Sciothericum telescopicum, or, A new contrivance of adapting a telescope to an horizontal dial for observing the moment of time by day or night useful in all astronomical observations, and for regulating and adjusting curious pendulum-watches and other time-keepers, with proper tables requisite thereto / by William Molyneux ...

Sciothericum Telescopicum, OR, A New Contrivance of Adapting a Telescope To a large Horizontal Dial, for observing the moment of Time by Day or Night.

CHAP. I. The Ʋse and Advantages of this Contrivance.

EVery one the least versed in Astronomy, does know of what great Concernment the Obser∣vation of the exact Moment of Time is therein. Without this no Celestial Observation can be per∣formed Accurately, and Astronomy is like to receive but little advancements. Hereby the Tables Astro∣nomical are approved or rejected, and Calculations found true or false. So that whatever advantages we propose to our selves by a Correct Astronomy, we shall find our present Indeavour to be helpful to∣wards them. And certainly there are some signal uses expected from it, since so many Kings, Princes, States, and Learned Men in all Ages, particularly our late and our present Soveraign of Great-Brittain, The present French King, and formerly some Kings

of Denmark, have been at such great expences both of Time, Labour, and Charges, for the advancement thereof. But I shall pass by all other excellent uses that are expected from an Accurate Theory of the motions of the Heavenly Bodies, and shall only insist on one particular, wherein the Observation of the exact Moment of Time does more immediately tend to the use of mankind. We all know how universaly the whole World is concern'd in Navi∣gation and Commerce, by Ships flying before the winds, and floating on the Seas; Nation converses with Nation, as every man with another by words flying in the Air; by this, Civility, Learning, and all Politeness is propagated; we are made acquain∣ted with one anothers Laws, Constitutions and Man∣ners, we mutually reap the Fruits of each others Countrys, and are no longer Strangers, but Fellow-Citizens of the World. And for all these advanta∣ges (at least for our more securely reaping these be∣nefits) we are in a great measure, if not wholly, beholding to Astronomy. For whoever has but in∣quired into the first Rudiments of that Science, does very well know, how far the determina∣tion of the Longitude of places, and consequently the advancement of Geography and Navigation de∣pends thereon. But whether this be attempted by Eclipses of the Sun, Moon, or Stars, or by the Immersi∣ons and Emersions of Jupiter's Satellits into or from his shadow, or by the Pendulum Clock, at Sea, &c. In

all these methods the Observation of the exact Mo∣ment of time is necessary, for otherwise the Horary distance of the place of Observation, and consequent∣ly the distance on the Aequator, or Longitude, from an assigned place shall be uncertain.

CHAP. II. Of the Methods used for observing the Exact Moment of Time, and their Inconveniencies and Troubles.

THE common ways used by Astronomers for observing the Time are, either by Dials, or by taking the Suns Altitude by day, or by the Altitude of fixt Stars by night, taken by large and accurate Instruments; or by observing the Altitude and Azimuth of the Sun or Stars, or lastly by the transits of Sun or Stars cross the Meridian, or the coming of some of the Circum-Polar Stars in the same Vertical with the Pole-Star. All these methods have their incon∣veniences, or at least, are attended with far greater trouble than that which I shall propose.

And first for Dials, unless they be very large they will not admit of divisions so minute, as are requisite to the nice determination of the Time, as into minutes, half-minutes, and quarter-mi∣nutes. And when they are so large as to admit such, the uncertain shadow that is cast from a long

Gnomon renders them useless for such niceness; for though your Dial have on it every quarter-mi∣nute, the most accurate eye cannot tell where the shadow determines to a minute. Another grand defect of Dials is, that they serve only in the day∣time, and that too, when the Sun shines out in∣tensely. So that for the night (which is the chief time of Astronomical Observation) Dials are perfectly useless.

Perhaps I need say no more to recommend my present contrivance, then to assert that it clearly takes off both these inconveniences. For thereby the larger the Dial is, and the more minute the divisions are, the more accurately is the Time ob∣served. A long Gnomon in our way hinders not at all, nor is there any uncertainty from a Penumbra. And moreover 'tis adapted as well to serve by the Stars at night, as by the Sun in the day, and gives the hour almost by inspection at a Star, as at the Sun. And withal has this advantage, that when the Sun is over-clouded, so as but just to be seen faintly, and casts no shadow at all on a Dial; yet in our way, if he be in the least perceivable by the eye, the Time may be exactly told by him.

I cannot say that there are inconveniences in observing the Time, by taking the Sun or Stars Altitudes and Azimuths by day and night; and yet if we reckon trouble an inconvenience, these me∣thods are not free from it. For, besides the dif∣ficulty

and charge of obtaining Instruments large and accurate enough for doing these, and the dex∣terity and long practice that is requisite for right∣ly managing them: This method is attended by the trouble of Calculating the most difficult of oblique spherical Triangles, viz. that wherein three sides are given to find an Angle; and this, if the observation be by the Altitude of the Sun in day∣time; for by the Altitudes of Stars by night, the Calculation is yet more tedious and troublesome. And if so, what a toil must it be to suppute twen∣ty or thirty of these in a night? Besides, the Al∣titudes of the Sun towards the meridian alter so slow∣ly, that for a good while both before and after noon, 'tis not safe to rely upon them. This incon∣venience indeed is something remedied at the Stars, where I can choose those that are of a pro∣per Altitude, and conveniently remote from the Meridian, and the observation of the Azimuth reme∣dies the other uncertainty proceeding from their vicinity to the Meridian. But, as I said before, the trouble of Calculation attends the observation ei∣ther of Altitudes or Azimuths; whereas the Instru∣ment I propose, does the matter with the greatest certainty, and greatest ease imaginable. There is requisite therein, besides a plain and simple obser∣vation, no Calculation by Triangles, or any other Operation, save only the addition and substraction of two or three small numbers, to be had in the

Tables ready Calculated; and that too, only when the observation is by the Stars at night.

The methods of observing the Time by the ap∣pulses of the Sun or fixt Stars to the Meridian, or the Circum-Polars coming in the same Vertical with the Pole, are plain, simple, and easy. We have the first described by Riccioli in his Almagestum Novum, Lib. 5. Cap. 15. Prob. 8. where he shews us how to perform it by his Triangulum Filare. The latter way is described by Sir Jonas Moore in his Compendium Mathematicum, p. 118. and more fully in the Royal Almanacks for the years 1676, 1677, 1678. And I have by me Tables laboriously and carefully Calculated by my esteemed Friend Henry Osburn Esq and excellent Astronomer and Mathematician for Dublin and other Latitudes in Ireland to years lately past, and to come, which are to be used in this way. But, though both these ways (as I said before) are very plain and easy, yet they serve ra∣ther to rectifie Watches and other Time-keepers, then to shew the Time themselves throughout the whole course of an observation; as, suppose it were an Eclipse of the Moon, perhaps when a spot ei∣ther immerges or emerges into or from the sha∣dow, there is not at that very instant, and perhaps will not be for many minutes after, a Star in the Meridian, or under the Pole-star, to tell me the mo∣ment of that time.

But what I propose does as constantly (and not

by fits) shew, and follow the time, if duly mana∣ged, as the Hand of a well-going Pendulum-Watch indicates the hour; that is to say, it tells you the present minute, and quarter of a minute, when∣ever you are pleased to look, as well as any other, past, or to come.

CHAP. III. A Description of the Instrument.

THE contrivance of this Instrument consists in making a very large Horizontal Dial, adap∣ted to your proper Latitude, and capable of recei∣ving divisions into minutes, and parts of a minute, fitted with a large, strong, and double Gnomon; I call that a double Gnomon that casts the morning-shadow from its Western-edge, and the afternoon-shadow from its Eastern-edge, and the noon-sha∣dow by its thickness. This Dial is to be furnished with two pair of Sights or Rulers; one to serve in the morning, or for Stars on the Eastern-side of the Meridian, t'other to serve in the afternoon, or for Stars on the Western-side of the Meridian. Each of these pair consists of two movable Rulers, one I will call the Horizontal-Ruler, t'other the Gnomo∣nick-Ruler, or Stile-Ruler. These two Rulers are to be so adapted, that their two edges that are next

the Gnomon, may be perpetually in the same plane with each other, and at the time of observation, that they both may be in the same plane with their correspondent edge of the Gnomon. On the Stile-Ruler are fixt Telescopick Sights, and the cross hairs in their due place. But all this will be made plainer by the first Figure, in which I shall repre∣sent that Instrument which by my directions was made in London in the Summer 1685 by Richard Whitehead Math. Inst. Maker, who took the dire∣ctions from my self, but made the Instrument in my absence.

The first Figure represents the Instrument in Perspective, having one pair of its Rulers in a po∣sture of observation; t'other pair lying carelesly on the plane of the Dial. 'Tis a large Octogonal Brass-plate, clear'd in the middle, except only the cross-bars zzz of the same piece with the Plate, left for strengthning the Instrument, and recei∣ving the Stile, the Plate is of a moderate thickness about 15/100 of an inch, the Diameter of the largest circle it receives is 18 inches, 'tis supported from the plane on which it stands about three quarters of an inch by three brass-feet 2. 2. 2. the bredth of the limb for receiving the Figures and Divisions, is 2 1/2 inches. The thickness or bredth of the face of the Stile malb is 7/10 of an inch. The Divisions actually expressed upon it are hours, half hours, quarters, five minutes, minutes, and half minutes,

and one may easily judge of the third part of an half minute, that is, 10 seconds. Down along the face of the Stile (some perhaps will call it the back of the Cock) there runs a deep Groove, to receive the screw m. l. which screw, by turning the handle n, raises and lets down the Nut op, on which the Stile-Ruler ef rests, and is thereby rai∣sed and let down, as the Sun or Star requires. This Nut op is furnish'd with a Return'd Fork, meer∣ly to keep the Stile-Ruler from an accidental fall, if any thing should chance to move it rudely. But I shall describe this Nut o. p. presently by it self. The screw m. l. is fixt both at top m and bottom l, so that it only is to be turn'd round by the handle n. the Stile is fixt most strongly by the screws, q. r. I come next to describe the Rulers, and first for the Horizontal Ruler cd, this turns most truly upon the Center of the hour-lines and divisions at k, and has so much of the root of the Stile clear'd off, as its thickness requires to permit its motion freely; the line cd of this Ruler cros∣ses the Center most exactly, and the edge cd is neatly cypher'd off (as the Workmen call it.) Wherefore the right line ab of the Stile, and the line of the under-edge of the Horizontal Ruler cd, meeting, and crossing perpetually in the same point k, they shall be always in the same plain, (by Prop. 2. Eucl. 11. Book.)

To the other end of this Horizontal Ruler there

is adapted the Stile-Ruler ef, which by means of the joynt vxy (which I shall describe by it self) obeys two several motions, viz. one upwards and downwards, as govern'd by the Nut and screw on the Stile; and t'other Eastward and West∣ward, according to the Azimuth, or as it follows the Horizontal Ruler. And in these two motions, 'tis so contrived, that the line cd and ef may per∣petually cross each other in one and the same Center at y. Hence it comes to pass, that the right line cd, and the right line ef, are always in the same plain. Wherefore laying the line ef to the edge of the Stile, the three lines ab, cd, ef, are in the same plain; and consequently direct∣ing the line ef to the Center of the Sun, the edge of the Gnomon, and the edges cd and ef of the Ru∣lers are in the plain of the shadow; and there∣fore the Ruler cd cuts the division on the limb of the Dial-Plate, where the shadow would cut it.

To the Stile-Ruler are fixt, the Eye-glass at h, the Ring that carries the cross hairs at g, and the Object-glass at i; The manner of adjusting all which, I shall shew presently.

But I must not forget to mention the Artificer, whose hands were imploy'd in this Instrument, Mr. Richard Whitehead living in Gunpowder-Alley in Shoo-Lane, by Fleetstreet, London, a most exact and careful Workman, of whose skill and curiosity in

making Mathematical Instruments, I have more than this one instance; And I dare venture to recommend any Gentleman to him, as a most ex∣act performer.

CHAP. IV. Of the Stile-Nut, and Ruler-Joynt.

IN the foregoing Chapter I have promised a particular description of some of the fore∣mentioned parts belonging to this contrivance; and first of the Nut op (Fig. 1.) This I have re∣presented by it self in Fig. 2. ss is the Stile-screw passing through the Nut n, which is lined with a female-screw; this Nut slides in the Groove a∣long the face of the Gnomon, so that the whole thickness of the screw lies under the said face: p p are two arms that clasp the Stile to make the motion of this Nut more even and steady. fab is the Return'd Fork to keep the Rulers, when they are supported on this Nut, from any accidental fall, and is very useful when the Ho∣rizontal Ruler is removed far from the Meridian. And least at any time, either of the Returns ab, may stand in the way of either of the Rulers mo∣tions, the parts ab are movable at a by a riveted joynt, and may be turn'd clearly downward out

of the way, as at ac, ac. At a there may be fixt a small gentle spring, that may lightly bear the edge of the Ruler constantly to the edge of the Stile; but this contrivance is not on my Instru∣ment, though it may be easily added.

The several parts of the Ruler-joynt (which in∣deed is the most curious piece of Mechanicks a∣bout the whole Instrument, and on which the whole affair does chiefly depend) are represented all apart in Figures by themselves. Fig. 3. shews the outward end of the Horizontal Ruler, aaa are the holes that admit the screws which fasten it to the other parts of the joynt, particularly to the socket shewn in Fig. 5, 6, 7, 8. at aaa. Fig. 4. shews the other end of the Horizontal Ruler, where it turns on the Pin in the Center of the Dial at the root of the Stile (at k Fig. 1.)

Fig. 5. expresses the appearance of the joynt, when discover'd of Fig. 3., ihi is a perfect hinge, the Center of whose motion is in the line fh, iii that part of the hinge belonging to the Ruler, hhh that part belonging to the Tumbler or Nut expressed in Fig. 7. hhh. aaa the socket wherein the Timbler hhh moves round and truly on the Center at middle h, which also is in the Center of the hinges motion. This socket aaa is repre∣sented in Fig. 8. bb are the screw-holes for the Ring and Snout of the Eye-glass.

Fig 6 shews the under-side of Fig. 5. where the

same parts are marked with the same letters; c is the round Pin of the same piece with the Nut hhh: This is more plain in Fig. 7, this Pin turns truly in the hole of the socket c in Fig. 8. whilst the Nut hhh of Fig. 7. rests and turns on the bottom of the said socket hhh Fig. 8. This Nut is kept close in the socket, and there made to move steadily and truly by the Pin e and springing Plate d Fig. 6. and 9. which Pin e passes over the Plate d through the Pin of the Nut c.

CHAP. V. Of the Telescopick Sights, and their true Adjusting.

FOr the true adjusting of the Telescopick Sights hgi (Fig. 1.) to the Stile-Ruler ef, there are three things requisite. But first I must advertise, that the Stile-Ruler ef ought to be so strength∣ned, that as it rests on the Nut op, it may not at all bend, but that the line ef may be one right line as nigh as possible. But in this particular the greatest niceness is not requisite, for if the Ruler chance a little to deviate from its exact straight∣ness, I shall shew a way of rectifying the error by the cross-hairs or Mensurator.

