre and comprized within two spherical superficies, to wit, one very high, and concave, and the other lower,Which ought to be accounted the sphere of the Universe. and convex, betwixt which I would constitute the innumerable multitude of stars, but yet at divers altitudes, and this might be called the Sphere of the Universe, conteining within it the Orbs of the planets already by us described.
Salv.But now we have all this while, Simplicius, disposed the mundane bodies exactly, according to the order of Copernicus, and we have done it with your hand; and moreover to each of them you have assigned peculiar motions of their own, except to the Sun, the Earth, and starry Sphere; and to Mercury with Venus, you have ascribed the circular motion about the Sun, ​without encompassing the Earth; about the same Sun you make the three superiour Planets Mars, Jupiter, and Saturn, to move, comprehending the Earth within their circles. The Moon in the next place can move in no other manner than about the Earth, without taking in the Sun, and in all these motions you agree also with the same Copernicus. There remains now three things to be decided between the Sun, the Earth, and fixed stars, namely, Rest,Rest, the annual motion and the diurnal ought to be distributed betwixt the Sun, Earth, and Firmament. which seemeth to belong to the Earth; the annual motion under the Zodiack, which appeareth to pertain to the Sun; and the diurnal motion, which seems to belong to the Starry Sphere, and to be by that imparted to all the rest of the Universe, the Earth excepted, And it being true that all the Orbs of the Planets, I mean of Mercury,In a moveable sphere, it seemeth more reasonable that its centre be stable, than any other of its parts.Venus, Mars, Jupiter, and Saturn, do move about the Sun as their centre; rest seemeth with so much more reason to belong to the said Sun, than to the Earth, in as much as in a moveable Sphere, it is more reasonable that the centre stand still, than any other place remote from the said centre; to the Earth therefore, which is constituted in the midst of moveable parts of the Universe, I mean between Venus and Mars, one of which maketh its revolution in nine moneths, and the other in two years, may the motion of a year very commodiously be assigned, leaving rest to the Sun.Granting to the Earth the annual, it must of necessity also have the diurnal motion assigned to it. And if that be so, it followeth of necessary consequence, that likewise the diurnal motion belongeth to the Earth; for, if the Sun standing still, the Earth should not revolve about its self, but have onely the annual motion about the Sun, our year would be no other than one day and one night, that is six moneths of day, and six moneths of night, as hath already been said. You may consider withal how commodiously the precipitate motion of 24 hours is taken away from the Universe, and the fixed stars that are so many Suns, are made in conformity to our Sun to enjoy a perpetual rest. You see moreover what facility one meets with in this rough draught to render the reason of so great appearances in the Celestial bodies.
Sagr.I very well perceive that facility, but as you from this simplicity collect great probabilities for the truth of that System, others haply could make thence contrary deductions; doubting, not without reason, why that same being the ancient Systeme of Pythagoreans, and so well accommodated to the Phænomena, hath in the succession of so many thousand years had so few followers, and hath been even by Aristotle himself refuted, and since that Copernicus himself hath had no better fortune.
Salv.If you had at any time been assaulted, as I have been, many and many a time, with the relation of such kind of frivolous reasons, as serve to make the vulgar contumacious, and difficult to be perswaded to hearken, (I will not say to consent) to this novel​ty, I believe that you wonder at the paucity of those who are followers of that opinion would be much diminished.Discourses more than childish, serve to keep fools in the opinion of the Earths stability. But small regard in my judgement, ought to be had of such thick sculs, as think it a most convincing proof to confirm, and steadfastly settle them in the belief of the earths immobility, to see that if this day they cannot Dine at Constantinople, nor Sup in Jappan, that then the Earth as being a most grave body cannot clamber above the Sun, and then slide headlong down again; Of such as these I say, whose number is infinite, we need not make any reckoning, nor need we to record their foolieries, or to strive to gain to our side as our partakers in subul and sublime opinions, men in whose definition the kind onely is concerned, and the difference is wanting. Moreover, what ground do you think you could be able to gain, with all the demonstrations of the World upon brains so stupid, as are not able of themselves to know their down right follies? But my admiration, Sagredus, is very different from yours, you wonder that so few are followers of the Pythagorean Opinion; and I am amazed how there could be any yet left till now that do embrace and follow it:A declaration of the improbability of Copernicus his opinion. Nor can I sufficiently admire the eminencie of those mens wits that have received and held it to be true, and with the sprightlinesse of their judgements offered such violence to their own sences, as that they have been able to prefer that which their reason dictated to them, to that which sensible experiments represented most manifestly on the contrary. That the reasons against the Diurnal virtiginous revolution of the Earth by you already examined, do carry great probability with them, we have already seen; as also that the Ptolomaicks, and Aristotelicks, with all their Sectators did receive them for true, is indeed a very great argument of their efficacie; but those experiments which apertly contradict the annual motion,Reasons and discourse in Aristarcus and Copernicus prevailed over manifest sence. are of yet so much more manifestly repugnant, that (I say it again) I cannot find any bounds for my admiration, how that reason was able in Aristarchus and Copernicus, to commit such a rape upon their Sences, as in despight thereof, to make her self mistress of their credulity.
Sagr.Are we then to have still more of these strong oppositions against this annual motion?
Salv.We are, and they be so evident and sensible, that if a sence more sublime and excellent than those common and vulgar, did not take part with reason, I much fear, that I also should have been much more averse to the Copernican Systeem than I have been since the time that a clearer lamp than ordinary hath enlightned me.
Sagr.Now therefore Salviatus, let us come to joyn battail for every word that is spent on any thing else, I take to be cast away.
​Salv.I am ready to serve you. You have already seen me draw the form of the Copernican Systeme;Mars makes an hot assault upon the Copernican Systeme. against the truth of which Mars himself, in the first place, makes an hot charge; who, in case it were true, that its distances from the earth should so much vary, as that from the least distance to the greatest, there were twice as much differences, as from the earth to the Sun; it would be necessary, that when it is nearest unto us, its discus would shew more than 60. times bigger than it seems, when it is farthest from us; nevertheless that diversity of apparent magnitude is not to be seen, nay in its opposition with the Sun, when its nearest to the Earth, it doth not shew so much as quadruple and quintuple in bigness, to what it is, when towards the conjunction it cometh to be occulted under the Suns rayes. Another and greater difficulty doth Venus exhibit; For if revolving about the Sun, as Copernicus affirmeth,The Phænomena of Venus appear contrary to the Systeme of Copernicus. it were one while above, & another while below the same, receding and approaching to us so much as the Diameter of the circle described would be, at such time as it should be below the Sun, and nearest to us, its discus would shew little less than 40 times bigger than when it is above the Sun, near to its other conjunction; yet neverthelesse,Another difficulty raised by Venus against Copernicus. the difference is almost imperceptible Let us add another difficulty, that in case the body of Venus be of it self dark, and onely shineth as the Moon, by the illumination of the Sun, which seemeth most reasonable; it would shew forked or horned at such time as it is under the Sun, as the Moon doth when she is in like manner near the Sun; an accident that is not to be discovered in her.Venus, according to Copernicus, either lucid in it self, or else of a transparent substance. Whereupon Copernicus affirmeth, that either she is light of her self, or else that her substance is of such a nature, that it can imbue the Solar light, and transmit the same through all its whole depth, so as to be able to appear to us alwayes shining; and in this manner Copernicus excuseth the not changing figure in Venus: but of her small variation of Magnitude,Copernicus speaketh nothing of the small variation of bigness in Venus and in Mars. he maketh no mention at all; and much less of Mars than was needful; I believe as being unable so well as he desired to salve a Phænomenon so contrary to his Hypothesis, and yet being convinced by so many other occurrences and reasons he maintained, and held the same Hypothesis to be true. Besides these things, to make the Planets, together with the Earth, to move above the Sun as the Centre of their conversions, and the Moon onely to break that order,The moon much disturbeth the order of the other Planets. and to have a motion by it self about the earth; and to make both her, the Earth, and the whole Elementary Sphere, to move all together about the Sun in a year, this seemeth to pervert the order of this Systeme, which rendreth it unlikely and false. These are those difficulties that make me wonder how Aristarchus and Copernicus, who must needs have observed them, not having been able for all that to salve them, have yet notwithstanding by other admirable occurrences been induced ​to confide so much in that which reason dictated to them, as that they have confidently affirmed that the structure of the Universe could have no other figure than that which they designed to themselves. There are also several other very serious and curious doubts, not so easie to be resolved by the middle sort of wits, but yet penetrated and declared by Coperninus, which we shall defer till by and by, after we have answered to other objections that seem to make against this opinion. Now coming to the declarations and answers to those three before named grand Objections, I say, that the two first not onely contradict not the Copernican Systeme,Answers to the three first objections against the Copernican Systeme. but greatly and absolutely favour it; For both Mars and Venus seems unequal to themselves, according to the proportions assigned; and Venus under the Sun seemeth horned, and goeth changing figures in it self exactly like the Moon.
Sagr.But how came this to be concealed from Copernicus, and revealed to you?
Salv.These things cannot be comprehended, save onely by the sense of seeing, the which by nature was not granted to man so perfect, as that it was able to attain to the discovery of such differences; nay even the very instrument of sight is an impediment to it self: But since that it hath pleased God in our age to vouchsafe to humane ingenuity, so admirable an invention of perfecting our sight, by multiplying it four, six, ten, twenty, thirty, and fourty times, infinite objects, that either by reason of their distance, or for their extream smallnesse were invisible unto us, have by help of the Telescope been rendered visible.
Sagr.But Venus and Mars are none of the objects invisible for their distance or smallnesse, yea, we do discern them with our bare natural sight; why then do we not distinguish the differences of their magnitudes and figures?
Salv.In this,The reason whence it happens that Venus and Mars do not appear to vary magnitude so much as is requisite. the impediment of our very eye it self hath a great share, as but even now I hinted, by which the resplendent and remote objects are not represented to us simple and pure; but gives them us fringed with strange and adventitious rayes, so long and dense, that their naked body sheweth to us agrandized, ten twenty, an hundred, yea a thousand times more than it would appear, if the capillitious rayes were taken away.
Sagr.Now I remember that I have read something on this subject, I know not whether in the Solar Letters, or in the Saggiatore of our common Friend, but it would be very good, aswell for recalling it into my memory, as for the information of Simplicius, who it may be never saw those writings, that you would declare unto us more distinctly how this businesse stands, the knowledge whereof I think to be very necessary for the assisting of us to understand that of which we now speak. ​Simpl.I must confesse that all that which Salviatus hath spoken is new unto me, for truth is, I never have had the curiosity to read those Books, nor have I hitherto given any great credit to the Telescope newly introduced;The operations of the Telescope accounted fallacies by the Peripateticks. rather treading in the steps of other Peripatetick Philosophers my companions, I have thought those things to be fallacies and delusions of the Chrystals, which others have so much admired for stupendious operations: and therefore if I have hitherto been in an errour, I shall be glad to be freed from it, and allured by these novelties already heard from you, I shall the more attentively hearken to the rest.
Salv.The confidence that these men have in their own apprehensivenesse, is no less unreasonable than the small esteem they have of the judgment of others: yet its much that should esteem themselves able to judge better of such an instrument, without ever having made trial of it, than those who have made, and daily do make a thousand experiments of the same: But I pray you, let us leave this kind of pertinacious men, whom we cannot so much as tax without doing them too great honour. And returning to our purpose,Shining objects seem environed with adventitious rayes. I say, that resplendent objects, whether it is that their light doth refract on the humidity that is upon the pupils, or that it doth reflect on the edges of the eye-browes, diffusing its reflex rayes upon the said pupils, or whether it is for some other reason, they do appear to our eye, as if they were environ'd with new rayes, and therefore much bigger than their bodies would represent themselves to us, were they divested of those irradiations. The reason why luminous bodies appear enlarged much the more, by how much they are lesser. And this aggrandizement is made with a greater and greater proportion, by how much those lucid objects are lesser and lesser; in the same manner for all the world, as if we should suppose that the augmentation of shining locks were v. g. four inches, which addition being made about a circle that hath four inches diameter would increase its appearance to nine times its former bignesse: but———
Simpl.I believe you would have said three times; for adding four inches to this side, and four inches to that side of the diameter of a circle, which is likewise four inches, its quantity is thereby tripled, and not made nine times bigger.
Salv.A little more Geometry would do well,Superficial figures encreasing proportion double to their lines.Simplicius. True it is, that the diameter is tripled, but the superficies, which is that of which we speak, increaseth nine times: for you must know, Simplicius, that the superficies of circles are to one another, as the squares of their diameters; and a circle that hath four inches diameter is to another that hath twelve, as the square of four to the square of twelve; that is, as 16. is to 144. and therefore it shall be increased nine times, and not three; this, by way of advertisement to Simplicius. And proceeding forwards, if we should add ​the said irradiation of four inches to a circle that hath but two inches of diameter onely, the diameter of the irradiation or Garland would be ten inches, and the superficial content of the circle would be the area of the naked body, as 100. to 4. for those are the squares of 10. and of 2. the agrandizement would 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.Objects the more vigorous they are in light, the more they do seem to increase.
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,An easie experiment that sheweth the increase in the stars, by means of the adventitious rays. 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,Jupiter augments lesse than the Dogstar. 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,The Sun and Moon increase little. 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,It is seen by manifest experience, that the more splendid bodies do much more irradiate than the lesse lucid. 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 means to take away the irradiations of the Stars. 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,Another second reason of the small apparent increase of Venus. 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.Tis true.Copernicus perswaded by reasons contrary to sensible experiments. 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:Mercury admitteth not of clear observations. 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 digrssieons 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,The difficulties removed that arise from the Earths moving about the Sun, not solitarily, but in consort with the Moon. so as to make them appear shaved round about. It remains, that we remove that which seemed a great inconvenience in the motion of the Earth, namely that all the Planets moving about the Sun, it alone, not solitary as the rest, but in company with the Moon, and the whole Elementary Sphear, should move round about the Sun in a year; and that the said Moon withal should move every moneth about the earth. Here it is necessary once again to exclaim and extol the admirable perspicacity of Copernicus, and withal to condole his misfortune, in that he is not now alive in our dayes, when for removing of the seeming absurdity of the Earth and Moons motion in consort we see Jupiter, as if it were another Earth, not in consort with the Moon, but accompanied by four Moons to rovolve about the Sun in 12. years together, with what ever things the Orbs of the four Medicaean Stars can contain within them.
Salv.Why do you call the four jovial Planets, Moons?
Sagr.Such they would seem to be to one that standing in Jupiter should behold them;The Medicean Stars are as it were four Moons about Jupiter. for they are of themselves dark, and receive their light from the Sun, which is manifest from their being eclipsed, when they enter into the cone of Jupiters shadow: and because onely those their Hemispheres, that look towards the Sun are illuminated, to us that are without their Orbs, and nearer to the Sun, they seem alwayes lucid, but to one that should be in Jupiter, they would shew all illuminated, at such time as they were in the upper parts of their circles; but in the parts inferiour, that is between Jupiter and the Sun, they would from Jupiter be observed to be horned; and in a word they would, to ​the observators standing in Jupiter, make the self same changes of Figure, that to us upon the Earth, the Moon doth make. You see now how these three things, which at first seemed dissonant, do admirably accord with the Copernican Systeme. Here also by the way may Simplicius see, with what probability one may conclude, that the Sun and not the Earth, is in the Centre of the Planetary conversions. And since the Earth is now placed amongst mundane Bodies, that undoubtedly move about the Sun, to wit, above Mercury and Venus, and below Saturn, Jupiter, and Mars; shall it not be in like manner probable, and perhaps necessary to grant, that it also moveth round?
Simpl.These accidents are so notable and conspicuous, that it is not possible, but that Ptolomy and others his Sectators, should have had knowledge of them, and having so, it is likewise necessary, that they have found a way to render reasons of such, and so sensible appearances that were sufficient, and also congruous and probable, seeing that they have for so long a time been received by such numbers of learned men.
Salv.You argue very well;The Principal scope of Astronomers, is to give a reason of appearances. but you know that the principal scope of Astronomers, is to render only reason for the appearances in the Cælestial Bodies, and to them, and to the motions of the Stars, to accomodate such structures and compositions of Circles, that the motions following those calculations, answer to the said appearances, little scrupling to admit of some exorbitances, that indeed upon other accounts they would much stick at. And Copernicus himself writes,Copernicus restored Astronomy upon the suppositions of Ptolomy: that he had in his first studies restored the Science of Astronomy upon the very suppositions of Ptolomy, and in such manner corrected the motions of the Planets, that the computations did very exactly agree with the Phænomena, and the Phænomena with the supputations, in case that he took the Planets severally one by one. But he addeth, that in going about to put together all the structures of the particular Fabricks, there resulted thence a Monster and Chimæra, composed of members most disproportionate to one another, and altogether incompatible; So that although it satisfied an Astronomer meerly Arithmetical, yet did it not afford satisfaction or content to the Astronomer Phylosophical.What moved Copernicus to establish his Systeme. And because he very well understood, that if one might salve the Cælestial appearances with false assumptions in nature, it might with much more ease be done by true suppositions, he set himself diligently to search whether any amongst the antient men of fame, had ascribed to the World any other structure, than that commonly received by Ptolomy; and finding that some Pythagoreans had in particular assigned the Diurnal conversion to the Earth, and others the annual motion also, he began to compare the appearances, and particulari​ties of the Planets motions, with these two new suppositions, all which things jumpt exactly with his purpose; and seeing the whole correspond, with admirable facility to its parts, he imbraced this new Systeme, and it took up his rest.
Simpl.But what great exorbitancies are there in the Ptolomaick Systeme, for which there are not greater to be found in this of Copernicus?
Salv.In the Ptolomaick Hypothesis there are diseases,Inconveniencies that are in the Systeme of Ptolomy. and in the Copernican their cures. And first will not all the Sects of Phylosophers, account it a great inconvenience, that a body naturally moveable in circumgyration, should move irregularly upon its own Centre, and regularly upon another point? And yet there are such deformed motions as these in the Ptolomæan Hypothesis, but in the Copernican all move evenly about their own Centres. In the Ptolomaick, it is necessary to assign to the Cælestial bodies, contrary motions, and to make them all to move, from East to West, and at the same time, from West to East; But in the Copernican, all the Cælestial revolutions are towards one onely way, from West to East. But what shall we say of the apparent motion of the Planets, so irregular, that they not only go one while swift, and another while slow, but sometimes wholly seace to move; and then after a long time return back again? To salve which appearances Ptolomie introduceth very great Epicicles, accommodating them one by one to each Planet, with some rules of incongruous motions, which are all with one single motion of the Earth taken away. And would not you, Simplicius, call it a great absurditie, if in the Ptolomaick Hypothesis, in which the particular Planets, have their peculiar Orbs assigned them one above another, one must be frequently forced to say, that Mars, constituted above the Sphære of the Sun, doth so descend, that breaking the Solar Orb, it goeth under it, and approacheth nearer to the Earth, than to the Body of the Sun, and by and by immeasurably ascendeth above the same? And yet this, and other exorbitancies are remedied by the sole and single annual motion of the Earth.
