Lectiones Cutlerianæ, or, A collection of lectures, physical, mechanical, geographical, & astronomical made before the Royal Society on several occasions at Gresham Colledge : to which are added divers miscellaneous discourses / by Robert Hooke ...

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 revi∣ved 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 cer∣tain manifestation either of the one or the other Doctrine. The more knowing and judicious have for many plausible reasons adhered to the Coperni∣can Hypothesis: But the generality of others, either out of ig∣norance or prejudice, have rejected it as a most extravagant o∣pinion. 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 perswade 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 do's so al∣ready. For such Persons I cannot suppose that they should under∣stand 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 prin∣ciples of Astronomy, there being already Introductions enough for that purpose: But rather to furnish the Learned with an ex∣perimentum crucis to determine between the Tychonick and Coperni∣can Hypotheses. That which hath hitherto continued the dispute hath been the plausibleness of some Arguments alledged 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 ex∣ceeding minuteness of the Globe of the Earth in comparison there∣with, who have confined their imaginations & fancies only with∣in 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 center 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 Hail-stones; and that will be martyr'd rather then grant that there may be Anti∣podes, believing it absolutely impossible, since they must necessa∣rily fall down into the Abyss below them: For how can they go with their feet towards ours, and their heads downwards, with∣out 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 uni∣formity and harmony of the Celestial bodies and motions, should be an Argument prevalent to perswade that the Earth moves a∣bout the Sun: Whereas that Hypothesis which shews 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 adhe∣red 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 fabrick of the world, which leave so deep an im∣pression 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 Ti∣chonick System, and by the Authority of their Tutors, over-awed into a belief, if not a veneration thereof: Whence for the most part such persons will not indure 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 imbrace the Copernican Arguments, as demonstration; 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 de∣monstration have we that the frame and constitution of the World is so harmonious according to our notion of its harmo∣ny, 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 Ticho 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 with∣out much art and difficulty, and taking many things for granted which are hard to be proved, that there is any body in the U∣niverse more considerable then the Earth we tread on. Is there not much reason for the Hypothesis of Ticho at least, when he with all the accurateness that he arrived to with his vast Instru∣ments

or Riccioli, who pretends much to out-strip him, were not able to find any sensible Parallax of the Earths Orb among the fixt 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 Chimera 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 it self 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 Worlds end; but there never was nor could have been any determina∣tion of the Controversie, without some positive observation for determining whether there were a Parallax or no of the Orb of the Earth; This Ticho 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 fixt Stars from the Suppellex of observations yet made either by Ticho, 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 un∣able to distinguish any angle less then a minute, and an obser∣vation requisite to determine this requiring a much greater ex∣actness then to a minute, it doth necessarily follow that this experimentum crucis was not in their power, whatever either Ticho 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 wayes of using them, we shall find that their performances thereby were far otherwise then what they would seem to make us believe. The Controversie therefore notwithstanding all that hath been said either by the one or by the other Party, remains yet undeter∣mined, Whether the Earth move above the Sun, or the Sun about the Earth; and all the Arguments alledged either on this or that side, are but probabilities at best, and admit not of a necessa∣ry 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 undenyable 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 harmoni∣ous constitution of the great bodies of the World compared one with another, as to their magnitudes, motions, and di∣stances, yet this objection was alwayes very plausible to most men, that it is affirmed by such as have written more particular∣ly of this subject, that there never was any sensible Parallax dis∣covered by the best observations of this supposed annual mo∣tion of the Earth about the Sun as its center, though moved in an Orb whose Diameter is by the greatest number of Astrono∣mers 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 thou∣sands; 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 re∣duced into miles, if we reckon with the most, amounting to 120 millions of English miles. It cannot, I confess, but seem ve∣ry 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 fixt Stars, and therefore 'twas in vain to indeavour to an∣swer that objection. For it is unreasonable to expect that the fancies of most men should be so far streined beyond their nar∣row dimensions, as to make them believe the extent of the Uni∣verse so immensly great as they must have granted it to be, sup∣posing 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 Paral∣lax 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 fail'd in disco∣vering a Parallax this way, as to my own thoughts and perswa∣sion, the almost infinite extension of the Universe had not to me seem'd 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 fixt Stars is meerly hypothetical, and not founded on any other ground or reason but fancy and suppo∣sition, and that there never was hitherto any Parallax observed, nor any other considerable Argument to prove the distances sup∣posed 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 then 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 then 'tis hitherto asserted by any Writer, when I consider the many differing magnitudes of the fixt 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 di∣stinguish what part of their appearing magnitude were to be at∣tributed to their bulk, and what to their brightness, I am apt to believe we should make another distribution of their magni∣tudes, then what is already made by Ptolomy, Ticho, Kepler, Bayer, Clavius, Grienbergerus, Piff, Hevelius and o∣thers.