The first thing requisite to the placing of the Telescopick Sights is, that the ring g, that carries

the cross-hairs or other Mensurator, be at a due and exact distance from the Object-glass i. This distance is to be exactly the total length of the Object-glass; but that we may get this total length more accurately than by any admeasure∣ment, the Eye-glass and Object-glass being adap∣ted together, and placing the Mensurator in the ring g between the Object-glass and Eye-glass at the distance of the Focus of the said Eye-glass, let us look at some object distant 4 or 5 miles, and moving your eye before the Eye-glass, observe whether the Mensurator seems to move upon the said object; for if it do, then the Mensurator is not at its exact distance from the Object-glass, but the Object-glass is to be removed farther or nigh∣er, till the eye looking at such a distant object, and moving before the Eye-glass, perceives the Mensurator as it were fixt and immovable on the object. If in raising the eye, the object seem to fall down on the Mensurator, or in depressing the eye, the object seem to rise on the Mensurator, then is the Object-glass too nigh the Mensurator. But if in raising the eye, the object seem to rise on the Mensurator; or in depressing the eye, the object seem to fall on the Mensurator, then is the Object-glass too far from the Mensurator. All which will be evident from the 10 Fig. wherein let AB be a distant object, whose middle point C is projected by the Object-glass D at k, let mn1 be the Men∣surator

to which the Object-glass is too nigh, and mn2 the Mensurator from which the Object-glass is too far, e, f, g, the eye placed at three different postures; in case of the first mensurator, if the eye rise from e to f it perceives the point k depressed from 1 to h; or if the eye fall from e to g, it per∣ceives the point k raised from 1 to l; and here the mensurator is too nigh the Object-glass. But in case of the second Mensurator, if the eye rise from e to f, the point k seems to rise on the Mensurator from 2 to r; or if the eye fall from e to g, it perceives the point k fallen from 2 to s, and in this case the Mensurator is too distant from the Object-glass; but if the mensurator be exactly in the Focus at k, let the eye rise or fall, the mensurator seems fixt and steddy upon the object. And this is the first thing requisite to the adjusting of these Sights.

This Affair is usually so well adjusted by the Workmen, and when once adjusted, is never al∣terable, that I need shew no way of providing for it. But in short, it may easily be provided for, by making the holes for the screws, that fixt the Object-glass-ring to the Stile-Ruler, long slits, so as to slip forwards and backwards on the necks of the screws; and when the Object-glass is at its right posture, the screw-heads may pinch and fix the Ring steddily.

The next requisite is, that the line of Collimation from the mensurator through the Object-glass, and

so to the object, run parallel to the line ef of the Stile-Ruler. This Parallelism consists in two man∣ner of ways, first, that the mensurator be neither more to the right or left-hand than requisite; or secondly, that it be neither higher or lower than it ought. The first error makes the Azimuths be shewn false, and the second error makes the Al∣titudes be shewn false: but an Horizontal Dial tells the time by both Altitude and Azimuth; therefore both these are to be taken care of.

And first for the Fabrick of the Ring g, that carries the mensurator; this is so to be order'd, that first the Ring may be moved more to the right or left-hand, and there to be fixt; and secondly, that the mensurator may be raised or depressed ac∣cording as is requisite, and there fixt. The first is obtain'd by making the holes for the screws, whereby this Ring g is fixt to the Stile-Ruler, long slits, so that they may slip on the necks of the screws before the Eye-glass, and when they are in their right posture, may be pinched close by the screw-heads, and there fixt. Thus there∣fore we give the mensurator a motion to the right or left-hand, by which 'tis brought to shew the Azimuth right, as I shall declare presently. Next, that the mensurator may be raised or depressed, in∣stead of cross-hairs in the Ring g, let there be placed therein a very strong Steel-needle, that may end in a most fine slender point: this needle

is to be a screw almost its whole length nigh to its smaller end, and to be screw'd through the top of the Ring g, so that its smaller end may pass through the center of the Ring; by screwing or unscrewing of this Needle, we depress or raise its fine point in the Ring. And thus much for the contrivance or Fabrick of the Ring.

I come now to shew the way of managing these two motions in the Mensurator, so as to bring it to its true posture, and there fix it. And first for rectifying the Mensurator so as to shew the true Azimuth. There are two manner of ways for do∣ing this. The first is more troublesome and tedi∣ous, but being most universal to the fixing of Telescopick Sights on all Rulers, I shall here describe it. In Fig. 11. let ABCD represent a Ruler, whose edge or side AC is exactly parallel to its side BD. To make a Ruler thus parallel, is not difficult to a good Artificer; but I shall shew how to try whether these sides are parallel or not. E is the Object-glass, F the Mensurator, G the Eye-glass. On a plain Board strike two round Brass-pins, as suppose at H and I, to these apply the side of the Ruler BD, so as it may rest against the pins, which are therefore not clearly buried into the Board, but stand out about 1/10 of an inch: then look through the Glasses, and observe where the men∣surator falls on an object distant a mile or two. Then remove the Ruler, and apply its other

side AC to the other side of the pins HI, and ob∣serve whether the mensurator falls on the same point of the object as before. If it do so, then are the sides of the Ruler AC, BD parallel; if not, then the sides are not parallel. The reason that so remote an object must be chosen, is, that the bredth of the Ruler may subsend an inconsidera∣ble Angle in a circle, whose Radius is the di∣stance of the object. Having found the sides of the Ruler to be parallel, the next thing is, to make the line of Sight, or line of Collimation LK parallel to these sides, for therein consists the first rectification of our Stile-Ruler. The method of do∣ing this is much the same with what immediate∣ly precedes, but requires another disposition of our pins; for now we are to raise our plain Board so as to stand edge-wise, nigh perpendicular to the Horizon, and the pins must stand an inch or more out from the Board, almost parallel to the Horizon; then resting the under-side of the Ruler on the pins, and applying its edge to the plain Board, observe the point of a remote object whereon the mensurator falls; in this posture the Glasses stand uppermost, or on the upper-side of the Ruler, and over-look the pins. Then remove the Ruler, and hang the other side thereof on the pins, that now the Glasses may be on the under∣side the Ruler, or under-look the pins, and resting the edge against the plain Board, observe whe∣ther

the mensurator fall on the same point as be∣fore; if it do, then is the line of Collimation LK pa∣rallel to the sides AC, BD; if it do not, but falls to the right-hand apparently of the said object, then is the mensurator to be removed (by means of the screws and slits in its Ring) to the left-hand: the contrary requiring the contrary. And thus by frequent repetitions and trials we at last bring all to rights. The most convenient Board or Ta∣ble for this Operation, is a Surveyors Plain-table; for these being usually made true, and readily and steddily obeying all motions and postures, and are easily fixt thereat; they are to be chosen before any other. Note also that the pins to be used with this or such like Table, are to be strong brass-wire, which having its roundness from its drawing, is sure to have its sides parallel. By this method, the line of sight of any Cylindrical or square Telescope may be made to run parallel to its sides, for finding the Declination of the Magnet accord∣ing to the methods lately proposed by Monsieur Hautefeville, and M^nsr. Sturmius, in the Journal des Scavans 23. Aug. 1683. and in the Acta Lipsiae, An. 1684. mens. Decemb. and for want of this method, what M^nsr. Sturmius says in the foresaid Act. Lips. pag. 579. is very defective. For thus he, Sola tubi locatio ut axis visionis per medias lentes excurrens me∣ridianae lineae exacte respondeat difficultatis quippiam ha∣bere videbatur, verum & huic infirmitati praesens, uti

credo, inventum est remedium, &c. And the remedy he tell us is, that the Tube be made a parallelipi∣ped of Wood or Brass; for then, says he, apply∣ing the side of your Tube to the meridian line, the Axis of vision will be parallel to the said meridian line. But I must crave leave to deny this, unless first it be rectified, so that this Axis runs parallel to the side of the Tube, which he was not aware of: and this is to be done by the method I have just now proposed, which serves likewise in ma∣ny other Occasions, Experiments and Practises, wherein a Ruler with Telescopick Sights is requi∣site.

The second method for effecting this said re∣ctification, is more easily applicable to our Dials, and withal is sufficiently accurate, as doing the business to 10″ or 15″ seconds of time at utmost, and by a careful and curious eye, may do it to half that or less. Place the Dial so before the Sun, that as nigh as possibly the eye can judge, the Gnomon may be equally enlightned on both sides, that is, that the shadow of the Stile may fall exactly on 12 a Clock, or the meridian line of the Dial. This perhaps will be said by some to be no fair pro∣ceeding, because in this we cannot tell where the shadow does exactly determine, and that this be∣ing one of the inconveniences our Dial pretends to remedy, if we rectify our Dial by supposing we can determine that; & if afterwards we determine

that by supposing our Dial rectified, it will seem a circle in Argumentation, but yet I say, they that will try it, will find it otherwise; for I can place the Dial so, that the shadow from the thickness of the Stile, or at least the Penumbra from both the Stiles edges, shall so equally fall upon the 12 a Clock-lines, that 10″ seconds of time, or less, shall sensibly alter the equality. And 'tis not the same case in telling when this shadow comes to an equality on both the 12 a Clock-lines, as in tel∣ling when the shadow of one of the single edges of the Gnomon comes to any of the other hour-lines. For in the first case I am only to judge by compa∣rison, when the shadow is come as much to one of the 12 a Clock-lines as to th'other; but in the latter case I am to judge positively without com∣parison. Wherefore having the Dial in this po∣sture, bring the Horizontal and Stile-Rulers just to 12 a Clock on the Dial-Plate, and observe whether your Mensurator divide the Sun equally into an Eastern and Western half; if it do so, then is your Mensurator right; if not, the mensurator is to be moved something to the right or left hand, as is requisite, till at last by frequent repetitions and tryals we obtain our desire. And thus much shall suffice concerning the rectification of the mensu∣rator to the right or left hand, so as to shew the Azimuths truly. I shall only take notice, that when one pair of the Rulers is rectified, the other

pair is easily rectified by them; for bring the rectified pair to the 12 a Clock-line on the Dial, and move the whole body of the Dial, till you get the center of the Sun, or any 〈◊〉〈◊〉 on the men∣surator, then immediately bring the unrectified pair of Rulers to the 12 a Clock-line on their side, and if the Sun or Star be not exactly on the men∣surator on this pair, the Mensurator is false, and must be rectified, as is requisite: but this be∣ing plain to the meanest capacity versed in these matters, I shall insist no longer there∣on.

But I proceed to the other Rectification of the Mensurator for rightly telling the Altitudes, as I have said before. And tho there be not so very great exactness required herein, especially in telling the time by the Sun or Stars when nigh the Meridian; yet a gross error herein must not be allow'd. This likewise is to be performed much after the same method with the former Rectifications, for 'tis but contriving some way for inverting the Ruler, so that its errors of this kind may be perceived, as by our former Inver∣sions we discovered the errors of another kind. But to make this a little more plain, this error consists in the line of Sight not running parallel with the under-side of the Ruler; wherefore if we have (suppose) a Deal-board whose two faces are exactly parallel, and this Board be raised and fixt

so as to lye steddily along one of its edges, and on each face of the Board there were a ledge to support the Ruler; and the Ruler be applyed by its under-side to one face of the Board, and the object marked out by the Mensurator, diligently observed; and then the Ruler applyed by the same under-side to the other face of the Board: If the same object be now cut as formerly, ly, all is right; if not, the Mensurator (being such as I have formerly described) must be screw'd or unscrew'd, so that the fine point thereof may be lower or higher in the Ring, according as is re∣quisite.

Another more easy way of discovering and rectifying this Error to sufficient accuracy, is thus: After you have by the former methods brought the Mensurator, and thereby the Ruler, to shew the true Azimuth; observe the time by the Dial when the Sun is very far removed from the Meridian, as early in the morning; and at the same time observe by a good Pendulum Clock the hour, minute, and second; and note the difference be∣tween the Dial and Clock. Proceed thus to make an observation every quarter of an hour through the whole morning, still noting the differences: And because we may well suppose that a good Pendulum Clock in so short a course of time goes equally, these differences should be always equal; but if they are unequal, then the Mensurator shews

the Altitudes falsely. As for instance, suppose I find that approaching towards Noon these dif∣ferences decrease, then does the Mensurator on the Telescopick Ruler shew the Altitudes too little, and therefore must be order'd so as to shew them more: if I find them increase, the contrary is to be done. The reason of this is plain, for an Ho∣rizontal Dial shews the time as well by the Altitudes as Azimuths; but as the time approaches towards Noon, the Altitudes are less concern'd in the mat∣ter than the Azimuths; and so less and less, till just at Noon the time is not at all shewn by the Altitude, but solely by the Azimuth. And conse∣quently, if there be any error in the time ari∣sing from a false Altitude, it will appear by com∣paring two times or more together; some, where∣in the Altitudes are much concern'd, and others, wherein the Altitudes are little or not at all con∣cern'd; but such times are, early in the morning, and towards noon.

CHAP. VI. The Way of Setting this Dial.

TO the true Setting of this Dial, there are two things requisite; First, that the plain of the Dial be in an exact Horizontal posture, this

is easily obtain'd by accurate levels, which are so common, that I shall mention nothing further hereof. The second requisite is, that the meridi∣an or 12 a Clock-line of the Dial be in an exact meridian line. This indeed is one of the chief par∣ticulars that we are to take care of, for thereon depends the accuracy of the whole. But that we may not over-turn or neglect the whole affair for the difficulty of this one particular, I shall shew that this is no such insuperable hardship as may be imagin'd. Let us therefore consider, that what is here alledged as a difficulty in this Dial, may as well be made against the large Azimuthal Quadrants used by Astronomers, and their observations of me∣ridional Altitudes, and transits through the Meridian; Ricciolis Triangulum Filare described Almag. Nov. Lib. 5. Cap. 15. Probl. 8. and all Enquiries after the Declination of the Magnet are to no purpose; for these wholly proceed on the discovery of an ex∣act meridian line. And indeed there are ways suf∣ficiently accurate described by several for finding the true meridian. Amongst others, Hevelius in the first Part of his Machinia Caelestis, Chap. 16. has many contrivances: And I shall presently set down an Instrument and way of my own for doing it, inferior, I think, to none. But let us a little consider, how much a meridian line must be erronious, to make a true Dial apply'd to it to err a minute in time; and this in our latitude of Dublin

will be 12 minutes of a Quadrant to make the Dial err a minute in time about noon; and for so much error in the meridian line the Dial shall err less than a minute in time about 5 and 6 a Clock, as is manifest to those that understand calculating hour distances for an Horizontal plain. Now 'tis a very rude way indeed that will not take a meri∣dian line more accurately than to half or quar∣ter 12 minutes error.

But last of all, (clearly to take off this difficul∣ty,) if it be allowed that there is any most accu∣rate way of telling the time of day or night, as by the Altitude of the Sun or Stars taken by large and curious Instruments, and Calculating there∣by; I say, by such a way as this I will set my Dial, and then surely it will be granted to be in a true Meridian. And perhaps this very hint may shew as accurate a way as any in the World for finding a meridian line; for the 12 a Clock line of a large and true Dial that is Set by such an accu∣rate observation must needs lye in a true meri∣dian line.