Sagr.I would gladly be bettter informed how these stations, and retrograde and direct motions, which did ever seem to me great improbalities, do accord in this Copernican Systeme.
Salv.You shall see them so to accord,Its a great Argument in favour of Copernicus, that he obviates the stations & retrogradations of the motions of the Planets. Sagredus, that this onely conjecture ought to be sufficient to make one that is not more than pertinacious or stupid, yield, assent to all the rest of this Doctrine. I tell you therefore, that nothing being altered in the motion of Saturn, which is 30 years, in that of Jupiter, which is 12, in that of Mars, which is 2, in that of Venus, which is 9. moneths, in that of Mercury, which is 80. ​dayes, or thereabouts, the sole annual motion of the Earth between Mars and Venus,The sole annual motion of the Earth causeth great inequality of motions in the five Planets. causeth the apparent inequalities in all the five stars before named. And for a facile and full understanding of the whole, I will describe this figure of it. Therefore suppose the Sun to be placed in the centre O, about which we will draw the Orb described by the Earth, with the annual motion BGM, and let the circle described, v. gr. by Jupiter about the Sun in 12. years, be this BGM, and in the starry sphere let us imagine the Zodiack YVS.
A demonstration of the inequalities of the three superiour Planets dependent on the annual motion of the Earth. Again, in the annual Orb of the Earth let us take certain equal arches, BC, CD, EF, FG, GH, HI, IK, KL, LM}}, and in the Sphere of Jupiter let us make certain other arches, passed in the same times in which the Earth passeth hers, which let be BC, CD, DE, EF, FG, GH, HI, IK, KL, LM, which shall each be proportionally lesse than these marked in the Earths Orb, like as the motion of Jupiter under the Zodiack is slower than the annual. Supposing now, that when the Earth is in B, Jupiter is in B, it shall appear to us in the Zodiack to be in P, describing ​the right line BbP. Next suppose the Earth to be moved from B to C, and Jupiter from B to C, in the same time; Iupiter shall appear to have passed in the Zodiack to Q, and to have moved straight forwards, according to the order of the signes PQ. In the next place, the Earth passing to D, and Iupiter to D, it shall be seen in the Zodiack in R, and from E, Iupiter being come to E; will appear in the Zodiack in S, having all this while moved right forwards. But the Earth afterwards beginning to interpose more directly between Iupiter and the Sun, she being come to F, and Iupiter to F, he will appear in T, to have already begun to return apparently back again under the Zodiack, and in that time that the Earth shall have pased the arch EF, Iupiter shall have entertained himself between the points ST, and shall have appeared to us almost motionlesse and stationary. The Earth being afterwards come to G, and Iupiter to G, in opposition to the Sun, it shall be visible in the Zodiack at V, and much returned backwards by all the arch of the Zodiack TV; howbeit that all the way pursuing its even course it hath really gone forwards not onely in its own circle, but in the Zodiack also in respect to the centre of the said Zodiack, and to the Sun placed in the same. The Earth and Iupiter again continuing their motions, when the Earth is come to H, and Iupiter to H, it shall seem very much gone backward in the Zodiack by all the arch VX. The Earth being come to I, and Iupiter to I, it shall be apparently moved in the Zodiack by the little space XY, and there it will seem stationary. When afterwards the Earth shall be come to K, and Iupiter to K; in the Zodiack he shall have passed the arch YN in a direct motion; and the Earth pursuing its course to L, shall see Iupiter in L, in the point Z. And lastly Iupiter in M shall be seen from the Earth M, to have passed to A, with a motion still right forwards; and its whole apparent retrogadation in the Zodiack shall answer to the arch SY, made by Iupiter, whilst that he in his own circle passeth the arch EI, and the Earth in hers the arch EI. And this which hath been said,Retrogradations more frequent in Saturn, lesse in Jupiter, and yet lesse in Mars, and why. is intended of Saturn and of Mars also; and in Saturn those retrogradations are somewhat more frequent than in Jupiter, by reason that its motion is a little slower than that of Jupiter, so that the Earth overtaketh it it in a shorter space of time; in Mars again they are more rare, for that its motion is more swift than that of Jupiter. Whereupon the Earth consumeth more time in recovering it. Next as to Venus and Mercury,The Retrogradation of Venus and Mercury demonstrated by Apollonius and Copernicus. whose Circles are comprehended by that of the Earth, their stations and regressions appear to be occasioned, not by their motions that really are such, but by the anual motion of the said Earth, as Copernicus exellently demonstrateth, ​together with Appollonius Pergæus in lib. 5. of his Revolutions, Chap. 35.
You see, Gentlemen, with what facility and simplicity the annual motion,The annual motion of the Earth most apt to render a reason of the exorbitances of the five Planets. were it appertaining to the Earth, is accommodated to render a reason of the apparent exorbitances, that are observed in the motions of the five Planets, Saturn, Jupiter, Mars, Venus and Mercury, taking them all away, and reducing them to equal and regular motions.The Sun it self testifieth the annual motion to belong to the Earth. And of this admirable effect, Nicholas Copernicus, hath been the first that hath made the reason plain unto us. But of another effect, no lesse admirable than this, and that with a knot, perhaps more difficult to unknit, bindeth the wit of man, to admit this annual conversion, and to leave it to our Terrestrial Globe; a new and unthought of conjecture ariseth from the Sun it self, which sheweth that it is unwilling to be singular in shifting, of this attestation of so eminent a conclusion, rather as a testimony beyond all exception, it hath desired to be heard apart. Hearken then to this great and new wonder.
The first discoverer and observer of the Solar spots,The Lyncæan Academick the first discoverer of the Solar spots, and all the other celestial novelties. as also of all the other Cœlestial novelties, was our Academick Lincæus; and he discovered them anno 1610. being at that time Reader of the Mathematicks, in the Colledge of Padua, and there, and in Venice,The history of the proceedings of the Academian for a long time about the observation of the Solar spots. he discoursed thereof with several persons, of which some are yet living: And the year following, he shewed them in Rome to many great personages, as he relates in the first of his Letters to Marcus Velserus, ** Duumviro Sheriffe of Augusta. He was the first that against the opinions of the too timorous and too jealous assertors of the Heavens inalterability, affirmed those spots to be matters, that in short times were produced and dissolved: for as to place, they were contiguous to the body of the Sun, and revolved about the same; or else being carried about by the said Solar body, which revolveth in it selfe about its own Centre, in the space almost of a moneth, do finish their course in that time; which motion he judged at first to have been made by the Sun about an Axis erected upon the plane of the Ecliptick; in regard that the arches described by the said spots upon the Discus of the Sun appear unto our eye right lines, and parallels to the plane of the Ecliptick: which therefore come to be altered, in part, with some accidental, wandring, and irregular motions, to which they are subject, and whereby tumultuarily, and without any order they successively change situations amongst themselves, one while crouding close together, another while dissevering, and some dividing themselves into many and very much changing figures, which, for the most part, are very unusual. And albeit those so inconstant mutations did somewhat alter the primary pe​riodick course of the said spots, yet did they not alter the opinion of our friend, so as to make him believe, that they were any essential and fixed cause of those deviations, but he continued to hold, that all the apparent alterations derived themselves from those accidental mutations: in like manner, just as it would happen to one that should from far distant Regions observe the motion of our Clouds; which would be discovered to move with a most swift, great, and constant motion, carried round by the diurnal Vertigo of the Earth (if haply that motion belong to the same) in twenty four hours, by circles parallel to the Equinoctial, but yet altered, in part, by the accidental motions caused by the winds, which drive them, at all adventures, towards different quarters of the World. While this was in agitation, it came to pass that Velserus sent him two Letters, written by a certain person, under the feigned name of ** This Authors true name is Christopher Scheinerus a Jesuit, and his Book here meant is intituled, Apelles post tabulam. Apelles, upon the subject of these Spots, requesting him, with importunity, to declare his thoughts freely upon those Letters, and withall to let him know what his opinion was touching the essence of those spots; which his request he satisfied in 3 Letters, shewing first of all how vain the conjectures of Apelles were; & discovering, secondly, his own opinions; withal foretelling to him, that Apelles would undoubtedly be better advised in time, and turn to his opinion, as it afterwards came to pass. And because that our Academian (as it was also the judgment of many others that were intelligent in Natures secrets) thought he had in those three Letters investigated and demonstrated, if not all that could be desired, or required by humane curiosity, at least all that could be attained by humane reason in such a matter, he, for some time (being busied in other studies) intermitted his continual observations, and onely in complacency to some friend, joyned with him, in making now and then an abrupt observation: till that he, and after some years, we, being then at my ** La mia villa delle Selue. Country-seat, met with one of the solitary Solar spots very big, and thick, invited withal by a clear and constant serenity of the Heavens, he, at my request, made observations of the whole progresse of the said spot, carefully marking upon a sheet of paper the places that it was in every day at the time of the Suns coming into the Meridian; and we having found that its course was not in a right line, but somewhat incurvated, we came to resolve, at last, to make other observations from time to time; to which undertaking we were strongly induced by a conceit, that accidentally came into the minde of my Guest, which he imparted to me in these or the like words.
In my opinion, Philip, there is a way opened to a business of very great consequence. For if the Axis about which the Sun turneth be not erect perpendicularly to the plane of the Eclip​tick, A concipt that came suddenly into the minde of the Academian Lyncæus concerning the great consequence that followed upon the motion of the Solar spots. but is inclined upon the same, as its crooked course, but even now observed, makes me believe, we shall be able to make such conjectures of the states of the Sun and Earth, as neither so solid or so rational have been hitherto deduced from any other accident whatsoever. I being awakened at so great a promise, importun'd him to make a free discovery of his conceit unto me. And he continued his discourse to this purpose.Extravagant mutations to be observed in the motions of the spots, foreseen by the Academick, in case the Earth had the annual motion. If the Earths motion were along the Ecliptique about the Sun; and the Sun were constituted in the centre of the said Ecliptick, and therein revolved in its self, not about the Axis of the said Ecliptique (which would be the Axis of the Earths annual motion) but upon one inclined, it must needs follow, that strange changes will represent themselves to us in the apparent motions of the Solar spots, although the said Axis of the Sun should be supposed to persist perpetually and immutably in the same inclination, and in one and the same direction towards the self-same point of the Universe. Therefore the Terrestrial Globe in the annual motion moving round it, it will first follow, that to us, carried about by the same, the courses of the spots shall sometimes seem to be made in right lines, but this only twice a year, and at all other times shall appear to be made by arches insensibly incurvated. Secondly, the curvity of those arches for one half of the year, will shew inclined the contrary way to what they will appear in the other half; that is, for six moneths the convexity of the arches shall be towards the upper part of the Solar Discus, and for the other six moneths towards the inferiour. Thirdly, the spots beginning to appear, and (if I may so speak) to rise to our eye from the left side of the Solar Discus, and going to hide themselves and to set in the right side, the Oriental termes, that is, of their first appearings for six moneths, shall be lower than the opposite termes of their occultations; and for other six moneths it shall happen contrarily, to wit, that the said spots rising from more elevated points, and from them descending, they shall, in their courses, go and hide themselves in lower points; and onely for two dayes in all the year shall those termes of risings and settings be equilibrated: after which freely beginning by small degrees the inclination of the courses of the spots, and day by day growing bigger, in three moneths, it shall arrive at its greatest obliquity, and from thence beginning to diminish, in such another time it shall reduce it self to the other Æquilibrium. It shall happen, for a fourth wonder, that the course of the greatest obliquity shall be the same with the course made by the right line, and in the day of the Libration the arch of the course shall seem more than ever incurvated. Again, in the other times, according as the pendency shall successively diminish, and make it ap​proach towards the Æquilibrium, the incurvation of the arches of the courses on the contrary shall, by degrees, increase.
Sagr.I confesse, Salviatus, that to interrupt you in your Discourse is ill manners, but I esteem it no lesse rudeness to permit you to run on any farther in words, whilst they are, as the saying is, cast into the air: for, to speak freely, I know not how to form any distinct conceit of so much as one of these conclusions, that you have pronounced; but because, as I thus generally and confusedly apprehend them, they hold forth things of admirable consequence, I would gladly, some way or other, be made to understand the same.
Salv.The same that befalls you, befell me also, whilst my Guest transported me with bare words; who afterwards assisted my capacity,The first Accident to be observed in the motion of the Solar spots; and consequently all the rest explained. by describing the businesse upon a material Instrument, which was no other than a simple Sphere, making use of some of its circles, but to a different purpose from that, to which they are commonly applied. Now I will supply the defect of the Sphere, by drawing the same upon a piece of paper, as need shall require. And to represent the first accident by me propounded, which was, that the courses or journeys of the spots, twice a year, and no more, might be seen to be made in right lines, let us suppose this point O [in Fig. 4.] to be the centre of the grand Orb, or, if you will, of the Ecliptick, and likewise also of the Globe of the Sun it self; of which, by reason of the great distance that is between it and the Earth, we that live upon the Earth, may suppose that we see the one half: we will therefore describe this circle ABCD about the said centre O, which representeth unto us the extream term that divideth and separates the Hemisphere of the Sun that is apparent to us, from the other that is occult. And because that our eye, no lesse than the centre of the Earth, is understood to be in the plane of the Ecliptick, in which is likewise the centre of the Sun, therefore, if we should fancy to our selves the body of the Sun to be cut thorow by the said plane, the section will appear to our eye a right line, which let be BOD, and upon that a perpendicular being let fall AOC, it shall be the Axis of the said Ecliptick, and of the annual motion of the Terrestrial Globe. Let us next suppose the Solar body (without changing centre) to revolve in it self, not about the Axis AOC (which is the erect Axis upon the plane of the Ecliptick) but about one somewhat inclined, which let be this EOI, the which fixed and unchangeable Axis maintaineth it self perpetually in the same inclination and direction towards the same points of the Firmament, and of the Universe. And because, in the revolutions of the Solar Globe, each point of its superficies (the Poles excepted) describeth the circumference of a ​circle, either bigger or lesser, according as it is more or lesse remote from the said Poles, let us take the point F, equally distant from them, and draw the diameter FOG, which shall be perpendicular to the Axis EI, and shall be the diameter of the grand circle described about the Poles EI. Supposing not that the Earth, and we with her be in such a place of the Ecliptick, that the Hemisphere of the Sun to us apparent is determin'd or bounded by the circle ABCD, which passing (as it alwayes doth) by the Poles AC, passeth also by EI. It is manifest, that the grand circle, whose diameter is FG, shall be erect to the circle ABCD, to which the ray that from our eye falleth upon the centre O, is perpendicular; so that the said ray falleth upon the plane of the circle, whose diameter is FG, and therefore its circumference will appear to us a right line, and the self same with FG, whereupon if there should be in the point F, a spot, it comming afterwards to be carried about by the Solar conversion, would, upon the surface of the Sun, trace out the circumference of that circle, which seems to us a right line. Its course or passage will therefore seem straight. And straight also will the motion of the other spots appear, which in the said revolution shall describe lesser circles, as being all parallel to the greater, and to our eye placed at an immense distance from them. Now, if you do but consider, how that after the Earth shall in six moneths have run thorow half the grand Orb, and shall be situate opposite to that Hemisphere of the Sun, which is now occult unto us, so as that the boundary of the part that then shall be seen, may be the self same ABCD, which also shall passe by the Poles EI; you shall understand that the same will evene in the courses of the spots, as before, to wit, that all will appear to be made by right lines. But because that that accident takes not place, save onely when the teminator or boundary passeth by the Poles EI, and the said terminator from moment to moment, by meanes of the Earths annual motion, continually altereth, therefore its passage by the fixed Poles EI, shall be momentary, and consequently momentary shall be the time, in which the motions of those spots shall appear straight. From what hath been hitherto spoken one may comprehend also how that the apparition and beginning of the motion of the spots from the part F, proceeding towards G, their passages or courses are from the left hand, ascending towards the right; but the Earth being placed in the part diametrically opposite the appearance of the spots about G, shall still be to the left hand of the beholder, but the passage shall be descending towards the right hand F. Let us now describe the Earth to be situate one fourth part farther distant from its present state, and let us draw, as in the other figure, the terminator ABCD, ​[as in Fig. 5.] and the Axis, as before AC, by which the plane of our Meridian would passe, in which plane should also be the Axis of the Suns revolution, with its Poles, one towards us, that is, in the apparent Hemisphere, which Pole we will represent by the point E, and the other shall fall in the occult Hemisphere, and I mark it I. Inclining therefore the Axis EI, with the superiour part E, towards us, the great circle described by the Suns conversion, shall be this BFDG, whose half by us seen, namely BFD, shall no longer seem unto us a right line, by reason the Poles EI are not in the circumference ABCD, but shall appear incurvated, and with its convexity towards the inferiour part C. And it is manifest, that the same will appear in all the lesser circles parallel to the same BFD. It is to be understood also, that when the Earth shall be diametrically opposite to this state, so that it seeth the other Hemisphere of the Sun, which now is hid, it shall of the said great circle behold the part DGB incurved, with its convexity towards the superiour part A; and the courses of the spots in these constitutions shall be first, by the arch BFD, and afterwards by the other DGB, and the first apparitions and ultimate occultations made about the points B and D, shall be equilibrated, and not those that are more or lesse elevated than these. But if we constitute the Earth in such a place of the Ecliptick, that neither the boundary ABCD, nor the Meridian AC, passeth by the Poles of the Axis EI, as I will shew you anon, drawing this other Figure [viz. Fig. 6.] wherein the apparent or visible Pole E falleth between the arch of the terminator AB, and the section of the Meridian AC; the diameter of the great circle shall be FOG, and the apparent semicircle FNG, and the occult semicircle GSF, the one incurvated with its convexity N towards the inferiour part, and the other also bending with its convexity S towards the upper part of the Sun. The ingressions and exitions of the spots, that is, the termes F and G shall not be librated, as the two others B and D; but F shall be lower, and G higher: but yet with lesser difference than in the first Figure. The arch also FNG shall be incurvated, but not so much as the precedent BFD; so that in this position the passages or motions of the spots shall be ascendent from the left side F, towards the right G, and shall be made by curved lines. And imagining the Earth to be constituted in the position diametrically opposite; so that the Hemisphere of the Sun, which was before the occult, may be the apparent, and terminated by the same boundary ABCD, it will be manifestly discerned, that the course of the spots shall be by the arch GSF, beginning from the upper point G, which shall then be likewise from the left hand of the beholder, and going to determine, des​cending towards the right, in the point F. What I have hitherto said, being understood, I believe that there remains no difficulty in conceiving how from the passing of the terminator of the Solar Hemispheres by the Poles of the Suns conversion, or neer or far from the same, do arise all the differences in the apparent courses of the spots; so that by how much the more those Poles shall be remote from the said terminator, by so much the more shall those courses be incurvated, and lesse oblique; whereupon at the same distance, that is, when those Poles are in the section of the Meridian, the incurvation is reduced to the greatest, but the obliquity to the least, that is to Æquilibrium, as the second of these three last figures [viz. Fig. 5.] demonstrateth. On the contrary, when the Poles are in the terminator, as the first of these three figures [viz. Fig. 4.] sheweth the inclination is at the greatest, but the incurvation at the least, and reduced to rectitude. The terminator departing from the Poles, the curvity begins to grow sensible, the obliquity all the way encreasing, and the inclination growing lesser.
