AN ATTEMPT To prove the MOTION OF THE EARTH FROM Observations MADE BY ROBERT HOOKE Fellow of the Royal Society.  Senec. Nat. Qu. lib. 1. cap. 30. Nè miremur tam tardè erui qua tam altè jacent. 
LONDON, Printed by T. R. for John Martin Printer to the Royal Society, at the Bell in St. Paul's Churchyard. 1674.   

TO THE TRULY HONOURABLE Sir John Cutler KNIGHT and BARONET, My Worthy PATRON.  
SIR,  
AMong several Eminent Marks of your Greatness of Mind for promoting the Public Good, that of your Bounty for the Advancement of Experimental and Real Knowledge, by the Founding a Physico-Mechanical Lecture, deserves to be Recorded as One, and more especially by me whom you have honoured by establishing your first Lecturer. As an Earnest of others more considerable shortly to follow, I here present you with one of my Discourses in that Employment, which though short and plain, contains somewhat of Information which the Learned have hitherto desired, though almost with despair. As I hope their kind Acceptance will produce their thanks to you to whom they are justly due, so your Acceptance will encourage me in the further prosecution of these Inquiries to approve myself,  
Noble Sir, Your most obliged, and most humble Servant From Gresham College, March 25. 1674. ROBERT HOOKE.   

READER,  
I Have formerly in the Preface of my Micrographia given the World an account of the founding a Physico-Mechanical Lecture in the Year 1665, by Sir John Cutler, for the promoting the History of Nature and of Art. In prosecution thereof, I have collected many Observations both of the one and the other kind, and from time to time (as obliged) I have acquainted the Royal Society at their Public Meetings, both at Gresham College and Arundel House therewith, by Discourses and Lectures thereupon.  
Now in order to the further promoting the End and Design of this Lecture, I have complied, with the desire of several of my Friends (though otherwise not thereunto obliged) to commit divers of those Discourses to the Public, though of themselves for the most part incomplete, and Essays or Attempts only upon several Subjects which have no dependency or coherency one with another. In the doing hereof, I design to avoid any kind of Method or Order that may require Apologies, Prefaces, or needless Repetitions of what is already known, or might have been said upon that Occasion, or may necessitate me to follow this or that Subject, that doth not some way or other offer itself as it were, and prompt me to the consideration thereof. But because they may possibly admit of some better order hereafter, I design to print them all of the same Volume, that so they may be, when ranged, either stitched or bound together, and may, as occasion requires, be referred to under the Title of their Number and Page. This way I choose as the best for promoting the Design of this Lecture; for as there is scarce one Subject of millions that may be pitched upon, but to write an exact and complete History thereof, would require the whole time and attention of a man's life, and some thousands of Inventions and Observations to accomplish it: So on the other side no man is able to say that he will complete this or that Inquiry, whatever it be, (The greatest part of Invention being but a luckey hit of chance, for the most part not in our own power, and like the wind, the Spirit of Invention bloweth where and when it listeth, and we scarce know whence it came, or whether 'tis gone.) 'Twill be much better therefore to embrace the influences of Providence, and to be diligent in the inquiry of every thing we meet with. For we shall quickly find that the number of considerable Observations and Inventions this way collected, will a hundred fold outstrip those that are found by Design. No man but hath some luckey hits and useful thoughts on this or that Subject he is conversant about, the regarding and communicating of which, might be a means to other Persons highly to improve them. Whence 'twere much to be wished, that others would take this Method in their Publications, and not torment their Readers with such nauseous Repetitions, and frivolous Apologies, as Method and Volumes do necessitate them to; But would rather enrich the Storehouse of Art and Nature with choice and excellent Seed, freed from the Chaff and Dross that do otherwise bury and corrupt it.  
The communicating such happy Thoughts and Occurrences need not much take up a man's time to fit it for the Press; the Relation being so much the better the plainer it is. And matter of Fact being the Kernel Readers generally desire (at least in these Subjects) it will be so much the readier for use if it be freed from the thick and hard shell of Impertinences. This way also is more grateful both to the Writer and the Reader, who proceed with a fresh stomach upon variety, but would be weary and dulled if necessitated to dwell too long upon one Subject. There are other conveniencies also in this Method of Communication not less considerable than the former, amongst the rest the securing of Inventions to their first Authors, which 'tis hardly possible to do by any other means; for there are a sort of Persons that make it their business to pump and spy out others Inventions, that they may vend them to Traders of that kind, who think they do ingenuously to print them for their own, since they have bought and paid for them. Of this there have lately been some Instances, and more may be expected, if this way prevent not.  
When things cannot be well explained by words only (which is frequent in Mathematical and Mechanical Discourses) I add Schemes and delineatious Descriptions of that kind being easier to be made and understood. As near as I can I omit the repeating things already printed, and endeavour to deliver such as are new and my own, being myself best pleased with such usage from other Authors.  
I have begun with a Discourse composed and read in Gresham College in the Year 1670. when I designed to have printed it, but was diverted by the advice of some Friends to stay the repeating the Observation, rather than publish it upon the Experience of one Year only. But finding that Sickness hath hitherto hindered me from repeating the Trials, and that some Years Observations have already been lost by the first delay: I do rather hast it out now, though imperfect, then detain it for a better completing, hoping it may be at least a Hint to others to prosecute and complete the Observation, which I much long for.  
This first Discourse is upon an Observation of Nature, and may therefore be properly referred to that Head, though it contain also somewhat of the Improvement of Art: The second speedily to follow, will more properly be referrable to Artificial Improvements, though it will contain also many Observations of Nature; and I design always to make them follow each other by turns, and as 'twere to interweave them, being apart but like the Warp or Woof before contexture, unfit either to Cloth, or adorn the Body of Philosophy.   

 
 
 
 
 
 
 
  

AN ATTEMPT To prove the Motion of the EARTH BY OBSERVATIONS.  