But I am mindful of my promise, Viz.

CHAP. VII. For Finding a Meridian Line.

THis is perform'd by means of the Instru∣ment represented Fig. 12. ABC is a Trian∣gle. (That which I have made is of Wood, but a good Mathematical-Instrument-maker would make one much better of Brass.) AB I call the Perpendicular side, BC the Horizontal side; in the end of the Horizontal side at E there is a screw, and from the said Horizontal side there strikes out a short arm D, in which also there is a screw; this arm D keeps the Instrument steddy from tottering. By means of these two screws at D and E, the side AB is brought to its exact perpendicu∣larity; but especially by means of the screw D, the edge xz of the side AB is brought to stand exactly in the same Vertical plain with the edge mn of the side BC, and this by help of a Plum∣line. F is a plate of Brass, having in it a center∣hole in the line m,n continued. G is a round, slen∣der, but strong Brass-pin arising perpendicularly from the face mn. 1, 2, 3, 4, 5, &c. are round Brass∣pins that rise and stick out from the face xz, at what distances we please. This Instrument be∣ing placed truly on an exquisite Horizontal plain,

so that its end E may something over-stretch the plain, and turning steddily on a pin in the cen∣ter-hole F, lay a Ruler adapted with Telescopick Sights over the pin G, and any of the other 1, 2, 3, &c. as is found most convenient and agreeable to the Altitude of the Sun or Stars you observe by, at convenient times both before and after Noon. 'Tis therefore requisite that in the under-side of your Telescopick Ruler towards the end next the eye, there be fixt a pin, that resting on the pin G may keep the Ruler from slipping down in this declining posture. Let us then suppose that a∣bout 9 a Clock in the morning on the Summer Solstice, the Telescopick Ruler resting on the pin G, and the third pin in the perpendicular side takes the Suns Altitude exactly, then on the Horizontal plain draw a line along the face m,n. Again, let us suppose that the Ruler removed upwards to the fourth pin, and there resting, takes the Suns Altitude the same morning about half an hour af∣ter 9; then by the face mn let us draw another line on the Horizontal plain, and so let us proceed to elevate the Ruler on other pins, to make ob∣servations at 10, at half an hour after 10 the same morning, still drawing lines on the Horizontal plain at each observation.

Then again in the afternoon let us descend by the same steps or pins, by which we rise in the morning, diligently observing when the Sun

comes to the corresponding Altitudes, and draw∣ing lines as before. Here we shall have three or four observations made in the morning, and as many in the afternoon. Then bisecting these An∣gles from the point F, if all their bisections are co∣incident in the same right line, we are sure that line is a true meridian line.

What is here said of the Sun, and of observing by it at the Summer Solstice, may be accommoda∣ted to the taking a meridian line at any time of the year by some fixt Stars, that being removed a∣bout 2 or 3 hours from the Meridian, have Alti∣tude convenient; though in choosing of a great Altitude there is no great nicety; for if Refraction do interpose in the morning-observation; it inter∣poses as much in the afternoon-observation; so that 'tis as if it did not interpose at all. And here we have a way of finding a Meridian line by the Stars at night, which is of no small advan∣tage, they being not subject to sudden alteration of their Declination, and consequently this me∣thod may be practised at all times of the year.

And indeed if we are careful to have all things exact, viz. an exact Horizontal plain, the face xz in an exact Vertical with the face mn, the Telesco∣pick Ruler and its Sights exactly adjusted by the methods in the foregoing 5th Chapt. and be very diligent and accurate in observing the true Alti∣tudes, this method of finding a meridian line will

appear inferior to none that has yet been propo∣sed.

Such a plain Telescopick Ruler as is expressed in the 11th. Figure, of a convenient length, is suffi∣cient in this practice.

CHAP. VIII. The Manner of observing the Time, and exactly deter∣mining it by the Sun or Stars.

ALL things being rightly adjusted, and the Dial placed in an exact level or Horizontal posture, and by a true meridian line, look at the Sun through the Telescopick or Stile-Ruler, and bring the Mensurator upon the Suns center, then shall the Horizontal Ruler cut the hour, minute, and part of a minute most exactly. But for Setting, or find∣ing the error of a Clock, the best way is to bring the Horizontal Ruler to some full Division, as, to some compleat minute; and by rightly managing the Stile-screw and Nut, and Stile-Ruler, observe when the center of the Sun and Mensurator come together, for that is the exact time to which you placed the Horizontal Ruler. And indeed through the Telescopick Sights we shall perceive the motion of the Sun so very quick, that we may determine its being on and off the mensurator to 2 beats of a

second Pendulum. So that if it be granted me that I can bring and settle the Horizontal-Ruler to a full division exactly, and not to err in placing it thereat over 3, 5, or 7 seconds, I can determine the time of day or night to 3, 5, or 7 seconds. But if this great exactness will not be allow'd me, I say it is not on the account of any fault in the Theory of this contrivance, which I dare assert to be most accurate in it self, but on the account of the workmanship or deficiency of some of its parts. And that strikes not at the Inventer; let those that use them, and adjust them, look to their truness in all particulars.

The way of using this Dial at the Stars by night is much the same, only for these there are requi∣site the Tables, at the end of this Book, of the Sun and Stars temporary Right Ascensions. In look∣ing at, or observing a Star through the Telescopick Ruler, the Horizontal Ruler cuts the said Stars hora∣ry distance from the Meridian, but then the hours are to be counted by the smaller Figures on the in-side of the limb. Thus, suppose I observe a Star, and find the Horizontal Ruler cut the ten a Clock line to which the great Figure of X is af∣fixt, the horary distance of that Star from the Me∣ridian is 22 hours, that is, twenty two hours are elapsed since that Star was last in our meridian, though really the Star be but 2 hours to the East of our meridian. This premised, the great Rule

for telling the time by the Stars is this; To the Stars horary distance from the meridian, add the Stars temporary Right Ascension, and from the Sum substract the Suns Right Ascension, the remainder (rejecting 24 hours if need be) gives the hour, minute, &c. of the night.

I shall declare this by an Example. Anno 1686. April the 5th. between 9 and 10 a Clock at night I desire to know the exact time. I observe by Spica Virginis, and find (suppose) its horary distance from the meridian 22 h. 03′ 15″. The temporary Right Ascension of that Star for that year is, 13 h. 08′. 46″, this added to the foresaid horary distance, the sum is 35 h. 12′. 01″. At the same time the Suns place is ♈. 26° 13′ 59″. Therefore its Right Ascension in time by the following Tables, is 1 h. 37′. 17″. this substracted from the foresaid sum (and rejecting 24 hours) leaves 9 h. 34′ 44″. the exact time of night. The reason and demonstra∣tion of this method depends on Astronomical Principles, which at present I must not undertake to illustrate, but are obvious enough to those that are versed in that Science, and will be very plain to those that consider the way of Calcula∣ting the hour of the night by the Altitude of a Star given, according to the most Learned and Inge∣nious Pere Tacquets Illustration thereof in his A∣stronomy, Lib. 5. Cap. 4. Num. 45.

And though there are other ways of ordering the foregoing Data, for getting the hour of the

night, yet what I propose is as plain and easy as any, and less embarras to the mind.

But here I must not omit one particular, and that is, that by our present contrivance, the Right Ascension, or place in the Aequator of any Star, is most easily and accurately obtained. How dif∣ficult and troublesome 'tis to obtain the Right Ascension of Stars, is known to Astronomers, and will appear to those that consult the foremen∣tioned Tacquet Astionom. Lib. 5. Cap. 1. num. 4, 5. but by this Instrument, and a truly rectify'd Pendu∣lum Clock, the business is easily perform'd: For, from the sum of the Suns Right Ascension, and hour of the night (known by the Clock) substract the Stars hour on the Dial, the remainder is the Stars Right Ascension in time, which converted into de∣grees and minutes, shews the Aequatorian distance of the Star from the first point of ♈, or its Right Ascension.

CHAP. IX. Of the Tables of the Suns and Stars Temporary Right Ascensions.

THe Table of the Stars Right Ascensions in time is plain enough of it self. 'Tis com∣puted to the year 1686, and will serve for ten years to come without the error of half a mi∣nute.

'Tis according to Riccioli's Catalogue of sixt Stars in his Astronomia Reformata. It consists of 5 Columns, the first contains the Magnitudes, the second shews the Greek Letters by which each Star is marked in Bayers Ʋranometria Printed at Ausburg, 1603. The third has the numbers by which each Star is noted in Tiho's Catalogue, which is followed by most Authors, but is to be found particularly in Tichonis Brahe Astronomiae In∣stauratae Progymnasmata, pag. 258. and at the end of the Rudolphine Tables published by Kepler. The fourth Column contains the Stars names, as they are in Bayer's Ʋranometria; and also after each name we express the common name in English, and as they are to be found on our common Globes. And here we must not won∣der to find that called Right or Left in the Latin names of Bayer, that is called Left or Right in the English common names; as for instance, Herculis Humerus Dexter, is in English, the left shoulder of Her∣cules. For the reason of this will appear plain to those that consider the Constellations of Bayer, and the common Constellations on our Globes. And I thought it not amiss to take all this care, and express all these marks for the sake of those that are not so well versed in the appearance of the Firmament, that they may the readier find out, and not so easily mistake any of the foremen∣tioned Stars. The fifth and last Column expres∣ses

the Right Ascension in time of each Star to the present year 1686.

The Tables of the Suns Right Ascension in time require the Suns place to be had from some good Tables or Ephemerides. They consist of four Co∣lumns, the first contains every degree and 10 mi∣nutes of the Suns place, the second contains the hours appropriated to the signs between the Ver∣nal and Autumnal Equinox, the third shews the hours appropriated to the signs between the Au∣tumnal and Vernal Equinox; and the fourth and last shews the parts of an hour, that is, minutes and seconds, that are common to the opposite signs. By the side of each division are expressed the dif∣ferences between every 10 minutes of the Suns place, for more ready making proportion. For Example, suppose the Suns place were ♈. 25°. 10″ I find its Right Ascension 1 h. 33′ 15″. But if his place were ♎ 25°. 10″. the Right Ascension would be 13 h. 33′. 15″. Where we see 33′. 15″. common to both places. But suppose I find by a good Ephemeris the Suns place about my required time to be ♈ 25°. 15″ then by making proportion I find by the Tables the Right Ascension to be 1 h. 33′. 34″. For I say if 10′ (the common difference of the minutes) give 38″, what shall 5′ (the difference between 10′ and 15′) give, and it will be 19″, which added to 1 h. 33′. 15″. makes 1 h. 33′ 34″.

I know the common way for giving the Suns

Right Ascension is by making a Table of the days of the month, and giving the Suns Right Ascension to the days. But this way, if it be general, and not appropriated to a certain year, is not accurate to a minute or two: and if it be adapted to a cer∣tain year, 'tis not general, and will not serve ano∣ther time. Whereas our Tables of the Suns Right Ascension are general, most accurate to a second, and perpetual.

CHAP. X. Concerning the Astronomical Equation of Time, and the Tables thereof.

BEing now upon the business of Time, and the accurate observation thereof, so as there∣by to regulate curious Time-keepers; it will not be improper to our subject to speak something of the Inequality of natural Days; a matter that has exercised the thoughts of all Astronomers in all ages: And though all have allowed that there really is such an Inequality, yet they have much disagreed in assigning its quantity, or demonstra∣ting the reason and affections thereof; till at last our most Learned and Ingenious English Astrono∣mer, and my Honoured Friend Mr. John Flamsteed Math. Regius, has determined the Controversy,

and by most evident demonstrations has put the matter beyond further dispute, clearly evincing both the Reasons, Affections, and Quantity of this Inequality. His Dissertation concerning this is an∣nex'd and publish'd at the end of the Opera Post∣huma Jeremiae Horroxcii, Lond. 1673. 4^to. From which (with my esteemed Friend's leave) I shall present the Reader with the following Schemes and De∣monstrations.

On account of the Suns Excentricity from the center of the Earths Annual Orbit, the Diurnal mo∣tion of the Earth is sometimes faster, and some∣times slower than the mean motion, and conse∣quently the apparent Day is sometimes longer, and sometimes shorter than the mean Day. Which Inequality, and the Quantity of the dif∣ference of the equal or mean Day from the ap∣parent, is thus demonstrated from the 13 Figure, according to the Copernican System.

Let ABPN be the great Orbit in which the Earth is yearly carried about the Sun, the center hereof is C, A the Aphelion, or the Earths place at Noon on that day that it is in its Aphelion, suppose the 18th. of June. B the Earths place at Noon the day following. AL an assigned Meridian of the Earth. The arch AB, or the angle ACB, the mean motion of the Earth from the Noon of a given day to the Noon of the day following. L a point in the given Meridian turn'd to the Sun; which

point, whilst the Earth is carried in its Orbit from A to B, is rould by the diurnal circumvolution of the Earth from L through O in the first place A to d in the second place B; to which place, when the said point arrives, 'tis manifest that the Earth has performed a compleat revolution about its own Axis; because the meridian Bd, in this its se∣cond posture at B, is made parallel to AL its yesterdays posture at A. But it is not yet appa∣rent Noon, till the same point of the Earth by its revolution by brought to e, where 'tis turn'd directly opposite to the Sun, who governs the Ci∣vil Days. And that this time is not the same with the Caelestial or equal Noon, will be proved, not only because the Earth has not yet performed its mean motion above its revolution, (tho this were a sufficient argument) but also because the diurnal motions about the Sun, and consequently the returns of any certain meridian to him, are ve∣ry unequal; neither can they possibly be equal in respect of any point about which the Earth is not carried equally, as is sufficiently manifest from the inspection of the Scheme only. Where∣fore the mean Noon and equal Time respects the point of the mean motion (that is the center of the Orbit C) and in our present instance is then when the meridian carried from e arrives at f, where 'tis directly opposite to the center of the Orbit C. And when it has gained this posture, the Earth has

performed its mean motion above a revolution requisite to compleat a mean day. For the arch df or the angle dBf is equal to the angle ACB the mean diurnal motion of the Earth. Also the arch de, which the Earth, or any meridian therein, must pass more than a revolution before it be apparent Noon, is equal to the angle ASB the apparent motion of the Earth at the Sun. From whence 'tis evident, that the arch ef, which the circumference of the rouling Earth performs be∣tween the apparent and mean Noon, and which shews the difference between the apparent and mean Day, is equal to the angle SBC, which is the Equation of the Orbit. Wherefore the Prosthaphae∣reses of the Orbit resolved into parts of time, shall be the Aequations of time; which Aequations, through∣out this semicircle of Anomoly are negative, or to be substracted from the apparent time, for herein the mean Noon succeeds the apparent.

