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 [Page 2]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 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 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 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 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 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 perswade that the Earth moves a­bout the Sun: Whereas that Hypothesis which shews how to [Page 3]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 fabrick 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, 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 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 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 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 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 Instru­ments [Page 4]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 determina­tion 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 un­able to distinguish any angle less then 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 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 undeter­mined, 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 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 [Page 5]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 harmoni­ous constitution of the great bodies of the World compared one with another, as to their magnitudes, motions, and di­stances, yet this objection was alwayes 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 center, 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 fixt Stars, and therefore 'twas in vain to indeavour to an­swer that objection. For it is unreasonable to expect that the fancies of most men should be so far streined 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 [Page 6]produced against it. Though yet I confess had I fail'd in disco­vering a Parallax this way, as to my own thoughts and perswa­sion, 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 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 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 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, then what is already made by Ptolomy, Ticho, Kepler, Bayer, Clavius, Grienbergerus, Piff, Hevelius and o­thers.

For supposing all the fixt 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 then 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 [Page 7]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 good­ness 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 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 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 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 al­wayes 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 incum­bred 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 [Page 8]there were any or no Parallax of this annual Orb; especially if it were less then 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 Ticho, 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 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 mate­rials 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 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 lyable 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 Ticho and Riccioli, who seem to have been aware thereof. But there was [Page 9]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 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 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 cal­culating 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 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 [Page 10]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 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 setled, 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 setling or swelling, &c.) I was destitute of such a con­venience 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 a­void: Namely, to that which hath hitherto made even the very [Page 11]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 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. 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 Eclip­tick 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 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 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 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 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 a­mongst the fixt Stars; this must necessarily happen, especially to those fixt Stars which were nearest the Pole of the Eclip­tick. And that this is so, any one may plainly perceive if he [Page 12]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 ♑ re­present 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 Col­ledge at noon, when the Earth is in Cancer, and A the Ze­nith point of the said Colledge at midnight in the aforesaid Orb A B C D when the Earth is in Capricorn, 'tis manifest there­fore that since the Poles of the Earth, the Poles of the Eclip­tick, 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 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 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 [Page 13]mid-day. But the nearer the Zenith of the place of observa­tion passeth to the Pole-point of the Ecliptick, the better; The Angle of Parallax being still the more sensible. There­fore the best place to compleat 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 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 Ze­nith 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, find­ing 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 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 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 Col­ledge 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 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 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 Radi­us. [Page 14]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 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 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 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 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 pla­ced 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 con­sequently perhaps as near again as one of the fourth, the An­gle 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 [Page 15]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 cer­tainly 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 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 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 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 Rayes 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 streight 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 [Page 16]have no need of Quadrant, Sextant, or Octant, nor of any o­ther 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 notwith­standing 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 irregulari­ties. Nay, notwithstanding the seemingly much greater curio­sity and expense of Hevelius, and his infinite labour and di­ligence 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 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 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 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 joyning the contempla­tion 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 consi­de [...]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 a­ble certainly to observe the transits of any Stars over or near [Page 17]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 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 rea­dy 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 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 skrew to be fixt in any place that was necessary: Within this Tube in a con­venient 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 Inter­stitia's, there was melted in hard Cement; this cell had a [Page 18]small barr that crossed under the center of the Glass, or the a­perture 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 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 Eye­glass 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 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 sur­prised [Page 19]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 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 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 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 Eye­glass placed in the cell, and so magnifying the Objects at the Mensurator more then sixteen times, 'tis easie enough to distin­guish it. But to proceed, I had one small arm m t in the Men­surator, 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 [Page 20]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 fixt 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 fixt 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 Pullies, 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 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 desi­red. Let this Rule, bezelled on each side, slip in a frame be­tween two cheeks q and r, upon the top of which strein ano­ther small hair as s t. This frame must be fastned to the Te­lescope, [Page 21]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 fast­ned 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 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 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 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 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 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 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 [Page 22]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 past exact­ly through the middle of the hole y. When I was sufficiently sa­tisfied 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 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 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 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 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 [Page 23]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 a­bove 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 In­struments sit for the observation, I began to observe the Tran­sits 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 [Page 24]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, 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 com­pleat 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 defle­cted the ray towards the thicker side, and so made the Perpendi­cular of the Mensurator to lye on that side of the true Perpen­dicular, 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 Perpen­dicular, is this, which is the way also of adjusting of Telescopi­cal 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 [Page 25]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 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 easie to deduce what the false refraction of the Object Glass is, and which way it lyes, 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 Earths Orb to the fixt 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 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 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 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 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 meer 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 [Page 26]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 impro­bable, 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 dimi­nish 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 fu­ture Observators to rectifie the apparent place of the Sun a­mongst the fixt 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 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 A­stronomical observations, but that I reserve them for some at­tempts 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 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 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 Mecha­nical Motions: This depends upon three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gra­vitating [Page 28]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 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 streight line, till they are by some o­ther effectual powers deflected and bent 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 Centers. 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 Coe­lestial 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 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 understand­ing thereof will be the true perfection of Astronomy.

SOME ANIMADVERSIONS On the first Part of HEVELIƲS His MACHINA COELESTIS, &c.

HAVING lately perused a Discourse of Hevelius, newly published, entituled, Johannis Hevelii Machina Coelestis, pars prior Organographiam sive instrumento­rum Astronomicorum omnium quibus Autor hactenus sidera rimatus & dimensus est accuratam delineationem & descrip­tionem plurimis Iconibus aeri incisis illustratam & exornatam ex­hibens, &c. and finding it a Discourse about practical and mechanical Knowledge, and of that kind wherein Geometry seems to be more then ordinarily concerned; I thought it might not be ungrateful to my Auditory, (nor improper to the Subject of Sr. JOHN CUTLER's Lecture, which is partly Mecha­nical and partly Physical) to consider a little the Contents there­of: And somewhat the rather too, because having heretofore communicated to him somewhat of this Subject, which I had oc­casion to read in this place in one of my former CUTLERIAN Lectures, I find he hath made some Animadversions and re­flections thereupon.

I find then that this excellent Person hath been for the most part exceedingly circumspect, to find out the inconveniences and difficulties that do accrew to the best Observators, even with the best instruments, and has not been less industrious to find out ways to obviate and overcome them; In the doing of which, he seems not to have spared either for labour and vigi­lancy, or for any cost and charges that might effect his pur­pose, for which he hath highly merited the esteem of all such as are lovers of that Science: But yet if he had prosecuted that way of improving Astronomical instruments, which I long since communicated to him, I am of opinion he would have done himself and the learned World a much greater piece of service, by saving himself more then 1/10 of the charge and trouble, and by publishing a Catalogue ten times more accurate. For though I doubt not in the least but that he hath by his own extraor­dinary diligence, care and cost, corrected several mistakes and errors committed by the assistants of the Noble Ticho: yet I am not satisfied that his Instruments are capable of making Ob­servations more accurately then those of Ticho, though 'tis pos­sible they may do it with somewhat less trouble and inconveni­ence. For first, I find that those of Ticho were as large as those of Hevelius, and consequently were capable of as accu­rate and minute divisions, and of as long and convenient Sights. Secondly, I find that the Sights made use of by Hevelius are the very same, at least not at all materially differing from those of Ticho, being only naked Sights, made by a slit and edge, serving only to regulate the direction of the naked eye, but no ways capable of assisting the eye to distinguish more accurately the object. Thirdly, I find that though the way of Division made use of by Hevelius, be a very ingenious invention, and that which is Geometrically true and certain, yet if we consider the great difficulty there is in Mechanically perform­ing it, we shall find it not much preferrable, if altogether as good as that of Ticho. And 'tis plain enough that Ticho him­self was not ignorant of it, though his particular reasons why he made no more use of it, we certainly know not: 'Tis very probable, because he thought it not altogether so accurate, as that he did make use of. For somewhat to this purpose he says himself, in the second Book of his Observations of the Comet of [Page 3]1577. pag. 461. Hanc graduum in singula minuta, meaning the Division by Diagonal Lines; & etiam horum in dena scrupula secunda subdivisionem in omnibus meis machinis Astronomicis usur­po, eo quod illam multis ab hinc annis exquisitissimam expertus sum. Licet enim ejus demonstratio in Rectilineis parallelogrammis pro­priè conveniat, nihilominus arcualibus etiam in tam exili intersti­tio quod à recta linea insensibiliter differt, citra omne erroris ve­stigium convenienter applicatur. 'Tis true, Ticho's Objection against this way of Division by Diagonals is material, as to a Ge­ometrical accurateness, but his Answer to it is altogether as material, that though it be not exactly true, yet it doth insensi­biliter differre, and so long as the error is not discovered by sense, there can be no error committed in observation; and indeed the whole matter both one way and the other is insigni­ficant, and but a vain curiosity to endeavour to divide an in­strument into seconds, or parts smaller then a minute, for I shall by and by shew that the eye can hardly distinguish minutes in the object: But were such niceness of Division of any use, 'tis easily enough to be done to Mathematical truth; for as I shall anon shew, there is a certain distance of each of the parallel Circles, which being given, the straight Diagonal Lines will divide the degree, by the intersection with those parallel Cir­cles, into exactly equal parts, which would have better an­swer'd Ticho's Objection, had he known it, which I wonder, I confess, how he could over-see, since he seems to have spent many thoughts on the matter; but this only by the By, because I shall speak more at large of it afterwards. But he proceeds to this other way of Divisions, which he, as well as Hevelius, ascribes to Nonnius, whereas the other that he approves of came first from England, as it appears by a passage in another Book of his, where he discourses somewhat of the same Subject.

Altera Divisio ad clarissimi Mathematici Petri Nonnii in Li­bello de crepusculis propositione tertia imitationem per plures qua­drantis arcus introrsum descriptos, & diversimodè subdivisos pro­cedit; etsi autem in hac ipsa apprime ingeniosa Nonnii inventione aliquid Auctuarii loco expeditius à nobis additum est, ita ut exte­rior arcus in plurimas partiunculas dividatur, ne (que) is ordo aut nu­merus arcuum sese introrsum concomitantium quem ille praesinivit [Page 4]sed multo expeditior & perfectior observetur; (I am apt to think he knew this very way, and here hints it:) Tamen quia haec sub­tilitas cum ad praxin deventum est plus habeat laboris quam fru­ctûs, neque id in recessu praestet quod prima fronte pollicetur, ut ali­bi plenius ostendemus, idcirco apud nos dudum in usu esse desiit. From which words, and also from what he says in his first Book of the new Star in 1572. pag 671, speaking of the com­parison between these two ways of Divisions, to wit, Sit cu­juscun (que) velit ingeniosa certe & apprime utilis est distributio, quam & ego postea arcualibus graduum divisionibus in quadrantibus sex­tantibus & armillis, non inconcinnè aut infrugiferè applicui. Li­cet enim demonstratio ejus in solis rectilineis superficiebus ad unguem se habeat; tamen cum quinorum vel denorum minutorum spatium in circumferentiis majusculis à rectilineo insensibiliter differat, hic quo (que) ejus usus satis commodus & ratus esse poterit, multo (que) Nonniana plurimorum arcuum intricata & difficili subdivisione ex­peditior aptior (que) deprehenditur. From his Discourse I say in these two places, and from several others dispers'd up and down his Works, which 'twould be too long now to quote, 'tis evident that Ticho was not ignorant of this way of Sub-divi­sion, so much applauded by Hevelius, invented by Petrus Nonnius, and promoted by Ticho himself; and yet we see he prefer'd that way of Diagonals, first made use of in England by the most skilful Mathematician Richard Cantzler, before it, re­jecting the one and making use of the other in all his Instru­ments. But either of them will do well enough if the Divisi­ons be done with great circumspection and care, and instru­ments of the size of those larger ones both of Hevelius and Ti­cho, are capable of Divisions ten times more accurate then are needful for common Sights, be they never so long, without making use of either Ticho's or Hevelius's way of Division, the eye being unable to distinguish a smaller Angle. To what purpose therefore is it to make the Divisions so fine, or any one part of the instrument or observation more accurate then another? since the power of distinguishing by the naked eye is that which bounds and limits all the other niceness, and what­ever part is more curious then that can equalize, is of no signi­ficancy. For instance, in taking the altitude of a Star, it would be but labour lost to distinguish by the Diagonals, or [Page 5]otherwise to Seconds, whilst in the mean time you are not cer­tain that the Plumb-line is true to a minute, or whilst you are not able to direct the Ruler, bearing the Sights to a greater cer­tainty then to that of a minute. And the like might be said of the extraordinary curiosity in any two parts, and the failure in any third, that is essential to an observation; as fruitless it is to calculate to seconds, when the observations are not true to minutes, or to be certain by the Sights and Divisions to se­conds, and uncertain in the Plumb-line to minutes.

There is therefore one thing in Hevelius his Instruments, that though they be never so large, never so accurately divi­ded, of never so choice and convenient materials, and never so tractable for use, and never so skilfully and industriously used, will notwithstanding make them all equal as to use, with one of about two or three foot radius of mettal with Ticho's Sights and Diagonal Divisions, which is occasioned by the limited power of distinguishing by the naked eye.

Something to this purpose I communicated to Hevelius in the year 65. and hoped that I might have thereby somewhat as­sisted him in his great and laborious Work, first by easing the eye, and next by making it capable of distinguishing more ex­actly, I having hinted to him the way how to reform and obvi­ate that inconvenience by Telescopical or Perspective Sights, as also the way of making instruments of much less bulk, to do ten times more then 'twas possible to do with the largest instru­ments made the common way. In answer to which he returns me this Discourse, in a Letter to the Royal Society, in the year 65.

MODUS ille observandi per Telescopia adminiculo Sex­tantis vel Quadrantis, videtur mihi vix adeò tutus, quam vulgaris, si pinnacidia rectè ac justè sint affixa. Haec enim sunt immobilia; Telescopia verò nullâ ratione adeò firmiter affigi possunt ut loco haud dimoveantur; etiamsi omni diligentiâ juxta methodum descriptum per totum Horizontem experiundo sint semel collocata. Adhuc quam arduum sit, eâ ratione-verum eorum locum indagare, satis super (que) expertus sum; sicut vix videam, an alicui [Page 6]circa restitutionem Fixarum Planetarum (que) adminiculo esse possint; in majoribus scilicet illis distantiis capiendis: In minoribus, largi­or, posse aliquid praestari; sed an Instrumenta, unius Spithamae radio instructa, elaborari possint multò exactius, quàm optima quoe­vis, vulgares Dioptras habentia, licet 60 pedum radio elaborata, nollem adhuc asseverare. Multa nam (que) in Theoriâ videntur cer­tissima, quae in praxi satis longe nonnumquam à vero recedunt. Si quis mihi certas observationes quarundam distantiarum & qui­dem Fixarum, circa Eclipticam & Aequatorem existentium, il­lis ipsis Instrumentis, Dioptris Telescopicis instructis habitas ex­hiberet: (utpote distantiam Lucidae ♈ à Palilicio; Palilicii à Pol­luce; Pollucis à Regulo; Reguli à Spicâ ♍ Spicae♍ à Boreal. sinist. manus Serpentarii; Boreal sinist. manus Serpentarii ab A­quilâ Aquila à Marcab; & Marcab à Lucidâ Arietis) vellem protinus de rei illius certitadine & meum quale quale judicium fer­re; sed antequam eas observationes obtineam, judicium suspendo. Interea utiq fateor; si quis adminiculo minoris cujusdam Instru­menti observationes corporum Coelestium peragere potest, multò sane illum esse feliciorem, variis de causis, eo, qui per majora id prae­stare allaborat. Rationes dividendi Instrumenta, diversae quidem mihi probè cognitae sunt; eas (que) etiam in usum transtuli; num autem sint eaedem quas Clarissimus Dominus Hookius novit, ac invenit, me prorsus latet: Si illi non adversum est, rogo, ut prae­cipuas communicet, ego ut meas intelligat rursùs studebo.

Since which time I have not sent any other description of instruments, save that of the manner of making and using a Tube for a 60 foot Glass, which I am much pleas'd to find he makes use of, and should gladly have communicated any thing fur­ther, if I had not found they were esteemed insignificant. It did much trouble me, I confess, that I could not prevail with him to make use of Telescopical Sights at least, since with less trouble he would have afforded the World Observations, and a Catalogue of the Stars, ten times more exact. And I am the more sorry to find that he hath proceeded to finish his Machina Coelestis, by instruments not more accurate then those of Ticho, and that he still remains in the same opinion of Telescopical Sights, and other improvements of instruments. For pag. 293. of this first Part of his Machina Coelestis, speaking concerning [Page 7]Sights, he says, Possibly some may wonder that I do not make use of Telescopical Sights, since they are by some accounted better and more accurate, insomuch that there is one in the World hath proceeded so far, as to suppose Telescopical Sights to be ten, twenty, thirty, nay forty times more accurate then the common Sights; and that 'tis possible to make an in­strument of a Span Radius to do more with Telescopical Sights, then an instrument of 60 foot with the common Sights. 'Twould be a thing of much moment could it be done, and not to be valued by money, but many things do seem true in the Theory, which do not answer upon Experience. You may perceive by comparing this slender Refutation with his Letter before, who he means by the Assertor of Telescopical Sights. But I am troubled he should think them so slight as not to deserve one tryal in seven years time, especially since by explaining the manner of making use of them much in the same sense with that which I sent him, he seems to have un­derstood enough of the way to have made use of it if he would. As to his Objection, That the Glasses are apt to be broke, and the Pins or Threads are apt to be bent and broke, there is not the least colour for it, for they cannot without much labour and design be broken or put out of order, but if they were, it might as well be said, that the Plumb-line of any of his instru­ments may be broken, or his Sights bended, and the like, and therefore those instruments, were not to be used. But these Objections I shall not urge against his instruments, nor a great many other I could produce of lesser moment, but only this one which is very fundamental, and cannot any ways be helped but by the help of Glasses, and that is, 'Tis impossible with Sights made after Ticho's or Hevelius his way, to distinguish any distance in the Heavens less then half a minute, or thirty Seconds, and hardly one of a hundred can distinguish a minute.

And this being proved, what will become of all the machi­nations and contrivances for greater instruments, to shew the Divisions of single or double Seconds? May not single minutes, nay half minutes, by the help of Diagonal Divisions, be suffi­ciently di [...]tinguished in an instrument of three foot Radius? What need is there then of all the other cumber? Certainly any one that will but try with the one and the other instrument, [Page 8]will find himself able to do as much with an instrument of three foot, as with one of threescore, since the eye cannot distinguish a less Angle, at least none that I have yet met with hitherto. Who is there that by his bare eye can distinguish any of the Te­lescopical spots in the Moon, though some of them are above a minute in Diameter? As for instance, Who can see Mount Si­nai, so call'd by Hevelius, which is a bright spot in a dark field, and consequently must appear near two minutes in Dia­meter to the naked eye? Or who can see the Palus Mareotis, or the Lacus niger, which are two dark spots in light fields, and each more then a minute in Diameter? Now if the eye cannot distinguish a smaller object then appears within the angle of half a minute, 'tis not possible to make any observation more accurate, be the instrument never so large.

Now that any one may presently satisfie himself of the truth of the I assert, concerning the limited power of the naked eye, as to the distinguishing of Angles; Let him take a sheet of white Paper, and thereon draw two parallel Lines, as O O, and P P, in the 28th. Figure, at four of five inches distance, then draw as many other small lines between them at right angles to them, and parallel one with another, as he thinks convenient, as aa, bb, cc, dd, ee, ff, gg, hh, ii, &c. and let them be drawn distant from each other an inch, then let him al­ternately blacken or shadow the spaces between them, as be­tween aa and bb, between cc and dd, between ee and ff, between gg and hh, between ii and kk, between ll and mm, &c. leaving the other alternately white, then let him expose this Paper against a Wall open to the light, and if it may be so that the Sun may shine on it, and removing himself backwards for the space of 287 ⅓ feet, let him try whether he can distinguish it, and number the dark and light spaces, and if his eyes be so good that he can, then let him still go further backwards and backwards from the same, till he finds his eyes unable any longer to distinguish those Divisions, there let him make a stand, and measure the distance from his eye to the a­foresaid Paper, and try by calculation under what Angle each of those black and while spaces appears to his eye, for by that means it will be manifest how small an Angle his eye is capable of distinguishing, and beyond which it cannot reach: Which [Page 9]being once known, he hath a Standard, by which he is able to limit the bigness and exactness of his Instruments, if he make use of common Sights, beyond which all magnitude and curi­osity is not only useless, but of much detriment upon many accounts.

This is that Consideration which I could wish had occur'd both to Ticho Brahe and to Hevelius, especially to the latter, who hath so earnestly endeavour'd to out-do the former, and for the accomplishment thereof, seems to have spared no charge, labour, or endeavour he was able to expend. I hope at least that this publick notice will for the future engage all such as shall attempt this Work, to be as sollicitous about as­sisting the Eye in the discovery of the parts of the Object, as of distinguishing the Divisions of the Instrument, for the doing of the one without being able to reach the other, will avail nothing.

Those therefore that desire or need Instruments to make Ob­servations to Seconds, must take another course then any that I know yet described. 'Tis true indeed, That Altitudes of the Sun may be taken, with the Sights commonly used for that pur­pose, to what accurateness is desired, if the Instrument be large enough, because the Image of the Sun being transmitted by the upper Sight through a small round hole, is represented within a Circle upon the lower Sight, and by means of the eyes ap­proaching near that Sight, 'tis possible by Instruments large enough, to arrive at the accurateness of a Second, in Observa­tions made of that kind. And somewhat of this may be done also by the Moon, when very bright and clear, but in all the other celestial Bodies it has never yet been done.

But then if we compare even this way with that of Teles­copes, caeteris paribus, we shall find it much short, both as to clearness and distinctness, and therefore even here also Teles­copical Sights are to be preferred, as I shall sufficiently mani­fest hereafter more at large, when I come to describe my own Instruments for this purpose; for I doubt not but to make it sufficiently plain, That by the help of an Instrument I have contrived, of three foot Radius, I will be able to make all Observations whatsoever, ten times more accurate, excepting those of the Sun, then any one can make with the largest In­strument, [Page 10]described either by Ticho or Hevelius, and to ma­nage the same with a quarter the trouble, clutter, and Appara­tus necessary to either of theirs, and to make the Divisions as accurate and sensible as can be desired.

For the doing of which, I will shew, First, How to make the Plain of the Instrument, that it shall not be subject to bend­ing or warping, and yet be so light as to be easily manageable. Secondly, How to make the Divisions on that Instrument, so as to distinguish certainly and exactly to Seconds, without any trouble, or wearying the sight. Thirdly, I will shew how to make the Sights of that Instrument, so as to distinguish the parts of the Object to Seconds, if need be, even by those who cannot distinguish to Minutes with common Sights, certainly, and without fallacy or error. Fourthly, How to make the Sights, so as to see two Objects, though never so far distant, with one glance of the eye. And Fifthly, I will shew how to adjust the Perpendicular, so as to set it exactly upright and plain to a Second, so that if it meets with a diligent, accurate, and experienced Observator, it will serve to make as curious Observations as are hitherto desirable. Sixthly, I will shew a way how to fix this Instrument, either for taking Altitudes or Azimiths, so as to be manageable with the least trouble imagi­nable, for Observations of that kind, and to be always steady and fixt in any Perpendicular posture, to whatever Azimith it be apply'd. Seventhly, I will explain an exact way for fixing the Instrument, so as to take the Distances of any two Stars, or celestial Object, and several other contrivances of the like nature. But of each of these hereafter, after I have examin'd over the several particulars mention'd by Hevelius, in his De­scriptions of the Instruments and Contrivances made use of by himself.

To pass by then his long Preface, and the Discourse of In­struments in general, which he hath premised in the first Chap­ter; I shall proceed to an examination of those Instruments of his own, which he doth more fully and particularly de­scribe.

The first of which kind I find to be a Quadrant of Brass, which he describes in the second Chapter, and begins with that first, as being an Instrument which he least esteem'd, and [Page 11]which at length he made no use of, though for many Reasons I think of a quantity big enough, to be as good, nay better, then any he made use of. But of that anon.

This Brass Quadrant was of three foot Radius, and so well fitted with cross Bars, and strengthned, that it was not subject to warp or bend; it had also a convenient Pedestal, and was made easie to be removed from place to place; it was suspend­ed by a Cylinder placed on the back-side, in the Center of Gravity of the Quadrant, and could by this means more easily be moved to and fro to take any Altitude, then that way of Ti­cho's, who fixt his Cylinder at the upper corner: But it hath this of inconvenience that Ticho's hath not, namely, That the Plumb-Line or Perpendicular will be longer before it settle, and the Instrument somewhat more apt to warp. The Sights of it are the same with that of Ticho, and indeed the best of Com­mon Sights, now commonly every where made use of in Instru­ments of that bigness, but far inferior to those which are made of Glasses, as I shall afterwards prove.

The way of Sights which he describes, pag. 98. for taking the Altitude of the Sun, is very good, but yet far inferior to one fitted with the Object-Glass of a Telescope, though he had omitted the Tube, for he might thereby have enlarged the hole of the upper Sight to what bigness he pleased, and consequent­ly have made the image of the Sun as bright as it should be thought convenient, and that without any manner of Penumbra, if the lower Sight were placed at the due distance of the Focus of that Object-Glass. And therefore I do wonder at his care­fulness to inform his Reader aright, for fear he should under­stand a Telescope by the Tube he made use of, to keep off the adventitious light from the lower Sight, saying, pag. 99. Per Tubum autem mi Lector non intelligo Telescopium aliquod lentibus instructum, sed plane nudum ex charta constructum Tubulum, as if he had some dread of making use of Glasses in any of his Sights. Whether it were, that he supposed Glasses to have some hid­den, un-intelligible, and mysterious way of representing the Object, or whether from their fragility, or from their uncer­tain refraction, or from a supposed impossibility of fixing them to the Sights, or whether from some other mysterious cause, which I am not able to think of or imagine, I cannot [Page 12]tell. Sure I am, that none of these I have named, are any thing at all considerable Objections against their use, and I have been so fully satisfied of the exceeding great use, nay ab­solute necessity of them in curious and exact Observations, that I do assure him there is not, nor can be any considerable Objection against them, which cannot easily be answer'd, nor any inconvenience, which cannot with ease be obviated and rectified; of which I shall say more hereafter.

The Divisions of it were made wholly by himself, with ex­traordinary labour and curiosity, insomuch that he says, he could not only distinguish each minute of a Degree, but almost every quarter of a minute, sufficiently accurate for his Com­mon Sights, if he could have only distinguished every half mi­nute, and indeed much more then most mens eyes are able to reach. He seems to have been at infinite trouble and pains, to perform the Divisions made by the help of Diagonals, cutting parallel Circles, a way made use of by Ticho, and now so com­monly known, that I think I need not spend time in the Expli­cation thereof; only I must take notice, That whereas he sup­poses these Circles to be equally distant, he ought to have pla­ced their Distances according to the Proportions of the diffe­rences of the Secants of some ten minutes, next successively fol­lowing one another in some Degree of the Quadrant, which is easie to determine, from the Distance of the two extream or bounding Circles; of which more hereafter.

Now though the Circles ought not according to the strict Rules of Geometry, to be equally distant from each other, as Hevelius seems to suppose, yet I confess, unless the space wherein these Circles lye be very large, and the parts of a De­gree that are to be distinguisht, very small, there is no necessi­ty of so curiously distinguishing those unequal Distances, but they may serve well enough for use, if they be taken equal, as Hevelius supposes, and indeed much more accurate, then 'tis possible to distinguish the Object by the bare eye; and there­fore I shall not need to insist upon the further Explication thereof, especially because when I come to shew a more accu­rate way of Sights, I shall also shew a much more accurate way of Division, then either of those two of Ticho Brahe, or this set down by Hevelius, which is much the same with one of those [Page 13]which was 100 years since made use of by Ticho, and descri­bed, and is by him attributed to an English Mathemati­cians.

But because this industrious and careful Person put himself to the trouble, of making and examining the Divisions himself, I could heartily have wisht he had thought upon some such way as this, which I here describe, and call a Compendium of Dia­gonal Divisions, it being a way, whereby as 89/90 of the trouble is saved, in performing the manual operation thereof, so I judg it to be much more certain, exact and plain, then the other way of Diagonals. My Reason for the first is plain, The Division of one Degree serving for the whole ninety: And my Reasons for the second are, First, Because it is much plainer to be di­stinguished, then by the help of the edge of a Ruler, lying over the Diagonals, one being able to see but one part of the Diagonal. And Secondly, I think it much better then a small fiducial Thread, which is very apt to be bended and broken, if it lyes close to the Superficies of the Diagonal, and if it lyes at a distance, a skew glance of the eye will much alter the seem­ing intersection of the Diagonals, which in this way are both prevented. The way then in short is nothing but this; Take a thin piece of clear Looking-glass Plate, well smoothed and polished on both sides, and large enough one way to cover the whole breadth of the Rim of the Quadrant, on which the Dia­gonals were to be made, and the other way to cover two or three Degrees, (this I do the bigger, that the sides of the Arm may not shadow or darken the Divisions and numbrings.) Sup­pose a a a a in the 29th. Figure, Plate 2. to represent such a Plate, upon this Plate describe with great care a Degree of the Quadrant you would have divided, and compleat it with all its parallel Circles and Diagonals, as you would have done any one Degree upon the Quadrant, and if the Rim of the Qua­drant be very broad in proportion to its Radius, you may by the Table of natural Secants or Tangents, set the parallels at their due Distances, but if the Rim be narrow, 'twill be suffi­ciently accurate to make their Distances equal. These Divisi­ons must be done with Compasses, pointed with small Diamant Points, in the manner of those wherewith Glasiers cut their Glass. The Glass being thus divided and lined, number the [Page 14]Diagonals, and place it in the Frame of the Ruler, with the lined side next the Quadrant, so that moving it to and fro, the side of the Glass may immediately touch the Brass Rim of the Quadrant. This Brass Rim must be divided into 90 equal parts or Degrees and at each Division straight Lines drawn from the Circumference to wards the Center, the whole breadth of the Limb, (at least as much as is made use of for the Glass-Plate, for the breadth of the Diagonals) the Frame to carry this Plate is a convenient Cavity, left in the moveable Arm of the Quadrant, the whole manner of which will be better under­stood by the Delineation thereof, to which I shall therefore refer the Reader. The Distances of the parallel Circles if un­equal, may be easily set down true, according to the numbers of natural Tangents or Secants, with a pair of Compasses, con­trived like Beam-Compasses, but having its Points to be set at any distance, desired by the help of a Screw, moving upon one side of the Beam, which I may have occasion to describe else­where more properly, and therefore will here omit it.

Next, If this way had not pleased, I could have wished he had known this following, which is altogether as easie, and as Geometrically true, which I have contrived, and have made small Instruments thereby to shew very minute Divisions, very easily and very plainly. I strike then upon the Limb of the Quadrant I would divide, being first made exceeding smooth and plain, a Circute very fine, and as lightly as possibly I can, so it be but discernable, and by the help of a very large Qua­drantal Dividing Plate of ten foot Radius, I divide the said Quadrant in the faint Circle above-mention'd, into 90 parts or Degrees, then by a peculiar contrivance of a very curious Point that strikes with a Spring, which I describe in another Discourse, the said Degrees are marked upon the Plate by cu­rious, small, round and deep holes, these are by another Line without it, which is divided and figured the Common way, distinguished and numbred by Figures, according to the Com­mon manner. Then for the sub-Divisions, I make a small Hold-fast by a Screw, which is fixed on to the moveable Arm of the Quadrant, this serves to hold the end of a Diagonal Hair, the other end of which is strain'd over the Supplementary Degree, till it lyeth directly over some prickt-Hole of the curi­ous [Page 15]Divisions, on the Limb of the Quadrant, this gives me the sub-Divisions of the Quadrant, to what accurateness I desire. The Supplementary Degree is a Degree of a very large Circle, put on upon a small Rule, fixed on to the side of the moveable Arm, whose Magnitude and Distance is found by this Propor­tion, as the Distance between the end of the small Hold-fast and the pointed Circle, is to the Radius of that Circle, so make the Distance between the said End and the Supplementary Cir­cle to the Radius of that Circle. This will be more plain by a Scheme.

Let a a a in the 32th. Figure represent a Quadrant, b b b a very fine Circle, struck on the Limb of the Quadrant, from the Center l, which by a large Quadrant of 10 foot Radius, I divide into Degrees, and by a springing Point strike so many small Points, and number them to 90. beginning at m, and numbring towards i. Let d d represent the moveable Arm, c c the hold-fast, fixed upon the side of that Arm, which by a small Screw pincheth and holds fast a very fine Hair at k, ee the small Ruler fixed at right Angles, with the Line l k f, in this Line (through the Points l and k) I take a Point, as f, and through f I strike a part of a Circle f g, whose Center is somewhere in the Line f k l produced, which I find by resolv­ing this Proportion, as k i is to l i, so will k f be to the Ra­dius of the Supplementary Circle f g, which will fall some­where in f k l produced, towards l, then take a Degree of that Circle, which will extend from f to g, and divide it in­to as minute Divisions as are necessary, and number them from f to g. Now to find what Angle the Sight d d maketh with the Sight m m, I strain the Hair h k, till I find it lye over the next Division Point towards the right hand, and observe in the Ruler e e, what part of a Degree is there marked, and on the Circle b b b, what Degree is marked, the sum of both which gives me the true Measure of the Angle d d l m. But this only by the By, and I will not now further enlarge on the Explication thereof, designing it for another Discourse, where I shall describe various, Mechanical and Practical ways, of accurately dividing Lines, into any assignable number of equal or proportional parts.

To proceed then where I left off, to the examination of [Page 16]the Instruments of Hevelius, I find that together with the Brass Quadrant I was speaking of, he describes two Contrivances about it; The first is, How to set it presently to an upright, without the trouble of turning the Screws in the Pedestal, which is plain enough, and so much the better; but it hath this of inconvenience, that it must be altered for every Azimith, which is a very great one, and which by another way altoge­ther as easie and plain, may be avoided; of which more here­after.

Another Contrivance about this Instrument, is a small Screw, for moving it and keeping it steady in any posture in the same Azimith, which is convenient enough, but will not perform what he afterwards supposes it capable of, as I shall afterwards shew.

The second Instrument, which in the third Chapter, pag. 102, 103, &c. 108. he describes, is a Sextant of Brass, of three foot Radius, carefully made, and divided with the same care and after the same way as the former. The Sights also are much the same, only whereas in the Quadrant he makes use of a Plate, with parallel edges for the Sight that is at the center, and furthest from the eye; in this he makes use of a Cylinder, which way also Ticho made use of 100 years ago, and hath been ever since made use of. The other Sights next the eye are the same with the former: There is nothing singular in the Pede­stal, nor in the Ball and Socket, only 'tis somewhat bigger then ordinary. His way of moving and fixing the Rule of it is convenient enough, and the same with his Instrument for moving and fixing his Quadrant, but 'tis not capable of performing what he promiseth for it.

The third Instrument, which in the fourth Chapter he de­scribes, is a Sextant of Iron, of four foot Radius, to be ma­naged only by one Observator, by putting the Center next the eye. The whole Instrument is little differing from the former, save only that the Cylinder at the Center which is here next the eye, is cover'd with another hollow Cylinder, which is voluble and convertible about the former, and carries two small Slits for the Sights, which performeth the same as the other Sights, but nothing more, and as the Author himself af­firms, is not so accurate for use as the other Sextant, where [Page 17]there are two Observators, and therefore was seldom made use of by him. But I shall anon shew a way by which one Obser­vator alone shall be able to take any Distance to a Semicircle with much more accurateness and conveniency then any two Observators can; and therefore will be an Instrument of the best use for Astronomical and Nautical affairs, for the perfecting both which I design it.

The fourth Instrument, which in the fifth Chapter, from pag. 114, &c. to 123. he describes, is a Quadrant of six foot Radius, whose Frame was all made of dry Oak, but the Limb, Sights, Sockets, &c. were made of Brass, divided so as to see every quarter of a Minute distinctly, the Sights the same as in the first Quadrant, and the way of suspending it not much differing, save only, whereas in the former the Pedestal was moveable, in this it is fixt, which is much better. And the Instrument is kept in an Aequilibrium, by the help of counter poises hung at the end of a string, and cast over a Pully, as is more visible by his De­scription. But this (as all other wooden Instruments do) he found to shrink and warp, and consequently to lose its exact­ness, and therefore he made little or no use thereof, but laid it aside, and made himself better of Brass.

The fifth Instrument described in the sixth Chapter, from pag. 123. to 132. is a Sextant of Wood of six foot Radius, made in all particulars like the former Sextant of Brass of three foot; nor has it any other contrivance about it considerable, save on­ly a rest made to slip up and down for the Observators to rest their Elbows upon. But this Instrument also he found to be vitiated by the shrinking and warping of the Wood, and there­fore he laid that by also, and seldom made use of it.

The sixth Instrument is a large Octant of Wood of eight foot Radius; this is made exactly according to the Form of Ticho's Octant, and serves for taking any Distance not exceeding 45 degrees. The Sights near the eye are made exactly as the former, but moveable, so as to slip upon the Limbs of the Octant; the Divisions of it are performed by Diagonals as before, and gives a greater niceness of Division then the Eye is capable of distin­guishing in the Object, and therefore of little use.

And thus far the Author proceeded in Ticho's way. But finding these Instruments which were made for the most [Page 18]part of Wood to be subject to faileur, he aspired to get better Instruments made all of Brass or Iron, and wholly laid aside the rest as altogether useless. And I cannot but very much ap­prove of his Judgment in so doing, for certainly caeteris paribus Instruments, well made of Brass or Iron, are much to be pre­ferred before the best of Wood. But yet neither are all man­ner of Wooden Instruments to be rejected; nor are all sorts of Metalline Instruments free from error, though 'tis confessed, if they be made and used with skill, they suffer not any conside­rable or sensible variation. First, I say, Wooden Instruments may be so contriv'd as very near to equalize those of Metal, the Joynts and Plates for Divisions only being made of Metal, they being very easie to be rectified before, and examined after eve­ry time of using. Such a one was contrived by Sir Christopher Wren, being two square Wooden Tubes or Telescopes, joyn'd together at the end next the Object by a Joynt of Brass, and the Angle made by the opening of them, measured by a straight Rule equal to half the Radius, divided by Diagonals into 5000 equal parts, which will by the help of a Table of natural Signs or Subtenses, shew the parts in Degrees, Minutes, and Seconds, of which I think I acquainted Hevelius some years since, Next Brass and Metalline Instruments, if they be not very carefully fortified against it, are more apt to bend then even those of Wood. And the best way I have found to secure them true and plain in all postures, is to lay them on a Table or Frame of Wood, well fortified underneath against bending, and by the help of small Screws in several parts of the Instrument to ad­just it upon that Frame; the whole Table and Quadrant being so counterpois'd, as to be easily moveable and fixt in any po­sture. But Hevelius is pleas'd, as I said before, wholly to lay aside all manner of Wooden Instruments as useless, and to indea­vour the obtaining of Instruments of Brass or Iron. Nam (sayes he pag. 136.) cùm longâ experientiâ probe tandem didicerim, multo securius esse ex solido prorsus metallo obtinere Instrumenta, tum quo majora & ampliora eo esse accuratiora & absolutiora, ad­haec prioribus admodum Tichonicum constructis plurima deesse qui­bus ditari merito deberent, & quod iisdem de causis omnino ne­cessum sit, ut parte corrigerentur & meliorentur, tam quà eorum materiam fructuram commotionem facilitandam divisionem quam [Page 19]alia diversa subsidia & adminicula, quo sic aptius, exquisitius, promp­tius, minorique labore, &c. ac temporis dispendio possent Astris ex­poni observationésque peragi. Idcirco omnem curam atque operam pro tenui ingenii mei facultatúmque mearum modulo à Deo concesso (reliqua sublimioribus ingeniis at que ampliori fortunâ Viris, five posteritati nostrae relinquens) adhibui: quo minora, tam lignea u­niversa ab Astris planè removerem, atque in ejus locum ex puro solidóque metallo, organa mihi compararem: & quidem ejusmodi, quae insigni amplitudine essent conspicua, simul commoditate regen­di, simul aliquanto accuratioribus adhuc divisionibus, ad paulò sub­tiliores observationes obtinendas gauderent. His Reasoning in­deed is very good, that since he had from much and long expe­rience learn'd, that Instruments of Wood after Ticho's manner, were not to be trusted to by reason of their warping and shrinking, and consequently that Instruments of solid Metall were much to be preferred before them, and also that the lar­ger the Instruments were, the more exactly they could be made and divided, and that the more easie they were to be moved, and the more steddy and sure they were to be fixt in any position, the more convenient they were for use, he had therefore reject­ed all those Instruments which he had made after Ticho's way; and had indeavoured to procure for his own use such as were compleat, both for their matter and form, having caused them to be made of Mettal that which could not be subject to the inconvenience of warping, swelling, or shrinking, with the variety of Weather, or length of Time: And likewise of such a bigness as was capable of receiving more nice and curious Divisions; and in the dividing them had found such contrivan­ces, and used such diligence, that they were more then ordi­narily true and exact. As far as he has gone on with these De­signs, he seems to have been even profuse in his expences, and exceeding bountiful of his own care, labour, and diligence; but I could have wish'd heartily that it had been some other way imploy'd. Those Instruments which he chiefly laboured to perfect, he professes to be Quadrants, Sectants, and Octants, after Ticho's manner, rejecting all other Instruments of whatsoe­ver Figures, whether Radii, Astrolabs, Zodiacal or Aequino­ctial Rings, Parallactical Instruments or Hoops, as more trou­blesome, and less accurate. But whether he hath in this his [Page 20]choice been rightly advised, I shall hereafter have more occasion to examine when I come to describe an Apparatus of In­struments necessary for such a one as designs to promote and perfect the knowledge of the Coelestial Bodies and their mo­tions; wherein I shall shew that of some Instruments rejected by him, there is a use absolutely necessary.