For supposing all the fixt Stars as so many Suns, and each of them to have a Sphere of activity or expansion pro∣portionate 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 then those already stated: Especially since we now find by observations, that of those which are ac∣counted single Stars, divers prove a congeries of many Stars, though from their near appearing to each other, the na∣ked

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, fourty times bigger then the Copernicans now suppose it between the Sun and the fixt Stars, and consequently sixty four thousand times in bulk. And if a Telescope of double or treble the good∣ness of one of fifteen should discover double or treble the said number of magnitudes, would it not be an Argument of doubling or trebling the former Diameter, and of in∣creasing the bulk eight or twenty seven times. Especially if their apparent Diameters shall be found reciprocal to their Di∣stances (for the determination of which I did make some ob∣servations, and design to compleat with what speed I am able.) But to digress no further, This grand objection of the Anti-copernicans, which to most men seem'd 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 alwayes suspected that though some great Astronomers had as∣serted that there was no Parallax to be found by their observati∣ons, though made with great accurateness, there might yet be a possibility that they might be mistaken; which made me al∣wayes look upon it as an inquiry well worth examining: first, Whether the wayes they had already attempted were not subject and lyable to great errors and uncertainties: and secondly, Whether there might not be some other wayes found out which should be free from all the exceptions the former were incum∣bred with, and be so far advanced beyond the former in cer∣tainty 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 al∣ready been performed by those who had asserted no sensible Pa∣rallax 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 then a minute, which Kepler and Riccioli hypotheti∣cally affirm it to be: The former making it about twenty four Seconds, and the latter about ten. For though Ticho, a man of unquestionable truth in his assertions, affirm it possible to observe with large Instruments; conveniently mounted and fur∣nished 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 Se∣conds; Yet Kepler did affirm, and that justly, that 'twas im∣possible to be sure to a less Angle then 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, then they had deceived others by their mistaken observations. And this mistake I found proceeded, from divers inconveniencies their wayes of observations were lyable to. As first from the shrinking and stretching of the mate∣rials wherewith their Instruments were made, I conceive a much greater angle then 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 moyst 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 fabrick 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 then to vary a minute: Both which incon∣veniencies ought to be removed. Next the bending and warp∣ing of an Instrument by its own weight, will make a very con∣siderable alteration. And thirdly, the common way of Divisi∣on is also lyable to many inconveniencies: And 'tis hardly pos∣sible to ascertain all the subdivisions of Degrees into minutes for the whole Quadrant, though that be not altogether impos∣sible. But I will suppose that they did foresee, and in some manner prevent all these inconveniencies, especially Ticho and Riccioli, who seem to have been aware thereof. But there was

one inconvenience which was worse the all the rest, which they seem not to have been sufficiently sensible of, from whence proceeded all their own mistakes, and their imposing upon o∣thers, 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 hard∣ly possible for any unarmed eye well to distinguish any Angle much smaller then that of a minute: and where two objects are not farther distant then 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 then 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 then 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 indeavour in directing the sight to the object: but since the naked eye cannot distinguish an Angle much smaller then a minute, and very few to a whole minute, all their charge and trouble in making and managing large Instruments, and in cal∣culating and deducing from them, was as to this use in vain. Hence I judged that whatever mens eyes were in the younger age of the World, our eyes in this old age of it needed Specta∣cles; and therefore I resolved to assist my eyes with a very large and good Telescope, instead of the common sights, where∣by 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 re∣mained