WHether the Earth move or stand still hath been a Problem, that since Copernicus revived it, hath much exercised the Wits of our best modern Astronomers and Philosophers, amongst which notwithstanding there hath not been any one who hath found out a certain manifestation either of the one or the other Doctrine. The more knowing and judicious have for many plausible reasons adhered to the Copernican Hypothesis: But the generality of others, either out of ignorance or prejudice, have rejected it as a most extravagant opinion. To those indeed who understand not the grounds and principles of Astronomy, the prejudice of common converse doth make it seem so absurd, that a man shall as soon persuade them that the Sun doth not shine, as that it doth not move; and as easily move the Earth as make them believe that it does so already. For such Persons I cannot suppose that they should understand the cogency of the Reasons here presented, drawn from the following observations of Parallax, much less therefore can I expect their belief and assent thereunto; to them I have only this to say, 'Tis not here my business to instruct them in the first principles of Astronomy, there being already Introductions enough for that purpose: But rather to furnish the Learned with an experimentum crucis to determine between the Tychonick and Copernican Hypotheses. That which hath hitherto continued the dispute hath been the plausibleness of some Arguments alleged by the one and the other party, with such who have been by nature or education prejudiced to this or that way. For to one that hath been conversant only with illiterate persons, or such as understand not the principles of Astronomy and Geometry, and have had no true notion of the vastness of the Universe, and the exceeding minuteness of the Globe of the Earth in comparison therewith, who have confined their imaginations & fancies only within the compass and pale of their own walk and prospect, who can scarce imagine that the Earth is globous, but rather like some of old, imagine it to be a round plain covered with the Sky as with a Hemisphere, and the Sun, Moon, and Stars to be holes through it by which the Light of Heaven comes down; that suppose themselves in the centre of this plain, and that the Sky doth touch that plain round the edges, supported in part by the Mountains; that suppose the Sun as big as a Sieve, and the Moon as a Chedder Cheese, and hardly a mile off. That wonder why the Sun, Moon, and Stars do not fall down like Hailstones; and that will be martyred rather than grant that there may be Antipodes, believing it absolutely impossible, since they must necessarily fall down into the Abyss below them: For how can they go with their feet towards ours, and their heads downwards, without making their brains addle. To one I say, thus prejudiced with these and a thousand other fancies and opinions more ridiculous and absurd to knowing men, who can ever imagine that the uniformity and harmony of the Celestial bodies and motions, should be an Argument prevalent to persuade that the Earth moves about the Sun: Whereas that Hypothesis which shows how to salve the appearances by the rest of the Earth and the motion of the Heavens, seems generally so plausible that none of these can resist it.  
Now though it may be said, 'Tis not only those but great Geometricians, Astronomers and Philosophers have also adhered to that side, yet generally the reason is the very same. For most of those, when young, have been imbued with principles as gross and rude as those of the Vulgar, especially as to the frame and fabric of the World, which leave so deep an impression upon the fancy, that they are not without great pain and trouble obliterated: Others, as a further confirmation in their childish opinion, have been instructed in the Ptolomaick or Tichonick System, and by the Authority of their Tutors, overawed into a belief, if not a veneration thereof: Whence for the most part such persons will not endure to hear Arguments against it, and if they do, 'tis only to find Answers to confute them.  
On the other side, some out of a contradicting nature to their Tutors; others, by as great a prejudice of institution; and some few others upon better reasoned grounds, from the proportion and harmony of the World, cannot but embrace the Copernican Arguments, as demonstrations that the Earth moves, and that the Sun and Stars stand still.  
I confess there is somewhat of reason on both sides, but there is also something of prejudice even on that side that seems the most rational. For by way of objection, what way of demonstration have we that the frame and constitution of the World is so harmonious according to our notion of its harmony, as we suppose? Is there not a possibility that the things may be otherwise? nay, is there not something of probability? may not the Sun move as Tycho supposes, and the Planets make their Revolutions about it whilst the Earth stands still, and by its magnetism attracts the Sun, and so keeps him moving about it, whilst at the same time ☿ and ♀ move about the Sun, after the same manner as ♄ and ♃ move about the Sun whilst the Satellites move about them? especially since it is not demonstrated without much art and difficulty, and taking many things for granted which are hard to be proved, that there is any body in the Universe more considerable than the Earth we tread on. Is there not much reason for the Hypothesis of Tycho at least, when he with all the accurateness that he arrived to with his vast Instruments, or Riccioli, who pretends much to outstrip him, were not able to find any sensible Parallax of the Earth's Orb among the fixed Stars, especially if the observations upon which they ground their assertions, were made to the accurateness of some few Seconds? What then, though we have a Chimaera or Idea of perfection and harmony in that Hypothesis we pitch upon, may there not be a much greater harmony and proportion in the constitution itself which we know not, though it be quite differing from what we fancy? Probable Arguments might thus have been urged both on the one and the other side to the World's end; but there never was nor could have been any determination of the Controversy, without some positive observation for determining whether there were a Parallax or no of the Orb of the Earth; This Tycho and Riccioli affirm in the Negative, that there is none at all: But I do affirm there is no one that can either prove that there is, or that there is not any Parallax of that Orb amongst the fixed Stars from the Suppellex of observations yet made either by Tycho, Riccioli, or any other Writer that I have yet met with from the beginning of writing to this day. For all Observators having hitherto made use of the naked eye for determining the exact place of the object, and the eye being unable to distinguish any angle less than a minute, and an observation requisite to determine this requiring a much greater exactness then to a minute, it doth necessarily follow that this experimentum crucis was not in their power, whatever either Tycho or Riccioli have said to the contrary, and would thence overthrow the Copernican System, and establish their own. We are not therefore wholly to acquiess in their determination, since if we examine more nicely into the observations made by them, together with their Instruments and ways of using them, we shall find that their performances thereby were far otherwise than what they would seem to make us believe. The Controversy therefore notwithstanding all that hath been said either by the one or by the other Party, remains yet undetermined, Whether the Earth move above the Sun, or the Sun about the Earth; and all the Arguments alleged either on this or that side, are but probabilities at best, and admit not of a necessary and positive conclusion. Nor is there indeed any other means left for humane industry to determine it, save this one which I have endeavoured to make; and the unquestionable certainty thereof is a most undeniable Argument of the truth of the Copernican Systeme; and the want thereof hath been the principal Argument that hath hitherto somewhat detained me from declaring absolutely for that Hypothesis, for though it doth in every particular almost seem to solve the appearances more naturally and easily, and to afford an exceeding harmonious constitution of the great bodies of the World compared one with another, as to their magnitudes, motions, and distances, yet this objection was always very plausible to most men, that it is affirmed by such as have written more particularly of this subject, that there never was any sensible Parallax discovered by the best observations of this supposed annual motion of the Earth about the Sun as its centre, though moved in an Orb whose Diameter is by the greatest number of Astronomers reckoned between 11 and 12 hundred Diameters of the Earth: Though some others make it between 3 and 4 thousand; others between 7 and 8; and others between 14 and 15 thousands; and I am apt to believe it may be yet much more, each Diameter of the Earth being supposed to be between 7 and 8 thousand English miles, and consequently the whole being reduced into miles, if we reckon with the most, amounting to 120 millions of English miles. It cannot, I confess, but seem very uncouth and strange to such as have been used to confine the World with less dimensions, that this annual Orb of the Earth of so vast a magnitude, should have no sensible Parallax amongst the fixed Stars, and therefore 'twas in vain to endeavour to answer that objection. For it is unreasonable to expect that the fancies of most men should be so far strained beyond their narrow dimensions, as to make them believe the extent of the Universe so immensly great as they must have granted it to be, supposing no Parallax could have been found.  
