A LIGHT to the LONGITUDE: OR The Use of an INSTRUMENT CALLED The SEAMAN'S DIRECTOR.  
SPEEDILY Resolving all Astronomical Cases and Questions Concerning the SUN, MOON, and STARS.  
WITH Several Propositions whereby Seamen may find at what Meridian and Longitude they are at, in all Parts of the WORLD.  
Published for the Advance of NAVIGATION.  
By Robert Theaker.  
LICENCED, June 28. 1665.  
Roger L'Estrange.  
LONDON, Printed by William Godbid for William Fisher at the Postern-Gate near Tower-Hill. 1665.   

The CONTENTS.  

THE Description of the Upper Moving-Sphere or Plain, representing the Celestial Globe. Pag. 3.  
Having the day of the Month known. To find the Sun's Declination, his place, Sign, and Degree in the Ecliptic, and his right Ascension in Degrees and Minutes or in Hours and Minutes. p. 5.  
The Sun's place in the Ecliptic being known, to find the Hour and Minute of the Sun's Rising or Setting any day of the Year. p. 6.  
To find any fixed Stars Declination, right Ascension in Degrees and Minutes, or in Hours and Minutes, his place, Sign, and Degree, or Longitude in the Ecliptic, and day of the Month belonging to that Star. p. 8.  
To find, every day in the Year, when any of the fixed Stars comes to the South. p. 10.  
To find, every day in the Year, when any of the fixed Stars Riseth or Setteth. p. 11.  
To find the Sun's Rising or Setting the same way as you find the Stars Rising or Setting. p. 12.  
To find the Sun's Altitude, every day of the year, when he comes to the Meridian. p. 14.  
To find, every day, how many Degrees the Sun or Stars dippeth or goeth under the Horizon at Midnight; Also to find the Amplitude of the Sun or Stars, every day in the year, at their Rising or Setting. p. 15.  
To find at all times when the North Star is directly South above the Pole, or North under the Pole. p. 17.  
To Draw the Parallels of the Sun or Stars Declinations, and thereby to know when they Rise or Set, or whether they Rise or Set at all. ibid.  
To find, every Day in the year, at what time any of the Planets cometh to the South. p. 18.  
To find the true Distance of the Moon's Motion from the Sun. p. 19  
To find the longitude, by knowing when any of the fixed Stars cometh to the South. p. 20.  
To find exactly the True Meridian and Longitude of the City of London. p. 22.  
The first of April, I demand how the proper and particular Meridian and Longitude of the City of London may be found and discovered, by this Instrument. p. 23.  
To find the true Longitude of the City of London, at the Sun's Setting. p. 24.  
To find the true Longitude of the City of London at the Sun's Rising. p. 25.  
To find the true Longitude of the City of London by the Moon when she cometh to the South. p. 26.  
To find the true Longitude of the City of London by the Moon when she cometh to the South. p. 27.  
Two several Questions by finding the Moon South to know what Meridian you are at. p. 29.  
The first Question. ibid.  
The Rule and reason for turning the upper Sphere is from 360 degrees. p. 31.  
To cut the Orisons for all Latitudes. p. 32.    

To the KING's most excellent Majesty.  
Dread Sovereign,  
THese following endeavours having been brought first of all before Your Sacred Majesty, who did not then despise the day of small things, but out of Your Princely Favour granted Access, and had the patience to hear the Reasons and Objections; Your Heroic Breast being truly inspired and persuaded, that the greatest Mysteries and Matters in the world, were first made known and discovered by plain men, and hid from the Learned; and so to this day the greatest pretended natural knowledges are still overruled by practical Proof-pieces; upon which considerations Your Majesty's faithful Subjects Robert Theaker and Charles Saltonstall, after much expenses of money and time, are now endeavouring to enable all practical Seamen, with the full knowledge of this Instrument; and in regard Charles Saltonstall hath made several long Voyages and Discoveries, instructed and brought up a considerable number of expert Navigators, (many of them being now in your Majesty's Service) it is hoped in time he will also enable them with this knowledge, that their Proof-pieces may give an end to all Objections: In which hope for the present I humbly lay all down at Your Majesty's Feet, beseeching a favourable acceptance of this Mite, which may prove more worth than the offerings of abundance. And so in all obedience I submit myself to Your Majesty's Princely good will and pleasure, desiring the great God of Heaven and Earth to grant Your Majesty a long, prosperous, and happy Reign.  
Your MAJESTY'S most humble and obedient Subject and Servant, Robert Theaker.   

To the READER.  
HAving for many years taken diligent notice of the Diurnal Motions of the Heavens, and how the Sun, Moon, and Stars did daily pass, and appear to be South once in 24 hours, at all the respective Meridian's in the world. I did apprehend that there might be contrived an Instrument which would readily distinguish to all men at what particular Meridian and Longitude they were at in all parts: And so did at last after many alterations and examinations complete this Instrument, now called, A Light to the Longitude; which doth in a plain and facile way speedily Answer all Astronomical Propositions concerning the Sun, Moon, and Stars, only by turning the upper Plain representing the Heavens or Terrestrial Globe, without the knowledge of the doctrine of Spherical Triangles, which many men did never attain to: Also by frequent practice and a little Instruction in using this Instrument, all the Constellations and fixed Stars in the heavens are readily found out and known in all places at any hour of the Night, very helpful to practical Seamen in the Art of Navigation, and being joined with the true nature and way of the turning this Instrument, I suppose they will speedily find at what particular Meridian they are at, which is indeed true Astronomical, Geographical, and Hydrographical Longitude, and is not the measuring of Distances betwixt any two Meridian's by Pendulums, Sand-glasses, Water-glasses, etc. but offereth to find under which of the 360 Meridian's all Islands, Head lands, Main-Lands, Cities and Towns are truly Situated and Placec, against which there hath been much opposition endeavouring to darken and put out this Light to the Longitude: But there was a person (very well known to most Navigators) which stood in the Gap, and defended it from being quite extinguished, whose further Study and endeavours I doubt not but will daily add more and more Light to this matter, until at last practical Seamen gain the honour, and bring home their undeniable Proof-pieces, and put an end to all Objections; And so for present I leave all my endeavours to your favourable Construction, hoping they will prove worthy of your Acceptance, and in time beneficial to all men.  
Your Friend Ro. Theaker.   

IF there be any one that desireth to be more fully instructed in the use of this Instrument, they may repair unto Charles Saltonstall Public Professor and Teacher of the Mathematics, living near the Postern-gate on East-Tower-hill, who will satisfy their desires.   