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 moveable 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 look'd upon as a new thought, and somewhat extravagant, and hardly practicable, until upon hearing my explication, and the various wayes how it might be reduced into practise, it was at length judged possible, and desirable to be tryed. 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 con∣veniencies and inconveniencies in each of them; for having se∣riously 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 setled, or of some large Rock or Hill whereunto I might fix my Glasses, so as to take the exact altitude of some e∣minent 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 obser∣vation. 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 setling or swelling, &c.) I was destitute of such a con∣venience near my habitation; besides, had I had my wish, I found that 'twas lyable to an inconvenience that would wholly overthrow my whole design, which I knew not well how to a∣void: 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 Ecliptick, 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 constitu∣tion 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. Adde to this, that it would have been no easie 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 Eclip∣tick distinctly to a Second.

The like difficulties I found if observations were made of the greatest altitude of the Pole of the Ecliptick in June and De∣cember, 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 considera∣ble, and in the later intolerable.

Having therefore examined the wayes 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 cer∣tainty 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 then was to observe by the passing of some considerable Star near the Zenith of Gresham Colledge, 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 a∣mongst the fixt Stars; this must necessarily happen, especially to those fixt Stars which were nearest the Pole of the Eclip∣tick. 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 center of the Planetary Orbs, A B C D an imaginary Orb of the fixt Stars of the first magnitude, whose center for demonstration sake we will suppose the Sun. Let ♈ ♋ ♎ ♑ represent the Orb in which the Earth is s••pposed to move about the Sun, obliquely projected on the Paper. Let ♑ re∣present the Earth in Capricorn, and ♋ the Earth in Cancer, let 1 2. 1 2. represent the imaginary Axis of the Earth, keeping continually a parallelism to its self, and let ♑ AICD ♋ represent an imaginary Plain passing through the center of the Star at D in the Solstitial Colure, and the two centers of the Earth in ♑ and ♋, and C represent the Zenith point of Gresham Col∣ledge at noon, when the Earth is in Cancer, and A the Ze∣nith point of the said Colledge at midnight in the aforesaid Orb A B C D when the Earth is in Capricorn, 'tis manifest there∣fore that since the Poles of the Earth, the Poles of the Eclip∣tick, 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 alwayes its parallelism, and that the Angles made by the Perpendiculars of Gresham Colledge, with the Axes are alwayes the same, that the aforesaid Perpendiculars of the said Colledge shall be parallel also one to another, and consequently deno••e 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 there∣of: and the difference between the Angle A ♑ D, and the An∣gle C ♋ D, will give the parallactical Angle ♑ D ♋ of the Orb of the Earth to the fixt 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 it self may easily prove, if the observation be made when the Zenith passes by the Star at midnight, and at

mid-day. But the nearer the Zenith of the place of observa∣tion passeth to the Pole-point of the Ecliptick, the better; The Angle of Parallax being still the more sensible. There∣fore the best place to compleat this observation were in some place under the Polar Circles, as in Iseland, where the Ze∣nith of the place at the times abovesaid, must consequently pass at one time to the North side of the Pole of the Ecliptick, and at the other on the South side, and the Zenith of March and Sept. must pass through the very Pole-point it self. 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 Ze∣nith point of Gresham Colledge in that Plain, then 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, find∣ing the Zenith point of Gresham Colledge to pass within some very few minutes of the Star it self; 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 ascention thereof being accord∣ing 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 perpendicu∣lar. Let p represent the Pole, e the Pole of the Ecliptick, I the bright Star in the head of Draco, and let a c c c represent an imaginary Circle described by the Zenith of Gresham Col∣ledge among the fixt Stars in June, and b d d d a like Circle described by the said Zenith in December, and e f f f a like Circle described as above in March, and g h h h 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 Ecliptick, to wit, in the head of the Constellation Draco, shall be to the true di∣stances of the said Zeniths in that part which is furthest from the said Pole, to wit, near the constellation of Auriga in conse∣quentia, 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 Colledge, to the Angle of Parallax in Iseland, or any other place under the Pole of the Ecliptick, or Artick Circle is, as the sign of seventy five to the sign of ninety or the Radi∣us.