The Inquisitive Jesuit Riccioli has taken great pains by 77 Arguments to overthrow the Copernican Hypothesis, and is therein so earnest and zealous, that though otherwise a very learned man and good Astronomer, he seems to believe his own Arguments; but all his other 76 Arguments might have been spared as to most men, if upon making observations as I have done, he could have proved there had been no sensible Parallax this way discoverable, as I believe this one Discovery will answer them, and 77 more, if so many can be thought of and produced against it. Though yet I confess had I failed in discovering a Parallax this way, as to my own thoughts and persuasion, the almost infinite extension of the Universe had not to me seemed altogether so great an absurdity to be believed as the Generality do esteem it; for since 'tis confessedly granted on all hands the distance of the fixed Stars is merely hypothetical, and not founded on any other ground or reason but fancy and supposition, and that there never was hitherto any Parallax observed, nor any other considerable Argument to prove the distances supposed by such as have been most curious and inquisitive in that particular, I see no Argument drawn from the nature of the thing that can have any necessary force in it to determine that the said distance cannot be more than this or that, whatever it be that is assigned. For the same God that did make this World that we would thus limit and bound, could as easily make it millions of millions of times bigger, as of that quantity we imagine; and all the other appearances except this of Parallax would be the very same that now they are. To me indeed the Universe seems to be vastly bigger than 'tis hitherto asserted by any Writer, when I consider the many differing magnitudes of the fixed Stars, and the continual increase of their number according as they are looked after with better and longer Telescopes. And could we certainly determine and measure their Diameters, and distinguish what part of their appearing magnitude were to be attributed to their bulk, and what to their brightness, I am apt to believe we should make another distribution of their magnitudes, than what is already made by Ptolemy, Tycho, Kepler, Bayer, Clavius, Grienbergerus, Piff, Hevelius and others.  
For supposing all the fixed Stars as so many Suns, and each of them to have a Sphere of activity or expansion proportionate to their solidity and activity, and a bigger and brighter bodied Star to have a proportionate bigger space or expansion belonging to it, we should from the knowledge of their Diameters and brightnesses be better able to judge of their distances, and consequently assign divers of them other magnitudes than those already stated: Especially since we now find by observations, that of those which are accounted single Stars, divers prove a congeries of many Stars, though from their near appearing to each other, the naked eye cannot distinguish them; Such as those Stars which are called Nebulous, and those in Orion Sword, and that in the head of Aries, and a multitude of others the Telescope doth now detect. And possibly we may find that those twenty magnitudes of Stars now discovered by a fifteen foot Glass, may be found to increase the magnitude of the Semidiameter of the visible World, forty times bigger than the Copernicans now suppose it between the Sun and the fixed Stars, and consequently sixty four thousand times in bulk. And if a Telescope of double or triple the goodness of one of fifteen should discover double or triple the said number of magnitudes, would it not be an Argument of doubling or trebling the former Diameter, and of increasing the bulk eight or twenty seven times. Especially if their apparent Diameters shall be found reciprocal to their Distances (for the determination of which I did make some observations, and design to complete with what speed I am able.) But to digress no further, This grand objection of the Anti-copernicans, which to most men seemed so plausible, that it was in vain to oppose it, though, I say, it kept me from declaring absolutely for the Copernican Hypothesis, yet I never found any absurdity or impossibility that followed thereupon: And I always suspected that though some great Astronomers had asserted that there was no Parallax to be found by their observations, though made with great accurateness, there might yet be a possibility that they might be mistaken; which made me always look upon it as an inquiry well worth examining: first, Whether the ways they had already attempted were not subject and liable to great errors and uncertainties: and secondly, Whether there might not be some other ways found out which should be free from all the exceptions the former were encumbered with, and be so far advanced beyond the former in certainty and accurateness, as that from the diligent and curious use thereof, not only all the objections against the former might be removed, but all other whatsoever that were material to prove the ineffectualness thereof for this purpose.  
I began therefore first to examine into the matter as it had already been performed by those who had asserted no sensible Parallax of the annual Orb of the Earth, and quickly found that (whatever they asserted) they could never determine whether there were any or no Parallax of this annual Orb; especially if it were less than a minute, which Kepler and Riccioli hypothetically affirm it to be: The former making it about twenty four Seconds, and the latter about ten. For though Tycho, a man of unquestionable truth in his assertions, affirm it possible to observe with large Instruments, conveniently mounted and furnished with sights contrived by himself (and now the common ones for Astronomical Instruments) to the accurateness of ten Seconds; and though Riccioli and his ingenious and accurate Companion Grimaldi affirm it possible to make observations by their way, with the naked edge to the accurateness of five Seconds; Yet Kepler did affirm, and that justly, that 'twas impossible to be sure to a less Angle than 12 Seconds: And I from my own experience do find it exceeding difficult by any of the common sights yet used to be sure to a minute. I quickly concluded therefore that all their endeavours must have hitherto been ineffectual to this purpose, and that they had not been less imposed on themselves, than they had deceived others by their mistaken observations. And this mistake I found proceeded from divers inconveniencies their ways of observations were liable to. As first from the shrinking and stretching of the materials wherewith their Instruments were made, I conceive a much greater angle than that of a minute may be mistaken in taking an altitude of fifty Degrees. For if the Instruments be made of Wood, 'tis manifest that moust weather will make the frame stretch, and dry weather will make it shrink a much greater quantity then to vary a minute: and if it be Metal, unless it be provided for in the fabric of the Instrument accordingly, the heat of Summer, when the Summer observations are to be made, will make the Quadrant swell, and the cold of Winter will make it shrink much more than to vary a minute: Both which inconveniencies ought to be removed. Next the bending and warping of an Instrument by its own weight, will make a very considerable alteration. And thirdly, the common way of Division is also liable to many inconveniencies: And 'tis hardly possible to ascertain all the subdivisions of Degrees into minutes for the whole Quadrant, though that be not altogether impossible. But I will suppose that they did foresee, and in some manner prevent all these inconveniencies, especially Tycho and Riccioli, who seem to have been aware thereof. But there was one inconvenience which was worse than all the rest, which they seem not to have been sufficiently sensible of, from whence proceeded all their own mistakes, and their imposing upon others, and that was from their opinion that the sight of the naked eye was able to distinguish the parts of the object as minutely as the limb of the Quadrant (of what largeness soever) was capable of Divisions; whereas 'tis hardly possible for any unarmed eye well to distinguish any Angle much smaller than that of a minute: and where two objects are not farther distant than a minute, if they are bright objects, they coaless and appear one, though I confess, if they be dark objects, and a light be interposed, the distance between them shall be visible, though really much less than a Second; and yet notwithstanding, my first assertion stands good; for though a bright object, as a candle or light at a distance, or a Star, or the like, can be seen by the eye, though its body do really not subtend an Angle of one third, yet it proceeds from a radiation (that is, from reflection and refraction together) in the air and in the eye, whereby the body thereof is represented to the naked eye some hundred times bigger than it really is. That this is so, any one that will but carefully examine will find it true.  