The full Description of an Instrument lately Invented by Robert Theaker, but now upon his request explained, and the manifold Uses thereof written for the general good, by Charles Saltonstal, Professor and Practitioner of the Mathematic, near the Postern-gate on East-Tower-hill.  
THIS Instrument consisteth of two Plains, the lowermost representeth the Terrestrial Globe, and standeth fixed, and is not to be removed at all, and thereupon is delineated and drawn three distinct hour Circles; the outwardmost Circle is divided into 24 Hours, ending at ♈ Aries, and numbered into the East with 1, 2, 3, 4, etc. until the whole Circle be counted round about to 24 hours ending again at ♈ Aries where it first began. In this hour Circleis reckoned the right Ascension of the Sun or fixed Stars, according to time, or in Hours and Minutes; The next, or second hour Circle I call ♈ Aries hour-Circle, because ♈ Aries stands there betwixt 24 hours in the outward hour-Circle, and 12 hours in the inward or third hour-Circle, and this hour-Circle is numbered from 12. of the Clock at Noon the Meridian of London, into the West, with 1, 2, 3, 4, etc. to 12 of the Clock at Night; and from thence back again with 1, 2, 3 4, etc. to 12. of the Clock at Noon the Meridian of London, where it first began; now in this hour-Circle is reckoned the time of Sunrising or Setting, the hour of any fixed Stars Rising or Setting, and coming to the Forth, as hereafter in the use of this Instrument will more evidently appear; The third hour-Circle beginneth at ♈ Aries with 12 of the Clock the beginning and ending of all Longitude in the Equinoctial, where is also placed 360 degrees, and is numbered into the West with 1, 2, 3, 4, etc. to 12 of the Clock, and from thence back again with 1, 2, 3, 4, etc. to 12 of the Clock where it first began, ♈ Aries; In this Circle is reckoned the difference of time, as hereafter will amply appear; The next and innermost Circle drawn upon this fixed Plain representing the Terrestrial Globe is the Equinoctial beginning and ending at ♈ Aries with 360 degrees, Numbered into the East with 10, 20, 30, etc. until it be counted round about, and then concludeth again with 360 degrees where it first began, the beginning and ending of all Longitude upon the Earth; Then upon this lower fixed plain representing the Terrestrial Globe, there are drawn at every tenth degree from the Equinoctial, strait Lines, all meeting in the Centre, which is here in this Projection counted the Pole of the World; then from that Centre or Pole, at every ten degrees Latitude or Breadth from the Equinoctial, there is drawn a Concentric Circle, which are numbered by Ten from the Equinoctial in this manner, 10, 20, 30, 40, etc. concluding with 90 degrees in the Centre, or Pole, all graduated upon a moving Meridian turning about in the Centre, which is here counted the Pole of the World, by which means the Latitude of all places upon the Terrestrial Globe are readily discovered and made known; Then there are also two small Protractors represented containing the 32 points of the Compass upon this fixed Plain, which may be made of Brass, Horn, or Pasteboard at pleasure, by which means all Courses and Bearings betwixt place and place according to the Terrestrial Globe, thus projected in Plano, wherein you may readily find the Latitude, Longitude, Course, and Distance, betwixt any two places howsoever situated upon the Terrestrial Globe: And by the Application of the upper Moving or Turning Plain representing the Celestial Globe, many excellent Matters, Operations and Conclusions in Astronomy are readily performed, and plainly demonstrated according to the Motions of the Heavens, as will be hereafter amply manifested.  

The Description of the Upper Moving-Sphere or Plain, representing the Celestial Globe.  
IN this Upper Moving Plain or Sphere, upon the outward edge there is drawn the Circle of Months numbered by ten, contrary to the Diurnal Motion, placing always the tenth day of March at ♈ Aries, by which means you may there find any day of the year you desire, and so know the exact time of the Sun or Stars Rising, Setting, and coming to the South, as hereafter will amply appear: The next and innermost Circle described upon that uppermost Moving Plain, or Sphere, is the Equinoctial Circle Numbered by 10 degrees, 20, 30, 40, etc. into the East, until you count round about to ♈ Aries again, and there end and finish with 360 degrees, where you first began, in the same manner as the Equinoctial is numbered and described on the lower fixed Plain; And from this Equinoctial is reckoned the Sun or Stars Declination, upon another moving Meridian called an Index, placed and turned about in the Centre of this upper moving-Plain, as hereafter in use will facilly appear; Then upon this upper Moving Sphere or Plain there is described the Ecliptic Circle, being the pathway of the Sun, and is numbered from ♈ Aries in the Northern Signs with 10 degrees, 20 degrees, and then 30 degrees, and then beginning again from ♉ with 10 degr. 20 degr. & then 30 degr. and so in the same manner numbering again from ♊ Gemini 10 degrees, 20 degrees, and 30 degrees to ♋ Cancer, attributing and allowing to each Sign 30 degrees; and so in the same manner are the Southern Signs numbered, beginning from ♎ Libra with 10 degrees, 20 degrees, and then 30 degrees; and then beginning again from ♏ Scorpio, with 10 degrees, 20 degrees, and then 30 degrees, etc. reckoning still on in the same manner, until you have counted round about and return again to ♈ Aries, where you first began; keeping the same order as you did in the Northern Signs, allowing 30 degrees to each Sign; And on this Moving Plain there is also a smaller Circle described representing the Tropics of ♋ Cancer and ♑ Capricorn touching the Ecliptic in the first minute of ♋ Cancer and ♑ Capricorn; Cancer showing that the Sun's greatest Declination North, is 23 degrees 30 Minutes; and ♑ Capricorn showeth the Sun's greatest declinations South is also 23 degrees and 30 minutes, the Tropics only showing the turnpoints in the Ecliptic, as the word signifies, declaring and setting bounds to the Sun's greatest Declinations North or South, not to exceed 23 degrees, 30 minutes, but must then turn back again. There is also belonging to this moving Plain, representing the Celestial Globe, a Moving Meridian I call an Index, graduated both ways from the Equinoctial, numbered with 10 degrees, 20, 30, 40, etc. concluding with 90 degrees in the Centre or Pole of the World, and the whole graduated Moving Meridian is exactly in length equal to the Diameter of the Equinoctial described on that upper Moving Plain, and the other parts of this Moving Meridian or Index, which are beyond or without the Graduated parts, serveth to cut the Circle of Months, the hour-Circles and Equinoctial described, on the fixed or lower Plain, as the Case shall require. Lastly, there is placed upon this Upper Sphere or Moving Plain, a Turning Horizon in the Centre, being to draw all Pannoles thereupon, and may be fitted for any Latitude required, having two Indices thereunto belonging, the Longer Index to be applied for the Rising or Setting of the Sun, when he is in the Northern Signs: or for the Southing, Rising, and Setting of the Northern Stars, and the shorter Index is to be applied to the Meridian for the Rising, Setting, and Southing the Southern Stars, or for the Sun when the Sun is in the Southern Signs. These are all the parts of this Instrument described on the lower fixed Plain representing the Terrestrial Globe; as also the Moving Upper Sphere, or Plain, representing the Celestial Globe, which being well understood, and rightly applied, will perform many excellent things in Navigation and Astronomy.   

Having the day of the Month known. To find the Sun's Declination, his place Sign, and Degree in the Ecliptic, and his right Ascension in Degrees and Minutes or in Hours and Minutes.  
THese propositions are all readily wrought by this Instrument by the Circles described on the uppermost plain representing the Celestial Globe, and by the outwardmost hour-Circle in the lower plain representing the Terrestrial Globe, between the Equinoctial and the Centre which is the Pole of the World: first than I say, turn the uppermost Sphere, being the Celestial Globe, until ♈ Aries there agree with ♈ Aries in the lowermost Shere representing the Terrestrial Globe, then bring the moving Meridian or Index to the day of the Month wherein you desire to know any of these several propositions, and you will then find that the distance at that time in the upper plain betwixt the Equinoctial & the Ecliptic, reckoned in the moving Meridian or Index, is the Sun's declination; and the point or place cut in the Ecliptic at the same time by the same moving Meridian or Index, showeth the Sign, Degree, and Minute that the Sun is in at that time. And the Degree and Minute then cut in the Equinoctial, by the same moving Meridian or Index, showeth the Sun's right Ascension in Degrees and Minutes, and then in the outwardmost Hour-Circle on the lower plain the same moving Meridian or Index showeth the Sun's right Ascension in time or Hours and Minutes. So the 23d day of February you will find by this Instrument that the Sun hath 6 Degrees South declination, his place and Sign in the Ecliptic 15 Degrees of ♓ Pisces one of the Southern Signs, his right Ascension in Degrees 346 Degrees, whose compliment to a whole Circle is 14 Degrees, the distance from ♈ Aries the next Equinoctial point, and the time of the Sun's right Ascension is in Hours and Minutes 23-4, and the compliment from ♈ Aries in time is 56 Minutes.  
So in the same manner, the 20th day of April, if you desire to know the Sun's Declination, his place, Sign, and Degree in the Ecliptic, his right Ascension, in Degrees and Minutes, as also in Hours and Minutes; fix this Instrument in all respects as before, making ♈ Aries in the upper plain and ♈ Aries in the lower plain to stand right against each other, and then bring the moving Meridian or Index to the 20th day of April, and you will then find the Sun's declination is 15 degrees North, his place in the Ecliptic 10-8 Degrees eight Minute's of ♉ Taurus, his right Ascension in Degrees from Aries; the next Equinoctial point is 38 degrees, which in time is 2-32 Hours thirty two Minutes, as appeareth in the outwardmost hour-Circle in the lower plain, where the moving Meridian cutteth,  
So the 31day of May you will find the Sun's declination 23-10 Degrees and ten Minute's North, his place in the Ecliptic 19-50 nineteen Degrees and 50 minutes of ♊ Gemini, his right Ascension 78 Degrees from ♈ which in time is 5-12 Hours and twelve Minutes, as appeareth in the lowermost outward hour Circle, and so in the same manner all sorts of propositions of the like Nature.  
Note all these five propositions: that is to say, the Sun's declination, the Sun's place, the Degree and Sign, which the Sun is in every day, the Sun's right Ascension in Degrees, the Sun's right Ascension in Hours, and Minutes, are all answered at one operation, only by bringing the moving Meridian or Index to the day of the Month, which is an exceeding great dispatch, and will prove very profitable in Astronomical practices.   