The Instruments therefore that he begins with are three small Quadrants of Brass; the first of two foot, the second of eigh­teen inches, and the third of one foot Radius. Each of these Instruments, he sayes, were made somewhat larger then common Quadrants, to wit, of an arch of 110 degrees, which is to no other end, but only in order to shew the subdivisions of each degree of the Quadrant, by the help of a new invented Per­pendicular of Brass wherewith each of them was furnisht. This Invention is by him highly extoll'd for most excellent and use­full; and to that end is made use of for the division of all his other Instruments, both great and small. Hear what he sayes of it: Quiscunque hujus rei (to wit, the new way of subdivi­ding the degrees of the Quadrant) primus fuerit repertor, subli­mes profecto cogitationes exercuit, hoc ipso ad congruentem effectum deducendo, & inter praestantissima inventa meritissimo refertur, quod etiam minora Instrumenta remotis omnibus transversalibus Lineis, in singula minuta corúmque particulas minimas subdividi liceat. He seems indeed both here, and elsewhere in many o­ther places of his Book to be highly possest with admiration of the sublimity, subtilty, and extream usefulness of this in­vention, and seems very much concern'd that the Author there­of should not certainly be known, but dares not father it upon any one positively. He sayes that one Benedictus Hedreus in a Work of his which he published Anno 1643. about the new and accurate Structure of the Geometrical Astrolab, describes it; but he gathers that he was not the Inventor himself, but ra­ther that he got both this Invention and the whole Quadrant, which he describes out of the Observatory, or rather Reposito­ry of Ticho Brahes Instruments, for that it seems Ticho was the Inventor of this way of division; and yet, as I noted before, he prefer'd the way by Diagonals much before it, whatever Reason Hevelius had to be of a contrary Judgment. What this way is I shall by and by explain. But in the mean time I am [Page 21]sorry to find Hevelius joyning with Hedreus in the Opinion or Demonstration, as Hevelius calls it, that the Sub-divisions by Diagonals is not capable of a Geometrical demonstration, espe­cially in lesser Instruments, which have need of many Circles. I confess I understand not their meaning nor reasoning, nor why it should be less demonstrable in lesser then in greater Instru­ments; since 'tis very easily demonstrable both in greater and lesser Instruments, and as Geometrical as any other way of Di­vision whatsoever: the Diagonal Line being alwayes a piece of a Tangent Line, that is to say, the spaces between the Parallel Circles upon the Diagonals are alwayes to be in proportion to the difference of some Tangent Lines, and the different distance of those Circles from the Center are alway in proportion of some Secants: And the way of finding what those Tangents or Secants are, and consequently what must be those Distances of the Parallel Circles I mentioned briefly before, and shall now more fully demonstrate. From which I will make it evident, that the Theory was not as Hedreus and Hevelius have suppo­sed, uncapable of Calculation or Mechanical Demonstra­tion.

But first give me leave to shew you what way Ticho Brahe made use of to demonstrate, or rather to find out the true An­gle unto each equal Distance, which I find set down at the lat­ter end of his Mechanicks, as a Supplement to the rest. Di­visionis puncta habentis transversalia modus talis est, ut 34 ex­primit figura in qua singula denominata per Lincolas in decem in­terstitia aequalia discriminatum punctis notata sunt, sicque regula fiducioe quodcunque horum inter observandum transiens ip sum mi­nutum gradus, quòd quaerebatur promit aut aliquotam ejus partem, prout ab hoc vel illo puncto removeri discernitur. Ut vero hoc e­tiam demonstratum hic addam ob sciolos fortè quosdam qui ea quae non satìs capiunt carpunt sic habe.

In Figura 34. Sit A centrum Instrumenti ejusque Semidiami­ter A O, assumitur autem O I, Particula in qua divisio ista per li­neas transver sas fit ea proportione quae est 1 ad 48. qualis in meis Instrumentis ut plurimum usurpatur. Cúmque A I ponatur partium 10000000000. integri canonis majoris Rhetici, erit earundem O I 208333333 utpote pars quadragesima octava radii Arcus I E sit 20′ & IV. 10′ horum sinus 29088779 Y I. Sinus autem secundus [Page 22]corundem 42308. V Y. qui additus N V quod aequale est O I facit N Y 208375641. In triangulo igitur NYI ad Y rectangulo nota sunt duo Latera N Y & Y I. quare datur basis I N 210396208. una cum angulo NIY 82°. 3′. 10″. 47‴. sui additus YIA 89°. 50′. conficit N I A. 171°. 53′. 10″. 47‴. Basis verò N I in triangulo rectangulo N V I dividatur in decem partes aequales ut conveniant uni minuto 21039621 representatae per I B. Moxque in triangulo obliquengulo BIA. dantur duo latera IB & IA. radius, una cum an­gulo BIA, qui idem est cum NIA 171°. 53′. 10″. 47‴. prius reperto: quare innotescit angulus IAB 1′. 1″. 7‴. qui tantummodo 1′. esse debe­ret, ità ut major sit saltem 1″. 7‴ differentia sanè insensibili: si­militer si F I assumatur, noven particularum erunt eae 189356587 habebimusque rursus triangulum F I A in quo dantur duo latera FI modo dictum una cum radio I A. & angulo F I A ab iisdem compre­henso velut antea exurgitque angulus I A F 9′. 1″. 6‴. qui debebat esse 9′ exacte deficiente in ultimo minuto F N. 1″. 6‴. Porrò ut circa medium idem tentetur quod nunc apud extremitates fecimus inveniuntur eadem qua antea primo Angulus NAH 5′. 3″. 6‴. abundans 3″. 6‴. Secundo Angulus N A H 4′. 56″. 55‴. deficiens 3″. 5‴. Patet itaque quod maxima differentia, five adjectiva, five ablativa in hac pragmatia proveniat minimum quid ultra 3″. quam subtilitatem visus acumen discernere in quocunque tandem instrumento nullatenus sustinet, quae etiam per se otiosa est, quare frustra nodum in Scirpo quaerunt, si qui hanc nostram satis accuratam distributionis formam cavillari praesumant. By which 'tis evident that Ticho understood an inequality, and what it was, and that it was insensible, and so not to be regarded. Now 'tis to me very wonderful indeed that Ticho having thought of a way of calculating this inequality, should not think of an easie expe­dient of reforming it by putting the Parallel Circles at unequal, but their due proportionate distances. And 'tis much more strange that Hevelius should still affirm it to be a way not Geo­metrical: For to any one that considers this proportion, the inclination of a Diagonal Line being given to find the true di­stances of the Parallel Circles that shall divide any assignable part thereof in any proportion assigned: Nothing can be more easie: and for more expedition use may be made of the Table of Natural Tangents which is ready calculated to hand. For instance: Let B C represent a Diagonal Line subtending an an­gul [Page 23]of 10 [...] at the Center A, produce the said Line BC to F, and let full a Perpendicular, from the Center A to E. Suppose then the Angle at B to be one Degree, then is B E the Tan­gent of 89°. to the Radius A E. and E C is the Tangent of 88. 50′. and the differences between the Tangents of 88 50, 88, 51.88, 52.88, 53.88, 54.88, 55.88, 56.88, 57. 88, 58.88, 59. and 89. gives the Distances of the several Cir­cles, C. 1 2 3 4 5 6 7 8 9 B. desired.

Since the Reading of this Lecture, Dr. Wallis hath also de­scribed another way of finding these Distances, which he hath communicated in a Letter to Hevelius, and I have prevailed with the said Doctor to permit it to be here printed, being very ingenious and accurate, and proceeding by a differing me­thod.

But to proceed. In the next place I think it will be sufflic­ently plain, to any one that shall try both the ways, that the Divi­sions are by Diagonals much easier distinguished by the eye, then by this way so applauded by Hevelius, and therefore I cannot choose but conclude with Hevelius, (pag. 140.) though to a quite differing end and sense: Sunt igitur splendidissimae tantum speculationes mentis (que) ideae quaecun (que) de Nomanis vel Hedrianis Divisionibus profe untur. But because perhaps there may be several persons that have not yet perused this Book of Heveli­us, nor that of Benedictus Hedreus, printed in 1643. nor Ti­cho's Mechanicks, of a much longer standing, and thence may perhaps not so well understand what this way of sub-dividing is; give me leave a little to explicate it, and shew you plainly what it is.

The way then as it is described by Ticho Brahe, and ascri­bed by him to Petrus Nonius, that excellent Spanish Mathe­matician, who publisht it in his learned Book, de Crepusculis, supposing it also to have been heretofore used by Prolomy, but (as Ticho is of opinion) without much reason, is this; Ut ducan­tur intra extremum quadrantem alii minores numero 44. successi­ve sese comitantes, quorum extimus in 89. sequens in 88. vertius in 87. & sic deinceps donec ad ultimum & intimum perventum fuerit qui 46. portiones habebit. To which Description pub­lished in his Mechanica, he adds in the second Book, de Mun­di AEtherei recenstoribus Phenomenis, pag. 461. Altern Di­visio ad Clarissimi Mathematici Petri Nonii—imitationem per plures quadrantis arcus introrsum descriptos & diversimode subdi­visos procedit. Etsi autem in hac ipsa imprimis ingenios [...] Nonii inventione; aliquid anctuarii loco expeditius à nobis additum est, ita ut exterior arcus in plurimas portiunculas dividatur; neque is ordo aut numerus arcuim sese introrsum concomitantium, quem ille praefinivit sed multo expeditior & perfectior observetur, camen quia haec subtilit as cum ad praxin deventum est plus habeat laboris quam fructus, ne (que) id in recessu praestet quod prime fronte pollicetur, ut alibi plenius ostendemus; ideirco apud nos dudum in u [...]uesse desiit. [See more of this, pag. 62. Epistolarum Astronomicarum.]

From which way of Division, this of Hevelius (which he ascribes to Hedreus, but is more properly ascribable to Pier­re Vernier, as I shall afterwards shew) is somewhat different, [Page 28]and possibly might be the same that Ticho Brahe contrived to compendifie that of Nonius.

The way then is this, described by Hevelius, pag. 141: Quadrantes contractiores ita à me sunt adornati, ut limbos corum tantum in integros & semigradus distinxerim; quae ut haec distinctio non nemini admodum rudis videatur, sufficit tamen affatim com­monstrandis singulis minutis primis; dummodo perpendiculi excen­tro appensi extremitas limbum stringens in certas particulas fit sub­divisa, imo quod magis de quo non nemo sane mirabitur, non solum haec rudior limbi subdivisio sufficiens exhibendis singulis minutis primis sed etiam pro denis quinis quinetiam singulis secundis in ma­joribus organis si videlicet nostrum Instrumentum directorium adhi­beas. Oportet ut inferior illius pars curiosissime & levissime sit li­mata & levigata, ut limbum totum aequabilissime quidem tangat, sed nullibi nimis adhaereat; tum quovis loco liberrime pendeat at (que) di­visionis tam quadrantis quam perpendiculi observator rite discer­nere valeat. Dividitur autem istud perpendiculum hac rations, si videlicet spatium 31 semigraduum in limbo perpendiculi accura­tissime denotes; id (que) primum in tres aequales partes, rursum quam­libet trientem in decem dividas; at (que) it a obtinebis spatiola paule admodum ampliora quam spatiola unius semigradûs, quia interca­pedo 31 partium in 30 transmutata necessario fiunt modice amplio­res. Attamen si divisiones perpendiculi ad limbum quadrantis accedant circa extremitates perpendiculi, discrepantiola illa divisio­num ab invicem vix ac ne vixcognoscitur; circa medietatem vero perpendiculi satis evidenter. In medio limbo perpendiculi & di­visionum parvulus index & quidem inter 15 & 16 spaciolum con­stituitur pro discernendis integris & semi gradibus; quos accurate dictus index indicat, quando totum spatium perpendiculi in 30 par­tibus divisum in ipso limbo quadrantis spatium 31 partium exquisite subtendit. Ea tamen expressa lege si totum Instrumentum absolute ab omni parte sit constructum; quando vero iste index pauxillum promotior existit integro aliquo vel semigradu certissimum est indi­cium, observation iminuta quidem adhaerere aut integro aut semi­gradui adnumeranda, si index huic vel illi vicinior est. Cognosci­tur autem minutorum numerus ex eo, quando lineola aliqua divisi­onum in perpendiculo cum una aliqua in limbo quadrant is prorsus in unam eandem (que) coincidit rectam. Nunquam enim nisi unica li­neola in perpendiculo cum altera in quadrante, si exquisite peracta [Page 29]sunt omnia omnino concurrit. In isto igitur utrius (que) lineolae concursu ubi una eadem (que) videlicet constituitur linea est terminus ipsorum minutorum vel integro gradui vel semi gradui adhaeren­tium.

This same way is also made use of by Hevelius, for the Divi­sion of all his larger Instruments, as well as for the Division of this smaller, by fixing it upon the Perpendicular, as he after­wards mentions, cap. 15. pag. 307. where he also gives a fuller description of it, to which I refer the Reader.

The way indeed is exceeding ingenious, and very much im­proved by Hevelius, but yet at the very best it is very diffi­cult, both to make the Divisions, and much more difficult to distinguish them, as may be plainly enough seen even by that very Specimen published by Hevelius, in the first and second Figure of the Plate T. especially if it be viewed with a magni­fying Glass or Lens; and I do wonder that Hevelius did not all this while think of making use of a Lens, to make the Divi­sions and Distinctions appear more plain, without which Se­conds are not to be distinguished, by those kinds of Divisions even in an Instrument of 10 foot Radius, and by the help of it they may be made and distinguished, in Instruments of a quarter that bulk, as he may find, if he please to make use of the shal­lowest Object-Glass of that Microscope which he had from London; he may, I say, by looking upon the Divisions of the first and second Figures of the Table T. with his Microscope, plainly detect how far those Divisions are short of accurat [...] ­ness, and how many faults and inequalities the naked eye and unmachined hand do commit.

It is therefore one of my ways for dividing and distinguish­ing Divisions, to make use of one, two, or three Lenses, where­by not only the eye is very much eased, but the judgment is ve­ry much augmented, and the hand directed, as I shall after­wards explain, when I come to shew some particular ways of making Divisions.

But because this Benedictus Hedreus, from whom Hevelius affirms he received this invention of dividing the Limb of the Quadrant, was not so ingenuous as to confess that he received this invention from another, and because perhaps the Book be­ing small, may have been long since lost and forgotten, having [Page 30]accidentally met with one, I shall acquaint Hevelius, that one Pierre Vernier (as he calls himself) Capitain & Chastelain pour sa Majesté au Chasteau Dornans, Conseiller, & General de ses Monnoies au Conté de Bourgongne, printed at Brussels, by Fran­cis Vivien, 1631. (to wit 12 years before Hedreus) a Treatise in French, which he calls, La construction l'Usage & les Propri­etes du quadrant nouveau Mathematique, comme aussi la constru­ction de la table des sinus de minute en minutes successivement par un seul maxime. De plus un abregé desdicts tables en une petite demi page avec son usage: & finallement la methode de trouver les angles d'un triangle par la cognoissance des costez & les costes par les angles sans l'ayde d'aucune table. In which he hath at large and very plainly described this way of dividing the Quadrant, to what accurateness is desired, and pretends it to be, as pos­sibly it was, an invention of his own.

But to return where I left to Hevelius his Division on the Quadrant by the help of the Brass arm, I say, against this way, besides what I have already mention'd, I have a second Obje­ction, and that is, that it requires a most exceeding great curio­sity and care to make that Metal Pendulum or Plumb of Brass, so as to be exactly of equal weight and make on both sides of the supposed middle Line, for if it be not so, it may easily vary not only some Seconds, but even some Minutes from its exact Perpendicularity, and if so, 'tis to little purpose all the for­mer curiosity about Subdivisions.

Thirdly, The Perpendicular ought alwayes to be kept very clean from Dust, for if a little more Dust settle on the one side then on the other, the Perpendicularity will be vitiated, and all the curiosity else about the Observation will be lost.

Fourthly, If the Pin on which this Brass Perpendicular hangs be not of some bigness, it may easily warp or bend; and if it be of a considerable bigness, it will not move easily, and consequently the Plumb will not hang tender, but stiff; in both which cases it can be of no use in the World for Astronomical Observations. Further, if it hang loose upon the Center, which it must do to hang tender, then there will lye as material an Objection against it, for its not moving true upon the Cen­ter of the Instrument; and therefore upon the whole matter I conclude it to be an Invention indeed of great sublimity and [Page 31]subtleness, but of little or no use for Astronomy, to which Heve­lius applies it. He had much better therefore have been content to have followed Ticho Brahe, and made use of a common Plumb Line and Diagonal Divisions; where there is occasion for them, for that is true and practicably capable of exhibiting the Subdi­visions of a Degree, as Minute, as are necessary to common Sights.

In the next place, before he leaves the Descriptions of these three smaller Quadrants, he mentions an Invention of his whereby he fixes the Quadrant in any altitude, and easily moves it steadily into any posture desired by the help of Screws. This Invention of his own contrivance he doth indeed very highly applaud, insomuch that he believes no good Astronomical Observations can be made without it. But he must pardon me if I am not altogether of his mind; I grant in­deed the thing is exceedingly convenient, in comparison with any yet used, if it be well made, and that the way of applying it to the Quadrant be very facil and easie. But 'tis not alway so necessary, but that Observations may be as conveniently made without it, as I shall afterward shew, in the Description of the moveable Axis, for continuing the Instrument in the Plain of the Object, whether a Distance or an Altitude be to be taken.

In the next place he proceeds to describe his large Qua­drant of Brass adjusted so as to take Altitudes and Azimuths, of which he makes a full and particular description; but the most considerable thing that is new in it is, that instead of a Screw used by Ticho for lifting and moving the Arm with Sights, he makes use of two Lines poys'd with Plumbets, by the pulling of this or that of which he is able to raise or sink the Ruler with Sights, all the rest of the contrivance being to make it stand perpendicularly in any Azimuth, which I think may be done to greater certainty with less trouble, by a way I shall afterwards shew: As an Essential part of this Instru­ment, he takes occasion to give the description of the Turret or Observatory which he built for it, and the several contri­vances about it, which I now omit.

The use he made of this Instrument was for the taking the Meridian Altitudes of the Sun, of which he affirms to have taken a very great number, especially such as were of princi­pal [Page 32]use for the regulating the motion of the Sun: Such as the Solstitial and Aequinoctial Altitudes, of which I hope we may expect an account in the second and third Part of his Machinae Caelestis. I know not to what exactness he hath proceeded in taking his Meridian Altitudes of the Sun; but had he proceeded in the way by Telescopes, he might have taken all his Alti­tudes of that kind to a single Second, with great ease and cer­tainty.

And upon this occasion I hope it will not be unacceptable to my Astronomical Reader to hint a very expeditious and ex­ceeding accurate way of making a Catalogue of all the visible, as well as the most considerable Telescopical Stars of the Hea­ven. For the doing of which there will not need a tenth part so much time as for the other wayes that have already been made use of, and yet will very much exceed them all in accu­rateness and certainty. The way then in short is nothing but this: Let there be made a very large mural Quadrant, or rather Semicircle, of 30 foot Radius, fixed exactly in the Meridian against a Wall made of squared Stones, well joynted and cramp­ed together, and setled on a foundation very firm and solid, to prevent all manner of slaking and swarving. Let the rim of this be made of Brass Plates, stayed in their due posture by cramps or bars of Iron fixed in the Wall, by running them with Lead: then having divided this Semicircle into 180 Degrees, and subdivided each Degree by the help of Diagonals, on a flat and well polisht Plate of Glass, according to the way I before described into Minutes and Seconds: adapt to it a 30 foot Te­lescope, so that the Tube shall not warp, nor the Glasses devi­ate out of their true posture; the Focus of the Object Glass make to be exactly upon the edge of the Brass Limb, so that by the help of the Eye-glass, which is a deep Convex, the punctu­al place or altitude of a Star to a quarter of a hairs breadth, e­ven to Seconds of a Minute, may be discover'd: the trouble of dividing this Quadrant will be no more then of one of an ordinary size, the subdivision of one Degree subdividing and examining all the rest. The way of making the Tube of the Telescope so as not considerably to bend, may be done some­what after that way of stiffning the Tubes of very long Tele­scopes, which I communicated to Hevelius, and you will find [Page 33]at large described in this Treatise of Hevelius: Save only, that instead of Ropes which I first made use of, I rather commend so many Braces of Wood. Now though notwithstanding all the Diligence that can be this way used, the Tube do somewhat bend in the middle, yet it can be of no manner of significancy as to the vitiating the Observation; since first, the Object Glass al­ways standeth in the same posture as to the Center, and secondly, the Focas thereof is exactly in the edge of the Limb.

Further, to prevent the inconvenience of looking up or in any other uneasie posture by the help of a reflex Metal one may al­ways look Horizontally, that is, perpendicularly to the plain of the Wall or Mural Quadrant. And to prevent the trouble and la­bour of moving or lifting the Tube by the help of a long yard poysed upon Centers on a Frame before the said Instrument, both the Tube & Arm for the Sight, and the Seat on which the Ob­servator sits, may be counterpoised, so that by turning a Win­dle, he may easily raise himself with the Tube to any posture desired. The Object Glass is just before the Center, and the Eye Glass looketh directly on the Divisions of the Limb, and there is nothing to strain or stir the Instrument it self, nor can the warping of the Tube, if there should be any, have any ef­fect on the Observation: Of this I may say more on another occasion. By this means (in one Nights Observation) the De­clinations of some hundreds of Stars may be taken to a Second by one single Observator, having only one or two Assistants to write down the Observations as fast as made. And at the same time the right Ascension of every one of them may be taken by the help of a very accurate. Compound-circular Pendulum Clock, which I shall elsewhere describe, denoting even to of a Second of time the appulse of the Star to the Meridian: There needs indeed great exactness in every part of this Appa­ratus, and 'twill not be done without a considerable charge, and much labour and diligence in the performance thereof; but if we compare it with the methods and wayes that have been hi­therto used, we shall certainly find that the Observations will be near 30 times more accurate, the charge not a quarter, and the labour not near a tenth part so much as in other wayes made use of by Ticho and Hevelius. And though it may be objected against this way (which indeed may be much more so against [Page 34]any other) that the refraction of the Air will considerably vary the Declination of such Stars as are very far South, yet since the same Instrument affords a way beyond any in the World for the discovering the several Refractions of the Air at several Altitudes above the Horizon, to the accurateness of a Second, by taking the Altitude of such Stars as never set in the North, in the greatest and least Altitude above the Horizon; a Table of such Refractions will easily rectifie the Declination of the other Stars to as great accurateness. This Subject doth deserve a much larger and more particular Description of every Branch thereof, and the Incouragement of some Prince, whose Name and Honour will thereby be Registred among those glorious Ce­lestial Bodies to all Posterity, and the succeeding Learned World will be obliged to celebrate his memory. But I fear this Age will hardly yield another Alphonsus, another Ticho, or another Hevelius, who have not spared to expend their utmost Indeavours in performing this task, though by other methods. But leaving this for another time, I shall proceed.

In the third place then he goes on to describe his great Ho­rizontal voluble Brass Quadrant, of which he says, he does not believe that ever the like was made by any, if the splendid Apparatus and the whole Fabrick thereof be consider'd. It is in Diameter six foot and an half, and serves, as he affirms, to take Altitudes to Seconds; but yet he is necessitated to allow, that it is short both of Ticho's large wooden Quadrant, and of his large mural Quadrant; nor do I see any reason why Ticho's mural Quadrant should not take Meridian Altitudes somewhat more accurately, since I believe his Sights every whit as good, and his Divisions altogether as exact; what he might fail in di­ligence, I cannot say. I do believe this Instrument to be an exceeding good one of the kind, and that he hath from much practice and experience found out many contrivances, in order to the making it convenient to make Observations, and he hath not spared for cost, pains, study and industry, for the com­pleating thereof; but still whether he be arrived to the greatest perfection, or to so great as to take Altitudes to Seconds, seems to me very dubious, and if he made use of the Sights before-de­scribed, wholly impossible. For first, a Degree upon the Limb is but about 6/3; of an inch, and consequently a Minute is [Page 35]but the 50th. part of an inch, and a Second but the 3000th. part of an inch, which he that can distinguish with his naked eye, hath better then I, or I fear, any man now living. Short­sighted men, I grant, can do much toward the distinguishing very minute Divisions, by being able to bring the Object very near the eye, but the most short-sighted must be yet very much shortned by Glasses, before he will be able to distinguish the 3000th. part of an inch, and when he hath distinguished it, which he may possibly do with a Microscope, how will he di­stinguish of the Penumbra, which is not certain even to a Mi­nute? And though it may be said, it is the same, round the Circle, and the Circle is the true bigness of the Sun, so that if a Circle of a bigness, answering to the Diameter of the Sun, and the Distance of the lower Sight from the upper be descri­bed on the lower Sight, it must bound the Limb of the Sun, and that consequently it will be easie to distinguish when that Circle is perfectly fill'd with the figure of the Sun, admitted through the hole in the upper Sight. I answer, That this seems very probable and easie, and is indeed believ'd and asserted so by Optical Writers: But yet 'tis quite otherwise; for not to mention that there is confessed by all, that the Penumbra of this Circle must be as big at least as the Diameter of the hole above, through which it is trajected, which cannot be less then a Mi­nute; I say, that experience doth demonstrate that it is quite otherways, and that the Limb of this Image painted on the low­er Sight is terminated with a Penumbra, which is sometimes five or six times bigger then the Diameter of the hole, and which is yet stranger, the smaller the hole be, the bigger is the Pen­umbra, and the bigger (to a certain Degree) the less, but there is no bigness which will take it off quite, and the Diameter of the Sun that way taken, is sometimes bigger and sometimes less then it ought, and that to a very considerable quantity: Of which, and several other very strange proprieties of Light, I shall hereafter say more on another Subject.

But to proceed. That he hath made this Instrument his chiefest, you may perceive by his pathetical describing thereof; for he says of it, pag. 184. Ad commodiorem hujus quadrantis usum, tot ac tot adminicula recens excogitata at (que) huic organo appli­cata fuere, ut nesciam à quibus primum inchoare debeam. Imo [Page 36]etiamsi vel maxime velim, nullo tamen modo omnia & singula adeo perspicue vel delineare vel describere potero, ut universi praeprimis qui similia haud ipsimet oculis usurparunt quaevis recte ac plane in­telligant, quinetiam credas velim utut aliis sunt attentiores at (que) hujus rei bene gnaros, aliquoties sane hocce Instrumentum visuros antequam dimidiam tantam partem debite animadvertant ac ple­nissime comprehendant. Quippe & verum fateor nec ipse ego, licet singula ex meo solo cerèbro prodierint ac confecta fuerint, possem adeo distincte tibi eum sub aspectum ponere nisi mihi hocce orga­num sub oculis assidue versaretur. Nihilotamen minus dabo ope­ram, ut quantum fieri poterit, dilucide omnia proponam, reliqua veri exercitatis caeli metaloribus ulterius rimanda & perquirenda commit am, &c.

And so he proceeds with the Description of this Quadrant, and the Apparatus about it, and first, he tells us of the weight of this Instrument, that it was 80 l. Next, of the shape of the Turret in which it was fixt, which is indeed very convenient and ingenious, it being so contrived, as to be voluble or con­vertible upon Truckles, having one only side open, and in­clos'd on all sides else, so that neither the Observator nor the Quadrant was much expos'd to the injury of the weather, which is indeed of no small use in Astronomical Observations. But this may be done many other ways also. He tells us fur­ther of the admirable and prodigious use of Screws, in order to the setting and fixing the Quadrant. Next, As to the giv­ing a motion to it, in order to follow the Sun and fixed Stars in their diurnal motion. Thirdly, As to perform all the Sub­divisions of a Degree, not only into Minutes but into single Se­conds. To all which I say first, As to the use of the small Hand-screws, I do grant, that in some cases they may have their conveniency, as to the moving and staying the Instru­ment. But then since he is fain to make use of two Screws, whereby both the hands must be imploy'd to manage these Screws, I judge them too troublesom for that use, and that there is a much better way, whereby the Quadrant being once set into the Azimuth of the Stars, it shall continue to be so, and to move along with it, without any trouble to the Obser­vator, so long as the Observator hath occasion to have it re­main so, which (that I may hint that only now by the By) is a [Page 37]small Automaton, which shall continue it for many hours ex­actly, in the Azimuth of the Star desired, of which more here­after.

Next, whereas he affirms this way capable to shew Seconds as well as Minutes, I grant it may be capable; but then I must further affirm, that he hath not at all shewed how that can be done, nor is it indeed feasible in his way, for he shews us not any way how to set it, that is, fix it certainly to any Degree: Now if he be not sure in the fixing it exactly to a Second, up­on that Degree where he would begin his Division, 'tis a vain thing to be so accurate in the other Dimension, for he cannot be more certain, (let him be never so curious in the Subdivisi­on with his Screw) then he is certain in the first fixing of his Screw to the Degree, for whatever he varies from the Degree in the setting, he varies at least as much in the Subdivisions, and consequently unless that be some ways taken care of, which I do not find, 'tis a nicety without use.

To conclude therefore, I say, the Frame of this Instrument is extraordinary good, and by the help of some additions, as to the Sights, Divisions, Perpendicular and Erection, might be made as good as need be desired for any use in Astronomy, and 40 times better then what it is now made and described by Hevelius, or then any I have yet heard of to be made in the world. But as it is, it is not more exact then the large Instru­ments of the Noble Ticho Brahe, which he used 100 years since, and much short of his mural Quadrant, for taking Meri­dional Heights.

He proceeds to the Description of his new and large Brass Sextant of six foot Radius: The Sights and the Divisions there­of are in nothing differing from those of the Quadrant, nor do I find any thing very considerable in the Description thereof; it was made use of by two persons in the same manner as the former Sextant, and like that of Ticho; but what grand incon­veniences do attend that way of Observation, I shall after­wards shew, when I come to explain how one person alone may be able to do it with less trouble by half, and ten times more exactness.

But by the way, I cannot but take notice of what Hevelius ingeniously confesses, of the great difficulty there is in taking [Page 38]the Distance of fixt Stars from the Moon, which is from no­thing else but the imperfections of his Common Sights, and all that difficulty vanishes, if the Sights be made another way. Next, He seems to make it a much more difficult business, to take the Distance of the Sun from Venus, when she is seen in the day-time; but by a way I shall hereafter shew, it will not only be easie to take the Distance of the Sun in the day-time from Ve­nus, but from Mars, from Jupiter, nay, from several of the fixt Stars.

I shall pass by therefore his Apparatus, which seems very great and chargeable, since I shall else-where shew a single, plain way, without any trouble or perplexity, how the mat­ter may be quite otherwise ordered, much to the advantage of the Observator.

As to what he asserts of his extraordinary care, diligence and pains, in dividing and examining the truth of his Instru­ment, I do no ways doubt it, but that he hath proceeded as far as it was possible for one to do in that way he made use of, but might have saved much of it, if he had thought of the way by Diagonals on Glass, which I have already described. Yet I should have been very glad to have seen the Distances, which he mentions to have taken of eight fixt Stars near the Eclip­tick, to wit, Lucidae Arietis & Palilicii, Palilicii & Pollucis, Pollucis & Reguli, Reguli & Spicae, Spicae & in manu Serpenta­rii, in manu Serpentarii & Aquilae, Aquilae & Marchab, Mar­chab & Lucidae Arietis, and that to so great exactness, as not to miss one single Second in the whole Circle of the Heavens, ta­ken at eight Observations. For to me indeed it seems one of the greatest affirmations I ever met withal, and not less then hu­manely impossible, were there no Refraction in the Air, and did all the Objects stand still in the Horizon, but the Refraction of the Air, were it much less then it is granted by all, would necessarily cause a variety of a great number of Seconds. And I durst undertake to demonstrate it to any, as plainly as any Geometrical Proposition, that it, was wholly impossible for him, with all or any of the Instruments he hath described, to make any one of these Observations, to the certainty of 30 Se­conds, whence if that uncertainty be 8 times multiplied, it will follow, he cannot be certain in the whole Circle to 240 [Page 39]Seconds, or 4 Minutes, which how much it is differing from one single Second, any one may judg.

I had many other things to have added, which have occurr'd to me in the perusing of Hevelius his Book, but I will say no more at present by way of Objection, having, I fear, wearied the Reader, with shewing him my doubts and scruples, espe­cially about the imperfection of that way of Sights and Divi­sions made use of by him: Only, to make my Reader some mends for his patience, I shall describe a short Apparatus, which I have contrived for this purpose, and in the doing there­of, shall be as plain and brief as possible the matter will bear.

Since the reading these Lectures, the Author having been acquainted, that some considerable Objections had been made against the certainty and accurateness of his Instruments, and that I had affirmed it impossible to perform what he had pro­mised in his Book, he returns his Sentiments thereof in a Letter to Mr. Oldenburg, to this effect:

—Caeterum percipio vestrates non omnes mihi adstipulari in isto Dioptrarum negotio, de quibus in machinae meae coelestis Organographia tractavi, verum etiamsi Cla. Hookius & Cla. Flamstedius alii (que) plane aliter sentiant, experientia tamen quotidi­ana me edocuit at (que) etiamnum docet, rem longe aliter se habere in magnis illis organis, quadrantibus scilicet sextantibus & octanti­bus imprimis quadrantibus Azimuthalibus aliisq, quadrantibus re­gulis constructis, quae nempe adeo procliviter commoveri & inver­ti (dum Dioptrae Telescopicae examinantur) imo nullo modo possunt, ut quidem Instrumenta illa trium quatuorve pedum perpendiculo constructa. Rei cum primis in eo consistit, quod nullam plane ob­servationem suscipere possint suis Dioptris Telescopicis nisiprius de­nuo eas examinent ac rectificent; in quo tamen examine varia viâ, tum jugiter utut studiosissime illud suscipiatur hallucinari da­tur. Adhaec in quadrantibus Azimuthalibus, octantibus & sex­tantibus, qua ratione examen istud adeo accurate nunquam non haud magno negotio temporis (que) dispendio institui possit, profecto non­dum capio, vix mihi persuadeo ullibi adhuc ullum aliquem magnum quoddam Instrumentum 6 vel 9 pedum utpote sext. octant. vel qua­drantem cum regula vel quadrant. Azim. cum pinnacidiis Dioptricis construisse, eum (que) ad coelum felici aliquo successu adhibuisse, & quicquam solide observasse; si tentasset ac per annos abiquot obser­vationibus [Page 40]continuo invigilasset sine dubio aliter sentiret. Hoc negotium enim non solum in eo consistit quod stellae aliquanto distin­ctius conspiciantur (quanquam fixae ab eo qui visu pollet & exerci­tatus est aequè bene nudis oculis discernantur) sed an Instrumenta ab omni parte correcte commonstrent, an pinnacidia Telescopica Instru­mentis toties ad quasvis observationes rite imponi & tuto conser­vari queant; de quibus quidem id omni tempore aequè praecise fieri posse valde dubito. Quare Clarissimos illos-viros humanissime roga­tos volo nisi jam possideant ejusmodi vastissima organa utpote sext. octant & quadrant. Azim. Dioptris Telescopicis munita, ea (que) cae­lo continuo admoneant, suspendant judicium paululum, donec longa annorum serie experti fuerint haud fuisse multoties egregie elusos. Nam ex una alterave observatione quadrant. aliquo leviori perpen­diculo gaudenti obtentâ, res haec non est decidenda, sed si quis per 10 & amplius annos assidue observaverint, tum ab ovo seriam stel­larum restitutionem per distantias susciperit, poterit quaedam cer­tiora in medium hac de re proferre. De reliquo satis mirari ne­queo, eas omnes qui ejusmodi Dioptris Telescopicis gaudent, non­dum locorum suorum, elevationem poli ubi degunt & observationes peragunt, quantum sciam recte & omnino praecise determinasse & stabilivisse. Hucus (que) enim ad aliquot minuta integra Parisiis ele­vatio poli nondum est definita, alii quippe eandem observationem 48.49′ alii 50′. alii 51′, alii 52′, alii 53′, alii 54′, 55′ imo am­pliorem adhuc statuerunt: sicuti legere est ex discertatione Petri Petiti de latitudine Lutetiae, sed nolo in his prolixius esse;ad obser­vationes ipsas provoco, tempus aliquando docebit quorum observati­ones universas accuratiores fuerint, si modo nonnulli censuram suam eo usq, rejicere possent. Nam video aliquos inter quos etiam Cl. Fl amstedit [...]s invenitur, prout ex Epistola ad Cassinum apparet, jam judicium de nostris qualibus observationibus tulisse, priusquam illas adhuc viderunt examinarunt vel quicquam de iis cognoverunt. Nolo quidem vanus esse rerum mearum jactator, nec unquam mihi imaginatus sum rem in omni isto negotio circa scilicet restitutionem ste llarum fixarum acu omnino tetigisse vel tangere posse. Sed hocce penitus mihi imaginor si totum istud negotium Dioptris Teles­copicis suscepissem, quod non solum plurimos annos examinibus tri­vissem, sed spe sine dubio varia via (de qua hic non est discerendi locus) cecidissem. Exinde gratulor mihi me ad eam sententiam non­dum transusse, ac me mea methodo universa perfecisse se quic quid [Page 41]praestitum Dei beneficio erit: an nibil amplius (ut putat Claris. Flamstedius) quam hactenus & quous (que) progressum fuerit, liberum erit cui (que) cum deinde viderit judicium suum exponere quinetiam integrum erit alium novum integrum catalogum super additis tot ac tot centenis nonis fixis, hactenus neglectis alia ratione construere. Verum nondum video an cura haec molestissima, taediosissima ac la­boriosissima, quae non nisi multorum annorum vigiliis suscipi & per­agi potest, aliquem adhuc serio tangat. Unam aut alteram stellam ope Telescopii vel Dioptrarum Telescopicarum, dum praecipuas ac majo­res fixas earum (que) intercapedines supponimus correctas ad debitum locum deducere, tum nonnunquam distantias nonnullas stellarum ca­pere haec ludicra sunt; sed omnes conjunctim secundum longum & latum restituere, tum ductu continuo singulis serenis diebus ac no­ctibus, tam altitudinum solarium quam reliquarum stellarum ob­servationibus operam dare, eas (que) orbi exponere ut pateat motuum harmonia at (que) Instrumentorum certitudo, hoc artis hoc laboris est. Quando observationes 20 vel 30 annorum spatio continuatas ab utra (que) parte aliquando habebimus, nimirum tam quae Dioptris Te­lescopicis quam quae solummodo nostris ex caelo deprompta sunt res omnino clarior erit. Interea quilibet fruatur suo ingenio, ac sua ratione pro libitu rem tentet. Honorificum nobis omnibus erit pro modulo nostro à Deo concesso, rei literariae incrementum varia via promovere.

To this Letter of Hevelius I have this to answer, That the Author neither hath, had, nor can have any experience, to shew Telescopical Sights not to be as good as the Common, or that they are less applicable to large Quadrants, Sextants, Octants, or Azimuth Quadrants, or to any other Quadrants furnished with Rules, and so fixt, that they cannot be easily inverted, or turned, then they are to Quadrants or Instru­ments of 3 or 4 foot Radius. Nor is his Reason against them of any validity, that no Observation can be made, without a repeated previous examination and rectification of the Sights, in which, says he, notwithstanding all the care and diligence, there is a Reason of failure and mistake. For first, I say, There is less need of rectifying the Instruments or Sights, af­ter they have been once adjusted, then of Instruments with Common Sights, all things being perfectly fixt, and so strong [Page 42]as not easily to be stirred or removed. I now begin to fear, that he hath not a true notion of the manner of performing the same, otherwise he would never have propounded such an Objection; and indeed he seems to say as much in the following words, Qua ratione examen illud omni tempore commode & sine magno temporis dispendio institui possit profecto nondum capio. Though I am very sorry that he should be so:for first, I thought I had about 9 years since, explain'd to him the way, when I ex­horted him by all means to the use thereof; at least if he had not understood it thereby, I should, upon his desire, have sent him a more ample and particular Description thereof, or have procured an Instrument of that kind made and fitted for him here. But I fear, he had been some ways or other pre­possest or prejudiced against them, before I writ first unto him concerning them, at least before he writ that Answer, which I have before printed in the 5 and 6 Pages, for there by it appears, that he was then of the same opinion he seems now to continue of. And whereas he thinks, that no tryal hath ever been made of Telescopical Sights, to a large Instrument of 6 or 9 foot, I do assure him, (and I mis-remember, if I did not then acquaint him with as much.) that I had then by me se­veral, and particularly one of Sr. Christopher Wren's inventi­on, furnished with two Perspective Sights of 6 foot long each, which I made use of for examining the motions of the Comet, in the year 1665. And if the same thing can be better done with a Quadrant of 6 inches Radius, then he can perform with one of 6 foot the common way, I think he might have con­cluded at least, that the same thing would be 10 times better done in one of 6 foot Radius, made after the same manner; of this, I am sure, I gave him then an account. Now it is not with these kinds of Instruments, as it is with Common Instru­ments, where 'tis not possible to make any better then one may be made of 3 foot Radius, because that is capable of Divisions, accurate enough to reach the power of the naked eye; but In­struments with Telescopical Sights, are capable to be made to distinguish minutes, seconds, nay single thirds, if they be pro­portionably augmented. Nor is there any need that a man must make 7 years tryal of an Instrument, before he can be cer­tain of the greater excellency thereof, for I can be as certain [Page 43]with 3 or 4 times viewing an Object through a Telescope, and with my naked eye, that I can see it better, and distinguish many more and much smaller parts in it through the Teles­cope, then I can with my naked eye, as I could be, supposing I had been viewing it 20 years together. But yet I must as­sure Hevelius, my experience hath not depended upon 3 or 4 tryals only; I cannot choose but wonder why he should be of that opinion, who hath not been less exercised in the use of the Telescope, then any at present in Europe: Possibly indeed his Telescopes were not altogether so good as now they are made, yet sure I am, he saw more with them then any one can see without them, as will sufficiently appear by his Phases of the Moon, Jupiter and Saturn. But I hope he will not won­der at me, though I do now venture to affirm, without staying 10 years or more to make Observations, that I can do more with a Quadrant, Sextant or Octant, of 1 foot Radius, fur­nished with Telescopical Sights and Screws, then can possibly be done with any other Instrument, furnished only with Com­mon Sights, though 10, 20, 30, nay threescore foot Radius; nor does it at all follow, that the Latitude of Paris is not yet exactly known, because Monsieur Petit was ignorant of it; but it rather shews, that Observations made with Common Sights, (such as I suppose Monsieur Petit's Instruments and others, before the publishing of his Book were) are no ways capable of certainty to a minute or two.

But I have done, and am sorry I have been forced to say so much in vindication of Telescopical Sights; and that in the doing thereof, I have been necessitated to take notice of the imperfections, that are the inseparable concomitants of In­struments made with Common Sights. Nor should I have pub­lished these my thoughts, had I not found them so highy de­cryed by a person of so great Authority, fearing that thereby other Observators might have been deterr'd from making any use of them, and so the further progress of Astronomy might have been hindred. Nor would I willingly be thought to de­pretiate or undervalue the Works and performances of a person, so highly meriting the thanks of all the learned World, both for his great and liberal expence, and for his vast pains, care and diligence, in the performing a Work so highly usefull to [Page 44]Astronomy and Navigation, and of such infinite tedium, trou­ble, labour and cost, to the undertaker. I do not in the least doubt, but that it will be a Work worthy so excellent a person, of perpetual esteem and fame, and much preferrable to any thing yet done of the like kind in the World, and that he hath gone as far as it was possible for humane industry to go with Instruments of that kind, and that his Instruments were as exact, and compleat, and fit for use, as such Instruments with Common Sights could be made, and that he hath calcula­ted them with all the skil and care imaginable, and deliver'd them with all the candor and integrity. But yet I would not have the World to look upon these as the bound or non ultra of humane industry, nor be perswaded from the use and im­provement of Telescopical Sights, nor from contriving other ways of dividing, fixing, managing and using Instruments for celestial Observations, then what are here prescribed by He­velius. For I can assure them, that I have my self thought of, and in small modules try'd some scores of ways, for perfecting Instruments for taking of Angles, Distances, Altitudes, Levels, and the like, very convenient and manageable, all of which may be used at Land, and some at Sea, and could describe 2 or 3 hundred sorts, each of which should be every whit as ac­curate as the largest of Hevelius here described, and some of them 40, 50, nay 60 times more accurate, and yet everyone differing one from another in some or other circumstantial and essential part. And that this may not seem altogether so strange, I will assure them, that I have contrived above 20 ways for dividing the Instrument, each of them as much di­stinct from each other as this of Hevelius, and that of Diago­nals, and yet every one capable of as great certainty and ex­actness at least, and some of them 100 times more. I have above a dozen several ways of adjusting the Perpendicularity or Horizontality of Instruments, all as exact as the common Per­pendicular, and some of them very much more, even to what accurateness shall be desired, and yet each of these very dif­fering one from another. I have as many differing kinds of Sights, for improving, directing, adjusting and ascertaining the Sight, some of which are applicable to some particular uses, but some for all, by means of which that part also may [Page 45]be improved to what accurateness is desired. I have various ways of fixing those Instruments, and appropriating them for this, that, or the other particular use. I have various mecha­nical ways for making and working the several parts of them with great expedition and certainty, which is a knowledge not less useful then the knowledge of the theory and use of them when made, there being so very few to be found in the World that can or will perform it. I have a mechanical way of cal­culating and performing Arithmetical operations, much quick­er and more certainly then can be done by the help of Loga­rithms, which compleats the whole business of measuring An­gles. These I mention, that I may excite the World to en­quire a little farther into the improvement of Sciences, and not think that either they or their predecessors have attained the utmost perfections of any one part of knowledge, and to throw off that lazy and pernitious principle, of being con­tented to know as much as their Fathers, Grandfathers, or great Grandfathers ever did, and to think they know enough, because they know somewhat more then the generality of the World besides: Reptat humi quicung; vult, Coelo restat itur, Coelo tentabimus ire. Let us see what the improvement of In­struments can produce.