It was, I doubt not, their extraordinary desire and care to be exact, that caused them to make their Instruments so large, and to subdivide them to such an exactness, as to distinguish, if possible, to Seconds; And I question not but that they used their utmost endeavour in directing the sight to the object: but since the naked eye cannot distinguish an Angle much smaller than a minute, and very few to a whole minute, all their charge and trouble in making and managing large Instruments, and in calculating and deducing from them, was as to this use in vain. Hence I judged that whatever men's eyes were in the younger age of the World, our eyes in this old age of it needed Spectacles; and therefore I resolved to assist my eyes with a very large and good Telescope, instead of the common sights, whereby I can with ease distinguish the parts of an object to Seconds: and I question not but that this way may be yet made capable of distinguishing much more curiously, possibly even to some few Thirds. This invention removed that grand inconvenience which all former observations were spoiled with: but there remained yet further this difficulty, How to make an Instrument large enough for this purpose, that I might be assured did not shrink, nor warp, nor stretch so much as to vary a Second; for such is the nature of all Materials that can be made use of for Instruments of the bigness I designed this, that 'tis almost impossible to make a movable Instrument that shall not be subject to a variation of divers Seconds: It was therefore my next inquiry where I might fix this Archimedean Engine that was to move the Earth. For the doing of which, I knew 'twas in vain to consult with any Writer or Astronomer, having never then heard of any person that had ever before that time had any thoughts thereof: and when I first propounded it to the Royal Society, 'twas looked upon as a new thought, and somewhat extravagant, and hardly practicable, until upon hearing my explication, and the various ways how it might be reduced into practice, it was at length judged possible, and desirable to be tried. I propounded therefore to them the several ways that it was possible to be performed, and what method was to be observed in every one of them, and somewhat of the conveniencies and inconveniencies in each of them; for having seriously meditated upon the Inquiry, I quickly thought of many expedients for the doing thereof. As first, I had thoughts of making use of some very great and massy Tower or Wall that were well settled, or of some large Rock or Hill whereunto I might fix my Glasses, so as to take the exact altitude of some eminent Star near the Pole of the Ecliptik, when at its greatest height, at two differing times of the year; to wit, about the Summer and Winter Solstice, to see if possibly I could discover any difference of altitude between the first and second observation. But to accomplish this (besides the vast difficulty there would have been to have measured such an Angle to the accurateness requisite, if at least it were desired to have the Angle of altitude to Minutes and Seconds, which ought also to have been repeated as oft as any observation had been made for fear of settling or swelling, etc.) I was destitute of such a convenience near my habitation; besides, had I had my wish, I found that 'twas liable to an inconvenience that would wholly overthrow my whole design, which I knew not well how to avoid: Namely, to that which hath hitherto made even the very best observations of Parallaxes ineffectual and uncertain, the refraction of the Air or Atmosphere, which though it could have been but very little at the greatest altitude of the Pole of the Ecliptic, yet it might have been enough plausibly to have spoiled the whole observation, and to have given the Anti-copernicans an opportunity of evading the Arguments taken from it, especially upon the account of the differing constitution of the Atmosphere in June and December, which might have caused so much a greater refraction of the same altitude at one time then another, as would have been sufficient to have made this observation ineffectual for what it was designed. Add to this, that it would have been no easy matter to have set the Glasses or Telescope exactly against the Meridian, so as to see the highest altitude of any Star near the Pole of the Ecliptic distinctly to a Second.  
The like difficulties I found if observations were made of the greatest altitude of the Pole of the Ecliptic in June and December, or the least altitude of the same in December and June. For besides all the uncertainties that the Instruments, be they what they will, are liable to, the grand inconvenience of the refraction of the Air, which is enough to spoil all observations if it be intermixed with uncertainty, in the former is considerable, and in the later intolerable.  
Having therefore examined the ways and Instruments for all manner of Astronomical observations hitherto made use of, and considered of the inconveniencies and imperfections of them; and having also duly weighed the great accurateness and certainty that this observation necessarily required: I did next contrive a way of making observations that might be free from all the former inconveniencies and exceptions, and as near as might be, fortified against any other that could be invented or raised against it. This way than was to observe by the passing of some considerable Star near the Zenith of Gresham College, whether it did not at one time of the year pass nearer to it, and at another further from it: for if the Earth did move in an Orb about the Sun, and that this Orb had any sensible Parallax amongst the fixed Stars; this must necessarily happen, especially to those fixed Stars which were nearest the Pole of the Ecliptic. And that this is so, any one may plainly perceive if he consider the annexed Scheme, Fig. I. where let S represent the Sun placed as it were in the centre of the Planetary Orbs, ABCD an imaginary Orb of the fixed Stars of the first magnitude, whose centre for demonstration sake we will suppose the Sun. Let ♈ ♋ ♎ ♑ represent the Orb in which the Earth is supposed to move about the Sun, obliquely projected on the Paper. Let ♑ represent the Earth in Capricorn, and ♋ the Earth in Cancer, let 12. 12. represent the imaginary Axis of the Earth, keeping continually a parallelism to its self, and let ♑ ABCD ♋ represent an imaginary Plain passing through the centre of the Star at D in the Solstitial Colour, and the two centres of the Earth in ♑ and ♋, and C represent the Zenith point of Gresham College at noon, when the Earth is in Cancer, and A the Zenith point of the said College at midnight in the aforesaid Orb ABCD when the Earth is in Capricorn, 'tis manifest therefore that since the Poles of the Earth, the Poles of the Ecliptic, and the Zenith points of the Earth at noon, when in Cancer, and at midnight, when in Capricorn, are all in the same Plain; and that the Axis of the Earth keeps always its parallelism, and that the Angles made by the Perpendiculars of Gresham College, with the Axes are always the same, that the aforesaid Perpendiculars of the said College shall be parallel also one to another, and consequently denote out two points in the abovesaid Orb A and C as far distant from each other as the parallel Lines A ♑ and C ♋ are, and consequently the point A shall be farther from the Star in D, and the point C shall be nearer to it, when in the Meridian near the Zenith of London, and consequently if the said Star be observed when in the Meridian of the place abovesaid, if there be any such difference considerable, it may be found if convenient Instruments and care be made use of for the observation thereof: and the difference between the Angle A ♑ D, and the Angle C ♋ D, will give the parallactical Angle ♑ D ♋ of the Orb of the Earth to the fixed Star D of the first magnitude. The same demonstration will hold mutatis mutandis, supposing the Star be not in the Meridian or Plain abovesaid, but in some other Meridian, as any one upon well considering the nature of the thing itself may easily prove, if the observation be made when the Zenith passes by the Star at midnight, and at midday. But the nearer the Zenith of the place of observation passeth to the Pole point of the Ecliptic, the better; The Angle of Parallax being still the more sensible. Therefore the best place to complete this observation were in some place under the Polar Circles, as in Iseland, where the Zenith of the place at the times abovesaid, must consequently pass at one time to the North side of the Pole of the Ecliptic, and at the other on the South side, and the Zenith of March and Sept. must pass through the very Pole-point itself. Now it falling out so, that there is no considerable Star in that part of the Heavens nearer the above said Plain, and nearer the Zenith point of Gresham College in that Plain, than the Bright Star in the head of the Dragon, I made choice of that Star for the object by which I designed to make this observation, finding the Zenith point of Gresham College to pass within some very few minutes of the Star itself; the declination thereof according to Riccioli being 51°. 36′. 7″. and the Plain the Star and Pole of the World, making an Angle with the aforesaid Plain but of 2°. 52. 36, the right ascension thereof being according to Riccioli 267°. 7′. 24″.  