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 Colledge in Draco: and LA, MB the perpendiculars of the same place to the Solstitial Colure near Auriga, the several di∣stances 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 tran∣sits of our Zenith from any other Star as well as from this of Draco, and the same Phenomena might have been observed, ta∣king 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 mid-day; 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 Colledge hath latitude. The principal dayes of do∣ing which will be about the 4 of April, when our Zenith pas∣seth by the said Star at midnight, and the 7 of October, when it passeth by it at noon or mid-day: the reason of all which will be sufficiently manifest to any one that shall well consider the preceeding explanation.

This Star I would the rather observe, because as it is pla∣ced so as that the Parallax thereof will be almost as great as of the Pole of the Ecliptick in Iseland, or under the Artick Circle, so it being a Star of the second magnitude, and con∣sequently perhaps as near again as one of the fourth, the An∣gle of Parallax will be near about twice as big, and the Star it self much more easie to be seen in the day time. This will be very easie to be understood, if we consider in the first Scheme the differing distances of the Orb A B C D, in which we may suppose the Stars of the second magnitude to be fixt, and of the Orb α β κ δ, in which we may suppose the Stars of the fourth magnitude, and a b c d in which we may suppose those of the third magnitude, and A B C D 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 easie to any one that shall consider that hereby, first, I avoid that grand inconvenience wherewith all ancient and modern observations have been perplext, 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 cer∣tainly much greater at one time then another, and never at any certainty; and secondly, 'Tis nor equally proportionable, for sometimes the refraction is greater at some distance above the Horizon, then in or nearer to the Horizon it self, and some∣times the quite contrary, which I have very often observed; and this to so exorbitant a difference, as to confound all Hy∣pothetical Calculations of Tables for this purpose. This a∣riseth 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 be∣ing 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 perplext, 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 uncer∣tain 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 Rayes above the Horizon; I will with ease make out all the visible Pheno∣mena of the Universe, Sun, Moon, and Stars, and yet not sup∣pose 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 cold∣er, 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 streight passage. In the next place, by this way of observing I avoid all the difficulties that attend the ma∣king, mounting, and managing of great Instruments: For I

have no need of Quadrant, Sextant, or Octant, nor of any o∣ther part or Circle bigger then 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 wayes or other lyable. And notwith∣standing the vast care and expence of the noble Ticho 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 irregulari∣ties. Nay, notwithstanding the seemingly much greater curio∣sity and expense of Hevelius, and his infinite labour and di∣ligence in the compleating and using of his vast Apparatus of Astronomical Instruments, I do not find them so well secured, but that some of the causes of erros that I have before men∣tioned, may have had a considerable effect upon them also; e∣specially 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 Ticho 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 uncertain∣ties, What shall we say of all that other farrage of trumpery that hath been made use of by most others? We see there∣fore the necessity of the conjunction of Physical and Philoso∣phical 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 ra∣tional grounds it was that Sir John Cutler, the Patron and Founder of this Lecture, proceeded in joyning the contempla∣tion of them both together.

The next thing was the Instrument for the making of this observations, such a one as should not be lyable to any of the former exceptions, nor any other new ones that were consi∣de••able. 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 a∣ble certainly to observe the transits of any Stars over or near

the Zenith, and furnishing it with perpendiculars and a con∣venient 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 Center or Zenith point of Gresham Colledge, 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 rea∣dy and better inabled to proceed with the same.

First then (finding a Tube would be very troublesome to the Rooms through which it past, 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 fixt 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 hindring, 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 there in fixt 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 n o p, which came down through the Tube to the place where I ob∣served. Within this perpendicular Tube a a, I made ano∣ther small square Tube b b, fit so as to slide upwards and down∣wards, as there was occasion, and by the help of a skrew to be fixt in any place that was necessary: Within this Tube in a con∣venient cell c, was fixt 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 it self 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 Inter∣stitia's, there was melted in hard Cement; this cell had a