In like manner, if we take the opposite parts of the Scheme, and consider the Earth in its Peri∣helion. The point g, or the meridian ng, being made parallel to its yesterdays posture, 'tis plain that the Earth has performed one compleat revolu∣tion. This point being carried to h, where 'tis op∣posite to the center of the Orbit, 'tis now mean Noon; for the arch gh, or the angle gNh equal to the mean diurnal motion of the Earth, is passed over. But it is not yet apparent Noon, till the

Earth by its rouling brings the same meridian to k, where 'tis directly opposite to the Sun. From whence 'tis manifest that the apparent Day ex∣ceeds the mean by so much time as is requisite for the earth to pass the arch hk, which arch is equal to the angle CNS the Prosthapheresis of the Orbit: wherefore resolving this into time, we have the Aequation of time, which throughout this semicircle of Anomoly is affirmative, or to be added to the ap∣parent time, because herein the mean Noon pre∣cedes the apparent.

'Tis manifest from what foregoes, that if the Sun were in the center of the great Orbit, and the Earths Axis were not inclined to its path or way, there would be no Inequality of time, but the mean Day and apparent would be equal. More∣over, if there were no excentricity of the Sun from the center of the Orbit, but there were the usual inclination of the Earths Axis to the Orbit, tho there would no Inequality of time arise such as is shewn in the foregoing demonstration; yet there would arise another Inequality from the said in∣clination of the Earths Axis, or as the Ptolomaicks would express it, from the inclination of the E∣cliptick to the Aequator; the quantity and affecti∣ons of which Inequality is thus shewn by the Analemma.

In Fig. 14. PCF is a Quadrant of the Solstitial Colure, P the Pole, AF a Radius of the Aequator, CA a

Radius of the Ecliptick, A the Equinoctial point, or the place of the Sun in the beginning of ♈ at noon on some certain day, ☉ the Suns place at noon the day following; through which place striking the arch P ☉ B perpendicular to the Aequator, A ☉ will express the diurnal motion of the Sun, and AB its Right ascension, or the arch of the Aequator that Culminates with the Sun. Which arch, seeing 'tis one of the sides of a Right-angled Triangle A ☉ B, cannot be equal to the Hypotenuse, that is, to the Suns motion A ☉. Wherefore seeing the revolu∣tions of the Aequator, and of its equal or like parts, are equable, and performed in equal times, but the Sun in passing equal parts of the Ecliptick applies to the meridian with unequal parts of the Aequator; it necessarily follows that the solar days are un∣equal. And that the difference between the Suns true place and its Right ascension being converted into time, is the true Aequation of time arising from this cause. Which Aequation, in the first and third Quadrants of the Zodiack is to be substracted from the apparent time, for in them the longitude of the Sun from the next Equinoctial point passes the meridian sooner than a like arch projected in the Aequator. But in the 2d and 4th Quadrants of the Zodiack this Aequation is to be added to the ap∣parent time to get the mean; for in these the lon∣gitude of the Sun from the Aequinox passes the me∣ridian later than the like Arch projected in the

Aequator. For example, let the longitude of the Sun from the first point of ♈ be ☉ A. 0°. 59′. 08″. its Right ascension, or the arch of the Aequator cul∣minating therewith AB will be 0°. 54′. 13″. their difference 4′. 55″. being converted into time is 00^h 00′. 19″.40‴, and by so much is the apparent day shorter than the mean. This therefore is the Aequation of time arising from this cause, and is negative, or to be substracted from the apparent time, to obtain the mean time; for the longitude of the Sun arrives at the meridian sooner than a like arch projected in the Aequator.

Here are therefore demonstrated two sorts of Aequations of time arising from two different cau∣ses, if they are both to be added, or both to be substracted, their sum is to be added or substra∣cted; but if one be to be added, and t'other sub∣stracted, their difference according to the nature of the greatest is to be added or substracted to or from the apparent time to get the mean.

And thus far I have presumed to borrow from my Learned and Ingenious Friend's Discourse; which is sufficient, I think, to put this matter out of all dispute.

After clearing the Theory of this Doctrine, I come next to apply it to practice in regulating curious Time-keepers, which indeed are very of∣ten abused for want of the due consideration and right application of this Aequation of time. For

at some time of the year it happens that if our Watches or Oscillating Pendulums do not differ above a quarter of an hour from the time shew'd by the Sun or Stars, they are false, and need a correction. And the reason of this is plain, for if a Pendulum-Watch goes true, it goes equal, that is, one 24 hours at any time of the year, is as long as another 24 hours at any other time of the year, and this per∣petually and constantly; that is, all Watches that go true, measure the equal or mean time, and con∣sequently ought to differ from the apparent time shewn by a Sun-dial or other Instrument, as much as is the Aequation of time in excess or defect; but the Aequation of time is sometimes above a quarter of an hour, therefore so much ought a good-going Pendulum-watch to differ sometimes from the Sun, if it be rightly adjusted. But this will be more evident by explaining the Tables. These are calculated by the foregoing Theory, and will serve very well for these 20 years to come; though it must be confest, that to have them most accurate, these Tables ought to be Calculated for every year, as is manifest to those that consider the foregoing Theory. Yet I say, these will serve very well for 20 years to come, without any con∣siderable error. Some few seconds error there may be, and he that desires them more exact, may be at the pains of Calculating them him∣self; the method whereof he may find laid down

in the forementioned Treatise at the end of Hor∣rox's Works; or in Mr. Flamsteed's Doctrine of the Sphere publish'd in Sir J. Moore's System of Mathe∣maticks. We see there are only four days in the year on which the aequations of days cease, that is, the apparent and mean time are then the same, viz. on the 4th. of April, June the 6th. Aug. the 21st. and Decemb. 13. If on any of these days we Set a wellregulated Pendulum-watch to the apparent time shewn by the Sun or Stars, on any day afterwards, it ought to differ from the apparent time shewn by the Sun so much as is the Aequation of time in the Table. If the Aequation is to be substracted, the Pendulum ought to be so much slower than (or behind) the Sun; if the Aequation is to be added, the Pendulum ought to be so much faster than (or before) the Sun. For upon any day of the year observing the time exactly by Sun or Stars, that time is the apparent time, and to gain the mean time which ought to be shewn by the Clock, we are to add too or to substract from the said apparent time, the Aequation answering to the day of our observa∣tion. Suppose for instance, on the 4th of April I observe the time by the Sun, here because the Aequation ceases, the apparent and mean time are the same, and therefore I am to set my Clock to the exact and full time, as the Sun or Stars shew it; but if the Pendulum go exactly true, and it move to the 4th of May, I shall find it 4′. 17″ behind

the Sun, for so much is the aequation on the 4th of May to be substracted from the apparent time of the Sun to gain the mean time of the Clock; that is, when the Sun shews it to be 9 a Clock in the morning, the Clock ought to be but 8h. 55′. 43″. And if I find the Pendulum more or less behind the Sun, it has not gone truly as it ought, but the Pendulum or swagg is to be lengthned or shortned as is requisite to make it gain or lose the differ∣ence betwixt the time shewn by the Clock, and 8h. 55′. 43″. in 30 days elapsed between the 4th of April, and 4th of May; according to a Table, whose use I shall declare presently. But if the Movement be exquisitely true, if it go to the 6th of June, it will again shew the same time with the Sun or Stars, for then again the Aequation is no∣thing. And if it go onwards exactly to the 3d of August, it will be 4′. 18″. before the Sun; for at that time so much is the aequation to be added to the apparent time to make it the mean. 'Till again on the 24th of October the Watch ought to be 16′. 4″. behind the Sun, for so much is the aequation on that day to be substracted.

Wherefore if at any time we set our Pendulum-Watch in order to rectify it, and bring it exactly to measure the mean day, we are to add to or substract from the apparent time shewn by the Sun so much as is the aequation of days at the time we set it. For example, at noon, or just when

the Sun is in the Meridian on the 9th of the September, that is, when the apparent time is exactly 12 a Clock, I set my Watch, the aequation is then 6′. 26″. subtr. Wherefore I set my Watch to 11h. 53′. 34″. Which, if it go right, that is equally as it ought, on the 9th of October will be 14′. 52″. behind the the Sun; if it be either more or less behind or be∣fore the Sun, it has gone false, and is to be recti∣fied by lengthning or shortning the Pendulum as much as is requisite to make it gain or lose the difference between 14′. 52″ behind the Sun and its error whatever it is in 30 days time elapsed be∣tween the 9th of Septemb. and 9th of Octob. But if at any other time of the year we set our Watch when the aequation is to be added, we must put it so much before the Sun as is the aequation. But this is plain enough without further Illustra∣tion.

Of the certainty and exactness of this aequation of time, I have made a most convincing Experi∣ment by an exquisitely rectified Pendulum-Clock, which I bought from Mr. Richard Jarrat Watch∣maker in Lothbury, London, whom I can therefore recommend for his honesty and ability.

And because I have spoken in this Chapter of lengthning or shortning of a Pendulum, so as to make it go slower or faster so much in a certain time; for doing this more regularly, and not by guess, I have here added a Table adapted to a Pen∣dulum

that Vibrates seconds, which is supposed to be 39.2. inches long. Sir Jonas Moore in his Mathema∣tical Compendium, pag. 113. gives us such a Table as this, but whether by the fault of the Printer or Calculator 'tis very erronious, as any one may find that will be at the pains to examine it by the fol∣lowing Rules for Calculating these Tables. The Rule is, the lengths of Pendulums are to each other re∣ciprocally as the squares of their vibrations in the same time. Thus, if a Pendulum 39.2 inches long vibrate 60 times in a minute, how oft will a Pendulum 9.8 (viz. quarter of 39.2) inches vibrate in a mi∣nute? by the foregoing Rule the proportion stands thus, 9.8: 39.2:: 3600:14400, whose square Root is 120; therefore a Pendulum 9.8 will vibrate 120 times in a minute. So if it be required how oft a Pendulum 39.0 inches vibrates in a minute, the Analogy will be this, 39.0: 39.2::3600:3618. whose square Root is 60.15. that is, a Pendulum 39.0 in∣ches long vibrates in a minute 60 times, and 15 hundreds of a vibration more than 60 times. So that multiplying 15 hundreds of a vibration by 1440 the number of minutes in 24 hours, we get the number of vibrations which a Pendulum 39.0 inches long vibrates in a day more than one of 39.2; and seeing each vibration of the Pendulum in a Clock adapted for it, sets the hand forward a second, by knowing the number of vibrations which a Pendulum 39.0 inches long performs in a

day more than a Pendulum 39.2 inches long, we may know the number of seconds which it will advance the Index of the Clock forward more than one 39.2 inches long. And by these Rules are the following Tables Calculated.

1	2	3	4
38.7	60″.3863	9′. 16″. 16‴	1′. 52″ 06‴
38.8	60.3084	7. 24. 10	1. 51. 40
38.9	60.2309	5. 32. 30	1. 51. 20
39.0	60.1536	3. 41. 10	1. 50. 40
39.1	60.0766	1. 50. 20	1. 50. 20
39.2	60.0000	0. 00. 00
39.3	59.9236	1. 50. 00	1. 50. 00
39.4	59.8475	3. 39. 36	1. 49. 36
39.5	59.7717	5. 28. 45	1. 49. 09
39.6	59.6962	7. 17. 30	1. 48. 45
39.7	59.6210	9. 05. 45	1. 48. 15

The first Column has in the middle the length of the Pendulum 39.2; upwards it diminisheth one tenth, and downwards it increaseth one tenth. The second Column is the vibrations and parts of a Vibration performed in a minute by the lengths

in the first. The third Column is the minutes and seconds that these lengthnings and short∣nings of the Pendulum will cause in a day, and are gotten by multiplying 1440′ the minutes in a day by the Decimals above or under 60″. The 4th and last Column are the differences of the 3d. The like Table may be made to any length of a Pen∣dulum, respect being had to the foregoing Rule.

I shall conclude all relating to my Dial with the Calculation of hours and minutes for an Ho∣rizontal Dial for the latitude of Dublin 53°. 20′. Which I believe will not be unacceptable to those that design curious Dials for that place.

The Tables follow amongst the others.

CHAP. XI. Of the Tables of the Circumpolar Stars, their Calculation and Ʋses.

I Shall here, as a conclusion to this Work, add something concerning very useful Tables for shewing the time of night very accurately, and other operations by the Circumpolars, or Stars that never set in our latitude of Dublin. Such Tables as these we have mentioned in Sir J. Moore's Mathe∣matical Compendium p. 118, 119. but they are for the latitude of London; neither does he give us all their

uses, or the method of Calculating them for other places. I shall do both in this place, and first for their use.

In any Northern Window, or other convenient place, hang up a good weighty Plummet by a fine and even silk or silver-wire, then placing your eye at some distance behind this thred, that is, to the South thereof, observe when any of the Stars mentioned in the Table are cut by this thred at the same time with the Pole-Star. From the Stars Right ascension in the Table (adding 24 hours if need be) substract the Suns right ascension, the remainder gives the hour, minute, and second of the night. The Tables consist of 6 Colums, the first shews the Magni∣tudes; the second contains the Stars names, as they are described on our common English Globes; the third shews the Right ascension of the Mid-heaven in time, when any of these Stars come in the same Vertical with the Pole-Star, by which (work∣ing according to the foregoing Rule) we find the hour of the night; the fourth Column gives the difference in time between the coming of any of these Stars under the Pole-star, and their coming under the Pole it self. Some of these Stars pass the Meridian, or come under the Pole before they come under the Pole-Star, such as are all the Stars whose Right ascensions are above 9°. 14′. 10″, and under 189°. 14′. 10″. And of these we say nothing in this place, only they are all marked in the Ta∣ble

with E, as having their Azimuth when under the Pole-star Eastward. But of these Stars in this Catalogue which pass the Meridian, or come under the Pole after they have left the Vertical of the Pole-star, we make this following use. All these are marked in the sixth Column with W, as ha∣ving a Western Azimuth when they are under the Pole-star. Wherefore placing a second line and plummet behind, or to the South of the former, then observe by the first when any of these Stars come under the Pole-star, and by a Pendulum from that instant count the time in this fourth Column, and placing your eye now behind both the lines, just at the end of your count by gently moving this last thred, make them both cut the Star you count for, then are these two lines exactly in the meridian; and is a curious way for finding a Me∣ridian line. The fifth and sixth Columns serve for the same use; for when any of these Stars are un∣der the Pole-star, making your two lines cut both Pole-star and t'other, these two lines hang so far out of the Meridian line, as is the Azimuth expressed in the Table, which Azimuth is shewn to be East or West by the 6th Column. Wherefore this angle being set off from the found line, shews the true Meridian. And we may observe, that there are three stars expressed in the Table, which being under the pole-star are insensibly nigh the Meri∣dian, these are Cassiopeid's Hipp, Cor Caroli, and Aliot

or the Great Bears Rump. Wherefore whenever we have any of these under the pole-star, we may by it find a Meridian line without any sensible er∣ror. Another use that we may make of this Ta∣ble, is for the true adjusting of Hour-glasses and other Time-keepers, as Pendulum-Watches, &c. for try∣ing their going, and bringing them to their right measure. Thus we shall find it just four hours (wanting one second) between the coming of Cor Caroli, and the 24th Star of Draco (in Tich. Catal.) under the Pole-star; for when Cor Caroli is under the pole-star, the Right Ascension of the Mid-heaven in time is 00h. 36′. 44″. And when the 24th of Draco is under the pole-star, the mid-heavens tempo∣rary Right Ascension is 4h. 36′. 43″. their difference is 3h. 59′. 59″. which wants only one second of four hours. Note that this 24th of Draco is mark∣ed in Bayer by.