And now to make my Reader some amends for his patience, I shall give a Specimen or two, of each of the several parts that belong to the perfecting of celestial Instruments: And this I shall do, in the Description of an Instrument for taking all manner of Angles and Distances in the Heavens, which if in­creased in bulk, is capable of as great accurateness, as the Air or Atmosphere will ever permit celestial Observations to be made. Its perfection consists in seven several particulars.

• 1. In the Sights, which are such as may be made to discover the minutest part discoverable in an Object, they do no ways strain the eye, and are fit for all Sights, whether short-sighted or old, &c.
• 2. In the Divisions, which are such as will distin­guish the Angle, as minutely as the Sights will distinguish the parts or Objects.
• 3. In the Sights, being so contrived, that with one glance of the eye, both the Objects though a Semi­circle distant, are at once distinguished and seen together.
• 4. In the method of setting it exactly perpendicular to a Se­cond, [Page 46]if need be.
• 5. In its fixation and motion, it being so fixed and moved, that if once set to the Objects, it continues to move along with them, so long as 'tis necessary to continue, or be very certain of any Observation.
• 6. In its not being difficult to be made and adjusted, and its not being without industry and design put out of order, and its being presently, and with all imaginable ease rectified and again adjusted.
• 7. In its not being very chargeable.

First, For the Sights, They are no other then plain Telescopes, made with two con­vex Glasses, an Object and an Eye-Glass, of what length and charge shall be thought most convenient, fixed into square Boxes or Tubes of Iron or Brass, and having cross Clews at the Focus, made with very sine Hair, or silk-Worms Clews. One of these is fixed upon the side of the moveable Bar or Plate of the Quadrant, the Object-Glass of which is next the Rim, and the Eye-Glass is next the Center. The other of these is fixed upon the side of the Quadrant by several Screws, and care is taken to keep it from bending or sagging. This Tube is made of twice the length of the former, and hath at each end an Object-Glass, each of them of the same length with the for­mer, and hath two Eye-Glasses in the middle, the manner of ordering which I shall shew by and by under the third head.

But first I shall explain the manner of fitting a Telescope for a Sight. Let a a b b in the 12th. Figure represent a Tube, in which let p represent the part toward the Object-Glass, whose Focus is at o, and let n represent the Eye-Glass, whose Focus also is at o, let s represent the point, where the eye being placed, the whole Eye-Glass n will be enlight­ned and fill'd with the Object, then make a small Tube about an inch in length, and of such bigness as it will just slide within the hollow of the Tube a a b b, and cross the Cavity of that strain two very fine Hairs or silk-Worms Clews, which may cross each other in the Center of the Cavity, by the means of which Box, the said crossing Clews or Hairs may be moved to and fro, till they are exactly placed in the very Focus both of the Object-Glass and Eye-Glass, for if they be not there, the moving of the eye to and fro over the hole at s, will make the Threads seem to move upon the Objects, but if they be exact­ly [Page 47]in both the aforesaid Focus's, the moving of the eye will not at all make the said Threads seem to move upon the Object, but they will appear as steady and fixt to the Object, as if they were strained and fastned to it. And though they are ex­ceeding small, even as small as the Web of a Spider or Silk-Worm, they will appear very big and distinct, and much plainer and bigger then a Thread in the Common Sights, at the further end thereof, will to the naked eye, though above 100, nay 1000 times the bigness, which at the first glance will sufficiently discover the vast advantage these kind of Sights have above the Common ones. Nor is this way of Sights at all confined, but may be made to distinguish the smallest part of the Object desirable, even the parts appearing to the naked eye, under the Angle of a single second or third of a Degree, which is some hundred of times more curious then the naked eye can distinguish, without the help of them, for the Teles­cope can be made longer, and the Eye-Glass can be made deep­er, and according as the Telescope is longer, and the Eye-Glass deeper, so will the Object appear bigger, and more mi­nute parts be distinguished, the power of the eye being in­creased proportionably to the length of the Object Glass, and the charge of the Eye-Glass, and the goodness of the both. Now as Sights this way made, are capable of the greatest accu­rateness desirable, so they are so appropriated to the eye, that they no ways strain it, for they may be so ordered, as to make all those parts that are to be distinguished, to appear to the eye under the Angle of 3 or 4 minutes, which most eyes are able well to distinguish, without using too much attention or straining to discover them. This is no small convenience, to one that is to make many Observations one after another, for the eye by too much attention is apt to be suddenly weary'd, and it doth very much harm and weaken the Sight, to endea­vour to distinguish parts so small, as appear to the eye under the Angle of a minute, very few eyes being able to reach it at all, and most others not without much difficulty and endea­vour. 'Tis further considerable upon this account, that 'tis fitted for all kinds of Sights: For a short-sighted person, the Eye-Glass may be made to slide a little nearer the Cross in the Focus; and for an old or decayed Sight, the Eye-Glass may be [Page 48]moved a little longer or further off from the said Cross or Fo­cus; for a dim Eye, the aperture of the Object-Glass may be augmented, and the Eye-Glass made shallower, or of a less charge; and for a weak, tender and curious Eye, the charge of the Eye-Glass may be augmented, and the aperture of the Object-Glass made less. And according to the several consti­tution of the Observators eyes, the manner of Sights may be ac­commodated, which the other Common Sights without the help of Glasses, are no ways capable of.

The second thing wherein the perfection of this Instrument consists, is the way of making the Divisions, which I think, is far beyond the Common way, both for the certainty and ease of making, and secondly, for the plainness and certainty of it, in being distinguished; nor is it capable of less accurateness for measuring, then the Sights are for distinguishing. And it excels all the Common ways of Division in these particulars:

• 1. That it is made certain and not by guess, we being not at all to depend upon the care, credit and diligence of the Instru­ment-maker, in dividing, graving or numbring his Divisions, for the same Screw makes it from end to end, as you will see by and by.
• 2. That the Divisions are not at all difficult to be di­stinguished, and there is no uncertainty in the Fabrick, nor can there be any reason of mistake, there being nothing to be looked after, but the Numbers expressed in Figures at large, sufficiently plain to any one that can read the Print of a large Church-Bible.

It excels the Common ways thirdly, upon the account of its Compendium; for whereas by Ticho's or He­velius's way, the Instrument must be made of 150 foot Radius at least, easily and certainly to discover and distinguish Se­conds, in this way it may be made to do it within the compass of 3 foot Radius. And whereas in either of their ways, even in an Instrument of 150 foot Radius, the Divisions are not easily distinguished and discover'd without the help of Glasses, in this way they are made so easie and plain, that a man cannot mistake, that is able by his naked eye to distinguish Decimals of an inch. Now that this is so, as I affirm, the Reader will easily understand, if he considers, first, that the bigness of a minute is hardly half an inch, in an Instrument of 150 foot Ra­dins, and consequently the bigness of a second is but [...]/120 of an [Page 49]inch, which to a good eye is but barely a visible point at the best advantage, and to most eyes is not distinguishable without much difficulty, and to very many not at all without the help of Glasses. Now though Hevelius pretends to be able to do much by the help of the new way of Nonnius, Vernier, or He­dreus, yet if he considers what I have now said, he will be of much another mind, a Radius of 10 foot being but a 15th. part of one of 150, and consequently every 120th. part of an inch, being no less then 15 whole Second. At least, I am sure, he will be convinced that his own is not true, if he look upon that Specimen of it which he hath printed in his Machina Coe­lestis, in the Plate T. with a moderately magnifying Glass, as I hinted to him before. He will further understand the truth of my Assertion, if he considers in the next place, that by the help of the Screw, I am able to make the bigness of a Minute as much as I please; for since in an Instrument of 5 foot Radi­us, a Degree is somewhat better then an inch, 'tis easie enough to understand, that there may be 30 Threads of a Screw in the length of an inch, and consequently there will be but 2 Mi­nutes to fill up the whole Circle of the Index-Plate, and conse­quently if the Circle be 7 inches Diameter, the Circumfe­rence will be almost 22 inches about, and consequently the bigness of a Minute not less then 11, and the bigness of a Se­cond not much less then the 5th. part of an inch. Now the Index-Plate e in the first and 11th. Figures, shews exactly the number of Revolutions, and the Hand 8 in the same Figures, shews the parts of a Revolution, and both these in Characters large and distinct enough; and therefore the certainty and truth of this Assertion cannot be further doubted.

The way then for these Divisions is this: Make a Frame of a Quadrant of hammer'd Iron, after the manner expressed in the first Figure, and in the Center hereof fix or raise a hollow Cy­linder, whose hollow may be about a 40th. part of its Radius, and whose convex part may be about a 30th; leave this stand­ing above the Plain of the Quadrant about 1/90 part of the Radi­us, let the out-side of this Cylinder be made as exactly round as 'tis possible to be turned or wrought, then make a Ruler or Plate, with a round hole in it at one end, turned, groun'd and fitted exactly about the above-mention'd Cylinder, and as [Page 50]long as you design the Telescope for the Sights of the Qua­drant, this by a Screw on the top thereof must be kept close and steady upon the said Cylindeer: Upon the end next the Limb is to be fitted a Socket or Frame with Screws, to carry the Screw-Frame steady and firm, according to the contrivance exprest in the first and 11 Figures; this Plate must be filed or bended at that part of it which touches the Limb of the Qua­drant, so as to lye obliquely to the Plain of the Quadrant, and to be parallel to the Plain of the Frame which carries the Screw, and upon the part beyond the Limb must be fixt with a Screw k, the Frame h h h, which carries of the Screw 9 9 9, and the Index Plate t t; the contrivance of this Frame h h, is to keep the Screw 9 9 9 close against, and very steady to the Limb of the Quadrant, and is moved to and fro upon the Limb of the Quadrant, b b b, by the help of the Screw turn­ing upon and against the edge of the Quadrant; and this Screw by reason of its distance from the center and eye, (the reason of the placing of which in that place you will understand by and by) being too far off to be reached by the hand, is turned by a small Rod of Iron, 0 0 0 in the first and 11 Fi­gures lying by the side of the Ruler or Plate, which hath a small Wheel q q, at the end next the Limb, by which the Screw is turn'd round with it, and hath a small Handle or Windle p p next the Center, by which it is made convenient to be so turned round. Upon the end of the above-mention'd Screw-Frame h h, is fixed a round Plate t t, which is divided into 1, 2, 3, 4, or 5 hundred equal parts, according as it is in bigness, and as it shall be thought convenient, which Divisi­ons are numbred and marked accordingly, serving to shew what part of a Revolution is made of the aforesaid Screw; for the end of the Screw 9 9 9 coming out through the middle thereof, and a Hand 8 being fastned upon the said end, every turn of the Screw doth make a Revolution of the Index upon the said Plate; and consequently the motion of the arm made by one turn of the Screw, is actually and sensibly divided into 1, 2, 3, 4, or 5 hundred equal parts, which is so exceeding exact, and withal so Mathematically and Mechanically true, that 'tis hardly to be equallized by any other way of proceed­ing. This Description will be much better understood by [Page 51]the Explication of the Figure, and the several parts there­of.

Let a a a a a, &c. represent the Frame of the Quadrant, consisting of 5 Bars, radiating from the Center, steadyed all of them by a Quadrantal Limb, and a straight subtending Chord Bar; this whole Frame is to be made of very good Iron, partly welded and partly sodered together with Brass; the breadth of the Bars may keep the same Proportions ex­press'd in the Figure, and the thickness may be about 180 part of the Radius in large Instruments. In the Center of this, out of the solid Bar, is to be raised a Cylinder, as d d, expressed above more plainly in the 2d. Figure; the out-side of this Cy­linder is to be turned and wrought, as Founders do their Stopcocks, as exactly as possibly it can be, and the end of the Iron Plate or moveable arm c c c c, shaped as is expressed in the 3d. and first Figure, must be bored and wrought upon it very well, so as they may turn exactly true, evenly and smoothly, without any manner of sticking or shaking, which a good Workman will easily perform. This arm being put on the Cylinder, is screwed down fast by the help of a Screw-Plate, expressed in the 4th. and first Figures by e e, which hath two notches in it f f, by means whereof a Handle g g in the 6th. Figure, doth readily screw and unscrew it, as there is occasion. Between this screw'd Plate and the hole of the Plate c c c c, is a thin Brass Plate, let on upon an 8 sided part of the Cylinder, that so the turning of the Plate c c c c, may not have any power to unscrew the Plate e e, which otherwise it is very apt to do. Why this Center is thus made, and a hole left in the middle thereof, you will shortly understand more plainly. Upon the Iron Limb of the Quadrant last menti­on'd, is screw'd and rivetted a Limb of fine Brass, first cast into that shape, and then very well hammer-hardned and filed, represented in the Figure by b b b b: This, as I said, by many holes drilled through the Iron and the Brass, is screw­ed and rivetted upon the iron Limb, so as about half an inch in a Quadrant of 5 foot Radius doth over-hang the iron Limb, and the ends thereof extend a considerable deal longer then the Quadrant, the reason and use of which you will by and by un­derstand, when I give the Description of the Screw-Frame. [Page 52]The edge of this Brass Limb must be, by the help of the Plate c c c c, and a File or Plain, cut very exactly round, to an­swer the Center of the Quadrant, and the upper side thereof must be plained exactly smooth and flat, upon which Plain-side the Loop-holed Plate c c c c must move, as is visible in the Figure. This Plate at i i must be wrenched or wreithed, so that the Plain thereof must stand parallel to the Plain of the Index-Frame, and by the wr [...]thing of it at i i, as aforesaid, there is room left for the Screw to lye obliquely, without the Screws touching the aforesaid Plate, or grating against it. The reason why I put the Screw obliquely to the Plain of the Quadrant is, that that part of the Thread which toucheth the edge of the Limb, may be exactly at right Angles, or perpen­dicular to that Plain, and consequently that the Teeth upon the said edge, may likewise be exactly cross or perpendicular also, and consequently that no bending of the Rule c c c c, (to the end of which the Frame of the Screw is fastned) may at all vary the Angle, nor any unequal thickness in the Limb of the Quadrant, but that the turning only of the Screw shall produce a variation, and that exactly proportionate to the number of Revolutions, and the parts thereof, shew'd by the Index.

The way to know exactly what the obliquity of the Screw ought to be, to make the Teeth upon the Limb perpendicu­lar, is to number how many Threads of the Screw there are in a known length, and what the Compass of the said Screw, or the Cylinder out of which it is made is, and multiplying the said Compass by the number of Revolutions into a Product, the Proportions of that Product to the known length, will give the obliquity of the Screw, the Product being the Radius, and the known length the Tangent of obliquity, thus; Sup­pose in the length of 4 inches, there be 83 Threads of the Screw, and that the Compass of the Cylinder of the Screw be ⌊92 Centesms of an inch, I multiply the ⌊92 by 83, the num­ber of Revolutions, and it giveth me 76⌊36, that is 76 inches, and 36 Centesms of an inch, making this Product the Radius, and the known length, viz. 4 inches, the Tangent of the ob­liquity of the Thread of the Screw to the Axis thereof, or of the Axis of the Screw to the Plain of the Quadrant. The de­monstration [Page 53]of this is so plain, that I need not insist upon it, for the length of the Thread of the Screw is the Secant, the Compass of the Cylinder is the Radius, and the bigness of the Thread, or the Distance between two Threads, is the Tangent, in a right angled Triangle, and the Screw is such a right ang­led Triangle, wound about a Cylinder, putting the Tangent thereof parallel to the Axis of the Cylinder, and consequent­ly in the Mechanical [...]ryal of these Proportions, the more Threads are taken to make that comparison or measurement, the more exact is the inclination found. The consideration of which doth plainly shew, how exact a way of Division this by the help of the Screw is, for the whole Quadrant is thereby resolved into one grand Diagonal, the same with Triangle, the length of the Thread upon the Compass of the Cylinder be­ing the Diagonal, and the Distance of the two ends of those Threads, in a Line parallel to the Axis, being the space to be divided by it, and consequently by augmenting the bigness or Compass of the Cylinder, and diminishing the Thread, you may augment the Diagonal in any Proportion assigned. Or by making the Hand or Index upon the end thereof, of double, treble, quadruple, decuple, &c. of the semi-Diameter of the Cylinder, out of which the Screw is made, you may dupli­cate, triplicate, quadruplicate, decuplicate, &c. the said length of the Diagonal, in Proportion to the space to be di­vided.

The next thing then to be described is the Screw-Frame, made of Iron, much of the shape represented by h h h, in the first and 11 Figures: This Frame, by the help of a Screw through the aforesaid Plate, whose head is expressed by the round head k, is fixed on to the long Plate from the center, and by the help of the Screw I, is forced and kept down very close, upon the edge of the Limb of the Quadrant; the Frame hath 4 Collers for the Screw-Pin to run against, which are in­deed but half Collers, serving only to keep the Screw steady; two of these are made with most care, marked with m m, in the 11th. Figure against m i, doth rest the Shoulder of the Screw-Pin 3, which is kept close home against it, by the Cy­linder g g, in the 10 and 11 Figures; the sharp Conical Point of this Screw 9 9, goeth into the Conical hole, at the [Page 54]end of the said Cylinder g g g. The shape of this Cylinder, and the Screw by which it is forced against the end of the Screw 99, is represented in the 10th. Figure; 7 in the 9th. Fi­gure represents the Conical Point; 3 the place lying against the Coller m i; 6 the Screw that moves upon the edge of the Limb of the Quadrant; 5 the Nut or Pinnion by which the Screw is turn'd by a Rod from the Center, exprest alone in the 8th. Figure, but the manner how it lyes in the Frame, is ex­prest by p p 0 0 0 in Fig. 1.0 0 0 representing the Rod; p p the Handle by which it is turned; q q the Nut or Pinnion that turneth the Pinnion 5 of the Screw; s r the Collers or Holes that hold it fast to the moveable Plate or arm of the Quadrant; s s representeth two small pieces that clip the edge of the Limb, and serve to keep the Screw-Frame steady and true in its oblique posture, and move equally on the Limb, by a strong springing of one side of it; t t representeth the Index-Plate, which is divided into what number of parts are thought neces­sary, 1, 2, 3, 4, or 5 hundred parts, according to the bigness of the Thread of the Screw at 6, a greater Thread requiring a more minute Division, and a smaller Thread requiring a more gross. These Divisions are pointed at by the Index 8 at the end of the Screw, and the number of Revolutions or Threads are marked on the Limb of the Quadrant, and pointed at by the Tongue e e, upon the which is fastned a small Pin f, serv­ing to carry a Lens over the Point of the Tongue, which maketh the number of Threads appear more plain and big: The manner of doing which upon the Frame of the Screw, is so easie, that I shall not spend more time in the Explication thereof, and the manner of making the whole Instrument, will be easie enough to any ingenious Workman; but if any person desire one of them to be made, without troubling himself to direct and oversee a Workman, he may imploy Mr. Tompion, a Watchmaker in Water-Lane near Fleetstreet; this person I re­commend, as having imploy'd him to make that which I have, whereby he hath seen and experienced the Difficulties that do occur therein, and finding him to be very careful and curious to observe and follow Directions, and to compleat and per­fect his Work, so as to make it accurate and fit for use.

By the help of these Indices, 'twill be easie and plain to see how many Revolutions of the Screw, and what parts of a Re­volution make a Quadrant of a Circle, and consequently 'twill be easie to make a small Table, which shall shew what parts of a Quadrant, divided into Degrees, Minutes and Seconds, will be designed by the Revolutions, and parts of the Revolutions of the Screw. As for instance, If I find that 1600 Revoluti­ons and ⌊912 make a Quadrant, then 17⌊788 Revolutions make a Degree, and ⌊296 Millesms of a Revolution make a Minute, and about 5 Millesms make a Second, thence 'twill be easie to find (if you observe) an Angle to contain 294⌊358, that is, 294 Revolutions, and 358 Millesms of a Revolution, that the Content of that Angle in Degreess, Minutes and Seconds, is 16 Degrees, 32 Minutes, and 47 Seconds, which is plain enough, and much less subject to mistake, then the common way made use of. I shall therefore proceed to

The third particular, wherein this Instrument excels all o­thers, and that, is, That one Observator with a single glance of his eye, at the same moment doth distinctly see, that both the Sights of the Instrument are exactly directed to the desired Points of the two Objects, and this, though they be removed by never so great an Angle, nay, though they are opposite to each other directly in a Line. This, I question not, will by all that know any thing of Instruments, or celestial Observations, be accounted one of the greatest helps to such Observations, that was ever found out. For whereas other Instruments re­quire two Observators, for taking a Distance in the Heavens, and Ticho generally made use of four, amongst which there was necessary so unanimous a concurrence in their readiness and certainty, that the failure of any one spoyl'd all the rest, and made the Observation become uncertain and of no use; and such Instruments as were contrived for one Observator, were accompany'd with so great difficulty, in the adjusting to both the Objects, being both in a continual and swift motion, and but one to be seen at once, that they were generally left off and dis-used, there being so vast a trouble and fatigue of looking now upon one, then upon another, by many repeated tryals, and so many new settings of the Instrument to the Objects in motion, before the Sights could be adjusted, besides the [Page 56]great uncertainty at the best, of several Minutes of truth In this way, the Observator has no farther trouble, then first, to set the Plain of the Quadrant in the Plain of the Objects, and by the Screw to move the arm of his Instrument, till he perceive both the Objects to touch each other, in those Points he would measure the Distance between. That this is so, he will easily perceive, when he understands the method of so adapting two Telescopes, that by looking in at one small hole in the side of one of them, he will be able to see both those Objects distinctly to which they are directed, how much soever separated. The way then of doing it is in short this.

Joyn them together at one end, by a hollow Joynt that has a hole through it, about ¾ of the hollow of the Tubes, prepare two square Tubes of Wood, Brass, Iron, &c. of what length you please, and directly against the Center of this hole in the Joynt, make a small hole, about the bigness of the blackest part or pupil of the eye, so as the eye looking in at that hole, may see perpendicularly into the lower Tube, then obliquely place two pieces of reflecting Metal, very well and truely po­lisht, so as to reflect the Axis of both those Tubes, perpendi­cular or at right Angles, which is by fixing the Plain of the Plates, inclined to the said Axis, in an Angle of 45 Degrees, let the upper reflex Plate reach from the upper side of the Tube, so low as to touch the Axis or middle of the Tube, and let the lower extend over the whole Tube, from the top to the bot­tom, and from one side to the other. These will be known to be duely placed, if looking in at the small hole against the Center of the Joynt, the two round holes of the Tube do ap­pear to the eye to coallesce into one, and that the eye sees di­rectly through the lengths of them both alike. Then into these Tubes fit two Telescopes, with convex Eye-Glasses, and cross Threads for Sights in their Foci, that they may be both of them at due distance from the eye, looking in at the side-hole, then opening those Tubes upon the said Joynt to any Angle, and looking in at the side hole, you shall plainly di­stinguish at once both the Objects, that are brought into the Tubes directly, and reflected up to the eye.

That this may be the plainer understood, I shall add a De­lineation thereof in plano.

Let a a b b in the 12th. Figure represent the upper Tube, and c c c c the lower Tube, and let d d represent that part of the Joynt, which belongs to the lower Tube, at one end, by which they are joyn'd together, and can be open'd in the manner of a Sector. Let i represent the hollow or center of this Joynt, which communicates the Cavities of the two Tubes. Let e e represent that part of the said Joynt which belongs to the upper Tube, being only a hole through the lower side, big enough to incompass the Cylinder d d of the lower Tube; and let r r represent a Plate screw'd or pinn'd on, to keep the parts of the Joynt together instead of rivetting, Let s re­present the hole in the side, by which the Eye h is to look in, and f the reflex Mettal in the upper Tube, reaching only half way the Tube, and g g the reflex Mettal in the under Tube, reaching over the whole Cavity; then will n o and p repre­sent the Eye-Glass, Sight-Threads, and Object-Glass of the upper Tube, and k l and m the same parts in the lower, and whatever Angle the Tubes make to each other, whilst they open upon the before-mention'd Joynt, the Eye h looking in at s, will see directly by the Axis of them both, and see the Sight-Threads distinctly crossing the Points of the Objects, whose Distances are to be measured.

These being thus explain'd, I suppose, it will be no diffi­cult matter for any man to conceive, how these may be apply'd to the above-described Quadrant; for 'tis but supposing c c, the upper side of the under Tube in this Figure, to represent a p a p, the fixt side arm of the Quadrant, and d d the Joynt of this, to represent d d the Joynt of the Quadrant, and b b the under side of the upper Tube, to represent c c c the move­able arm of the Quadrant, and applying two Tubes to these parts, and fitting them with reflecting Plates, Eye-Glasses, Sight-Threads, and Object-Glasses, at due Distances, the whole will be performed.

These Tubes thus fitted, will serve to take any Angle less then a Quadrant, to what exactness is desired, but for bigger Angles, the Contrivance must be somewhat varied, the De­scription of which I shall now add.

Let either of the two Tubes for the Sights, be made dou­ble the length of the other, that is, let it be as long behind the [Page 58]Center as before it, and make the Reflex-Glass, that it may be turned round, and reflect the Ray exactly backwards, as before it did forward, then fix into this other half of the Tube a Telescope-Sight, in all things fitted, adjusted, and like the other two, then adjust them, that they may look forwards and backwards in the same like, which being done, the Reader will easily understand how any Angle may be taken, even to the extent of two right ones: For 'tis plain enough, that the two Tubes I first described, apply'd to the Quadrant, will measure any Angle to a Quadrant or right Angle; and 'twill be as easie to understand, how by the help of the Reverse-Tube, any Angle between a Quadrant and two right Angles may be measured.

To make this a little plainer to the Reader, let c c c c c in the 12th. Figure represent the under Tube or fixed Sight, s the hole or Eye-cell, t r a round piece carrying the reflex Mettal g g; this is made to turn round, and the reflecting Mettal g g being fixed to it within the Tube, is carried round also with it. Let s i k l m x represent the Ray passing forwards by the Eye-Glass, Thread-Sight, and Object-Glass; then this round piece t r being turned and made r t, as in the 13th. Figure, is represented, and with it the reflecting Mettal g g, here marked q q, being turned also: the Line s q k l m y will represent the Ray reflected, and passing backwards by the reflex-Mettal q q, Eye-Glass k, Thread-Sight l, and Object-Glass y.

The measure of the Angle is found by the same Apparatus or Screw-Plate; for as much as the Screw-Plate would shew the Angle less then a Quadrant, if the fore-part of the Tube were used, by so much is the Angle more then a Quadrant, if the reverse or back part of the Tube be used; and the same reason of the accurateness and certainty for the one, is good for the other, without being lyable to any manner of Objection or In­convenience.

It remains therefore now only to shew, First, How these two Perspective or Telescope Sights, placed within the same Tube, may be made to look exactly forwards or backwards in the same Line. And secondly, How they shall be adjusted to the Telescope, fixt upon the moveable arm of the Quadrant, [Page 59]so as to know when the Division-Angle begins, and when they are open'd to a Quadrant, right Angle, or 90 Degrees; for unless these be ascertain'd, and fixt to as great a measure of ac­curateness, as the contrivance of the Screw is capable of divi­ding, or the Telescope-Sights are capable of distinguishing, or the Perpendicularity ascertain'd, all the pains, care, in­dustry, and curiosity, bestow'd about the other, are of no use.

First then, For fixing the Thread-Sights of the two Teles­copes within the same Tube, so as to look directly forward and backwards, care must be taken, that every one of the four Glasses, that is to say, the two Object-Glasses, and the two Eye-Glasses, must be so steadily and securely fixt into the Tube, that they cannot by any means be stirr'd or removed; the manner of doing which, I suppose, so exceeding easie, that I need not spend time in describing a way to do it. Next, Sufficient care must be taken of the stiffness of the Tubes, that they may not warp or bend. Thirdly, One of the Thread-Sights must be fixt as firmly and securely as the Glasses, and so, that the crossing of the Threads may be, as near as possible, in the Axis of the Object and Eye-Glass, the other Thread-Sight must be left free, till by several tryals it be found to stand ex­actly in the same Line with the first; the manner of doing which, I shall now describe.

There being two Threads which cross each other, the one Perpendicular and the other Horizontal, care must be taken, that both these lye exactly in the same Lines with the Horizon­tal and Perpendicular Threads in the other Sights; and in order thereunto, there must be two Frames of Brass, repre­sented in the 29 and 30 Figures of the 2d. Plate, of the big­ness of the hollow of the Tube; these must have groves made in the Tube fit to receive them, in which they may by the help of Screws be moved, and made to slide to and fro, as there is occasion, for their adjusting. Next, They must lye so close together, that the Hairs may touch each other. And thirdly, They must cross exactly in the Focus of the Object and Eye-Glass. One of these Frames must carry the Perpendicular Thread, and by a Screw in the side of the Tube, must be move­able to the right or left side, as there is occasion; the other [Page 60]Frame must carry the Horizontal Thread, and by a Screw in the top of the Tube, must be made to rise or fall in the Tube, as there is need. The Mechanical Fabrick of which is so easie, that, I hope, I need not spend time in the further De­scription thereof, but refer the Reader to the 29 and 30 Fi­gures.

These things being thus done, from the top of some Turret, or any other Station, where two opposite places at a conside­rable distance, as half a mile, or a mile or two, can be plainly seen, find out two Points, which, at the first looking through your Glasses, you find to be shewn out by the Crosses of the Thread-Sights, then note those Points very diligently, that you may be sure to find them and know them again, when you have removed the Glasses; this done, turn the ends of the Tube, and (if you were looking Eastwards and Westwards) turn that part towards the East which before looked West­wards, and vice versâ, and find out the two Points you saw in the former Observation, then directing that part that hath the fixt Threads, to the Point that was seen before by the move­able Threads, find out the other Point, which you will be sure to see within the compass of your Eye-Glass, and observe how far the cross Threads are now removed from it, either North­wards or Southwards, upwards or downwards, then, as near as you can, by your judgement half that Difference, and by the Screws move the Frames, that the Threads may stand in the middle between the two Points, then take notice again of the Points shewn by the Threads, and turn the Tube again: Do this so many times, till you find upon converting the Tubes, that you see the same Points to be marked by the Crosses of the Thread-Sights, with which end soever you look on them, and then the Tube will be exact and fit for use.

The reason of this adjusting will be sufficiently plain, to any one that shall consider the 14th. Figure: Where let v re­present the middle of the Tube t u b, or the place of the Eye, and let w represent the Object seen Westwards, and e the Object Eastwards, at the first view; then keeping the middle of the Tube exactly upon the same Point u, turn the end of the Tube t towards the East, and the end b towards the West, and find out first the Eastern Object e, and finding the [Page 61]other Cross to direct now to the Point p, and not to w, di­vide the Distance between the Point w, and the Point p, as exactly as you can, in half, which if you chance to hit exactly at first, it will be the middle Point m, but if you do not, but you rectifie it only to r, then by the next turning of your Tube you will find s, where you must again rectifie to half the Dif­ference between s and r; now the Difference being grown yet less, you will a 3d. or 4th. time set it so exactly, as to see the Points m and e, which lye in the straight Line with the Center of the double Tube.

The 4th. thing wherein this Quadrant exceeds the Common, is for its accurateness for taking Altitudes; and this is done by the help of a Water-Level, for adjusting the exact Perpendi­cularity thereof. This Level may be made and fixed so exact­ly, that any Observator may be sure of the Level of his Instru­ment to a Second or two. The Level it self is nothing but a short Tube of Glass, about 6 or 8 inches long, Hermetically sealed at each end, and filled with a Liquor that will not freeze nor grow foul with standing.

The Glass, as near as can be gotten, should be Cylindrical and straight, it being the better the nearer it be to a straight, provided it have a sensible bending or swelling in the middle, the gibbous part of which should be set upwards, and a pro­per Cell and Box made for it of Brass.

This Glass is to be filled almost full of distill'd Water, to which about a 3d. part of good Aqua-fortis or spirit of Niter hath been put, to keep the same from freezing, and also from growing foul, then carefully sealed up Hermetically, and pla­ced in its Box of Brass, and with hard Cement fixed into the same, which by Screws is fixed to that side of the Quadrant, that is to lye Horizontal.

The Brass Box being thus fixed to the right side of the long fixt Tube ap ap ap, and underneath the Quadrant, so as not to hinder the free movement of the arm c c c, as at x x; the next thing to be done, is by it to set the Quadrant truly Hori­zontal, which is thus performed.

Setting the side a p a p a p Horizontal, and the Limb of the Quadrant upwards, and looking in at the Center, take notice of two Objects in the Horizon opposite to each other, [Page 62]observe the limits of the bubble of Air on the top of the Li­quor, on each side of the middle of the Level, and make a mark, then turning the ends of the Quadrant, set it, till the ends of the bubble stand as in the former Observation; then look again at those Objects in the Horizon, and find what the difference is between these opposite Objects, and those in the former Observation; then halve the difference between them as near as you can, and by your eye set the Sights to the middle between them, by inclining the Quadrant, then by the Screw that rectifies the Level, set the Glass-Level so, that the ends of the bubble may be equally distant from the middle, and con­vert the Quadrant again, and see if the ends of the bubble standing at the same marks, the two opposite Telescope-Sights do see the same Objects, for if so, you are assured of the per­fect Horizontality of the Sights, upon the fixt arm of a p a p; but if you do not find it to direct to the same Objects, continue examining and converting, till you find it per­fect.

Now this way of Perpendicular being subject to the incon­venience of heat and cold, which doth rarifie and condense the Liquor, and consequently make the bubble of Air less or more, care must be taken, to mark all the varieties of those kinds of the bubble, that are caused by the degrees of heat and cold, which you may thus easily effect.

Reduce the Liquor in the Tube of the 24th. Figure, by the help of Ice and Salt, to as great a degree of cold as you can, then by the method newly directed, set the Quadrant Hori­zontal, and mark the two ends of the bubble with 44, then by gently applying heat to the ambient Air warm likewise the Water, and observe the expansion thereof at both its ends, and mark them on the Glass with the point of a Diamant, as 33. 22. 11. 00. which being done, it will be exceeding easie at any time, to adjust the Quadrant to any accurateness desi­red, by being careful to see, that the two ends of the bubble be proportionably extended, as to 00. 11, 22. 33. 44, &c. or to any intermediate space.

The Contrivance of fastening and adjusting this Level to the Quadrant or other Instrument, will be very easily understood, by the Delineation thereof in the 24th. Figure.

Let a a a a represent the Frame or Plate of Brass, which by four Screws d d d d, is fixed to the Tube, as before. This Plate hath 4 upright Cheeks, b b, c c, between which the Brass Box e e e e, (into which the Cylindrical Glass-Le­vel f f, is fixed with hard Cement) is held steady, without any manner of shaking. This Brass Box, at the end of it near the right hand, hath 2 Pevots, which are fitted exactly into 2 small holes in the Cheeks c c, and at the other end next the left hand, hath a small Screw-Pin g, which holds it down fast to the bottom Plate, and keeps it from rising out from between the Cheeks b b, which a very strong Spring lying underneath it, between the Plate a a, and the Box e e, would otherwise force it to do. By this Screw the Level is to be adjusted to the Sights of the Quadrant, by the way I just now described, and being once thus adjusted and fixed, 'tis not easily put out of order, without moving or altering the Screw g, which may easily be prevented by 100 Contrivances.

The Reason of the accurateness of this kind of Level, will be easily discover'd, if we consider, that the upper part of the Tube being very near to a straight Line, is consequently ei­ther a part of a Circle of a very great Radius, or of some ir­regular Curve, very near of the same nature with a Circle, as to this business of Levelling, and consequently a Degree of the same will be proportionably large, and the flexure of the Tube may be made of a Curve of so large a Radius, that every Se­cond of Inclination may cause a change in the Level of a very sensible length.

This can hardly be performed by the ordinary way of Plumbets, without hanging from a vast height, which is not practicably to be performed, without almost infinite trouble, expence and difficulty, and when done, can be of no use in the World, as any one will grant, that considers the vast Appa­ratus that is requisite to obviate the great unsteadiness of Buildings, the motion of the Air, and a multitude of other in­cumbrances.

Now the Curvature this way made may be a portion of a Sphere of 1000 foot Radius, or more, if it be desired, and consequently a Minute of the same will not be less then 20/100 of a foot, and every Second will be almost half a Centesm of a [Page 64]foot, which is sufficiently distinguishable to the naked eye. So if the Glass Cylinder be 9 inches long, it may contain two whole Minutes of such a Circle between f and f, and one be­tween 4 and 4, and consequently the said Glass may be set Ho­rizontal to the certainty of a Second, which is hardly to be ascertain'd any other way.

But there remains yet one great Difficulty, how to be able to make such a Curviture, for though the thing be true in the­ory, yet is it not without some trouble, put in practice. Ve­ry few Glass Canes are so conveniently bent, as is desirable, and 'tis as difficult to find them true straight.

To prevent this, If Glass Canes be used, there must be much care taken, and many tryals made, for the finding what pieces, and what side of those pieces will be most fit for this purpose, for our Glass-House Workmen know not yet a way, certainly to draw them of this or that curviture or straightness, nor are they easily ground into a straightness or curviture by the Glass­grinder afterwards, though that can be done with some troub­le. But diligence and tryal will quickly find some piece or other, that will be sufficiently exact for any tryal, among those which are only drawn at the Glass-House. I made use of one of another form, such as is described in the 25th. Figure, which I found to do exceeding well, the dark part represent­ing the Water, and the lighter part the Air. This was made of two Glasses, drawn in distinct Pipes at the Glass-House, but joyn'd together in the Lamp, and the upper part of the larger or under Tube, was incurvated with its convexity downwards, so that the Water touched the middle part, and the bubbles of Air at each end thereof, communicated toge­ther by the small Pipe above. I tryed also another way, by which I was more certain of the truth of the Curvity, and could make the Curvity of a greater Circle: This was by a long piece of a Looking-Glass-Plate, ground very smooth and polished, which by the help of Screws I bent upon the circu­lar edges of a brass prismatical Box, and cemented the same very tight, with hard and soft Cement; this Plate had a hol­low Channel ground in it the length thereof, which serv'd to keep the bubble in the middle. By this means, 'tis not diffi­cult to bend such a Plate, into the Curviture of a Circle of 50, [Page 65]60, 100, 1000 foot Radius, and the Brass Box can easily be made to fill or empty, as there shall be occasion for the use thereof, so that the Bubble may be at any time left, of what bigness shall be desired. It will be convenient also to varnish the in-side of this Brass Box with Lacker-Varnish, very thick and close, both to keep it from rust [...]ng, and also to preserve it from being corroded by Aqua fortis, whensoever there shall be occasion to put it in, for the cleansing he inward tarnish and foulness of the Glass-Plate. This Curvity of the upper side of the Level may be made, by grinding the under side of such a long Plate of Looking Glass, upon a Convex Glass-Tool of 50, 60, 100, 1000 foot Radius, and polishing the samé ac­cordingly of that Figure: The Curvity of the said Plate is ex­press'd in the 26th. Figure. Now what by this way may be done with Water and Bubbles of Air, the same may be done with the same Glasses turned upside-down, by the help of an exactly round and polisht Cylinder or Globule of Glass, Chry­stal, Cornelian, Agate, or other exceedingly hard and close Stone, after the manner represented in the 27th. Figure, for the Ball or Cylinder will naturally roll to the lowest part of the Concavity, and there stand. But in the doing of this, great care must be taken, that the Globule be exactly round and po­lisht, and that they Concavity of the Plate be as smooth and well polisht, and that they be both very clean and free from dust, otherwise the Cylinder or Globule will be apt to stand in a place where it should not, and consequently produce conside­rable errors.

And here I cannot omit to take notice of a very curious Le­vel, invented by Sr. Chr. Wren, for the taking the Horizon every way in a Circle. Which is done by a large Concave, ground and polisht on a very large Sphere, and the Limb of it ground and polisht on a flat, for by placing the same Horizon­tal, and rectifying it by a small quantity of Quick-silver, pour­ed into the Concavity thereof, 'twill be easie, by looking by the flat polisht Limb, to discover the true Horizon. The only inconvenience I find in it is, that the ☿ hath some kind of stick­ing to the Glass, but a small Chrystal Bowl, I suppose, may re­medy that inconvenience, and make it fit for use.

The 5th. thing wherein this Instrument is made to excell [Page 66]others, is in its easinesses to be adjusted to the Objects, and in this, that being once adjusted, the whole Instrument is so or­der'd, as that it will remain constant to those Objects, though they are moved. The want of this is so great an inconvenience, in all other Instruments hitherto made use of, that almost all Observations have been thereby vitiated. And Hevelius, to prevent and obviate this, hath found out many contrivances, but they are such, as though they do it in part, yet 'tis but in part, and that with much trouble and inconvenience. I need not spend time to shew, how many inconveniences his way by 4 several Hand-Screws, to be managed by 2 Observators at the least, is subject to; they are indeed so many and so great, that it was not without very good reason, that he so often appeals to experience, for the truth is, there was great need of long practice and much experience, to be able to make an Observa­tion in that way well, the removal of every one of those Screws, having an influence upon every one of the other, so as no Screw could be turn'd, but the whole Instrument was put out of its due situation, and both the Objects being continually in moti­on, the whole Instrument was to be rectifi'd every moment. There was therefore necessary so great a judgement and dexterity, to manage every one of those Screws, that without an acquired habitude and handiness by long practice and experience, no­thing could be done to any certainty, nay, not even to that lit­tle accurateness that the common Sights are able to reach. But this, though it were a very great unhappiness to Hevelius, that he was not furnished with better Contrivances, yet it no ways tends to his dispraise, for his most extraordinary and indefa­tigable care, pains and industry, is so much the more to be ad­mired, esteem'd and honour'd, and will be so much the more, by such as have by experience found the difficulty, of making any one Observation certain in that way.