These are those admirable and extravagant mutations, that my Guest told me would from time to time appear in the progresses of the Solar spots, if so be it should be true that the annual motion belonged to the Earth, and that the Sun being constituted in the centre of the Ecliptick, were revolved in it self upon an Axis, not erect, but inclined to the Plane of the said Ecliptick.
Sagr.I do now very well apprehend these consequences, and believe that they will be better imprinted in my fancy, when I shall come to reflect upon them, accommodating a Globe to those inclinations, and then beholding them from several places. It now remains that you tell us what followed afterwards touching the event of these imaginary consequences.
The events being observed, were answerable to the predictions.Salv.It came to passe thereupon, that continuing many several moneths to make most accurate observations, noting down with great exactnesse the courses or transitions of sundry spots at divers times of the year, we found the events punctually to correspond to the predictions.
Sagr.Simplicius, if this which Salviatus saith be true; (nor can we distrust him upon his word) the Ptolomeans and Aristoteleans had need of solid arguments, strong conjectures, and well grounded experiments to counterpoise an objection of so much weight, and to support their opinion from its final overthrow.
Simpl.Fair and softly good Sir, for haply you may not yet be got so far as you perswade your self you are gone. And though I am not an absolute master of the subject of that narra​tion given us by Salviatus;Though the annual motion assigned to the Earth answerth to the Phænomena of the solar spots, yet doth it not follow by conversion that from the Phænomena of the spots one may infor the annual motion to belong to the Earth. yet do I not find that my Logick, whilst I have a regard to form, teacheth me, that that kind of argumentation affords me any necessary reason to conclude in favour of the Copernican Hypothesis, that is, of the stability of the Sun in the centre of the Zodiack, and of the mobility of the Earth under its circumference. For although it be true, that the said conversion of the Sun, and cirnition of the Earth being granted, there be a necessity of discerning such and such strange extravagancies as these in the spots of the Sun, yet doth it not follow that arguing per conversum, from finding such like unusual accidents in the Sun, one must of necssity conclude the Earth to move by the circumference, and the Sun to be placed in the centre of the Zodiack. For who shall assertain me that the like irregularities may not as well be visible in the Sun, it being moveable by the Ecliptick, to the inhabitants of the Earth, it being also immoveable in the centre of the same? Unlesse you demonstrate to me, that there can be no reason given for that appearance, when the Sun is made moveable, and the Earth stable, I will not alter my opinion and belief that the Sun moveth, and the Earth standeth still.
Sagr.Simplicius behaveth himself very bravely, and argueth very subtilly in defence of the cause of Aristotle and Ptolomy; and if I may speak the truth, mythinks that the conversation of Salviatus, though it have been but of small continuance, hath much farthered him in discoursing silogistically. An effect which I know to be wrought in others as well as him. But as to finding and judging whether competent reason may be rendered of the apparent exorbitancies and irregularities in the motions of the spots, supposing the Earth to be immoveable, and the Sun moveable, I shall expect that Salviatus manifest his opinion to us, for it is very probable that he he hath considered of the same, and collected together whatever may be said upon the point.
Salv.I have often thought thereon, and also discoursed thereof with my Friend and Guest afore-named; and touching what is to be produced by Philosophers and Astronomers, in defence of the ancient Systeme, we are on one hand certain, certain I say,The Pure Peripatetick Philosophers will laugh at the spots and their Phænomena, as illusions of the Chrystals in the Telescope. that the true and pure Peripateticks laughing at such as employ themselves in such, to their thinking, insipid fooleries, will censure all these Phænomena to be vain illusions of the Christals; and in this manner will with little trouble free themselves from the obligation of studying any more upon the same. Again, as to the Astronomical Philosophers, after we have with some diligence weighed that which may be alledged as a mean between those two others, we have not been able to find out an ​answer that sufficeth to satisfie at once the course of the spots, and the discourse of the Mind. I will explain unto you so much as I remember thereof, that so you may judge thereon as seems best unto you.
Supposing that the apparent motions of the Solar spots are the same with those that have been above declared, and supposing the Earth to be immoveable in the centre of the Ecliptick, in whose circumference let the center of the Sun be placed; it is necessary that of all the differences that are seen in those motions, the causes do reside in the motions that are in the body of the Sun: Which in the first place must necessarily revolve in it self (i. e. about its own axis) carrying the spots along therewith;If the Earth be immoveable in the centre of the Zodiack, there must be ascribed to the Sun four several motions, as is declared at length. which spots have been supposed, yea and proved to adhere to the Solar superficies. It must secondly be confest, that the Axis of the Solar conversion is not parallel to the Axis of the Ecliptick, that is as much as to say, that it is not perpendicularly erected upon the Plane of the Ecliptick, because if it were so, the courses and exitions of those spots would seem to be made by right lines parallel to the Ecliptick. The said Axis therefore is inclining, in regard the said courses are for the most part made by curve lines. It will be necessary in the third place to grant that the inclination of this Axis is not fixed, and continually extended towards one and the same point of the Universe, but rather that it doth alwayes from moment to moment go changing its direction; for if the pendency should always look towards the self same point, the courses of the spots would never change appearance; but appearing at one time either right or curved, bending upwards or downwards, ascending or descending, they would appear the same at all times. It is therefore necessary to say, that the said Axis is convertible; and is sometimes found to be in the Plane of the circle that is extreme, terminate, or of the visible Hemisphere, I mean at such time as the courses of the spots seem to be made in right lines, and more than ever pendent, which happeneth twice a year; and at other times found to be in the Plane of the Meridian of the Observator, in such sort that one of its Poles falleth in the visible Hemisphere of the Sun, and the other in the occult; and both of them remote from the extreme points, or we may say, from the poles of another Axis of the Sun, which is parallel to the Axis of the Ecliptick; (which second Axis must necessarily be assigned to the Solar Globe) remote, I say, as far as the inclination of the Axis of the revolution of the spots doth import; and moreover that the Pole falling in the apparent Hemisphere, is one while in the superiour, another while in the inferiour part thereof; for that it must be so, the courses themselves do manifestly evince at such time as they are ​equilibrated, and in their greatest curvity, one while with their convexity towards the upper part, and another while towards the lower part of the Solar Discus. And because those positions are in continuall alteration, making the inclinations and incurvations now greater, now lesser, and sometimes reduce themselves, the first sort to perfect libration, and the second to perfect perpendicularity, it is necessary to assert that the self same Axis of the monethly revolution of the spots hath a particular revolution of its own, whereby its Poles describe two circles about the Poles of another Axis, which for that reason ought (as I have said) to be assigned to the Sun, the semidiameter of which circles answereth to the quantity of the inclination of the said Axis. And it is necessary, that the time of its Period be a year; for that such is the time in which all the appearances and differences in the courses of the spots do return. And that the revolution of this Axis, is made about the Poles of the other Axis parallel to that of the Ecliptick, & not about other points, the greatest inclinations and greatest incurvations, which are always of the same bigness, do clearly prove. So that finally, to maintain the Earth fixed in the centre, it will be necessary to assign to the Sun, two motions about its own centre, upon two several Axes, one of which finisheth its conversion in a year, and the other in lesse than a moneth; which assumption seemeth, to my understanding, very hard, and almost impossible; and this dependeth on the necessity of ascribing to the said Solar body two other motions about the Earth upon different Axes, describing with one the Ecliptick in a year, and with the other forming spirals, or circles parallel to the Equinoctial one every day: whereupon that third motion which ought to be assigned to the Solar Clobe about its own centre (I mean not that almost monethly, which carrieth the spots about, but I speak of that other which ought to passe thorow the Axis and Poles of this monethly one) ought not, for any reason that I see, to finish its Period rather in a year, as depending on the annual motion by the Ecliptick, than in twenty four hours, as depending on the diurnal motion upon the Poles of the Equinoctial. I know, that what I now speak is very obscure, but I shall make it plain unto you, when we come to speak of the third motion annual, assigned by Copernicus, to the Earth. Now if these four motions, so incongruous with each other, (all which it would be necessary to assign to the self same body of the Sun) may be reduced to one sole and simple motion, assigned the Sun upon an Axis that never changeth position, and that without innovating any thing in the motions for so many other causes assigned to the Terrestrial Globe, may so easily salve so many extravagant appearances in ​the motions of the Solar spots, it seemeth really that such an Hypothesis ought not to be rejected.
This, Simplicius, is all that came into the minds of our friend, and my self, that could be alledged in explanation of this Phænomenon by the Copernicans, and by the Ptolomæans, in defence of their opinions. Do you inferre from thence what your judgment perswades you.
Simpl.I acknowledge my self unable to interpose in so important a decision: And, as to my particular thoughts, I will stand neutral; and yet neverthelesse I hope that a time will come, when our minds being illumin'd by more lofty contemplations than these our humane reasonings, we shall be awakened and freed from that mist which now is so great an hinderance to our sight.
Sagr.Excellent and pious is the counsel taken by Simplicius, and worthy to be entertained and followed by all, as that which being derived from the highest wisdome and supreamest authority, may onely, with security be received. But yet so far as humane reason is permitted to penetrate, confining my self within the bounds of conjectures, and probable reasons, I will say a little more resolutely than Simplicius doth, that amongst all the ingenuous subtilties I ever heard, I have never met with any thing of greater admiration to my intellect, nor that hath more absolutely captivated my judgment, (alwayes excepting pure Geometrical and Arithmetical Demonstrations) than these two conjectures taken, the one from the stations and retrogradations of the five Planets, and the other from these irregularities of the motions of the Solar spots: and because they seem to me so easily and clearly to assign the true reason of so extravagant appearances, shewing as if they were but one sole simple motion, mixed with so many others, simple likewise, but different from each other, without introducing any difficulty, rather with obviating those that accompany the other Hypothesis; I am thinking that I may rationally conclude, that those who contumaciously withstand this Doctrine, either never heard, or never understood, these so convincing arguments.
Salv.I will not ascribe unto them the title either of convincing, or non-convincing; in regard my intention is not, as I have several times told you, to resolve any thing upon so high a question, but onely to propose those natural and Astronomicall reasons, which, for the one and other Systeme, may be produced by me, leaving the determination to others; which determination cannot at last, but be very manifest: for one of the two positions being of necessity to be true, and the other of necessity to be false, it is a thing impossible that (alwayes confining our selves ​within the limits of humane doctrine) the reasons alledged for the true Hypothesis should not manifest themselves as concludent as those for the contrary vain and ineffectual.
Sagr.It will be time therefore, that we hear the objections of the little Book of ** I should have told you, that the true name of this concealed Authour is Christopher Scheinerus, and its title Disquisitiones Mathematicæ. Conclusions, or Disquisitions which Simplicius did bring with him.
Simpl.Here is the Book, and this is the place where the Author first briefly describeth the Systeme of the world, according to the Hypothesis of Copernicus, saying, Terram igitur unà cum Luna, totoque hoc elementari mundo Copernicus, &c.
Salv.Forbear a little, Simplicius, for methinks that this Authour, in this first entrance, shews himself to be but very ill verst in the Hypothesis which he goeth about to confute, in regard, he saith that Copernicus maketh the Earth, together with the Moon, to describe the ** i.e. the Ecliptick grand Orb in a year moving from East to West; a thing that as it is false and impossible, so was it never affirmed by Copernicus, who rather maketh it to move the contrary way, I mean from West to East, that is, according to the order of the Signes; whereupon we come to think the same to be the annual motion of the Sun, constituted immoveable in the centre of the Zodiack. See the too adventurous confidence of this man; to undertake the confutation of anothers Doctrine, and yet to be ignorant of the primary fundamentals; upon which his adversary layeth the greatest and most important part of all the Fabrick. This is a bad beginning to gain himself credit with his Reader; but let us go on.
Simpl.Having explained the Universal Systeme, he beginneth to propound his objections against this annual motion: and the first are these, which he citeth Ironically, and in derision of Copernicus,Instances of a certain Book Ironically propounded against Copernicus. and of his followers, writing that in this phantastical Hypothesis of the World one must necessarily maintain very grosse absurdities; namely, that the Sun, Venus, and Mercury are below the Earth; and that grave matters go naturally upwards, and the light downwards; and that Christ, our Lord and Redeemer, ascended into Hell, and descended into Heaven, when he approached towards the Sun, and that when Joshuah commanded the Sun to stand still, the Earth stood still, or the Sun moved a contrary way to that of the Earth; and that when the Sun is in Cancer, the Earth runneth through Capricorn; and that the Hyemal (or Winter) Signes make the Summer, and the Æstival Winter; and that the Stars do not rise and set to the Earth, but the Earth to the Stars; and that the East beginneth in the West, and the West in the East; and, in a word, that almost the whole course of the World is inverted.
Salv.Every thing pleaseth me, except it be his having inter​mixed places out of the sacred Scriptures (alwayes venerable, and to be rever'd) amongst these, but two scurrilous fooleries, and attempting to wound with holy Weapons, those who Philosophating in jest, and for divertisement, neither affirm nor deny, but, some presupposals and positions being assumed, do familiarly argue.
Simpl.Truth is, he hath displeased me also, and that not a little; and especially, by adding presently after that, howbeit, the Copernichists answer, though but very impertinently to these and such like other reasons, yet can they not reconcile nor answer those things that follow.
Salv.This is worse than all the rest; for he pretendeth to have things more efficacious and concludent than the Authorities of the sacred Leaves; But I pray you, let us reverence them, and passe on to natural and humane reasons: and yet if he give us amongst his natural arguments, things of no more solidity, than those hitherto alleadged, we may wholly decline this undertaking, for I as to my own parricular, do not think it fit to spend words in answering such trifling impertinencies. And as to what he saith, that the Copernicans answer to these objections, it is most false, nor may it be thought, that any man should set him self to wast his time so unprofitably.
Simpl.I concur with you in the same judgement;Supposing the annual motion to belong to the Earth, it followeth, that one fixed Star, is bigger than the whole grand Orb. therefore let us hear the other instances that he brings, as much stronger. And observe here, how he with very exact computations concludeth, that if the grand Orb of the Earth, or the ecliptick, in which Copernicus maketh it to run in a year round the Sun, should be as it were, insensible, in respect of the immensitie of the Starry Sphære, according as the said Copernicus, saith it is to be supposed, it would be necessary to grant and confirm, that the fixed Stars were remote from us, an unconceivable distance, and that the lesser of them, were bigger than the whole grand Orb aforesaid, and some other much bigger than the whole Sphære of Saturn; Masses certainly too excessively vast, unimaginable, and incredible.
Salv.I have heretofore seen such another objection brought by Tycho against Copernicus,Tycho his Argument grounded upon a false Hypothesis. and this is not the first time that I have discovered the fallacy, or, to say better, the fallacies of this Argumemtation, founded upon a most false Hypothesis, and upon a Proposition of the said Copernicus,Litigious Lawyers that are entertained in an ill cause, keep close to some expression fallen from the adverse party at unawares. understood by his adversaries, with too punctual a nicity, according to the practise of those pleaders, who finding the flaw to be in the very merit of their cause, keep to some one word, fallen unawares from the contrary partie, and fly out into loud and tedious descants upon that. But for your better information; Copernicus having declared ​those admirable consequences which are derived from the Earths annual motion, to the other Planets, that is to say, of the ** Or progressions. directions and retrogradations of the three uppermost in particular;The apparent diversity of motion in the Planets, is insensible in the fixed Start. he subjoyneth, that this apparent mutation (which is discerned more in Mars than in Jupiter, by reason Jupiter is more remote, and yet lesse in Saturn, by reason it is more remote than Jupiter) in the fixed Stars, did remain imperceptible, by reason of their immense remotenesse from us, in comparison of the distances of Jupiter or Saturn. Here the Adversaries of this opinion rise up, and supposing that fore-named imperceptibility of Copernicus, as if it had been taken by him, for a real and absolute thing of nothing, and adding, that a fixed Star of one of the lesser magnitudes, is notwithstanding perceptible, seeing that it cometh under the sence of seeing, they go on to calculate with the intervention of other false assumptions, and concluding that it is necessary by the Copernican Doctrine, to admit, that a fixed Star is much bigger than the whole grand Orb.Supposing that a fixed Star of the sixth magnitude is no bigger than the Sun, the diversitie which is so great in the Planets, in the fixed Stars is almost insensible. Now to discover the vanity of this their whole proceeding, I shall shew that a fixed Star of the sixth magnitude, being supposed to be no bigger than the Sun, one may thence conclude with true demonstrations, that the distance of the said fixed Stars from us, cometh to be so great, that the annual motion of the Earth, which causeth so great and notable variations in the Planets, appears scarce observable in them; and at the same time, I will distinctly shew the gross fallacies, in the assumptions of Copernicus his Adversaries.
And first of all,The distance of the Sun, containeth 1208 Semid. of the Earth. I suppose with the said Copernicus, and also with his opposers, that the Semidiameter of the grand Orb, which is the distance of the Earth from the Sun, containeth 1208 Semidiameters of the said Earth. Secondly, I premise with the allowance aforesaid, and of truth, that the ** The Diameter of the Sun, half a degree. apparent diameter of the Sun in its mean distance, to be about half a degree, that is, 30. min. prim. which are 1800. seconds, that is, 108000. thirds. And because the The Diameter of a fixed Star, of the first magnitude, and of one of the sixth. apparent Diameter of a fixed Star of the first magnitude, is no more than 5. seconds, that is, 300. thirds, and the Diameter of a fixed Star of the sixth magnitude, 50. thirds, (and herein is the greatest errour of the Anti-Copernicans) Therefore the Diameter of the Sun,The apparent Diameter of the Sun, how much it is bigger than that of a fixed star. containeth the Diameter of a fixed Star of the sixth magnitude 2160. times. And therefore if a fixed Star of the sixth magnitude, were supposed to be really equal to the Sun, and not bigger, which is the same as to say, if the Sun were so far removed, that its Diameter should seem to be one of the 2160. parts of what it now appeareth, its distance ought of necessity to be 2160. times greater than now in effect it is, which is as much as to say, that the distance of the fixed Stars of the sixth magnitude, is 2160. Semidiameters of the grand ​Orb.The distance of a fixed star of the sixth magnitude, how much it is, the star being supposed to be equal to the Sun. And because the distance of the Sun from the Earth, contains by common consent 1208. Semidiameters of the said Earth, and the distance of the fixed Stars (as hath been said) 2160. Semediameters of the grand Orb, therefore the Semidiameter of the Earth is much greater (that is almost double) in comparison of the grand Orb, than the Semidiameter of the grand Orb, in relation to the distance of the Starry Sphære;In the fixed stars the diversitie of aspect, caused by the grand Orb, is little more then that caused by the Earth in the Snn. and therefore the variation of aspect in the fixed Stars, caused by the Diameter of the grand Orb, can be but little more observable, than that which is observed in the Sun, occasioned by the Semidiameter of the Earth.
Sagr.This is a great fall for the first step.
Salv.It is doubtlesse an errour; for a fixed Star of the sixth magnitude,A star of the sixth magnitude, supposed by Tycho and the Authour of the Book of Conclusions, an hundred and six millions of times bigger than needs. which by the computation of this Authour, ought, for the upholding the proposition of Copernicus, to be as big as the whole grand Orb, onely by supposing it equal to the Sun, which Sun is lesse by far, than the hundred and six millionth part of the said grand Orb, maketh the starry Sphære so great and high as sufficeth to overthrow the instance brought against the said Copernicus.