And that this may be made a little plainer, let us suppose in the third Figure, the North part of the Heavens projected stereographical upon a Plain to which the Axis is perpendicular. Let p represent the Pole, e the Pole of the Ecliptic, l the bright Star in the head of Draco, and let accc represent an imaginary Circle described by the Zenith of Gresham College among the fixed Stars in June, and bddd a like Circle described by the said Zenith in December, and efff a like Circle described as above in March, and ghhh in September. It is very evident that the true distances of the Zeniths in that part of the Meridian which is next the Pole of the Ecliptic, to wit, in the head of the Constellation Draco, shall be to the true distances of the said Zeniths in that part which is furthest from the said Pole, to wit, near the constellation of Auriga in consequentia, as the sign of 75 degrees to the sign of 14°. 54′, and the variation of the Zeniths, or the Angle of Parallax here at Gresham College, to the Angle of Parallax in Iseland, or any other place under the Pole of the Ecliptic, or Arctic Circle is, as the sign of seventy five to the sign of ninety or the Radius. This will be very evident if we consider in the second Scheme; AB to represent the Diameter of the great Orb: AC and BD the perpendiculars of Iseland, or some other place under the Polar Circle. GA', HB the perpendiculars of Gresham College in Draco: and LA, MB the perpendiculars of the same place to the Solstitial Colour near Auriga, the several distances CD, GH, IK, LM, will be as the signs of 90°75° 66°. 30′ 14°. 54′. to wit, as the Lines or Cords AB. AO. PB. QB.  
I might have made observations of the distances of the transits of our Zenith from any other Star as well as from this of Draco, and the same Phenomena might have been observed, taking care to make one of the observations when the Star is in the Zenith at midnight, and the other when the same Star is in the Zenith at noon or midday; and upon this account when I next observe, I design to observe the transits of our Zenith by Benenaim, or the ultima caudae ursae majoris, it being a Star of the second magnitude, and having almost as much declination as Gresham College hath latitude. The principal days of doing which will be about the 4 of April, when our Zenith passeth by the said Star at midnight, and the 7 of October, when it passeth by it at noon or midday: the reason of all which will be sufficiently manifest to any one that shall well consider the preceding explanation.  
This Star I would the rather observe, because as it is placed so as that the Parallax thereof will be almost as great as of the Pole of the Ecliptic in Iseland, or under the Arctic Circle, so it being a Star of the second magnitude, and consequently perhaps as near again as one of the fourth, the Angle of Parallax will be near about twice as big, and the Star itself much more easy to be seen in the day time. This will be very easy to be understood, if we consider in the first Scheme the differing distances of the Orb ABCD, in which we may suppose the Stars of the second magnitude to be fixed, and of the Orb α β χ δ, in which we may suppose the Stars of the fourth magnitude, and abcd in which we may suppose those of the third magnitude, and ABCD in which we may suppose those of the first; for if the Stars are further and further removed from the Sun, according as they appear less and less to us, the parallactical difference found by observation must necessarily be less and less, according as the observation is made of less and less Stars.  
The reasons then why I made choice of this way of observing will be easy to any one that shall consider that hereby, first, I avoid that grand inconvenience wherewith all ancient and modern observations have been perplexed, and as to Parallax insignificant, and that is the refraction of the Air or Atmosphere. How great an inconvenience that was is obvious, since 'tis certainly much greater at one time then another, and never at any certainty; and secondly, 'Tis not equally proportionable, for sometimes the refraction is greater at some distance above the Horizon, then in or nearer to the Horizon itself, and sometimes the quite contrary, which I have very often observed; and this to so exorbitant a difference, as to confound all Hypothetical Calculations of Tables for this purpose. This ariseth from the uncertain and sudden variations of the Air or Atmosphere, either from heat and cold, from the thickness and thinness of Vapours, from the differing gravity and levity, from the winds, currents, and eddyes thereof, all which being not so well understood by what way, and in what degree, and at what time they work and operate upon the Air, must needs make the refraction thereof exceedingly perplexed, and the reduction thereof to any certain theory fit for practice, a thing almost impossible. Now if we are uncertain what part of the observed Angle is to be ascribed to refraction, we are uncertain of the whole observation as far as the possible uncertainty of refraction. Let me have but the liberty of supposing the refraction what I please, and of fixing the proportional decrease thereof according to the various elevation of the Rays above the Horizon; I will with ease make out all the visible Phenomena of the Universe, Sun, Moon, and Stars, and yet not suppose them above a Diameter of the Earth distant. Now in this observation there is no refraction at all, and consequently be the Air thicker or thinner, heavier or lighter, hotter or colder, be it in Summer or Winter, in the night or the day, the ray continually passeth directly, and is not at all refracted and deflected from its straight passage. In the next place, by this way of observing I avoid all the difficulties that attend the making, mounting, and managing of great Instruments: For I have no need of Quadrant, Sextant, or Octant, nor of any other part or Circle bigger than a Degree at most; nor have I need to take care of the divisions and subdivisions thereof, nor of the substance whether made of Iron, Brass, Copper, or Wood, nor whether the parts thereof shrink or swell, or bend or warp, to all which the best Instruments hitherto made use of, have been some ways or other liable. And notwithstanding the vast care and expense of the noble Tycho about the making, fixing, and using his great Instruments; yet I do not find them so well secured from divers of these inconveniences, but that they were still subject to some considerable irregularities. Nay, notwithstanding the seemingly much greater curiosity and expense of Hevelius, and his infinite labour and diligence in the completing and using of his vast Apparatus of Astronomical Instruments, I do not find them so well secured, but that some of the causes of errors that I have before mentioned, may have had a considerable effect upon them also; especially if they were supposed to measure an Angle to some few Seconds, as I shall hereafter perhaps have more occasion to manifest. Now, if the Instruments of Tycho and Hevelius, (who had certainly two of the most curious and magnificent Collections of Astronomical Instruments that were ever yet got together or made use of) were subject to these uncertainties, What shall we say of all that other farrage of trumpery that hath been made use of by most others? We see therefore the necessity of the conjunction of Physical and Philosophical with Mechanical and Experimental Knowledge, how lame and imperfect the study of Art doth often prove without the conjunction of the study of Nature, and upon what rational grounds it was that Sir John Cutler, the Patron and Founder of this Lecture, proceeded in joining the contemplation of them both together.  