But that he or any other, that hath a mind to make further Tryals and Observations, may be freed from this intollerable trouble and difficulty, I have thought of this following Instru­ment, by means whereof the Quadrant being once adjusted, and set to the Objects, will continue to be so, for as long a time as shall be desired, without at all requiring the help of any one hand of the Observator, though he be but one.

My way then in short is this: I make an Axis of very dry and strong Dram-Fir, of a bigness thick enough for its length, to desend it from bending; at the lower end of this, I fix into the middle of it, (well bound and hoop'd about with Iron) a Center or Point of Steel, very well turn'd, hardned and sharp, which is to move in a conical hole fit to receive it, of as good and well hardned Steel; at the other end of this Rod, I fix ano­ther piece of Steel into the middle thereof, that, immediately contiguous to the Wood, hath a Neck very well turn'd and hardned, a little tapering from the Wood outward, which is to be moved in a Collar fit for it, as I shall shew by and by; and at a convenient Distance from the said Neck, as at somewhat more then half the Radius of the Instrument, is made a Cylin­drical Neck, fitted with a Collar of Brass, with a Joynt, and other Apparatus, large enough to carry the Table and Instru­ment firm and true, without sliding or yielding in its Socker, after it be once set. This Axis by the Collar and conical hole below, I place parallel to the Axis, which by some tryals is ea­sily enough adjusted; about the Cylindrical Neck, at the up­per end of this Axis, is a Socket of Brass fastned with a Screw, which Socket claspeth in a Joynt, a short Arm, which hath at one end a Ball that is fitted into a Socket, that is fixed under the Table and Frame of the Quadrant, and at the other end a Counterpoise of Lead, to ballance the weight of the whole Ap­paratus, about the Quadrant, upon the middle Line of the long Axis, then the Table and Quadrant is rectifi'd, so as to lye in the Plain of the two celestial Objects, whether Planets or fixt Stars, and by the small Screws in the Sockets it is fixt in that Plain. What further adjusting is requisite, is done by the help of small Screws in the Quadiant it self, which are easi­ly enough conceiv'd without Description. The Table being adjusted to the Plain of the Objects, with the Quadrant on it, and all counterpois'd pretty near by the poises underneath the Table, and the fixed Sight directed to one of the said Ob­jects, the said Table and Instrument continues to be in that Plain, so long as is desired, without any father trouble to the Observer, though the Objects continually change their places, and the fixt Sight remains directed at one of the Objects, till the other can be found by the moveable Sight. To effect which [Page 68]motion of the Table and Instrument, a Watch-work is fitted to the Axis, so as to make it move round in the same time, with a diurnal revolution of the Earth, and consequently to keep even pace with the seeming motion of the fixt Stars; the manner of doing which is thus: About some part of the Axis, where 'tis most convenient for the Room in which 'tis to be used, six an Octant of a Wheel of 3 foot Radius, let the Rim of this be turn'd true to the Centers of the Axis, and cut the edge there of into 360 Teeth, there being so many half minutes of an hour in the 8th. part of a whole Revolution, though these minutes and hours which respect the fixt Stars, will be considerably short­er then the solar hours; then sit a Worm or Screw to these Teeth, that one revolution of the Worm being made in ½, a mi­nute may move one Tooth forward; the revolution of the Worm is adjusted by a circular Pendulum, which is carried round by a Flie, moved in the form of a one wheel'd Jack, from a swash toothed Wheel, fastned upon the shank of the Worm or Screw above-mention'd; the weight that carries round this Wheel must hang upon the shank of the Worm, and must be of about a 3d. or 4th. part of the weight of the Qua­drant and Table, that it may carry it round steadily and strong­ly; and the circular Pendulum must be so order'd, that the Ob­servator may at any time of his Observation either shorten or produce the length thereof, so as to make it move quicker or slower, as there shall be occasion, which is done, by sliding the hole upon which the Pendulum makes its conical motion, a little higher or lower, without listing up or letting down the Pendulum, or else by winding up the Thread of the Pendulum a little shorter, or letting it down a little longer, by the help of a Cylinder, above the hole or apex of the Cone, in which the Pendulum is moved.

This whole Contrivance will be somewhat better under­stood by a Delineation. Let a b then in the 15th. Figure re­present the Axis of Fir or Iron, c the conical Point at the bot­tom, d the conical center or hole in which it is to move, e the Collar above, in which the tapering Neck of the iron Par f is to be moved. The Axis of this is to be placed as exactly as may be, parallel to the Axis of the Earth: at the end or head of the Iron f g, is fitted a Socket b h, with a Screw 4, which [Page 69]will fix it to the head in any posture. This Socket hh in the 15 and 16 Figures, hath a large Joynt to be stiffned by a Screw 5, in which Joynt is moved a strong Bar of Iron, about 4 foot in length, to wit, 2 foot on each side of the Joynt, the one end 6 hath a large weight or counter poise of Lead 8, which serveth to counter ballance the whole weight of the Frame and Instru­ment upon the other, and can be screw'd either nearer to or farther from the Joynt, as there shall be occasion for poising; at the other end of the Iron is a large Ball of Iron 7, to which is fitted also a Socket of Brass 9, with a Screw to fix it and move it, as there shall be occasion. This Socket is fastned un­der the middle of a Table s s, upon the plain side of which the Quadrant is to lye. Upon some convenient part of this Axis is fixed an Octant or Sextant of a Circle, represented in the 15th. Figure edge-ways, and in the 17th. Figure broad­ways, by 3 3 ii, whose circular edge 3 3 is cut into Teeth, as before is directed; unto these is adjusted a Worm or Screw k, which is the Axis or Arbor of the Wheel PII; this Wheel is moved round by the weight x, whose Line is coiled round the Barrel u u, and with it it turneth round the Flie n n, by the help of a Screw m, fixed upon the Arbor o o, in the manner of the Flie of a one wheel'd Jack; this Flie moveth circularly the Pendulum p p, in the 15th. and 29th? Figures, which is shortned or lengthned, by slipping up and down the Cylin­der q q, the Thread of the Pendulum being fastned at r.

I shall not now spend any more time in the Explication of the making or contriving the circular Pendulum, reserving it for another opportunity and Discourse, wherein I shall shew several useful Contrivances and Inventions about the same, and particularly about this and some other Experiments of motion, which was the cause of the Invention thereof by me long since, in the year 65. Upon which occasion, I cannot but take no­tice of a Publication, made by Christianus Hugenius Zuliche­mius Const. F. in his Book call'd, Horologium Oscillatorium sive demotu Pendulorum ad Horologia aptato demonstrationes Geome tricae; containing a short Description of a circular Pendulum-with somewhat about the Explication of it, without naming, me at all, as concern'd therein, though I invented it, and brought it into use in the year 1665, and in the year 1666, I [Page 70]communicated it to the Royal Society, at their publick Meet­ings, both as to the Theory and Practick thereof, and did more particularly explain the Isocrone motion of the Ball of a Pen­dulum, in a parabolical Superficies, and the Geometrical and Mechanical way of making the same move in such a Superficies, by the help of a Paraboloeid, which I caused also to be made and shew'd before the same Society, upon several days of their publick Meeting, where besides many of the Society, were divers strangers of forreign parts. This many of the Royal So­ciety can bear me witness, and the publick Registers thereof do testifie and make appear, and I was told by Sr. Robert Mo­ray, that he did then write to Monsieur Zulichem concerning the same. But of this more hereafter, when I examine some other things in that Book, about finding the descent of heavy Bodies, and of finding the Longitude of places, and publish some more certain and practicable ways of doing them.

This puts me in mind of publishing an Invention, which I made and produced before the Royal Society, in the same year 1666, much about the same time that I produced the Theory and Experiment of the circular Pendulum compleat, which I call'd the perfection of Wheel-work, as being indeed founded on a principle capable of the greatest perfection can be imagined. It is in short, First, To make a piece of Wheel­work so, that both the Wheel and Pinnion, though of never so small a size, shall have as great a number of Teeth as shall be desired, and yet neither weaken the Work, nor make the Teeth so small, as not to be practicable by any ordinary Workman. Next, That the motion shall be so equally communicated from the Wheel to the Pinnion, that the Work being well made, there can be no inequality of force or motion communicated. Thirdly, That the Point of touching and bearing, shall be al­ways in the Line that joyns the 2 Centers together. Fourthly, That it shall have no manner of rubbing, nor be more difficult to be made then the common way of Wheel-work, save only that Workmen have not been accustomed to make it.

First then, If there be a certain number, and no more of Teeth required to be made in a small Wheel, them must the Wheel and Pinnion consist of several Plates or Wheels, lying one besides the other, in the manner they appear in the 20th. [Page 71]Figure. Where suppose it be required, that the Wheel shall have 1000 Teeth, and the Pinnion 100, and yet that the Teeth both of the Wheel and Pinnion have sufficient strength; take 10 Plates all of equal bigness and thickness, and by 2 or more Screws fix them firmly together, as if one Wheel, cut this Wheel into 100 Teeth, and compleat it, then fit the middle hole upon the round neck of an Arbor, then unscrew the Plates, and place them in such order, that the Teeth may gradually follow each other, much after the manner as is exprest in the 20th. Figure, (though it be there very ill exprest, by reason of the mistake and failure of the Graver) and with such steps, that the last Tooth of one Degree, may within one step answer to the first Tooth of the next Degree. I call the 10 Teeth comprehended within the lighter part, a b c d, or e f g h, or i k l m, a Degree of Teeth in steps, and d c f e, or h g k i, are Degrees of Notches between the Teeth, and the Tooth b c, which is the last to wards the right hand, should have been pla­ced within one step as low as e h, the first of the next Degree on the left side, (though it be much otherwise here graven) whence all the inequality in the touching, bearing or rubbing, in a Wheel-work thus well made, would be no more then what could be between the 2 next Teeth in one of the Degrees, which would be much less then a 10th. part, of what must necessarily happen in a Wheel of one Plate of 100 Teeth only.

Secondly, If it be desired, that the Wheel and Pinnion should have infinite Teeth, all the ends of the Teeth in the Degrees of the 20th. Figure, must by a Diagonal slope be filed off, and re­duced to a straight, as in the 21, which may indeed be best made by one Plate of a convenient thickness, which thickness must be more or less according to the bigness of the sloped Tooth. And this is to be always observed in the cutting there­of, (though it be otherwise and very falsly exprest in the 21 Figure) that the end of one slope Tooth on the one side, be full as forward as the beginning of the next Tooth on the other, that is, that the end b c of one Tooth on the right side, be full as low as e h, the beginning of the next Tooth on the left side, (though by the Gravers mistake it be here quite otherwise exprest.) I shall not spend more time in explicating the Pinni­ons, r s t u, r s t u, of the 20 and 21 Figures, which are to an­swer [Page 72]the Teeth of the Wheels, they being plain enough to any person a little versed in Mechanicks, and because the further and more full Explication of the form and reason of this and other Wheel-work, is comprised in another Discourse, which I may after wards publish.

But to proceed where I left at this Digression, to the finish­ing of the Description of the Instrument for moving the Qua­drant, so as alway to respect the Object. The conical hole, in which the end of the Axis is to move, may be made after the form expressed in the 18th. Figure, where a a a a represents an iron Frame screw'd fast to the Floor, b b b b the iron piece, containing the conical steel hole, c c c c 4 long Screws, by which the piece is moved and fixed in any part of the space, in­cluded within the Frame a a a a; this by a strong springing Frame underneath, is kept down close to the Superficies of the Floor, and cannot in any wise totter or shake. There is no great difficulty in the Contrivance, and therefore I shall pro­ceed.

In the next place then, having shew'd the way how to keep the Instrument, in the Plain of two Objects that are to be ob­serv'd, I shall shew, by what means a Quadrant may be kept always Perpendicular, and in the Azimuth of the celestial Ob­ject. And this I do, by a small addition to the former Con­trivance; that is, Let a b in the 22 Figure, represent the Axis described in the former Contrivance, accommodated with all the Contrivances of the moveable Center below, of the Clock-work of the circular Pendulum, to keep it moving equally round in the middle, and of the Collar e above. But unto the small Neck f must be joyn'd a semi-circular piece of Iron c d, with a Center-hole in each arm at c and d, to re­ceive the Pevots i i, of the circular piece of Iron x, in the 22 and 23 Figures; upon the second Floor o o, must be sted­fastly fixed a Bow or Frame of Iron h h, which must have a hole through it, exactly over the middle of the Plate x, this is to be a Collar for the Neck k, of a perpendicular Axis l k, which by means of a moveable Center fixed in the cieling, in which the Point l moves, may be exactly adjusted to a Per­pendicularity; to this Axis at right Angles is fixed a Frame m m, steadied by the Brakets or Braces n n; upon this Frame [Page 73]the fixed Sights of the Quadrant, are laid and adjusted to an exact Horizontality, and the Plain of the Quadrant being once adjusted to the Plain of the celestial Object, will by the circu­lar Pendulum moving the Axis a b, in an equal motion with that of the Object about the Axis of the Earth, be always kept in the Plain of the Object, whose Azimuth and Altitude is to be observed. Now the motion of the under or inclining Axis a b, is communicated to the perpendicular Axis l k, by means of the circular Plate x, in the 22 and 23 Figures, for the semi-circular Arms c d of the lower Axis, taking hold of the Points 11 of the Plate x, and the semi-circular Arms of the upper Axis, taking hold of the Points 22 of the said Plate, the perpendicular Axis is moved in a proportionate motion with the inclining Axis a b, which Proportion is Geometri­cally and strictly such as it ought to be, to keep the Plain of the Quadrant exactly in the Azimuth of the celestial Object, as any one never so little versed in Geometry, will easily find; and I shall hereafter more at large demonstrate, when I come to shew, what use I have made of this Joynt, for a universal In­strument for Dialling, for equalling of Time, for making the Hand of a Clock move in the Shadow of a Style, and for per­forming a multitude of other Mechanical Operations.

The next thing I have to explain, is the way of finding how many Revolutions of the Screw, and what parts of a Revoluti­on go to make a right Angle, or 90 Degrees upon the Quadrant. For the doing of which, I must, in a place where I can have a good Prospect for a semi-Circle, first direct both the Sights of the Telescopes directly at the same Object, and the same Point thereof, and then rectifie the Indices to o, or the beginning of the Divisions; then I turn the Screw, till as near as I can mea­sure with Compasses, the moveable Telescope hath moved a Quadrant, and through the three Telescopes take notice of three Points in the Horizon, that is to say, two Points exactly opposite one to another, in respect of the Center of the Qua­drant, and a third pretty near the middle between them, in the same respect, which I further adjust thus; I shew'd before how I rectifi'd the fixed Sights, so as to look exactly forwards and backwards, which being accordingly done, I observe the supposed right Angle, with the moveable Sight on the Quadrant, [Page 74]and with the Sight fixt on the Quadrant looking forwards, and note diligently the two Objects pointed at; then without moving the Screw, or moveable Arm upon the Quadrant, I find those Ob­jects through the moveable Sight, and the fixt Sight, looking back­wards, and directing one of the Sights exactly to one Point, I ob­serve, how much the other doth vary from the other Object, either by being within it or without it; then I half that Difference, as near as I can judge by my Sight, and move the moveable Sight by the help of the Screw, so as to respect the middle Point: Then I observe this second found Angle, by the fixt Sight looking forwards, and by the moveable Sight, and see whether there be any Difference, and if I find any, as near as possible, I adjust it again, to half this last Difference, and so continue to examine and adjust, till I am certain, that the Angles on each side of the moveable Tube, between the same and the Sights, looking for­wards and backwards, are equal to each other, and conse­quently are both right Angles, or Quadrants of a Circle. Which when I have found, I observe, by the Indices on the Screw-Plate and Limb, how many Revolutions, and what part of a Revolution, the Screw hath been turned to open that An­gle; this Number I set, as the Number answering to 90 De­grees, and dividing that Number into 90 equal parts, I have the Numbers that belong to every Degree, and dividing the common Difference between them into 60 parts, I find the Numbers answering to the Minutes of the Quadrant, and di­viding the common Difference between the Minutes into 60 parts, I easily make the Numbers answering to the Seconds; but these will be needless, for subducting the next Number, less then it in the Table from the Number observed, you have the Degree and Minute, and some Number perhaps over, which may presently be found by one small Table of the com­mon Differences of Seconds. See page 55.

Here methinks I hear some object possibly, That the Divisi­ons on the Quadrant, do not exactly correspond to the Divi­sions made on the Plate. I answer, That in part they do, and in part they do not. First, They concur, in that all the Di­visions made by whole Revolutions, shew exactly the same by the Indices, that they do upon the Quadrant. Secondly, I say, in part they do not, that is, the parts of any single Revo­lution, [Page 75]are not exactly and Mathematically the same pointed out by the Index, upon a Ring equally divided, that are made upon the Limb of the Quadrant. But yet, I say, they are sensibly equal even to the sense, assisted by a 60 foot Teles­cope, and consequently need no manner of rectification; but yet if any one will be so curious and nice, he may make the Divisions on the Index-Ring, according to the proportion of the Differences of the Tangents, that are subtended within half the compass of the distance of the two next Threads. As suppose in the above-mention'd instance, half the Distance of two Threads be the Tangent of three Minutes, or thereabout; if we examine any large Table of Natural Tangents, we shall find the Differences between the Minutes themselves, even till six Minutes, (which is much more then double three) doth not differ above one or two parts of a thousand thousand, which is 1000 times more nice, then our Sight, even with Glasses, can arrive to, much less then will be the difference between the Differences of the Seconds; and therefore it will be a niceness meerly notional, and of no use, and as such, ought to be omitted, and the plain and equal Divisions made use of, they being as to all sense true and perfect, and proper Divisions, though as to curiosity of Theory and Calculation, unequal.

Now I have done, possibly some may say, To what pur­pose all this curiosity? To which I answer, That though pos­sibly in many common cases 'tis of but little value, yet I con­ceive in general, that it is of infinite value, to any that shall de­sign to improve Geography, Astronomy, Navigation, Philoso­phy, Physicks, &c. And to instance in some particulars, I conceive,

First, That one use of this Instrument, may be for taking the exact Refraction of the Air, from the Horizon to the Ze­nith; by which we shall be able not only to rectifie all Ob­servations, and clear them from Refractions, which in some Observations, especially those of Parallax, is absolutely ne­cessary, but it may give us a new means to judge of the quali­ties and constitutions of the Air, as to the seasons of the year, and the temperature of the weather, which are to succeed. For 'tis most certain, that there is as great a variety in the re­fractive, [Page 76]of the Air, as there is in the heat and cold, gravity and levity, dryness and moisture, rarefaction and condensati­on thereof, and sometimes when none of those do seem at all to be sensibly alter'd, its refractiveness hath been very much va­ried, which change does seem to proceed from some alterati­ons in the upper Regions thereof, far removed from the Super­ficies of the Earth, and is sometimes many days in descending and fermenting, as it were deeper and deeper, into the lower Regions of the Air, before it descend so low as the bottom thereof next the Earth. But of this much more in another place.

A second use is for regulating the places of the fixt Stars, as to their Longitudes and Latitudes, and Distances from one ano­ther, especially those within the Zodiack, by which we shall in a short time be able to judge, whether those Bodies that we account so fixt and constant, do not vary their Positions one to another, which I have very good grounds to believe they do.

A third use of this Instrument, is for regulating the places of the Planets, by their Appulses to those fixt Stars, so that not only Astronomy will be perfected, but the Longitude of places upon the Earth, (a thing so highly advantageous for Trade and Navigation) will of consequence follow, which without such an Instrument as this, is in vain expected from the Heavens.

A fourth use of this may be for stating the exact Latitude of places to a Second, whereby we shall quickly know, whe­ther those Latitudes do vary, as well as the variation of the Loadstone, which hath been conjectur'd, not without some­what of probability, but is hardly to be determined, without some such accurate way of Tryal, as this Instrument is capable of performing.

A fifth use of it may be, for examining what influence the approach or recess of the other Planets have upon the Earth, as to its Periodical motion, and what influence the Earth hath upon them as to theirs; for I have good ground to believe, each of these to have influence upon one another, and to cause such motions, as have hitherto much confounded all Astrono­mical Hypotheses and Calculations: Of which I shall say more on another occasion.

A sixth use may be for measuring the quantity of a Degree upon the Earth; the best Experiment of that kind, that is yet publick to the World, is that of Mr. Norwood, made between London and York: But if we examine with what Instruments he made it, we shall find, that he was not certain in either of his Latitudes to a Minute, and consequently could not be certain of the quantity of the Earth, answering to his supposed mark to two miles, and consequently it could not be made the com­mon standard of all measure. But by the means of this Qua­drant, all Latitudes may be certainly taken to a Second, and consequently the error in 150 miles, cannot be more then the 30th. part of a mile, and consequently a foot, or yard, or rod, this way stated, cannot vary above a 6000 part of its length, which is sufficiently accurate for a universal and common standard of all measure and quantity, to which all other mea­sures in the World should be referr'd and proportioned. this was the occasion of the contriving and making thereof; His Sacred Majesty having commanded me to see that Experi­ment accurately performed, and to give Him a true Account thereof, which had been before this performed, had not my indisposition of health prevented.

A seventh use may be for measuring the Distance between two places, exactly in a straight Line. This it will perform to admiration, by the exactness of taking the Angles, if some length be exactly measured at the place that is to be the Ob­ject, insomuch that 'tis hardly possible, by any other means in the World, to come to that exactness, nay, though there were a continued Plain extended between the two places, whose Distances are to be found, and the same were carefully measu­red with Chains, Rods, or Wheels. By this means the Di­stance of a Ship on the Sea, can be found more exactly, then any other way whatsoever, by one or two Stations, and a multitude of Philosophical Tryals under this Head, which are not practicably to be done with any tolerable accurateness, by other ways.

An eight use may be for taking the exact Diameters of the Sun, Moon, and Planets, even to a Second, and the Distance of the smaller appearing Planets from the fixt Stars, near adjoyning. Now because for this Design, it may perhaps seem a little too [Page 78]cumbersom, and by reason of its short Tubes, somewhat too small, I have therefore contrived an Instrument of 6 times the length or radius, which will take in an Angle of about 5 De­grees, and yet take in the whole Angle by one glance of the eye, and determine the measure thereof to less then a Second. I have likewise invented and made a new Helioscope, by which the Body of the Sun may be look'd on as inoffensively to the eye; as a sheet of white Paper; of great use for such, as will make Physical Observations of that glorious Body. These I will in some ensuing Papers describe.

A ninth may be for exactly taking the Level, for the con­veyance of a River or Water from place to place; and under that Head of performing infinite of Philosophical Experiments, which can hardly be try'd by any other way in the World, about the Refractiveness of the Air near the Earth, whereby distant places sometimes appear, and sometimes disappear, under the Horizon. By this means also the Rotundity of the Earth may be truely found, vastly surpassing any thing per­formed by the best Levels yet known. To this we may add, the height of Hils, if their distance be known, or their di­stance, if their height be known.

I could have enlarged upon these, and have named divers others; but designing it only as an Answer to such, as may captiously put such a Question, I shall rather leave the plea­sure of finding them, to such as shall really seek them, to be as­sisted thereby in their own undertakings.

A DESCRIPTION OF HELIOSCOPES, And some other INSTRUMENTS.

THE necessary avocations of business, and the urgent importunity of some, for the speedy publication of my Animadversions, made me conclude them in the Eleventh sheet, without staying to Explicate several things which I designed to go along with them. But having now retrieved a little more of leasure, both for Delineation and Description, for a further elucidation of what I have said, I shall make it my third Attempt, to explain;

First, A Helioscope to look upon the body of the Sun, without any offence to the Observers eye.

Secondly, A way of shortning reflective and refractive Tele­scopes.

Thirdly, A way for using a Glass of any length, without mo­ving the Tube.

Fourthly, An Instrument for taking the Diameters of the Sun, Moon and Planets, or for taking any other Distances, to five or ten Degrees, to the certainty of a Second. Two of these I promised in the 78th. or last page of my Animadversions, and the other fall in as analogous to them.

Fifthly, An Instrument for describing all manner of Dials, by the tangent projection.

Sixthly, The uses thereof;

• 1. For adjusting the Hand of a Clock, so as to make it move in the shadow of a Dial, whose style is parallel to the Axis: Or,
• 2. In the Azimuth of any Celestial Body, that is, in the shadow of an upright, or any other way inclining Style, upon any plain.
• 3. For making a Hand move according to the true ae­quation of Time.
• 4. For making all manner of Elliptical Dials, in Mr. Foster's way, &c.
• 5. For communicating a circular motion in a Curve Line, without any shaking: And for divers other excellent purposes.

And first, For a HELIOSCOPE which shall so take off the brightness of the Sun, as that the weakest eye may look upon it, at any time, without the least offence. My contrivance is, By often reflecting the Rayes from the surfaces of black Glasses, which are grownd very exactly, flat, and very well polished so to diminish the Radiations, that at length they become as weak and faint as those of the Moon in the twilight, so that one may with ease, and very much pleasure, view, examine and describe the phase of the Sun, and the maculae and faculae thereof, if any such happen to appear when the Observation is made, and it gives a good opportunity of discovering them, before we have any advertisement thereof from others. The reason of which will be sufficiently plain to such as consider, how great a quantity of the rays of Light [Page 3]is lost by every reflection, and that every reflection doth duplicate, triplicate, quadruplicate, quintuplicate, &c. the first proportion of loss. For Instance:

Suppose I have a Helioscope made of an Object Glass, an Eye Glass, and four Reflecting Glasses, and that, by the first reflection, I lose ¾ of the Direct light, I affirm there will re­main but 1/256 part of the Direct rays of the Sun, which can fall upon the eye at the last, for if every reflection doth lose ¾ of its Rays, and reflect but ¼, and that quarter loseth ¾, and reflects only ¼ of its received Light, there will remain but 1/16 part of the whole, and if this sixteenth part loseth three quarters of its Rays, and reflects only a fourth, it will follow, the remainder will only be 1/64 part of the whole, and if that be once more reflected, the Ray will return but with 1/2 [...]6 part of its first light.

This, although it be obvious, and easie enough now it is known, yet I do not find that any Person hath yet had thoughts of applying it to this use. The generality of Observers have hitherto made use of, either some very opacous and thick Glasses next the Eye, whether of red, green, blew, or purple Glass; others have diminished the Radiation, by covering the Glasses with a very thick and close coat of the soot of a Lamp; others, by casting the figure upon a piece of white Paper, whence 'tis reflected to the eye; Others have contra­cted the Aperture into a less circle, and thereby let in less Light, and so make use of one single Ray instead of a pencil of Rayes; Others have expanded the figure of the Sun, by the help of Eye Glasses, into a circle of ten, twenty, or an hundred times its Diameter. But none of all these waies do come near this which I now describe by the help of three, four, or more Reflections, as any one upon trial will very plain­ly discover.

First, As to the coloured Glasses, I cannot at all approve of them, because they tinge the Rayes into the same colour, and consequently take off the truth of the appearance, as to Colour; besides, it superinduces a haziness and dimness upon the Figure, so that it doth not appear sharp and di­stinct. The same inconvenience is also produced by Monsieur Hugenius's way, of covering the Glass with the soot of a [Page 4]Lamp, though not to so great a degree. The Figure on paper, or a smooth white surface is not magnified enough, nor the difference of shadows so very distinct, though that doth very well, if the surface be very smooth, and the Object be magni­fied by a Hand Glass. That by the contracted Aperture is the worst of all, by reason of a certain propriety of Light not taken notice of yet by Optick Writers, the edges of Ob­jects seeming ragged, of which I have hinted somewhat in my Animadversions, pag. 35, and shall shortly say much more, the whole ground of Opticks depending thereon.

The way of expanding the figure of the Sun by the Eye Glass, to me seems the best of all the rest, but that is apt to vitiate the Figure, to super-induce somewhat of Colour, and doth not give the smallest distinctions of lights and shadows, without somewhat of colour, and somewhat of haziness and dimness.

The Glasses of this HELIOSCOPE may be made ei­ther by refracting or reflecting Spherical Glasses. The best way for taking in a large Angle, is, the using refracting Glasses, both for the Object and Eye Glasses; but the best way for taking in a small part, and for avoiding haziness, dimness, and colours, is, by Reflection, either in part, or in whole; that is, either to make the Object Glass only by way of Refle­ction, and the Eye Glass by that of Refraction, or, both the Object-glass and Eye Glass also by reflection, and to have no refraction at all. The several waies of doing which I have represented in the adjoyning Table, wherein I have expressed ten several waies of placing the several Glasses, so as to be fit for the use designed.

The first way represented in the first Figure, is, a sixty foot Object-Glass, contracted into a twelve foot Tube, by the help of four several Reflecting-plates placed between the Object-Glass and Eye-Glass. The Experiment of doing which, I produced and shewed before the Royal Society, at divers of their publick Meetings at Arundel house, in the year 1668, and it remains upon their Register.

This (as I then shewed) would be of exceeding great use in all manner of Perspectives and Telescopes, if we could find a good material that would make the Reflections very strong [Page 5]and full. And that would not be subject to lose its Figure, which all our specular Mettals are very apt to do; for, by it, 'twould be possible to contract the Tubes for long Glasses into very short lengths, and so make them of easie use and ma­nage.

This I attempted with several sorts of Mettal, made with ♃, ♀, ♂, Antimony and Arsenick, but most of these compound Mettals I found to be very spongy, and consequently in the last polish to receive, though a very glaring polish, yet such as did much confound the Object by a kind of haziness, espe­cially if Putty be used to glase it, and, for this purpose, Putty must not in any wise, that I yet know of, be used, it being so very apt to round off the edges of pores or scratches, which does much contribute to the haziness and confusion of the Ob­ject.

If I made use of Glasses foil'd with Quicksilver, which I found to give much the best reflection, yet I found this incon­venience, that a considerable part of the Ray was lost, by the double reflection at the unfoil'd superficies of the Glass. The first from the surface of the Glass before it entred; this, as it weakned the Ray, so mingling with the other reflection that came from the bottom, it created some kind of haziness and confusion, if the two superficies of the Glass were parallel, but if they were not parallel, it superinduced somewhat of Colour, unless it were helped by a contrary refraction in a second Reflecting-glass, after the manner of that which is de­lineated in the fifth Figure, where let a b represent the Object-Glass, c g the first Reflecting-plate, whose thinnest side is to c, and d θ the second Reflecting-plate, whose thinnest part is towards θ, which doth thereby take off the first Refraction of c g, and destroy the Colours superinduced by the first. The Ray also was weakned much more from the second reflection it suffered at the unfoil'd superficies of the Glass, from the reflection of the Air, or aether, which is much stronger than that of Glass, at its re-entring into the Air. Besides this, I find that the substance of most Glass is so imperfectly mixt, that there is in the very best much of veinyness and inequa­lity of Refraction in the parts thereof, and thence, though [Page 6]there were no visible vein appearing in the body of the Glass, and though both the surfaces thereof were very truly figured and polished, yet there was some kind of dimness superindu­ced upon the Objects, by the rays passing through those Glasses. But this was not in all, for I found some that did very well answer my expectation, and I am very apt to be­lieve, that if a pot of Glass were made on purpose, by a way I know, the body thereof might be made perfectly clear, uniform, and transparent, without blebs, veins, or sands, which, when I have leasure and opportunity I design to ex­perience farther. But this only by the by, in relation to the shortning the Tubes of Telescopes for the Moon, Planets, and other Objects, because it is not at all to our present purpose of making a Helioscope, where we make use only of the reflection of the first superficies of the Glass, and where our main aim and design is, the loss of the strength and brightness of the Rays, and not for preserving the strength and briskness of the Rays, or augmenting them. And therefore for this use, the best material I have yet met with, is, black Glass, black Marble, and Glass of Antimony. For these substances being very dark and opaque, do reflect but a very small part of the Raies that fall upon it, and none of those that penetrate into it, especially if they be thick; and being of a very hard and permanent substance, are capable of receiving a very curious and exact polish, and qualified sufficiently to retain and keep it, without receiving injury from the Air, or ordinary wiping.

But in the making of these Glasses for Long Telescopes, very great care and diligence must be used to make them of a true flat, and so much the more, by how much the nearer they are placed to the Object-Glass, and the further from the Eye-Glass; a little err our at a great distance from the eye being vastly mag­nified to the eye at that distance, whereas a greater becomes insensible, if it be near the eye. Let a b, in the first; represent a sixty foot Glass, whose focus is at o; let a c d e f o, and b g h i k o, represent the two side Rayes of the pencil of light, this Pencil, by the four Reflecting surfaces (γ η, δ θ, ε ι, ζ κ) is broken into five shorter lengths (η δ answering to c d, γ θ to g h, δ ε to d e, θ ι to h i, ε ζ to e f; and ι κ to i k, and [Page 7]lastly, ζ ο and κ ο to f o and k o) as will be sufficiently plain to any one that will but consider the Scheme.

By this way four fifths of the length of the Tube is taken away, which is the most that can be taken away by four Re­flections, every reflection running the whole length of the Tube, a lesser part of the length may be taken away in any proportion assigned, as in the second contrivance, described in the second Figure, two thirds are taken off, when the same Letters answer to the Object-Glass, Eye-Glass, the flexures of the side Rays of the Pencil, and the Reflecting-plates that make those flexures. The third and fourteenth Figures represent the Tube shortned by two or three reflections, and so serves to shorten the Tube by two thirds only. These are of use for a very strong Eye and with a small aperture of the Object-Glass, and when the Sun is near the Horizon, or its light is a little diminished, by a Fogg, thin Clouds, or the like.

If it be thought more convenient to have this long Tube to lie alwaies Horizontal, and consequently, that there should be no need of having a Pole or Engine to raise the Tube: It may be framed somewhat like that in the fourth Figure, where the same Letters answer to all the parts above-mentioned, or else like that in the sixth Figure, the Letters of both which being the same with the former, will easily explain them.

Now in all these, and 20 other contrivances of this nature; with one, two, three, or four Reflecting-plates which may be presently thought of, the sight is directed exactly at the Sun, so that there will be little difficulty of finding it after the Glasses are fixt to their due lengths and positions.

I explained also at the same time to the Royal Society, at their publick Meeting at Arundel-house, several other waies of facilitating the use of very long Glasses, for other Objects in the heaven, by the help of one Reflecting plate only, and that was by a Tube fixed, either perpendicularly, horizontally, or obliquely, for it mattered not whether as to the seeing the Object in any part of the Heaven, supposing other circum­stances hindred not, and the object could be as easily found as by the common Telescopes of the same length. But of these elsewhere.

These contrivances with four Reflections, may be made use [Page 8]of by such whose sight is weak, but such as can endure it somewhat brighter, and would see the parts more strong, may make use of one of three Reflections only, like that of Fig. 14. which doth best suit my eye.

Next, this Helioscope may be made by Reflection only, with­out any Refraction, and that may be done either in the man­ner of that in the seventh Figure, when a b represents a con­cave surface of a black Glass, whose focus is o, which, for In­stance, we will suppose at the distance of forty foot, c d repre­sents a clear plate of Glass of two flat surfaces, which are made not parallel but a little inclining, so as the reflection from that side which is furthest from the concave may be cast another way; and not fall at all upon the third Reflecting-plate [...] ζ, and because the wedg-like form of this transparent plate of Glass, c d, will cause a refraction, and consequently a coloration of the Ray; therefore there must be another wedg-like Plate exactly as may be like the former, which at some distance, as at m p, where the reflection will not come to fall upon the Plate, [...] ζ must be so fixed that the thinnest part of this may lie just upon the thickest part of c d, and the thickest of this over the thinnest of that, by which means both the false refle­ctions and refractions will be removed. From [...] ζ that Rays are reflected to γ θ, and from γ θ to o the focus, and so through the lens, z, to the eye x. This I take to be the best by Reflection; but it may be twenty other waies contrived, which I shall not now spend more time in describing, it being so easie a mat­ter from the consideration of these I have mentioned, to make an hundred other variations of the principle.

To this Helioscope may be fitted Instruments for measuring the Maculae, faculae, and Nebulae, visible in the body of the Sun, as also the spaces passed by them in a day, two, three, ten, &c. together with the variation of their Figures and Mag­nitudes; but the diameter of the body of the Sun will be bet­ter taken by the following Instrument. And by reason that it will be often necessary to draw their figures more exactly, the Engine that I have described in my Animadversions, in the 67, 68, and 69 pages, may be made use of to keep the Helioscope alwaies directed at the body of the Sun, which will be no small ease to an Observer, that is to delineate the figures on Paper. [Page 9]When the brightness and radiation of the Moon, Venus or Ju­piter, do somewhat offend the eye, they will presently lose their beards and look very distinct, if one reflection from glass be made use of in the Telescope.

Another Instrument I promised to describe, is, for taking any such Diameters transits, or distance to the certainty of a second Minute, by which more may be done for the finding the Parallax of the superiour Planets, and the Longitude on the Earth, then hath been ever yet done by all the Instru­ments that have been used in the World.

1. This is made exactly, in all particulars like the Qua­drant, as to its hollow centre, Screwd-limb, Screw-frame, and long Rod to turn the Screw from the Centre; and that the Screw-frame may be kept down the truer, upon the edge of the Limb, there should be made a small Arm to clasp behind the inward limb of the Instrument, after the manner represented in the 8th. Figure by w, by which means the Screw will be kept close, steady, and eaven to the outward edge of the Limb. The Letters in this 8th. Figure being the same with those of the 1 and 11th. Figures of the Animadver­sions, and representing the same parts, need no further expla­nation.

2. Instead of this Screw upon a circular Limb, a Screw may be made to move upon a straight Limb, or Ruler; the end of which must move upon Centres or Rowlers, the centres or axes of which Rowlers must be exactly in the same line, when both the Perspective-sights are adjusted to the same Ob­ject, and the divisions began. The same thing may be done by a straight Screw, in the manner of a pair of dividing Com­passes, where the same care must also be had, that the axes of the Rowlers must be exactly in the same line, and the sides of the Incompassing-screw, being made of steel, must be made to spring about the long Straight-screw; this long Screw must be made of steel of half an inch of diameter at least, if it be made 18 inches long, and 'twill be best to screw it with a small thred, otherwise it will be apt to be moved out of a straight by screwing a large thred; and the thred, whether greater or less, must be made by degrees with a pair of cutting-stocks, that may be set closer every time of screwing.

The manner of contriving the Centres and Sockets may be seen in the 12 and 13 Figures, where the 13 represents it in an end way Prospect, and the 12 in a lateral or side-Prospect; 1 is the Rowler of the upper Tube, and 2 of the under, 33 the Screws to fasten them in the holes, 44 the incompassing or Socket-screw which springeth close to the Cylinder 5, 6 the Cylinderical smooth Socket which guides the Cylindrical­screw, so as to make its Axis pass exactly over the center of the Rowler 22, and which, by means of a Ring 7 on the screw, keepeth the pointed-end thereof 8 against the stay or por­tance 9; 'tis not difficult how to make a Dividing-plate, and an Hand or Index thereunto, nor how it may be turned from the centre of the two Tubes by a long Rod, as in the 8th. Fi­gure; nor vvill it be difficult, after it is known by Observa­tion, how many Revolutions, and vvhat part of a Revolution answers to five whole degrees, to calculate a Table of Sub­tenses, which shall shew vvhat part thereof goeth to make the subtense of every Minute and Second of the said angle.

3. The same thing in the year 1665, I performed by a Rowler, rowling upon the limb of the Quadrant, by the help of two Wires vvhich vvere coyled about those Rowlers, and the ends thereof were fastned upon the limb of the Quadrant; for, by a large index on the end of this Rowler, I was able to move the arm of the Instrument to any fifth Second of the Qua­drant, vvith great ease and certainty.

I also at the same time made another Frame with a straight Screw, vvhich opened to five degrees only, vvith Tumbrels or Rowlers like a pair of dividing Compasses (after the same manner vvith this I have newly described, for taking Dia­meters or Distances to five degrees) and by the help of very curious Lines drawn upon a smooth Glass-plate, and Points very curiously made at every five degrees on the limb of the Quadrant, or Instrument on vvhich it vvas fixt, and the help of a very deep Plano convex lens, vvhose plain side vvas turned downwards towards the Plate, and the convex side towards the eye, the said Frame vvas moveable from five degrees to five degrees, upon the whole limb of the Quadrant or Instru­ment, by vvhich Instrument I could vvith great ease actu­ally and accurate divide an angle into every five Seconds, [Page 11]and consequently take any angle to the accurateness of sive Seconds; for, removing the Frame to the next division, less than the Angle desired, and then by the Glass, fixing one of the Arms that had the plate, exactly over the hole or point of division, by the Screw the remaining part of the Angle could be exactly measured.

As to the method of dividing any of these, the best vvay vvill be to measure upon some Plain 1000, 1500, or 2000 foot in length, by two Rods of twenty foot long a piece, or else by Wires strained vvith vveights, the vvay of which I shall shortly describe: Beginning from the very centre of the In­strument, and at the end thereof, to set up so many Deal­boards joyned to the end of each other in a streight line, or else to strain a pretty big Line, vvhich shall cut the measured line of distance from the center of the Instrument at Right­angles, and then by a Table of natural tangents, according to the distance from the centre of the Quadrant, put as Radius, to set and mark off upon those Boards or Lines the divisions of Degrees and Minutes, by Compasses or Rules, as exactly as may be, and mark them accordingly, that the Degrees may be distinguished very plainly from the Minutes: Then having ad­justed the Instrument, so as to see the beginning of those Divi­sions through both the Tubes at once, to set both the Indices to o, or the beginning of the divisions, then keeping the under­most of the two Tubes fixt to the same place, so as still to respect the same point or beginning of the Divisions upon the Boards or Line, by the help of the Rod to turn the Screw or Rowl, till you find the upper Tube to respect the first mi­nute, and then the first degree, and so till you see the last mi­nute of the five vvhole degrees, or vvhatever Angle else you design it to take in; then (for the first and third way) reckon how many vvhole Revolutions, and vvhat part of a Revolu­tion goeth to make up that vvhole Angle, and subdivide the same by a small Table into Minutes and Seconds, and you vvill presently find by the Trial, that you vvill be able to di­vide to a strange accurateness upon those Boards, by the help of your Tubes and Screw, even at the distance of 1000, 1500, or 2000 foot, and even almost to equalize the Divisions by your Compasses, when at the very Boards. And by this you [Page 12]may easily examine, whether your Instrument doth make the sub-divisions exactly or not, which will be a great confirma­tion of the certainty and truth of your Instrument. But for the second way, by streight Screws, the Table of Sub-divi­sion into degrees, minutes, and seconds, must be proportioned according to the length of Subtenses answering to the Radius, which is the distance of the centre of the Rowlers from the cen­tre of the Instrument.

