A LIGHT to the LONGITVDE 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 Sea-men 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 LICENSED June 28. 1665. Roger L'Estrange LONDON Printed by William Godbid for William Fisher at the Postern-Gate neer Tower-Hill 1665. The CONTENTS THE Description of the Vpper 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 Ecliptick and his right Ascension in Degrees and Minutes or in Hours and Minutes p. 5. The Sun's place in the Ecliptick 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 Ecliptick 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 Horizons for all Latitudes p. 32. To the KING 's most excellent Majesty Dread Soveraign THese following endevours 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 Heroick 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 over-ruled by practical Proof-pieces upon which considerations Your Majesties faithful Subjects Robert Theaker and Charles Saltonstall after much expences of money and time are now endevouring to enable all practical Sea-men with the full knowledg 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 Majesties Service it is hoped in time he will also enable them with this knowledg that their Proof-pieces may give an end to all Objections In which hope for the present I humbly lay all down at Your Majesties 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 my self to Your Majesties Princely good will and pleasure desiring the great God of Heaven and Earth to grant Your Majesty a long prosperous and happy Reign Your MAJESTIES 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 Meridians in the world I did apprehend that there might be contrived an Instrument which would readily distinguish to all men at what perticular 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 facil 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 joyned 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 Meridians by Pendulums Sand-glasses Water-glasses c. but offereth to find under which of the 360 Meridians all Islands Head lands Main-Lands Cities and Towns are truly Situated and Placec against which there hath been much opposition endevouring 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 endevours I doubt not but will daily add more and more Light to this matter until at last practical Sea-men 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 endevours to your favourable Construction hoping they will prove worthy of your Acceptance and in time beneficial to all men Your Friend Ro. Theaker IF
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 Rumpe or the hindmost of the 3 in Charles his Waine 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 c. 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 wayes to cut the outward edg of that plain Horizon with points or Crossings in the edg 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 Complement 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 edg therefore that Star sets not at all And so if any Star hath South declination equal or greater than the Complement 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 Ecliptick 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 Ecliptick 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 Ecliptick the 15 day of March being 14 degrees 3 minutes in ♒ Aquarius cometh to the South at 8 of the Clock 46 Minutes past 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 past 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 past in the Afternoon allowing 2 minutes in the Ecliptick 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 Ephemerides find the Moon 's place in the Ecliptick then bring the moving Meridian to 12 hours and 20 degrees the Longitude of London and then bring the Moon 's place in the Ecliptick 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 Ecliptick 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 alwayes in work remembring when you have found 9 hours to allow two Minutes for each hour which here is 18 Minutes which 18 minutes in the Ecliptick at the Rate of 4 minutes for a degree is 4 degrees ◠and that joyned 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 minuts past in the afternoon which is now the direct true time of the Moon 's coming to the South Note 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 shal 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 Indexes 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 applyed 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 Ecliptick 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 Center which is the Pole of the World first then I say turn the uppermost Sphere being the Celestial Globe untill ♈ 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 Moneth 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 Ecliptick reckoned in the moving Meridian or Index is the Sun's declination and the point or place cut in the Ecliptick at the same time by the same moving Meridian or Index sheweth 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 moveing Meridian or Index sheweth 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 sheweth 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 Ecliptick 15 Degrees of ♓ Pisces one of the Southern Signs his right Ascension in Degrees 346 Degrees whose complement 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 complement from ♈ Aries in time is 56 Minutes So in the same manner the 20th day of Aprill if you desire to know the Sun's Declination his place Sign and Degree in the Ecliptick 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 Aprill and you will then find the Suns declination is 15 degrees North his place in the Ecliptick 10-8 Degrees eight Minuts 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 Minutes North his place in the Ecliptick 19-50 nineteen Degrees and 50 Minuts 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 Moneth which is an exceeding great dispatch and will prove very profitable in Astronomical practices The Sun's place in the Ecliptick 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 untill the place of the Sun in the Ecliptick come exactly to the plain Horizon at which edg interâ—ecting or touch point keep the Ecliptick 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 shew the Hour and Minute of Sun Setting also at the same time the moving Meridian will shew the Sun's declination in the moving Meridian and day of the Month in the Circle of daies 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 untill the first Minute of ♉ Taurus in the Ecliptick intersect touch or joyneth with the edge of the plain Horizon and there hold all fast together and then bring the moveing Meridian or Index to that point or intersection in the Horizon one end in ♈ Aries hour Circle in the East Hemisphere will shew 