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A64474 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 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. Theaker, Robert. 1665 (1665) Wing T844; ESTC R1274 25,756 42

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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 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 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
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