The Sun's place in the Ecliptic being known, to find the Hour and Minute of the Sun's Rising or Setting any day of the Year.  
THe Sun's place being found by this Instrument, as hath been formerly taught; bring the longest Index of the Horizontal plain having nothing but the pannage there on graduated unto 12 a clock in ♈ Aries hour-Circle, the same Index then cutting 20 Degrees of longitude in the lowermost plain, the longitude of the City of London, and there keep that Horizontal Index fast, and then turn the upper moving plain, representing the Celestial Globe, until the place of the Sun in the Ecliptic come exactly to the plain Horizon, at which edge inter●ecting or touch point keep the Ecliptic farst, and then bring the moving Meridian or Index to that intersection, made by the meeting of the Sun in that point in the Horizon, and then at that time in the East Hemisphere in ♈ Aries hour-Circle, you will find the moving Meridian doth there cut the Hour and Minute of Sun rising, and in the West Hemisphere, the other end of the moving Meridian in ♈ Aries hour-Circle doth at the same time show the Hour and Minute of Sun Setting; also at the same time the moving Meridian will show the Sun's declination in the moving Meridian and day of the Month in the Circle of days and Months, whether the Sun be either in any of the Northern Signs or Southern Signs.  
So the Sun being in the first Minute of ♉ Taurus, bring the longest Index of the Horizon to 12 Hours and 20 Degrees in the lowermost fixed plain, and there keep that Index fast; then turn about the upper moving Sphere until the first Minute of ♉ Taurus in the Ecliptic intersect, touch or joineth with the edge of the plain Horizon, and there hold all fast together, and then bring the moving Meridian or Index to that point or intersection in the Horizon, & one end in ♈ Aries hour Circle in the East Hemisphere will show the Sun Riseth then at 5 a clock in the Morning; and the other end at the same time in the West Semicircle of the Sphere in ♈ Aries hour-Circle will show the Sun than Setteth at 7 a clock in the Afternoon. Note when you would know the time of Sun Rising, you must count the hour from 12 in ♈ Aries hour-Circle backwards calling 11one, 10 two, 9 three 8 four, 7 five, 6 six, 5 seven etc. or having the hour of Sun Setting if you subtract that from 12, there will rest the hour of Sun Rising: so if the Sun Riseth at 5 that substracted from 12 resteth 7 a clock for Sun Setting, or if the Sun Setteth at 7 a clock that substracted from 12 resteth 5 hours for the time of Sun Rising. Also now at the same time that end of the moving Meridian or Index which cuts the Sun's place brought to the Horizon in the Circle of days and months, will show that it is now the 10th day of April, and that the Sun hath now 11 Degrees and 35 minute's North declination accounted in the moving Meridian or Index.  
So in the same manner the 20 day of October, the Sun being then in the 7 Degree of ♏ Scorpio, by this Instrument, as hath been formerly taught, you will find the Sun Riseth at 7 a clock 13 minutes passed in the morning and Setteth at 4 a clock 47 minutes passed in the Afternoon: and in the Circle of Months the moving Meridian will show then that it is the 20 day of October, and at the same time on the moving Meridian or Index you will see the Sun hath 14 Degrees South declination; and so in the same manner you may find all these several propositions: the Sun being in any Sign and Degree in the Ecliptic, in all which you may facilly perceive, very great expedition and dispatch, which will prove very useful to all practical Seamen, and such as have occasion to inquire into these Astronomical cases.   

To find any fixed Stars Declination, right Ascension in Degrees and Minutes, or in Hours and Minutes, his place, Sign, and Degree, or Longitude in the Ecliptic, and day of the Month belonging to that Star.  
THese propositions are all readily wrought by this Instrument, by the application of the great Circles, described on the uppermost moving Sphere or plain representing the Terrestrial Globe, and by the moving Meridian or Index thereon placed, with the help of the outwardmost hour-Circle placed on the lower fixed plain representing the Terrestrial Globe; for if you turn the upper plain until ♈ Aries in that plain agree or point directly with ♈ Aries in the lower fixed plain representing the Terrestrial Globe, and there hold it fast, and then bring the moving Meridian or Index to that Star whereof you desire to know the declination, right Ascension in Degrees or Time, his place and Degree or longitude in the Ecliptic, with the day of the Month belonging to that Star, and there also hold that moving Meridian fast; and you will then find in the moving Meridian that the distance betwixt the Equinoctial and the Star is his declination, the Degrees cut in the Equinoctial his right Ascension in Degrees, and the hour cut by the same moving Meridian or Index at the same time in the outwardmost hour-Circle upon the lowermost fixed plain showeth his right Ascension in hours and minutes; also at the same time this moving Meridian or Index doth then cut in the Ecliptic the place, Sign, Degree, and longitude of that Star: and lastly, this moving Meridian doth then show in the Circle of months the day of that month belonging to that Star wherein all these Astronomical effects, cases, and conclusions come to pass.  
So if you desire at any time to know the declination, right Ascension in Degrees and Time, the place, Sign, Degree, and longitude of the fixed Star called Orion's left shoulder: First turn the upper plain until ♈ Aries in that moving plain be right against ♈ Aries in the lower fixed plain, and there keep them together, then bring the moving Meridian or Index unto the Star called Orion's left shoulder, and there also stay and hold fast that moving Meridian, and then you will readily find the distance between that Star and the Equinoctial reckoned in the moving Meridian is 6 Degrees, which is his declination, North; and the same moving Meridian will then at the same time cut 77 Degrees in the Equinoctial, which is his right Ascension in Degrees, and al●o at the same time cutteth in the outward hour Circle on the fixed plain 5 hours and 8 minutes, which is his right Ascension in time; and in the Ecliptic the same moving Meridian at the same time cutteth 18 of ♊ Gemini which is his place or longitude; and lastly, the same Index at the same time in the Circle of Months showeth that it is the 29th day of May, all which by this Instrument is apparently manifested at one and the same time, which is a notable dispatch, and worthy of observation. So again in the same manner, if you desire to find all these Astronomical propositions concerning the Star called the Grea● Dog, move as before the upper plain until ♈ Aries there stand right against ♈ Aries in the lower fixed plain, then bring the moving. Meridian or Index to the Star called the Great Dog, and you find the distance betwixt that Star and the Equinoctial reckoned in the moving Merridian, is 16 Degrees 32 minutes, which is his declination South, and at the same time this moving Meridian in the Equinoctial showeth his right Ascension is 98 Degrees, and in the outward hour-Circle in the fixed plain showeth 6 hours 32 minutes is the Great Dog's right Ascension in time and then lastly cuts in the Ecliptic 7 Degrees of ♋ Cancer which is the Great Dog's place or longitude, and in the Circle of Months 17 day 2 minutes of June, and so of all other Stars whatsoever.   