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 shew the Sun then 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 c. or having the hour of Sun Setting if you substract 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 daies and months will shew that it is now the 10th day of Aprill and that the Sun hath now 11 Degrees and 35 minuts 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 â™ Scorpio by this Instrument as hath been formerly taught you will find the Sun Riseth at 7 a clock 13 minuts past in the morning and Setteth at 4 a clock 47 minutes past in the Afternoon and in the Circle of Months the moving Meridian will shew 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 Ecliptick in all which you may facilly perceive very great expedition and dispatch which will prove very usefull to all practical Sea-men 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 Ecliptick 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 untill ♈ 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 Ecliptick 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 sheweth his right Ascension in hours and minutes also at the same time this moving Meridian or Index doth then cut in the Ecliptick the place Sign Degree and longitude of that Star and lastly this moving Meridian doth then shew 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 untill ♈ 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 alâ—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 Ecliptick 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 sheweth 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 Greaâ— Dog move as before the upper plain untill ♈ 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 sheweth his right Ascension is 98 Degrees and in the outward hour-Circle in the fixed plain sheweth 6 hours 32 minutes is the Great Dog 's right Ascension in time and then lastly cuts in the Ecliptick 7 Degrees of ♋ Cancer which is the Great Dog's place or longitude and in the Circle of Months 17 day 2 minuts 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 then 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 untill the moving Meridian also cut the Starr 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 shew 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 shew 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 shew 3 a clock 24 minuts in the morning which is the time when the Great Dog cometh to the South and on the first day of December the Index sheweth 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 shew 9 a clock 37 minuts past 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 ost fixed Equinoctial as before and there keep the Horizontal Index fastand turn the upper moving Sphere or plain representing the Celestial Globe untill 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 untill the Star come to the Circular edg of the moving Horizon in the West Semicircle of the moving Sphere I call the East Semicircle that which is conteined betwixt ♈ Aries and ♎ Libra the Ecliptick having thereon placed the six Northern Signs viz. ♈ Aries ♉ Taurus ♊ Gemini ♋ Cancer ♌ Leo ♠Virgo and in the Circle of months Aprill May June July August September and the other Semicircle betwixt ♈ Aries and ♎ Libra contein the Southern Signs and the Circle of months March February January December November I call the West Semicircle and in the East Semicircle I alwaies contein 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 shew in ♈ Aries hour-Circle the time of that Stars Rising if the Star touch the Horrizontal edg in the East Semicircle or in ♈ Aries hour-Circle will shew the time of the Stars Setting if the Star touch the edg of the moveing 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 edg of the Horizon in the East Semicircle and then the moving Index or Meridian brought to the 10 day of March will shew 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 edg 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 edg 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 shew 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 edg of the moving Horizon in the West Semicircle and then the moving Meridian brought to the 10. of March the same Index will shew 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 shewed 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 then 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 shew 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 then 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 shew 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 shewed the time of that Star's Setting So in the same manner if you please you may imploy 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 shew 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 shew the time of Sun Setting Provided alwayes if the Sun be in any of the Northern Signs and so hath North declination then 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 Ecliptick 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 shew in ♈ Aries hour-Circle that the Sun Riseth at 4 of the Clock 41 Minutes past in the morning Setteth at 7 of the Clock 41 minutes past 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 shew the Sun then Riseth at 7 of the Clock 13 minutes past in the morning and sets at 4 of the Clock 47 minutes past 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 shew 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 dayes 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 edg 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 substract it when it is South from 38 degrees and 30 minutes the height of the Equinoctial it will shew the height of the Sun that day upon his Meridian so the 20 day of April the Suns Declination is 15 degrees North which added to the 38 degrees 30 minutes sheweth 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 degreet 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 streight 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 joyn it to the point of Latitude in the Quadrant of Latitudes towards ♈ Aries and then lay a streight 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 streight 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 streight 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 alwayes 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 joyn the Declination 23 degrees and 30 minutes and then from that point lay a streight 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 streight 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