Sagr.Favour me with this computation.
Salv.The supputation is easie and short. The Diameter of the Sun,The computation of the magnitude of the fixed Stars, in respect to the grand Orb. is eleven semidiameters of the Earth, and the Diameter of the grand Orb, contains 2416. of those same semidiameters, by the ascent of both parties; so that the Diameter of the said Orb, contains the Suns Diameter 220. times very near. And because the Spheres are to one another, as the Cubes of their Diameters, let us make the Cube of 220. which is 106480000. and we shall have the grand Orb, an hundred and six millions, four hundred and eighty thousand times bigger than the Sun, to which grand Orb, a star of the sixth magnitude, ought to be equal, according to the assertion of this Authour.
Sagr.The errour then of these men, consisteth in being extreamly mistaken, in taking the apparent Diameter of the fixed Stars.
Salv.This is one, but not the onely errour of them; and indeed,A common errour of all the Astronomers, touching the magnitude of the stars. I do very much admire how so many Astronomers, and those very famous, as are Alfagranus, Albategnus, Tebizius, and much more modernly the Tycho's and Clavins's, and in sum, all the predecessors of our Academian, should have been so grosly mistaken, in determining the magnitudes of all the Stars, as well fixed as moveable, the two Luminaries excepted out of that number; and that they have not taken any heed to the adventitious irradiations that deceitfully represent them an hundred and more times bigger, than when they are beheld, without those capilli​ous rayes, nor can this their inadvertency be excused, in regard that it was in their power to have beheld them at their pleasure without those tresses, which is done, by looking upon them at their first appearance in the evening,Venus renders the errour of Astronomers in determining the magnitudes of stars inexcusable. or their last occultation in the comming on of day; and if none of the rest, yet Venus, which oft times is seen at noon day, so small, that one must sharpen the sight in discerning it; and again, in the following night, seemeth a great flake of light, might advertise them of their fallacy; for I will not believe that they thought the true Discus to be that which is seen in the obscurest darknesses, and not that which is discerned in the luminous Medium: for our lights, which seen by night afar off appear great, and neer at hand shew their true lustre to be terminate and small, might have easily have made them cautious; nay, if I may freely speak my thoughts, I absolutely believe that none of them, no not Tycho himself, so accurate in handling Astronomical Instruments, and that so great and accurate, without sparing very great cost in their construction, did ever go about to take and measure the apparent diameter of any Star, the Sun and Moon excepted; but I think, that arbitrarily, and as we say, with the eye, some one of the more antient of them pronounced the thing to be so and so, and that all that followed him afterwards, without more ado, kept close to what the first had said; for if any one of them had applied himself to have made some new proof of the same, he would doubtlesse have discovered the fraud.
Sagr.But if they wanted the Telescope, and you have already said, that our Friend with that same Instrument came to the knowledge of the truth, they ought to be excused, and not accused of ignorance.
Salv.This would hold good, if without the Telescope the businesse could not be effected. Its true, that this Instrument by shewing the Discus of the Star naked, and magnified an hundred or a thousand times, rendereth the operation much more easie, but the same thing may be done, although not altogether so exactly, without the Instrument, and I have many times done the same, and my method therein was this. I have caused a rope to be hanged towards some Star,A way to measure the apparent diameter of a star. and I have made use of the Constellation, called the Harp, which riseth between the North and ** Rendred in Latine Corum, that is to say, Northwest. North-east, and then by going towards, and from the said rope, interposed between me and the Star, I have found the place from whence the thicknesse of the rope hath just hid the Star from me: this done, I have taken the distance from the eye to the rope, which was one of the sides including the angle that was composed in the eye, and ** i.e. Is subtended by. which insisteth upon the thicknesse of the rope, and which is like, yea the same with the ​angle in the Starry Sphere, that insisteth upon the diameter of the Star, and by the proportion of the ropes thicknesse to the distance from the eye to the rope, by the table of Arches and Chords, I have immediately found the quantity of the angle; using all the while the wonted caution that is observed in taking angles so acute, not to forme the concourse of the visive rayes in the centre of the eye, where they are onely refracted, but beyond the eye, where really the pupils greatnesse maketh them to concur.
Sagr.I apprehend this your cautelous procedure, albeit I have a kind of hæsitancy touching the same, but that which most puzzleth me is, that in this operation, if it be made in the dark of night, methinks that you measure the diameter of the irradiated Discus, and not the true and naked face of the Star.
Salv.Not so, Sir, for the rope in covering the naked body of the Star, taketh away the rayes, which belong not to it, but to our eye, of which it is deprived so soon as the true Discus thereof is hid; and in making the observation, you shall see, how unexpectedly a little cord will cover that reasonable big body of light, which seemed impossible to be hid, unlesse it were with a much broader Screene: to measure, in the next place, and exactly to find out, how many of those thicknesses of the rope interpose in the distance between the said rope and the eye, I take not onely one diameter of the rope, but laying many pieces of the same together upon a Table, so that they touch, I take with a pair of Compasses the whole space occupied by fifteen, or twenty of them, and with that measure I commensurate the distance before with another smaller cord taken from the rope to the concourse of the visive rayes. And with this sufficiently-exact operation I finde the apparent diameter of a fixed Star of the first magnitude, commonly esteemed to be 2 min. pri. and also 3 min. prim. by Tycho in his Astronomical Letters,The diameter of a fixed star of the first magnitude not more than five sec. min. cap. 167. to be no more than 5 seconds, which is one of the 24. or 36. parts of what they have held it: see now upon what grosse errours their Doctrines are founded.
Sagr.I see and comprehend this very well, but before we passe any further, I would propound the doubt that ariseth in me in the finding the concourse [or intersection] of the visual rayes beyond the eye, when observation is made of objects comprehended between very acute angles; and my scruple proceeds from thinking, that the said concourse may be sometimes more remote, and sometimes lesse; and this not so much, by meanes of the greater or lesser magnitude of the object that is beheld, as because that in observing objects of the same bignesse, it seems to me that the concourse of the rayes, for certain other re​spects ought to be made more and lesse remote from the eye.
Salv.I see already, whither the apprehension of Sagredus, a most diligent observer of Natures secrets, tendeth; and I would lay any wager,The circle of the pupil of the eye enlargeth and contracteth. that amongst the thousands that have observed Cats to contract and inlarge the pupils of their eyes very much, there are not two, nor haply one that hath observed the like effect to be wrought by the pupils of men in seeing, whilst the medium is much or little illumin'd, and that in the open light the circlet of the pupil diminisheth considerably: so that in looking upon the face or Discus of the Sun, it is reduced to a smallnesse lesser than a grain of * * Panicum, a small grain like to Mill, I take it to be the same with that called Bird Seed.Panick, and in beholding objects that do not shine, and are in a lesse luminous medium, it is inlarged to the bignesse of a Lintel or more; and in summe this expansion and contraction differeth in more than decuple proportion: From whence it is manifest, that when the pupil is much dilated, it is necessary that the angle of the rayes concourse be more remote from the eye; which happeneth in beholding objects little luminated. This is a Doctrine which Sagredus hath, just now, given me the hint of, whereby, if we were to make 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 ** Strisce. How to find the distance of the rays concourse from the pupil. 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 op​posite 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.
Simpl.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.All Astronomers agree that the greater magnitudes of the Orbes is the cause of the tardity of the conversions. 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. considering 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,By another supposition taken from Astronomers, the distance of the fixed Stars is calculated to be 10800 semidiameters of the grand Orb. 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,By the proportion of Jupiter and of Mars, the starry Sphere is found to be yet more remote. and from Mars, that would give it us to be 15000. and this 27000 semidiameters of the grand Orb, to wit, the first seven, and the second twelve times bigger than what the magnitude of the fixed Star, supposed equal to the Sun, did make it.
Simpl.Methinks that to this might be answered, that the motion of the starry Sphere hath, since Ptolomy, been observed not to be so slow as he accounted it; yea, if I mistake not, I have heard that Copernicus himself made the Observation. ​Salv.You say very well; but you alledge nothing in that which may favour the cause of the Ptolomæans in the least, who did never yet reject the motion of 36000. years in the starry Sphere, for that the said tardity would make it too vast and immense. For if that the said immensity was not to be supposed in Nature, they ought before now to to have denied a conversion so slow as that it could not with good proportion adapt it self, save onely to a Sphere of monstrous magnitude.
Sagr.Pray you, Salviatus, let us lose no more time in proceeding, by the way of these proportions with people that are apt to admit things most dis-proportionate; so that its impossible to win any thing upon them this way: and what more disproportionate proportion can be imagined than that which these men swallow down, and admit, in that writing, that there cannot be a more convenient way to dispose the Cœlestial Spheres, in order, than to regulate them by the differences of the times of their periods, placing from one degree to another the more slow above the more swift, when they have constituted the Starry Sphere higher than the rest, as being the slowest, they frame another higher still than that, and consequently greater, and make it revolve in twenty four hours, whilst the next below, it moves not round under 36000. years?
Salv.I could wish, Simplicius, that suspending for a time the affection rhat you bear to the followers of your opinion, you would sincerely tell me, whether you think that they do in their minds comprehend that magnitude, which they reject afterwards as uncapable for its immensity to be ascribed to the Universe. For I,Immense magnitudes and numbers are incomprehensible by our understanding. as to my own part, think that they do not; But believe, that like as in the apprehension of numbers, when once a man begins to passe those millions of millions, the imagination is confounded, and can no longer form a conceipt of the same, so it happens also in comprehending immense magnitudes and distances; so that there intervenes to the comprehension an effect like to that which befalleth the sense; For whilest that in a serene night I look towards the Stars, I judge, according to sense, that their distance is but a few miles, and that the fixed Stars are not a jot more remote than Jupiter or Saturn, nay than the Moon. But without more ado, consider the controversies that have past between the Astronomers and Peripatetick Philosophers, upon occasion of the new Stars of Cassiopeia and of Sagittary, the Astronomers placing them amongst the fixed Stars, and the Philosophers believing them to be below the Moon. So unable is our sense to distinguish great distances from the greatest, though these be in reality many thousand times greater than those. In a word, I ask of thee, O foolish man! Doth thy imagination comprehend ​that vast magnitude of the Universe, which thou afterwards judgest to be too immense? If thou comprehendest it; wilt thou hold that thy apprehension extendeth it self farther than the Divine Power? wilt thou say, that thou canst imagine greater things than those which God can bring to passe? But if thou apprehendest it not, why wilt thou passe thy verdict upon things beyond thy comprehension?
Simpl.All this is very well, nor can it be denied, but that Heaven may in greatnesse surpasse our imagination, as also that God might have created it thousands of times vaster than now it is; but we ought not to grant any thing to have been made in vain, and to be idle in the Universe. Now, in that we see this admirable order of the Planets, disposed about the Earth in distances proportionate for producing their effects for our advantage, to what purpose is it to interpose afterwards between the sublime Orb of Saturn and the starry Sphere, a vast vacancy, without any star that is superfluous, and to no purpose? To what end? For whose profit and advantage?
Salv.Methinks we arrogate too much to our selves, Simplicius, whilst we will have it, that the onely care of us, is the adaequate work, and bound, beyond which the Divine Wisdome and Power doth, or disposeth of nothing. But I will not consent, that we should so much shorten its hand, but desire that we may content our selves with an assurance that God and Nature are so imployed in the governing of humane affairs,God & Nature do imploy themselves in caring for men, as if they minded nothing else. that they could not more apply themselves thereto, although they had no other care than onely that of mankind; and this, I think, I am able to make out by a most pertinent and most noble example, taken from the operation of the Suns light, which whilest it attracteth these vapours,An example of Gods care of mankind taken from the Sun. or scorcheth that plant, it attracteth, it scorcheth them, as if it had no more to do; yea, in ripening that bunch of grapes, nay that one single grape, it doth apply it self so, that it could not be more intense, if the sum of all its business had been the only maturation of that grape. Now if this grape receiveth all that it is possible for it to receive from the Sun, not suffering the least injury by the Suns production of a thousand other effects at the same time; it would be either envy or folly to blame that grape, if it should think or wish that the Sun would onely appropriate its rayes to its advantage. I am confident that nothing is omitted by the Divine Providence, of what concernes the government of humane affairs; but that there may not be other things in the Universe, that depend upon the same infinite Wisdome, I cannot, of my self, by what my reason holds forth to me, bring my self to believe. However, if it were not so, yet should I not forbear to believe the reasons laid before me by ​some more sublime intelligence. In the mean time, if one should tell me, that an immense space interposed between the Orbs of the Planets and the Starry Sphere, deprived of stars and idle, would be vain and uselesse, as likewise that so great an immensity for receipt of the fixed stars, as exceeds our utmost comprehension would be superfluous, I would reply, that it is rashnesse to go about to make our shallow reason judg of the Works of God, and to call vain and superfluous, whatsoever thing in the Universe is not subservient to us.
It is great rashnesse to censure that to be superfluous in the Universe, which we do not perceive to be made for us.Sagr.Say rather, and I believe you would say better, that we know not what is subservient to us; and I hold it one of the greatest vanities, yea follies, that can be in the World, to say, because I know not of what use Jupiter or Saturn are to me, that therefore these Planets are superfluous, yea more, that there are no such things in rerum natura; when as, oh foolish man! I know not so much as to what purpose the arteries, the gristles, the spleen, the gall do serve; nay I should not know that I have a gall, spleen, or kidneys, if in many desected Corps, they were not shewn unto me; and then onely shall I be able to know what the spleen worketh in me, when it comes to be taken from me. To be able to know what this or that Cœlestial body worketh in me (seeing you will have it that all their influences direct themselves to us) it would be requisite to remove that body for some time;By depriving Heaven of some star, one might come to know what influence it hath upon us. and then whatsoever effect I should find wanting in me, I would say that it depended on that star. Moreover, who will presume to say that the space which they call too vast and uselesse between Saturn and the fixed stars, is void of other mundane bodies? Must it be so,Many things may be in Heauen, that are invisible to us because we do not see them? Then the four Medicean Planets, and the companions of Saturn came first into Heaven, when we began to see them, and not before? And by this rule the innumerable other fixed stars had no existence before that men did look on them? and the cloudy constellations called Nebulosæ were at first only white flakes, but afterwards with the Telescope we made them to become constellations of many lucid and bright stars. Oh presumptious, rather oh rash ignorance of man!
Salv.It's to no purpose Sagredus, to sally out any more into these unprofitable exaggerations: Let us pursue our intended designe of examining the validity of the reasons alledged on either side, without determining any thing, remitting the judgment thereof when we have done, to such as are more knowing. Returning therefore to our natural and humane disquisitions, I say,Great, small, immense, &c. are relative terms. that great, little, immense, small, &c. are not absolute, but relative terms, so that the self same thing compared with divers others, may one while be called immense, and another ​while imperceptible, not to say small. This being so, I demand in relation to what the Starry Sphere of Copernicus may be called over vast. In my judgment it cannot be compared, or said to be such, unlesse it be in relation to some other thing of the same kind;Vanity of those mens discourse who judg the starry sphere too vast in the Copernican Hypothesis. now let us take the very least of the same kind, which shall be the Lunar Orb; and if the Starry Orb may be so censured to be too big in respect to that of the Moon, every other magnitude that with like or greater proportion exceedeth another of the same kind, ought to be adjudged too vast, and for the same reason to be denied that they are to be found in the World; and thus an Elephant, and a Whale, shall without more ado be condemned for Chymæra's, and Poetical fictions, because that the one as being too vast in relation to an Ant, which is a Terrestrial animal, and the other in respect to the ** Spilloncola, which is here put for the least of Fishes. Gudgeon, which is a Fish, and are certainly seen to be in rerum natura, would be too immeasurable; for without all dispute, the Elephant and Whale exceed the Ant and Gudgeon in a much greater proportion than the Starry Sphere doth that of the Moon, although we should fancy the said Sphere to be as big as the Copernican Systeme maketh it.The space assigned to a fixed star, is much lesse than that of a Planet. Moreover, how hugely big is the Sphere of Jupiter, or that of Saturn, designed for a receptacle but for one single star; and that very small in comparison of one of the fixed? Certainly if we should assign to every one of the fixed stars for its receptacle so great a part of the Worlds space, it would be necessary to make the Orb wherein such innumerable multitudes of them reside, very many thousands of times bigger than that which serveth the purpose of Copernicus.A star is called in respect of the space that environs it. Besides, do not you call a fixed star very small, I mean even one of the most apparent, and not one of those which shun our sight; and do we not call them so in respect of the vast space circumfused? Now if the whole Starry Sphere were one entire lucid body;The whole starry sphere beheld from a great distance might appear as small as one single star. who is there, that doth not know that in an infinite space there might be assigned a distance so great, as that the said lucid Sphere might from thence shew as little, yea lesse than a fixed star, now appeareth beheld from the Earth? From thence therefore we should then judg that self same thing to be little, which now from hence we esteem to be immeasurably great.
Sagr.Great in my judgment, is the folly of those who would have had God to have made the World more proportinal to the narrow capacities of their reason, than to his immense, rather infinite power.
Simpl.All this that you say is very true; but that upon which the adversary makes a scruple, is, to grant that a fixed star should be not onely equal to, but so much bigger than the Sun; when as they both are particular bodies situate within the ​Starry Orb: "And indeed in my opinion this Authour very pertinently questioneth and asketh: To what end, and for whose sake are such huge machines made?Instances of the Authour of the Conclusions by way of interrogation. Were they produced for the Earth, for an inconsiderable point? And why so remote? To the end they might seem so very small, and might have no influence at all upon the Earth? To what purpose is such a needlesse monstrous ** Or Gulph. immensity between them and Saturn? All those assertions fall to the ground that are not upheld by probable reasons."
Salv.I conceive by the questions which this person asketh, that one may collect,Answers to the interrogatories of the said Authour. that in case the Heavens, the Stars, and the quantity of their distances and magnitudes which he hath hitherto held, be let alone, (although he never certainly fancied to himself any conceivable magnitude thereof) he perfectly discerns and comprehends the benefits that flow from thence to the Earth, which is no longer an inconsiderable thing; nor are they any longer so remote as to appeare so very small, but big enough to be able to operate on the Earth; and that the distance between them and Saturn is very well proportioned, and that he, for all these things, hath very probable reasons; of which I would gladly have heard some one:The Authour of the Conclusions confound and contradicts himself in his interrogations. but being that in these few words he confounds and contradicts himself, it maketh me think that he is very poor and ill furnished with those probable reasons, and that those which he calls reasons, are rather fallacies, or dreams of an over-weening fancy. For I ask of him, whether these Celestial bodies truly operate on the Earth,Interrogatories put to the Authour of the Conclusions, by which the weaknesse of his is made appear. and whether for the working of those effects they were produced of such and such magnitudes, and disposed at such and such distances, or else whether they have nothing at all to do with Terrene mattets. If they have nothing to do with the Earth; it is a great folly for us that are Earth-born, to offer to make our selves arbitrators of their magnitudes, and regulators of their local dispositions, seeing that we are altogether ignorant of their whole businesse and concerns; but if he shall say that they do operate, and that they are directed to this end, he doth affirm the same thing which a little before he denied, and praiseth that which even now he condemned, in that he said, that the Celestial bodies situate so far remote as that they appear very small, cannot have any influence at all upon the Earth. But, good Sir, in the Starry Sphere pre-established at its present distance, and which you did acknowledg to be in your judgment, well proportioned to have an influence upon these Terrene bodies, many stars appear very small, and an hundred times as many more are wholly invisible unto us (which is an appearing yet lesse than very small) therefore it is necessary that (contradicting your self) you do ​now deny their operation upon the Earth; or else that (still contradicting your self) you grant that their appearing very small doth not in the least lessen their influence; or else that (and this shall be a more sincere and modest concession) you acknowledg and freely confesse, that our passing judgment upon their magnitudes and distances is a vanity, not to say presumption or rashnesse.