small barr that crossed under the center of the Glass, or the a∣perture thereof; in which barr were drill'd two small holes at equal distance from the middle of the Glass, through which the upper ends of the two perpendiculars d d were fastned; 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 barr lye as exactly North and South as could be, though that were not altogether so absolutely necessary to this observation. These perpendiculars d d fastned to the barr 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 perpen∣dicularly under this Tube a hole r r a foot square in the floor below, which with shutters could be closed or opened up∣on 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; under∣neath 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 it self, 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 compleat the observation, but might have been otherwise sur∣prised

by the suddain 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 shew 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 Me∣ridian, 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 crost 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 easie to divide a part of c d, which subtended a minute into sixty parts, and conse∣quently to subdivide it into Seconds. Now though the sixti∣eth 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 then sixteen times, 'tis easie enough to distin∣guish it. But to proceed, I had one small arm m t in the Men∣surator, to which the Diagonal thred was fastned at the point m, which served for the more nice subdivisions into Seconds; The other Diagonal thred which was fastned at u, served for such observations where so great niceness was not so necessary, distinguishing only every four Seconds. The points where these Diagonal threds were fastned, 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 ex∣actly 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 Diago∣nal line be fixt in a hole, and move round in it.

This was the Mensurator by which I measured the exact di∣stance 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 fixt Stars; for measuring the distances of the Satellites of Jupiter and Sa∣turn from their discks, for taking the diameters and magnitudes of the spots of the Moon, and for taking the distances of ap∣proaching Stars, and for many other mensurations made by Te∣lescopes or Microscopes, if it be so placed as to be in the fo∣cus 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 Com∣passes, others by wheels, others by the way of the Leaver, others by the way of Pullies, and the like; any one of which is accu∣rate 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 sim∣ple and plain as this I have described, and altogether as accu∣rate; but for some accidental circumstances in the place where I made my observation, was not altogether so convenient as the former. This Mensurator then 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 a b in the Eighth Figure, divide this into 100, 1000, 10000 equal parts, with what accurateness 'tis possible, between the points a b. On the top of this Rule, at each end fix two cross pieces g h and e f, then from the two cross pieces e f and g h, 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 desi∣red. Let this Rule, bezelled on each side, slip in a frame be∣tween two cheeks q and r, upon the top of which strein ano∣ther small hair as s t. This frame must be fastned to the Te∣lescope,

so as s t may lye in a due position to the Eye Glass of it. Now in the time of observation the frame q r being fast∣ned to the Telescope as above, by sliding the Rule a b to and fro, you give upon the line s t any length desired, which is noted out by the line s t upon the rule; for if o p be put one inch, then x y will be 494/1000 of an inch, and if o p be the subtense of 10 minutes, then x y will be the subtense of 4/94; this is so plain, simple, and easie, that as any ordi∣nary Workman will be able to make it, so I doubt not but e∣very 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 then 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 dif∣ficulty 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 perpendicu∣lars, 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 perpen∣dicularity: which by the way makes me very fearful that all common Instruments have hitherto been lyable 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 per∣pendicularly, 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 Bras, such as are described in the Seventh Figure by z z, z z, which had small holes at the extreams, 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 accurate∣ness I could so fix the said arm, that the plumb line past exact∣ly through the middle of the hole y. When I was sufficiently sa∣tisfied that the plumb line past exactly through the middle of the trying arms, I fixed those arms zz, zz, and removed the plumb lines, then I laid the Mensurator l l in the Fourth Fi∣gure, 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 fixt the Mensurator fast to the Table, and prepared for the observations, putting in the slider g g in the Fourth Figure, that carried the cell f, and lying down upon a Counch (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 (r m 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 d c, 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 r cut upon the Rule o p.