To find, every day in the Year, when any of the fixed Stars comes to the South.  
FIrst, bring the moving Meridian or Index to 12 hours in the lower fixed plain in ♈ Aries hour-Circle, than the same Index at the same time will also cut 20 Degrees in the Equinoctial, described on the lower fixed plain, which is in this projection accounted the longitude of the City of London, and there keeping the moving Meridian fast, turn the upper plain representing the Celestial Globe until the moving Meridian also cut the Star which you desire to know at what time it comes to be South, and there keep the Star fast, and then turn the moving Index or Meridian to the day of any Month, and in ♈ Aries hour-Circle the same moving Meridian will show the hour when that Star cometh to the South.  
So the Star called the Great Dog being brought to stand right against 12 hours and 20 Degrees in the lower fixed plain, and there kept fast, and then if you turn the moving Index or Meridian to the first day of January, the same Index will then show in ♈ Aries hour-Circle 11 a clock at night at which hour the Star called the Great Dog cometh to the South; and if you then keep the Instrument unaltred, and turn the same moving Meridian to the first day of November, the Index then in ♈ Aries hour-Circle will show 3 a clock 24 minutes in the morning, which is the time when the Great Dog cometh to the South: and on the first day of December the Index showeth 1 a clock 16 minutes in the morning for the hour when the Great Dog cometh to the South.  
So in the same manner, if you would know when the Star called Orion's left shoulder cometh to the South, that Star brought to 12 hours and 20 Degrees in the lowermost fixed plain, the longitude of London as before, the moving Meridian brought to the first day of January will show 9 a clock 37 minutes passed in the afternoon, and then the Star called Orion's left shoulder cometh to the South.   

To find, every day in the Year, when any of the fixed Stars Riseth or Setteth.  
HEre in this case, if it be a Star that hath North declination, bring the longest Index of the moving Horizon, to 12 a clock in ♈ Aries hour-Circle, which will then also cut the fixed Equinoctial 20 Degrees, the longitude of the City of London according to this projection: but if it be a Star that hath South declination then bring the shortest Index of the moving Horizon, to 12 a clock in ♈ Aries hour-Circle and 20 Degrees in the lowerm  fixed Equinoctial as before, and there keep the Horizontal Index fastand turn the upper moving Sphere, or plain representing the Celestial Globe, until the Star, the time of whose Rising you desire to know come exactly to touch the Circular edge of the moving Horizon in the East Semicircle of the moving Sphere; or if you desire to know the time of the Stars setting, turn the whole moving Sphere or plain until the Star come to the Circular edge of the moving Horizon in the West Semicircle of the moving Sphere; I call the East Semicircle that which is contained betwixt ♈ Aries and ♎ Libra, the Ecliptic having thereon placed the six Northern Signs viz. ♈ Aries, ♉ Taurus, ♊ Gemini, ♋ Cancer, ♌ Leo, ♍ Virgo, and in the Circle of months, April, May, June, July, August, September; and the other Semicircle betwixt ♈ Aries and ♎ Libra contain the Southern Signs and the Circle of months, March, February, January, December, November, I call the West Semicircle: and in the East Semicircle I always contain the Sun or Stars Rising, and in the West the Sun or Stars Setting: now the Star thus stated keep all, turn the moving Index or Meridian to the day in the Circle of month wherein you desire to know the time of that Stars Rising or setting, and the same Index at the same time will show in ♈ Aries hour-Circle, the time of that Stars Rising, if the Star touch the Horrizontal edge in the East Semicircle, or in ♈ Aries hour-Circle, will show the time of the Stars Setting if the Star touch the edge of the moving Horizon in the West Semicircle of the Spheer.  
So the Star called the Great Dog, if you desire to know the time of his Rising the 10 day of March, (being the Star's declination is South) bring the shortest Index of the moving Horizon to 12 of the Clock in ♈ Aries hour Circle, and to 20 degrees in the lower fixed Equinoctial; then keeping that Index there fast, turn the whole moving Sphere or Plain until the Star called the Great Dog come exactly to the edge of the Horizon in the East Semicircle, and then the moving Index or Meridian brought to the 10 day of March, will show in ♈ Aries hour-Circle, that the Great Dog riseth at 1 of the Clock, 52 minutes in the Afternoon, and sets at a 11 of the Clock and 8 minutes in the Afternoon, when the Star is at the edge of the Moving Horizon, in the West Semicircle.  
And after the same manner, if you desire to know when the Star called Orion's left shoulder riseth or setteth the 10. day of March; now because the Star hath North declination, keep the longest Index of the moving Horizon on 12 of the Clock in ♈ Aries hour Circle, and 20 degrees in the lower fixed Equinoctial as before, then turn the upper Sphere or moving Plain until the Star, called Orion's left shoulder, come to the edge of the Horizon in the East Semicircle, and there keeping all fast, bring the moving Meridian to the 10 day of March, and the same Index in Aries hour Circle will show that Orion's left shoulder riseth at 10 of the Clock and 40 minutes in the morning; and if the same Star be brought to the edge of the moving Horizon, in the West Semicircle, and then the moving Meridian brought to the 10. of March, the same Index will show in ♈ Aries hour-Circle that the Orion's left shoulder sets at 11 of the Clock and 40 minutes in the Afternoon: and so of all others.   

To find the Sun's Rising or Setting the same way as you find the Stars Rising or Setting.  
FOrmerly it hath been showed, that when the Index of the Horizon was placed upon the Meridian of London, at 12 hours and 20 degrees Longitude in the lower fixed Plain, and there kept fast, than the place of the Sun brought to the Horizon, and the moving Meridian to the day of the Month desired, one end of that Index in the East Semicircle would then show the time of Sun Rising, and the other the time of Sun Setting, but the Rising and Setting of the fixed Stars could not be so found; for after the Index of the Horizon was kept at the Meridian and Longitude of London, than the same Star was brought first to touch the East part of the Horizon, and then according to the day proposed, the moving Meridian did in ♈ Aries hour-Circle show the time of that Star's Rising, and then the same Star brought again to touch the West part of the Horizon, and the moving Meridian turned to the same day in ♈ Aries hour-Circle shown the time of that Star's Setting; So in the same manner, if you please, you may employ the place of the Sun to the East part of the Horizon for his Rising, and the West part for his Setting; and the moving Meridian brought to the proposed day, when the Sun is at the East part of the Horizon, will in ♈ Aries hour-Circle show the time of Sun Rising; and on the same day, when the Sun cometh to the West part of the Horizon, the same moving Meridian in ♈ Aries hour-Circle will show the time of Sun Setting: Provided always if the Sun be in any of the Northern Signs, and so hath North declination, than you must bring the longest Index of the Horizon to 12 hours and 20 degrees in the fixed Plain, the Longitude of London, and then proceed as before hath been taught: But if the Sun be in the Southern Signs, and so hath South declination, then bring the shortest Index of the Horizon to 12 Hours and 20 degrees, in the lower fixed Plain, the Meridian and Longitude of London, and then proceed to find the Rising and Setting of the Sun upon the day proposed.  
So the 20 day of April, the Sun's place being 10 degrees 12 Minutes of ♉ Taurus; now because ♉ Taurus is one of the Northern Signs, and so the Sun hath North declination, bring the longest Index of the moving Horizon to 12 hours 20 degrees in the lower fixed Plain, the Meridian of London, then bring the Sun's place in the Ecliptic first to the East part of the Horizon, and so keep all fast, and then turn the moving Meridian to the 20 day of April, and it will then show in ♈ Aries hour-Circle that the Sun Riseth at 4 of the Clock 41 Minutes passed in the morning, & Setteth at 7 of the Clock 41 minutes passed in the Afternoon; Or if you desire to know the 20 day of October, at what time the Sun Riseth or Setteth. Now again, because the Sun's place is 7 degrees of ♏ Scorpio, one of the Southern Signs, and so hath South declination, bring the shortest Index of the moving Horizon to 12 of the Clock and 20 degrees in the lower fixed Plain, and there keep it fast; and then turn the upper moving Plain, until the Sun's place 7 degrees of ♏ Scorpio come to the East part of the Horizon, and then the moving Index brought to the 20 day of October, will show the Sun than Riseth at 7 of the Clock 13 minutes passed in the morning, and sets at 4 of the Clock 47 minutes passed in the Afternoon; which is a much better way then to count one end of the Morning Index to cut the Hour of Sun setting, and the other end counted back from 12 in Aries hour Circle for the time of Sun Rising, as hath been formerly taught; Also by this means the whole moving upper Plain representing the celestial Globe, being turned about in this Diurnal Motion upon any day required, will show the time of the Sun's Rising or Setting, and all the Stars Rising, Setting, and coming to the South in order, from whence in Astronomy, many beneficial conclusions may be readily drawn; Seeing this Instrument is so exact, and maketh such extraordinary dispatch answering many varieties all at once, which by proportion and the doctrine of Spherical Triangles, will require longer time, notwithstanding the help of the Logarithmes and Natural Signs provided in our days.   