Simpl.Truth is, I my self did also, in reading this passage perceive the manifest contradiction, in saying, that the Stars (if one may so speak) of Copernicus appearing so very small, could not operate on the Earth, and not perceiving that he had granted an influence upon the Earth to those of Ptolomy, and his sectators, which appear not only very small, but are, for the most part, very invisible.
Salv.But I proceed to another consideration: What is the reason, doth he say, why the stars appear so little? Is it haply, because they seem so to us?That remote objects appeare so small, is the defect of the eye, as is demonstrated. Doth not he know, that this commeth from the Instrument that we imploy in beholding them, to wit, from our eye? And that this is true, by changing Instrument, we shall see them bigger and bigger, as much as we will. And who knows but that to the Earth, which beholdeth them without eyes, they may not shew very great, and such as in reality they are? But it's time that, omitting these trifles, we come to things of more moment; and therefore I having already demonstrated these two things: First, how far off the Firmament ought to be placed to make, that the grand Orb causeth no greater difference than that which the Terrestrial Orb occasioneth in the remotenesse of the Sun; And next, how likewise to make that a star of the Firmament appear to us of the same bignesse, as now we see it, it is not necessary to suppose it bigger than the Sun; I would know whether Tycho, or any of his adherents hath ever attempted to find out, by any means, whether any appearance be to be discovered in the starry Sphere, upon which one may the more resolutely deny or admit the annual motion of the Earth.
Sagr.I would answer for them, that there is not, no nor is there any need there should;Tycho nor his followers ever attempted to see whether there are any appearances in the Firmament for or against the annual motion. seeing that it is Copernicus himself that saith, that no such diversity is there: and they, arguing ad hominem, admit him the same; and upon this assumption they demonstrate the improbability that followeth thereupon, namely, that it would be necessary to make the Sphere so immense, that a fixed star, to appear unto us as great as it now seems, ought of necessity to be of so immense a magnitude, as that it would exceed the bignesse of the whole grand Orb, a thing, which notwithstanding, as they say, is altogether incredible.
​Salv.I am of the same judgment, and verily believe that they argue contra hominem, studying more to defend another man, than desiring to come to the knowledge of the truth. And I do not only believe,Astronomers, perhaps, have not known what appearances ought to follow upon the annual motion of the Earth. that none of them ever applied themselves to make any such observation, but I am also uncertain, whether any of them do know what alteration the Earths annual motion ought to produce in the fixed stars, in case the starry Sphere were not so far distant, as that in them the said diversity, by reason of its minuity dis-appeareth; for their surceasing that inquisition, and referring themselves to the meer assertion of Copernicus, may very well serve to convict a man, but not to acquit him of the fact:Copernicus understood not some things for want of Instruments. For its possible that such a diversity may be, and yet not have been sought for; or that either by reason of its minuity, or for want of exact Instruments it was not discovered by Copernicus; for though it were so, this would not be the first thing, that he either for want of Instruments, or for some other defect hath not known; and yet he proceeding upon other solid and rational conjectures, affirmeth that, which the things by him not discovered do seem to contradict: for, as hath been said already, without the Telescope, neither could Mars be discerned to increase 60. times; nor Venus 40. more in that than in this position; yea, their differences appear much lesse than really they are and yet neverthelesse it is certainly discovered at length, that those mutations are the same, to an hair that the Copernican Systeme required.Tycho and others argue against the annual motion, from the invariable elevation of the Pole. Now it would be very well, if with the greatest accuratenesse possible one should enquire whether such a mutation as ought to be discoverable in the fixed stars, supposing the annual motion of the Earth, would be observed really and in effect, a thing which I verily believe hath never as yet been done by any; done, said I? no, nor haply (as I said before) by many well understood how it ought to be done. Nor speak I this at randome, for I have heretofore seen a certain Manuscript of one of these Anti-Copernicans, which said, that there would necessarily follow, in case that opinion were true, a continual rising and falling of the Pole from six moneths to six moneths, according as the Earth in such a time, by such a space as is the diameter of the grand Orb, retireth one while towards the North, and another while towards the South; and yet it seemed to him reasonable, yea necessary, that we, following the Earth, when we were towards the North should have the Pole more elevated than when we are towards the South. In this very error did one fall that was otherwise a very skilful Mathematician, & a follower of Copernic. as Tycho relateth in his * * Christophorus Rothmannus.Progymnasma. pag. 684. which said, that he had observed the Polar altitude to vary, and to differ in Summer from what it is in Winter: and because Tycho denieth the merit ​of the cause, but findeth no fault with the method of it; that is, denieth that there is any mutation to be seen in the altitude of the Pole, but doth not blame the inquisition, for not being adapted to the finding of what is sought, he thereby sheweth, that he also esteeemed the Polar altitude varied, or not varied every six moneths, to be a good testimony to disprove or inferre the annual motion of the Earth.
Simpl.In truth, Salviatus, my opinion also tells me, that the same must necessarily ensue: for I do not think that you will deny me, but that if we walk only 60. miles towards the North, the Pole will rise unto us a degree higher, and that if we move 60. miles farther Northwards, the Pole will be elevated to us a degree more, &c. Now if the approaching or receding 60. miles onely, make so notable a change in the Polar altitudes, what alteration would follow, if the Earth and we with it, should be transported, I will not say 60. miles, but 60. thousand miles that way.
Salv.It would follow (if it should proceed in the same proportion) that the Pole shall be elevated a thousand degrees. See, Simplicius, what a long rooted opinion can do. Yea, by reason you have fixed it in your mind for so many years, that it is Heaven, that revolveth in twenty four hours, and not the Earth, and that consequently the Poles of that Revolution are in Heaven, and not in the Terrestrial Globe, cannot now, in an hours time shake off this habituated conceipt, and take up the contrary, fancying to your self, that the Earth is that which moveth, only for so long time as may suffice to conceive of what would follow, thereupon should that lye be a truth. If the Earth Simplicius, be that which moveth in its self in twenty four hours, in it are the Poles, in it is the Axis, in it is the Equinoctial, that is, the grand Circle, described by the point, equidistant from the Poles, in it are the infinite Parallels bigger and lesser described by the points of the superficies more and lesse distant from the Poles, in it are all these things, and not in the starry Sphere, which, as being immoveable, wants them all, and can only by the imagination be conceived to be therein, prolonging the Axis of the Earth so far, till that determining, it shall mark out two points placed right over our Poles, and the plane of the Equinoctial being extended, it shall describe in Heaven a circle like it self. Now if the true Axis, the true Poles, the true Equinoctial, do not change in the Earth so long as you continue in the same place of the Earth, and though the Earth be transported, as you do please, yet you shall not change your habitude either to the Poles, or to the circles, or to any other Earthly thing; and this because, that that transposition being common to you and to all Terrestrial ​things;Motion where it is common, is as if it never were. and that motion where it is common, is as if it never were; and as you change not habitude to the Terrestrial Poles (habitude I say, whether that they rise, or descend) so neither shall you change position to the Poles imagined in Heaven; alwayes provided that by Celestial Poles we understand (as hath been already defined) those two points that come to be marked out by the prolongation of the Terrestrial Axis unto that length. Tis true those points in Heaven do change, when the Earths transportment is made after such a manner, that its Axis cometh to passe by other and other points of the immoveable Celestial Sphere, but our habitude thereunto changeth not, so as that the second should be more elevated to us than the first. If any one will have one of the points of the Firmament, which do answer to the Poles of the Earth to ascend, and the other to descend, he must walk along the Earth towards the one, receding from the other, for the transportment of the Earth, and with it us our selves, (as I told you before) operates nothing at all.
Sagr.Permit me, I beseech you Salviatus, to make this a little more clear by an example, which although grosse, is acommodated to this purpose.An example fitted to prove that the altitude of the Pole ought not to vary by means of the Earths annual motion. Suppose your self, Simplicius, to be aboard a Ship, and that standing in the Poope, or Hin-deck; you have directed a Quadrant, or some other Astronomical Instrument, towards the top of the Top-gallant-Mast, as if you would take its height, which suppose it were v. gr. 40. degrees, there is no doubt, but that if you walk along the ** Corsia, the bank or bench on which slaves sit in a Gally. Hatches towards the Mast 25. or 30. paces; and then again direct the said Instrument to the same Top-Gallant-Top. You shall find its elevation to be greater, and to be encreased v. gr. 10. degrees; but if instead of walking those 25. or 30. paces towards the Mast, you stand still at the Sterne, and make the whole Ship to move thitherwards, do you believe that by reason of the 25. or 30. paces that it had past, the elevation of the Top-Gallant-Top would shew 10. degrees encreased?
Simpl.I believe and know that it would not gain an hairs breadth in the passing of 30. paces, nor of a thousand, no nor of an hundred thousand miles; but yet I believe withal that looking through the sights at the Top and Top-Gallant, if I should find a fixed Star that was in the same elevation, I believe I say, that, holding still the Quadrant, after I had sailed towards the star 60. miles, the eye would meet with the top of the said Mast, as before, but not with the star, which would be elevated to me one degree.
Sagr.Then you do not think that the sight would fall upon that point of the Starry Sphere, that answereth to the direction of the Top-Gallant Top?
​Simpl.No: For the point would be changed, and would be beneath the star first observed.
Sagr.You are in the right. Now like as that which in this example answereth to the elevation of the Top-Gallant-Top, is not the star, but the point of the Firmament that lyeth in a right line with the eye, and the said top of the Mast, so in the case exemplified, that which in the Firmament answers to the Pole of the Earth, is not a star, or other fixed thing in the Firmament; but is that point in which the Axis of the Earth continued streight out, till it cometh thither doth determine, which point is not fixed, but obeyeth the mutations that the Pole of the Earth doth make.Upon the annual motion of the Earth, alteration may ensue in some fixed star, not in the Pole. And therefore Tycho, or who ever else that did alledg this objection, ought to have said that upon that same motion of the Earth, were it true, one might observe some difference in the elevation and depression (not of the Pole, but) of some fixed star toward that part which answereth to our Pole.
Simpl.I already very well understand the mistake by them committed; but yet therefore (which to me seems very great) of the argument brought on the contrary is not lessened, supposing relation to be had to the variation of the stars, and not of the Pole; for if the moving of the Ship but 60. miles, make a fixed star rise to me one degree, shall I not find alike, yea and very much greater mutation, if the Ship should sail towards the said star for so much space as is the Diameter of the Grand Orb, which you affirm to be double the distance that is between the Earth and Sun?
Sagr.Herein Simplicius, there is another fallacy, which, truth is,The equivoke of those who believe that in the annual motion great mutations are to be made about the elevation of a fixed star, is confuted. you understand, but do not upon the sudden think of the same, but I will try to bring it to your remembrance: Tell me therefore; if when after you have directed the Quadrant to a fixed star, and found v. g. its elevation to be 40. degrees, you should without stirring from the place, incline the side of the Quadrant, so as that the star might remain elevated above that direction, would you thereupon say that the star had acquired greater elevation?
Simpl.Certainly no: For the mutation was made in the Instrument and not in the Observer, that did change place, moving towards the same.
Sagr.But if you sail or walk along the surface of the Terrestrial Globe, will you say that there is no alteration made in the said Quadrant, but that the same elevation is still retained in respect of the Heavens, so long as you your self do not incline it, but let it stand at its first constitution? Simpl.
Give me leave to think of it. I would say without more ado, that it would not retain the same, in regard the pro​gresse I make is not in plano, but about the circumference of the Terrestrial Globe, which at every step changeth inclination in respect to Heaven, and consequently maketh the same change in the Instrument which is erected upon the same.
Sagr.You say very well: And you know withal, that by how much the bigger that circle shall be upon which you move, so many more miles you are to walk, to make the said star to rise that same degree higher; and that finally if the motion towards the star should be in a right line, you ought to move yet farther, than if it were about the circumference of never so great a circle?
Salv.True:The right line, and circumference of an infinite circle, are the same thing. For in short the circumference of an infinite circle, and a right line are the same thing.
Sagr.But this I do not understand, nor as I believe, doth Simplicius apprehend the same; and it must needs be concealed from us under some mistery, for we know that Salviatus never speaks at random, nor proposeth any Paradox, which doth not break forth into some conceit, not trivial in the least. Therefore in due time and place I will put you in mind to demonstrate this, that the right line is the same with the circumference of an infinite circle, but at present I am unwilling that we should interrupt the discourse in hand. Returning then to the case, I propose to the consideration of Simplicius, how the accession and recession that the Earth makes from the said fixed star which is neer the Pole can be made as it were by a right line, for such is the Diameter of the Grand Orb, so that the attempting to regulate the elevation and depression of the Polar star by the motion along the said Diameter, as if it were by the motion about the little circle of the Earth, is a great argument of but little judgment.
Simpl.But we continue still unsatisfied, in regard that the said small mutation that should be therein, would not be discerned; and if this be null, then must the annual motion about the Grand Orb ascribed to the Earth, be null also.
Sagr.Here now I give Salviatus leave to go on, who as I believe will not overpasse the elevation and depression of the Polar star or any other of those that are fixed as null, although not discovered by any one, and affirmed by Copernicus himself to be, I will not say null, but unobservable by reason of its minuity.
Salv.I have already said above, that I do not think that any one did ever set himself to observe,Enquiry is made what mutations, & in what stars, are to be discovered, by means of the annual motion of the Earth. whether in different times of the year there is any mutation to be seen in the fixed stars, that may have a dependance on the annual motion of the Earth, and added withal, that I doubted least haply some might never have ​understood what those mutations are, and amongst what stars they should be discerned; therefore it would be necessary that we in the next place narrowly examine this particular.Astronomers having omitted to instance what alterations those are that may be derived from the annual motion of the Earth, do thereby testifie that they never rightly understood the same. My having onely found written in general terms that the annual motion of the Earth about the Grand Orb, ought not to be admitted, because it is not probable but that by means of the same there would be discoverd some apparent mutation in the fixed stars, and not hearing say what those apparent mutations ought to be in particular, and in what stars, maketh me very reasonably to infer that they who rely upon that general position, have not understood, no nor possibly endeavoured to understand, how the businesse of these mutations goeth, nor what things those are which they say ought to be seen.The mutations of the fixed stars ought to be in some greater, in others lesser, and in others nothing at all. And to this judgment I am the rather induced; knowing that the annual motion ascribed by Copernicus to the Earth, if it should appear sensible in the Starry Sphere, is not to make apparent mutations equal in respect to all the stars, but those appearances ought to be made in some greater, in others lesser, and in others yet lesser; and lastly, in others absolutely nothing at all, by reason of the vast magnitude that the circle of this annual motion is supposed to be of. As for the mutations that should b• seen, they are of two kinds, one is the said stars changing apparent magnitude, and the other their variation of altitudes in the Meridian. Upon which necessarily followeth the mutation of risings and settings, and of their distances from the Zenith, &c.
Sagr.Methinks I see preparing for me such a skean of these revolutions, that I wish it may never be my task to dis-intangle them, for to confesse my infirmity to Salviatus, I have sometimes thought thereon, but could never find the ** Bandola that end of a skeen where with housewives fasten their hankes of yarn, thread or silk. Lay-band of it, and I speak not so much of this which pertains to the fixed stars, as of another more terrible labour which you bring to my remembrance by maintaining these Meridian Altitudes, Ortive Latitudes and distances from the Vertex, &c.The grand difficulty in Copernicus his Doctrine, is that which concerns the Phænomena of the Sun and fixed stars. And that which puzzleth my brains, ariseth from what I am now about to tell you. Copernicus supposeth the Starry Sphere immoveable, and the Sun in the centre thereof immoveable also. Therefore every mutation which seemeth unto us to be made in the Sun or in the fixed stars, must of necessity befall the Earth and be ous. But the Sun riseth and declineth in our Meridian by a very great arch of almost 47. degrees, and by arches yet greater and greatet, varieth its Ortive and Occidual Latitudes in the oblique Horizons. Now how can the Earth ever incline and elevate so notably to the Sun, and nothing at all to the fixed stars, or so little, that it is not to be perceived? This is that knot which could never get thorow my ** Pettine, it is the stay in a Weavets Loom, that permitteth no knot or snarle to passe it, called by them the Combe of the Loom. Loom-Combe; and if you shall ​untie it, I shall hold you for more than an Alexander.
Salv.These are scruples worthy of the ingenuity of Sagredus, and this doubt is so intricate, that even Copernicus himself almost despaired of being able to explain the same, so as to render it intelligible, which we see as well by his own confession of its obscurity, as also by his, at two several times, taking two different wayes to make it out. And, I ingenuously confesse that I understood not his explanation, till such time as another method more plain and manifest, had rendred it intelligible; and yet neither was that done without a long and laborious application of my thoughts to the same.
Simpl.Aristotle saw the same scruple,Aristotles argument against the Ancients, who held that the Earth was a Planet. and makes use thereof to oppose certain of the Ancients, who held that the Earth was a Planet; against whom he argueth, that if it were so, it would follow that it also, as the rest of the Planets, should have a plurality of motions, from whence would follow these variations in the risings and settings of the fixed stars, and likewise in the Meridian Altitudes. And in regard that he propoundeth the difficulty, and doth not answer it, it must needs be, if not impossible, at least very difficult to be resolved.