I come now to shew the method of Calcula∣ting this Table, for which see the 15 and 16 Fi∣gures. Wherein axbp is the circle described by the pole-star x round the pole p, z the Zenith, zn the meridian, whose North part is pn, s is any other Circumpolar stars, zxs a Vertical circle, hn the Horizon, aeq the Aequator, po the Axis Mundi. There are here given (or at least may be known from the Tables) px the Complement of the pole-stars De∣clination, ps the Complement of the other stars De∣clination, xps the difference of the Right Ascensions

of the pole-star, and other star, also zp the Comple∣ment of the Poles Elevation. Wherefore, in the Triangle spx, having sp, px, and the angle spx, we may find the angle sxp; and having that, we have the angle pxz, for this is the Complement of sxp to 180 degrees. Then in the Triangle zpx, we have zp, px, and the angle pxz, to find the angle pzx, which is the Azimuth that these two Stars have, when they come in the same Vertical, and makes the fifth Column in our Table. And from the same Data, we may find the angle zpx. Therefore in the Triangle zps, we have found the angle zps, for zps is equal to the sum of zpx and spx. Now the difference between zps and 180 degrees is equal to the difference in time between the Star s coming under the Pole-star and coming, under the Pole, or its being in the Meridian, and consequently its having its own Right Ascension, or its Complement; and this makes the fourth Column in our Table. Now this difference in time between the Pole and Pole-star being added to or substracted from the true Right Ascension of the Star s in time, gives the Right Ascension in time of the Star s (or of the mid-heaven) when 'tis under the Pole-star; and this makes our third Column in the Table. The Rule to know when this dif∣ference in time between the Pole and Pole-star is to be added, and when to be substracted, will be evi∣dent by observing, that all such Stars whose Right

Ascensions are above the Right Ascension of the Pole-star (for the year, as for 1680) 9°. 14′. 10″, and un∣der 189°. 14′. 10″. pass the meridian before they come under the Pole-star; all the other semicircle, contrarily; for if the Star pass the meridian before it comes under the Pole-star, this difference in time between the Pole and Pole-star is to be added to the Right Ascension of the Star; if the contrary, 'tis to be substracted.

FINIS.

TABLES OF THE Suns Right Ascension in Time TO EVERY Ten Minutes of the ECLIPTICK.

D. m.	♈ H	♎ H	Com. ′ Pts ″	X
0.0	0	12	0.0
10	0	12	0.37
			″
20	0	12	1.13
			37
30	0	12	1.50
40	0	12	2.27
50	0	12	3.3
1.0	0	12	3.40
10	0	12	4.17
			″
20	0	12	4.53
			37
30	0	12	5.30
40	0	12	6.7
50	0	12	6.43
2.0	0	12	7.20
10	0	12	7.57
			″
20	0	12	8.33
			″
30	0	12	9 10
40	0	12	9 46
50	0	12	10.23
3.0	0	12	11.0
10	0	12	11.37
			11
20	0	12	12.13
			37
30	0	12	12.50
40	0	12	13.26
50	0	12	14.3
4.0	0	0	12	14.40
10	0	12	15.17
			11
20	0	12	15.53
			37
30	0	12	16.30
40	0	12	17.6
50	0	12	17.43
5.0	0	12	18.20
10	0	12	18.57
			11
20	0	12	19.33
			37
30	0	12	20.10
40	0	12	20.46
50	0	12	21.23
6.0	0	12	22.0
10	0	12	22.37
			11
20	0	12	23.13
			37
30	0	12	23.50
40	0	12	24.26
50	0	12	25.3
7.0	0	12	25.41
10	0	12	26.18
			11
20	0	12	26.55
			37
30	0	12	27.32
40	0	12	28.9
50	0	12	28.46
8.0	0	12	29.23
10	0	12	30.0
			11
20	0	12	30.36
			37
30	0	12	31.13
40	0	12	31.50
50	0	12	32.26
9.0	0	12	33.3
10	0	12	33.40
			11
20	0	12	34.16
			37
30	0	12	34.53
40	0	12	35.30
50	0	12	36.7

10.0	0	12	36 44
10	0	12	37.21
				″
20	0	12	37.58
				37
30	0	12	38.35
40	0	12	39 12
50	0	12	39 49
11.0	0	12	40.26
10	0	12	41.••3
				″
20	0	12	41.40
				37
30	0	12	42.17
40	0	12	42.54
50	0	12	43 31
12.0	0	12	44.7
10	0	12	44 44
				″
20	0	12	45.21
				37
30	0	12	45.58
40	0	12	46 35
50	0	12	47.12
13.0	0	12	47.49
10	0	12	48.26
				″
20	0	12	49 03
				37
30	0	12	49 40
40	0	12	50.17
50	0	12	50.54
14.0	0	12	51.31
10	0	12	52.8
				″
20	0	12	52.45
				37
30	0	12	53.22
40	0	12	53.59
50	0	12	54.36
15.0	0	12	55.1••
10	0	12	55.50
				″
20	0	12	56.27
				37
30	0	12	57.••4
40	0	12	57.4••
50	0	12	58.19
16.0	0	12	58.5••
10	0	12	59.3••
				″
20	1	13	00.••0
				37
30	1	13	00.47
40	1	13	1. 24
50	1	13	2.2
17 0	1	13	2.3••
10	1	13	3.16
				″
20	1	13	3.53
				37
30	1	13	4 30
40	1	13	5.7
50	1	13	5.45
18.0	1	13	6.22
10	1	13	6.59
				″
20	1	13	7 37
				37
30	1	13	8.14
40	1	13	8 52
50	1	13	9 29
19.0	1	13	10.6
10	1	13	10.43
				″
20	1	13	11.21
				37
30	1	13	11.58
40	1	13	12.36
50	1	13	13.13

20.0	1	13	13.50
10	1	13	14.27
				″
20	1	13	15.5
				38
30	1	13	15.42
40	1	13	16.20
50	1	13	16.57
21.0	1	13	17.34
10	1	13	18.12
				″
20	1	13	18.50
				38
30	1	13	19.27
40	1	13	20.5
50	1	13	20.43
22.0	1	13	21.19
10	1	13	21.57
				″
20	1	13	22.35
				39
30	1	13	23.12
40	1	13	23.50
50	1	13	24.28
23.0	1	13	25.5
10	1	13	25.42
				″
20	1	13	26.20
				39
30	1	13	26.57
50	1	13	27.35
50	1	13	28.13
24.0	1	13	28.50
10	1	13	29.28
				″
20	1	13	30.6
				39
30	1	13	30.44
40	1	13	31.22
50	1	13	32.0
25.0	1	13	32.37
10	1	13	33.15
				″
20	1	13	33.53
				38
30	1	13	34.31
40	1	13	35.9
50	1	13	35.46
26.0	1	13	36.24
10	1	13	37.2
				″
20	1	13	37.40
				38
30	1	13	38.18
40	1	13	38.56
50	1	13	39.33
27.0	1	13	40.11
10	1	13	40.49
				″
20	1	13	41.27
				38
30	1	13	42.5
40	1	13	42.43
50	1	13	43.21
28.0	1	13	43.59
10	1	13	44.37
				″
20	1	13	45.15
				38
30	1	13	45.53
40	1	13	46.31
50	1	13	47.9
29.0	1	13	47.47
10	1	13	48.25
				″
20	1	13	49.03
				39
30	1	13	50.41
40	1	13	51.19
50	1	13	51.58

D. m.	♉ H	♏ H	Com. ′ Pts. ″
0.0	1	13	51.36
10	1	13	52.14
				″
20	1	13	52.52
				38
30	1	13	53.30
40	1	13	54.8
50	1	13	54.47
1.0	1	13	55.25
10	1	13	56.4
				″
20	1	13	56.42
				38
30	1	13	57.21
40	1	13	57.59
50	1	13	58.38
2.0	1	13	59.15
10	1	13	59.54
				″
20	2	14	0.32
				39
30	2	14	1.11
40	2	14	1.49
50	2	14	2.27
3.0	2	14	3.6
10	2	14	3.45
				″
20	2	14	4.23
				39
30	2	14	5.1
50	2	14	5.39
50	2	14	6.18
4.0	2	14	6.57
10	2	14	7.36
				″
20	2	14	8.15
				39
30	2	14	8.53
40	2	14	9.32
50	2	14	10.11
5.0	2	14	10.49
10	2	14	11.28
				″
20	2	14	12.7
				39
30	2	14	12.46
40	2	14	13.25
50	2	14	14.4
6.0	2	14	14.42
10	2	14	15.21
				″
20	2	14	16.0
				39
30	2	14	16.39
40	2	14	17.18
50	2	14	17.57
7.0	2	14	18.35
10	2	14	19.14
				″
20	2	14	19.53
				39
30	2	14	20.32
40	2	14	21.11
50	2	14	21.50
8.0	2	14	22.29
10	2	14	23.8
				″
20	2	14	23.47
				39
30	2	14	24.26
40	2	14	25.5
50	2	14	25.44
9.0	2	14	26.24
10	2	14	27.3
				″
20	2	14	27.41
				39
30	2	14	28.20
40	2	14	28.59
50	2	14	29.38

10.0	2	14	30.19
10	2	14	30.59
				″
20	2	14	31.38
				39
30	2	14	32.17
40	2	14	33.7
50	2	14	33.46
11.0	2	14	34.15
10	2	14	34.54
				″
20	2	14	35.34
				39
30	2	14	36.13
40	2	14	36.51
50	2	14	37.31
12.0	2	14	38.11
10	2	14	38.51
				″
20	2	14	39.31
				40
30	2	14	40.11
40	2	14	40.51
50	2	14	41.31
13.0	2	14	42.9
10	2	14	42.49
				″
20	2	14	43.29
				40
30	2	14	44.8
40	2	14	44.48
50	2	14	45.27
14.0	2	14	46.7
10	2	14	46.47
				″
20	2	14	47.27
				40
30	2	14	48.6
40	2	14	48.46
50	2	14	49.25
15.0	2	14	50.5
10	2	14	50.45
				″
20	2	14	51.25
				40
30	2	14	52.5
40	2	14	52.45
50	2	14	53.25
16.0	2	14	54.5
10	2	14	54.45
				″
20	2	14	55.25
				40
30	2	14	56.5
40	2	14	56.45
50	2	14	57.25
17.0	2	14	58.5
10	2	14	58.45
				″
20	2	14	59.25
				40
30	3	15	0.5
40	3	15	0.46
50	3	15	1.26
18.0	3	15	2.6
10	3	15	2.46
				″
20	3	15	3.27
				40
30	3	15	4.7
40	3	15	4.47
50	3	15	5.28
19.0	3	15	6.8
10	3	15	6.49
				″
20	3	15	7.29
				40
30	3	15	8.10
40	3	15	8.50
50	3	15	9.30

20.0	3	15	10.10
10	3	15	10.51
				″
20	3	15	11.30
				41
30	3	15	12.11
40	3	15	12.51
50	3	15	13.32
21.0	3	15	14.13
10	3	15	14.53
				″
20	3	15	15.34
				41
30	3	15	16.15
40	3	15	16.55
50	3	15	17.36
22.0	3	15	18.17
10	3	15	18.58
				″
20	3	15	19.39
				41
30	3	15	20.20
40	3	15	21.1
50	3	15	21.41
23.0	3	15	22.22
10	3	15	23.03
				″
20	3	15	23.44
				41
30	3	15	24.25
40	3	15	25.06
50	3	15	25.47
24.0	3	15	26.27
10	3	15	27.08
				″
20	5	15	27.49
				41
30	3	15	28.30
40	3	15	29.11
50	3	15	29.52
25.0	3	15	30.33
10	3	15	31.14
				″
20	3	15	31.55
				41
30	3	15	32.36
40	3	15	33.17
50	3	15	33.58
26.0	3	15	34 40
10	3	15	35.21
				″
20	3	15	36.02
				41
30	3	15	36.44
40	3	15	37 25
50	3	15	38.06
27.0	3	15	38 47
10	3	15	39.29
				″
20	3	15	40.11
				41
30	3	15	40 53
40	3	15	41.34
50	3	15	42.15
28.0	3	15	42.55
10	3	15	43.37
				″
20	3	15	44.19
				41
30	3	15	45 01
40	3	15	45.43
50	3	15	46.21
29.0	3	15	47.4
10	3	15	47.46
				″
20	3	15	48.28
				42
30	3	15	49 10
40	3	15	49.52
50	3	15	50.33

D. m.	♊ H.	♐ H.	Com. ′ Pts. ″
0.0	3	15	51.14
10	3	15	51.56
				″
20	3	15	52.37
				42
30	3	15	53.19
40	3	15	54.••0
50	3	15	54 42
1.0	3	15	55.24
10	3	15	56.••6
				″
20	3	15	56.47
				42
30	3	15	57.29
40	3	15	58.10
50	3	15	58.52
2.0	3	15	59.35
10	4	16	00.17
				″
20	4	16	00.59
				42
30	4	16	01.40
40	4	16	2••.22
50	4	16	3.4
3.0	4	16	3.46
10	4	16	4.28
				″
20	4	16	5.9
				42
30	4	16	5.51
40	4	16	6.33
50	4	16	7.15
4.0	4	16	7.59
10	4	16	8.41
				″
20	4	16	9.23
				42
30	4	16	10.5
40	4	16	10.47
50	4	16	11.29
5.0	4	16	12.11
10	4	16	12.53
				″
20	4	16	13 35
				42
30	4	16	14.17
40	4	16	14 59
50	4	16	15.41
6.0	4	16	16.25
10	4	16	17.7
				″
20	4	16	17.50
				42
30	4	16	18.32
40	4	16	19.15
50	4	16	19.57
7.0	4	16	20.39
10	4	16	21.21
				″
20	4	16	22.4
				43
30	4	16	22.47
40	4	19	23.30
50	4	16	24.12
8.0	4	16	24.54
10	4	16	25.36
				″
20	4	16	26.19
				43
30	4	16	27.1
40	4	16	27.44
50	4	16	28.26
9.0	4	16	29.9
10	4	16	29.51
				″
20	4	16	30.34
				43
30	4	16	31.16
40	4	16	31.59
50	4	16	32.42

10.0	4	16	33.25
10	4	16	34.8
				″
20	4	16	34.51
				43
30	4	16	35.34
40	4	16	36.15
50	4	16	36.58
11.0	4	16	37.41
10	4	16	38.24
				″
20	4	16	39.7
				43
30	4	16	39.49
40	4	16	40.32
50	4	16	41.14
12.0	4	16	41.57
10	4	16	42.40
				″
20	4	16	43.23
				43
30	4	16	44.05
40	4	16	44.48
50	4	16	45.31
13.0	4	16	46.15
10	4	16	46.58
				″
20	4	16	47.41
				43
30	4	16	48.23
40	4	16	49.5
50	4	16	49.48
14.0	4	16	50.32
10	4	16	51.15
				″
20	4	16	51.58
				43
30	4	16	52.41
40	4	16	53.23
50	4	16	54.5
15.0	4	16	54.51
10	4	16	55.34
				″
20	4	16	56.17
				43
30	4	16	57.00
40	4	16	57.43
50	4	16	58.26
16.0	4	16	59.9
10	4	16	59.52
				″
20	5	6	00.35
				43
30	5	6	1.18
40	5	6	2.01
50	5	6	2.44
17.0	5	17	3.28
10	5	17	4.11
				″
20	5	17	4.54
				43
30	5	17	5.37
40	5	17	6.20
50	5	17	7.04
18.0	5	17	7.48
10	5	17	8.31
				″
20	5	17	9.14
				43
30	5	17	9.58
40	5	17	10.41
50	5	17	11.24
19.0	5	17	12.8
10	5	17	12.52
				″
20	5	17	13.35
				43
30	5	17	14.18
40	5	17	15.01
50	5	17	15.44