To find the Sun's Altitude every day of the year when he comes to the Meridian.  
THIS proposition is very useful for all Seamen readily to set the shadow vein in observation at Sea to find the Latitude; First then, if you turn the moving Meridian and shorter Index of the Horizon both together, to ♈ Aries in the moving Plain, the edge of the Horizon will then cut the moving Meridian in 38 degrees and 30 minutes, the height of the Sun upon the Meridian the 10 day of March in the Latitude of 51 degrees and 30 minutes, and is also the height of the Equinoctial in that Latitude for ever; Therefore at any time, if you add the Sun's declination when it is North, or subtract it when it is South from 38 degrees and 30 minutes, the height of the Equinoctial, it will show the height of the Sun that day upon his Meridian; so the 20 day of April the Sun's Declination is 15 degrees North, which added to the 38 degrees 30 minutes, showeth the Altitude of the Sun that day upon the Meridian is 53 degrees 30 minutes; and the 18 of October the Sun hath 13 degrees 30 minutes South declination, which substracted from 38 degrees 30 minutes, resteth 25 degree, which is the height of the Sun that day upon his Meridian here in the North Latitude of 51 degrees 30 minutes; and so of all others.   

To find every day how many Degrees the Sun or Stars dippeth or goeth under the Horizon at Midnight; Also to find the Amplitude of the Sun or Stars every day in the year at their Rising or Setting.  
TO find the Sun's Amplitude at his rising or setting by this Instrument; there must also be provided a straight Ruler, to be employed as occasion shall require: First then, when you desire to know the Sun's Amplitude, you must grant the Diameter betwixt ♈ Aries and ♎ Libra to represent the prime vertical Circle, or Circle of the East and West, and the Quadrant from ♈ Aries to 90 degrees, reckoned in the Equinoctial, the Quadrant of Latitudes and the Diameter, betwixt 90 degrees, and 270 degrees, the Horizon Circle; then having the Latitude of any place, and declination of the Sun, bring the moving Meridian to the Latitude, and there keep it fast, then with a pair of Compasses take the declination out of the Equinoctial being one of the great Circles, and join it to the point of Latitude, in the Quadrant of Latitudes towards ♈ Aries, and then lay a straight Ruler from that point parallel to the moving Meridian, which is held fast at the point of Latitude, and then observe where the Ruler cuts or crosseth the Diameter now representing the Horizon; and then also observe under the Horizon where that straight Ruler cutteh the Equinoctial, and so many degrees doth the Sun or Star dip or go under the Horizon or Midnight; then from the same point in the Horizon, turn or lay the straight Ruler parallel to the prime vertical, and then in the Equinoctial, being one of the great Circles, it will cut the true Amplitude of the Sun or Stars, which is always the distance contained betwixt ♈ Aries and that point so cut.  
So in the North Latitude of 51 degrees 30 minutes, the greatest Declination of the Sun being 23 degrees, 30 minutes, if you bring the moving Index to 51 degrees 30 minutes in the Quadrant of Latitude, and thereunto join the Declination 23 degrees and 30 minutes, and then from that point lay a straight Ruler parallel to the moving Meridian or Index, it will cut under the Horizon in the Equinoctial 15 degrees, and so much goeth the Sun then under the Horizon at Midnight; also at the same time note the place or point cut in the Horizon by the same straight Ruler, and then turn or lay the Ruler from that point in the Horizon parallel to the prime vertical, and where it cutteth the Equinoctial, the distance betwixt ♈ Aries and that point is the Amplitude, which here at this time appeareth to be 39 degrees and 50 minutes, being the greatest Amplitude the Sun can possibly have here at London in the North Latitude of 51 degrees 30 minutes; And so in the same manner you may find the Amplitude of any of the fixed Stars at their rising or setting.  
Note, If the Sun hath North declination, it is called North Amplitude; and if it hath South declination, it is called South Amplitude, and the greater Latitude the greater Amplitude; and so of the fixed Stars.  
Note also, Until the Sun be 18 degrees under the Horizon it is the Crepusculum or Twilight; therefore here at London when the Sun hath 23 degrees 30 minutes North declination, the Sun dippeth but 15 degrees under the Horizon; Therefore here at London at that time, it is not perfect Night at all, but the Twilight continueth.   

To find at all Altines when the North Star is directly South above the Pole, or North under the Pole.  
TO know at what hour, every Day and Night, the North Star is directly North or South, above or under the Pole; bring the moving Meridian to 12 of the Clock in ♈ Aries hour-Circle and 20 degrees, the Longitude of London, then turn the upper Plain, until the Star called Aliot, being a Star in the Great Bear's Rump, or the hindmost of the 3 in Charles his Wain, unto that Index on the North or Southside, and then if that Star be on the South side, the North Star is then 2 degrees 30 minutes under the Pole, and if Aliot be on the Northside, the North Star is then 2 degrees 30 minutes above the Pole.  
So the 22 day of March, Aliot is South at 12 of the Clock at Night, and so the North Star is then 2 degrees 30 minutes under the Pole; and the 4 day of February, Aliot is South at 5 of the Clock in the morning, and so the North Star is then also 2 degrees 30 minutes under the Pole: And the 9 day of September, Aliot is North at 12 of the Clock at Night, and the North Star is then 2 degrees 30 minutes above the Pole; And the 25 day of October, Aliot is North at 9 of the Clock at Night, and then the North Star is 2 degrees 30 minutes above the Pole.   

To Draw the Parallels of the Sun or Stars Declinations, and thereby to know when they Rise or Set, or whether they Rise or Set at all.  
TO draw the parallels of Declination; First, set one Foot of the Compasses in the Pole or Centre of the moving Meridian, and then extend the other foot to 5 degrees, 10, 15, 20, 25, 30, etc. in the same moving Meridian, according as the Declination may require; then with the same extent so taken out of the moving Meridian, set one foot in the Centre of the moving Horizon, and from the Diameter sweep an arch of a Circle both ways to cut the outward edge of that plain Horizon, with points or Cross in the edge of the Horizon, are the direct places where those Stars come unto at their rising or setting; Note, if any Star here in the Latitude of 51 degrees 30 minutes, hath his Declination North equal or more than the Compliment of the Latitude, that Star (I say) sets not at all, for then the Compasses in the plain Horizon will sweep an Arch of a Circle within the plain Horizon, and will not reach the outward edge, therefore that Star sets not at all; And so if any Star hath South declination equal or greater than the Compliment of the Latitude, that Star riseth not at all in our Horizon, and so of all others.   