Salv.The stresse and strength of the knot rendereth the solution thereof more commendable and admirable; but I do not promise you the same at this time, and pray you to dispense with me therein till too morrow, and for the present we will go considering and explaining those mutations and differences that by means of the annual motion ought to be discerned in the fixed stars, like as even now we said, for the explication whereof certain preparatory points offer themselves, which may facilitate the answer to the grand objection. Now reassuming the two motions ascribed to the Earth (two I say, for the third is no motion, as in its place I will declare) that is the annual and diurnal,The annual motion made by the centre of the Earth under the Ecliptick and the diurnal motion made by the Earth about its own centre. the first is to be understood to be made by the centre of the Earth in or about the circumference of the grand Orb, that is of a very great circle described in the plain of the fixed and immutable Ecliptick; the other, namely the diurnal, is made by the Globe of the Earth in it self about its own centre, and own Axis, not erect, but inclined to the Plane of the Ecliptick, with the inclination of 23. degrees and an half, or thereabouts, the which inclination is maintained all the year about, and that which ought especially to be observed, is alwayes situate towards the same point of Heaven:The axis of the Earth continueth alwayes parallel to it self, and describeth a Cylindraical superficies, inclining to the grand Orb. in so much that the Axis of the diurnal motion doth alwayes remain parallel to it self; so that if we imagine that same Axis to be continued out until it reach the fixed stars, whilst the centre of the Earth is encircling the whole Ecliptick in a year, the said Axis describeth the super​ficies of an oblique Cylinder, which hath for one of its bases the said annual circle, and for the other a like circle imaginarily described by its extremity, or, (if you will) Pole, amongst the fixed stars. And this same cylinder is oblique to the Plane of the Ecliptick, according to the inclination of the Axis that describeth it, which we have said to be 23 degrees and an half, the which continuing perpetually the same (save onely, that in many thousands of years it maketh some very small mutation, which nothing importeth in our present businesse) causeth that the Terrestrial Globe doth never more incline or elevate,The Orb of the Earth never inclineth, but is immutably the same. but still conserveth the same state without mutation. From whence ensueth, that as to what pertaineth to the mutations to be observed in the fixed stars dependant on the sole annual motion, the same shall happen to any point whatsoever of the Earths surface, as befalleth unto the centre of the Earth it self; and therefore in the present explanations we will make use of the centre, as if it were any whatsoever point of the superficies. And for a more facile understanding of the whole,The fixed stars placed in the Ecliptick never elevate nor descend, on account of the annual motion, but yet approach and recede. let us design the same in lineal figures: And first of all let us describe in the Plane of the Ecliptick the circle ANBO [in Fig. 7.] and let us understand the points A and B, to be the extreams towards the North and South; that is, the beginning of [or entrance into] Cancer or Capricorn, and let us prolong the Diameter AB, indeterminately by D and C towards the Starry Sphere. I say now in the first place, that none of the fixed stars placed in the Ecliptick, shall ever vary elevation, by reason of any whatsoever mutation made by the Earth along the said Plane of the Ecliptick, but shall alwayes appear in the same superficies, although the Earth shall approach and recede as great a space as is that of the diameter of the Grand Orb, as may plainly be seen in the said figure. For whether the Earth be in the point A or in B, the star C alwayes appeareth in the same line ABC; although the distance BC, be lesse than AC, by the whole diameter AB. The most therefore that can be discovered in the star C, and in any other placed in the Ecliptick, is the augmented or diminished apparent magnitude, by reason of the approximation or recession of the Earth.
Sagr.Stay a while I pray you, for I meet with a certain scruple, which much troubleth me, and it is this: That the star C may be seen by the same line ABC, as wel when the Earth is in A, as when it is in B, I understand very well, as also furthermore I apprehend that the same would happen in all the points of the line AB,Objections against the Earths annual motion taken from the fixed stars placed in the Ecliptick. so long as the Earth should passe from A to B by the said line; but it passing thither, as is to be supposed, by the arch ANB, it is manifest that when it shall be in the ​point N, and in any other except those two A and B, the said star shall no longer be observed in the line AB; but in others. So that, if the appearing under several lines ought to cause apparent mutations, some difference must needs appear in this case. Nay more, I will speak it with that Philosophical freedom, which ought to be allowed amongst Philosophick friends, methinks that you, contradicting your self, deny that now, which but even now to our admiration, you proved to be really true, and considerable; I mean that which happeneth in the Planets, and particularly in the three superiour ones, that being constantly in the Ecliptick, or very near unto it, do not onely shew themselves one while near unto us, and another while remote, but so deformed in their regular motions, that they seem sometimes immoveable, and sometimes many degrees retrograde; and all upon no other occasion than the annual motion of the Earth.
Salv.Though by a thousand accidents I have been heretofore assured of the wittinesse of Sagredus, yet I had a desire by this one experiment more to ascertain me of what I may expect from his ingenuity, and all this for my own interest, for in case my Propositions stand but proof against the hammer and furnace of his judgment, I shall be confident that they will abide the ** Or will prove of good alloy. test of all Touch-stones. I say therefore that I had purposely dissembled this objection, but yet not with any intent to deceive you, and to put any falshood upon you, as it might have happened if the objection by me disguised, and by you over-lookt, had been the same in effect as it seemed to be in appearance, that is, really valid and conclusive; but it is not so; nay I rather suspect that to try me, you make as if you did not see its nullity. But I will herein be too hard for you, and force from your tongue, that which you would so artificially conceal; and therefore tell me, what that thing should be, whereby you come to know the station and retrogradation of the Planets, which is derived from the annual motion, aud which is so great, that at least some foot-steps of such an effect ought to appear in the stars of the Ecliptick?
Sagr.This demand of yours containeth two questions, to which it is necessary that I make reply; the first relates to the imputation which you lay upon me of a Dissembler; the other concerneth that which may appear in the stars, &c. As to the first, I will say with your permission, that it is not true, that I have dissembled my knowing the nullity of that objection; and to assure you of the same, I now tell you that I very well understand the nullity thereof.
Salv.But yet I do not understand how it can be, that you ​spake not friendly, when you said you did not know that same fallacy which you now confesse that you know very well.
Sagr.The very confession of knowing it may assure you that I did not dissemble, when I said that I did not understand it; for if I had had a mind, and would dissemble, who could hinder me from continuing in the same simulation, and denying still that I understand the fallacy? I say therefore that I understood not the same, at that time, but that I do now at this present apprehend it, for that you have prompted my intellect, first by telling me resolutely that it is null, and then by beginning to question me so at large what thing that might be, whereby I might come to know the station and retrogradation of the Planets;The station, direction and retrogradation of the Planets is known, in relation to the fixed stars. and because this is known by comparing them with the fixed stars, in relation to which, they are seen to vary their motions, one while towards the West, and another towards the East, and sometimes to abide immoveable; and because there is not any thing above the Starry Sphere, immensely more remote from us, and visible unto us, wherewith we may compare our fixed stars, therefore we cannot discover in the fixed stars any foot-steps of what appeareth to us in the Planets. This I believe is the substance of that which you would force from me.
An Indice in the fixed stars like to that which is seen in the Planets, is an argument of the Earths annual motion.Salv.It is so, with the addition moreover of your admirable ingenuity; and if with half a word I did open your eyes, you by the like have remembred me that it is not altogether impossible, but that sometime or other something observable may be found amongst the fixed stars, by which it may be gathered wherein the annual conversion resides, so as that they also no lesse than the Planets and Sun it self, may appear in judgment to bear witnesse of that motion, in favour of the Earth; for I do not think that the stas are spread in a spherical superficies equally remote from a common centre, but hold, that their distances from us are so various, that some of them may be twice and thrice as remote as others; so that if with the Telescope one should observe a very small star neer to one of the bigger, and which therefore was very exceeding high, it might happen, that some sensible mutation might fall out between them, correspondent to that of the superiour Planets. And so much shall serve to have spoken at this time touching the stars placed in the Ecliptick.The fixed stars without the Ecliptick elevate and descend more or lesse, according to their distance from the said Ecliptick. Let us now come to the fixed stars, placed out of the Ecliptick, and let us suppose a great circle erect upon [i. e. at right angles to] the Plane of the ** i. e. of the Ecliptick. same; and let it, for example, be a circle that in the Starry Sphere answers to the Solstitial Colure, and let us mark it CEH [in Fig. 8.] which shall happen to be withal a Meridian, and in it we will take a star without the Ecliptick, which let be E. Now this star will indeed vary its elevati​on upon the Earths motion; for from the Earth in A it shall be seen according to the ray AE, with the elevation of the angle EAC; but from the Earth placed in B, it shall be seen according to the ray BE, with the elevation of the angle EBC, bigger than the other EAC, that being extern, and this intern and opposite in the triangle EAB, the distance therefore of the star E from the Ecliptick, shall appear changed; and likewise its altitude in the Meridian shall become greater in the position B, than in the place A, according as the angle EBC exceeds the angle EAC, which excesse is the quantity of the angle AEB: For in the triangle EAB, the side AB being continued to C, the exteriour angle EBC (as being equal to the two interiour and opposite E and A) exceedeth the said angle A, by the quantity of the angle E. And if we should take another star in the same Meridian, more remote from the Ecliptick, as for instance the star H, the diversity in it shall be greater by being observed from the two stations A and B, according as the angle AHB is greater than the other E; which angle shall encrease continually according as the observed star shall be farther and farther from the Ecliptick, till that at last the greatest mutation will appear in that star that should be placed in the very Pole of the Ecliptick. As for a full understanding thereof we thus demonstrate. Suppose the diameter of the Grand Orb to be AB, whose centre [in the same Figure] is G, and let it be supposed to be continued out as far as the Starry Sphere in the points D and C, and from the centre G let there be erected the Axis of the Ecliptick GF, prolonged till it arrive at the said Sphere, in which a Meridian DFC is supposed to be described, that shall be perpendicular to the Plane of the Ecliptick; and in the arch FC any points H and E, are imagined to be taken, as places of fixed stars: Let the lines FA, FB, AH, HG, HB, AE, GE, BE, be conjoyned. And let the angle of difference, or, if you will, the Parallax of the star placed in the Pole F, be AFB, and let that of the star placed in H, be the angle AHB, and let that of the star in E, be the angle AEB. I say, that the angle of difference of the Polar star F, is the greatest, and that of the rest, those that are nearer to the greatest are bigger than the more remote; that is to say, that the angle F is bigger than the angle H, and this bigger than the angle E. Now about the triangle FAB, let us suppose a circle to be described. And because the angle F is acute, (by reason that its base AB is lesse than the diameter DC, of the semicircle DFC) it shall be placed in the greater portion of the circumscribed circle cut by the base AB. And because the said AB is divided in the midst, and at right angles by FG, the centre of the circumscri​bed circle shall be in the line FG, which let be the point I; and because that of such lines as are drawn from the point G, which is not the centre, unto the circumference of the circumscribed circle, the biggest is that which passeth by the centre, GF shall be bigger than any other that is drawn from the point G, to the circumference of the said circle; and therefore that circumference will cut the line GH (which is equal to the line GF) and cutting GH, it will also cut AH. Let it cut it in L, and conjoyn the line LB. These two angles, therefore, AFB and ALB shall be equal, as being in the same portion of the circle circumscribed. But ALB external, is bigger than the internal H; therefore the angle F is bigger than the angle H. And by the same method we might demonstrate the angle H to be bigger than the angle E, because that of the circle described about the triangle AHB, the centre is in the perpendicular GF, to which the line GH is nearer than the line GE, and therefore the circumference of it cutteth GE, and also AE, whereupon the proposition is manifest. We will conclude from hence, that the difference of appearance, (which with the proper term of art, we might call the Parallax of the fixed stars) is greater, or lesse, according as the Stars observed are more or lesse adjacent to the Pole of the Ecliptick, so that, in conclusion of those Stars that are in the Ecliptick it self, the said diversity is reduced to nothing. In the next place,The Earth approacheth or recedeth from the fixed stars of the Ecliptick, the quantity of the Diameter of the Grand Orb. as to the Earths accession by that motion to, or recession from the Stars, it appeareth to, and recedeth from those that are in the Ecliptick, the quantity of the whole diameter of the grand Orb, as we did see even now, but that accession or recession to, or from the stars about the Pole of the Ecliptick, is almost nothing; and in going to and from others, this difference groweth greater, according as they are neerer to the Ecliptick. We may,The stars nearer to us make greater differences than the more remote. in the third place, know, that the said difference of Aspect groweth greater or lesser, according as the Star observed shall be neerer to us, or farther from us. For if we draw another Meridian, lesse distant from the Earth; as for example, this DFI [in Fig. 7.] a Star placed in F, and seen by the same ray AFE, the Earth being in A, would, in case it should be observed from the Earth in B, appear according to the ray BF, and would make the angle of difference, namely, BFA, bigger than the former AEB, being the exteriour angle of the triangle BFE.
Sagr.With great delight, and also benefit have I heard your discourse;The Epilogue of the Phænomena of the fixed stars caused by the annual motion of the Earth. and that I may be certain, whether I have rightly understood the same, I shall give you the summe of the Conclusions in a few words. As I take it, you have explained to us the different appearances, that by means of the Earths annual mo​tion, may be by us observed in the fixed stars to be of two kinds: The one is, that of their apparent magnitudes varied, according as we, transported by the Earth, approach or recede from the same: The other (which likewise dependeth on the same accession and recession) their appearing unto us in the same Meridian, one while more elevated, and another while lesse. Moreover, you tell us (and I understand it very well) that the one and other of these mutations are not made alike in all the stars, but in some greater, and in others lesser, and in others not at all. The accession and recession whereby the same star ought to appear, one while bigger, and another while lesser, is insensible, and almost nothing in the stars neer unto the pole of the Ecliptick, but is greatest in the stars placed in the Ecliptick it self, and indifferent in the intermediate: the contrary happens in the other difference, that is, the elevation or depression of the stars placed in the Ecliptick is nothing at all, greatest in those neerest to the Pole of the said Ecliptick, and indifferent in the intermediate. Besides, both these differences are more sensible in the Stars neerest to us, in the more remote lesse sensible, and in those that are very far distant wholly disappear. This is, as to what concerns my self; it remaineth now, as I conceive, that something be said for the satisfaction of Simplicius, who, as I believe, will not easily be made to over-passe those differences, as insensible that are derived from a motion of the Earth so vast, and from a mutation that transports the Earth into places twice as far distant from us as the Sun.
Simpl.Truth is, to speak freely, I am very loth to confesse, that the distance of the fixed Stars ought to be such, that in them the fore-mentioned differences should be wholly imperceptible.
Salv.Do not throw your self into absolute despair, Simplicius, for there may perhaps yet some qualification be found for your difficulties. And first, that the apparent magnitude of the stars is not seen to make any sensible alteration, ought not to be judged by you a thing improbable, in regard you see the guesses of men in this particular to be so grossely erroneous, especially in looking upon splendid objects; and you your self beholding v. g. a lighted Torch at the distance of 200 paces,In objects far remote, and luminous, a small approach or recession is imperceptible. if it approach nearer to you 3. or 4. yards, do you think that it will shew any whit encreased in magnitude? I for my part should not perceive it certainly, although it should approach 20. or 30. yards nearer; nay it hath sometimes happened that in seeing such a light at that distance I know not how to resolve whether it came towards me, or retreated from me, when as it did in reality approach nearer to me. But what need I speak of this? If the self same accession and recession (I speak of a distance ​twice as great as that from the Sun to us) in the star of Saturn is almost totally imperceptible, and in Jupiter not very observable, what shall we think of the fixed stars, which I believe you will not scruple to place twice as far off as Saturn? In Mars, which for that it is nearer to us———
Simpl.Pray Sir, put your self to no farther trouble in this particular, for I already conceive that what hath been spoken touching the unaltered apparent magnitude of the fixed stars may very well come to passe, but what shall we say of the other difficulty that proceeds from not perceiving any variation in the mutation of aspect?
Salv.We will say that which peradventure may satisfie you also in this particular. And to make short, would you not be satisfied if there should be discovered in the stars face mutations that you think ought to be discovered, in case the annual motion belonged to the Earth?
Simpl.I should so doubtlesse, as to what concerns this particular.
Salv.I could wish you would say that in case such a difference were discovered,If in the fixed stars one should discover any annual mutation, the motion of the Earth would be undeniable. nothing more would remain behind, that might render the mobility of the Earth questionable. But although yet that should not sensibly appear▪ yet is not its mobility removed, nor its immobility necessarily proved, it being possible, (as Copernicus affirmeth) that the immense distance of the Starry Sphere rendereth such very small Phænomena unobservable; the which as already hath been said, may possibly not have been hitherto so much as sought for, or if sought for, yet not sought for in such a way as they ought,It is proved what small credit is to be given to Astronomical Instruments in minute observations. to wit, with that exactnesse which to so minute a punctuality would be necessary; which exactnesse is very difficult to obtain, as well by reason of the deficiency of Astronomical Instruments, subject to many alterations, as also through the fault of those that manage them with less diligence then is requisite. A necessary argument how little credit is to be given to those observations may be deduced from the differences which we find amongst Astronomers in assigning the places, I will not say, of the new Stars or Comets, but of the fixed stars themselves, even to the altitudes of the very Poles, in which, most an end, they are found to differ from one another many minutes. And to speak the truth, who can in a Quadrant, or Sextant, that at most shall have its side ** Braccia Italian. 3. or 4. yards long, ascertain himself in the incidence of the perpendicular, or in the direction of the sights, not to erre two or three minutes, which in its circumference shall not amount to the breadth of a grain of ** Or Mill. Mylet? Besides that, it is almost impossible, that the Instrument should be made, and kept with absolute exactnesse. Ptolomey ​sheweth his distrust of a Spherical Instrument composed by Archimedes hismelf to take the Suns ingression into the Æquinoctial.Ptolomy did not trust to an Instrument made by Archimedes.
Simpl.But if the Instruments be so suspitious,Instruments of Tycho made with great expence. and the observations so dubious, how can we ever come to any certainty of things, or free our selves from mistakes? I have heard strange things of the Instruments of Tycho made with extraordinary cost, and of his singular diligence in observations.
Salv.All this I grant you; but neither one nor other of these is sufficient to ascertain us in a businesse of this importance. I desire that we may make use of Instruments greater by far,What Instruments are apt for most exact observation. and by far certainer than those of Tycho, made with a very small charge; the sides of which are of 4. 6. 20. 30. and 50. miles, so as that a degree is a mile broad, a minute prim. 50 ** Italian braces. yards, a second but little lesse than a yard, and in short we may without a farthing expence procure them of what bignesse we please. I being in a Countrey Seat of mine near to Florence,An exquisite observation of the approach and departure of the Sun from the Summer Solstice. did plainly observe the Suns arrival at, and departure from the Summer Solstice, whilst one Evening at the time of its going down it appeared upon the top of a Rock on the Mountains of Pietrapana, about 60. miles from thence, leaving discovered of it a small streak or filament towards the North, whose breadth was not the hundredth part of its Diameter; and the following Evening at the like setting, it shew'd such another part of it, but notably more small, a necessary argument, that it had begun to recede from the Tropick; and the regression of the Sun from the first to the second observation, doth not import doubtlesse a second minute in the East.A place accommodated for the observation of the fixed stars, as to what concers the annual motion of the Earth. The observation made afterwards with an exquisite Telescope, and that multiplyeth the Discus of the Sun more than a thousand times, would prove easie, and with all delightful. Now with such an Instrument as this, I would have observations to be made in the fixed stars, making use of some of those wherein the mutation ought to appear more conspicuous, such as are (as hath already been declared) the more remote from the Ecliptick, amongst which the Harp a very great star, and near to the Pole of the Ecliptick, would be very proper in Countries far North, proceeding according to the manner that I shall shew by and by, but in the use of another star; and I have already fancied to my self a place very well adapted for such an observation. The place is an open Plane, upon which towards the North there riseth a very eminent Mountain, in the apex or top whereof is built a little Chappel, situate East and West, so as that the ridg of its Roof may intersect at right angles, the meridian of some building standing in the Plane. I will place a beam parallel to the said ridg, or top of the Roof, ​and distant from it a yard or thereabouts. This being placed, I will seek in the Plain the place from whence one of the stars of Charls's Waine, in passing by the Meridian, cometh to hide it self behind the beam so placed, or in case the beam should not be so big as to hide the star, I will finde a station where one may see the said beam to cut the said star into two equal parts; an effect that with an * exquisite Telescope may be perfectly discerned. And if in the place where the said accident is discovered, there were some building, it will be the more commodious; but if not, I will cause a Pole to be stuck very fast in the ground, with some standing mark to direct where to place the eye anew, when ever I have a mind to repeat the observation. The first of which observations I will make about the Summer Solstice, to continue afterwards from Moneth to Moneth, or when I shall so please, to the other Solstice; with which observation one may discover the elevation and depression of the star, though it be very small. And if in that operation it shall happen, that any mutation shall discover it self, what and how great benefit will it bring to Astronomy? Seeing that thereby, besides our being assured of the annual motion, we may come to know the grandure and distance of the same star.