20.0	5	17	16.28
10	5	17	17.12
				″
20	5	17	17.55
				44
30	5	17	18.39
40	5	17	19.23
50	5	17	20.5
21.0	5	17	20.48
10	5	17	21.32
				″
20	5	17	22 15
				44
30	5	17	22.59
40	5	17	23.42
50	5	17	24.26
22.0	5	17	25.9
10	5	17	25 53
				″
20	5	17	26.37
				44
30	5	17	27.21
40	5	17	28 04
50	5	17	28.47
23.0	5	17	29.30
10	5	17	30.14
				″
20	5	17	30.58
				44
30	5	17	31.41
40	5	17	32.25
50	5	17	33.08
24.0	5	17	33.51
10	5	17	34.35
				″
20	5	17	35.18
				44
30	5	17	36 02
40	5	17	36.46
50	5	17	37.30
25.0	5	17	38.12
10	5	17	38.56
				″
20	5	17	39.39
				44
30	5	17	40.23
40	5	17	41.06
50	5	17	41.50
26.0	5	17	42.33
10	5	17	43.17
				″
20	5	17	44.00
				44
30	5	17	44.44
40	5	17	45.27
50	5	17	46.11
27.0	5	17	46.55
10	5	17	47.39
				″
20	5	17	48.22
				44
30	5	17	49.06
40	5	17	49.49
50	5	17	50.33
28.0	5	17	51.17
10	5	17	52.01
				″
20	5	17	52 44
				44
30	5	17	53.27
40	5	17	54.11
50	5	17	54.54
29.0	5	17	55.38
10	5	17	56.22
				″
20	5	17	57 06
				44
30	5	17	57 49
40	5	17	58.33
50	5	17	59.16

D. m.	♋ H	♑ H	Com. ′ pts. ″
0.0	6	18	0.0
10	6	18	00.44
				″
20	6	18	1.27
				44
30	6	18	2 01
40	6	18	2.44
50	6	18	3.28
1.0	6	18	4.22
10	6	18	5.06
				″
20	6	18	5.50
				44
30	6	18	6.34
40	6	18	7 18
50	6	18	8.02
2.0	6	18	8.43
10	6	18	9.26
				″
20	6	18	10.10
				44
30	6	18	10.54
40	6	18	11.37
50	6	18	12.20
3.0	6	18	13.5
10	6	18	13.49
				″
20	6	18	14.32
				44
30	6	18	15.16
40	6	18	15.59
50	6	18	16.43
4.0	6	18	17.27
10	6	18	18.11
				″
20	6	18	18.54
				44
30	6	18	19 38
40	6	18	20.22
50	6	18	21.05
5.0	6	18	21.48
10	6	18	22.31
				″
20	6	18	23.15
				44
30	6	18	23.59
40	6	18	24.••2
50	6	18	25.25
6.0	6	18	26.••9
10	6	18	26.53
				″
20	6	18	27.37
				44
30	6	11	28.20
40	6	18	29.04
50	6	18	29.47
7.0	6	18	30.30
10	6	18	31.14
				″
20	6	18	31.57
				44
30	6	18	32.41
40	6	18	33.24
50	6	18	34.17
8.0	6	18	34.51
10	6	18	35.34
				″
20	6	18	36.18
				44
30	6	18	37.01
40	6	18	37.45
50	6	18	38.28
9.0	6	18	39.11
10	6	18	39.54
				″
20	6	18	40.48
				44
30	6	18	41.31
40	6	18	42.15
50	6	18	42.58

10.0	6	18	43.32
10	6	18	44.15
				″
20	6	18	44.59
				43
30	6	18	45.42
40	6	18	46.25
50	6	18	47.••9
11.0	6	18	47 52
10	6	18	48.35
				″
20	6	18	49.18
				43
30	6	18	50.2
40	6	18	50.45
50	6	18	51.29
12.0	6	18	52.12
10	6	18	52.55
				″
20	6	18	53.38
				43
30	6	18	54 22
40	6	18	55.5
50	6	18	55.48
13.0	6	18	56.31
10	6	18	57.14
				″
20	6	18	57.57
				43
30	6	18	58.41
40	6	18	59.24
50	7	19	0.7
14.0	7	19	0.50
10	7	19	1.33
				″
20	7	19	2.16
				43
30	7	19	3.••0
40	7	19	3.43
50	7	19	4 26
15.0	7	19	5.••9
10	7	19	5.52
				″
20	7	19	6.35
				43
30	7	19	7.18
40	7	19	8.••1
50	7	19	8.44
16.0	7	19	9.27
10	7	19	10.10
				″
20	7	19	10.53
				43
30	7	19	11.36
40	7	19	12.19
50	7	19	13.2
17.0	7	19	13.45
10	7	19	14.28
				″
20	7	19	15.11
				43
30	7	19	15.54
40	7	19	16.36
50	7	19	17.19
18.0	7	19	18.••2
10	7	19	18.45
				″
20	7	19	19.28
				43
30	7	19	20.11
40	7	19	20 53
50	7	19	21.36
19.0	7	19	22.19
10	7	19	23.2
				″
20	7	19	23.45
				43
30	7	19	24.27
40	7	19	25.10
50	7	19	25.53

20.0	7	19	26.35
10	7	19	27.18
				″
20	7	19	28.0
				43
30	7	19	28.43
40	7	19	29.25
50	7	19	30.8
21.0	7	19	30.51
10	7	19	31.34
				″
20	7	19	32.16
				43
30	7	19	32.59
40	7	19	33.41
50	7	19	34 24
22.0	7	19	35.6
10	7	19	35.49
				″
20	7	19	36.31
				43
30	7	19	37.14
40	7	19	37 56
50	7	19	38 39
23.0	7	19	39.21
10	7	19	40.3
				″
20	7	19	40.46
				42
30	7	19	41 28
40	7	19	42.10
50	7	19	42.52
24.0	7	19	43.35
10	7	19	44.17
				″
20	7	19	45.0
				42
30	7	19	45.42
40	7	19	46.24
50	7	19	47.7
25.0	7	19	47.49
10	7	19	48.31
				″
20	7	19	49.13
				42
30	7	19	49.56
40	7	19	50 38
50	7	19	51.20
26.0	7	19	52.01
10	7	19	52 43
				″
20	7	19	53.25
				42
30	7	19	54.••7
40	7	19	54.50
50	7	19	55.32
27.0	7	19	56.13
10	7	19	56.55
				″
20	7	19	57.37
				42
30	7	19	58.20
40	7	19	59.2
50	7	19	59 43
28.0	8	20	0.25
10	8	20	1.7
				″
20	8	20	1.49
				42
30	8	20	2.30
40	8	20	3.12
50	8	20	3.54
29.0	8	20	4.36
10	8	20	5.18
				″
20	8	20	6.0
				42
30	8	20	6.41
40	8	20	7.23
50	8	20	8.4

D.m.	♌ H	♒ H	Com. ′ Pts. ″
0.0	8	30	8.46
10	8	20	9.28
				″
20	8	20	10.10
				42
30	8	20	10.52
40	8	20	11.34
50	8	20	12.16
1.0	8	20	12.55
10	8	20	13.36
				″
20	8	20	14.17
				41
30	8	20	14.58
40	8	20	15.39
50	8	20	16.20
2.0	8	20	17.4
10	8	20	17.45
				″
20	8	20	18.26
				41
30	8	20	19.07
40	8	20	19.48
50	8	20	20.29
3.0	8	20	21.12
10	8	20	21.53
				″
20	8	20	22.34
				41
30	8	20	23.15
40	8	20	23.56
50	8	20	24.37
4.0	8	20	25.20
10	8	20	16.01
				″
20	8	20	26.42
				41
30	8	20	27.23
40	8	20	28.04
50	8	20	28.45
5.0	8	20	29.27
10	8	20	30 08
				″
20	8	20	30.49
				41
30	8	20	31.30
40	8	20	32.11
50	8	20	32.52
6.0	8	20	33.33
10	8	20	34.14
				″
20	8	20	34.55
				41
30	8	20	35.36
40	8	20	36.17
50	8	20	36.58
7.0	8	20	37.38
10	8	20	38.19
				″
20	8	20	39.00
				41
30	8	20	39.41
40	8	20	40.22
50	8	20	41.03
8.0	8	20	41.42
10	8	20	42.23
				″
20	8	20	43.04
				41
30	8	20	43.45
40	8	20	44.26
50	8	20	45.07
9.0	8	20	45.46
10	8	20	46.26
				″
20	8	20	47.06
				40
30	8	20	47.46
40	8	20	48.26
50	8	20	49.06

D. m.	♌H	♒H	Com. ′ Pts. ″
10.0	8	30	49.50
10	8	20	50.30
				″
20	8	20	51.10
				40
30	8	20	51.50
40	8	20	52.30
50	8	20	53.10
11.0	8	20	53.53
10	8	20	54.33
				″
20	8	20	55.13
				40
30	8	20	55.53
40	8	20	56 33
50	8	20	57.13
12.0	8	20	57.55
10	8	20	58.35
				″
20	8	20	59.15
				40
30	8	20	59.55
40	9	21	00.35
50	9	21	1.15
13.0	9	21	1.55
10	9	21	2.35
				″
20	9	21	3.15
				40
30	9	21	3.55
40	9	21	4.35
50	9	21	5.15
14.0	9	21	5.35
10	9	21	6.35
				″
20	9	21	7.15
				40
30	9	21	7.55
40	9	21	8.35
50	9	21	9.15
15.0	9	21	9.55
10	9	21	10.35
				″
20	9	21	11.15
				40
30	9	21	11.55
40	9	21	12.35
50	9	21	13.15
16.0	9	21	13.53
10	9	21	14.33
				″
20	9	21	15.13
				40
30	9	21	15.53
40	9	21	16.33
50	9	21	17.13
17.0	9	21	17.51
10	9	21	18.31
				″
20	9	21	19.11
				40
30	9	21	19.51
40	9	21	20.31
50	9	21	21.11
18.0	9	21	21.48
10	9	21	22.27
				″
20	9	21	23.06
				39
30	9	21	23 45
40	9	21	24.24
50	9	21	25 03
19.0	9	21	25.45
10	9	21	26.24
				″
20	9	21	27.03
				39
30	9	21	27.42
40	9	21	28.21
50	9	21	29.00

20.0	9	21	29.41
10	9	21	30.20
				″
20	9	21	30.59
				39
30	9	21	31.38
40	9	21	32.17
50	9	21	32.56
21.0	9	21	33.36
10	9	21	34.15
				″
20	9	21	34.54
				39
30	9	21	35.33
40	9	21	36.12
50	9	21	36.51
22.0	9	21	37.30
10	9	21	38.9
				″
20	9	21	38.48
				39
30	9	21	39.27
40	9	21	40.06
50	9	21	40.45
23.0	9	21	41.24
10	9	21	42.03
				″
20	9	21	42.42
				39
30	9	21	43.21
40	9	21	44.00
50	9	21	44.39
24.0	9	21	45.17
10	9	21	45.56
				″
20	9	21	46.35
				39
30	9	21	47.14
40	9	21	47.53
50	9	21	48.32
25.0	9	21	49.11
10	9	21	49 50
				″
20	9	21	50.29
				39
30	9	21	51.08
40	9	21	51.47
50	9	21	52.26
26.0	9	21	53.2
10	9	21	53.41
				″
20	9	21	54.9
				39
30	9	21	54 58
40	9	21	55.36
50	9	21	56.14
27.0	9	21	56 53
10	9	21	57.32
				″
20	9	21	58.10
				39
30	9	21	58.49
40	9	21	59.27
50	10	22	00.06
28.0	10	22	0.44
10	10	22	1.22
				″
20	10	22	2.00
				38
30	10	22	2.39
40	10	22	3.17
50	10	22	3.55
29.0	10	22	4.34
10	10	22	5.12
				″
20	10	22	5.50
				38
30	10	22	6.29
40	10	22	7.08
50	10	22	7.46

D. m.	♍ H	♓ H	Com. ′ Pts. ″
0.0	10	22	8.24
10	10	22	9.02
				″
20	10	22	9.40
				38
30	10	22	10.19
40	10	22	10.57
50	10	22	11.35
1.0	10	22	12.13
10	10	22	12.51
				″
20	10	22	13.29
				38
30	10	22	14.07
40	10	22	14.45
50	10	22	15.23
2.0	10	22	16.1
10	10	22	16.39
				″
20	10	22	17.17
				38
30	10	22	17.55
40	10	22	18.33
50	10	22	19.11
3.0	10	22	19.49
10	10	22	20.27
				″
20	10	22	21.05
				38
30	10	22	21.43
40	10	22	22.21
50	10	22	22.59
4.0	10	22	23.36
10	10	22	24.14
				″
20	10	22	24.52
				38
30	10	22	25.30
40	10	22	26.08
50	10	22	26.46
5.0	10	22	27.23
10	10	22	28.01
				″
20	10	22	28.39
				38
30	10	22	29.16
40	10	22	29.54
50	10	22	30.32
6.0	10	22	31.9
10	10	22	31.46
				″
20	10	22	32.24
				38
30	10	22	33.01
40	10	22	33.39
50	10	22	34.17
7.0	10	22	34.55
10	10	22	35.33
				″
20	10	22	36.10
				38
30	10	22	36.48
40	10	22	37.25
50	10	22	38.03
8.0	10	22	38 40
10	10	22	39.••8
				″
20	10	22	39.56
				38
30	10	22	40 33
40	10	22	41.10
50	10	22	41.48
9.0	10	22	42 25
10	10	22	43.02
				″
20	10	22	43.40
				38
30	10	22	44.17
40	10	22	44.54
50	10	22	45.32