Now, because in an Instrument of this bigness it will be somewhat troublesome to turn the whole Angle by the help of the Screw upon the Limb, vvhich I find also is somewhat troublesome in the Instrument of three foot Radius, vvhen the Angle is large, therefore for preventing of that trouble, and to be able immediately to open the Instrument to the Angle desired, or very near it. The Screw l (in the first Figure of my A­nimadv.) at the end of the moveable Arm, is made, by unscrew­ing, to draw off the long Screw from touching the threds on the Limb, which being done, the Arm is at liberty to be moved to any part of the Quadrant, when by returning the Screw l, the Screw-frame and Screw is brought down again to take hold of the Threds of the Limb of the Instrument. The on­ly care to be taken in this action, is, that neither the Index e e be at all moved out of its posture to the Index-frame h h, nor the Index 8 be moved at all about the rod of the Screw 999. It matters not at all though the Screw-rod 999 be turned round or moved, so as it be done by the Rod 000, and the handle thereof p p, or by the small handle x at the end of the Screw-rod, and that the Index 8 being very stiffly fixt to the said Rod, be moved round with it by the same motion, with­out varying its position to the Rod; for being again brought down by the return of the Screw l, to take hold of the Threds of the Limb, into which it must be steadily guided by hand, the Index e e will shew upon the Limb the number of Threds or Revolutions from the beginning, and the Index 8 will shew what part of a Revolution there is to be joyned to it.

I hope I shall not need to spend time to explicate, how the Centre of these Tubes are to be made, nor how the Glasses and Thred-sights are to be fixt, nor need I much to shew, how the Tubes may be stiffned to keep them from warping very [Page 13]much; A small matter of warping not creating any sensible errour, I am not much concerned to prevent.

If it be desired to make the Screw less, and only long e­nough to subtend one whole degree, which is enough in In­struments of fisty or sixty foot Radius, it may be done by a straight Screw very well, if care be used, which will very exactly take Diameters and Transits to a single Second.

Another thing I promised further to explain, was, the contrivance of the Arms and Joynt, mentioned in page 73, as a Universal Instrument for describing all manner of Dials. For adjusting the-Hand of a Clock, so as to make it move in the shadow of the Style of a Dial, that is, in the Plain of the right ascension of any Point, of the Ecliptick, or of the Heaven; or secondly, in the shadow of a perpendicular, or inelined Style: For dividing and describing all manner of Ellipses in any Ana­lematical projection; and also, For making all manner of Ellipti­cal Dials in Mr. Foster's way. For communicating a round motion through any irregularly bent way, without shaking or variation, and the like.

First, The Instrument for describing all manner of Dials by the Tangent projection, must be made in this manner, described in the 11th. Figure, in which there are two Axes or rods of Wire that are joyned together by a Joynt, which from the applicability of it to, and fitness for all kinds of motions and flexures, I call a Universal Joynt. One of these Rods b b, is, by the help of a Frame a a, placed perpendicularly over the centre of the Dial, the sharp or pointed end thereof c being sunk into the Centre, about which it is to be moved ac­cording as it shall be guided by the motion of the second Rod or Axis d d. This second Rod or Axis, is, by its Frame, to be moved and set so as to be parallel to the Axis of the World; then the Hand e e of this last being turned to the hour of Twelve on the Plate f f, the Hand of the first g g will point out upon the Dial-plain, the Meridian or Twelve of Clock Line.

And so for describing any manner of Dial, you have no­thing to do but to find the Substile, and the altitude of the Stile above the Plain, and to put the Axis in its due scituation accordingly, that is, parallel to the Axis of the Earth, and [Page 14]then by the Plumbet at the end thereof to rectifie the Meri­dian or Twelve of clock point: For then, by turning round the Axis or Rod d d by the handle, till you see the Index e e on the Axis to point at those Hours, halfs, quarters, or minutes you have a mind to take notice of in your Dial; by the second Index g g, you are directed to the true corresponding point in the Plain of the Dial it self. But in such Dials as are in or near a Polar-plain, it will be convenient to make use of a small Thred to extend from the Cross, till it touch the Plain in the several hours, halfs, quarters, minutes, &c. The Arms of the Joynt in this Operation are to be so fixed, that the axis of the Plate may cross the axis of the Rod at right An­gles.

The Universal Joynt for all these manner of Operations, having not had time to describe the last Exercise, I shall now more particularly explain. It consisteth then of five several parts, each of which I shall describe in the 9 and 10 Fig.

The two first parts are, the Rods and Axes A and B, on which the Semicircular Arms are fastned, which are to be joyned together so, as that the motion of the one may commu­nicate a motion to the other according to a proportion, which, for distinctions sake, I call Elliptical or Ob­lique.

The two next parts are, the two Semicircular Arms C C and D D, which are fastned to the ends of those Rods, which serve to take hold of the four Points of the Ball, Circle, Me­dium, or Cross in the middle, X; each of these pair of Arms have two Centre-holes into which the sharp ends of the Me­dium are put, and by which the Elliptical or oblique pro­portion of Motion, is steadily, exactly, and most easily com­municated from the one Rod or Axis to the other. These Centre-holes I call the Hands.

The fifth and last thing, is, the Ball, Round-plate, Cross, or Medium X in the middle, taken hold of by the hands both of one and the other pair of Semicircular Arms, which, for distinctions sake, I henceforth call the Medium, and the two Points 11, taken hold of by the Hands of the Axis, I call the Points, and the other two Points 22, taken hold of by the second pair of Arms, I call the Pivots.

First, for the Rods, they may be made of what bigness you think fit, according to the use for which you design the In­strument. The only care to be taken in the making of them, is, first that they may be exactly Cylindrical in those parts that move in Collers, and secondly, that the Axis or middle line of them do cut each other exactly in one point, which point must not vary upon any alteration or change of the Joynt by bending the angle they make with each other, more or less, nor with the inclination of the Semicircular-arms to any de­sired obliquity, nor with the rotation or turning round of the whole Instrument. They require therefore a very dexte­rous, and a very knowing Artist, to make them as they ought to be, to perform their motion with exactness. Let a b then represent one of those Rods, and c d a second, which are turned exactly cylindrical within the Collers e f g and h, and these Collers are so disposed and fixed on some frame, that the middle line or axis of both these Cylinders may cut each o­ther in the point e; if then both their necks and collers be wrought true and exact, the Axis or middle lines of them will alwaies cut each other in the same point, howsoever they be turned round within their Collers; nor must this point i be varied, howsoever those two Axes are inclined to each other, so that though c d be inflected to l m, or n o, and so make either an obtuser or acuter Angle, yet the point i must be the centre of the Medium, where both the Axes concur and cut each other.

Secondly, The Semicircular-arms may be made of what bigness, thickness, or strength, the occasion for which they are designed shall require; that is, if they are only to carry the Hand of a Clock in the shadow of a Common Dial, whether made after the Orthographical, Stereographical, or Horological projection; or if they are by an Annual motion to shew the motion of the Sun in the Ecliptick, or the aequation of Time, a very small strength is sufficient; but if they are for carrying round a great Quadrant, such as that I have heretofore de­scribed, there they must be made stronger and more substan­tial. Care also must be had, that the inclining the Arms to any angle may not vary the centre of the Ball or Cross out of the point, where the two Axes cut each other. Both these [Page 16]Arms are to be made so as to be inclined to any angle; that is, that the Axis of the Medium, taken hold of by the Arms of Iron, may be made to incline to the axis of the Rod, on which they are in any angle desired, and being set to that Angle, to be steadily fixed, which may be done by a pin, screw or wedge; the way I make use of for the Azimuth-Instrument, described in the 73 p. of my Animadversions, is this which is delineated and explained in the 9th. Fig., where G re­presents a socket of Brass, movable cylindrically round about the end or neck B, of the Axis or Rod B B, the same with a b, in the 22 Fig. of my Animadversions, and fixable in any posture desired, by help of a side-Screw h, such as is very commonly made use of for most Instruments that are fixed upon the end of a three legg'd Staff, and is commonly called a Cylinder and Socket; this Socket of Brass hath a small Rod of Iron, k, fixed in­to it at k, which is near the middle of its concave part, through this Rod there is made a small eye or hole, and through that hole a wedge-like pin m being thrust, serves to keep the Semi­circular Iron-arms C C, steady and fixed in any posture they shall be rectified to. The Semicircular-arms C C, are to be made of very good Iron, or rather Steel, and to have a chan­nel or grove quite through the middle of one of them, and extending the whole length of a quadrant of a Circle, namely from n to o, because, according to the variety of occasions, it may be varied to any point between n and o; and 'tis to be observed, that the Iron-rod k must be so far fixed out of the axis of the Socket g, as n is distant from i, or o from p the middle of the Iron-arms between i and i, that so when there is occasion, the Centre-hole or hands i may be moved to p and fastned. At q must be made a Joynt in the Semicircular-arms, so that when the end n of the Arms is fixed in or near k, the other arm C may fall back from the point i, otherwise the circular motion, in many cases, cannot be continued quite round, and communicated from one Rod to the other, by help of the Me­dium or Plate x. The several pieces of this Joynt, as they are apart and distinct, you may see in the 9th. Figure, and as they are joyned all together sit for motion you may see in the tenth Figure, to which also the description of every part is ad­joyned in words referred to by the help of Literal marks, [Page 17]I hope, will make it sufficiently plain to any Artist to understand.

Thirdly, The medium Ball or Cross X, must be made of a bigness suitable to the Arms and Cylinders, and great care must be had that all the ends, points, or handles, lie exactly in the same plain, and that they be all equally distant from their Center, at least, that any two opposite ones be so made, because it is not absolutely necessary that they should be so all four, though in most cases it be best; and farther, the Handles or Pivots ought to be exactly round, conical, or cylindrical, and the middle lines of them to cut each other at right angles, or upon a square; and in general, that all things about the said Joynt be so contrived and wrought that the Axis of the two Rods may alwaies cut each other in the centre of the medium Cross or Plate, and that the said Centre, whatever change happens to the Joynt, may alwaies keep exactly in the same very point, without any alteration.

The shape of this Medium may be either, a Cross whose four ends hath each of them a Cylinder, which is the weakest way, 'tis described in the 9 and 10th. Figures by the Cross X; or secondly, it may be made of a thick plate of Brass, upon the edge of which are fixed four Pivots, which serve for the handles of the Iron-arms to take hold of; this is much better than the former, but hath not that strength and steadi­ness that a large Ball hath, which is the way I most approve of, as being strong, steady, and handsome; these are deline­ated in the aforesaid Figures, by X x, and X x x.

If it be an Elliptical Dial to be described by the Ortho­graphical projection, the former way for describing Tangent Dials, gives the lines that divide the Ellipsis of the Equinox in its true proportions: and if you would have the Lines that divide the Ellipsis of either Tropick, or of any other pa­rallel Circle, you must rectifie the Semicircular Arms C C of the Axis B B, to the degree of the declination of that Paral­lel, and them proceeding as before, you have the Lines which from the aforesaid Circle divide the Ellipsis of that Parallel accordingly. Perpendiculars also, let fall from the ends of the Cross 11, give the true Ellipsis in the Orthographical projection answering to that Parallel.

These Lines thus found, are the true azimuth Lines of the points or divisions of that Parallel, and are this way traced out exactly, without any trouble of Calculation, which for some purposes, in Surveying, Navigation, &c. are of very great use, as I shall afterwards shew.

The Universality of this Contrivance, for resolving almost all Spherical Questions, makes it of very great use in Navi­gation, if it be adapted as it ought to be, especially for the Common Sea-mans use, who, with a very few Rules, will be able immediately to find the hour, and azimuth of any point in the Heaven, sufficiently accurate for most Observations that can be made at Sea; of which more hereafter.

For making the Hand or Index of a Clock move in the sha­dow of the Style, made upon the Face of the Dial, and ex­posed to the Sun, this Joynt, being made to joyn the arbor of the Wheel that goeth round in twenty four hours, with the arbor of the hand, performeth it without any other Wheel or Pinion in the Dial or Face part of the Clock; if the Arbor of the Clock that should have carried the Hand round in twenty four hours, be made to have the same inclination to the plain of the Dial that the Axis hath, whether parallel to the Axis or not, it matters not at all, so that the Hand be rectified accordingly as it ought to be, and that the Style of the Dial ariseth from the centre of the Dial, out-through which the Arbor is produced for carrying the Hand, and placed in its Parallel respect to the Axis, as it ought to be for a Tangent Dial. For the shadow-Line of the Axis upon the plain of the Dial, being alwaies carried round the centre of a Dial in a plain, which passeth through the Axis or Style, and maketh equal progressions about it in equal spaces of Time, and unequal pro­gressions upon the Dial-plain, according to the proportion of Inclination, and the whole Revolution being performed in twenty four hours, and the Hand of the Clock upon the Face of the Dial being alwaies moved in a plain which passeth through the Arbor of the Clock, and maketh equal pro­gressions in equal spaces about the said Arbor, but unequal progression about the Centre of the Dial, according to the differing Inclinations: And those Inclinations being both in the Sun-Dial and Clock-Dial the same, it will follow, that the [Page 19]Hand of the Clock must alwaies move in the shadow of the Style, if the Hand be once rectified to the true Plain, and the Axis or Arbor make its Revolution as it ought to do in twenty four hours.

If it be further desired, for the ease of taking Azimuths and Altitudes, that the Arm of the Azimuth quadrant that is once adjusted to the Coelestial Object, should, by the aforesaid Joynt or Instrument, be kept alwaies respecting and follow­ing the said Object in its Diurnal motion, it may be very easily performed by the help of a small perpendicular Ruler, whose lower end is Joynted into either of the Arms 11, of the cir­cular Plate X, in the 22 and 23d. Figure of my Animadver­sions, and the upper end joynted into the movable Arm, at the same distance from the Centre of the Quadrant that the lower end is from the centre of the Plate X, and that the centre of the Quadrant be set exactly perpendicular over the centre of X; but then the divisions by the help of the Screw cannot be made use of, because the Clock-work it self is to turn and move the Arm: But it may be done by any Quadrant, where the minute Divisions are performed by the help of Diagonals. For the Arms of the Circular-plate 11 being alwaies moved in the superficies of the Cone described, by the radiation from the Coelestial Object to the centre of the Plate X, that is to say, the Line that passes through the Centre of the said Plate, and through the two Points 11, being alwaies directed to the Coelestial Object, if the Arm of the Quadrant be moved per­pendicular over it, and parallel to it, that also must be alwaies directed to it. And hence it may very easily be conceived, how the aforesaid Semicircular Arms may be readily and cer­tainly rectified to any Coelestial Object; that is, by fixing Te­lescopes or Common-sights upon the Circular-plate, so as the Axis of them may be parallel to the Line through 11, and loosing the Screw h to rectifie it to the Object by the sight, and then immediately to fix it in the said posture by the afore­said Screw; the Clock-work of the said Instrument having been before that put into motion. The reason of all which will easily appear to any one that throughly considers, that all Celestial Objects seem, by the diurnal motion of the Earth, to move equally from East to West about the Axis of it, and [Page 20]would all do exactly so, were they not somewhat varied by their own proper periodical revolutions, which though it doth indeed make a real difference between their velocities about the Axis of the Earth, yet that difference is but small; and the same circular Pendulum will serve both for the Sun, Moon, Planets, and Stars, if at least the Pendulum p, in the fifteenth Figure, be a little lengthened or shortened, by lifting up or letting down the Rod q q, in proportion as the Body k moves swifter or flower. And 'twill not be difficult to mark upon the Rod q q, the appropriated length of the Pendulum for the Sun, Moon, or Stars; but this only by the by.

If in the next place it be desired, that the Hand of the Clock should be alwaies carried round upon the face of the Clock, in the shadow of a Style perpendicular to that plain, by reason that the declination of the Sun daily varieth, the angles of the shadow about that Style varieth also, and con­sequently the inclination of the plate of the Joynt to the Axis or Arbor must vary also, and that variation must al­waies be the same with the variation of the declination of the Sun, which is twenty waies mechanically performable in Clock-work, so that the motion shall be performed by the Clock-work alone, without touching it with the hand. All the other directions that are requisite to adjust the Clock-work to such a Dial, is, only to make the Arbor of the Clock-work to have the same inclination to the plain of the Dial, that the Axis of the Earth, or a line paralel to it hath; and rectifying the Hand into the true plain of the Axis, or Inclined arbor, the equality of the motion of the Clock-work, according to the diurnal and annual motion of the Sun, we suppose also to be provided for.

If the Hand of the Clock be desired to be moved in the shadow of any other streight Style, howsoever inclined to the plain of the Dial, then must there be another Joynt like the former, added to the end of that Axis which was per­pendicular to the plain of the Dial, and all the three Axes must be scituate in respect of the Plain, in which the Hand on the end of the last is to move, that the inclination of the said Axes to each other, may represent the inclination of the Axis to the perpendicular axis of the Plain, and of [Page 21]that perpendicular Axis to the axis of the Style. Or, which is somewhat shorter, and may be made handsome enough, Let the two ends of the Hand represent the two points of the second circular Plate or Globe, extended long enough to reach to the hour Circle, then let the axis of this second Arm be placed in the axis of the inclined Style, and let the axis of equal motion, representing the axis of the diurnal motion of the Earth, be placed with such inclination to it, as the axis of the Earth hath to the oblique Axis or Style of the Dial, and the motion will be most exactly performed me­chanically, and according to the truth of Geometry and Cal­culation.

Now, in all these motions, care must be taken, to provide that the inclination of the declination of the Sun from the E­quinoctial, be exprest by the ends 11, in the 22 and 23 Figures of the second Plate of my Animadversions, of the Cross, taken hold of by the semicircular arms c d, upon the end of the first Axis; that is, that the said arms may, by their revo­lution, make the line of the Cross describe such a cone about the first Axis, as the motion of the Sun doth about the axis of the Earth, making the centre of the Earth the apex of that Cone; which will be done, if the said semicircular Arms be moved, and set to the declination of the Sun for that day. Or, that an additional motion be added to the first Axis, that the Clock it self may perform it. This may be done twenty waies easily enough, which I suppose will be suffi­ciently obvious to any knowing Mechanick, and that with­out the help of Tooth-wheels or Pinions, which in works of this nature are in no wise to be made use of, by reason of their shaking and uncertainty, which I shall elsewhere describe.

There is one only difficulty in this motion, and that is only in such Objects as pass over, or very near the Zenith or Nadir of the place, for in those cases, when the Object comes very near the Zenith, the obliquity of the motion of the one to the other is so very great, that the first Axis doth not move the second without some difficulty: But to remedy this, the expedient is as easie, and that is, by having a little barrel about the perpendicular Arm, to carry it forward as far and as fast as the first Inclined axis will permit it; which weight [Page 22]may be removed as soon as the Object is a little way past the Zenith.

The next use that may be made of this, is, for carrying the Hand of a Clock so, as alwaies to move over that point of the Ecliptick in which the Sun is, in a Stereographical projection of the Sphere upon the Plain of the Equinoctial, or in an Orthographical projection of the said Sphere upon the same Plain, so as to express thereby not only the differing right ascensions, but the anomaly also of the Suns motion in the excentrick of the Ecliptick. And by this means the Face of the Clock may be made by a Planispherical pro­jection, to represent the motion of all the Stars appearing in any Horizon that is not too near the Equinoctial, their Risings, settings, culminatings, azimuths, and almicauters; Risings and settings of the Sun, the lengths of the Days and Nights, and of the Twilights and Dawnings, and many other Problems of the Sphere. And, which is a consequent of this, it may be made to shew the equation of Time, which is ne­cessary to be made use of for setting a pendulum Clock by the Sun, the manner of doing which I must refer to another opportunity, as I must also the use of this Joynt, for draw­ing Ellipses, drilling and boring of bending Holes, for turning Elliptical and Swash-work, till I publish my description of a Turning Engine, capable to turn all manner of Conical Lines, and Conoeidical; all manner of Foliage and Flower-work, all variety of Basket or Breaded-work, all variety of Spiral and Helical-work, serving for the imitation of the various forms and carvings of all sorts of Shells; for cylindrical and conical Screws; all variety of Embossments and Statues; all variety of edged and Wheel-like work; all variety of Regularly shaped Bodies, whe­ther the five Regular bodies of Plato, or produced from those by various sections or additions, of which the variety is in­finite; all variety of bended Cylinders or Cones, and those whether round, in the manner of an Oxes-horn, or compres­sed and angular, like those of a Ram or Goat; for all manner of Swasht-work, Comprest-work, &c. every of which prin­cipal parts hath a vast variety, and the compound and decompound principles have a variety almost infinite.

LAMPAS: OR, A DESCRIPTION OF SOME Mechanical Improvements OF LAMPS.

THe Hypothesis of Fire and Flame I did about eleven years since publish in the 16. Observation Pag. 103, 104, and 105. of my Micrographia, which hath so far obtained, that many Au­thors have since made use of it, and asserted it; nor have I yet met with one considerable objection against it. It shall not therefore be my business at present to dis­course of, or farther explain that Theory, which any one upon a strict inquiry into, I question not, will find cause sufficient to confirm him in, but rather to mention some pleasant and beneficial uses thereof, and to hint some Mechanical contrivances for the supplying the Pabulum Oyl or Spirit by the same Degrees by which it is consumed in the flame of a Lamp, that great dissolvent.

I do not here design to shew a way how to make a per­petual Lamp, that being a Chimera which my Hypothe­sis of flame doth seem to destroy, for the dissolvend must in time be dissolved: But to shew a way how to make [Page 2]the Receptacle of a Lamp in such manner as that it shall continue to supply the Pabulum to the flame equally and for a very long time till it be all consumed. The con­sideration of which Problem first put me upon the en­quiry after a counterpoise for Liquors of Fluids, which is also of very great use in Hydraulicks, as I shall here­after have occasion to manifest.

This I can do by very many contrivances, depending from very differing Principles, all and every of which may be fitted so as to supply the Oyl or Pabulum of the Lamp in such quantity, and after such manner and pro­portion as shall be desired. I shall now omit all the other ways of performing this effect, though divers of them are as much or more considerable than any of these I here mention. And having promised in the 32 Page of my description of Helioscopes to publish a Counterpoise for Liquors, I shall only explain several ways by the help of these Counterpoises to do whatsoever can be required, as to the manner and quantity of supplying Oyl to the flame.

The chief design of the Counterpoise in this inquisiti­on is to keep the Superficies of the Liquor (whether Oyl, Spirit of Wine, Oyl of Turpentine, or the like) whatever quantity there be in the Vessel, always to the same height, so that the said Pabulum shall always be equally distant from the bottom of the flame, and the Wick or flame being once placed at a convenient height or distance above the Superficies of the Oyl, shall not be deserted by the said Superficies till the whole quantity be consumed; but it is as easie to contrive it, to supply it by decreasing or increasing degrees, which are conveniences that none of all the Lamps I have ever yet met with have had, that was tolerable for use. The most ingenious is that which is commonly known by the name of Car­dans Lamp, as being published and very probably inven­ted by Cardan, which doth in some manner supply the wasting and decay of the Oyl caused by the flames Con­sumption. But then it is subject to a great many incon­veniences, [Page 3]which make it intollerable and disused: The first is, though it doth supply the defects of the Oyl to the Wick, yet it doth it not constantly and equally, but by starts and gluts; for after the receptacle by the Wick is filled, the Superficies of the Oyl continues to sink by degrees a considerable space below the flame, before there be any more supply added from the great Magazine or Repository, and till the Air can break in, (which it doth very unequally) so that there sometimes comes down so great a quantity that the receptacle is over-filled, and the flame extinguished, and these gluts are more unequal the bigger the Magazine be in proportion to the Recep­tacle by the flame, and the more the quantity of the Oyl be that is suspended, and the more the Air space be above the Oyl, and the more tenacious or sluggish the constitution of the Oyl is.

The second inconvenience of Cardans Lamp is that the Air is apt to rarifie it with heat, so as sometimes to drive down so much Oyl as to overflow the receptacle, and choak the flame.

The third Inconvenience is, that the Wick by the sink­ing of the oyl doth sooner decay the flame, being sometimes a little higher and sometimes lower upon the Wick; for if the Wick rise up into the hollow dead part of the Cone of the flame, the streams and coals of the Oyl will be so caked together as to dead the flame and much to diminish the light and heat thereof, whereas if the Wick be but short, and suffered only to go but a very little within the under-Superficies of the flame, it will not be so stopped and caked with those feculencies. The reason of which is evident, for the flame, as I formerly proved, being nothing but the parts of the Oyl rarified and raised by heat into the form of a vapour, smoak, or steam, the free Air that incompasseth this steam keepeth it into a Cy­lindrical form, and by its dissolving property preyeth upon or dissolveth those parts of it that are outwards and next to the Air, so as by the said dissolution it continueth the heat, and produceth the light which we observe; but [Page 4]those parts of the body of steams that rise from the Wick; which are in the middle, and not contiguous to the out­ward Air, are not dissolved or turned into shining flame by the Air till they rise towards the top of the Cone of flame where the free Air can come to reach, and so to dis­solve them, and thence gathering about the Wick in the Center of the Cone of flame they choak, clog, and quite stifle it that the flame will quickly go out. That this is so, any one may easily find if he examine the flame of a Lamp or Candle by the help of a piece of glass: For by the transparency thereof he will plainly perceive that all the middle of the Cone of flame neither shines nor burns but only the outward Superficies thereof that is contiguous to the free and unsatiated Air, and that the middle parts may be collected in the form of Soot, or very fine powdered coal dust.

Take then a piece of Glass, whether Window-Glass, Looking-glass Plate, or the side of a Viol, it matters not, or, which is best of all, a thin Plate of Selenitis or Musco­via Talk, and hold it Horizontally in the middle of the flame, so as to cut off the top or upper part of the Cone thereof, then presently, before it be choaked with soot, look down upon it, and you shall plainly see that all the middle parts of the Flame and the Wick have no shining power or light at all; nor are they dissolved by the Air, but remain in the form of Soot, but that only the Super­ficies or outside of the said Cone doth burn, shine, and consume into and mix with the ambient Air.

In the same manner, if you hold the Glass or Selenitis perpendicularly, and apply the side of it so as to cut the flame per axin coni, that the Air cannot come to one side thereof, you may plainly perceive that the shining part of the flame is only that which is contiguous to, and preyed upon by the free and unsatiated Air, and that where that Air cannot come free without being glutted and satiated in its way, there neither the consumption of the Oyl, nor the heat and light of the flame is produced, but only a sooty, choaking, and stifling substance.

To make then the reason of the Phaenomena observa­ble about the lasting or stifling of the flame of a Lamp the more clear and easie to be understood and compre­hended, give me leave to explain the manner of its pro­duction and continuation by a Scheme, delineation, and description thereof.

Let A A then in the second Table represent a body of Oyl, or any other combustible fluid substance, the Superfi­cies whereof B B is Horizontal, and pretty near plain. [I say, pretty near, because it is always either Concave, or Convex, more or less according to several circumstances; to wit, the capacity and the nature of the Vessel E E, in which it is contained; for if the Vessel be small, and that the Oyl hath a greater congruity with it than the Air, the Superficies of the Oyl will be very much concavated especially towards the sides of the Vessel as at C C; but if the Vessel be incongruous to Oyl, the Superficies will be Convex as at D D, the reason of which I have long since explained in another place.]

Let F F then in the third figure represent the Wick, which consists of a great number of very fine Cylinders or hairs of Cotton f f f twisted and laid very close together, into, and between which the Oyl (having a very great congruity therewith) doth readily insinuate it self and ad­here, and is by the pressure of the Air (much greater without than between those Cylinders or hairs) forced up to a considerable height between them, (as to the height of an inch and half, or two Inches) and if by any means the Oyl be taken out at the top thereof, the remaining part of the Oyl in the Vessel will ascend to supply the va­cancy of the part drawn off, which is evident in Filtra­tion. About the sides of this Wick the Oyl will be sure to ascend, and the Superficies thereof will be concava­ted as at G G, because unless there be a congruity be­tween the Oyl and the Wick there will be no ascent of the Oyl therein, and therefore that substance that the Oyl doth not readily adhere to cannot be a fit material for that purpose.

Now to this Wick thus filled with Oyl apply the flame of a Lamp or Candle, or any other substance ex­tremely hot, as a glowing piece of Iron, Copper, or the like, and by this means the parts of the Oyl in the Wick will be very much heated, and expand themselves in va­pours into the contiguous Air by the steams h h h h h, and fill all the Ambient space of the Air H H therewith, which vapours being very much rarified, and conse­quently lighter than the incompassing Air, are by the grea­ter gravity and pressure thereof carried upwards by the Curve Lines h i k. These at first gush out of the Wick at Right Angles, but by the protrusion of the Air are quickly turned into a kind of Parabolick Curve h i k The motion of the Particles in which is swiftest in k k, that is to a certain degree of Altitude. The motion of ascent increasing somewhat after the nature of the motion of descent in heavy bodies, I say somewhat in that nature, for if the ascending bodies were uniformly lighter than the Ambient they would be the same, but because the rarefaction and nature of them is varied by Circumstances, therefore it hath but part of that Analogy.

To proceed then with the Explication: I say, these steams of the Oyl thus ascending, if they are heated to a sufficient degree of heat are preyed upon, and dissolved or burned by the Ambient Air; which dissolu­tion hath this effect, first, that it produceth light; next, that it produceth heat enough to make the succeeding parts of the steams that rush out of the Wick and follow after it to be sufficiently heated for dissolution by the Air, the heat of which produceth the same operation upon a third, and that upon a fourth, and that upon a fifth, and so successively so long as there are steams of Oyl to be dissolved, and plenty of fresh and unsatiated Air to dissolve. The action also of this dissolution causeth heat sufficient to raise up the succeeding parts of the Oyl into the Wick, and expand them into vapours, and so to make them fit to be further heated and dissolved. It is further observable in the flame of a Lamp, that those vapours [Page 7]that issue out of the Wick are by degrees dissolved, and not all in a moment, for the parts of the flame that are lowermost about H have a kind of faint blew light until they come to I, where they seem to have their brightest and clearest light and heat, the said vapours not being hea­ted to that degree at their first breaking out that they af­terwards acquire by the farther action of the Air upon them. At I they seem to be in their highest degree of disso­lution, and from thence upwards are made one with the dissolving Air, so that they are not but by other means discernable to the eye of the observer; so that the shining part of this Conical shaped space of the flame is only the outside of the Cone, it being that part where the Ambient Air preys upon the ascending eruptions of the Oyl, namely, where the Chain of small Circles intercept the Curve lines of the motion of the ascending eruptions.

This Figure and shape of the flame and vapours may be plainly seen by the help of a Metalline Concave placed at a certain distance and Position, and also by ob­serving the shadow of the Candle cast by the beams of the Sun upon a sheet of white Paper, or white Wall, but that way of a Concave speculum is incomparably beyond it, because it doth so very plainly shew the form and manner of the steams rising above i i i i, as about k k k k, &c.

The Air after it hath performed the action of Disso­lution, and is satiated and incorporated with the parts of the Oyl at i i i, ascend by k k k, but shine not. All the steams or eruption of the vapours of the Oyl out of the Wick f f f shine not between the Wick f f and i i, but begin to be dissolved, and to shine as they approach the fresh Air at ii, where the dissolution is compleated.

The upper parts of the flame shine more than the lower, the parts having been heated to a much greater degree by the longer space of passage they have had through the hot Concave part of the flame, and contigu­ous or very near to the glowing sides thereof at i i i.

All the under parts of the Wick neither shine nor [Page 8]burn, but are as it were charkd by the extremity of the heat of the Conical Superficies of the flame, they are de­fended from burning at the bottom by the fresh access of new Oyl from the Vessel underneath; and the middle parts are defended from burning or shining by reason the Air cannot approach them before it be satiated at the Conical Superficies i i i by the dissolution of the steams of the Oyl it there meeteth with. But the upper parts of the Wick do burn and shine, if they be high enough, into the smaller part of the Cone of flame that the Air before it be satiated can reach at them. And if any part of the Wick fall into the said Conical and shining Superficies of the flame, it doth both shine and consume, and suffers the same dissolution into the Air as the steams of the Oyl, and if any part of this Wick be without this Conical Su­perficies at i i i, it is presently consumed and reduced to Ashes; as by many experiments differing ways made is very plainly visible.

This plainly gives the cause why knots and Tophus's do as it were grow to the Wick of the Lamp like so many Mushrooms on a rotten Tree, which as soon as they are removed out of the middle and dead part of the flame are immediately consumed by, and dissolved into the Air, and shine like a coal of fire, as being indeed nothing else.

Hence we may give a plain Reason why upon applying any cool Superficies very low into the flame of a Lamp, there is immediately condensed upon it a great quantity of soot, namely, that the middle parts of the Cone of flame, being nothing but a great number of oyly steams ascending, are not fired nor consumed by the Air, till they can come to be wrought upon by the free and unsatiated Air. Now if the Air be so intercepted that it cannot come at them, and the steams be cooled by the plates coldness that the Air is not able to prey upon or dissolve them for want of a preparatory heat sufficient, they must remain in the form of burnt Oyl, or Lamp-black.

I have been somewhat the longer and more particular [Page 9]in this description and explanation of my Theory of the flame of a Lamp or Candle, that so the Reader under­standing the nature and causes thereof the more fully and plainly, he may the easier discover the inconveniences that may occur in the burning, heating, shining, durati­on, &c. thereof, and the sooner and more readily and scientifically find a cure and prevention of those inconve­niences, which he that is ignorant of can but hood­winked grope after, and at best can but hope possibly after long puzling himself in vain attempts and blind trials, nothing to the purpose, he may at length stumble upon that which had he been inlightned by the true The­ory, he would have readily gone to at the first glance.

I could have further expatiated into the contem­plation of this most admirable Phenomenon of flame, producing heat and light, the two most spirituous and most potent Agents in Nature, and the ways of Intending and Diminishing them, and the uses that may be made of them, but that it is not my present design to annex a discourse on those subjects, which doth more properly belong to another Lecture I shall short­ly publish. I shall therefore at present proceed only to shew some Mechanical contrivances for counter­poising Liquors in Vessels, so as to keep them running or supplying a stream always with equal swiftness, what­ever quantity there be of the said Fluid; which as they are very convenient for perfecting Lamps for divers uses, which they could not otherwise perform, so in Hydrau­lick they are of most admirable benefit for divers effects, hardly to be performed without them, as I shall hereafter manifest. But first, I will explain some few ways by which more conveniences may be obtained, and more inconveniences prevented in the use of Lamps for Chymical, Mechanical, and Philosophical uses than by this way of Cardan, or any other I have met with: For this I look upon as one of the Tools to be made use of in the Work-house or Elaboratory of Nature, without a good Apparatus of which, be the Workman otherwise [Page 10]never so well accomplished, he will never be able to pro­duce any very considerable effect; and with them, even a Bungler otherwise, will, if well furnished, do won­ders to such as know not the means by which they are done.

It may possibly seem very strange to some to hear, that by the flame of a Lamp Plants may be made to grow, bear Leaves, blow Flowers, ripen Seeds; that the Eggs of Fowls and Insects may be hatched, and brought to life and perfection; that Metals, even the hardest, Glass, Stones, &c. may be almost in a moment melted, soft­ned, liquified, hardned, &c. that thousands of separa­tions of conjoyned and naturally united bodies may be effected, and they reserved distinct; and as many other bodies, naturally distinct, and very differing, may be united and compounded into Homogeneous mixtures, some scarce separable afterwards; that Glass may be shaped and moulded like Wax; that almost all the sen­sible qualities of bodies may be increased, diminished, annihilated, and created; and some also of the qualities insensible (otherwise than by the effects;) and yet even these, and many more, may be effected by this Tool or Instrument, if rightly used, as I could manifest if I had now time. But I shall not here any further expatiate on it, possibly I may hereafter but at present I shall only proceed to the description of one sort of those In­struments which serve to supply the Oyl or Pabulum of a Lamp conveniently by any degrees, and in what quan­tity is desired. This sort doth depend upon some con­trivance of Counterpoises for the Liquor in the Re­ceptacle that is to feed the Lamp, and may be made use of in Hydralicks as well as Lamps to feed and continue any running stream any time desired.

These Counter poises then of Fluids might be made to feed the flame of a Lamp equally for any time assigned, and consequently would make a kind of Perpetual Lamp, but the Pabulum it self will be some ways or other unapt for such an effect; as Oyl hath a foulness whereby the [Page 11]Wick is choaked or stopped, so as that it will no longer ascend in it; Spirit of Wine will in length of time eva­porate and lose much of its nature; and other Oyls have their several defects which make them uncapable of con­tinuing the flame very long. But there are none of these that I have met with but may be in great measure avoided by the help of some Chymical or Mechanical contri­vances, some instances whereof I shall hereafter give, which the Theory of Fire and Flame doth readily hint.

The first way then I shall now describe is by a round Box, the inward Cavity of which is divided by a Dia­phragm into two equal parts, and fitted with a proper Counterpoise, the Axis of whose motion lieth Horizon­tally. The contrivance of which will be more plainly understood by the Delineation thereof in the first place, where the second Figure represents the whole Instrument, with its Globe, Frame, Pedestal, Socket, and lighted Lamp.

A represents the Pedestal or foot upon which the In­strument stands, which may be made of Silver, Brass, Wood, or the like. B C D E F, the Frame fastned to the Pedestal, and shaped in the form of a Snake, perforated at B and D to receive the Pivots or Gudgeons of the Lamp G H, and hollow from E to F to serve to convey the Oyl or Spirit of Wine from the end of the hollow Gudgeon H to the Wick I, to feed the Flame K; the hole at E to receive the end of the hollow Gudgeon; H is made a little ta­pering, and the end of the Gudgeon H is ground fit into it, so as to turn easily, and yet so true, as not to let any Oyl there leak out, the said Gudgeon being kept close home by the springing of the Arm B; the Supersicies of the Oyl or Spirit for the Pabulum is always kept by the motion of the said Globe upon its Axis G H, exactly in the Line L M, untill it be all consumed, which how it is done will be better conceived by shewing the contrivance of the inside of the aforesaid Globe, how the same is divi­ded, how filled, and how counterpoised.

Suppose then the aforesaid Globe cut in sunder by the middle Line or Circle N O, and discovering the In­side or Cavity thereof to be represented in the first Fi­gure, where P A H R Z P represents the aforesaid Circle, or half shell of the Globe; O represents the middle of the hollow Gudgeon H, which is the Pole or Axis about which the said Globe doth move. H O Z represents the Horizontal Line or Plain passing through the aforesaid Axis; P R the Perpendicular to that Plain. Let H Z then represent a Diaphragm or Partition of the same material with the Globe, by which the Concavity thereof is divi­ded into an upper Hemisphere H P Z O H, and into an under Hemisphere H R Z O H. Let the under Hemi­sphere be filled with Oyl, Spirit of Wine, &c. or the like fit material for a Lamp to burn; and let the upper part be filled with some material of half the weight of the Oyl, Spirit, or other material, or because that will be somewhat difficult to do, let there be a counterpoise of Lead or other ponderous matter fixed somewhere in the Line P O, so that the said upper Hemisphere shall have half the gravity of the under Hemisphere upon the Center of motion O. I say, whatever quantity of the Fluid Pabulum is in the Cavity of the said under He­misphere, the Superficies thereof shall always be in the Horizontal Line or Plain O Z, the counterpoised upper Hemisphere keeping it always up to that height. For instance, supposing the said Hemisphere full, there is no doubt but that the under Hemisphere being double the weight of the uppermost will be lowermost, and that Horizontal Line will lie Horizontally, since it is evident, that the Center of gravity of the whole will be below the Center of motion O, and somewhere in the Line O R, which is Perpendicular to the aforesaid Plain. Next, suppose so much of the aforesaid Liquid Pabulum con­sumed as to leave enough only to fill the space C O Z B R C, and the Diaphragm be moved from its Ho­rizontal Position H Z, and placed in the Oblique Posi­tion C O D. I say, the said upper Hemisphere [Page 13]CHAPDOC shall exactly counterpoise the said under Hemisphere C R B Z D O C, so as the Superficies of Li­quor shall be in the Horizontal Plain O Z. Make A P equal to P D, and draw the Line A O B through the Center O, it is manifest then that the Wedge C O R of the Liquor doth counterpoise the Wedge R O B on the other side the Perpendicular, and that the Wedge P O D of the upper Hemisphere doth counterpoise the Wedge P O A on the other side of the Perpendicular, so that neither of these have any prepollency to move the Globe out of this Posture. Next, it is plain that the Wedge B O Z of the Liquor will be counterpoised by the Wedge A O C, which is double the bigness of B O Z, and con­sequently of equal weight, the parts of the upper He­misphere being put of half the gravity or weight of the under Hemisphere.

Next, suppose half the Oyl be consumed, and there be only left enough to fill the quadrantal Wedge Z O R, I say, the Superficies thereof shall be in the Horizontal Line O Z; for since the upper Hemisphere is half the weight of the under, the two quadrantal Wedges P O H and H O R must necessarily counterpoise the quadrantal Wedge R O Z of the Oyl.

Thirdly, Suppose that more than half the said Oyl or liquid Pabulum be consumed, and that there be only left enough to fill the Wedge B O Z, I say, the counterpoi­sing upper Hemisphere now made the under, and placed in the Position A H C R B O A shall exactly counterpoise the said Wedge of Liquor, so as that the Superficies thereof shall be in the Line O Z; for the Wedge R O B of the aforesaid upper Hemisphere doth counterpoise the Wedge C O R on the other side of the Perpendicu­lar, and the double Wedge A O H and H O C will coun­terpoise the Wedge B O Z.

Nor can the Superficies of the Liquor be any whit higher or lower than the Line O Z, for if it be any whit higher as at E F, the Liquor must necessarily overpoise the aforesaid Wedge A O C, by all the weight of the [Page 14]Liquor contained in F G O Z F. And if it be any whit lower as at I K, the Wedge K I B must be too light for the counterpoising Wedge A O C by the weight of the Liquor contained in the space Z O T K Z, since I just now shewed that A O C did just counterpoise Z O B, which was the thing to be proved.

Now though in this Instance I have chosen to explicate I have made choice of a Globe, yet that form is not ne­cessary, but it may be made of any Figure whatsoever that is turned upon an Axis or Poles, so as wheresoever the said Figure be cut by a Plain to which the Axis is Per­pendicular, the Superficies of the said Figure shall de­scribe a Circle, the Center whereof is in the said Axis, whether the said Figure be a Cylinder Cone, or any other Conoeidical, mixt, or otherwise, regular, or irre­gular figure. Such as the Figures A B C D E F G, which represent the Section of the said Vessel through the Axis.

The second way for the poysing the Liquor, and keeping the Superficies thereof always to an equal height, is this:

Make a Concave Receptacle for the Oyl or Liquor of a Hemispherical, Semicylindrical, Semiconical, or of any other half-round hollow Figure, where the turned Figure is cut in two parts per Axin, and whereof the Axis is placed Horizontal, and the plain Section per Axin like­wise Horizontally, so as it may be filled with any Liquor up to that Plain; and that the Liquor may not be apt to dash, be shaken, or filter over, it will be convenient to extend the brims of that Receptacle somewhat above the half-Round, that there may be about half or three quarters of an Inch of space above the Superficies of the Oyl vacant or empty. And that upon whatever Plain the foot stand, the Plain per Axin may stand Horizontal, it will be good to suspend the Receptacle in the same man­ner as a Sea-mans Compass is suspended, within a frame: [Page 15]Fix this Receptacle, or the Frame that is to keep the Receptacle, Horizontal upon a convenient Pedestal; and fit within the Hollow or Concavity of the Recepta­cle a half-round solid poise, turned of the same form with the hollow of the Receptacle, and cut exactly through the Axis in two equal parts. Let this solid poise be made exactly half the weight of the Liquor that is to be poised, and fit to it two Pivots or Pins at each end of the Axis, which may be exactly in the Poles of the half-Round, and fit to those Pins make two holes in the Centers of the Ends of the Concave Receptacle, in which the Pins may freely move, and suffer the half-Round poise to move round within the hollow of the Receptacle, according as the quantity of the Oyl or Li­quor is increased or diminished. Fit to this Receptacle a neck and socket fit for the Wick and flame of the Lamp, and the same operation will be performed by this as by the first contrivance; to wit, the Oyl will be kept al­ways to the same height in the Receptacle.