Sagr.I very well comprehend your whole proceedings; and the operation seems to me so easie, and so commodious for the purpose, that it may very rationally be thought, that either Copernicus himself, or some other Astronomer had made trial of it.
Salv.But I judg the quite contrary, for it is not probable, that if any one had experimented it, he would not have mentioned the event, whether it fell out in favour of this, or that opinion; besides that, no man that I can find, either for this, or any other end, did ever go about to make such an Observation; which also without an exact Telescope could but badly be effected.
Simpl.I am fully satisfied with what you say. But seeing that it is a great while to night, if you desire that I shall passe the same quietly, let it not be a trouble to you to explain unto us those Problems, the declaration whereof you did even now request might be deferred until too morrow. Be pleased to grant us your promised indulgence, and, laying aside all other discourses, proceed to shew us, that the motions which Copernicus assigns to the Earth being taken for granted, and supposing the Sun and fixed stars immoveable, there may follow the same accidents touching the elevations and depressions of the Sun, touching the mutations of the Seasons, and the inequality of dayes and nights, &c. in the self same manner, just as they are with ​facility apprehended in the Ptolomaick Systeme.
Salv.I neither ought, nor can deny any thing that Sagredus shall request: And the delay by me desired was to no other end, save only that I might have time once again to methodize those prefatory points, in my fancy, that serve for a large and plain declaration of the manner how the forenamed accidents follow, as well in the Copernican position, as in the Ptolomaick: nay, with much greater facility and simplicity in that than in this.The Copernican Systeme difficult to be understood, but easie to be effected. Whence one may manifestly conceive that Hypothesis to be as easie to be effected by nature, as difficult to be apprehended by the understanding: yet neverthelesse, I hope by making use of another kind of explanation,Necessary prepositions for the better conceiving of the consequences of the Earths motion. than that used by Copernicus, to render likewise the apprehending of it somewhat lesse obscure. Which that I may do, I will propose certain suppositions of themselves known and manifest, and they shall be these that follow.
First, I suppose that the Earth is a spherical body, turning round upon its own Axis and Poles, and that each point assigned in its superficies, describeth the circumference of a circle, greater or lesser, according as the point assigned shall be neerer or farther from the Poles: And that of these circles the greatest is that which is described by a point equidistant from the said Poles; and all these circles are parallel to each other; and Parallels we will call them.
Secondly, The Earth being of a Spherical Figure, and of an opacous substance, it is continually illuminated by the Sun, according to the half of its surface, the other half remaining obscure, and the boundary that distinguisheth the illuminated part from the dark being a grand circle, we will call that circle the terminator of the light.
Thirdly, If the Circle that is terminator of the light should passe by the Poles of the Earth, it would cut (being a grand and principal circle) all the parallels into equal parts; but not passing by the Poles, it would cut them all in parts unequal, except only the circle in the middle, which, as being a grand circle will be cut into equal parts.
Fourthly, The Earth turning round upon its own Poles, the quantities of dayes and nights are termined by the arches of the Parallels, intersected by the circle, that is, the terminator of the light, and the arch that is scituate in the illuminated Hemisphere prescribeth the length of the day, and the remainer is the quantity of the night.
These things being presupposed,A plain Scheme representing the Copernican Hypothesis, and its consequences. for the more clear understanding of that which remaines to be said, we will lay it down in a Figure. And first, we will draw the circumference of a circle, that shall represent unto us that of the grand Orb descri​bed in the plain of the Ecliptick, and this we will divide into four equal parts with the two diameters Capricorn Cancer, and Libra Aries, which, at the same time, shall represent unto us the four Cardinal points, that is, the two Solstices, and the two Equinoctials; and in the centre of that circle we will place the Sun O, fixed and immoveable.
Let us next draw about the four points, Capricorn, Cancer, Libra and Aries, as centres, four equal circles, which represent unto us the Earth placed in them at four several times of the year. The which, with its centre, in the space of a year, passeth through the whole circumference, Capricorn, Aries, Cancer, Libra, moving from East to West, that is, according to the order of the Signes. It is already manifest, that whilst the Earth is in Capricorn,The Suns annual motion, how it comes to passe, according to Copernicus. the Sun will appear in Cancer, and the Earth moving along the arch Capricorn Aries, the Sun will seem to move along the arch Cancer Libra, and in short, will run thorow the Zodiack according to the order of the Signes, in the space of a year; and by this first assumption, without all question, full satisfaction is given for the Suns apparent annual motion under the Ecliptick. Now, coming to the other, that is, the diurnal motion of the Earth in it self, it is necessary to establish its Poles and its Axis, the which must be understood not to be erect perpendicularly upon the plain of the Ecliptick, that is, not to be parallel to the Axis of the grand Orb, but declining from a right angle 23 degrees and an half, or thereabouts, with its North Pole towards ​the Axis of the grand Orb, the Earths centre being in the Solstitial point of Capricorn. Supposing therefore the Terrestrial Globe to have its centre in the point Capricorn, we will describe its Poles and Axis AB, inclined upon the diameter Capricorn Cancer 23 degrees and an half; so that the angle A Capricorn Cancer cometh to be the complement of a Quadrant or Radius, that is, 66 degrees and an half; and this inclination must be understood to be immutable, and we will suppose the superiour Pole A to be Boreal, or North, and the other Austral, or South. Now imagining the Earth to revolve in it self about the Axis AB in twenty four hours, from West to East, there shall by all the points assigned in its superficies, be circles described parallel to each other. We will draw, in this first position of the Earth, the greatest CD, and those two distant from it gr. 23. and an half, EF above, and GM beneath, and the other two extream ones IK and LM remote, by those intervals from the Poles A and B; and as we have marked these five, so we may imagine innumerable others, parallel to these, described by the innumerable points of the Terrestrial surface. Next let us suppose the Earth, with the annual motion of its centre, to transferre it self into the other places already marked; but to passe thither in such a manner, that its own Axis AB shall not only not change inclination upon the plain of the Ecliptick, but shall also never vary direction; so that alwayes keeping parallel to it self, it may continually tend towards the same part of the Universe, or, if you will, of the Firmament, whereas, if we do but suppose it prolonged, it will, with its extream termes, designe a Circle parallel and equal to the grand Orb, Libra Capricorn Aries Cancer, as the superiour base of a Cylinder described by it self in the annual motion above the inferiour base, Libra Capricorn Aries Cancer. And therefore this immutability of inclination continuing, we will design these other three figures about the centres Aries, Cancer, and Libra, alike in every thing to that first described about the centre Capricorn. Now we will consider the first figure of the Earth, in which, in regard the Axis AB is declined from perpendicularity upon the diameter Capricorn Cancer 23 degrees and an half towards the Sun O, and the arch AI being also 23 degrees and an half, the illumination of the Sun will illustrate the Hemisphere of the Terrestrial Globe exposed towards the Sun (of which, in this place, half is to be seen) divided from the obscure part by the Terminator of the light IM, by which the parallel CD, as being a grand circle, shall come to be divided into equal parts, but all the rest into parts unequal; being that the terminator of the light IM passeth not by their Poles AB, and the parallel IK, together with all the rest ​described within the same, and neerer to the pole A, shall wholly be included in the illuminated part; as on the contrary, the opposite ones towards the Pole B, contained within the parallel LM, shall remain in the dark. Moreover, the arch AI being equal to the arch FD, and the arch AF, common to them both, the two arches IKF and AFD shall be equal, and each a quadrant or 90 degrees. And because the whole arch IFM is a semicircle, the arch FM shall be a quadrant, and equal to the other FKI; and therefore the Sun O shall be in this state of the Earth vertical to one that stands in the point F. But by the revolution diurnal about the standing Axis AB, all the points of the parallel EF passe by the same point F: and therefore in that same day the Sun, at noon, shall be vertical to all the inhabitants of the Parallel EF, and will seem to them to describe in its apparent motion the circle which we call the Tropick of Cancer. But to the inhabitants of all the Parallels that are above the parallel EF, towards the North pole A, the Sun declineth from their Vertex or Zenith towards the South; and on the contrary, to all the inhabitants of the Parallels that are beneath EF, towards the Equinoctial CD, and the South Pole B, the Meridian Sun is elevated beyond their Vertex towards the North Pole A. Next, it is visible that of all the Parallels, only the greatest CD is cut in equal parts by the Terminator of the light IM. But the rest, that are beneath and above the said grand circle, are all intersected in parts unequal: and of the superiour ones, the semidiurnal arches, namely those of the part of the Terrestrial surface, illustrated by the Sun, are bigger than the seminocturnal ones that remain in the dark: and the contrary befalls in the remainder, that are under the great one CD, towards the pole B, of which the semidiurnal arches are lesser than the seminocturnal, It is likewise apparently manifest, that the differences of the said arches go augmenting, according as the Parallels are neerer to the Poles, till such time as the parallel IK comes to be wholly in the part illuminated, and the inhabitants thereof have a day of twenty four hours long, without any night; and on the contrary, the Parallel LM, remaining all in obscurity, hath a night of twenty four hours, without any day. Come we next to the third Figure of the Earth, placed with its centre in the point Cancer, where the Sun seemeth to be in the first point of Capricorn. We have already seen very manifestly, that by reason the Axis AB doth not change inclination, but continueth parallel to it self, the aspect and situation of the Earth is the same to an hair with that in the first Figure; save onely that that Hemisphere which in the first was illuminated by the Sun, in this remaineth obtenebrated, and that cometh to be luminous, which in ​the first was tenebrous: whereupon that which happened before concerning the differences of dayes and nights, touching the dayes being greater or lesser than the nights, now falls out quite contrary. And first, we see, that whereas in the first Figure the circle IK was wholly in the light, it is now wholly in the dark; and the opposite arch LM is now wholly in the light, which was before wholly in the dark. Of the parallels between the grand circle CD, and the Pole A, the semidiurnal arches are now lesser than the seminocturnal, which before were the contrary. Of the others likewise towards the Pole B, the semidiurnal arches are now bigger than the seminocturnal, the contrary to what happened in the other position of the Earth. We now see the Sun made vertical to the inhabitants of the Tropick GN, and to be depressed towards the South, with those of the Parallel EF, by all the arch ECG, that is, 47 degrees; and in summe, to have passed from one to the other Tropick, traversing the Equinoctial, elevating and declining in the Meridians the said space of 47 degrees. And all this mutation is derived not from the inclination or elevation of the Earth, but on the contrary, from its not inclining or elevating at all; and in a word, by continuing always in the same position, in respect of the Universe, onely with turning about the Sun situate iu the midst of the said plane, in which it moveth it self about circularly with its annual motion. And here is to be noted an admirable accident,An admirable accident depending on the not inclining of the Earths axis which is, that like as the Axis of the Earth conserving the same direction towards the Universe, or we may say, towards the highest Sphere of the fixed stars, causeth the Sun to appear to elevate and incline so great a space, namely, for 47 degrees, and the fixed Stars to incline or elevate nothing at all; so, on the contrary, if the same Axis of the Earth should maintain it self continually in the same inclination towards the Sun, or, if you will, towards the Axis of the Zodiack, no mutation would appear to be made in the Sun about its elevating or declining, whereupon the inhabitants of one and the same place would alwayes have one and the same difference of dayes and nights, and one and the same constitution of Seasons, that is, some alwayes Winter, others alwayes Summer, others Spring, &c. but, on the contrary, the alterations in the fixed Stars would appear very great, as touching their elevation, and inclination to us, which would amount to the same 47 degrees. For the understanding of which let us return to consider the position of the Earth, in its first Figure, where we see the Axis AB, with the superiour Pole A, to incline towards the Sun; but in its third Figure, the same Axis having kept the same direction towards the highest Sphere, by keeping parallel to it self, inclines no longer towards the Sun with its superiour Pole A, but ​on the contrary reclines from its former position gr. 47. and inclineth towards the opposite part, so that to restore the same inclination of the said Pole A towards the Sun, it would be requisite by turning round the Terrestrial Globe, according to the circumference ACBD, to transport it towards E those same gr. 47. and for so many degrees, any whatsoever fixed star observed in the Meridian, would appear to be elevated, or inclined. Let us come now to the explanation of that which remains, and let us consider the Earth placed in the fourth Figure, that is, with its centre in the first point of Libra; upon which the Sun will appear in the beginning of Aries. And because the Axis of the Earth, which in the first Figure is supposed to be inclined upon the diameter Capricorn Cancer, and therefore to be in that same plane, which cutting the plane of the grand Orb, according to the line Capricorn Cancer, was erected perpendicularly upon the same, transposed into the fourth Figure, and maintained, as hath alwayes been said, parallel to it self, it shall come to be in a plane in like manner erected to the superficies of the Grand Orbe, and parallel to the plane, which at right angles cuts the same superficies, according to the diameter Capricorn Cancer. And therefore the line which goeth from the centre of the Sunne to the centre of the Earth, that is, O Libra, shall be perpendicular to the Axis BA: but the same line which goeth from the centre of the Sunne to the centre of the Earth, is also alwayes perpendicular to the ​circle that is the Terminator of the light; therefore this same circle shall passe by the Poles AB in the fourth figure, and in its plain the Axis AB shall fall, but the greatest circle passing by the Poles of the Parallels, divideth them all in equal parts; therefore the arches IK, EF, CD, GN, LM, shall be all semicircles, and the illumin'd Hemisphere shall be this which looketh towards us, and the Sun, and the Terminator of the light shall be one and the same circle ACBD, and the Earth being in this place shall make it Equinoctial to all its Inhabitants. And the same happeneth in the second figure, where the Earth having its illuminated Hemisphere towards the Sun, sheweth us the other that is obscure, with its nocturnal arches, which in like manner are all semicircles, and consequently, here also it maketh the Equinoctial. And lastly in regard that the line produced from the centre of the Sun to the centre of the Earth, is perpendicular to the Axis AB, to which the greatest circle of the parallels CD, is likewise erect, the said line O Libra shall passe of necessity by the same Plain of the parallel CD, cutting its circumference in the midst of the diurnal arch CD; and therefore the Sun shall be vertical to any one that shall stand where that intersection is made; but all the Inhabitants of that Parallel shall passe the same, as being carried about by the Earths diurnal conversion; therefore all thes upon that day shall have the Meridian Sun in their vertex. And the Sun at the same time to all the Inhabitants of the Earth shall seem to describe the Grand Parallel called the Equinoctial. Furthermore, forasmuch as the Earth being in both the Solstitial points of the Polar circles IK and LM, the one is wholly in the light, and the other wholly in the dark; but when the Earth is in the Equinoctial points, the halves of those same polar circles are in the light, the remainder of them being in the dark; it should not be hard to understand, how that the Earth v. gr. from Cancer (where the parallel IK is wholly in the dark) to Leo, one part of the parallel towards the point I, beginneth to enter into the light, and that the Terminator of the light IM beginneth to retreat towards the Pole AB, intersecting the circle ACBD no longer in IM, but in two other points falling between the terms IA and MB, of the arches IA and MB; whereupon the Inhabitants of the circle begin to enjoy the light, and the other Inhabitants of the circle LM to partake of night. And thus you see that by two simple motions made in times proportionate to their bignesses, and not contrary to one another, but performed, as all others that belong to moveable mundane bodies, from West to East assigned to the Terrestrial Globe, adequate reasons are rendred of all those Phænomena or appearances, for the accommodating of ​which to the stability of the Earth it is necessary (forsaking that Symetry which is observed to be between the velocities and magnitudes of moveables) to ascribe to a Sphere, vast above all others, an unconceiveable celerity, whilst the other lesser Spheres move extream slowly; and which is more, to make that motion contrary to all their motions; and, yet again to adde to the improbability, to make that superiour Sphere forcibly to transport all the inferiour ones along with it contrary to their proper inclination. And here I refer it to your judgment to determine which of the two is the most probable.
Sagr.To me, as far as concerneth sense, there appeareth no small difference betwixt the simplicity and facility of operating effects by the means assigned in this new constitution, and the multiplicity, confusion, and difficulty, that is found in the ancient and commonly received Hypothesis. For if the Universe were disposed according to this multiplicity, it would be necessary to renounce many Maximes in Philosophy commonly received by Philosophers,Axiomes commonly admitted by all Philosophers. as for instance, That Nature doth not multiply things without necessity; and, That She makes use of the most facile and simple means in producing her effects; and, That She doth nothing in vain, and the like. I do confesse that I never heard any thing more admirable than this, nor can I believe that Humane Understanding ever penetrated a more sublime speculation. I know not what Simplicius may think of it.
Simpl.These (if I may speak my judgment freely) do seem to me some of those Geometrical subtilties which Aristotle finds fault with in Plato,Aristotle taxeth Plato for being too studious of Geometry. when he accuseth him that by his too much studying of Geometry he forsook solid Philosophy; and I have known and heard very great Peripatetick Philosophers to disswade their Scholars from the Study of the Mathematicks, as those that render the wit cavilous, and unable to philosophate well; an Institute diametrically contrary to that of Plato, who admitted one to Philosophy, unlesse he was first well entered in Geometry.
Salv.I commend the policy of these your Peripateticks,Peripatetick Philosophers condemn the Study of Geometry, and why. in dehorting their Disciples from the Study of Geometry, for that there is not art more commodious for detecting their fallacies; but see how they differ from the Mathematical Philosophers, who much more willingly converse with those that are well verst in the commune Peripatetick Philosophy, than with those that are destitute of that knowledg, who for want thereof cannot distinguish between doctrine and doctrine. But passing by this, tell me I beseech you, what are those extravagancies and those too affected subtilties that make you think this Copernican Systeme the lesse plausible?
​Simpl.To tell you true, I do not very well know; perhaps, because I have not so much as learnt the reasons that are by Ptolomy produced, of those effects, I mean of those stations, retrogradations, accessions, recessions of the Planets; lengthenings and shortnings of dayes, changes of seasons, &c. But omitting the consequences that depend on the first suppositions, I find in the suppositions themselves no small difficulties; which suppositions, if once they be overthrown, they draw along with them the ruine of the whole fabrick. Now forasmuch as because the whole module of Copernicus seemeth in my opinion to be built upon infirm foundations, in that it relyeth upon the mobility of the earth, if this should happen to be disproved, there would be no need of farther dispute. And to disprove this, the Axiom of Aristotle is in my judgement most sufficient, That of one simple body, one sole simple motion can be natural: but here in this case, to the Earth,Four several motions assigned to the Earth. a simple body, there are assigned 3. if not 4. motions, and all very different from each other. For besides the right motion, as a grave body towards its centre, which cannot be denied it, there is assigned to it a circular motion in a great circle about the Sun in a year, and a vertiginous conversion about its own centre in twenty four hours. And that in the next place which is more exorbitant, & which happly for that reason you pass over in silence, there is ascribed to it another revolution about its own centre, contrary to the former of twenty four hours, and which finisheth its period in a year. In this my understanding apprehendeth a very great contradiction.