10.0	10	22	46.10
10	10	22	46.47
				″
20	10	22	47.25
				37
30	10	22	48.03
40	10	22	48.40
50	10	22	49.17
11.0	10	22	49.54
10	10	22	50.31
				″
20	10	22	51.09
				37
30	10	22	51.46
40	10	22	52.23
50	10	22	53.01
12.0	10	22	53.38
10	10	22	54.15
				″
20	10	22	54.52
				37
30	10	22	55.29
40	10	22	56.07
50	10	22	56.44
13.0	10	22	57.21
10	10	22	57.58
				″
20	10	22	58.34
				37
30	10	22	59.12
40	10	22	59.49
50	11	23	00.27
14.0	11	23	1.4
10	11	23	1.41
				″
20	11	23	2.18
				37
30	11	23	2.55
40	11	23	3.32
50	11	23	4.09
15.0	11	23	4.47
10	11	23	5.24
				″
20	11	23	6.01
				37
30	11	23	6.39
40	11	23	7.16
50	11	23	7.53
16.0	11	23	8.29
10	11	23	9.06
				″
20	11	23	9.43
				37
30	11	23	10.20
40	11	23	10.57
50	11	23	11.34
17.0	11	23	12.11
10	11	23	12.48
				″
20	11	23	13.25
				37
30	11	23	14.02
40	11	23	14.39
50	11	23	15.16
18.0	11	23	15.53
10	11	23	16.30
				″
20	11	23	17.07
				37
30	11	23	17 44
40	11	23	18.21
50	11	23	18.58
19.0	11	23	19.34
10	11	23	20.11
				″
20	11	23	20 48
				37
30	11	23	21.25
40	11	23	22.02
50	11	23	22 39

20. 0	11	23	23.16
10	11	23	23.53
				″
20	11	23	24.30
				37
30	11	23	25.07
40	11	23	25.44
50	11	23	26.21
21. 0	11	23	26.56
10	11	23	27.33
				″
20	11	23	28.10
				37
30	11	23	28.46
40	11	23	29.23
50	11	23	30.00
22. 0	11	23	30.37
10	11	23	31.14
				″
20	11	23	31.51
				37
30	11	23	32.27
40	11	23	33.04
50	11	23	33.41
23. 0	11	23	34.18
10	11	23	34 55
				″
20	11	23	35.32
				37
30	11	23	36 08
40	11	23	36.45
50	11	23	37.22
24. 0	11	23	37.59
10	11	23	38.36
				″
20	11	23	39.13
				37
30	11	23	39.59
40	11	23	40.36
50	11	23	41.13
25. 0	11	23	41.40
10	11	23	42.17
				″
20	11	23	42.54
				37
30	11	23	43 30
40	11	23	44 07
50	11	23	44 43
26. 0	11	23	45.20
10	11	23	45.57
				″
20	11	23	46.34
				37
30	11	23	47.10
40	11	23	47.47
50	11	23	48.23
27. 0	11	23	49.0
10	11	23	49.37
				″
20	11	23	50.14
				37
30	11	23	50.50
40	11	23	51.27
50	11	23	52.03
28. 0	11	23	52.40
10	11	23	53.17
				″
20	11	23	53.54
				37
30	11	23	54.30
40	11	23	55.06
50	11	23	55.43
29. 0	11	23	56.20
10	11	23	56.57
				″
20	11	23	57 34
				37
30	11	23	58 10
40	11	23	58.46
50	11	23	59.23

A Catalogue of some Noted fix'd Stars, with their Temporary Right Ascensions to the Year 1686. The first Column shews their Magnitudes. The second Bayer's Notes. The third the Numbers in Ticho's Catalogue. The fourth Bayer's Latin Names, and common English Names. The fifth their Tem∣porary Right Ascensions.

Mag	Not. Bay.	Num Cat. Tich	Stars Names.	Rt. Ascens. H. ′ ″
3	ι	21	In Extremitate Boreali Caudae Ceti	00.03.32
			Northern in the Whales Tail
2	β	22	In Extremitate Australi Caudae Ceti	00. 28. 17
			Southern in the Whales Tail
3	κ	16	Praecedens in Eductione Caudae Ceti	00. 54. 13
			Western in the Back of the Whale
3	θ	15	Sequens in Eductione Caudae Ceti	01. 08. 40
			Eastern in the Back of the Whale
3	ζ	14	In medio corpore Ceti trium Septentrionalior	01. 36. 05
			Northern in the Whales Beily
4	γ	1	Prima Stella Arietis	01. 36. 22
			First Star of Aries
4	β	2	In sinistro Cornu Arietis	01. 37. 04
			Second Star of Aries
3	α	19	In Nodo Vinculorum Piscium	01. 45. 49
			Br ⋆ in the Knot of the Fishes Line
3	α	14	Lucidae Arietis	01. 49. 29
			Bright Star of Aries
3	δ	4	Trium in Collo Ceti Australior	02. 23. 43
			In the Whales Cheek
3	ι	10	Laeteris Sequentis Quadrilateri Borea in Pectore Ceti	02. 24. 40
			On the Whales Brest
3	γ	3	Media Trium in Collo Ceti	02. 27. 16
			In the Whales Mouth.

2	α	2	Lucida in Naribus, Menkar, Ceti	02. 45. 50
			Whales Jaw
3	α	32	Lucida Pleiadum Tauri	03. 29. 01
			Brightest of the Pleiades
3	γ	11	In Vultu Tauri illa in Naribus	04. 01. 50
			The lowest of the Hyades
3	ι	15	Ad Oculum Boreum Tauri	04. 10. 08
			North Eye of Taurus
1	α	14	Tauri Oculus Austrinus. Aldebaran	04. 17. 56
			Bulls South Eye
3	β	2	Supra Pedem Orionis in Flumine Erid.	04. 52. 32
			Orions Foot in Eridanus
1	β	35	Pes Dexter Orionis. Rigel	04. 59. 29
			Bright Star in Orions Foot
2	β		Tauri Cornu Septentrionale	05 06. 27
			Bulls North Horn
2	γ	3	In humero Dextro Orionis Duarum Borealior	05. 08. 22
			First or left Shoulder of Orion
2	δ	26	In Baltheo Orionis Fulgentium 3um precedens	05. 15. 55
			First in Orions Belt
3	ζ	19	Extrema Cornu Australis Tauri	05. 18. 50
			Bulls South Horn
2	φ	27	Media Balthei Orionis	05. 20. 08
			The second or middle in Orions Belt
2	ξ	28	Sequens seu tertia Balthei Orionis	05. 24. 30
			Third or last in Orions Belt
1	α	2	Lucida in Humero sinistro Orionis	05. 38. 07
			The latter or right Shoulder of Orion
3	••	15	Calx Castoris	05. 56. 05
			The Heel of Gemini

2	β	9	In Collario Canis Majoris	06. 09. 13
			The fore-foot of the Great Dog
2	γ	17	In summo Pede sinistro sequentis ♊	06. 19. 25
			Bright Star on the Foot of ♊
1	α	1	Syrius seu Canis Major	06. 31. 11
			The Great Dog Star
3	ζ	11	In Dextro Genu Herculis ♊	06. 45. 38
			Left Knee of Gemini
3	γ	4	Ad Aurem Dextram Canis Majoris	07. 11. 00
			On the Neck of Canis Major
1	α	2	Procyon seu Canis Minor	07. 22. 53
			The Little Dog
2	α	12	Cor Hydrae, Alphard	09. 12. 07
			Hydra's Heart
3	κ	7	Trium in Cervice Leonis Australio••	09. 50. 22
			Southern in the Neck of Leo
1	••	8	Lor Leonis	09. 51. 31
			Lions Heart
3	ζ	5	Trium in Cervice Leonis Borealior	09. 59. 06
			Northern in the Neck of Leo
2	γ	6	Trium in Cervice Leonis Media. Juba	10. 02. 27
			Lions Crest
2	δ	20	In Lumbis Leonis Duarum quae Sequitur	10. 57. 21
			In the Loyn of Leo
3	θ	21	In Vertebra Femoris Dextri Leonis	10. 57. 50
			On the Buttock of Leo
1	β	27	Cauda Leonis	11. 32. 58
			Lions Tail
3	ι	23	In Femore Dextro Leonis	11. 07. 44
			On the Thigh of Leo

3	β	5	In Extremo Alae sinistra Virginis	11. 34. 31
			Above the left wing of Virgo
3	γ	7	Sub strophio seu Castula Virginis	12. 25. 43
			On the left wing of Virgo
3	δ	10	Ad Cingulum Virginis	12. 39. 58
			In the Girdle of Virgo
3	ι	13	Alae Dextra ♍ precedens. Vindemiatrix	12. 46. 46
			Virgo's right wing. Vindemiatrix
1	α	14	Spica Virginis	13. 08. 46
			Virgins Spike
3	ζ	15	Sub Perizomate ad pedem dextrum ♏	13. 13. 38
			On the Buttock of Virgo
3	κ	20	In sinistra Tibia Bootis trium Borealior	13. 32. 33
			Most Northern on the left knee of Bootes
1	α	23	Arcturus	14. 01. 24
			Arcturus
3	ζ	19	In Dextra Tibia Bootis	14. 26. 20
			Bend of Bootes right knee
2	α	1	Lanx A••stralis	14. 33. 46
			Southern Ballance
2	β	3	Lanx Borealis	15. 00. 15
			Northern Ballance
3	γ	7	In media lance Boreali Prima & Superior	15. 18. 13
			Middle of the Northern Ballance
2	α	9	Precedens trium in medio neru colli serpentis	15. 28. 54
			Bright Star in the Serpents neck
2	β	1	In fronte ♏ ad Boream prima fulgens	15. 46. 04
			Highest in Scorpio's forehead
3	δ	2	In dextra manu serpentarii Borealior	15. 58. 23
			Northern in the left hand of Serpentarius

3	γ	5	Ad Originem Alae Dextrae Aquilae	19. 31. 38
			Pinion of Aquila's Right Wing
2	α	3	Lucida in Eductione Colli Aquila	19. 35. 51
			Aquila's Bright Star
3	β	2	In Collo Aquilae	19. 39. 57
			Neck of Aquila
3	α	1	Septentrionalis duplex in Cornu Capricorn	20. 00. 50
			Northern in the Horn of Capricorn
3	ι	1	Luoida Cauda Delphini trium Antecedens.	20. 18. 23
			Dolphins Tail
3	β	4	In Humero Dextro Aquarii	21. 14. 58
			Left Shoulder of Aquary
3	γ	23	In Eductione Caudae Capricorni Antecedens	21. 22. 57
			First in the Tail of Capricorn
3	ι	1	In Rictu Pegasi Enif.	21. 28. 44
			Mouth of Pegasus
3	δ	24	In Eductione Caudae Capricorni succedens	21. 30. 07
			Last in the Tail of Capricorn
3	α	2	Humerus sinister Aquarii	21. 49. 43
			Right Shoulder of Aquary
3	γ	9	In Lavo Cubito Aquarii	22. 05. 37
			Right Elbow of Aquary
3	δ	18	In sinistra Tibia Aquarii	22. 38. 15
			Right shin or knee of Aquary
2	β	18	In Eductione Cruris Pegasi. Scheat	22. 48. 43
			Pegasus Thigh
2	α	17	Ala Pegasi. Marchab	22. 49. 05
			Pegasus Wing
2	γ	19	In Exteema Ala Pegasi	23. 57. 03
			End of Pegasus Wing

3	ι	8	Australior in Dextra manu Serpentarii	16. 01. 57
			Southern in the left hand of Serpentarius
3	γ	3	In sinist. Humero Herculis trium Australior	16. 08. 07
			Hercules Right Shoulder
1	α	8	Cor Scorpii	16. 10. 18
			Scorpius Heart
3	β	2	In sinist. Humero Herculis trium Borealior	16. 16. 41
			Northern in Hercules Right Shoulder
3	ζ	19	In Femore Dextro Serpentarii	16. 19. 59
			Serpentarius left knee
3	θ	13	In Femore sinistro Serpentarii 3um Borealior	16. 52. 02
			Right Ham of Serpentarius
3	α	1	Caput Herculis	17. 00. 23
			Hercules Head
3	δ	5	Herculis Humerus Dexter	17. 01. 57
			Left Shoulder of Hercules
2	α	1	Caput Serpentarii	17. 20. 22
			Serpentarius Head
3	β	5	In sinist. Humero Serpentarii 2rum Superior	17. 27. 55
			Northern in Serpentarius right Shoulder
3	γ	3	In eodem duarum Inferior	17. 32. 23
			Southern in Serpentarius Right Shoulder
3	ζ	16	Prima post Serpentarium in Cauda Serpentis	17. 44. 09
			Last but two in the Serpents Tail
3	κ	17	In Penultima Flexione Caudae Serpentis	18. 05. 20
			Last but one in the Serpents Tail
3	θ	18	Extrema Caudae Serpentis	18. 40 37
			Last in the Serpents Tail
3	ι	11	Extrema Caudae Aquilae	18. 51. 06
			Last in the Eagles Tail

TABLES OF AEQUATION OF Natural Days.

A Table of Aequation of Natural Days.

Day	Jan	Dif.	Feb.	X	March	X	Apr.	X	May	X	June	X
	′ ″	″	′ ″	″	′ ″	″	′ ″	″	′ ″	″	′ ″	″
1	8.55		14.54		10.16		0.51		4.12		1.10
		22		1		18		16		2		13
2	9.17		14.53		9.58		0.35		4.14		0.57
		23		2		18		17		2		12
3	9.40		14.51		9.41		0.18		4.16		0.45
		22		3		17		17		1		12
4	10.02		14.48		9.24		0.01		4.17		0.33
		21		3		15		1		14
5	10.23		14.45		9.06		0.14		4.16		0.19
		21		5		17		15		1		12
6	10.44	14.40	8.49	9.29	4.15		0.07
		18		5		17		14		1		13
7	11.02		14.35		8.32		0.43		4.14		0.06
		18		6		18		15		2		13
8	11.20		14.29		8.14		9.58		4.12		0.19
		18		6		19		14		2		13
9	11.38		14.23		7.55		1.12		4.10		0.32
		17		7		18		14		2		12
10	11.55		14.16		7.37		1.26		4.08		0.44
		17		9		19		14		3		13
11	12.12		14.07		7.18		1.40		4.05		0.57
		16		8		20		12		4		13
12	12.28		13.59		6.58		1.52		4.01		1.01
		15		9		19		11		4		13
13	12.43		13.50		6.39		2.03		3.57		1.23
		15		9		19		12		5		13
14	12.58		13.41		6.20		2.15		3.52		1.36
		13		10		19		11		5		14
15	13.11		13.31		6.01		2.26		3.47		1.50
	Add	12	Add	11	Add	19	Substract	11	Substract	5	Add	12
16	13.23	13.20	5.42	2.37	3.42	2.02
		12		11		15		11		7		12
17	13.35		13.09		5.23		2.48		3.35		2.14
		11		12		19		9		7		12
18	13.46		12.57		5.04		2.57		3.28		2.26
		11		12		19		9		7		12
19	13.57		12.45		4.46		3.06		3.21		2.38
		9		14		19		9		8		12
20	14.06		12.31		4.27		3.15		3.13		2.50
		9		14		19		8		9		12
21	14.15		12.17		4.08		3.23		3.04		3.02
		8		13		18		7		8		12
22	14.23		12.04		3.50		3.30		2.56		3.14
		6		14		19		7		9		11
23	14.29		11.56		3.31		3.37		2.47		3.25
		6		13		19		7		10		10
24	14.35		11.37		3.12		3.44		2.37		3.35
		5		15		19		6		9		10
25	14.40		11.22		2.53		3.50		2.28		3.45
		4		16		18		5		10		12
26	14.44		11.06		2.35		3.55		2.18		3.57
		4		16		19		4		11		10
27	14.48		10.50		2.16		3.59		2.07		4.07
		2		16		18		4		11		10
28	14.50		10.34		1.58		4.03		1.56		4.17
		1				17		3		11		8
29	14.51				1.41		4.07		1.45		4.25
		1				17		3	11		8
30	14.52				1.24		4.10			1.34		4.33
		1				17				12
31	14.53				1.07				1.22