To find, every Day in the year, at what time any of the Planets cometh to the South.  
FIrst, bring the moving Meridian to 12 of the Clock and 20 degrees, the Longitude of London, and there keep it fast, and then find the Sign and Degree that the Planet is in at that time, and then turn the whole upper Plain until that Sign and degree come to the moving Meridian placed at 12 of the Clock 20 degrees, and there keep them both fast together, and then look in the Circle of Months for the Day you desire to know the time of that Planets coming to the South, and right against that day in ♈ Aries hour-Circle, you will see at what of the Clock that Planet comes to the South.  
So ♄ Saturn's place or Longitude in the Ecliptic the 15 day of March, being 8 degrees 56 minutes of ♑ Capricorn, if you turn the whole upper moving Sphere until that Sign and degree in the Ecliptic come to the Meridian placed at 12 of the Clock 20 degrees, and there hold them both fast together, and then right against the 15 day ♈ Aries hour-Circle, it will appear that ♄ Saturn cometh to the South at 6 of the Clock 20 minutes in the morning; and ♃ Jupiter's place or Longitude in the Ecliptic the 15 day of March, being 14 degrees 3 minutes, in ♒ Aquarius cometh to the South at 8 of the Clock 46 Minutes passed in the Morning; and the same day Mars being in 3 degrees 4 minutes of ♓ Pisces, cometh to the South at 10 of the Clock in the morning; and ♀ Venus the same day being in 18 degrees 50 minutes of ♉ Taurus, cometh to the South at 2 of the Clock 46 minutes in the Afternoon; and ☿ Mercury being then in 8 degrees 46 minutes of ♒ Aquarius, cometh to the South at 8 of the Clock 46 minutes passed in the Morning: and the same day ☽ Luna being in 19 degrees 22 minutes of ♋ Cancer, cometh to the South at 7 of the Clock 21 minutes passed in the Afternoon, allowing 2 minutes in the Ecliptic for each hour to be added to the place of the Moon, so here was added 14 minutes; Note, if the day whereon you desire to know when the Star cometh to the South be in the East Semicircle, they are Morning hours; or if they be in the West Semicircle, they are Afternoon hours.   

To find the true Distance of the Moon's Motion from the Sun.  
FIrst, by the Ephemerideses find the Moon's place in the Ecliptic, then bring the moving Meridian to 12 hours and 20 degrees, the Longitude of London, and then bring the Moon's place in the Ecliptic also to that Meridian; and there hold them both fast together, and then in the Circle of Months find the day you desire to know, at what hour the Moon cometh to the Meridian, and right against that day you will find the hour of the Moon's then coming to the South.  
So the 17 day of March, the Moon being in 18 degrees of ♌ Leo, being the moving Meridian to 12 hours and 20 degrees, the Meridian and Longitude of London, then turn the whole upper Sphere until the Moon's place in the Ecliptic also come to that Meridian, and there keep them both fast together, and then in the Circle of Months you will find right against the 17 day of March 9 hours 13 minutes in the Afternoon, which is the time of the Moon's coming to the South that day, always in work remembering when you have found 9 hours to allow two Minutes for each hour, which here is 18 Minutes, which 18 minutes in the Ecliptic, at the Rate of 4 minutes for a degree, is 4 degrees ● and that joined to 18 degrees of ♌ Leo the Moon's place maketh 22½ degrees, which is the true place that the Moon is then in; which brought to the Index placed at 12 hours and 20 degrees as before, and there kept fast right against the 17 day of March will appear 9 of the Clock 13 minutes passed in the afternoon, which is now the direct true time of the Moon's coming to the South.  
Note, On the lower fixed plain in this Instrument, are placed 3 hour-Circles, the outwardmost with 24 hours at ♈ Aries is to measure the right Ascension in time; the middle hour-Circle, which I call ♈ Aries hour-Circle beginning at 12 a Clock and 20 degrees longitude, is proper for the Meridian of London, to measure the hour of the day or night; the third, next the Equinoctial, is to measure time from the general or first Astronomical Meridian according to the distance betwixt the Sun or Stars.   

To find the longitude, by knowing when any of the fixed Stars cometh to the South.  
FIrst, you must observe, that by this projection in the lower fixed plain representing the Terrestrial Globe, at one single certain point take in the Equinoctial, there is set and placed 360 degrees with 12 of the Clock at noon in the next hour-Circle, and ♈ Aries in the second hour-Circle, and 24 hours in the outward hour-Circle, and this Meridian thus stated is the first Meridian of the World, and declareth the beginning and ending of all longitude; which formerly by Geographers hath been placed at several parts of the World, some assigning it to pass through St. Michael's Island, one of the Azores, others will have it to pass through Tenaref one of the Canary Islands, and some again will have it pass by or through, the Westermost parts of Africa; all as yet grounding themselves, from courses, distances, departures, differences of latitude and longitude, found by expert skilful practical Navigators according to their Sea observations and reckon; for I suppose there have been as yet but few Eclipses observed to contradict the expert Navigators endeavours, who indeed deserve the honour and thanks for the originals which built that demonstrative Figure and Type called the Terrestrial Globe, and I suppose will in the future gain the like honour in this great matter, by practical proof confirming a true Meridian and Longitude properly and peculiarly belonging to each particular part and place upon the Terrestrial Globe, being the most competent Judges grounding their knowledge upon their great Attempts and remote Discoveries, which others, not versed in those things, must come far short off. Now Astronomically we say 360 degrees must be accounted for the beginning and ending of all Longitude, but we cannot place that Meridian upon the earth at pleasure, for that is absurd and improper; but Astronomically, by knowing the time of any of the fixed Stars coming to the South, and the place or Longitude of the Sun in the Ecliptic that day, the distance then indeed betwixt the Sun and Star reckoned in the Equinoctial, showeth both their respective right Ascensions and also the Longitude in degrees or time contained betwixt them, by which means this Instrument will readily show the true Meridian and Longitude in all places upon the Terrestrial Globe, provided it be granted, that at every minute of Time in one place or other, the Sun and Stars are always Rising, Setting, and coming to the Meridian (which is not to be denied) than I say, each particular Meridian and Longitude, upon the Terrestrial Globe, may undoubtedly be clearly discovered: For if it were inquired at what Meridian and Longitude the City of London was truly seated, if we should search the Terrestrial Globes they would show us several Longitude, according to the several places, where they appointed the first Meridian to begin and end all Longitude, and so in effect will show us just nothing; for indeed there is but one single proper Meridian belonging to the City of London, or any other place whatsoever, which may as surely be pointed out and shown which is it in particular by this Instrument, as any Astronomical Calculator can tell you the very Day, Hour, & Minute of the Stars coming to the South, which many will affirm they can infallibly perform, and several Authors have already drawn out Tables to that purpose, some of which I can testify are exceeding well, true, and perfectly done and performed; but I have not observed that any of them, hath truly stated and discovered the Meridian properly belonging to the particular Longitude of London, or pointed out which or where it is; I suppose the reason hath been, because they found the Longitude of places upon the earth were variously affirmed, and therefore they meddled with none of them.   

To find exactly the True Meridian and Longitude of the City of London.  
FIrst, by this Instrument to find the true Longitude of London, you must consider the day of what month you will employ for this service, which day I then call the day of the Sun; then always bring the day of the Sun to 360 degrees, the beginning and ending of all Longitude, then take notice of any of the fixed Stars placed upon the upper moving Plain in this Instrument, and bring the moving Index to cut that Star, and in the outward hour-Circle you will find the hour and minute of that Stars coming to the South, when the day of the Sun standeth at 360 degrees in the Equinoctial, which on the same day of the Sun will show one and the same hour and minute, for the Stars being South in all the particular Longituds of the World; and so that hour, common to all Longituds, cannot distinguish the particular Meridian of any of them, but this Instrument from that ground will show each proper and particular Meridian and Longitude of all places upon the Terrestrial Globe which cannot be removed or altered; for, if you count in the lower hour-Circle placed next the Equinoctial, 1 hour, 2 hours, 3 hours, 4 hours &c. according to the diurnal motion, until you bring the day of the Sun to such an hour as right against it will stand the hour and minute in ♈ Aries hour-Circle, answerable and equal to the hour first found in the outward Circle containing 24 hours a Natural day, at which time the day of the Sun was first brought to 360 degrees in the Equinoctial, and so the hour of the Star was that day one and the same in all Longitudes: but now (I say) if the day of the Sun be turned to so many hours and minutes in the lower hour-Circle that then against the same day of the Sun in ♈ Aries hour-Circle there appear the hours and minutes equal to the hours and minutes first found in the outward Circle of 24 hours, I say, the Star proposed will then stand right against the proper and particular Meridian and Longitude of the place desired, and cannot possibly be removed or constrained to stand against any other Meridian or Longitude, but that which properly and particularly belongeth to that one single part, point, or place upon the Terrestrial Globe.  