This will be easier understood by explaining a De­signation thereof which is shadowed forth in the fourth Figure: Where

A A A represents a Pedestal, which may be made with three claws or toes to make it stand the steadier and even­ner upon any Plain or Table.

B B represent one of the Semicircular Arms that are fix'd to the top of the Pedestal, this hath two holes in it at the ends or extremities, as at C is one, the other hole being in the other arm which goes behind the Globe, and therefore cannot be seen, is supposed to be Diametri­cally opposite to this at C. These two holes are the Cen­ter holes in which two small Pins or Centers, fastned into two opposite points of the Hoop or Frame are made fit to move, by which means the said Hoop is preserved in an horizontal Position.

D D is this Hoop or Frame, which is made to incom­pass the Vessel or Receptacle of the Oyl, and is shaped exactly like it. This is made strong enough of Brass, [Page 16]Iron, Silver, or other material to bear the Receptacle, Poise and Oyl without bending, and hath, as I said be­fore, two Pins or Gudgeons at C, and opposite to it Di­ametrically, or Semicircularly, upon which the said Hoop always hangeth Horizontally. It hath also on each side in the middle between the aforesaid Pivots, two Centers as at F and E to receive the ends of the Axis of the Receptacle appearing at F and E, by which the said Receptacle is always free to hang plumb or in its Perpen­dicularity, so as that the upper edge thereof at F F will al­ways lie Horizontally.

One of these Pivots, namely, that on the Right hand is the Pipe to convey the Oyl to the Socket of the Lamp I, in which is fitted a Wick of Cotton to serve for the flame, K G G represents the Vessel or Receptacle of Oyl, which is here described Hemispherical, that being the most capacious uniform Figure, but may be of any other, qualified as those I mentioned in the first contrivance. The Brims of this are extended somewhat higher than a Semicircle, namely, to F F, to keep the Oyl from flashing or filtring over. This is always kept full with Oyl or other Liquor to the Horizontal prick'd Line L L, which passeth through the Center or Axis of its Cavity by the Counterpoise moved on the Center C.

H H H represents that Counterpoise which is made ex­actly half the weight of the Oyl or Liquor, and the Cen­ter of gravity of it must be somewhere in the Line M M; and it ought to be fitted as exactly into the hollow of the Receptacle as it is possible, that there may be left as little space as may be between its convex sides and the Con­cave of the Receptacle, but yet so much must be left that it may move very freely upon its Center C a whole Semicircle. This done, and the Receptacle being fil­led with Oyl, the same effect will follow as in the first contrivance, and the Demonstration of it being much the same, I shall not now spend time to explain it. But rather proceed to the description of a third way of keeping the Liquor counterpoised to the same level.

The third way then is:

Take any round Vessel, whose Concavity and Con­vexity is turned upon an Axis, and suspend that Vessel upon two small Pivots (but yet big enough to bear the said Vessel filled with Oyl, &c.) fastned in the Poles of that Axis; and leave or cut open a sixth part more or less as you please of the side thereof, that thereby any thing may be put into or taken out of the Cavity of the Vessel; then poise the Vessel exactly on those Centers, that no side be heavier than the other; then fit into it a float of Brass, Silver, Tin, Lead, &c. Convex on the under side, so as just to fill to the Cavity of the Vessel. And on the upper side, Plain, or Convex, or any other convenient Figure, it matters not much. Make this float as heavy as you can at the bottom, and as light as may be at the top, but yet of such weight as may well float upon the top of the Oyl, &c. Let one end of this be fastned by a wire or string, so as that end thereof may always touch that point of the Concave of the Vessel to which it is tied, and that the rest thereof may turn and follow the sink­ing of the Oyl; and through the end of it, near the place where it is fastned, let a Pipe go through it to receive the Wick, which Pipe hath no communication with the Ca­vity of the hollow float. This done, fill the Vessel as full as convenient with Oyl, and light the Wick, and you shall find that as the fire consumeth the Oyl, the Vessel will turn upon its Poles and keep the Superficies of the Oyl always at the same distance from the flame that it was put at at first till the whole be consumed.

This will be made more conceivable by a figure and explanation thereof, which therefore take as follows in the fifth figure.

A C B B represents a hollow Vessel, the Cavity where­of is very exactly turned upon an Axis whose Poles are in P, the space between A and B in the side thereof is left open into the Cavity of it. This Vessel is suspended [Page 18]upon its Poles at P, so as to be free to move round upon them, and exactly poised as no one side thereof be hea­vier than another. To the hollow of this Vessel is fitted a float D of Brass, Latton, Silver, Lead, &c. whose under­side is made of a Convexity just fit for the Concavity of the Vessel, as may be seen at K D I, and the upper straight or Plain. Let this float be made somewhat lighter than the Oyl or Liquor on which it is to swim, so that a part thereof may float above the Superficies thereof. Let one end thereof E be fastned to the side of the Vessel a little below the Brim B; through the end of this float is put a Pipe and Wick h, for the flame i, then pouring in Oyl by the open side A Q B, fill the same till it carry the float up to touch the hollow of the Vessel; then light the Wick, and you will find that the Lamp will consume the Oyl, and this contrivance will continually supply it till the whole be consumed, and the Poise be moved to touch the Concave of the aforesaid Vessel; for when the Vessel is filled up to f g, the float D will touch at O and E, and the Cavity above f g being empty, the Vessel will be as is described in the Figure, the open part A B being upwards. And as the flame consumeth the Oyl, the side of the Vessel B will descend downward towards B 1; and so by B 1, B 2, B 3, to B 4, where the whole quanti­ty of Oyl will be consumed, and the bottom of the float will touch the hollow side of the Vessel; in all which gradual wasting of the Oyl the Superficies thereof will lie at the same distance below the upper side of the float D that it had at first, and consequently at the same distance from the bottom of the flame. The reason of all which will be very easie to be understood by any one that shall seriously on this Delineation consider that the float D must necessitate the Vessel A C B to move on its Axis B ac­cording as its Oyl wasts, because one end thereof E being fastned to the brim of the Vessel B, the other end O be­ing loose will as the Oyl wasts descend towards N, whence the end E must hang heavier on the brim B, and conse­quently must move it down towards B, till the upper [Page 19]side f g of the float be reduced to a Parallelism with the Superficies of the remaining Oyl, and the end E have no gravitation on the brim B, which motion will be continu­ed as the Oyl wasts, and the brim B will be moved down­wards by the points B 1, B 2, B 3, to B 4. I shall not therefore spend any more time in the Geometrical demon­stration thereof, but proceed to explain a fourth way by which the Flame and Superficies of the Oyl keep always at the distance they were first put at.

The Fourth way then is, the making the Socket of the Wick to swim upon the top of the Oyl, so that the Socket may sink as well as the Oyl, by reason it is sustai­ned by that, and by that only. The Vessel or Receptacle is generally made of Glass, and it is best of a Hemisphe­rical Figure, the light casting it self through the body of the Oyl as well as of the Glass. This is so plain and obvi­ous, and so commonly used and practised, that I need not spend more time in the explanation or demonstration thereof, but proceed to describe a Fifth way.

The Fifth way then is much upon the same principle with the Fourth, but avoids several inconveniences to which that is subject: For whereas the Flame in the Fourth is necessitated to be within the capacity or the Receptacle in this Fifth, it may be at any distance, and so is made much more convenient to be come at, and to be dressed and trimmed. Take then a Vessel of Glass, Cy­lindrical is best, as a Glass Bottle, and fit to it a Siphon, long enough to draw the Oyl from the bottom of the said Ves­sel, make the one end of this Siphon extend at what di­stance you think convenient for the placing the flame of the Lamp, and so order it that it may always draw from the Receptacle by its arms to feed the flame, which it will do if the end of the Siphon be made where the Socket of the Lamp is placed to return or bend upwards again. So that the Plain of the upper Superficies of the Oyl may cut that end of the Siphon where the flame is [Page 20]between the top of the mouth of it next the Socket and the return thereof upwards; then by a counterpoise so suspend this Siphon that it may follow the Oyl as it wasts, and fit into the return of the Siphon a Socket and Wick for the flame to be continued. A contrivance somewhat of this kind you have in divers Authors, and therefore I shall spend less time in the description thereof. Let A A A A in the Sixth Figure then represent a large Cylin­drical Viol of Glass through the mouth B of which the Cavity thereof may be filled with Oyl, and also the end D and float C of a convenient Siphon may be put in. This Siphon D D D P G must be made long enough that the float C may reach the bottom of the Vessel when the Oyl is spent, and the other end thereof must be so curved that the knee of the Siphon P may be below the Super­ficies of the Oyl E F, and yet that the Socket H made for holding the Wick for the flame I may be somewhat above it, this Siphon D D D P G with its Socket and float should be so counterpoised with a weight M, hung over a Pulley K, by a string L, that the float may not sink deep into the Surface of the Liquor, but swim as it were at the top. This done, if the Wick I be lighted, the Surface of the Oyl will be kept always at the same distance below the flame that it was first put at.

In the first, third, fourth, and fifth ways the flame of the Lamp descends equal spaces with the Superficies of the Oyl in the Vessel, and therefore though for some uses it be very convenient, as in annealings, where things are to be cooled by degrees, yet for many other it is not; Especially in Lamp Furnaces, where the same heat is to be continued, and in some cases gradually increased. For such cases therefore the first and second ways will be very convenient. In some other cases the sixth and seventh ways, which do much the same thing.

The sixth way then is this: Through an arm or Siphon (like the Branch of a Lamp hung against a Wall) fixed in any convenient place, the Oyl from the Receptacle is [Page 21]continually and equally supplied to the flame of the Lamp by the raising of the Receptacle as fast as the Oyl wasts, so as to keep the Superficies of the Oyl alway in the same Horizontal Plain. The Receptacle is raised by a Counterpoise hung upon a Fusey, which Fusey is a part of an Archimedean Spiral.

Let C C then in the seventh Figure represent the Recep­tacle for the Oyl, being a Cylindrical or Prismatical Vessel, of what Bigness or Length you please; to this by two Ears at L L fasten two Lines or Ropes K K, the ends of both which are fastned to the Wheel or Pulley G, though one of them do run over the Pulley F. Fit into this Receptacle is made a Cylindrical or Prismatical Plug A A, which is fixed in some convenient place, so as not to rise or sink, and through the middle thereof pas­seth a Siphon B B B, the one end whereof extended like the branch of a Candle or Lamp sustains the Socket D for the Flame E, which is fed with Oyl through the Si­phon B B B by the rising Receptacle C C.

To the side of the Pulley G is fastned a Fusey H, made with very great care of one Revolution of an Archimedean Spiral, not beginning from the Center, but from some convenient distance from it, where the weight I hanging, may just counterpoise the Receptacle C C, when quite empty of Oyl, the other hanging coun­terpoise (Tangent to the largest part of this Spiral) must be so far distant from the Center of the Wheel G, that the same weight I may just counterpoise the said Re­ceptacle filled top-full of Oyl, and the Fusey must be filed true to a Spiral, drawn with great care of one Revolution between those two points. I say here of one Revolution, because I have supposed the Wheel or Pulley G big enough, by one Revolution of it to draw up the Receptacle the whole space it is to be rai­sed; for if the said Pulley be so small as to require two, three, four, or more Revolutions, then must the piece of the Spiral between those points be drawn of two, three, four, or more Revolutions proportionably, which [Page 22]being very Artificially and Mechanically performed, the Receptacle C C will be raised by the same Degrees by which the Oyl is consumed at E, and the upper Super­ficies thereof shall always be in the same Horizontal Line MM. The Geometrical and Mechanical Reason of which being so very plain, I hope I shall not need to spend any more time in the explication thereof than only to say, that by means of the Archimedean Spiral-Fusey the Power of the weight I upon the Pulley G decreaseth in the same proportion as the weight of the Oyl in the Receptacle C C is diminished by its consumption.

The seventh way then is, by a Cylindrical or Prisma­tical Plug fitted into a Cylindrical or Prismatical Re­ceptacle, and let down into it by a Counterpoise, hung upon a Spiral Fusey, the Oyl is so raised in that Recepta­cle as always to stand Brimfull, or to the same Horizon­tal height till the whole Oyl be consumed.

The contrivance of this way will be very easily under­stood by any one that shall peruse the Delineation in the eighth Figure, and examine it by this following descri­ption.

Let A A in the eighth Figure then represent a Cylin­drical or Prismatical Receptacle, standing fixt upon a Table or Pedestal, from the side of which issues a hol­low Arm or Branch B B, bearing the Socket for the Wick C, where the flame D is continued. Into the Ca­vity of this Receptacle is fitted a Cylindrical or Prisma­tical Plug E E, big enough to fill the whole capacity thereof, and yet not so close but that it may freely slip up and down the Cavity of the said Receptacle without sinking. Let this Plug be made considerably heavier than the Oyl of the Receptacle; that is, let the Counterpoise L, hanging upon the little Wheel M just reduce its gra­vity to be equal to that of the Oyl; then let the point I, where the Perpendicular toucheth the Spiral, be so far removed from the Center of the Wheel H, that the coun­terpoise [Page 23]L may just take off its whole gravity, and suffer it to have no degree of gravity or pressure downwards. Then draw the Spiral n o p according to the direction I gave in the former way, and the effect will be produced. The Geometrical and Mechanical Demonstration of which is very plain to any one that shall consider, that, As the Plug E E by sinking into the Receptacle A A so far as to raise the Oyl to the Horizontal Superficies M M will lose its gravity by the same Degrees by which it sinketh into the Receptacle, and that is alway propor­tionable to the diminishing of the Oyl in the Receptacle by the flame: So the weight L will lose its power upon the Wheel H, by the same degrees by which the Plug de­scendeth, by reason the Line by which it is suspended becomes a Tangent to a proportionately shorter Radius of the Spiral, of the Rays of the Spiral.

I know indeed that both in this and the former Fusey there lies an objection against the true form of the Spiral, because the Line K K of the weight L doth not touch the Spiral in a point level with the Center, but in one some­what above it, and in this latter somewhat beneath it; but though that be a seeming material one, yet as to practice it signifies very little. For first, it will not be difficult to prove that this may be Mechanically drawn true enough, that there shall be no sensible error, and if the error be not sensible, it is no error in practical Mechanicks. Next, were it the true Spiral, yet it would not be more Geometrically Delineated than this which is here requi­red, and at best it would prove but a Mechanical ap­proach, which is sufficient for the effect to be produced by it.

These two last contrivances do keep the flame of the Lamp always in the same place, and of the same strength and fulness. But the succeeding ways, though they maintain the flame in the same degree of strength and nourishment, yet by their motion upwards they may be made to increase, and intend the heat produced by them in the bodies posited above them, which is of great [Page 24]use in many Chymical and Philosophical Experi­ments.

The eighth way then is this: Make a Cylindrical or Prismatical Receptacle for the Oyl exactly like the for­mer, with its Arm, Socket, Wick, &c. and fit into it a Cylindrical or Prismatical Plug, as in the former, that may be able to fill the said Receptacle. Fix this Plug fast into some Wall or Standard, so that it shall not be able to stir; Then by the help of two Lines fastned to a Coun­terpoise at one end, and the other to the Ears of the Re­ceptacle, so counterpoise the said Receptacle that it shall have no weight or gravity downwards, but hang in a perfect equilibrium; I say, whatever quantity of Oyl there be in the said Vessel, the Superficies thereof shall always be in the Plain which is equal to the top of the Oyl when the Vessel is filled as high as is desired, which will very plainly appear to any one that shall examine and consider well this following description, and com­pare it with the Delineation of the Instrument in the ninth Figure, where A A represents a Receptacle for the Oyl of any convenient capacity, made Cylindrical or Prismatical, to which is fastned a hollow Neck or Arm B B for bearing the Socket C, to which through its Ca­vity (being made hollow) is conveyed the Oyl or Pa­bulum for the continuance of the Flame D; into this Re­ceptacle fit a Cylindrical or Prismatical Plug, so as it may pretty equally fill the said Cavity of the Receptacle, yet not so as any ways to hinder the sliding on upon it of the Receptacle. Let this Plug then be fixt by the top in any convenient place Perpendicularly, and setting the Receptacle underneath it, Counterpoise the same when filled up with Oyl by a Counterpoise I, which is fastned to the two strings F F F F, by which the Receptacle is to hang, which two strings for their more easie sliding to and fro move upon the two Pulleys or Truckles G G, that are fixed to the same frame to which the Plug E E is fixed; which being so adjusted, as fast as the flame D consumeth the Oyl out of the Receptacle A A, the [Page 25]Counterpoise I raiseth the said Receptacle on upon the Plug so far till the top of the Oyl be equal to the height it was at first counterpoised at, to which height it always keeps it till the whole be consumed.

This last way of poising the Liquor or Oyl doth make the Superficies thereof run higher and higher as the quantity thereof is more and more consumed, which for divers Expedients in Mechanicks, Natural Philosophy, and Chymistry is of excellent use, as I may hereafter have opportunity to manifest upon many occasions where I shall make use of them; and it would be, I fear, too tedious to the Reader to have them here enumerated.

But because it may not possibly be ungrateful to him to have some uses of this Principle here hinted, I shall now specifie a few, and hereafter add many more, toge­ther with a great number of other Poises for Liquors which serve for very differing effects in their kinds, not less considerable, but rather somewhat more strange, as being yet farther removed from the common practices and discourses of Hydraulicks.

The first use then that I shall mention of this Liquor­poise shall be in Hydraulicks, viz. to make a Cistern of whatever bigness and depth is required to deliver all its water at the top, or so near unto it as it shall be de­sired: By which means nothing of the Descent of the water falling into the Cistern is lost, but without any la­bour or trouble the whole quantity of water that is de­livered at the top into the Cistern is re-delivered again out of the Cistern at the top. This may be done by the first, second, and seventh ways of poising Liquors; this, that, or the other, of which may be more convenient to this, that, or another effect or operation to be per­formed by it, which must be chosen and applied with judgment, according to the occasion, and the circum­stances of it. Every of the three, though they all agree together in the producing the effect of keeping the Su­perficies [Page 26]perficies of the water to the same Level, and there de­livering it, have yet each of them their several proprie­ties, which maketh some one of the three more proper and adapted to one design than either of the other two, and each of the other two in some other effects and ap­plications may be much more usefully applied than the first. By this means the whole depth of the Cistern is gained, and all that water that was used to be delivered at the bottom is now delivered at the top, and conse­quently gains the advantage of the Perpendicular height of the Cistern to be imployed, for any use, for turning an Automaton, or conveying the Stream farther, or to a higher level.

A second effect performable by these Poises may be for delivering any quantity of water with an equal de­gree of swiftness, so as to continue an equal supply of water till the whole Cistern or Receptacle be emptied, the spending of the water in the Cistern not at all abating the stream without, the Counterpoise always keeping the Cistern full, and maintaining the current till the last. This may be useful for sawing or grinding stones by an Engine; for gauging of Glass Tools, or grinding glasses by an Automaton, in all which cases there is need of a constant and equal supply of water and sand; as also for washing and Fulling of Cloth; it may also serve for various sorts of Clepsydras, or mea­suring the quantity of time by the quantity of the cur­rent of water, as I shall by and by shew. And thirdly, for maintaining any slow and constant motion, as that of a Jack, or Clock; an Engine for continually stirring of a liquid body, or shaking, tumbling, and turning of dry Solids and powders, of which sort there are a great number of uses in Chymistry for the operations of Digestion, Calcination, Pounding, Grinding, Trituration, Searcing, and the like; which operations being certainly, evenly, and constantly performed by an Engine supplied by such a stream of water will far exceed the same kind [Page 27]of work done by the hands of men, especially in such operations where the Labour and Diligence is to last divers days and nights together without any intermission, which are Requisites not at all strange to Chymistry, and which will weary the diligence of the best Laborant and his Attendants.

A third effect performable by these Poises is the ma­king a perpetual and constant stream in imitation of that of a natural Spring or Fountain in the Earth. This may be done if the Cistern be once in twenty four hours re­cruted and supplied with a new access of water from some Pipes, which is usual enough here in London, and elsewhere, where there are Waterworks and Convey­ances of water. For as the wasting of the water in the Cistern does no ways abate or diminish the stream of the water from the Cistern, so the new access of other wa­ter for a supply to refill the Cistern does not at all accele­rate it, but the stream remains equal; And hence, con­sequently constant, and, as it were, perpetual.

A fourth effect is, the delivering any quantity of wa­ter to any degree of swiftness, and the whole quantity of the water by the same degree. This is performed by tapping the Cistern at any part of the depth thereof, for according as the Vessel is tapp'd lower under the Sur­face, so will the motion of the water be swifter; and here the depths must be in a duplicate proportion to the Velocity desired: As for instance, the Cistern being tap­ped with a hole of a quarter of an Inch bore, at the depth of an Inch below the Surface, is found to de­liver a certain quantity of water in a minute; if it be desired that through a Tap of the same bore there should be delivered twice that quantity, the Cistern must be tapp'd at four Inches deep; and if thrice that quantity in the same time, it must be tapp'd at nine Inches deep; and so forwards, as is already demonstrated by Mersennus, and other Authors. For since the pressure of Fluids upon the parts thereof increase, in the same proportion [Page 28]with the depth below the Surface. And since the forces requisite to accelerate motions must always be in du­plicate proportion to the Accelerations, it follows, that the perpendicular depths of the Tap under the Super­ficies of the water must be always in duplicate proportion to the Velocities required.

The plainness and certainty of this truth in Hydro­staticks, long since so fully and excellently demonstrated by Stivinus of all Fluids, and so highly improved of late in the particular applications thereof by many more modern Authors, who have writ most learnedly and clearly thereof, as well as experimentally and practically, makes me much admire at the learned Doctor More, who in his Enchiridion Metaphysicum, in the 11, 12, and 13 Chapters, and in a Book, newly published, called, Remarks upon two late ingenious discourses, &c. does not only deny this Gravitation in the parts of Air, but of Water, quicksilver, and other Liquors. And instead thereof, to solve the Phenomena, would introduce into the World a Principle, which he terms an Hylarchick Spirit, which at command acts and performs whatsoever is necessary to solve all the Phenomena of Mechanical, Hy­drostatical, and, in a word, all Physical motions and effects.

In answer to whose Doctrine about Hydrostaticks I shall only urge this one Experiment of the Velocity of the current of Fluids, tapp'd and running at several depths under the Superficies of that Fluid, which can no ways be solved by the Hylarchick Spirit, and we must be fain to come to the Mechanical and plain Rules of moti­on, and to allow every particular of that Fluid to press with its own gravity where ever placed. And this I will prove from his own words in his Enchiridion Metaphy­sicum, pag. 113. where explaining very ingeniously the Hypothesis of Gravitation of the parts of Fluids one upon another by the similitude of six men standing in a Line, and pressing against a Wall, (which men he marks with A B C D E F, and the Wall with G) He says, that A the first man cannot press F the last against the Wall [Page 29]G, but by pressing B against C, and C against D, and D against E, and E against F; nor can A press B against C, nor C press D against E, nor E press F against the Wall G, but at the same time it must be understood that B presses D towards F, and D presses F towards the Wall G, for A C and E, says he, are here put for Des Cartes Materia Coelestis, pressing the parts of the water within the pores, and B D and F for those parts of the water pressing the bottom of the Vessel. But, says he, that B presses D, and D presses F appears from this, that casting out E and F, D doth run to the Wall G, and casting out C D E and F, B also will run to the said Wall. And so, says he, the state of the matter would be if Gravity did proceed from the meer Mechanical motion imparted to the Terrestrial parts of the Fluid by the Materia Coelestis of Des Cartes, to wit, the Elements would actually gravi­tate in their proper places. But since there is no such thing, it is a sure sign that Gravity doth arise from a higher cause, which higher cause he elsewhere supposes to be an Hylarchick Spirit. This from so plain reasoning is a strange Conclusion, and contrary to all experience.

Now though, I confess, I suppose Gravity to be other­wise performed than as Des Cartes has supposed, yet do I believe his Suppositions so Rational and Ingenious, and so much above the Objections brought against them, and so much better than any other I have yet met with, as no wise to deserve to be esteemed foeda deliria, as the lear­ned Doctor is pleased to term them, pag. 125.

It shall not be my business to defend Des Cartes Prin­ciples at the present, nor to set up any new Hypothe­sis instead thereof, but only to urge this Experiment of the running of a Liquor swifter and swifter, according as the hole through which it runs is deeper and deeper placed below the Surface of the said Liquor or Fluid, and that the Velocities of those streams are always in a subduple proportion to the Altitude of the Fluid above those holes; whence it is evident, that the force that makes that Fluid run is always in the same proportion [Page 30]with the Altitude of the fluid parts above those holes; and consequently, that the motion of them is exactly according to the plain and obvious Rules of Mechanical motions. And consequently for the solving all the Phe­nomena of Hydrostaticks there is no need of any other Principles than the plain Mechanical Principles, which supposeth every Terrestrial Body to have a Gravity in it, which is always the same, and always communicates its Gravity to the Terrestrial Bodies subjected under it, and not only its own, but the Gravity of all other Bo­dies above it, which have communicated their Gravity to it, and that this Gravitation is always the same, and acteth continually by continual repetitions indefinitely swift. And that this gravitating or communicating of its weight, together with the weight of all other Bodies communicated to it, is no ways differing from all other communications or propagations of motion, which the Doctor must confess to be meerly Mechanical, if at least he will admit of any such thing as Mechanical motion. For I cannot conceive any Reason why the Doctor should not allow for instance the parts of a Cylinder of Lead to press upon one another as much when they are kept melted in an Iron Cylinder into a Cylindrical form part over part as when the Lead is cold and divided into several parts, and laid one over another in the same form that they were kept in by the incompassing Iron Cylinder. Since if the Iron Cylinder and melted Lead, and the Iron Cylinder and cold Lead be weighed, it will be found that they have both the same weight or gravity downwards, and do communicate continu­ally the same force, pressure, indeavour, impetus, strength, gravity, power, motion, or whatever else you will call it to the Scale. And I suppose the Doctor will grant, that if the cold Cylinder of Lead, weighing ten pounds, be divided into ten shorter Cylinders, that are each a tenth part of the whole, and do each weigh a pound alone, every one of the upper shall gravitate upon every one of the lower; and that the tenth, with the other nine [Page 31]upon it, shall press the Scale with ten pound weight, and consequently, that the tenth doth not only commu­nicate its own gravity of one pound, but the gravity of all the other nine above it, which is nine pounds; and, if the tenth be taken away, and the ninth be put to touch the Scale, with the other eight upon it, it is certain that the ninth will not only communicate its motion, or press the Scale with its own weight of a pound, but will communicate the motion to, or press the Scale with the weight of eight pounds more, or of all the eight Cy­linders superincumbent, and the like Ratiocination may be upon the eighth, seventh, sixth, fifth, fourth, and second, but the last will only press the Scale with its own weight, unless we take in the consideration of the weight of the Air, which in this Ratiocination is not neces­sary. Since then I think it cannot be denied but that the whole tenstanding in a Cylinder one over another, the tenth is pressed by nine, and presses with ten pound weight; the ninth presses with nine, and is pressed with eight; the eighth is pressed with seven, and presses with eight, and so onwards, and that the pressure of the lowest downward is always proportionable to the height of this Cylinder. Supposing these to be all melted in an Iron Cylinder, but kept in the same position and situa­tion, and finding the whole to keep the same weight, why should we not believe that each of those parts will exert the same effects, as to gravity, on those be­neath it as the same parts cold, and in the same posture did; since if the Cylinder of the Fluid be shortned by 1, 2, 3, or 4, tenths of its height, the same abatement of weight or gravity will appear. Having seriously perused all the Ratiocination that the Doctor hath produced, both in this late Book, and in his Enchiridion Metaphysi­cum, I cannot find any convincing reason against it, but what seems grounded upon some pre-conceived Notions and Hypotheses which I cannot understand; and I can­not see how he can avoid acknowledging this to be a Mechanical motion, if at least he will allow any Me­chanical [Page 32]motion at all, since it doth so perfectly, and in all circumstances so exactly conform and agree with the Laws of Mechanical motion, that I do not know any difference, nor any one Phenomenon of Hydrostaticks or Gravity but what may be clearly solved by the common Rules of Mechanicks.

But to pass by all other Mediums to prove this Gra­vitation or pressure of the parts of Fluids one upon another, I shall only insist upon this one Experiment of the Velocity of Fluids, vented or running at several depths below the Superficies of that Fluid. In which it is observable, that the quantity of water running with­in a certain space of time is always in a Subduple propor­tion to the height of the pressing Fluid above the hole. That is, the quantities of water are in proportion to one another as the square Roots of the several Alti­tudes. As for instance, it is the observation of Mersennus in his Hydraulicks, that a Tap of an Inch bore, four foot under the Superficies of the water will yield a pound or pint of water in 13 Seconds of time; now, if it be desired to make the water run through a Tap of the same bore twice as fast, that is, to yeild a quart or two pounds of water. This new Altitude must be made to the former Altitude, as the square of two to the square of one, that is, as four to one; whence it will follow, that the Altitude of the water above the Tap must be made sixteen foot to make the Tap run a quart of water in 13 Seconds of time. And if it be desired to have the Tap run a Gallon or eight pints in 13 Seconds, the proportion of the new Altitude to the first must be as the square of eight to the square of one, that is, as 64 to 1, whence the Altitude of the water must be 256 foot, and the like for any other quantity or Velocity desired. As if it be desired that the Tap should only run half a pint in 13 Seconds, the Tap must be placed at one foot under the Superficies, which is a quarter of the former Alti­tude. Now this is exactly according to the General Rule of Mechanicks. Which is, that the proportion of [Page 33]the strength or power of moving any Body is always in a duplicate proportion of the Velocity it receives from it; that is, if any Body whatsoever be moved with one degree of Velocity, by a determinate quantity of strength, that body will require four times that strength to be moved twice as fast, and nine times the strength to be moved thrice as fast, and sixteen times the strength to be moved four times as fast, and so forwards. This is most certainly true in the motion of Bullets shot out of Cannons, Muskets, Pistols, Wind-guns, Cross-bows, Spitting-Trunks, and the like; as likewise in the motion of Arrows shot with Bows or Ballistae; of Stones thrown by the hand, or with Slings; of Pendulums mo­ved by Gravity or Weights; of Musical Strings; of Springs, and all other vibrating Bodies; of the motion of Wheels, Flies, &c. drawn and turned by Weights or Springs; of the motion of Perpendicularly or Ob­liquely falling Bodies; and in a word, of all other Me­chanical and Local motions, allowance only being made for the impediment of the Air or other Fluid Medium, through which the Body is moved. Now if the Doctor will contend for an Hylarchick Spirit to perform all these, he may plausibly enough contend for it also in the Experiment of the Gravitation of the parts of Fluids one upon another.

We see then how needless it is to have recourse to an Hylarchick Spirit to perform all those things which are plainly and clearly performed by the common and known Rules of Mechanicks, which are easily to be understood and imagined, and are most obvious and clear to sense, and do not perplex our minds with unintelligible Idea's of things, which do no ways tend to knowledge and practice, but end in amazement and confusion.

For supposing the Doctor had proved there were such an Hylarchick Spirit, what were we the better or the wiser unless we also know how to rule and govern this Spirit? And that we could, like Conjurers, command this Spirit, and set it at work upon whatever we had occa­sion [Page 34]for it to do. If it were a Spirit that Regulated the motion of the water in its running faster or flower, I am yet to learn by what Charm or Incantation I should be able to incite the Spirit to be less or more active, in such proportion as I had occasion for, and desired; how should I signifie to it that I had occasion for a current of water that should run eight Gallons in a minute through a hole of an Inch bore? If the Doctor should tell me, that I must make the Tap at such a depth under the Superficies of the water, and then the Hylarchick Spirit will make the water run as I desire, I would then inquire how he comes to call that an Hylarchick, or matter-governing Spirit, which is rather commanded by matter, and sub­jected to its Laws, and is necessitated to act exactly ac­cording to the quantity and position of matter, by what means soever it be so placed? This Principle therefore at best tends to nothing but the discouraging Industry from searching into, and finding out the true causes of the Phenomena of Nature: And incourages Ignorance and. Superstition by perswading nothing more can be known, and that the Spirit will do what it pleases. For if all things be done by an Hylarchick Spirit, that is, I know not what, and to be found I know not when or where, and acts all things I know not how, what should should I trouble my self to enquire into that which is never to be understood, and is beyond the reach of my Faculties to comprehend? Whereas on the other side, if I understand or am informed, that these Phenomena do proceed from the quantity of matter and motion, and that the regulating and ordering of them is clearly with­in the power and reach of mans Industry and Invention; I have incouragement to be stirring and active in this in­quiry and scrutiny, as where I have to do with matter and motion that fall under the reach of my senses, and have no need of such Rarified Notions as do exceed Imagination and the plain deductions of Reasons there­from.

For what is clearer to be seen and tried by Experi­ment, [Page 35]and what more easie to be imagined and under­stood than that a Cylinder of water, or any other Ho­mogeneous substance of twice the height should have twice the gravity or pressure: of thrice the height, thrice the pressure: of ten times the height, ten times the pres­sure: of 100 times the height, 100 times the pressure, and consequently, to imagine that as in all other Mechani­cal motion, four times the pressure will double the Velo­city, nine times the pressure will treble it, sixteen times will quadruple it, and 100 times will decuple it, and so forward; So in this Experiment the same pressure will perform the same effect, and a proportionate pressure a proportionate effect. And since we find that the effect does most exactly answer the Theory (as most certainly, evidently, and undeniably it doth) why should we doubt of the cause which is so certain and Regular a Con­comitant, that it is always present when the effect is performed? And where ever it is present, (if other Circumstances hinder not) the effect certainly follows. I could have gone over all the other Ratiocinations of the Doctor for an Hylarchick Spirit to perform the effects which do clearly belong to Mechanical motions and powers, and are performed and regulated exactly according to the quantity and quality of matter, and ac­cording to the general and universal Laws of motion, and not otherwise. But that is not my present business, but rather to explain how this contrivance of Poises doth serve to make a Cistern or Vessel to run any quan­tity of water required in any space of time. And that to run the whole quantity either with an equal Velocity or stream, or by any desired degrees to be accelerated or retarded from the beginning to the end, which for some occasions in Mechanicks is of great use, and hath not been explained by any Writer of Hydraulicks hi­therto.

I should have here left this Digression, but that I find a little further in the aforesaid Doctors Enchiridion, to wit, in theninereenth Chapter, in the fifth, sixth, seventh, [Page 36]and eighth Sections, continued from the 246. to the 256. Page, some Animadversions upon an Explication of Co­lours which I did formerly publish in my Micrographia, from the confutation of which he endeavours to assert this Hylarchick Spirit. But in this he doth Canere trium­phum ante victoriam, and seems to make very slight of that which he neither hath hitherto by all he hath said in his Enchiridion Metaphysicum, nor can by all other Argu­ments he can produce answer. For if the Doctor had pleased to have confidered the Objections I made against the Hypothesis of the Rotation of the Cartesian Globuli, with a little more seriousness and deliberation, he would not, I conceive, have believed that one that understood the Objection would be satisfied with so slight and insig­nificant answers, as he is pleased to make to them. His Answer then to the first Objection which I brought against this Hypothesis, which was raised from Experi­ments made with thin plated bodies, producing colours, though the refracting Superficies were parallel, is no more but this: That it is not every second Refraction of the Ray in a Parallelipiped that doth destroy the Rota­tion generated by the first, but only that which entring at one side, passeth through, and goeth out again with the same refraction it entered. In which case only, says he, the Rotation of the Globuli, generated in the first Superficies, is destroyed in the second. But, says he, a Ray falling upon a Parallelipiped, and being reflected from the second Superficies, suffers a double Refraction in the same Superficies, the one at entring, and the other at going out again; both which Refractions, says he, do promote the Rotation of the Globuli the same way. This he says very positively, but gives no reason for it. Nor indeed could he, since it is expresly contrary to Des Cartes Principles, and to all the Phenomena of such Parallel sided bodies until they come to a certain degree of thinness: For if his Affirmation were true, then must all Reflections from the Quicksilver, or foil of Looking­glasses, especially if a little oblique, make the Object [Page 37]spread, and become coloured in the same manner as Ob­jects do which are look'd at through Prismes. But this is contrary both to Experience, and the Laws of Reflecti­on; for the Refractions in the Parallelipiped B are the very same with the Refractions in the Parallelipiped A, the Reflection at D making the Ray to be refracted at F, in the same manner as if it were refracted at G by G H, and the Parallelipiped were twice as thick, and conse­quently the colour generated in E must be destroyed in F, and consequently produce no colours, as really it doth not in plates beyond such a thickness; whereas if the Refraction at F did promote the Rotation, as he affirms, then must the reflected Superficies I K not be Parallel to E F, but inclined to it with an Angle at L M. Then G N would represent F O, which is impossible, and con­trary to the Laws of all reflection, as he might have understood if he had considered my Demonstration about the Reflections of a Globe. Nor will the Doctors adding, Sed de hac prima objectione non est quod sumus adeo soliciti, cum sit in materia magis incerta ac inequali cujus interna contextura videatur Globulorum motus variis modis posse mutari. For since all transparent bodies whatsoever produce the same effect, that Subterfuge of supposing some strange invisible texture in the body of Muscovy Glass, differing from that of other transparent bodies, will prove but a lame help, for this interna contextura must be common to all transparent Bodies. And why it should do it at one time, and not at another, the Doctor doth no where shew, nor seems to understand.

Next, whereas in the seventh Section of the said nine­teenth Chapter he says, Verum in materia illa idonea Gutta scilicet Pluvia, si nullus Demonstrationis. Scopo subsit error, actum est de Globulis Cartesianis. Sed videtur (says he) ingeniosus demonstrator non satis intellexisse scopum quo collinneare debeat ipsius Demonstratio. To which I an­swer, that I perceive by the Learned Doctors endea­vours to refute it, that he neither understood that, nor the Laws of Reflection and Refraction according [Page 38]to Des Cartes Hypothesis. Neque enim satis erat probare (quod agnosco eum fecisse scite & eleganter) Refractiones in gutta pluvia ita fieri, ut si in duobus pellucidi Parallelipipedi Lateribus oppositis, factae essent, sed oportebat praeterea evi­cisse quod eodem modo refringatur radius in utrisque Locis quo in Parallelipipedo A refringitur, hoc est ut Radius B C quamvis oblique, perpetuo tamen currat versus candem ex­tremitatem tam in F quam in D Parallepipedi A puta versus extremitatem E, nam in hoc casu Rotatio ad D dissolvitur iterum ad F ut supra dictum est; sed Demonstratio Inge­niosi Micrographi huc non attingit; sed probat secundam re­fractionem in opposito Latere fieri ad modum refractionis in Parallelipipedo C ubi Radius B N primo refringitur in D & procurrens versus extremitatem E ibique inflexus pergit postea versus alteram extremitatem G & Refringitur in F, quae refractio non diluit Rotationem prioris refractionis in D, quippe quod tendentia Radii sit in partem oppositam. If the Learned Doctor had better consulted Des Cartes Doctrine, or the common Laws of Reflection and Re­fraction, he would have been of quite another mind, and would not so positively have asserted a Proposition so positively contrary to the Principles of Des Cartes, and all Experiments. For if what he affirms were so, then (as I urged before) according to Des Cartes Doctrine, and the Doctrine he would defend, the Image from a Looking-glass must be returned coloured, and the same also from a plain sided Prisme, where the refracting sides are Perpendicular or equally inclined, but contrary ways to the Reflecting Superficies. But this is contrary to Experiment, he must therefore once again consider how to find out a Reason why there is no colour generated, where, according to his Assertion, there is so great a re­fraction, and a doubly promoted Rotation made in both the refracting Superficies the same way, and both so much promoting the said Rotation of the Globuli. He might therefore, if he had pleased, have suspended his Conclusion. Adeo ut Doctrina Cartesiana de Globulis eo­rumque Rotationibus nihil periclitetur ab hac Demonstra­tione [Page 39]quae quamvis satis elegans sit & concinna, debitum ta­men scopum non omnino attingit, until he had a little far­ther considered the nature of Reflection and Refraction. Now, because I find that the Learned Doctor is not the only person that hath not rightly apprehended this Theory, give me leave to explain a little more particu­larly the manner thereof: Suppose we then in the three Figures D E and F, that the space between the two Parallel Lines a c and b d doth represent a Ray or Radia­tion of light; Not a Mathematical Line, but a Physical one of some Latitude, between which Lines is propa­gated a motion, or something equivalent thereunto, which serves to produce the effect of light. This motion we suppose to be propagated by a Pulse or Wave in all uncoloured Rays at Right Angles with the Line of Di­rection, but in coloured Rays more or less obliquely ac­cording to the greater or less refraction. We will sup­pose the stroke of the Pulse to be the length of the space between 1 and 2, or 2 and 3, or 3 and 4, &c. and con­sequently, in a uniform medium the pulse will continue the same, and the expansion of it will be Perpendicular to the Line of Direction or progress; but when it comes to the Refracting Superficies c d, Obliquely the side of the Pulse c touches the refracting Superficies first, and be­ing propagated into the refracting medium by a longer and quicker Pulse, it is propagated to 4 below c before the other side of the Pulse touches the Superficies at d, the Pulse therefore 44, 55, 66, &c. becomes Oblique to the tendency of the Radiation; and by the Superfi­cies ef it is reflected by 77, 77, 77, till it touches the second refracting Superficies g h; where it is observable, that the same side of the Ray that entred first the Super­ficies c d enters first into the Superficies g h, in the same manner as if it had proceeded on by the straight Lines f m e l till it met with a Parallel Superficies l m to the first c d; for the Ray between the two Parallel Lines f h, e g, hath the same inclination and respect to the Refracting Superficies h g, that the Ray between f m and e l would [Page 40]have to the Superficies m l, supposing there were no Re­flecting Superficies at e f. I shall not need, I hope, more particularly to demonstrate every part of this Explana­tion, the very observing the Delineation of the Scheme being enough to make it plain to any one never so little versed in Geometry, from which he will plainly per­ceive that what I endeavour to demonstrate was really so, and that I did understand what scope my De­monstration aimed at, so far as to hit the Mark, which was to shew that Colours were generated, where, ac­cording to Des Cartes own Principles, there could be no Rotation of the Globuli. Now, though the Learned Doctor would not admit of this Demonstration to be sufficient to do the work, yet he says, Pag. 252. Verun­tamen dissimulandum non est, non pauca me meapte opera excogitasse quibus pro persuasissimo habeo eorum motus & rotationes modis pure mechanicis semper fieri non posse. And in prosecution of the destruction of this Rotation of the Globuli, which he hath hitherto seemed to defend, he adds four several Arguments, I shall not now stay to re­peat them. But whosoever will please to read what the Learned Doctor hath suapte opera excogitated against the Cartesian Hypothesis, and set down in the 252, 253, 254, and 255. pages. And compare them with what I have said in the forementioned place, to wit, at the latter end of the 60. and the beginning of the 61. pages of my Micrographia, may plainly find the Arguments brought by the Doctor do very little, if at all, differ from those I there published.