Day	July	X	August	X	Sept.	X	Octob.	X	Novemb	X	Decemb	X
	′ ″	″	′ ″	″	′ ″	″	′ ″	″	′ ″	″	′ ″	″
1	4.43		4.36		3.41		13.13		15.28		5.51
		8		9		21		13		8		28
2	4.51		4.27		4.02		13.26		15.20		5.23
		7		9		21		14		9		28
3	4.58		4.18		4.23		13.40		15.11		4.55
		7		12	21		13		10		29
4	5.5		4.06		4.44		13.53		15.01		4.2
		7		11		20		13		10		30
5	5.12		3.55		5.04		14.06		14.51		3.56
		6		11		20		13		12	Substract	29
6	5.18		3.44		5.24		14.19		14.39		3.27
		6		13		21		12	13		29
7	5.24		3.31		5.45		14.31		14.26		3.58
		5		13		20		11		13		30
8	5.29		3.18		6.05		14.42		14.13		2.28
		4		13		21		10		13		30
9	5.33		3.05		6.26		14.52		14.00		2.58
		4		13		20		09		15		30
10	5.37		2.52		6.46		15.01		13.45		1.28
		4	Add	14		21		9		1••		30
11	5.41		2.38		7.07		15.10		13.29		0.58
		3		14		21		8		10		31
12	5.44		2.24		7.28		15.18		13.13		0.28
		2		16		21	8		1••		30
13	5.46		2.08		7.49		15.26		12.56		0.03
		2		16		20		8		18		30
14	5.48		1.52		8.09		15.34		12.38		0.33
		1		16		22		6		19		30
15	5.49		1.36		8.30		15.40		12.19		1.03
Add	••		16	Substract	20	Substract	6	Substract	19		30
16	5.49		1.20		8.50		15.46		12.00		1.33
		0		16		19		5		21		29
17	5.49		1.04		9.09		15.51		11.39		2.02
		1		17		20		4		21		30
18	5.48		0.47		9.29		15.55		11.18		2.32
		1		17		19		3		22		29
19	5.47		0.30		9.48		15.58		10.56		3.01
		2		18		18		2		22		30
20	5.45		0.12		10.6		16.00		10.34		3.31
		2		17		19		2		23		29
21	5.43		0.05		10.25		16.02		10.11		1.00
		3		19		19		1		2••		28
22	5.40		0.24		10.44		16.03		9.47		1.28
		4		19		19		1		24		28
23	5.36		0.43		11.03		1••.04		9.23		4.56
		4		20		17		0		24		27
24	5.3••		1.03		11.20	16.04	8.59	5.23
		4		19		17		2	25		27
25	5.28		1.22		11.37		16.02		8.34		5.50
		6	Substract	19		17		3		26		27
26	5.22		1.41		11.54		15.59		8.08		6.17
		7		19		17	3		27		27
27	5.15		2.00		12.11		15.56		7.41		6.44
		7		20		16		4		26		26
28	5.08		2.20		12.27	15.52		7.15	7.10
		8		20		16		5		27		26
29	5.00		2.40		12.43		15.4••		6.48		7.36
		7	20		16		6		29		24
30	4.53		3.00		12.59		15.41		6.19		8.00
		8		20				7					24
31	4.45		3.20					15.34				8.24

CALCULATION OF Hours and Minutes for an HORIZONTAL-DIAL. DUBLIN Lat. 53°. 20′.

Calculation of Hours and Minutes for an Horizontal Dial: Dublin Lat: 53° 20°.

Time from Noon	Hour dist. on the Plain
h ′	0 ′
XIi.00	00.00
1	0.12
2	0.24
3	0.36
4	0.48
5	1.0
6	1.12
7	1.24
8	1.36
9	1.48
10	2.0
11	2.12
12	2.25
13	2.37
14	2.49
15	3.1
16	3.13
17	3.25
18	3.37
19	3.49
20	4.1
21	4.13
22	4.25
23	4.37
24	4.49
25	5.1
26	5.13
27	5.25
28	5.37
29	5.49
30	6.1
XII.30	6.1
31	6.14
32	6.26
33	6.38
34	6.50
35	7.2
36	7.14
37	7.27
38	7.39
39	7.51
40	8.3
41	8.15
42	8.28
43	8.39
44	8.51
45	9.4
46	9.16
47	9.28
48	9.40
49	9.52
50	10.5
51	10.17
52	10.29
53	10.42
54	10.54
55	11.6
56	11.18
57	11.31
58	11.43
59	11.55
60	12.8
I.00	12.8
1	12.20
2	12.33
3	12.45
4	12.57
5	13.9
6	13.22
7	13.34
8	13.47
9	13.59
10	14.11
11	14.24
12	14.37
13	14.49
14	14.1
15	15.14
16	15.26
17	15.39
18	15.51
19	16.4
20	16.17
21	16.29
22	16.41
23	16.54
24	17.7
25	17.20
26	17.32
27	17.45
28	17.57
29	18.10
30	18.23
I.30	18.23
31	18.35
32	18.48
33	19.1
34	19.14
35	19.27
36	19.39
37	19.52
38	20.4
39	20.17
40	20.30
41	20.43
42	20.56
43	21.9
44	21.22
45	21.35
46	21.48
47	22.1
48	22.14
49	22.27
50	22.40
41	22.53
52	23.6
53	23.19
54	23.32
55	23.45
56	23.58
57	24.11
58	24.24
59	24.38
60	24.51

II.00	24.51
1	25.5
2	25.18
3	25.31
4	25.44
5	25.57
6	26.10
7	26.24
8	26.38
9	26.51
10	27.4
11	27.18
12	27.31
13	27.44
14	27.58
15	28.11
16	28.25
17	28.39
18	28.52
19	29.6
20	29.19
21	29.33
22	29.47
23	30.0
24	30.14
25	30.28
26	30.41
27	30.55
28	31.9
29	31.23
30	31.37
II.30	31.37
31	31.51
32	32.4
33	32.18
34	32.32
35	32.46
36	33.0
37	33.••••
38	33.28
39	33.43
40	33.57
41	34.11
42	34.25
43	34.39
44	34.53
45	35.8
46	35.22
47	35.36
48	35.50
49	36.5
50	36.19
51	36.34
52	36.48
53	37.2
54	37.17
55	37.31
56	37.46
57	38.0
58	38.15
59	38.29
60	38.44
III.00	38.44
1	38.59
2	39.14
3	39.28
4	39.43
5	39.57
6	40.12
7	40.27
8	40.42
9	40.57
10	41.12
11	41.27
12	41.42
13	41.57
14	42.12
15	42.27
16	42.42
17	42.57
18	43.12
19	43.27
20	43.42
21	43.57
22	44.13
23	44.29
24	44.44
25	44.59
26	45.15
27	45.30
28	45.45
29	46.1
30	46.16
III.30	46.16
31	46.32
32	46.47
33	47.3
34	47.19
35	47.35
36	47.50
37	48.5
38	48.21
39	48.37
40	48.53
41	49.9
42	49.25
43	49.40
44	49.56
45	50.12
46	50.28
47	50.44
48	51.0
49	51.16
50	51.33
51	51.49
52	52.5
53	52.21
54	52.37
55	52.54
56	53.10
57	53.26
58	53.43
59	53.59
60	54.15

IIII.00	54.15
1	54.32
2	54.48
3	55.5
4	55.21
5	55.37
6	55.54
7	56.11
8	56.28
9	56.45
10	57.1
11	57.18
12	57.35
13	57.51
14	58.8
15	58.25
16	58.42
17	58.59
18	59.16
19	59.32
20	59.49
21	60.7
22	60.24
23	60.41
24	60.58
25	61.15
26	61.32
27	61.50
28	62.7
29	62.24
30	62.42
IIII.30	62.42
31	62.••••
32	63.••6
33	63.33
34	63.51
35	64.8
36	64.26
37	64.43
38	65.1
39	65.18
40	65.36
41	65.53
42	66.11
43	66.28
44	66.46
45	67.4
46	67.22
47	67.39
48	67.57
49	68.14
50	68.32
51	68.50
52	69.8
53	69.26
54	69.44
55	70.2
56	70.20
57	70.38
58	70.56
59	71.14
60	71.32
V.00	71.32
1	71.50
2	72.8
3	72.26
4	72.44
5	73.2
6	73.20
7	73.38
8	73.56
9	74.14
10	74.33
11	74.51
12	75.9
13	75.28
14	75.46
15	76.4
16	76.23
17	76.41
18	76.59
19	77.17
20	77.36
21	77.55
22	78.13
23	78.31
24	78.50
25	79.8
26	79.27
27	79.45
28	80.4
29	80.22
30	80.40
V.30	80.40
31	80.59
32	81.18
33	81.37
34	81.55
35	82.14
36	82.32
37	82.51
38	83.9
39	83.28
40	83.47
41	84.5
42	84.24
43	84.43
44	85.2
45	85.20
46	85.38
47	85.57
48	86.16
49	86.34
50	86.53
51	87.11
52	87.31
53	87.50
54	88.9
55	88.28
56	88.47
57	89.6
58	89.25
59	89.44
60	90.00

A Table of the most noted Circumpolar-Stars, or those that set not in the Lat. 53°. 20′. for shewing the time of Night by a Line and Plummet, to the year 1680, and serves for 20 years to come.

Mag	Stars Names.	Rt. Ascension in Time under the Pole-star	Diff. in Time betwixt the polestar & pole	Azimuth un∣der the Pole-star	Coast
	H	H ′ ″	H ′ ″	° ′ ″
Ursa Major
2	On his Back	00. 03. 53	0. 04. 26	0. 37. 12	E
3	Penult in Dracos Tail	00. 20. 17	0. 03. 19	0. 19. 12	E
2	Cor Caroli	00. 36. 44	0. 0. 05	0. 00. 54	E
2	His Rump Aliot	00. 39. 25	0. 0. 14	0. 02. 06	W
2	Middle of its Tail	01. 07. 02	0. 03. 44	0. 33. 00	W
2	End of the Tail	01. 28. 56	0. 05. 49	0. 57. 00	W
2	Last but two in Dracos Tail	01. 47. 40	0. 10. 58	1. 16. 48	W
	Ursa Minor
2	Higher Guard	02. 26. 05	0. 24. 10	1. 55. 48	W
3	Lower Guard	02. 57. 15	0. 26. 50	2. 24. 36	W
Draco
3	27 in Ticho's Cat.	02. 59. 49	0. 18. 01	2. 27. 00	W
3	26	03. 35. 17	0. 21. 04	2. 55. 48	W
3	25	03. 54. 54	0. 24. 39	3. 10. 12	W
3	20	03. 58. 34	0. 30. 43	3. 12. 36	W
3	24	04. 36. 43	0. 30. 49	3. 34. 48	W
3	First in the Head	04. 59. 30	0. 23. 42	3. 45. 00	W
2	Bright in the Head	05. 25. 01	0. 24. 11	3. 53. 24	W
1	Lucida Lyrae	06. 05. 34	0. 20. 30	4. 00. 36	W

3	N. in the upper turn	06. 37. 04	0. 35. 44	4. 01. 12	W
3	S. in the upper turn	07. 11. 22	0. 37. 56	3. 56. 24	W
	Cygnus
3	Ʋpper Wing	07. 13. 26	0. 21. 49	3. 56. 24	W
3	Her Brest	07. 51. 26	0. 19. 20	3. 45. 00	W
4	N. Cepheus R. Arm	07. 55. 07	0. 28. 46	3. 44. 00	W
2	Swans Tail	08. 10. 30	0. 19. 59	3. 37. 12	W
	Cephus
4	S. on his R. Arm	08. 11. 32	0. 26. 57	3. 36. 36	W
2	Right shoulder	08. 45. 35	0. 25. 02	3. 18. 36	W
3	His Girdle	08. 53. 30	0. 30. 44	3. 13. 48	W
4	N. in his Cap	09. 41. 52	0. 18. 16	2. 40. 48	W
4	Before his Head	10. 09. 17	0. 15. 56	2. 19. 12	W
4	Left shoulder	10. 20. 44	0. 17. 48	2. 09. 36	W
3	His Knee	11. 10. 00	0. 17. 59	1. 25. 48	W
	Cassiopea
3	Her Chair	11. 46. 07	0. 05. 54	0. 51. 00	W
4	Seat of the Chair	12. 11. 48	0. 03. 14	0. 25. 48	W
4	Head	12. 17. 20	0. 02. 07	0. 20. 24	W
3	Brest	12. 20. 48	0. 01. 50	0. 16. 48	W
4	Girdle	12. 28. 46	0. 00. 59	0. 09. 00	W
3	H••pp	12. 37. 50	0. 00. 02	0. 00. 10	W
3	Knee	13. 08. 45	0. 03. 41	0. 31. 12	E
3	Legg	13. 39. 38	0. 07. 53	1. 01. 12	E
2	Foot of Androm.	13. 50. 37	0. 06. 19	1. 12. 00	E

	Perseus	H ′ ″	H ′ ″	° ′ ″
4	Left shoulder	14. 33. 32	0. 10. 52	1. 51. 36	E
3	Bend of his side	14. 43. 40	0. 11. 03	2. 00. 36	E
3	Right shoulder	14. 55. 31	0. 13. 42	2. 10. 48	E
3	Medusa's Head	14. 59. 14	0. 11. 45	2. 13. 48	E
					E
2	Bright * in his side	15. 14. 59	0. 14. 29	2. 26. 24	E
4	Left Thigh	15. 37. 56	0. 14. 35	2. 44. 24	E
3	Left Knee	15. 51. 39	0. 14. 57	2. 54. 36	E
4	Before his Right Knee	16. 01. 08	0. 18. 05	3. 00. 36	E
4	Middle of his Right Knee	16. 09. 47	0. 18. 06	3. 06. 36	E
	Auriga
4	Left Elbow	16. 58. 15	0. 19. 27	3. 33. 36	E
1	Capella	17. 13. 55	0. 20. 49	3. 40. 48	E
2	Right shoulder	17. 58. 07	0. 21. 55	3. 55. 12	E
	Ursa Major
4	His Lipp	20. 31. 52	0. 27. 38	3. 37. 48	E
3	N. in his Right Foot	20. 50. 49	0. 20. 53	3. 28. 12	E
3	S. in the same	20. 55. 23	0. 20. 13	3. 21. 00	E
3	Left Knee	21. 24. 15	0. 19. 57	3. 07. 12	E
4	Higher in his hind Foot	22. 11. 32	0. 13. 56	2. 30. 36	E
2	Lower Leader in □	22. 54. 50	0. 12. 57	1. 50. 24	E
2	Higher Leader	22. 57. 59	0. 14. 20	1. 47. 24	E
3	Last in Draco's Tail	23. 24. 13	0. 13. 36	1. 20. 24	E
2	Bears Left Thigh	23. 43. 36	0. 06. 38	0. 59. 24	E

FINIS.