The motion of descent belongs not to the terrestrial Globe, but to its parts.Salv.As to the motion of descent, it hath already been concluded not to belong to the Terrestrial Globe which did never move with any such motion, nor never shall do; but is (if there be such a thing) that propension of its parts to reunite themselves to their whole. As, in the next place, to the Annual motion, and the Diurnal,The annual and diurnal motion are compatible in the Earth. these being both made towards one way, are very compatible, in the same manner just as if we should let a Ball trundle downwards upon a declining superficies, it would in its descent along the same spontaneously revolve in it self. As to the third motion assigned it by Copernicus, namely about it self in a year, onely to keep its Axis inclined and directed towards the same part of the Firmament, I will tell you a thing worthy of great consideration: namely ut tantum abest (although it be made contrary to the other annual) it is so far from having any repugnance or difficulty in it,Every pensil and librated, body carryed round in the circumference of a circle, acquireth of it self a motion in it self contrary to that. that naturally and without any moving cause, it agreeth to any whatsoever suspended and librated body, which if it shall be carried round in the circumference of a circle, immediate of it self, it acquireth a conversion about its own centre, contrary to that which carrieth it about, and of ​such velocity, that they both finish one revolution in the same time precisely. You may see this admirable, and to our purpose accommodate experience,An Experiment which sensibly shews that two contrary motions may naturally agree in the same moveable. if putting in a Bason of water a Ball that will swim; and holding the Bason in your hand, you turn round upon your toe, for you shall immediatly see the Ball begin to revolve in it self with a motion, contrary to that of the Bason, and it shall finish its revolution, when that of the Bason it shall finish. Now what other is the Earth than a pensil Globe librated in tenuous and yielding aire, which being carried about in a year along the circumference of a great circle,The third motion ascribed to the Earth is rather a resting immoveable. must needs acquire, without any other mover, a revolution about its own centre, annual, and yet contrary to the other motion in like manner annual? You shall see this effect I say, but if afterwards you more narrowly consider it, you shall find this to be no real thing, but a meer appearance; and that which you think to be a revolution in it self, you will find to be a not moving at all, but a continuing altogether immoveable in respect of all that which without you, and without the vessel is immoveable: for if in that Ball you shall make some mark, and consider to what part of the Room where you are, or of the Field, or of Heaven it is situate, you shall see that mark in yours, and the vessels revolution to look alwayes towards that same part; but comparing it to the vessel and to your self that are moveable, it will appear to go altering its direction, and with a motion contrary to yours, and that of the vessel, to go seeking all the points of its circumgyration; so that with more reason you and the bason may be said to turn round the immoveable Ball, than that it moveth round in the bason. In the same manner the Earth suspended and librated in the circumference of the Grand Orbe, and scituate in such sort that one of its notes, as for example, its North Pole, looketh towards such a Star or other part of the Firmament, it always keepeth directed towards the same, although carried round by the annual motion about the circumference of the said Grand Orbe. This alone is sufficient to make the Wonder cease, and to remove all difficulties. But what will Simplicius say, if to this non-indigence of the co-operating cause we should adde an admirable intrinsick vertue of the Terrestrial Globe,An admirable intern vertue of the terrestrial Globe of alwayes beholding the same part of Heaven. of looking with its determinate parts towards determinate parts of the Firmament, I speak of the Magnetick vertue constantly participated by any whatsoever piece of Loade-stone. And if every minute particle of that S•one have in it such a vertue,The terrestriæl Globe made of Loade-stone. who will question but that the same more powerfully resides in this whole Terrestrial Globe, abounding in that Magnetick matter, and which happily it self, as to its internal and primary substance, is nothing else but a huge masse of Loade-stone.
​Simpl.Then you are one of those it seems that hold the Magnetick Phylosophy * An eminent Doctor of Physick, our Countreyman, born at Colchester, and famous for this his learned Treatise, published about 60 years since at London, The Magnetick Philosophy of William Gilbert. * William Gilbert.
Salv.I am for certain, and think that all those that have seriously read his Book, and tried his experiments, will bear me company therein; nor should I despair, that what hath befallen me in this case, might possibly happen to you also, if so be a curiosity, like to mine, and a notice that infinite things in Nature are still conceal'd from the wits of mankind, by delivering you from being captivated by this or that particular writer in natural things, should but slacken the reines of your Reason, and mollifie the contumacy and tenaceousnesse of your sense; so as that they would not refuse to hearken sometimes to novelties never before spoken of.The Pusillanimity of Popular Wits. But (permit me to use this phrase) the pusillanimity of vulgar Wits is come to that passe, that not only like blind men, they make a gift, nay tribute of their own assent to whatsoever they find written by those Authours, which in the infancy of their Studies were laid before them, as authentick by their Tutors, but refuse to hear (not to say examine) any new Proposition or Probleme, although it not only never hath been confuted, but not so much as examined or considered by their Authours. Amongst which, one is this, of investigating what is the true, proper, primary, interne, and general matter and substance of this our Terrestrial Globe; For although it never came into the mind either of Aristotle, or of any one else, before William Gilbert to think that it might be a Magnet, so far are Aristotle and the rest from confuting this opinion, yet neverthelesse I have met with many, that at the very first mention of it, as a Horse at his own shadow, have start back, and refused to discourse thereof, and censured the conceipt for a vain Chymæra, yea, for a solemn madnesse: and its possible the Book of Gilbert had never come to my hands, if a Peripatetick Philosopher, of great fame, as I believe, to free his Library from its contagion, had not given it me.
Simpl.I, who ingenuously confesse my self to be one of those vulgar Wits, and never till within these few dayes that I have been admitted to a share in your conferences, could I pretend to have in the least withdrawn from those trite and popular paths, yet, for all that, I think I have advantaged my self so much, as that I could without much trouble or difficulty, master the roughnesses of these novel and fantastical opinions.
Salv.If that which Gilbert writeth be true, then is it no opinion, but the subject of Science; nor is it new, but as antient as the Earth it self; nor can it (being true) be rugged or difficult, but plain and easie; and when you please I shall make you feel the same in your hand, for that you of your self fancy it to ​be a Ghost, and stand in fear of that which hath nothing in it of dreadfull, like as a little child doth fear the Hobgoblin, without knowing any more of it, save the name; as that which besides the name is nothing.
Simpl.I should be glad to be informed, and reclaimed from an errour.
Salv.Answer me then to the questions that I shall ask you. And first of all, Tell me whether you believe, that this our Globe, which we inhabit and call Earth, consisteth of one sole and simple matter, or else that it is an aggregate of matters different from each other.
Simpl.I see it to be composed of substances and bodies very different;The Terrestrial Globe composed of sundry matters. and first, for the greatest parts of the composition, I see the Water and the Earth, which extreamly differ from one another.
Salv.Let us, for this once, lay aside the Seas and other Waters, and let us consider the solid parts, and tell me, if you think them one and the same thing, or else different.
Simpl.As to appearance, I see that they are different things, there being very great heaps of unfruitful sands, and others of fruitful soiles; There are infinite sharp and steril mountains, full of hard stones and quarries of several kinds, as Porphyre, Alablaster, Jasper, and a thousand other kinds of Marbles: There are vast Minerals of so many kinds of metals; and in a word, such varieties of matters, that a whole day would not suffice only to enumerate them.
Salv.Now of all these different matters, do you think, that in the composition of this grand masse, there do concur portions, or else that amongst them all there is one part that far exceeds the rest, and is as it were the matter and substance of the immense lump?
Simpl.I believe that the Stones, Marbles, Metals, Gems, and the so many other several matters are as it were Jewels, and exteriour and superficial Ornaments of the primary Globe, which in grosse, as I believe, doth without compare exceed all these things put together.
Salv.And this principal and vast masse, of which those things above named are as it were excressences and ornaments, of what matter do you think that it is composed?
Simpl.I think that it is the simple, or lesse impure element of Earth.
Salv.But what do you understand by Earth? Is it haply that which is dispersed all over the fields, which is broke up with Mattocks and Ploughs, wherein we sowe corne, and plant fruits, and in which great boscages grow up, without the help of cul​ture, and which is, in a word, the habitation of all animals, and the womb of all vegetables?
Simpl.Tis this that I would affirm to be the substance of this our Globe.
Salv.But in this you do, in my judgment, affirm that which is not right: for this Earth which is broke up, is sowed, and is fertile, is but one part, and that very small of the surface of the Globe, which doth not go very deep, yea, its depth is very small, in comparison of the distance to the centre: and experience sheweth us, that one shall not dig very low, but one shall finde matters very different from this exteriour scurf, more solid, and not good for the production of vegetables. Besides the interne parts, as being compressed by very huge weights that lie upon them, are, in all probability, slived, and made as hard as any hard rock. One may adde to this, that fecundity would be in vain conferred upon those matters which never were designed to bear fruit, but to rest eternally buried in the profound and dark abysses of the Earth.
Simpl.But who shall assure us, that the parts more inward and near to the centre are unfruitful? They also may, perhaps, have their productions of things unknown to us?
Salv.You may aswell be assured thereof, as any man else, as being very capable to comprehend, that if the integral bodies of the Universe be produced onely for the benefit of Mankind, this above all the rest ought to be destin'd to the sole conveniences of us its inhabitants. But what benefit can we draw from matters so hid and remote from us, as that we shall never be able to make use of them?The interne parts of the terrestrial Globe must of necessity be solid. Therefore the interne substance of this our Globe cannot be a matter frangible, dissipable, and non-coherent, like this superficial part which we call ** Or MOULD. Earth: but it must, of necessity, be a most dense and solid body, and in a word, a most hard stone. And, if it ought to be so, what reason is there that should make you more scrupulous to believe that it is a Loadstone than a Porphiry, a Jasper, or other hard Marble? Happily if Gilbert had written, that this Globe is all compounded within of ** Of which with the Latin translatour, I must once more professe my self ignorant.Pietra Serena, or of Chalcedon, the paradox would have seemed to you lesse exorbitant?
Simpl.That the parts of this Globe more intern are more compressed, and so more slived together and solid, and more and more so, according as they lie lower, I do grant, and so likewise doth Aristotle, but that they degenerate and become other than Earth, of the same sort with this of the superficial parts, I see nothing that obliegeth me to believe.
Salv.I undertook not this discourse with an intent to prove demonstratively that the primary and real substance of this our ​Globe is Load-stone; but onely to shew that no reason could be given why one should be more unwilling to grant that it is of Load-stone,Our Globe would have been called stone, in stead of Earth, if that name had been giuen it in the beginning. than of some other matter. And if you will but seriously consider, you shall find that it is not improbable, that one sole, pure, and arbitrary name, hath moved men to think that it consists of Earth; and that is their having made use commonly from the beginning of this word Earth, as well to signifie that matter which is plowed and sowed, as to name this our Globe. The denomination of which if it had been taken from stone, as that it might as well have been taken from that as from the Earth; the saying that its primary substance was stone, would doubtlesse have found no scruple or opposition in any man. And is so much the more probable, in that I verily believe, that if one could but pare off the scurf of this great Globe, taking away but one full thousand or two thousand yards; and afterwards seperate the Stones from the Earth, the accumulation of the stones would be very much biger than that of the fertile Mould. But as for the reasons which concludently prove de facto, that is our Globe is a Magnet, I have mentioned none of them, nor is this a time to alledg them, and the rather, for that to your benefit you may read them in Gilbert; onely to encourage you to the perusal of them, I will set before you, in a similitude of my own,The method of Gilbert in his Philosophy. 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,Many properties 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.An Argument proving the terrestrial Globe to be a Magnet. 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, to make 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, ot Tin.
Simpl.I would say, without the least hæsitation, 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 Æquilibrium, 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,The Magnet armed takes up much more Iron, than when unarmed. 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 †† Or Closet of rarities. 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. The first observers and inventers of things ought to be admired.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,The true cause of the multiplication of vertue in the Magnet, by means of the arming. 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,Of a new effect its necessary that the cause be likewise new. 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, It is proved, that Iron consists of parts more subtil, pure, and compact than the magnet.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 compact​ed 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.A sensible proof of the impurity of the 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 ** The Author hereby meaneth that the stone doth not all consist of magnetick matter, but that the whiter specks being weak, those other parts of the Loadstone of a more dark & constant colour, contain all that vertue wherewith bodies are attracted. 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 ** A common sewing needle. 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 happen to me in the present Probleme, for being desirous to assure my self, by some other accident, whether the reason of the Proposition, by me found, were true; namely, whether the substance of the Magnet were really much lesse continuate than that of Iron or of Steel, I made the Artists that work in the Gallery of my Lord the Grand Duke, to smooth one side of that piece of Magnet, which formerly was yours, and then to polish and burnish it; upon which to my satisfaction I found what I desired. For I discovered many specks of colour different from the rest, but as splendid and bright, as any of the harder sort of stones; the rest of the Magnet was polite, but to the tact onely, not being in the least splendid; but rather as if it were smeered over with foot; and this was the substance of the Load-stone, and the shining part was the fragments of other stones intermixt therewith, as was sensibly made known by presenting the face thereof to filings of Iron, the which in great number leapt to the Load-stone, but not so much as one grain did stick to the said spots, which were many, some as big as the fourth part of the nail of a mans finger, others somewhat lesser, the least of all very many, and those that were scarce visible almost innumerable. So that I did assure my self, that my conjecture was true, when I first thought that the substance of the Magnet was not close and compact, but porous, or to say better, spongy; but with this difference, that whereas the sponge in its cavities and little cels conteineth Air or Water, the Magnet hath its pores full of hard and heavy stone, as appears by the exquisite lustre which those specks receive. Whereupon, as I have said from the beginning, applying the surface of the Iron to the superficies of the Magnet the minute particles of the Iron, though perhaps more continuate than these of any other body (as its ​shining more than any other matter doth shew) do not all, nay but very few of them incounter pure Magnet; and the contacts being few, the union is but weak. But because the cap of the Load-stone, besides the contact of a great part of its superficies, invests its self also with the virtue of the parts adjoyning, although they touch not; that side of it being exactly smoothed to which the other face, in like manner well polisht of the Iron to be attracted, is applyed, the contract is made by innumerable minute particles, if not haply by the infinite points of both the superficies, whereupon the union becometh very strong. This observation of smoothing the surfaces of the Irons that are to touch, came not into the thoughts of Gilbert, for he makes the Irons convex, so that their contact is very small; and thereupon it cometh to passe that the tenacity, wherewith those Irons conjoyn, is much lesser.
Sagr.I am, as I told you before, little lesse satisfied with this reason, that if it were a pure Geometrical Demonstration; and because we speak of a Physical Problem, I believe that also Simplicius will find himself satisfied as far as natural science admits, in which he knows that Geometrical evidence is not to be required.
Simpl.I think indeed,Sympathy and Antipathy, terms used by Philosophers to give a reason easily of many natural effests. that Salviatus with a fine circumlocution hath so manifestly displayed the cause of this effect, that any indifferent wit, though not verst in the Sciences, may apprehend the same; but we, confining our selves to the terms of Art, reduce the cause of these and other the like natural effects to Sympathy, which is a certain agreemet and mutual appetite which ariseth between things that are semblable to one another in qualities; as likewise on the contrary that hatred & enmity for which other things shun & abhor one another we call Antipathy.
Sagr.And thus with these two words men come to render reasons of a great number of accidents and effects which we see not without admiration to be produced in nature. But this kind of philosophating seems to me to have great sympathy with a certain way of Painting that a Friend of mine used,A pleasant example declaring the invalidity of some Phylosophical argumentations. who writ upon the Tele or Canvasse in chalk, here I will have the Fountain with Diana and her Nimphs, there certain Hariers, in this corner I will have a Hunts-man with the Head of a Stag, the rest shall be Lanes, Woods, and Hills; and left the remainder for the Painter to set forth with Colours; and thus he perswaded himself that he had painted the Story of Acteon, when as he had contributed thereto nothing of his own more than the names. But whether are we wandred with so long a digression, contrary to our former resolutions? I have almost forgot what the point was that we were upon when we fell into this magnetick dis​course: and yet I had something in my mind that I intended to have spoken upon that subject.
Salv.We were about to demonstrate that third motion ascribed by Copernicus to the Earth to be no motion but a quiescence and maintaining of it self immutably directed with its determinate parts towards the same & determinate parts of the Universe, that is a perpetual conservation of the Axis of its diurnal revolution parallel to it self, and looking towards such and such fixed stars; which most constant position we said did naturally agree with every librated body suspended in a fluid and yielding medium, which although carried about, yet did it not change direction in respect of things external, but onely seemed to revolve in its self, in respect of that which carryed it round, and to the vessel in which it was transported. And then we added to this simple and natural accident the magnetick virtue, whereby the self Terrestrial Globe might so much the more constantly keep it immutable,———
Sagr.Now I remember the whole businesse; and that which then came into my minde, & which I would have intimated, was a certain consideration touching the scruple and objection of Simplicius, which he propounded against the mobility of the Earth, taken from the multiplicity of motions,The several natural motions of the Magnet. impossible to be assigned to a simple body, of which but one sole and simple motion, according to the doctrine of Aristotle, can be natural; and that which I would have proposed to consideration, was the Magnet, to which we manifestly see three motions naturally to agree: one towards the centre of the Earth, as a Grave; the second is the circular Horizontal Motion, whereby it restores and conserves its Axis towards determinate parts of the Universe; and the third is this, newly discovered by Gilbert, of inclining its Axis, being in the plane of a Meridian towards the surface of the Earth, and this more and lesse, according as it shall be distant from the Equinoctial, under which it is parallel to the Axis of the Earth. Besides these three, it is not perhaps improbable, but that it may have a fourth, of revolving upon its own Axis, in case it were librated and suspended in the air or other fluid and yielding Medium, so that 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.
Simpl.This doth uot 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.Aristole grants a compound motion to mixt bodies. 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.
Simpl.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?
Simpl.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.The motion of mixt bodies ought to be such as may result from the composition of the motions of the simple bodies compounding.
Simpl.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,With two right motions one cannot compose circular motions. 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 cœlestial, if you will maintain that the straight motion is a peculiar to the Elements, and the circular to the cœlestial 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,Philosophers are forced to confesse that the Magnet is compounded of cœlestial substances, and of elementary. and integral substance of our Globe, pertaketh of the same qualities with it. The errour of those who call the Magnet a mixt body, and the terrestrial Globe a simble body.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 * Ogliopotrida a Spanish dish of many ingredients boild together. 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,The Discourses of Peripateticks, full of errours and contradictions. 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;An improbable effect admired by Gilbertus in the Loadstone. 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,The vain argumentation of some to prove the Element of Water to be of a Spherical superficies. 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.