The next thing was the Instrument for the making of this observation, such a one as should not be liable to any of the former exceptions, nor any other new ones that were considerable. To this purpose I pitched upon a Telescope, the largest I could get and make use of, which I designed so to fix upright, as that looking directly upwards, I could be able certainly to observe the transits of any Stars over or near the Zenith, and furnishing it with perpendiculars and a convenient dividing Instrument, I should be able not only to know exactly when the Star came to cross the Meridian, but also how far it crossed it from the Centre or Zenith point of Gresham College, either towards the North, or towards the South. All which Particulars, how I performed, I shall now in order describe, and this somewhat the more distinctly, that such as have a desire to do the like, may be the more ready and better enabled to proceed with the same.  
First then (finding a Tube would be very troublesome to the Rooms through which it passed, especially if it were placed pretty far in the Room, and that one wanted so free an access as was necessary if it were planted nigh the wall, and that there was no absolute necessity of such an intermediate Tube, supposing there were a cell to direct the eye fixed to the Eye Glass, and that there were some short cell to carry the Object Glass in at the top, so as to keep it steady, when raised upward or let downwards, the light in the intermediate Rooms not at all hindering, but rather proving of good use to this purpose for seeing the Mensurator) I opened a passage of about a foot square through the roof of my lodgings (see the Fourth Figure) and therein fixed a Tube a a perpendicular and upright, of about ten or twelve foot in length, and a foot square, so as that the lower end thereof came through the Ceiling, and was open into the Chamber underneath: This Tube I covered with a lid at the top q, housed so as to throw off the rain, and so contrived, as I could easily open or shut it by a small string nop, which came down through the Tube to the place where I observed. Within this perpendicular Tube a a, I made another small square Tube b b, fit so as to slide upwards and downwards, as there was occasion, and by the help of a screw to be fixed in any place that was necessary: Within this Tube in a convenient cell c, was fixed the Object Glass of the Telescope (that which I made use of was thirty six foot in length, having none longer by me, but one of sixty foot, and so too long to be made use of in my Rooms) the manner of fixing which was this: The Glass itself was fixed into a cell or frame of Brass, so exactly fitted to it, that it went in stiff; and to fill up all the Interstitia's, there was melted in hard Cement; this cell had a small bar that crossed under the centre of the Glass, or the aperture thereof; in which bar were drilled two small holes at equal distance from the middle of the Glass, through which the upper ends of the two perpendiculars d d were fastened; and in the fixing this brass cell or frame into the square Tube that was to slide up and down, care was taken to make the bar lie as exactly North and South as could be, though that were not altogether so absolutely necessary to this observation. These perpendiculars d d fastened to the bar hung 36 foot and better in length, and had at the lower ends of them two balls of lead e e as big as the Silks could bear, by which the lowest parts of this Instrument were adjusted, as I shall by and by explain. But first, I must acquaint the Reader, that I opened a so perpendicularly under this Tube a hole r r a foot square in the floor below, which with shutters could be closed or opened upon occasion; by this means I had a perpendicular Well-hole of about forty foot long, from the top of a to the lower floor s s. Upon the second floor s s I fixed the frame that carried the Eye-glass and the other Apparatus fit to make this observation. I made then a Stool or Table, such as is described in the same Fourth Figure i h h i, having a hole through the top or cover thereof h h, of about nine inches over; the middle of which I placed as near as I could perpendicularly under the middle of the Object Glass in the cell above, and then nailed the frame fast to the floor by the brackets i i, that it could not stir; underneath the cover of this Table I made a slider g g, in which was fixed in a cell an eye Glass f, so as that I could through the eye Glass moved to and fro, see any part of the hole in the Table that I desired, without stirring the stool from its fixtness. This was necessary, because many Stars which were forerunners of this Star in Draco, and served as warning to prepare for the approaching Star, went pretty wide from the parallel that passed over our Zenith; by this means also I took notice of the Star itself, at above half a degree distance from the Zenith to the East, and so followed the motion of it with my eye Glass, and also with my measuring Clew, and at the same time told the Seconds beat by a Pendulum Clock, and so was very well prepared to take notice of all things necessary to complete the observation, but might have been otherwise surprised by the sudden approach and swift motion of the said Star. The measuring Instrument or Mensurator was a round thin plate or circle of Brass, delineated in the Seventh Figure, the aperture a b of which was about nine inches over, crossed in the middle by two very small hairs a b and c d, which served to show the Zenith point at e, by which the Star was to pass; there were also two other small hairs f g and i h drawn parallel to that which was to represent the East and West line, that past under our Zenith, these cut the Clue that represented the Meridian, or North and South Line at the places k and l, where the perpendicular points were made by the two long plumb lines: This Instrument was produced on the side a to n, n e being made fifteen times the length of e m, so that e m being one inch and two thirds, e n was twenty five inches: at n the line n e was crossed by a rule of about 3½ foot long o p, which from the point n was divided each way into inches and parts, each inch being subdivided into thirty parts, which served to determine, though not precisely, the Seconds on the line c d, for a minute of a degree to a thirty six foot Glass, being very near one eighth part of an inch, and this eighth part, by the help of the Diagonal, being extended to two whole inches upon the three foot Rule o p, it became very easy to divide a part of c d, which subtended a minute into sixty parts, and consequently to subdivide it into Seconds. Now though the sixtieth part of an eighth of an inch be very hardly distinguishable by the naked eye, yet by the help of looking through the Eye-glass placed in the cell, and so magnifying the Objects at the Mensurator more than sixteen times, 'tis easy enough to distinguish it. But to proceed, I had one small arm m t in the Mensurator, to which the Diagonal thread was fastened at the point m, which served for the more nice subdivisions into Seconds; The other Diagonal thread which was fastened at u, served for such observations where so great niceness was not so necessary, distinguishing only every four Seconds. The points where these Diagonal threads were fastened, were exactly over the line a b, and the distances e m and e u were an inch and two thirds, and five inches.  
There is somewhat of niceness requisite to the fixing these Diagonal threads (which is very material) at m and u, and that is that there be a small springing slit to pinch the hair fast exactly over the line a b, so that the point of its motion may be precisely in the said East and West line, and not sometimes in it, and sometimes out of it, which it is apt to be, if the Diagonal line be fixed in a hole, and move round in it.  