Example. The first of April, I demand how the proper and particular Meridian and Longitude of the City of London may be found and discovered, by this Instrument.  
BRing the first day of April to 360 degrees, which I now call the day of the Sun, then find on the upper plain or Sphere the fixed Star called the Lion's Tail, and thereon place the moving Meridian or Index, and then in the outward hour-Circle it will show that Star cometh to the South at 10 a clock 13 minutes in the afternoon, which is the common hour for all Meridian's in the World for that day; therefore now turn about the upper moving Plain or Sphere until the first day of April the day of the Sun come to 8 hours 52 minutes in the lowermost hour-Circle, and then right against the same hour and day of the Sun in ♈ Aries hour-Circle you will then find 10 a Clock 13 minutes at night equal to the hour first found in the outward hour-Circle, and so the Star called the Lion's Tail will now stand exactly against 20 degrees in the Equinoctial, placed upon the fixed plain at 10 a Clock 13 minutes at night, which is the proper and particular Meridian and Longitude of the City of London, which cannot possibly be removed, changed, or altered, and was never truly found or thus stated by any Man before.  
So in like manner, if you will the same first day of April employ the fixed Star called Hidra's Heart, to find the true Meridian and Longitude of London, bring again the first day of April the day of the Sun as before to 360 degrees, and then place the moving Meridian upon that Star, and in the outward hour-Circle it will show 7 a Clock 52 minutes; therefore now turn the day of the Sun to 6 hours 32 minutes in the lowermost hour-Circle, and then right against that in ♈ Aries hour-Circle you will find again 7 a Clock 52 minutes, and then you will find Hidra's Heart, will stand again directly right against 20 degrees, the proper Meridian and Longitude of London as before at 7 a Clock and 52 minutes.  
So in like manner if you will the same first day of April employ the Star called Virgin Spick bring the day of the Sun to 360 degrees and place the moving Meridian upon the Star, which will then in the outward hour Circle show 11 a Clock 48 minutes, therefore now turn the day of the Sun to 10 hours 28 minutes, and at the same time right against that, in ♈ Aries hour-Circle, you will find 11 a Clock 48 minutes at night, and then the Virgin Spike will stand right against 20 degrees, the true Meridian and Longitude of London as before, and so in the same manner you may employ any of the fixed Stars which you think convenient, and they will all affirm the true, proper, and particular Meridian and Longitude of London is directly 20 degrees, which cannot be removed, altered, or contradicted by any Man; and so being at any place or point upon the Terrestrial Globe, by this Instrument, and the same Rule, you may find the proper and particular Meridian and Longitude of that place, which cannot be removed, altered, or denied by any one.   

To find the true Longitude of the City of London, at the Sun's Setting. Example.  
SUppose the tenth day of April it be required to find the true Longitude of the City of London at the setting of the Sun; bring the longest Meridian of the moving Horizon to 360 degrees the first Index of the world, and there keep it fast, then turn the upper moving Sphere until the place of the Sun, being then the first minute of ♉ Taurus, come to the edge of the Horizon in the West Semicircle of the Instrument; then bring the moving Meridian or Index to the place of the Sun, which Index will then at the same time in the Circle of days and months cut or show the 10 day of April the day of the Sun; and now the Instrument thus stated, keep all the Indices and Horizon unaltered, and then turn the whole upper moving Sphere, until that Index which cuts the day and place of the Sun come to 360 degrees, the first Meridian, and then the longest Index of the Horizon in the outward hour-Circle will cut 4 hours, which is the distance that day betwixt the Sun when he is on the Meridian, and the time of his setting when he is in the Horizon, and so continues at the same distance, for that day, upon all Meridian's and Longitudes until the Sun, by the force of Primum Mobile, is carried round about the world; Therefore now again turn the whole moving Sphere unaltered according to his Diurnal motion, until the Index at the day of the Sun cut in the innermost hour-Circle 5 hours 40 minutes, and then at the same time the same Index will also cut in ♈ Aries hour-Circle 7 of the Clock in the Afternoon, the time of Sun setting, which was also the first distance cut in the outward hour-Circle; and then the longest Index of the Horizon will stay at 20 degrees, the true Meridian and Longitude of the City of London, which cannot be removed, altered, or contradicted, and was never before found, known, or truly stated by any man until Now: and by the same Rule and Directions, being in any part of the world, we can as truly and exactly find the proper and particular Meridian and Longitude belonging to that place, as we have now settled and discovered a true, proper, and particular Meridian and Longitude, not to be changed, removed, or altered for the City of London, which was never known or found before, confirmed both by the Southing of a Star, and Setting of the Sun.   

THE THIRD WAY. To find the true Longitude of the City of London: at the Sun's Rising.  
SUppose the same tenth day of April it be required to find the true Meridian and Longitude of the City of London at the Sun's Rising; bring the longest Index of the Horizon to 360 degrees, the first Meridian as before, and there keep it fast; then turn the upper moving Sphere, until the place of the Sun, being now the first minute of ♉ Taurus, come to the edge of the Horizon in the East Semicircle of the Instrument; then bring the moving Meridian or Index to the place of the Sun, which will then also cut the tenth day of April, in the Circle of Months, which is now the day of the Sun; and so the Instrument thus stated, keep all the Indices and Horizon unaltered; and now being it is Sun Rising, turn the whole moving upper Sphere, until the Index which cuts the day and place of the Sun to 180 degrees, or 12 of the Clock at night, and then the longest Index of the Horizon will show in the outward hour-Circle 7 hours, which is the distance being upon the first Meridian Now at 180 degrees 12 of the Clock at Night, which is the distance of the Sun that day betwixt the time when he's upon the Meridian, and riseth in the Horizon, round about the world in all respective Meridian's and Longitudes; Therefore now turn again the whole moving Sphere, according to his Diurnal Motion, until the Index at the day of the Sun in the innermost hour-Circle, cut 3 Hours 40 minutes, and then the same Index in ♈ Aries hour-Circle, will show 5 of the Clock the time of Sun Rising, and the longest Index of the Horizon at the same time will stay again at 20 degrees as before, the true Meridian and Longitude of the City of London, confirmed by three several ways, and cannot be removed or altered to any other point, which point of Longitude was never found before.   

THE FOURTH WAY. To find the true Longitude of the City of London by the Moon when she cometh to the South.  
SUppose the 11 day of May, the Moon being then in 2 degrees of ♌ Leo, it were required to show then the true Longitude of the City of London; first bring one Index in the Circle of Months to the 11th day of May the day of the Sun, then bring another Index to the 25 degrees of ♌ Leo, the Moon's place that day, and then the distance betwixt those Indices will appear in the Equinoctial to be 88 degrees, which in time is 5 a Clock 52 minutes; therefore now turn the whole moving upper Sphere, keeping the two Indices unaltred, and bring the Index placed at the day of the Sun to 360 the first Meridian and beginning and ending of Longitude, and then the Index of the Moon, in the Equinoctial on the fixed Plain, will show 88 degrees which is 5 hours 32 minutes in time: but in regard the Moon for this distance of time must have 2 minutes allowed for each hour, take with a pair of compasses 15 degrees of the fixed Equinoctial, and then set one foot in 88 degrees, and turn over the compasses until they come to 360 degrees, and count how many times they are turned over which here will appear to be 6 times, therefore at 2 minutes for an hour, is 12 minutes, which added to 5 hours 52 minutes maketh 6 a Clock 4 minutes agreeing with Mr. Wings calculation, within 2 minutes; with 12 minutes add to 88 make 91 degrees, the true distance, the Moon's Index now standing there. Then the Indexces still unaltred, turn the whole moving Sphere until the Moon's Index cometh to 6 a Clock 6 minutes, which will also cut 111 degrees in the Equinoctial, and then the Index of the Sun will then stay again at 20 degrees the true Longitude of the City of London as before, which cannot be removed, altered or contradicted by any one. And thus hath the true Longitude of London been confirmed by four several ways to be directly 20 degrees and no more, no Man having before now ever discovered what it was, and so by the same Rule, may the true Longitude of any part of the world be speedily found.   