I could heartily therefore have wished that the Lear­ned Doctor had made use of some other Mediums to prove the Existence of an Hylarchick Spirit, and not have medled with Arguments drawn either from Me­chanicks or Opticks; for I doubt, that such as understand those subjects well, will plainly see that there is no need of any such Hylarchick Spirit; and if there be no need of it, but that all the Phenomena may be done with­out it, then it is probable that there is none there, for [Page 41] Natura nihil agit frustra. It had been much easier to have proved the existence of it by Arguments drawn from sub­jects we less perfectly understand, as from the generati­on, nutrition, vegetation, and propagating of Vegetables, and animal substances; for there the manner of the progress of Nature being infinitely more curious and abstruse, and further removed beyond the reach of our senses and un­derstandings, one may more boldly assert strange things of this Hylarchick Spirit without fear of controul or contradiction, and from whence possibly it may never lie within the power of Reasoning to banish him.

But to leave this Digression, and return to the use of these water-poises.

A fifth effect may be for washing and refining of Earth, Clays, Powders, and the like; the clear water by these contrivances being made to run over gently at the top, and so leaving all the settlement from the water at the bottom.

By any one of these, with a receptacle Cistern added to it, the stream of water from that Cistern may be acce­lerated or retarded by any degrees desirable. This doth de­pend partly from the proportion of the Tap of the Recep­tacle Cistern to the Tap of the counterpoised Cistern, and partly from the shape and make of the Receptacle Cistern, by the proportion and shape of which the stream of Li­quor through the Tap of the Receptacle Cistern may be modulated at pleasure, as any one, a little versed in Hy­drostaticks, will easily perceive and demonstrate.

A sixth effect may be for governing the heat of Lamps for Distillations, Digestions, Fermentations, Putrefacti­ons, Dissolutions, hatching the Eggs of Birds or Insects; accelerating, and seasoning, or timing the growth of Plants; nealing of Glasses and Metals by the gradual ac­cess of the heat, so as to make them fit for stronger [Page 42]degrees, or by the gradual recess to bring them out of the greater degrees to make them tough and capable to re­ceive the cold of the Air.

It would be too long to give instances of contrivances for every of these operations but the skilful Mechanist, Philosopher or Chymist will easily supply his own desires by some one of these I have instanced in, or at least by a composition of them. I shall therefore only add a descri­ption of a Clepsydra or time-keeper or two, and so leave this subject for the present.

COMETA, OR, Remarks about Comets.

ON Saturday morning, April 21. 1677. I first saw the Comet, of which I had been advertised the day before. It appeared in the Sign Taurus, be­tween the base of the Triangle, and the unformed Stars in the Cloud of Aries, dignified by P. Pardies, with the figure of the Flower-de-luce. The head of it was in a right line, with the heart of Cassiopea, and Alamak, or the South foot of Andromeda. and as near as I could judge by my naked eye (having no Instrument or help by me) it was ⅚ of the distance between the feet and the Girdle of Andromeda, distant from the said Alamak towards the South.

Its tail sometimes as the Air was clearer and darker, extended about three quarters of its distance from the aforesaid Alamak, and pointed directly at the Star in the nose of Cassiopea of the fourth Magnitude, and conse­quently the head of the Comet pointed not directly at the Sun (the Sun then being about the eleventh degree of Taurus) but rather towards the fourteenth degree of the same Sign. Its appearance was very small and slender, and as people commonly ghessed, about two yards long; and the head about the bigness of a Star of the first magnitude, but of a much fainter and duller light. Its blaze about three o'the clock seemed to rise straight up­ward, [Page 2]before that about half an hour after two it lean­ed a little Eastwards, or towards the right hand, and after three, as it rose higher, inclined towards the left side or Westwards. The head to the naked eye was brighter than the blaze, and seemed to be somewhat bigger than that part of it which immediately joyn'd to the head; but those parts of it which were farther di­stant, were of a much greater breadth; spreading wi­der and wider, as they were more remote from the head, and in the same proportion also growing fainter and fainter in their light, especially towards the out­sides: but the middle parts or medulla appear'd much longer, and the brightness much greater, which made the whole blaze to seem to taper, or be pointed towards the top.

The length of the Blaze appeared sometimes shor­ter, and sometimes longer, by several vicissitudes; and as the day-break, or dawning increased, so the Blaze shortened, and especially towards the sides near the top, and shortly after before the Sun rose, disappeared.

But notwithstanding this shortning and lengthening of the Blaze, I could not perceive any kind of motion in the parts of it, such as is observable in flame, smoke, or other steams rising from a burning or hot body: but the same parts of the Blaze seemed to appear and disap­pear in their proper places as if they had been fixed and a solid body.

The first Figure I have here annexed will with some short explications, represent the appearance of it to the eye, more plainly than by a multitude of words, with­out it 'tis possible to express.

A, represents the head of the Comet, the middle of which appeared brighter than any other part; about which was a hazy light somewhat like the shining of a Star through a thin cloud; the lower part of which was pretty round and defined. B, the neck of it, which seemed to the naked eye of less Diameter, and less bright than the head, but through a six-foot glass, as I [Page 3]shall mention by and by, it appeared bigger, though not so bright. The middle of this was very bright, and seemed to issue from the Nucleus or Star in the middle of the head. C, the brushy parts which were fainter and paler towards the sides, especially nearer the top, which made the whole seem to taper and resemble the Figure here exprest: Observing it with Telescopes (one of which was fifteen foot, and the other six foot long) I found the shape of it much like this, which I have re­presented in the second Figure.

It had a pretty bright Star (if I may so call it) near the middle of the head, seeming much about the bright­ness of ♄ when near the Horizon, and was about 25 seconds in Diameter; as is represented by A, not per­fectly defined, but hazy; the cloudy part or beard of the body encompassing it on all sides: but that part of the Coma B, which was next towards the Sun, was the narrowest: nor was this Coma well defined, but the outward parts of it were fainter and fainter. However they were regularly enough terminated to make the out­ward most bounds of it of a kind of Parabolical figure; the most bent part of which was towards the Sun, and most defined: And the bright Star of it was, as I have expressed it about four of its Diameters di­stant from the said parabolical limb. The light parts of the ambient Cloud seemed to spread gradually towards that side of it, which was opposite to the Sun; but those which were next the middle were the brightest: and al­ways as they were farther and farther from the Star in the head, the fainter and paler they were.

I could not observe any representations like those which are given us by Mr. Hevelius, in his Cometogra­phy, neither in the Head, nor the Blaze, no more than I could in those which appeared in the years 1664. and 1665. as may be easily taken notice of by comparing these which I have here delineated with those.

The middle part of the Blaze CC, which ascended from the Star in the middle, seemed the brightest, and [Page 4]of this medulla or stem, those parts were brightest which were nearest situated to the said Star. The sides of it grew fainter and fainter, as they were farther from the head; and though they had brightness enough to make them appear in a dark and clear sky, yet the dawning quickly made them vanish, and disappear, as did any haziness of the Sky: and according as the light increa­sed, so was the Blaze diminished, after the order of the tapering prickt lines exprest in the third Figure by a a a, b b b, c c c, d d d, &c. and even in a clear and dark Sky, towards the farther end of the Blaze they of­ten disappeared for some short space of time, though the middle or stem continued; and so it caused the re­maining appearance to resemble the figure of a very slender birchen whisk or brush, much like that represen­ted in the first figure.

The 22. from half an hour after two, till half an hour after three, the North-east part of the Heavens to me was cloudy, and the Sky between the Clouds was ha­zy, and the dawning struck much higher than the day before, so that I could not find it.

The 23. with several friends I observed it again, the Sky being clear, and confirmed my self in all my for­mer observations, taking again diligent notice of all circumstances remarkable, both with my naked eye, and with Perspective-glasses. And I had this morning a very notable observation in order to measure the bigness of the Star and its Coma which encompassed it, by compa­ring it with somewhat fixt: for some few minutes be­fore three of the Clock the head of it past just behind the type or top-post of a tower not far distant, and was quite eclipsed by it; and as soon as it appeared to have past it, seeming yet contiguous, I observed it with my six foot Telescope, and found the Coma or whole head to appear full as big as the said type or timber post, and the Nucleus or Star in the middle of it, to be very near of the same bigness of the iron spindle, upon which the weather-cock was fixt. Whence upon examining the [Page 5]bigness of the said parts, since by an accurate Instru­ment I judge the head or Coma was about 4 ⅙ minutes in Diameter, and the Nucleus or Star about 25 seconds. I took notice this morning that it had much altered the position in the Heavens, which it had upon Saturday morning, and that the Blaze of it was very much de­flected out of the line it appeared in the last time. And with a small crossstaff, taking the distance of it from Alamak, and from Genib, in the left side of Perseus. I judged it to be in the mid-way between the Flower-de­luce aforesaid, and Algol, or the head of Medusa, that is, about 14 degrees of ♉, and 17 degrees of Nor­thern Latitude: so that I judged its motion almost East, but a little deflecting South. I was not much solicitous of making observations of its true place, as not de­signing my present enquiry to be for what kind of moti­on it had, conceiving its motion to be towards the Sun, and so of very little duration: and expecting to hear an account of that from other places, and persons that were better furnished with Instruments and convenien­ces for observations of that kind than I was then.

The Blaze extended it self in a right line towards the Star in the right thigh of Cassiopea, being a Star of the third magnitude. Its length at first was about 7 or 8 degrees, and did sometimes seem longer, sometimes shorter, as I noted before, without seeming to have any other motion in it but the Diurnal motion, the same with the fixt Stars on Earth. Whence I collected, that the head of it pointed towards the seventeenth degree of Taurus in the Ecliptick, though the Sun at that time was about the thirteenth degree of the same Sign.

The 24. with several others, I attended the appea­rance of it, but the Sky in that part of the Heavens was over-cast with Clouds.

The 25. I expected to have a farther Observation of it from half an hour after two, till a quarter after four; but notwithstanding the South-easterly wind, and the clarifying quality of the air, which before half an hour [Page 6]after three had partly carried off, and partly dissolved the black thick Clouds (with which the North-east parts of this Horizon was over-cast about three of the Clock) and left that part of the Heavens where the Co­met should have appeared clear, and without Clouds. Yet the air being very high and heavy, as the Barome­ter shewed, the upper parts of it were so filled with the dawning light of the morning, that neither the Blaze head or Star of the Comet appeared to me in the least: nor had I any sight of it since.

The like appearance of the great height of vapors in the air, when it is very heavy, I have often taken no­tice of, and have observed, that the twy-light and dawning between the night, and appearing of the Sun is very much altered thereby. And that a heavy air, when the vapors are raised high, will make the length of them much greater, and consequently the night short­er. And a light air, on the contrary, shortning them, doth lengthen the night.

These were the most remarkable circumstances I took notice of in this Comet, being altogether Physical, and designed only for enquirng into the constitution of these wonderful bodies: the accounts and opinions we have hitherto had of them of that kind, being very unfatis­factory. Though other Observations, to wit, Mathe­matical, of the way, celerity, and magnitude of Comets have been prosecuted with very much care, and great skill; such as those of the noble Tycho, and the learned and diligent Hevelius, insomuch that I could not expect to have better; yet as to Physical remarks, I wanted much information to be able to satisfie many difficulties that occurr'd to my thoughts, upon enquiry into the particular natures of them. I did therefore, as I de­signed, employ all the time I could get of observing this Comet, in taking notice of such circumstances as I judged would be pertinent to resolve any of those Que­ries I had formerly made, in order to find out the nature of Comets in general. And though the little oppor­tunity [Page 7]I now had, and the disadvantageous appearance of this last were very short of giving me that satisfacti­on in many particulars which I wish'd for, and expected at first, yet since they may possibly serve for hints to others that may hereafter have better oportunity than I, and that I might understand what material objections could be made by observers from preceding Comets, and that they might for the future more diligently take notice of what from these queries and hints may be judged sig­nificant to this design, such as they are I have here pub­lished as I had done formerly by my Lectures in Gre­sham-Colledge, those which I had made of those in 1664. and 1665.

Now before I come to make relexions upon these re­marks, I thought it might not be improper to add some few of those things concerning those two former Co­mets observed by me in the said years. I say, some few, because it would be needless to set down all, especially such of mine as do agree with others since published. I did therefore soon after I had seen the first Comet, to wit, December 23. 1664. propound to my self certain Queries necessary to be answered, in order to find out a true theory of them, and directed my Observations accordingly; and they were these.

Of what substance its body, beard, and blaze is? and next, of what magnitude each of those parts appear, and of what real magnitude they are?

Other Queries were concerning its density and rari­ty, its mutability or immutability; that is, whether it dissolved and wasted or not? whether it were fluid or solid? whether it participated of gravity or levity?

Whence it had its light, colour, &c.

What was the sigure of the Star, Radiation, Blaze, &c.

Whether the Blaze were always opposite to the Sun, or deflected? whether straight or bended, &c.

What kind of motion it was carried with? whether in a straight or bended line? and if bended, whether in a circular or other curve, as elliptical or other com­pounded [Page 8]line, whether the convex or concave side of that curve were turned towards the earth? Whether in any of those lines it moved equal or unequal spaces in equal times?

Through what parts of the universe it moved, and how far distant it was at several times? Whether in the lower Regions near the Earth in the Atmosphere, or near it, or in the Heavens, or fluid AEther, with which the space of the Heavens is filled? Whether above or below the Moon, &c.

Whether it wasts, and is dispersed and consumed? or whether it lasts and endures for a longer time? If it lasts, Whether it ever appears again, being moved in a circle; or be carried clear away, and never appear a­gain, being moved in a straight or paraboloeidical line? Whether it be collected or generated when it first ap­pears? and dissipated or destroyed when it disap­pears; or whether the several distances of it do not make that appearance?

Whether it may not have some such propriety, as the Star in Cete, whereby it may shine and appear for a cer­tain period, and again lose its light, and disappear by several vicissitudes? and whether that may not give some account of the appearance of so many Comets about Aries?

First, As concerning the matter or substance of the Nu­eleus Star or body, of the hazy shining part encompassing it, and of the Tail or Blaze: I say, that by comparing all the circumstances that I was able to take notice of from the beginning to the end, I found that the Star in the head was of a very compacted and dense light, and almost equalled that of Saturn; though it were not like that confined by an equal limb: that there were some parts distinguishable in this body, some having a bright­er, others a fainter light. That these parts did not continue the same, but considerably varied, which might in part be caused by the differing position of those parts which were seen before, from the same seen afterwards, [Page 9]in respect of the eye, situate on the surface of the Earth, moved one way, and the Comet moved ano­ther; though I do not conceive it wholly ascribable to that, but partly also to a real alteration of the parts of the Comet. That I did very diligently watch to ob­serve if it were possible, when it pass'd over any fix'd Star to find whether it were transparent; as I had se­veral times observed the tail of it to be even in its brightest parts, but I had not the opportunity; but that I did several times observe the tail of it transparent, not only with the naked eye, but through a Telescope: if at least the fixed Stars be above it, which I think few doubt, that the light diminish'd by degrees towards the extremes of the hazy part encompassing it; and yet the extremes of it as to that part of it which respe­cted the Sun, seemed pretty evenly and smoothly de­fined, especially through a Telescope: From all which remarks, and from the velocity of its motion, I con­jecture it to be made up of solid matter, not fluid; that the body of it especially, is considerably dense, but that the haziness or Coma about it is much more rarified, and the tail thereof is most of all. That this body is en­compassed with a body most fluid, and easily permea­ble, and which doth with very little resistance give way to the motion of it, or any other body through it, that it doth easily admit at least (if not actually take in­to it self) the parts of this body, Coma, and Blaze. I say, admit at least, (though there may be many reasons alledged that it doth actually prey upon, and dissolve those parts into it self, as I shall shew by and by) be­cause that we find that the extreme parts do extend but to such a distance, and beyond that there is no appea­rance of light, and that the light is from it self, and not produced by refraction or reflexion of the beams of the Sun, I shall shew reasons by and by. And consequent­ly, where there is most light appears, there are the great­est number, and there is the greatest density of the Cometical parts. The middle of the body may be as [Page 10]dense as the body of the earth; and I have not obser­ved my self, nor met with any body else that hath taken notice of any thing to the contrary: If I could have seen any Comet to have covered any Star in its way, it would have afforded a very circumstantial information, especially if for this purpose it had been taken notice of with a good Telescope. What the density of the in­nermost parts of this Earth we live on is, none knows; for though we find the parts on which we tread to be very compact, and though by the industry of Miners it hath been proved so also to the depth of many hundred foot, as Georgius Agricola relates: and though it hath been found so even to a greater depth by the soundings of the bottom of the Sea, yet none can bring an unde­niable proof that the same is so solid to 25 miles deep; much less that it is so to the center: if therefore the ex­ternal shell of this Globe were broken, and removed, 'tis not impossible but that the middle parts thereof may be of the same nature with the middle parts of the Comets body; and that those parts (were the superfi­cial parts or shell removed) might, like these of Co­mets expand themselves into the encompassing AEther. Nay we find, that notwithstanding the compacted­ness of the superficial parts of this Earth, yet the AEther is able to take up into it self vast quantities of them, and to keep them suspended, some of them, even to the height of many miles, if any argument may be drawn from the height or length of the dawning or Crepuscu­lum; and this, notwithstanding the attraction of the Earth in its perfect vigor, or the gravitation of these parts thus taken up, or their endeavour towards the center of the Earth. How much more freely then might we imagine the encompassing AEther to prey up­on, and take up into it self the internal parts, if they were of a loose and pervious texture, and almost in a state of fluidity, like a heap of Sand, or a vessel of Ala­baster-dust in boyling, and were not so firmly united by the bonds of gravity, and the vinculum of petrifa­ction, [Page 11]as we find the superficial parts of the earth now are. There is one argument to prove to us, that there may be such a looseness of the internal parts of the earth, and that is that the magnetical virtue varies, which virtue without controyersie diffused through the whole body of the Earth, and which hath a relation to the whole Globe, and to every magnetical part thereof. For by observation 'tis found, that the magnetical virtue acts upon a needle without it, as the magnetical virtue of a round Loadstone doth on a Needle applied without that, which, as I may elsewhere shew, hath a respect to the center of the stone differing from all the respects that Authors have hitherto ascribed to it, even of Gil­bert, Kepler, Kircher, Descartes, and our Country­man Mr. Bond, who I think was the first man that endeavoured to reduce the variations observed by Wright, Gellibrand, Coster, &c. into a Theory and calcu­lation. Now this magnetical virtue, (which may be cal­led one emanation of the Anima mundi, as gravity may be called another) being diffused through every part of it, and seeming to be, as it were Tota in toto & tota in qualibet parte, and to be more spiritual, and to act more according to Magical and Mystical Laws than Light, Sound, or the like, it giving to every mag­netical body, and every piece of it, though infinitely divided, the same proprieties it hath it self; This magnetical virtue, I say, having such a relation, and be­ing forced thus to vary, 'tis very probable that the in­ternal parts to which it hath a respect, have a variation likewise; and consequently, that these internal parts which are supposed generally very dense, compact, and very closely and solidly united, may be notwithstanding more loose, and ununited, and movable from certain causes.

To proceed therefore, I say, that it seems very pro­bable to me, that the body of Comets may be of the same nature and constitution with that of the internal parts of the Earth, that these parts may, by the help of the [Page 12]Aether, be so agitated and blended together, as to make them work upon, and dissolve each other in the same manner, as we have often had examples of some of the parts of the Earth; a late instance of which was at Mongibel or Aetna in Sicily, where the Fire continued for a long time, and produced very considerable effects. That this internal agitation may confound the gravita­ting principle, and so leave the parts in a greater free­dom to be dissolved by the encompassing Aether, which is the agent that sets the other two at work to destroy each other, that it may at length prey upon both, and dissolve them both into it self; and consequently, not only the parts thus dissolved are elevated to a greater distance from the center of the Star or Nucleus, or the superficies of it, whose gravitating or attractive princi­ple is much destroyed, the Coma being in this Comet four or five Diameters of the Star or Nucleus: but ha­ving given those parts leave thus far to ramble, the gra­vitating principle of another body more potent acts up­on it, and makes those parts seem to recede from the center thereof, though really they are but as it were, left behind the body of the Star, which is more powerfully attracted than the minuter steaming parts: for, I suppose the gravitating power of the Sun in the center of this part of the Heaven in which we are, hath an attractive power upon all the bodies of the Planets, and of the Earth that move about it, and that each of those again have a respect answerable, whereby they may be said to attract the Sun in the same manner as the Load-stone hath to Iron, and the Iron hath to the Load-stone. I conceive also that this attractive virtue may act likewise upon several other bodies that come within the center of its sphere of activity, though 'tis not improba­ble also but that as on some bodies it may have no effect at all, no more than the Load-stone which acts on Iron, hath upon a bar of Tin, Lead, Glass, Wood, &c. so on other bodies, it may have a clean contrary effect, that is, of protrusion, thrusting off, or driving away, as [Page 13]we find one Pole of the Magnet doth the end of a Needle touched on the opposite part; whence it is, I conceive, that the parts of the body of this Comet (be­ing confounded or jumbled, as 'twere together, and so the gravitating principle destroyed) become of other natures than they were before, and so the bo­dy may cease to maintain its place in the Universe, where first it was placed. Whence instead of continu­ing to move round some central body, whether Sun or Planet, as it did whilst it maintained it self entire, and so had its magnetical quality (as I may so call it) uncon­founded, it now leaves that circular way and by its motion (which always tends to a straight line, and would be so were it not bended into a curve by the at­tractive virtue of the central body) it flies away from its former center by the Tangent line to the last place, where it was before this confusion was caused in the body of it. In this line ('tis probable) it passes from one part of the Heavens to another, and so passes through the spheres of the activity of multitudes of central bodies; in the passing through which spheres, 'tis not improbable that those parts which by their disso­lution are made of a nature differing from the body in the center, are rather expelled from, than attracted to­wards it; and so being by this dissolution rarified, and loosened from the middle, and by their acting upon one another, and dissolution of the Aether made of another nature, after they have every way dispersed themselves to a considerable distance from their proper body, are converted and driven in a way almost opposite to that expelling body, and so continue to be driven away to such a vast distance, as to make out that prodigious length of the tail or Blaze of some Comets (such as was that of 1618. which, as Kepler reports, was exten­ded to 70 degrees from the body or head of it) till at last they are dissolved also, and commixed with the Aether within them. So that though I suppose the at­tractive power of the Sun, or other central body may [Page 14]draw the body towards it, and so bend the motion of the Comet from the streight line, in which it tends, in­to a kind of curve, whose concave part is towards the Sun, by reason that there are some central parts of it, which are not yet destroyed, and so retain somewhat of its gravitating principle: yet I conceive that all those parts of the Comet which are thus wrought upon by the other, and changed into another state, and are ve­ry much rarified, and produce light, are of a clean con­trary nature, and recede from the center of the Sun: much after the same manner as we find any combustible body with us; as Coal, &c. where we find that the body of the Coal, before it be resolv'd into smoke, is a very dense, and very heavy body, and tends to the center of the earth; but the parts thereof agitated by the Air and Aether into steams and smoke, and those yet farther dissolved into flame, do tend upwards, and from the center of the earth. Now though one cause of the recess of flame from the center of the Earth be the gravity of the ambient Air. Yet 'tis not impossible, but that there may be somewhat also of positive levi­ty conjoyned therewith. Most certain it is, that there must be a tendency of receding, as well as a tendency of approaching the center of the Earth, and other at­tracting body. And there may be much said for the supposition, that the recess of the purest Aether, from the center, is the cause of the motion of the grosser Aether, and of all other bodies towards it, though there are also very considerable arguments against it. But this discourse is not my present business, though it may hereafter be the subject of a Lecture in this place; for upon it do depend some of the greatest operations in the universe. And as in the History of the Creation, we have an account of the production of light, imme­diately after the making of matter, which is a motion of recess from the center of the shining body. Next that, a Firmament which divided between the waters or the fluids of the one, and the fluids of another part of [Page 15]the world. And in the third place, the collections of particular fluids to one center, as the center of the Earth: and lastly, out of that collection of fluids ap­peared the dry and solid land. So I conceive the most proper way of speculating on these great productions of the omnipotent Creator, may be to begin with the consideration of light, or the motion of recess from the center of a body. Next, with the consideration of the cause of the separating of fluid from fluid, as Ae­ther from Aether, as I may so call differing Aethers; be­cause we have not yet distinct names in use, and the reason of their conglobation, the Aether from the Air, the Air from the Water, the Water from Quicksilver, Oyl, or other fluid. Thirdly, the cause of the conglo­bating property of each of these fluids when separa­ted, how they accept and embrace Homogenea, and reject or expel Heterogenea. And fourthly, how they condense and settle together, and produce a solid bo­dy: whence proceeds the confirmation of attraction or gravitation, &c. But to digress no further, but con­clude this part of enquiry in short, I suppose the Nu­cleus or Star of the Comet may be much of the like na­ture with the central parts of the Earth, Moon, Mars, Jupiter, Saturn, or other Planets, but much impaired in its attractive or gravitating power.

Next, that the Coma or Hazy Cloud about it, may be of the nature of the Atmosphere or Air about the Earth, or the Smoke or steams about a heated or burning body, before they are quite kindled, converted into Flame, or dissolved into the ambient Air.

Thirdly, that the Tail or Blaze is much of the nature of the parts of Flame, though with those differences I conceive, that the parts of these steams are not so close together, as are those of Smoke: nor doth the motion of them, though much swifter upwards than that of our Flame, serve to make them appear a shining line; but being at that distance, they appear much slower to the eye, and so discontinue the appearance; whence every [Page 16]shining particle appears only a shining point, though in the parts of flame (where notwithstanding the motion be much slower, yet being nearer; and so varying the position to the eye much quicker) each of the shining parts makes an appearance of a line of light, and all of them passing pretty near together, make the appea­rance of a continued fluid flame; though that indeed be nothing but a great number of single parcels of the burning body, raised up in the particles of Smoke. This will appear evident if we consider the appearan­ces easily to be taken notice of in light: for 'tis obvi­ous from multitudes of experiments, that any shining body, as a candle or brands end, being moved very quick, makes the same impression on the eye, that a line of light doth standing still: And as obvious also that any very light body incompassed with a dark medium appears to the eye under an angle bigger than really it is, and a dark body encompassed with a light medium much less. This any one may presently find, if he make a small hole through a thin plate of metal, and holding it first between the light and the eye, and so seeing the light appear through it, and then placing it so as there is nothing but darkness appears through the said hole, for he will plainly perceive that the same hole will ap­pear much bigger in the former position than in the lat­ter. Upon this account indeed each of the shining parts of the Comet seems to fill and occupy a much greater space than really it doth: and so, as 'tis obser­vable in the milky way, a great number of these small shining bodies though dispersed at a pretty distance one from another, yet by reason of the imperceptibleness of each of them they all seem to coalesce into a stream or Blaze of light, the brightness of which is yet farther augmented by a clear and unenlightened air, and by such a part of the Heaven wherein there appears fewest of the Stars, whether they be greater or lesser.

To the Query, Of what magnitude the Body, Coma, and Blaze of Comets may be? No answer can be given until an­other question be first answered; and that is, What is the place of Comets, and what is their distance from the Earth? It was the opinion of most Modern Writers before Tycho Brahe and Kepler (I know divers of the Antients thought otherwise) that Comets were sublunary Me­teors, drawn up into the higher Regions of the Air, and there set on sire, and so continued burning till the Meteor were consumed; and as the matter increased, or wasted, so did the appearance of the Comet. But this noble Dane, and several others about that time found by accurate observations made, that its Parallax was less than that of the Moon; and consequently, that it was farther distant from the earth: that it must be a body of another magnitude, and nature, than most before that time had imagined; and therefore that it ought to be otherwise thought of than the generality of mankind believed concerning it. Many had been the attempts of former Writers concerning them, to find out their parallax; and whether from their unac­curate instruments, or from their less skill and diligence in using them, or from an imagination of the solidity, and impenetrability of the Coelestial Orbs, or from er­ror in their calculations, or from comparing Observations made at distant places, one or both whereof were un­accurate, or from a prepossession of Tradition or com­mon Fame, or from what other cause soever it were is uncertain; but 'twas generally concluded by them, that all Comets were sublunary Meteors: and there are not even at this day wanting some of the same opinion, though for what reason I know not. 'Twill be hard to convince some of these, that the opinion they have hitherto received for good, is not so, because they will hardly give themselves the trouble of examining strictly into the matter: And to understand the nature of Parallaxes, and how significant they are in deter­mining the distances of bodies from the surface of the [Page 18]Earth, to certain degrees thereof; beyond which, by reason of the imperfections in Instruments, and Obser­vations, and the exceeding niceness and curiosity neces­sary, they signifie very little. It is not my present de­sign to explain what Parallax is, that I would suppose my Reader to understand; otherwise there can be no reason shewn him to convince him that 'tis possible to prove that this or that Comet was not nearer than so many semidiameters of the Earth, nor farther off than so many. There are then two ways, by which we may come to some certainty of what distance a Comet is; and those are, first the Parallax of its Diurnal motion, or its Parallax caused by the Diurnal motion of the Earth. And secondly, the Parallax of its proper motion compared with the Periodick or Annual motion of the Earth. The first of these may be observed two ways; either by two Observers at parts of the Earth very far distant from each other, but as near as may be under the same Meri­dian: as suppose the one in London, the other in St. He­lens; both conspiring in their observing of the place of the Comet amongst the fix'd Stars at the same time. Or secondly, by one Observer in the same place, by ob­serving the place of it amongst the fix'd Stars, in its ri­sing or setting, and in a greater, or if it may be, its greatest height: The noble Tycho by very accurate Observations of the Parallax, proves the Comet of 1577. to be above the Moon. Kepler by his own Observations proves that of 1607. at its begin­ning to be four times farther distant; and I doubt not but some may have been above forty times farther. But I do not yet find that any Observations have accurately de­termined that which is indeed the great help by which we are inabled to judge of the nature, and all the o­ther accidents and proprieties of Comets. The Aristo­telian Philosophy for a long time prevailing, made the world believe them to be nothing but Exhalations from the Earth, drawn up into the higher Regions of the Air. But Tycho by his Observations of their Parallax, raises [Page 19]them out of that confinement, but yet he seems to place them in an Orb about the Sun. But Kepler frees them from that confinement, and assigns them the Universe to expatiate in. But none of all these do accurately prove the true distance of them, their Parallax being for the most part so very small, that I fear Instruments with common lights will hardly reach them. But we must expect from future observations made with Tele­scopical Instruments to receive a certain Answer to this Query. Certain I am, that the Comet which began to appear in November 1664. and disappear'd in March following, was far removed beyond the distance assign­ed by Kepler. For by my own Observations divers times repeated, I could not find any senfible Parallax, though I endeavoured by a new method to make my Observations more accurate. Now though I had not the convenience of making use of a Quadrant, or any such Instrument, to observe its place when near the Ho­rizon, yet the way I took, would, I think, be as good; which was this: With a very good six foot Perspective­glass or Telescope, I observed the place of the Comet, in respect of the adjacent small Stars, as soon as it ap­peared, and so traced its way till it disappeared in the vapors of the Horizon: the like I did several other days successively, taking notice by what degrees, in what times it made its progress, to see whether by its Parallax, when near the Horizon, it would have been deprest below that line of its motion, which it kept, when at a greater height above it. But though I tried this several times, yet I was not able to discern that the Parallax of it caused either any sensible bending of the line, or any sensible inequality in its progress, by which I should have sooner found it, than by taking its altitudes with common Instruments: though I confess these Obser­vations were made when the motion of the Comet was slow, and consequently, when in probability it was far distant from the earth. To me there seems no doubt but that it was a long way removed above the Moon [Page 20]when I made these Observations: for had it been of an equal distance with that they allow the Moon, it must this way have manifested a very sensible Parallax of di­vers minutes: but whereas I could not certainly distin­guish any sensible at all, it must be many times higher than the Moon. Now that this way is abundantly to be preferred before an Observation made with a Qua­drant for the taking of its altitude, is pretty evident; because, by this means the greatest part of the irregu­larity, caused by the refraction or inflection of the Air is removed; for by this means, though the Parallax be very large, yet the refraction or inflection of the Air will not amount to many seconds, both the objects be­ing almost equally raised by refraction, especially when 5 or 10 degrees high; nearer than which the small Stars vanished out of sight by the thickness of our air. It follows therefore that a Semidiameter of the Earth must be a very inconsiderable measure in its distance.

This part therefore of the Theory of Comets hath been much defective hitherto. If we enquire the Parallax of them from the Observation of divers men made in differing places. we shall find them so differing one from another, that there is great reason to suspect them all: Nay, not only so, but in this Comet of 1664. by comparing two Tables or Charts of the Stars, and Constellations of that part of the Heavens, through which the Comet past, on which was also markt out its way and place from day to day, both of them Prin­ted from Copper Plates, I find that strange errors and mistakes may be created, notwithstanding all the Au­thors thors care and accurateness possible, from the carelesness or neglect of the Graver: This I noted in the two Tables of the learned and accurate Mathematician, P. Aegidius Franciscus de Gotignies, (whose skill and care from other works of his and other Observations of this Comet I am sufficiently assured of) and found that by the first table upon the ⅔½ of December, 1664. it [Page 21]was in 4½ of II in Longitude, and in 33⅔ of Southern Latitude; but by the second it is placed at the same time in 4°II for its Longitude, and in 34½ of South La­titude. And this error is not only committed in the place of the Comet, but also in the place of the fix'd Stars: for Riget in the first Table is placed in 30¾ South Latitude, and in 12¾II for Longitude, but in the se­cond in 31½ South Latitude, and in II ½ II for Longi­tude: both which differ considerably from the place of it assigned by Riccioli and Grimaldi; according to whose Observations it should be in 31. II′ South La­titude, and 12°. II′. 40″. II in Longitude.

Now if there be these differences to be remarked in the Observations of one, we cannot but expect that much more disagreement should be found between those which have been made by differing persons in dif­fering places, and with differing ways, and differing Instruments. And upon examination I have found it no better: for from comparing such Observations as I have received from several parts of the world, even of those which have seemed more than ordinarily exact, I find them for the most part so unaccurate, that though they sufficiently manifest that the Comet of 1664. which lasted above four months, was visible in most parts of the world, and seen to pass in all those places pretty near in the same way amongst the fixed Stars. Yet they are so far from manifesting the Parallax, that some of them make the place of the Comet to be quite contrary to what parallax would make it; some of the Southern Observators placing it much more South­wardly than those of the North. Others indeed of them make the Parallax so great, that one might ghess it to be not so far removed from the Earth Something indeed in the general might be ghest of the way of that Comet amongst the fix'd Stars, especially when it ap­proaches them pretty near: but for exactness of Calcula­tion for Parallax, they were no way useful. And even­in [Page 22]the former use too it seems very doubtful for com­paring the Charts of the Comets way amongst the fix'd Stars published by that diligent and unwearied Obser­ver Mr. Hevelius of Dantzick, the above-mentioned P. Gottignies, Professor at Rome, and Monsieur Petit of Paris, I find, that the two former make the way of the Comet to lie below the Star in the Bill of Corvus; whereas the later, though in a Latitude interposed be­tween the parallels of the former, makes it to lie a­bove, or to the North of it: and with him agree some Observations which I have seen of Monsieur Hugenius. Other differences I found between those Tables in the way of the Comet of 64. near the middle of its arch; wherein Monsieur Hevelius all the way places it more Southward than either Monsieur Petit, or P. Gottig­nies: for whereas both P. Gottignies, and Mounsieur Petit make it pass above the Star of the third magni­tude in the right shoulder of Lepus, Monsieur Heve­lius makes it move below it, which seem to be ascribable to Parallax. But I fear much cannot be concluded of certainty from them.

I shall not trouble the Reader with a multitude of other Histories, which I have received concerning that Comet of 64. nor with the disagreements of them one with another, and perhaps of most with the truth. They have given me sufficient trouble in the examinati­on of them, having little other benefit from them, save only this, that I was thereby informed what a man might think of a great number of Astronomical Obser­vations that have been made: for, saving the exact Ob­servations of some few such, as Mr. Hevelius, Mr. Aurout, P. Gottignies, &c. truly diligent and accurate men, the greater the Collections of Observations are, the more trouble and difficulty is created to the Examiner; they not only confounding one another, but perplex­ing those also which are real and perfect.

Now the reasons or causes of these inconveniences seem to be these.

First, the want of accurate and knowing Observa­tors.

Secondly, The scarcity of convenient Instruments.

Thirdly, The Imperfection of the Tables of the fix'd Stars.

For the Observators, 'tis not enough to know how to manage an instrument, or to have a good eye, or a dextrous and steady hand; but with these there must be joyned a skilfulness in the theorical and speculative part, and add to all a love and delight in the thing it self; and even all these will signifie but little, without convenient and accurate Instruments, such as may be easily manageable and sufficiently exact.

The first of these the love of the study being in it self the most excellent, or the encouragement of Prin­ces, Noblemen, and other Patrons of this Learning must procure: and where both of these concur, thence most is to be expected, and most fruit hath hitherto been proceeded; though there are not wanting divers eminent instances where the first reason hath been the only inducement.

As to the second, I have already in some of my for­mer Lectures described several convenient ones for these purposes; and therefore I shall not here add any more concerning it.

But as to the third, I hope the indefatigable labour and skill of Monsieur Hevelius will shortly supply the present defect, though it had been much to be wish'd, that the Instruments he had made use of had been fitted with Telescopical sights. These Tables, if well done, will alone (as to the business of Comets at least) supply the place of all other Instruments almost, save only a thread, especially if they be so delineated in Tables af­ter the Tangent projection, as that the minutes of eve­ry degree may be very distinguishable, which will not swell the Maps of the Heavens into an extraordinary large volume, and may possibly be the cheapest Instru­ment for this purpose an Astronomer can be furnished [Page 24]withal; for having such a volume of Tables, it will be very easie with a thread and one's eye, screen'd only with a spectacle made of a thin plate of Brass, with a small hole through it, instead of a glass, to observe what place the Comet possesseth amongst the fixt Stars: for having by the help of the said thread observed what two Stars lie in the same line with the Comet on one side of it, and what other two Stars lie in a line with it, which is at right angles (as near as may be) with the former line, by finding out those four Stars in the Ta­bles, ordered according to the Tangent projection, and with a Ruler, drawing lines over them respective­ly, where those lines do intersect, there will be the true place of the Comet, from which it will not be difficult to find out the true Longitude and Latitude of it by a Sector with Tangents. Now as these Tables of all the fixt Stars visible to the naked eye, would serve for find­ing its place whilst very big and swift of motion; so the like Tables of the small Telescopical Stars that lie near its way, when almost disappearing, and moving very slow, will by the help of a pair of measuring Compas­ses placed within the eye-glass of the Telescope, and a straight line or hair drawn cross it, serve to find the true motion and way of it, when only visible with a Tele­scope: according to which method I made the annexed Schemes, and Observations of the last appearances of the Comet.

Now since neither from my own, nor from any other Observations that I have hitherto met with, there can be any certain conclusion drawn of the distance of these Comets, save only this, that their distance was very great, and much higher than the body of the Moon, because else there must have been a considerable Pa­rallax caused by the Diurnal motion. The next enqui­ry will be, what other ways there are of knowing its distance. Now though none could be more demonstra­tive than the Parallax found this way by the Diurnal motion, yet there are some other which seem more easie [Page 25]arising from the consideration of the motions that may be thought to be concern'd in the producing the appea­rances. And though they be wholly hypothetical, and so need some other arguments to prove the ground and principles on which they are founded, yet since there are not very many considerable ones wanting to make them probable and rational, I shall here add somewhat of my inquiries after the distance, position, motion, magnitude, &c. of these Comets by these means.

Of these ways there are several depending upon se­veral suppositions which produce very differing effects, as to the magnitude, distance, motion, and way of the same Comet.

The suppositions are these:

Either that the Earth moves in an annual orb about the Sun, as the Sun is supposed by others to move about the Earth: Or that the Earth is perfectly fix'd, and hath no such motion.

Next, that the Comet moves either in a straight line, or in a curve line; and the curve is either a circle, or some other regular or irregular curve.

Further that the motion of the Comets in these lines is either by equal or unequal spaces in equal times.

Now according as we take this, or those of these dif­fering suppositions, and compound them together, so will the product of them be strangely differing. Amongst the great variety of compositions of these principles or suppositions, these seem the most simple, and conse­quently being any otherwise proved, will best deter­mine the true distance and way of the Comet.

First, To suppose the Earth to stand still, and the Comet to move equal spaces in equal times in a circle.

Secondly, To suppose the Earth to move in an an­nual Orb about the Sun, and the Comet to move through the Aether or Expansum, equal spaces in equal times in a straight line.

Thirdly, To suppose the Earth to move (as above) [Page 26]in its annual Orb, and the Comet also to move equal spaces in equal lines in a circle.

The other are indeterminate and infinite, and no­thing can be concluded from them as to the distance, magnitude, motion, &c. of Comets; for the line or way of the Comet may be placed at any distance, if we will suppose it moved in an uncertain curve, with une­qual degrees of velocity: And indeed, upon a suppo­sal of an inequality of motion, nothing of its way or distance can by any of these suppositions be found out. This fault had that of Tycho Brahe, where he supposed an unequal motion of it in its Orb about the Orb of Venus, which was founded upon the first Hypothesis, but had introduced into it some inequality of motion; besides his own supposition, that it was moved about the Sun, and the Sun about the Earth. See the fifth Figure. Keplers way, which was after the second Hypothesis, had the same fault; for he supposed the annual motion of the Earth, and the motion of the Comet in a straight line, but introduces an accelera­tion of motion in the Tangent towards the latter end.