This was the Mensurator by which I measured the exact distance of the Stars from our Zenith: it may be also made use of for the measuring the Diameters of the Planets; for the examining the exact distances of them from any near approaching fixed Stars; for measuring the distances of the Satellites of Jupiter and Saturn from their discks, for taking the diameters and magnitudes of the spots of the Moon, and for taking the distances of approaching Stars, and for many other mensurations made by Telescopes or Microscopes, if it be so placed as to be in the focus of the Object Glass and Eye Glass. I could here describe at least thirty other sorts, some by the help of screws, others by the help of wedges, some after the way of proportional Compasses, others by wheels, others by the way of the Leaver, others by the way of Pulleys, and the like; any one of which is accurate enough to divide an inch into 100, 1000, 10000 parts if it be necessary; but I must here omit them, they being more proper in another place, and shall only name one other, because I sometimes made use of it in this observation, which is as simple and plain as this I have described, and altogether as accurate; but for some accidental circumstances in the place where I made my observation, was not altogether so convenient as the former. This Mensurator than is made thus: take a Rule of what length it seems most convenient for the present occasion, as two, three, or four foot long, represented by ab in the Eighth Figure, divide this into 100, 1000, 10000 equal parts, with what accurateness 'tis possible, between the points ab. On the top of this Rule, at each end fix two cross pieces gh and of, then from the two cross pieces of and gh, strain two very fine and even clues, as Silkworms clues, curious small hairs, or the like, so as that they cross each other at n, and be distant at o and p, an inch, or any other certain measure desired. Let this Rule, bezelled on each side, slip in a frame between two cheeks q and r, upon the top of which strain another small hair as saint. This frame must be fastened to the Telescope, so as st may lie in a due position to the Eye Glass of it. Now in the time of observation the frame qr being fastened to the Telescope as above, by sliding the Rule ab to and fro, you give upon the line st any length desired, which is noted out by the line st upon the rule; for if op be put one inch, than xy will be 494/1000 of an inch, and if op be the subtense of 10 minutes, than xy will be the subtense of ; this is so plain, simple, and easy, that as any ordinary Workman will be able to make it, so I doubt not but every Reader will, without more application, understand both the description and use thereof. I shall return therefore to the description of the former Mensurator.  
The next thing than is the way of fixing this Mensurator, so as to set the threads in their due posture, that is East and West, and North and South, and that they cut each other under the middle of the Glass. This last was that which had the most of difficulty in the whole Experiment. For the performing of this I removed the slider underneath the Table that carried the Eye Glass, and also the Mensurator, and suffered the plumb lines to hang down through the aperture of the Table, and that the Balls might come the sooner to their perpendicularity, I suffered them to hang into a vessel of water, deep and wide enough, that they might not touch either side or bottom.  
This expedient of hanging the plumbets in water I mention, because without it 'tis not to be imagined how much time is lost by expectation of the settlement of the said perpendiculars, and how very apt they are to be made to vibrate by the little imperceptible motion of the Air, and by any small hair or other impediment how apt to be put out of their perpendicularity: which by the way makes me very fearful that all common Instruments have hitherto been liable to very great errors, by the unaccurate hanging of their plumb lines, being made for the most part to hang and play against the side of the Instrument. By this means they would soon come to hang perpendicularly, and be so detained when in that posture; not being apt to be stirred by the motion of the Air, or their own swing; and whilst thus steady, I fixed two small arms of Brass, such as are described in the Seventh Figure by z z, z z, which had small holes at the extremes, with a small slit on the side to admit or emit the plumb line as there was occasion; one of these is more at large described in the Sixth Figure. Now the plumb line being let into the middle of this, I did with all the accurateness I could so fix the said arm, that the plumb line passed exactly through the middle of the hole y. When I was sufficiently satisfied that the plumb line passed exactly through the middle of the trying arms, I fixed those arms zz, zz, and removed the plumb lines, than I laid the Mensurator l l in the Fourth Figure, upon the surface of the Table, and took great care that the crosses k and l in the Seventh Figure, lay exactly under the middle of the holes in the arms, which having done by the help of certain screws, I fixed the Mensurator fast to the Table, and prepared for the observations, putting in the slider gg in the Fourth Figure, that carried the cell f, and lying down upon a Couch (k of the Fourth Figure) made purposely for this observation, I could look directly upward, and with my left hand move the Cell and Eye Glass so as to find any Star which passed within the hole of the Table, and at the same time with my right hand I could move the Diagonal thread (rm of the Seventh Figure) so as to find exactly how far distant from the Zenith e, either Northwards or Southwards, the Stars past the Meridian dc, and giving notice to my Assistant to prepare, he upon the sign given took notice exactly by a Pendulum Clock to the parts of a Second when the said Stars past, and also took notice what division the Diagonal thread m cut upon the Rule op.  
With all these difficulties I was forced to adjust the Instrument every observation I made, both before and after it was made, which hath often made me wish that I were near some great and solid Tower, or some great Rock or deep well, that so I might fix all things at once, and not be troubled continually thus to adjust the parts of the said Instrument; for whoever hath that opportunity will, I question not, especially if the lines of his Mensurator be made of the single clues of a Silkworm, with much ease discover plainly a change of the distance of Stars of the greater magnitude from the Zenith, in a much shorter time than six months. This variation also will be much more easy to be discovered, if instead of a thirty six foot Glass, there be made use of one of four times that length, to wit, one of one hundred forty four foot; and if instead of a Tower some deep and dry Well be made use of, such as I have seen at a Gentleman's house not far from Bansted Downs in Surry, which is dug through a body of chalk, and is near three hundred and sixty foot deep, and yet dry almost to the very bottom: For such a one is much less subject to any kind of alteration, either from the settling towards this or that side, which most Towers and high Buildings, whether new or old, are liable to. This also is safe from bending and shaking with the wind, which I find the strongest Houses, Towers, and Walls, if of any considerable height, are apt to do, nor would the wind have any power to swerve the perpendiculars, which 'tis almost impossible to prevent in high Buildings above ground. But this I can only wish it were performed, but cannot hope to have any opportunity of Doing it myself. But certainly the discovery of the observation will abundantly recompense those that have the curiosity to make it.  
Having thus resolved upon the way, and prepared the Instruments fit for the observation, I began to observe the Transits of the bright Star in the head of Draco; and always both before and after the observation, I adjusted the Mensurator by the Perpendiculars, that I might be the more certain of the exactness of the Instrument; for I often found that when I came to examine the Instrument, a day, or two, or three, or more, after a former observation, that there had been wrought a considerable change in the Perpendiculars, in so much as to vary above a minute from the place where I left them, which I ascribe chiefly to the warping of the Tube that rose above the roof of the House, finding sensibly that a warm day would bend it considerably towards the South, and that a moist Air would make it bend from the quarter of the wind: But yet I am apt to think there might be somewhat also of that variation ascribable to the whole Fabric of the Roof, and possibly also to some variation of the Floors; but yet I never found these variations so sudden, as to be perceptible in the time of a single observation, finding always the preceding and subsequent adjusting to answer.  
The first observation I made was the Sixth of July, 1669. when I observed the bright Star of Draco to pass the Meridian Northwards of the Zenith point of the Mensurator, at about two Minutes and twelve Seconds.  
The second observation I made was upon the Ninth of July following, when I found it to pass to the Northwards of the said Zenith or cross of the Mensurator, near about the same place, not sensibly differing.  
The third observation I made upon the Sixth of August following; then I observed its transitus North of the aforesaid Zenith, to be about two Minutes and six Seconds.  
The last observation I made upon the One and twentieth of October following, when I observed it to pass to the North of the Zenith, at one Minute and about 48 or 50 Seconds.  
Inconvenient weather and great indisposition in my health, hindered me from proceeding any further with the observation that time, which hath been no small trouble to me, having an extraordinary desire to have made other observations with much more accurateness than I was able to make these, having since found several inconveniencies in my Instruments, which I have now regulated.  