ANOTHER WAY. To find the true Longitude of the City of London by the Moon when she cometh to the South.  
SUppose the eleventh day of May, the Moon being then in 25 degrees of ♌ Leo, it were required to find the true Longitude of the City of London; First bring the 11th day of May now the day of the Sun to 360 degrees the first Meridian, and turn the Index to 25 degrees of ♌ Leo the Moon's place, that day, and then the distance betwixt the Sun and the Moon will appear, in the Equinoctial upon the fixed Plain, to be 88 degrees, and in the outward hour-Circle 5 a Clock 52 minutes; but now in regard the Moon must be allowed 2 minutes for each hour to be added to this distance take 15 degrees with a pair of Compasses out of the Equinoctial and set one foot in 88 degrees, and you will find you may turn them over near fix times before you come to 360 degrees the first Meridian, therefore you must allow 12 minutes which is 3 degrees more in the Equinoctial, and the Moon's Index must now stand at 91 degrees in the Equinoctial, and then in the outward hour-Circle will now show 6 a Clock 4 minutes. Therefore now, keeping the Moon's Index unaltred, turn the whole moving Sphere, until the Index of the Moon cut in ♈ Aries hour-Circle to 6 a Clock 6 minutes in the morning, and then the 11th day of May the day of the Sun will stand right against 20 degrees in the Equinoctial, again the true Longitude of the City of London, as before, which cannot be altered or contradicted by any one And thus we have stated the true Longitude of London four several ways to be directly 20 degrees and no more; which was not known or discovered before this time by any Man.  
1. Note, the outward hour-Circle always showeth the Sun's distance from the Star, from the Horizon, or from the Moon in hours and minutes, and the Equinoctial showeth the distance in degrees.  
2. And the Innermost hour-Circle showeth how many hours and minutes you may turn the day of the Sun or the place of the Moon.  
3. And ♈ Aries hour-Circle in the middle always in his own account showeth the same hour with the outward hour-Circle, and so determineth the hour of the day proper for that Latitude and Longitude which you are at.    

Two several Questions by finding the Moon South to know what Meridian you are at.  

The first Question.  
THe 10th day of June 1665 three Men being at Sea, the first Man had the Moon South at 6 hours 18 minutes; the second Man, at 6 hours 29 minutes; and the third Man had the Moon South at 6 hours 32 minutes. I demand what Meridian and Longitude each of those Men were then at?   

Example.  
FIrst, the 10th day of June, you may then readily find that the Sun is then in 29 degrees of ♊ Gemini at 20 degrees the Meridian of London, and the Moon at that time in 3 degrees 50 minutes of ♎ Libra; therefore now set one Index to the 10th day of June the day of the Sun, and the same Index in the Ecliptic will then cut 29 degrees of ♊ Gemini, the place of the Sun: then lay the other Index on 3 degrees 50 minutes of ♎ Libra, the place of the Moon, and with the Indices unaltred turn the upper Sphere until the Index of the Sun cut 20 degrees the Meridian of London, and the distance betwixt the two Indices in the Equinoctial will be 94½ degrees which is 6 hours 18 minutes, the first Man's hour of having the Moon South: but the Index of the Moon then in the Equinoctial will also cut 115 degrees, the first Man's Meridian and Longitude that he was at.  

The second Man having the Moon South at 6 hours 29 minutes.  
THE Indices remaining as before turn the upper Sphere until the Index of the Moon come to 20 degrees the Longitude of London; but now in regard there must be allowed 2 minutes for an hour for the Moon's depression, which is 12 minutes, therefore turn back the Index of the Moon 3 degrees, and then turn again the moving upper Sphere until the Index of the Moon cut 20 degrees, the Longitude of London; and the Index of the Sun will then cut 6 hours 29 minutes: so the second Man had the Moon South at 20 degrees the Meridian of London.   

The third Man having the Moon South at 6 hours 32 minutes.  
THE Indices not altered from the last proposition, turn the upper Sphere until the Index of the Moon come to 320 degrees, but now having 3 hours' difference, allowing 2 minutes for an hour, turn back the Index of the Moon 1½ degree, and then turn again the upper Sphere until the Index of the Moon cut 320 degrees, and then the Index of the Sun will cut 6 hours 32 minutes: so the third Man had the Moon South at the Meridian and Longitude of 320 degrees.    

The Second Question.  
THe 17th day of June 1665 five Men being at Sea, the Moon then at the full at 10 a Clock 24 minutes passed in the morning, the Sun in the 6 degree of ♋ Cancer and the Moon in the 6 degree of ♑ Capricorn South at 22 a Clock, at 224 degrees the first Man's Meridian and Longitude; but the Second Man hath the Moon South at 12 minutes after 12 a Clock; the third Man 24 minutes after 12; the fourth Man 28 minutes after 12; and the fifth Man 34 minutes after 12 a Clock. I demand, what Meridian and Longitude each of these particular Men were then at?   

Example.  
FIrst, lay the Index one end on the 17th day of June which will then also cut 6 degrees of ♋ Cancer the Sun's place, and the other end will then cut 6 degrees of ♑ Capricorn the Moon's place, then move the upper Sphere until the Sun's end of the Index cut 10 a Clock 24 minutes passed in the morning, the time of full Moon, and the Moon's end will then cut 224 degrees in the Equinoctial, which is the first Man's Longitude at 12 a Clock; then allowing 2 minutes for each 15 degrees, or one hour of time for the Moon's depression, you will then first find that betwixt 224 degrees and 134 degrees is contained 90 degrees, which is 6 hours of time; now allowing 2 minutes for each hours depression, in all 12 minutes, which is 3 degrees, turn the upper Sphere, the Index unaltred, until the Moons end come to 134 degrees then 3 degrees allowed for depression maketh exactly 12 a Clock 12 minutes past: So the second Man's Longitude must be 134 degrees at that time and place. The third Man having the Moon South 24 minutes after 12 a Clock, allowing 2 minute's depression for each hour, it appeareth that his Meridian and Longitude, when he hath the Moon South, must be 44 degrees: because the distance betwixt 44 degrees and 224 degrees in the Equinoctial is 180 degrees, or 12 hours, and then 24 minutes which is 6 degrees allowed for depression maketh 24 minutes after 12 a Clock: so the third Man must have the Moon South at the Meridian and Longitude of 44 degrees. The fourth Man had the Moon South at 20 degrees 28 minutes after 12 a Clock, because the distance betwixt 20 degrees and 224 degrees in the Equinoctial is 204 degrees or 13 hours 9 minutes: therefore allowing 2 minute's depression for an hour maketh 28 minutes after 12 a Clock: so the fourth Man, had the Moon South at 20 degrees the Meridian and Longitude of London. The fifth Man had the Moon South at 334 degrees 34 minutes after 12 a Clock, because the distance according to the Diurnal motion betwixt 334 degrees and 224 degrees is 250 degrees or 17 hours, allowing 2 minute's depression for an hour, maketh 34 minutes: so the fifth Man had the Moon South at 334 degrees 34 minutes after 12 a Clock; which is all that was required.  

The Rule and reason for turning the upper Shere is from 360 degrees.  
THE rule is to see how many hours and minutes the Sun can be turned from the first point of ♈ Aries, before t●e Star can come to be South: and the reason is because the Star cannot be South but at one time at one Meridian.   

To cut the Orisons for all Latituds.  
UPon a piece of pasteboard draw two lines Squarewise, that is perpendicular to each other, and let the longest line be the diameter of the upper Sphere, and the shorter the perpendicular, the Latitude from the Centre of the Index, by which means, from the Centre where the two lines cross each other there is got or found 3 points; now find the Centre to those 3 points, and strike an arch, and cut out by that arch the Horizon required.     
THE END.   

Errata.  
PAg. 6. l. 28. for pannage read parallels, p. 8. l. 17. for Terrestrial r. Celestial, p. 11. l. 26. for contain r. count, p. 17. l. 1. for all Altines r. all Times, p. 24. l. 27. for first Index r. first Meridian.