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. Michaels 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 reckonings for I suppose there have been as yet but few Eclipses observed to contradict the expert Navigators indeavours 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 knowledg 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 Ecliptick that day the distance then indeed betwixt the Sun and Star reckoned in the Equinoctial sheweth both their respective right Ascensions and also the Longitude in degrees or time conteined betwixt them by which means this Instrument will readily shew 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 alwaies Rising Setting and coming to the Meridian which is not to be denied then I say each particular Meridian and Longitude upon the Terrestrial Globe may undoubtedly be cleerly 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 shew 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 shew 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 shewed which is it in particular by this Instrument as any Astronomical Calculator can tell you the very Day Hour Minut 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 medled 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 imploy for this service which day I then call the day of the Sun then alwaies 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 shew 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 shew each proper and particular Meridian and Longitude of all places upon the Terrestrial Globe which cannot be removed or altred 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 untill 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 conteining 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 minuts 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 Lyons
Tayl and thereon place the moving Meridian or Index and then in the outward hour-Circle it will shew that Star cometh to the South at 10 a clock 13 minutes in the afternoon which is the common hour for all Meridians in the World for that day therefore now turn about the upper moving Plain or Sphere untill 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 Lyons Tayl 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 altred 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 imploy 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 shew 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 Aprill imploy the Star called Virgin Spik 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 shew 11 a Clock 48 minuts therefore now turn the day of the Sun to 10 hours 28 minuts 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 imploy 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 altred 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 altred 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 edg 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 dayes and months cut or shew the 10 day of April the day of the Sun and now the Instrument thus stated keep all the Indexes 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 Meridians 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 setled 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 edg 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 Indexes 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 shew 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 Meridians 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 shew 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 wayes and cannot be removed or altered to any other point which point of Longitude was never found before THE FOVRTH 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 shew 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 Moons place that day and then the distance betwixt those Indexes 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 Indexes unaltred and bring the Index placed at the day of the Sun to 360 the first Meridian and begining and ending of Longitude and then the Index of the Moon in the Equinoctial on the fixed Plain will shew 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 untill 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 minuts 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 Moons Index now standing there Then the Indexces still unaltred turn the whole moving Sphere untill the Moons 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 altred or contradicted by any one And thus hath the true Longitude of London been confirmed by four several waies 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 neer 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 Moons Index must now stand at 91 degrees in the Equinoctial and then in the outward hour-Circle will now shew 6 a Clock 4 minutes Therefore now keeping the Moons Index unaltred turn the whole moving Sphere untill 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 altred or contradicted by any one And thus we have stated the true Longitude of London four several wayes 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 alwaies sheweth the Suns distance from the Star from the Horizon or from the Moon in hours and minutes and the Equinoctial sheweth the distance in degrees 2. And the Innermost hour-Circle sheweth 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 alwaies in his own accompt sheweth 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 Ecliptick 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 Indexes unaltred turn the upper Sphere untill the Index of the Sun cut 20 degrees the Meridian of London and the distance betwixt the two Indexes 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 minuts THE Indexes remaining as before turn the upper Sphere untill 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 Moons depression which is 12 minutes therefore turn back the Index of the Moon 3 degrees and then turn again the moving upper Sphere untill 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 Indexes not altred from the last proposition turn the upper Sphere untill 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 untill 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 minuts past 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 Suns place and the other end will then cut 6 degrees of ♑ Capricorn the Moons place then move the upper Sphere untill the Suns end of the Index cut 10 a Clock 24 minutes past 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 untill 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 minutes 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 minutes 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 minutes 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 tâ—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 Horizons for all Latituds UPon a peice of pastboard 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 Center of the Index by which means from the Center where the two lines cross each other there is got or found 3 points now find the Center 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 contein r. count p. 17. l. 1. for all Altines r. all Times p. 24. l. 27. for first Index r. first Meridian