With all these difficulties I was forced to adjust the In∣strument 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 continu∣ally thus to adjust the parts of the said Instrument; for who∣ever hath that opportunity will, I question not, especially if the lines of his Mensurator be made of the single clues of a Silk∣worm, with much ease discover plainly a change of the distance of Stars of the greater magnitude from the Zenith, in a much shorter time then six moneths. This variation also will be much more easie 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 fourty four foot; and if instead of a Tower some deep and dry Well be made use of, such as I have seen at a Gentlemans house not far from Bansted Downs in Surry, which is dugg 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 lyable 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 a∣bove ground. But this I can only wish it were perfo••••ed, but cannot hope to have any opportunity of Doing it my self. 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 In∣struments sit for the observation, I began to observe the Tran∣sits of the bright Star in the head of Draco; and alwayes 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 Fabrick of the Roof, and possibly also to some variation of the Floors; but yet I never f••und these variations so sudden, as to be perceptible in the time of a single observation, finding alwayes the preceding and subsequent adjustings 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 fol∣lowing; 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, hindred 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 then 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 Colledge, 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 com∣pleat the observation) for whether it were, or were not, it is certain that it alwayes 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 seldome otherwise) and consequently defle∣cted the ray towards the thicker side, and so made the Perpendi∣cular of the Mensurator to lye on that side of the true Perpen∣dicular, that the thicker side of the Object Glass respected, yet it being alwayes 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 Perpen∣dicular, is this, which is the way also of adjusting of Telescopi∣cal sights, as I shall afterwards have occasion to shew. 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 fixt 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 South∣wards, 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 easie to deduce what the false refraction of the Object Glass is, and which way it lyes, and consequently to regulate the ap∣parent 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 Earths Orb to the fixt Star in the head of Draco, and consequently a confirmation of the Copernican Sy∣stem 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 rayes 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 Dragons head to pass by the Zenith as distinctly and clear∣ly 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 vanisht: The like I found it divers other dayes before, when I observed it, the Sun shining very cleer into both the aforesaid Rooms, which by the way I suppose was the first time that the fixt Stars were seen when the Sun shin'd very bright, without any obscuring of its light by E∣clipse 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 meer fiction, without any ground: For the being placed at the bot∣tom of a Well doth not at all take away the light of the Atmo∣sphere from affecting the eye in and near the Axis of vision, though

indeed the sides thereof may much take off the lateral rayes; but unless the radiation of the false rayes of the Star be brighter then that of the Air, the true rayes 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 rayes that do beard it in the night being cleerly shaved away, and the naked body thereof left a very small white point.

The smalness of this body thus discovered does very fully answer a grand objection alledged 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 then the Sun, thereby hoping to make it seem so impro∣bable, as to be rejected by all parties. But they that shall by this means examine the Diameter of the fixt 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 fixt 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 dimi∣nish the apparent bulk of the Stars by bringing fewer false rayes to the eye that are the occasion of the glaring and magnifying of the said bodies. It may for the present suffice to shew that even with this Glass we find the Diameter of this Star considerably smaller then 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 then 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 then the Diameter of the Sun in the Center thereof; and therefore if the parallactical difference be found to be two hundred times more then 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 fixt 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 Ecliptick at any time of the year; for since by this means 'tis easie 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 fu∣ture Observators to rectifie the apparent place of the Sun a∣mongst the fixt Stars to a Second, or very near, which is one hundred times greater accurateness, then has hitherto been at∣tained by the best Astronomers. The like use there may be made of it for observing any notable appulse of the ☽, ♃, ♄, ♂, and ♀, to any notable fixt 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 A∣stronomical observations, but that I reserve them for some at∣tempts that are hereafter to follow, about the various wayes I have tryed, not without good success of improving Clocks and Watches, and adapting them for various uses, as for accurating Astronomy, compleating the Tables of the fixt 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 o∣ther 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 it self, which perhaps were not dreamt of before, which I shall hereafter more at large describe, when further tryals have more fully confirmed and compleated these beginings. 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 Mecha∣nical Motions: This depends upon three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gra∣vitating

power towards their own Centers, 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 Coelestial 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 mo∣tions also. The second supposition is this, That all bodies what∣soever that are put into a direct and simple motion, will so con∣tinue to move forward in a streight line, till they are by some o∣ther effectual powers deflected and bent into a Motion, descri∣bing 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 Centers. Now what these several degrees are I have not yet experimentally ve∣rified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Coe∣lestial 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 directi∣on in Nature for the true stating thereof. This I only hint at pre∣sent 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 my self many other things in hand which I would first compleat, 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 understand∣ing thereof will be the true perfection of Astronomy.