The third way I have here taken, and from the best observation I could meet with, I have delineated its re­spects or angles to the Sun: and accordingly supposing it to move equal spaces in equal times, in a curve which for so much of it as the Comet was observed to pass was very near a Circle, I found this Circle would fall as it is express'd in the seventh Figure, where 'tis obvious to take notice, that when the Comet was nearest to the Earth, namely, about the 19. or 20. of December, that it was not nearer than an eleventh part of the di­stance of the Sun, that on the 23, it was twice as far, that on the 29. it was four times as far; that on the 15. of January it was as far as the Sun, and on the 14. of February it was above twice as far distant as the Sun. That this way or Orb of the Comet is here bended so as (if it were an entire Circle;) one part of it would [Page 27]go without the Orb of Jupiter, as the other which is here delineated comes within the Orb of the Earth; that the plain of this Orb is inclined to the plain of the Ecliptick about 18 degrees, that if from several parts this Orb perpendiculars be let fall upon the Plain of the Ecliptick, those perpendiculars shall fall in an Ellipsis, part whereof shall fall within the Orb of the Earth in ♌, and the opposite without the Orb of ♃ ♒. That the Comet moves a Sextant of this Orb in about 130 days, and consequently if its motion should continue the same in such a Circle, it would appear about Fe­bruary, March, or April, 1667. but being so far remo­ved towards the South Pole, will here hardly be seen: but by those that live towards the South, it may appear to have some such motion by the South Pole, as that of 1618. had by the North. And 'tis not impossible, but that the Comet of 1618. might be the same with this, if we suppose the Nodes of it to have a motion contrary to the order of Signs: and that the same Node which in this Comet, according to this supposition was in ♊, was then about ♍ or ♐: but these as conjectures I shall not insist on, because neither in this, nor in that have we Observations sufficiently accurate to build any Theory upon. Now though upon these suppositi­ons the motion and appearances of the Comet seem to be very regularly, and very naturally made out, yet 'tis not the only Hypothesis for that design: nor do I believe it so evident a demonstration for that end, as some would suppose; though for other reasons I am apt enough to think that opinion of the Earths motion very probable: but the motion of this Comet is so well made out, by the contrary supposition, that I think it may be alledged for a greater argument against the mo­tion of the Earth, than for it: for if we only grant one of the former postulata, namely, that the body of the Comet is moved equal spaces in equal times, and a quite contrary postulatum to the former; namely, that the Earth remains fix'd as to an annual motion, we may [Page 28]find all the observations of this Comet, especially the most accurate of them, to happen so, that the Comet being supposed to be moved in a great Circle, whose convex side is turned towards the Earth, whose center is extended towards the fix'd * in ♋; and whose Semi­diameter is about sixscore times the nearest distance of the Comet from the Earth, and the Comet be supposed to be moved very near equal spaces in equal times, we shall find, I say, all the appearances most exactly solved, and indeed much more exactly than by the other supposition I was able to find any; for by this supposition both the magnitude, longitude, latitude, re­trogradation, station, and direction of the Comet is most exactly made out as any one might have found that should have by this means examined with me the observations I have hitherto either made or met with: and indeed all the Observations hitherto have so well answered this Hypothesis, that I do almost promise my self to be able to see this Comet a month or six weeks hence, after the Sun has past by it; if by its exceeding elongation it be not quite grown out of sight, as it is now indeed already so exceeding dim, and faint, that it cannot be seen without a very good glass, which will endure an exceeding big aperture: nor could I these two last nights perceive it, though the Air were clear; but the reason I attribute to its nearness to a fixed * of ♈: This Hypothesis is explained in the seventh Figure. By this supposition the return of the Comet will be much longer, and the time of seeing of it much more uncertain; because the curvature is so little that the making the circle a twentieth, or a sixteenth part bigger or less, does not much alter the regularity; whence 'tis exceeding difficult, unless we had much more accurate Observations than I have hitherto met with, to determine exactly the bigness of the circle, and consequently the time of the return. And by this supposition the Comet may be supposed either nearer or farther from the Earth at any distance, which is not [Page 29]contradicted by a Diurnal Parallax; that is, it may be supposed either above Saturn, or below the Moon, or in any place between; by supposing only, that the farther the nearest part of the Circle is distant from the Earth, the greater must that Circle be, and the swifter the motion of the Comet in it: to prove which affirmation, let in the Eighth figure A be the Earth, BCD the Orb of the Comet supposed very near the Earth, and E F G the Orb of it supposed at a greater distance: let H be the center of B C D, and I of E F G, and let A C, be to C H, as A F, to F I, all the lines drawn from the point A, so as to cut the Circles B C D and E F G, shall divide those Circles E F G, and B C D, into simi­lar segments: as let A B E be a line drawn cutting those Circles in B and E: I say, the Arch B C shall be similar to E F. In which Hypothesis if we have toge­ther with the place of the Comet when stationary, the place of it when in its greatest celerity, perige, or the places of it when of the same celerity on each side of its perige, we have from thence the proportion of the Radius of its Orb to the perigean distance, and conse­quently all the other distances, the line in which it ap­pears when stationary, being the Tangent to the Circle in which it moves, as A B E, to which a Perpendicular raised at B B E, and produced till it cut the line A C, (produced) at H H I, it gives the Center of its Orb H H I, and the proportions of the lines A B, AC, B H=H C, or of A E, A F, E I=F I, the Angle B A C, being given by observation. So that by this Hypo­thesis the Phaenomena of the motion and bigness of the Comet will be solved, though supposed of any distance. Nor are these the only Hypotheses by which the hitherto observ'd Phaenomena may be solv'd: for if we will admit an unequal motion, such as is now gran­ted to all the Planets: and if further we will admit it to be moved in an Elleipsis, or other such like curve, there may be divers other Hypotheses that will solve the Phaenomena; so that the Comet may be supposed to [Page 30]have no motion at all as to Longitude, but only as to Latitude: that is, it may be supposed to be moved in an Elleipsis, described in a plain which shall be at right Angles with the plain of the Ecliptick, and the ways of the Earth in it: it may be supposed also to have been mov'd direct, according to the order of the signs, that is, to have been first about Gemini, in respect of the Sun, and to be now in some part of Leo: And it is not impos­sible to solve the phaenomena of its periodick or proper motion, though it be supposed not so high as the Moon, and that the motion of the Earth passing by it did real­ly alter its motions, had there not been made some Ob­servations about the Parallax of it, which prove it higher: so that according to this or that Hypothesis which we take, the time of its return, if permanent, will be longer or sooner.

And these Hypotheses may be so various, that till re­gulated by very exact Observation of the Parallax, 'tis not to be hoped that the appearance of a Comet can be certainly predicted: So that I fear the prophetick say­ing of Seneca, Erit qui demonstret aliquando in quibus Cometae partibus errent, cur tam seducti à caeteris eant, quanti qualesque sint, will hardly be verified at this time by the help of this present Comet. Though in truth I cannot find by the examination of several of them, but that they all seem to promise very fairly a return of it: for all the Calculations I have hitherto made of its motion, seem to cast it into a circular, and not a into straight line, as Kepler supposed; and indeed upon examining even Keplers own Calculations of those Comets which he observed, and has endeavoured to make to move in a straight line, I cannot find that any of them will be found to move equally in such a line: but to solve the appearances, he is fain to make them move in such sup­posed straight lines, by a line of Tangents, that is, to make the motion of Comets accelerated the further they are moved; all which Phaenomena may be very easily solved by supposing them to have moved equal spaces [Page 31]in a curve or circle. The physical reason indeed seems pretty difficult, by what means it should be confin'd or bound so as to move in a Circle: but this is no more than is usually supposed in all the Planets, and with­out supposing a kind of gravitation throughout the whole Vortice or Coelum of the Sun, by which the Planets are attracted, or have a tendency towards the Sun, as terrestrial bodies have towards the center of the Earth. I cannot imagin how their various moti­ons can with any satisfaction be imagined, but that be­ing granted (for which had I now time, I could alledg many reasons, and may do it hereafter on another occa­sion) not only the reason of all the irregular motion of the Planets may be easily found, but the reason also of the strange and various motions of the Comets. The reason why its Beard is for the most part opposite to the Sun, which was another Query, of which I have already said somewhat of my suppositions, and shall now add, that the brighter spot or kernel in the middle did seem to be some kind of body, which though it be not actually burnt, may yet by the en­compassing fluid Aether be dissolved and wasted, and those dissolved parts may ascend upwards, or from the center of the Sun, (which seems indeed to be the cen­ter of gravitation throughout the whole systeme of it.) To illustrate which explication, I could produce seve­ral experiments which would make a perfect represen­tation of the phaenomena of the body, and beard of the Comet: I shall only instance in one. Take a very clear long Cylindrical Glass, which may hold about a quart of water; fill it three quarters full with water, and put into it a quarter of a pound of Oyl of Vitriol, and in the midst of this suspend by a small silver wire, a small wax-ball, rould in filings of iron or steel, and you may plainly observe a perfect representation of the Head, Halo, and Beard of the Comet; for the menstruum falling on, or dissolving the iron, there is a continual erup­tion of small bubbles, and dissolv'd particles from all the [Page 32]sides of this body; and after the eruption they all af­cend upwards from the center of the earth; for being of a much lighter consistence than the anbient liquor, they are by the greater gravity of that, continually protruded upwards. The same appearance may be made with any kind of menstruum, and a convenient dissoluble body suspended in it; so that if we suppose the Aether to be somewhat analogous to a menstruum, and that there is a gravitation towards the center of the Sun, if the Nucleus or head of the Comet be sup­posed such a dissoluble substance, the phaenomena of the shape of the Comet may, I think, be rationally ex­plained. Now that the Aether may have such a kind of propriety, seems to me to be argued from this, that the Air about the Earth seems to owe its original to it, it being only a dissolution of terrestrial bodies into the Aether, the Aether being the principal fluid body, and greatest part of this dissolution; and the substance of the Air, some very few and small saline and earthy particles: of which elsewhere. By this Hypothesis the phaenomena of the Comet may be solved; for hence 'tis easie to deduce the reason why the Beard grows broader and broader, and fainter and fainter towards the top: why there is a Halo about the body; for this will appear clearly in the experiment: why the Beard becomes a little deflected from the body of the Sun; for if the dissolving Ball be by the wire mov'd either this way or that way, the arising stream or bubbles will bend the contrary: and to countenance this supposition, both in those Comets observed by Tycho, Kepler, and also in this last the beard was contrary to the motion; so that the head or body going faster, seemed to leave the beard or tail somewhat behind: by this supposition also 'twill be easie to explicate why the beard is sometime bended, and not straight, and why it is sometimes brighter upon one side than upon another? why the bottom of it is more round, and the other sides more undesin'd; and divers of the like phaenomena. Against [Page 33]this supposition it seems difficult to conceive whence so vast a body should be generated; next, how it should be able to supply such a constant stream of a­scending parts, and yet last so long as this has done, al­most a quarter of a year. Thirdly, Whence such a newly generated body should receive so great a degree of motion. In answer to which, I say, 'tis not impossi­ble but that the body of it may be as old as the world, and that it may have then received its first determina­tion, or laws of motion, and may have ever since pre­served them, that it may have been all this time also in dissolution, and yet not be quite wasted; and that it may continue yet for many ages before it be quite dissolved into the Aether. And to make this probable, divers experiments and reasons might be alledged, as that of the slowness of the wasting of many bodies, by the dissolution made on them by the fire: the slowness also of the dissolution of multitudes of bodies in menstruums. And I have already shewn how small a quantity of dis­solved particles will be able to make as great a shew of light: besides that, the motion of the ascending stream or beard being but slow, there needs no very quick supply of other parts. We see also into what a vast quantity of smoke a small parcel of a combustible body may be turn'd. From all which particulars, 'tis not un­likely but that the Comet may be a body moved with a regular circular or elliptical motion as the Planets are, that it may be a body of such a constitution, as that the fluid Aether through which it passes, may dis­solve it much after the manner as a me [...]struum; (such as Aquafortis, Spirit of Niter, &c.) does a dissoluble body; that by this means there may be a slow, but continual eruption of somewhat opacous parts, which may by their dissolution afford a sufficient quantity of light to make as great an appearance as any of the Comets, that this stream or beard may by the resistance of the Aether be a little deflected back wards in the same manner as an ascending stream of smoke will be by the resistance of [Page 34]the Air, if the burning body be mov'd this or that way through it, that the body of the Comet may be both as ancient and as lasting as the world; and that this which has lately appeared may have appeared heretofore, and may likewise hereafter appear again; that 'tis probable the nearest distance of it was much greater than that of the Moon, that the length of its Beard was longer than its distance from the Earth, and consequently several times longer than the distance between the Earth and the Moon; that its visible way among the Stars was very differing from a great circle, especially towards the latter end, when it became retrograde; that its way through the Aether could not be supposed equal in a straight line, though it might be supposed equal in a curve or circle, that the exact way of it could not be certainly determined by the best Observations I have yet met with: and that therefore the best help we have to ghess of its way and distance, is by its manner of mo­ving, as to appearance among the fixed Stars, which I have already shewn to be explicable by various Hy­potheses: for both the Earth and Comet may be sup­posed to be moved, either both one way, or contrary ways, or cross ways, the Earth may be supposed to stand still, and the Comet only to be moved, and the like.

These Requisites therefore being hitherto wanting in the Observations I have met with of this Comet, all that can be said of it will at best be but conjectural and hypothetical; since nothing can be reasonably built upon those Observations where the truth of them is du­bious; wanting therefore sound materials to work upon in this Comet, I had recourse to the Observations of the noble Dane Tycho Brahe, being sufficiently satisfied both of the ability, industry, and veracity of that ex­cellent Author, who left nothing unattempted for the perfecting of such Observations as seem'd to him requi­site for the compleating a History of that Comet which appeared in 1577. And from those Observations of his [Page 35]I endeavoured to trace the way of it according to se­veral hypotheses; and found, that supposing the Earth not to be moved with an annual motion, but only a diurnal about its own Axis, the way of Comets will fall in a line very near approaching the nature of a circle, though neither into an exact circle, nor an exact ellipse; and therefore seems irregular, and not at all probable. Again, supposing it moved about the Sun, as Tycho has done, we find from his Calculation of it, he was fain to allow it a quicker and slower motion in its Orbit, to solve the Phaenomena, which seems to me but a shift, that will serve to help out any lame Hypothesis what­soever: And that granted, and the Parallax of the Comet unknown, I will undertake very easily to make out almost any Hypothesis, which is the fault also of Mr. Horox his Hypothesis, wherein he supposes the Earth to be moved about the Sun, and the Comet like a Rocket to be shot out of the Sun, and by degrees to return to it again; in which Hypothesis indeed there seems to be much more reason for aninequality of mo­tion, though not in the manner as he has placed it; 'twas very rational that the motion of it at first, if cast out of the Sun, should be very swift; but then it ought likewise to have accelerated its motion in the same manner in its return back to it again, which it does not in his Hypothesis; for a stone or any other heavy body being shot up into the Air, does make its return back again to the Earth, almost by the same degrees of velo­city, by which it ascended from it: almost, I say, be­cause the resistance of the Air does so far impede the motion of the body through it, that it never suffers it to acquire the same degree of velocity with which it was first shot upward. This is sufficiently evident from a Pendulum, which if it be thrown upwards, and be suffered to return back, it will never rise again on the opposite side to an equal height, with that it descended from, on that side towards which it was thrown: but besides, in his Hypothesis he seems to take no notice at [Page 36]all of the Latitude of the Comet, which seemed to carry it much farther off from the Sun, when he sup­poses it to be returning nearer. And indeed upon the whole his Hypothesis seems rather a product of chance than of any contrivance. For he in endea­vouring to set off the Longitude of the Comet ac­cording to Tycho's Tables, and to trace its way by supposing the Earths annual motion, making use al­ways of the same Radius to set off the aspect, or ap­parent angle of it with the Sun, his line of Chords he made use of did always direct the point of his Compas­ses to the place where he situates the Comet, as may be easily found by examining the ninth figure; where you may find that he places the Comet always equally distant from the Earth, and that distance is always equal to the distance of the Sun, which has so many in­conveniencies and improbabilities, that I shall not in­sist farther on it; especially since I do not find that he bestowed any farther pains in explicating or cultiva­ting this his Hypothesis, than only the bare delineati­on of this ninth figure. But to return to Tycho's Hy­pothesis, if that be true, why did not the Comet again appear after a certain space of time? and why could not he have foretold when it should again ap­pear, as well as he could predict the appearance of Venus, about whose Orb he supposes it to circulate? I shall pass by several other very material objections that might be made against that his supposition, because many of them might be made also against his Hypothe­fis of the Heavens in general, which I shall the rather omit, because I do not find he has many followers in that supposition; the generality of Astronomers em­bracing rather the Copernican System, especially as it is refined and rectified by the ingenious Kepler.

Lastly, I endeavoured to trace the way of the Co­met from Tycho's Tables, according to Keplers Hypo­thesis; which was, that the appearances of the mo­tion of the Comet were ascribable to two causes; [Page 37]namely, the motion of the Earth about the Sun in its annual Orbit, and the motion of the Comet in a straight line, not accelerated according to the proportion of the increase of Tangents; but upon supposition that it mov'd equal spaces in equal times: (for I cannot imagine what reason he had to suppose its motion to be accele­rated, and much less why he should assert it to be ac­cording to the proportion of Tangents, which in a lit­tle time must necessarily come to move infinitely swift: than which nothing is more hard to be granted.) And I found it after many trials and essays to fall in a straight line, inclining to the plain of the Ecliptick by anangle of 47.40. and cutting it in 9 degrees of Scorpio, if computed out of the Sun, and moved faster by half than the Earth in its Orb; and this to so great an ex­actness to answer all the Observations of Tycho, that from a very large Scheme which I drew of it on a plain, I could never find many minutes difference; so that I concluded that to be the most likely Hypothesis for that Comet, it seeming to solve all the several Phaeno­mena of the motion and magnitude of the Comet, with the least imaginable difficulty, and to be most agree­able with my physical notions of Comets: For, first it only supposes a solid body moved in a fluid, with an almost direct motion. I say, almost direct, because for some physical reasons, as I have said before, I imagine it not exactly straight, but inflected a little towards the curvity of a circle, which I shall presently endeavour to explain farther in this Comet. Next, it supposes that body to move in that line almost equal spaces in equal times; I say, almost equal, because some of those equal spaces may be increased by an accelerating cause or principle, such as that of a gravitation towards the bo­dy of the Sun, placed in the center of its Vortice or System, when the motion of the Comet carries it to­wards the Sun, and may be diminish'd from other impe­ding causes, such as the impediment of the fluid me­dium through which it passes, and the attraction of the [Page 38]Sun operating on it when its motion carries it farther and farther off from it: besides, 'tis not unlikely, but that the attraction of the Earth, or some of the other Planets may have some kind of influence on it, especi­ally, when its line of Direction does somewhat nearer approach those attractive points. But the deslection from a straight line is always so much the less by how much the swifter the body is moved, and by how much the farther off its line of trajection is perpendicularly distant from those attracting bodies. According to this supposition of mine, I have endeavoured to make out all the appearances of this last Comet, taken no­tice of in the best observations I have yet met with, amongst which I find no one of the Parallax satisfacto­ry, as in the tenth figure, let S represent the Sun, O R B, the Orb of the Earth, A C D E F, a bended or curve line in which the Comet is supposed to move: the Comet then coming into the Sphere of the attractive power of the Sun, by the straight line P A G, at A, the power of the Sun worketh on it, and by degrees at­tracting it towards its own Center by that time the Comet hath moved to C, the attractive power hath de­flected its direct course from P A G, to C H, and so the Comet would continue to move in that straight line C H, but it is still deflected so, that at D, it moves to­wards I, but the gravitation of the Sun attracting it, deflects it from that line towards E, and so from E to F, when it begins again to Jet out of the attractive beams of the Sun, and so it will continue to proceed, as if it had come to that point by the line M F L, the reason of which is the great velocity of these bodies, which are generally much swifter in their motions than the Earth or other Planets are supposed to be, in theirs. We must seek out some other way therefore of finding of the distance of Comets than the commonly used: I shall therefore somewhat further explain the contrivance I newly invented for this purpose, by which not only the Parallax of the Comet but of the Pla­nets [Page 39]also may be found with great facility and ex­actness.

Having a large Telescope prepared (as I formerly directed) with Eye-glasses capable of taking in an Angle of about two degrees at once, and furnished with a dividing Scale, observe when the motion of the Comet or Planets is not too fast, the position and distances of the small fixed Stars which are next ad­joyning to the moved body whose Parallax you would find; of these small fixed Stars you shall seldom miss a sufficient number, which will be taken into the glass at once, if at least the object-glass be allowed a very large aperture; and having found such Stars as will be convenient for your purpose, be very diligent in taking, by the help of the dividing Scale, the exact distance of them one from an other, and when the body is high­est above the Horizon, viz. in or near the Meridian, by the same means take the exact distance of it from two or three of the nearest and most conspicuous fixt Stars about it, and by the help of a plumb-line, hung likewise within the cell, near the dividing Ruler, find exactly the positions of all those bodies you take no­tice of to the Perpendicular or Horizon, which may be easily enough done, if together with a Plumb-line or Perpendicular plac'd within the glass you have also a small Diagonal thred fastned to a ring, whose circum­ference is divided into 360 degrees, and moveable so as by the finger easily to be turn'd any way, by which means this Diagonal thred may be made to cross over any two of the bodies you observe, and by observing what division of this divided limb the Perpendicular cuts, it will be easie to determine the exact position of those Stars to the Horizon; this same may be done by the dividing Scale also, if that be fixt in a divided Circle which is movable, in the same manner as the thred is supposed to be. This Observation, with all other circumstances of it is likewise to be repeated at the setting or rising of the Planet or Comet, and a­gain [Page 40]the next night when it comes to the Meridian, and in each of those observations the exact time is to be noted by a time-keeper, and the altitude by some of those I have before described, for by comparing these three observations together it will be very easie to find what irregularity in its motion is ascribable to its Paral­lax. And this will be so much the easier because the examination and reduction of it may be done (with as great exactness as the observation can be made,) by the help only of Ruler and Compasses, for all the distan­ces will be set off by equal divisions of straight lines, the line also of the periodick motion, whether of the Comet or Planet, especially if the observations be made when the body is near an opposition with the Sun, which is much the best time, will be with sufficient ex­actness taken for a straight line, and the motion in that line may be supposed by equal spaces in equal times; for the difference between the Tangents of the centesms of a degree to two degrees is not increased much more then 2/1745 that is not a quarter of a centesm of the hundredth part of a degree, which is much more exact than I fear our observations will ever be.

Another way of finding the Parallax may be by the help of exact observations made by several persons at the same time, in places much differing in Latitude, though as near as may be under the same Meridian (because of saving the trouble of Calculation, and for being assured that the observations were both made exactly at the same time) each person by the help of ve­ry long Telescopes observing the exact distance of the body from the small fixt Stars next adjoyning.

A third way of finding the Parallax of Comets is wholly new, and though hypothetical (as supposing the annual motion of the Earth, and the motion of the Comet in a right line through equal spaces in equal times) yet 'tis founded upon a Problem in Geometry (invented by the incomparable Mathematician, Doctor C. Wren) which is truly noble and wholly new, and [Page 41]though it had been of no use in Astronomy, deserves none of the meanest places in Geometry, by the help of which (which is much more than either of the other ways is capable of) one may easily find the true parallax of the Comet, from any four exact observations of it, made at differing times in the same place: Nor does it require so nice and accurate Instru­ments and Observators as are altogether necessary in the other ways. The Problem as I received it, is this.

From the invention of which Problem 'twill be very easie by any four observations Graphically to describe, or Geometrically to calculate the true di­stance of the line of the trajection of the Comet, and consequently to answer all those questions that can be demanded concerning the bigness of the body and head, and concerning the bigness and length of the blaze, and concerning the distance of it from the Earth in eve­ry part of its way when it was nearest the Earth, when nearest the Sun, where it cuts the Plain of the Ecliptick, seen from the Sun, and where seen from the Earth, with what Angle it was inclined to the said Plain, how swift the motion was, that is, what length it passed, in what time, when it must appear Stationary, when Retro­grade, when disappear, and the like.

According to this method I received at the same time, (whilst it yet appeared very visible to the Eye, and was not Retrograde,) the way of the first Comet de­lineated by the said person, which did very near solve all the appearances preceding and subsequent, which I have therefore here annexed in the Table expressed in the 19.20. and 21. figures, where in the 19. is delineated the Place of the Sun in the Center of the Circle ♈, N, D, I, ♎, which represents the annual Orb of the Earth about the Sun, the points between N and D represent the places of the Earth in that Orbit in the days of November, and the lines drawn from them to the points in the straight line, represent the lines in which the Comet appeared in respect to the Sun; in like manner the points between D and I, the places of the Earth in December, and the lines drawn from them to the straight line, as before the visible places of the Comet at those times, &c. The 20. figure represents singly the several Longitudes of the Comet at several times seen from the Earth. And the 21. represents the se­veral Latitudes, at the several times, together with the [Page 43]true distances of the Comet at those times, both which are made out of the 19. figure, where E at the end of the line represents the Center of the Earth, from which to the figures in the prickt curve-line, are the true di­stances of the Comet, the Perpendiculars from those fi­gures to the line E C are the signs of the Latitude of the Comet from the plane of the Ecliptick E C, the aforesaid distances being made the Radii.

Now though according to my former Delineation the Comet seemed to take a circuit, as if it would within three years return to its former position, yet I am not wholly convinced that it moves in a circle or Ellipse, but I rather incline to the incomparable Kep­lers opinion, that its natural motion tends towards a straight line, though in some other suppositions I dif­fer from him.

As first that the Comet perseveres exactly in a straight line. Secondly, that after it has past its Pe­rige it accelerates its motion in proportion to Tangents of equal Angles. Thirdly, that it either is extinguisht dissipated, broken in pieces, or burnt out into ashes. Fourthly, that it receives all its light from the Sun. Fifthly, that if the blaze were not made by the beams of the Sun passing through the head of the Comet, and so carrying the parts along with them, the blaze would not be opposite to the Sun. Sixthly, that the cause of the bending of the blaze is the refraction of the Suns raies in the body, and their being bent by the Aether as with a wind (which is the opinion that the Ingenious Descartes follows also.) To these I cannot consent, and I have many objections to several other of his opinions concerning this matter, which would be too tedious to insert; only I shall add, that having traced several of the Comets according to the best observations I could get, I found it very difficult to make their motion fall in a straight line, unless it be granted that their motions are really accelerated and retarded in that line, which seems not so probable, at [Page 44]least not in those parts of their transit where he places them. And particularly by tracing the way of this Comet of 1664. it is very evident that either the ob­servations are false, or its appearances cannot be solved by that supposition, without supposing the way of it a little incurvated by the attractive power of the Sun, through whose system it was passing, though it were not wholly stayed and circumflected into a Circle, as I have already mentioned.

That it is not extinguisht or quite burnt out, when it ceases to appear, I argue from this, that I was able to see it with a Telescope above a month after it disappeared to the naked Eye, as may be seen by the observations I have annext in Fig. 4. and had not the cloudy weather and the light of the Moon, and nearness of the Crepuscu­lum hindred, I suppose I might have seen it much longer, as I am apt to believe the great one in 1618. might have been seen several months longer, if it had been diligent­ly followed with Telescopes, it disappearing in such a part of the Heavens as might have been seen every clear night between the Crepusculum and Dawning.

Nor can I suppose it to receive all its light from the Sun, since if so it would follow, that the Nucleus in the head, would have a dark shadow opposite to the Sun, the contrary of which has always been ob­served. Nor can I well understand that the Sun beams are like a stream of water, carrying the parts of the Comet along with them so as to make its blaze, since no such effect is found of them here with us upon the Earth: Nor how they should come to be bended like smoke, since we observe no such property of light in a uniform medium, such as in probability the Aether is.

These were my thoughts about those Comets which appeared in 1664. and 1665. which I have found in several loose papers of Lectures, read in the beginning of 1665. And I have not had the op­portunity of making many observations since, con­cerning Comets, save these two last, in which I had [Page 45]not the convenience of observing any thing certain concerning its motion or Parallax. And therefore I applyed my self to mark as near as I could the true fi­gure of it, through a six foot Telescope, and to take notice of as many circumstances as the short time I had would permit, which though they were very short and transitory observations, and I wanted time to repeat them so often as I could have desired, yet even from them I was sufficiently satisfied, that I had reason to adhere to my former conjecture, that the light of the Comet did not depend wholly from the reflection of the Sun beams, from the parts thereof, but rather from its own light, for upon well considering of the form of this Comet, I manifestly saw that the middle of the blaze was brighter than the side parts thereof, and especially that part which was immediatly opposite to the Sun, was the brightest of all, which would have been otherwise if the light had depended wholly from the deflection of the rays of the Sun, for one might rationally conclude that the Nucleus or Star in the mid­dle, which reflected so great a quantity of light should have caused a darkness in the parts behind it, as we see all strong reflecting bodies do, and consequently that the middle part of the stream or blaze, especially that which was next the body should not have been so bright as those other parts to which the light of the Sun had a more free access, unless it may be said that even the Star it self, though it seem so bright, is not­withstanding not so Dense, but that it admits rays e­nough to pass through it unreflected, to inlighten the parts behind it. But this seems not so likely, since be the body of the Star supposed a thousand times thinner than a Cloud (which yet tis hard to suppose, since it gives so considerable a reflection,) yet it being in all probability ten thousand times bigger in bulk, the rays in passing through so great a bulk, must needs meet with more obstruction than in the thinnest Cloud, and yet we find that there is no Cloud so thin, but casts [Page 46]shadow opposite to the Sun, and therefore in probabi­lity this would do the like, but I diligently observed that there was no such appearance here, but the con­trary, that is, that where the shadow should have been, there was the lightest part of all the blaze, and con­sequently in probability it did depend upon some other cause than a reflection of light.

It is a hard matter to assign the particular cause of its light, but it seems from these circumstances to be very probable that it was (in part at least) from its own nature, whether that might be somewhat of that of the Sun and Stars, or of that of our fire, or of that of decaying fish, rotten wood, glow-worms, &c. or of that of the Ignis Fatuus, at Land or Sea, or like that of Sea-water, or a Diamond, or like that of the falling meteors, or Star-shoots, it will be very hard to determine, unless one had a much greater stock of observations to build upon. But it may possibly be somewhat of the nature of them all, though it agree not in all particulars with any one of them. All these ways that I have named seeming to agree in one parti­cular, and that is an internal motion of the parts which shine, whether that motion be caused by some exter­nal menstruum dissolving it as in fire, and Ignes fatui, or an external motion, stroke, or impulse as in a Dia­mond, Sea-water, and possibly some Ignes fatui, or from the parts of the bodies working and dissolving one another, as in decaying fish, rotten wood, glow-worms, or whether it be susceptible of a much more subtil impulse, even from light it self, as the Bononian stone, and Bladwines Phsophorus, which seems to be so harmo­nious (as I may so speak) to the motion of light, that a new motion is thereby raised in it, and continues for some time to move of it self after the impulse or influence ceases, not much unlike the unison string, or other sounding body, which in Musick receives a tre­mulation and sound from the motion and sound of the unison body, or string that is struck.

To me It seems most probable that the body and parts of the Comet are in a state of dissolution, whether that dissolution be caused by the parts of the Aether through which it passes, after the manner as a Torch is dissolved by the air, or whether by the internal working of the constituent parts one upon the other, as in Gun-powder, shining Fish and rotten Wood, I can­not determine; but I rather guess it to be in some things analogous to the one, and somewhat to the other, though not exactly the same with either. And this I conceive from the figure and make of the shining parts, for if it had been of the same nature with a Torch, the blaze would have resembled that of the flame of a Torch or Candle, that is, the sides would have been brighter, and the middle darker, as I have shewn in my Lampas; whereas it was very manifest that the mid­dle of the blaze was brightest, and of that blaze that which was next the Star or Nucleus was brighter than that which was further off: whereas in flame the con­trary is very observable, as I have in the said Trea­tise shewn.

From the shape of the figure, the manner of its disso­lution seems to be thus. The Star or Nucleus in the mid­dle, seems to be the fomes or source from whence all the light proceeds: this we suppose to be a dense body en­compast with a very fluid body (such as the Aether seems to be) but of such a loose and spongy nature, as that the Aether doth cause those parts which are contiguous to it, to be dissolved and expanded into it self. This dissolution and expansion I conceive doth generate or cause the light that seems to proceed from it, that dissolution causing such a motion of the Aether, as is necessary to produce the appearance of light; now so long as any part thereof remains in dissolution, so long doth it continue to shine, as is also observable in the flame of any body burning in the air, but when the part separated from the body is quite dissolved in­to the Aether, the effect of shining ceases, as it doth [Page 48]also in the parts of flame. Now I have observed that the blaze is so very much rarified, that first the Aether I conceive comes very freely to every particle of the body after it is separated from it, but especially to the outermost, and continues to be incompassed with it so long as till it be quite dissolved into it, which I con­ceive to be at a little farther distance from the head than the greatest length of the blaze seems to be to our sight. And further I conceive that the outward parts being thus incompassed more perfectly with the free and un­disturbed Aether, are sooner dissolved into it than those of the middle, and consequently the sides seem first to disappear, and the middle parts continue their shining to a much greater distance from the Star in the head, though somewhat also of that appearance may be ascribed to the dispersing and rarity of the parts near the sides.

The Nucleus or Ball in the middle of the head, which I have called the Star, I conceive to be dissol­ved equally on all sides, and the parts which are dissol­ved or separated from it, I conceive to fly every way from the center of it, with pretty near equal celerity or power, like so many blazing Granadoes or Fire-balls, these continue their motion so far toward the way they are shot, till the Levitation from the body of the Sun deflect them upwards, or in opposition to the Sun into a Parabolick curve, in which Parabolick curve, eve­ry single particle continues its motion till it be wholly burnt out, or dissolved into the Aether. These are con­tinually succeeded by new separations from the afore­said body in the same manner as tis observable in a burning, steaming, or smoaking body in our air, or a dissolving body incompassed with its proper menstru­um, as I before mentioned, and will so continue until the whole be at length dissolved into the Aether, through which it passes.

It hath been demonstrated by Torricellius, of bul­lets or other bodies cast or shot upwards, that the same [Page 49]or equal bullets discharged or shot out from the same point, with the same degree of strength, but with differing degrees of inclination to the Horizon, each of them shall be moved in a parabolical line, and every one of those parabolical lines shall touch a paraboli­cal line, whose axis is the perpendicular, and whose apex is distant from the said point, the full altitude of the perpendicular shot; So that supposing in the twenty second figure, A to be the point from whence all the shots are made with equal velocity, A C the greatest height of the perpendicular shot, and A D the greatest Horizontal random at 45 degrees of inclination, and suppose E D C D E a parabola passing through those points D C D, all the shots made with equal bullets, with equal velocity from A, but with all variety of in­clination between the perpendicular upwards, and the perpendicular downwards that touch the said paraboli­cal line, and consequently if there be an indefinite number of such balls continually flowing out of the point A, with equal degrees of celerity every way dispersing themselves equally in orbem, the whole ag­gregate of such an emanation will make a solid para­bolical conoeid E D C D E. Now about the point A, if we suppose a Sphere as B B B B, and from this Sphere an indefinite number of such equal Balls be thrown off perpendicularly to the superficies of it, from every point thereof, with equal ce­lerity at their leaving it, those emanations will form also a conoeid, which will be very near the same with the former: And if this Ball in the middle be supposed a burning and shining body, and that all these emana­tions have every one of them equal light in proportion to the Globe B B B B A, the effect produced hereby will perfectly resemble the appearance and figure of Comets, if at least the Parabolical conoeid be inver­ted; which will somewhat explain the manner how I conceive the figure of the Cometical body is naturally, and most proportionably formed; for if the effect of [Page 50]such an emanation of shining bodies be examined, it will very plainly exhibit the exact and true apparent figure of Comets, as they may be seen through a good Telescope, which is to me a very great argument, that 'tis the genuine cause of its shape and figure: Now though the Comets appearance be this way caused, and so a man might conceive the Globous body would in a little time (by so copious an emanation) be consumed, yet I do not believe that it doth in a short time wast and disperse the whole Ball, nor can I con­ceive that the disappearing of those blazing bodies to­ward the latter end, does depend upon their dissoluti­on (though possibly that may somewhat diminish them) but that rather is to be ascribed to their distance and position in respect of us: Though this I remember I observed very manifestly in that of 1664. that the body toward the latter end of its appearing was very much less in proportion to the radiations about it, than it seemed to be at the beginning, but whether that might not be partly ascribed to the great distance it then was from us, and the turning of the head pretty near to­wards us, and thence the spreading of the Tail (appear­ing beyond it,) might add to the breadth of the radia­tion about the Nucleus, I will not positively determine. Now though for explication sake, I have compared the parts separated from the body of the Comet to blazing Granadoes or Fire-balls, yet I would not be understood to suppose these parts so separated to be of any very large bulk, for I see no necessity to sup­pose them bigger than the Atoms of smoke, or the particles of any other steaming body, or than the parts of the Air, which make the body of it appear thick and hazy; nor do I believe that all the light of the Star, head, and blaze, does depend only upon the shining of the dissolving body and particles thereof: but I do suppose that it doth proceed both from the reflection of the Sun-beams from those parts, and also from an innate and momentaneous light produced by [Page 51]the action of dissolution wrought on the parts by the incompassing Aether.

It may possibly seem very difficult to suppose that the dissolution of the parts of the Nucleus, by the in­compassing Aether, should cause or impress so violent a motion into the separated parts, as to make them depart from it to the space of four or five Diameters, before it be over-powered by the power of Levitation from the body of the Sun, and so deflected into a pa­rabolical line upwards. It may likewise seem strange to suppose that the Aether should have such power in it, as first to dissolve a body into it self, and secondly to cause a shining, and thirdly to cause a Levitation of the dissolved parts upwards; whereas I supposed be­fore (and I think 'tis very manifest) that they cause a gravitation downwards, towards the Center of the Sun: But to these for explication, I answer that we need not go far for instances to make these things probable, the Atmosphere about the Earth, as I have formerly mentioned in my Micrographia, I take to be nothing else but the dissolution of the parts of the Earth into the incompassing Aether; for the proof of which, I could bring many arguments, were it here a proper place, by which I could most evidently de­monstrate the thing to be as I have asserted. It is here evident that this Aether doth take up the particles of bodies to a very great distance from the surface from which they were separated, and it doth not only raise them but susteins them at those heights, nor is this pecu­liar only to the Aether when a menstruum, but to all dissolving menstruums in general.

As to give one instance, in stead of many, we find that Gold (the heaviest of all Terrestrial bodies we yet know,) being dissolved by Aqua Regis, is taken up in­to it, and kept suspended therein, though the parts of the Gold be fifteen times heavier than the parts of the Aqua Regis. So Pit-coal though very heavy, is yet taken up into the Air, and kept suspended there­in, [Page 52]though it will be found to be some thousands of times more ponderous than the menstruum of the Air that keeps it suspended.

Many reasons I could produce to shew the great power of the Aether, and the universality of its acti­vity almost in all sensible motions, but reserving them for another Discourse hereafter, I shall at present, on­ly mention those suppositions which seem to have the greatest difficulty, in this Theory, viz. how the dissolution of the parts of the Star by the incompassing Aether should cause light, and secondly how it should cause an actual Levitation of the dissolving particles up­wards. For the explication of these two difficulties, I must at present crave favour to explain them by ex­amples taken from operations of Nature in the At­mosphere wherein we live, very similar and analogous to them. First, for the production of light, we find that the Air incompassing the steams of bodies pre­pared by heat or otherwise, and made fit for dissolu­tion, doth so operate upon them, as to make them fly and part asunder with a very impetuous motion, inso­much that the small particles or Atoms of the dissolved bodies, do not only leave one another, but depart and dart out with so great an impetuosity, as to drive off all the incompassing Air from their Center from whence they flew, and this I take to be the cause not only of their Light, but also of their Levity upwards, this may be seen very plainly by the small parts of crackling Char-coal, which upon the blowing them with Bellows, and so crowding a great quantity of the fresh menstruum on them, fly and dart asunder with great celerity and noise, but is abundantly more evi­dent in the kindling of Gun-powder, where the im­petuosity is so very great as to drive away not only all the incompassing Air but all other bodies, though ne­ver so solid, that hinder its expansion, in the perform­ing of which operation the Aether hath a great share, as I may hereafter shew, 'tis very probable that the [Page 53]Aether in the same manner dissolving the particles of the Star, causeth the Atoms thereof to fly asunder with so great an impetuosity as to leave a vacuity even of the parts of the Aether, which flying asun­der doth not only cause light by impressing on the Aether a stroke or pulse which propagates every way in Orbem, but maketh such an agitation of the the Aether, as causes a rarefaction in the parts thereof, whilst the parts that are once actually separated, by continual rebounding one against another before they come to be at rest and quietly to touch each other, prolong that first separation or vacuity be­tween them.

This Explication, though it be somewhat difficult, yet I hope it is intelligible, and may be, with proba­bility enough, supposed to be the true cause of the appearance, whilst there is nothing therein supposed which is not manifestly the method of Nature in other operations; and though the supposition even of the Aether, may seem to be a Chimera and groundless; yet had I now time, I could by many very sensible and undeniable experiments, prove the existence and reality thereof, and that it doth actually produce not only as sensible effects as these I have named, but very much the same, and many others much more cosidera­ble, which by Philosophers have hitherto been ascri­bed to quite different causes.

Had I been able to have made some other observati­ons (which I designed, if I had had the opportunity of seeing it, some of the succeeding Nights,) I should have hoped to have explained several other difficulties con­cerning the nature of the body and blaze of Comets, but being therein prevented, I must leave them till I can make some further observations on some Comets that may hereafter appear.

In the mean time that what I have discoursed con­cerning the light of Comets, may not seen so altoge­ther paradoxical and unintelligible as some may ima­gine, [Page 54]I have here added an account of some trials and observations made on shining substances of natures ex­ceedingly differing from those that are commonly to be met withal. And this I the rather do, not only because it affords an instance of shining where there is no Air, but that hereby I may enlarge the limits of their imagination, who shall consider of this subject. For nothing is more apt to misguide our reasoning than a narrow and limited knowledg of causes, we are not to conclude the body of a Comet a sulphureous vapour exhaled from the Earth and kindled above, because here are such vapours observed and such ef­fects produced, nor a collection of Sun beams made by a Lentiformed vapour, after the manner of a Burning­glass (as some eminent Writers have lately done,) be­cause some such appearances may be Artificially pro­duced in a smoaky or thickned Air; since if we dili­gently inquire, we may find that light which is the most sensible quality of Comets that affects our senses, may be, and really is produced by very many, and those very differing ways. In Nitre and Sulphur kindling each other by heat, we have one way; in a body burning in the Air a second, in a heated Iron or Glass a third, in a piece of Iron hammered till red hot a fourth, in rotten Wood and decayed Fish a fifth, in Glow-worms, Scolopondras, and other living Worms, and in the sweat and excrements of other living crea­tures a sixth, in a Diamond rubbed a seventh, in Dews Ignes fatui, &c. an eighth, in Sea-water a ninth, in the Bononian stone, and in the Phosphorus Baldwini (which I take to be much of the same nature) a tenth, in the Phosphorus of Mr. Kraft an eleventh, and possibly wholly differing from all these, may be the light of the Sun, a twelfth, and that of the Star may dif­fer from that of Sun, and the Comet may be differing from all the rest. Whether they be so or not, the be­ing acquainted with the several proprieties of them will the better enable one to judg of what is perti­nent [Page 55]to be observed in Comets, in order to find out which is concerned.

The Phaenomena of most of these shining bodies are very common and obvious, and therefore need­less to be added; but that of the Bononian stone pre­pared, and that of the Phosphorus Baldwini (lately discovered by Mr. Baldwine) are rare and hard to be got, and the effects of them are wholly differing from all the ways I have yet met with, and will therefore prove Experimenta Crucis, highly instructive in the Theory of Light, of which more hereafter. As for the Phospho­ros Fulgurans of Mr. Kraft (more scarce and rare than the other) 'tis wholly differing from any of the rest, and very strange and surprising, at least it appeared so to me, who had the good fortune to be present at a good part of the experiments made by the Author in the presence and at the Chamber of the Honourable Robert Boyle, Esq; that great Judg and Promoter of all curious inquiries into Nature and Art, who at my ear­nest intreaty, was not only pleased to commit to wri­ting what he observed, but (for the information of Curious and Inquisitive Naturalists,) to give me liber­ty here to publish it.