Whether this Zenith so found out upon the Mensurator, be the true Zenith of Gresham College, is not in this inquiry very material (though that also I designed to examine, had not an unhappy accident broken my Object Glass before I could complete the observation) for whether it were, or were not, it is certain that it always had the same position to the true Zenith, the Object Glass and Perpendiculars having not been in all that time removed out of the Cell, whence if the said Object Glass were thicker upon one side then upon the other (which is very common and very seldom otherwise) and consequently deflected the ray towards the thicker side, and so made the Perpendicular of the Mensurator to lie on that side of the true Perpendicular, that the thicker side of the Object Glass respected, yet it being always so if the transitus of the Star varied from this false Perpendicular, it must also vary from the true one. The manner how I designed to examine and find out the true Perpendicular, is this, which is the way also of adjusting of Telescopical sights, as I shall afterwards have occasion to show. Having marked the four sides of the Glass, the North with N, the East with E, the South with S, and the West with W, about the first of June I begin to observe and measure the true distance of some remarkable fixed Star, as of this of Draco from the Zenith found one night when the side N of the Glass stood North. Then I change the side of the Object Glass, and put the North side Southwards, and the South, Northwards, and observe the Transitus of the same Star the next night, and note down the same; the third night following I put the East side or E North, and observe the transit of the same Star over the Meridian; and the fourth night I put the West side or W North, and observe the transit of the said Star. Now by comparing all these together, it will be very easy to deduce what the false refraction of the Object Glass is, and which way it lies, and consequently to regulate the apparent Zenith by the true one. But this only by the by.  
'Tis manifest then by the observations of July the Sixth and Ninth: and that of the One and twentieth of October, that there is a sensible parallax of the Earth's Orb to the fixed Star in the head of Draco, and consequently a confirmation of the Copernican System against the Ptolomaick and Tichonick.  
Before I leave this Discourse, I must not forget to take notice of some things which are very remarkable in the last observation made upon the 21 of October. And those were these. First, that about 17 minutes after three a-clock the same day, the Sun being then a good way above the Horizon, and shining very clear into the Room where I lay to observe, and having nothing to screen off the rays of light, either in the Room where I was, or in the next Room through which I looked, I observed the bright Star in the Dragon's head to pass by the Zenith as distinctly and clearly as if the Sun had been set, though I must confess it had lost much of the glaring brightness and magnitude it was wont to have in the night, and its concomitants were vanished: The like I found it divers other days before, when I observed it, the Sun shining very clear into both the aforesaid Rooms, which by the way I suppose was the first time that the fixed Stars were seen when the Sun shined very bright, without any obscuring of its light by Eclipse or otherwise. And though we have a great tradition that the Stars may be seen with the naked eye out of a very deep Well or Mine in the day, yet I judge it impossible, and to have been a mere fiction, without any ground: For the being placed at the bottom of a Well doth not at all take away the light of the Atmosphere from affecting the eye in and near the Axis of vision, though indeed the sides thereof may much take off the lateral rays; but unless the radiation of the false rays of the Star be brighter than that of the Air, the true rays from the body are so very small, that 'tis impossible the naked eye should ever be affected by them. For in the second place, by this observation of the Star in the day time when the Sun shined, with my 36 foot Glass I found the body of the Star so very small, that it was but some few thirds in Diameter, all the spurious rays that do beard it in the night being clearly shaved away, and the naked body thereof left a very small white point.  
The smallness of this body thus discovered does very fully answer a grand objection alleged by divers of the great Anti-copernicans with great vehemency and insulting; amongst which we may reckon Ricciolus and Tacquet, who would fain make the apparent Diameters of the Stars so big, as that the body of the Star should contain the great Orb many times, which would indeed swell the Stars to a magnitude vastly bigger than the Sun, thereby hoping to make it seem so improbable, as to be rejected by all parties. But they that shall by this means examine the Diameter of the fixed Stars, will find them so very small, that according to these distances and Parallax they will not much differ in magnitude from the body of the Sun, some of them proving bigger, but others proving less; for the Diameter of the parallactical Circle among the fixed Stars, seems to exceed the Diameter of the Star almost as much as the Diameter of the annual Orb of the Earth doth that of the Sun. And possibly longer and better Telescopes will yet much diminish the apparent bulk of the Stars by bringing fewer false rays to the eye that are the occasion of the glaring and magnifying of the said bodies. It may for the present suffice to show that even with this Glass we find the Diameter of this Star considerably smaller than a Second, and the Parallax we judge may be about 27 or 30 Seconds. It will not therefore be difficult to find many Stars whose Diameters shall be less than a two hundredth part of this Parallax, as possibly upon more accurate observation this very Star may be found to be. Now we find that the Diameter of the Orb of the Earth is but two hundred times bigger than the Diameter of the Sun in the Centre thereof; and therefore if the parallactical difference be found to be two hundred times more than the visible Diameter of the Star, the Star will prove but of the same magnitude with the Sun.  
This Discovery of the possibility and facility of seeing the fixed Stars in the day time when the Sun shines, as I think it is the first instance that hath been given of this kind, so I judge it will be a discovery of great use for the perfecting Astronomy; as first, for the rectifying the true place of the Sun in the Ecliptic at any time of the year; for since by this means 'tis easy to find any Star of the first, second, or third magnitude at any time of the day, if it be above the Horizon, and not too near the body of the Sun: And since by a way I shall shortly publish any Angle to a Semicircle in the Heavens, may be taken to the exactness of a Second by one single observator: It will not be difficult for future Observators to rectify the apparent place of the Sun amongst the fixed Stars to a Second, or very near, which is one hundred times greater accurateness, then has hitherto been attained by the best Astronomers. The like use there may be made of it for observing any notable appulse of the ☽, ♃, ♄, ♂, and ♀, to any notable fixed Star that shall happen in the day time, which may serve for discovering their true places and parallaxes. The Refractions also of the Air in the day time may by this means be experimentally detected.  
I should have here described some Clocks and Time-keepers of great use, nay absolute necessity in these and many other Astronomical observations, but that I reserve them for some attempts that are hereafter to follow, about the various ways I have tried, not without good success of improving Clocks and Watches, and adapting them for various uses, as for accurating Astronomy, completing the Tables of the fixed Stars to Seconds, discovery of Longitude, regulating Navigation and Geography, detecting the proprieties and effects of motions for promoting secret and swift conveyance and correspondence, and many other considerable scrutinies of nature: And shall only for the present hint that I have in some of my foregoing observations discovered some new Motions even in the Earth itself, which perhaps were not dreamt of before, which I shall hereafter more at large describe, when further trials have more fully confirmed and completed these beginnings. At which time also I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Celestial Bodies whatsoever, have an attraction or gravitating power towards their own Centres, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Celestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that ☿ also ♀, ♂, ♄, and ♃ by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a straight line, till they are by some other effectual powers deflected and bend into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centres. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Celestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first complete, and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.   

LONDON, Printed for John Martin, Printer to the Royal Society. 1674.