Anno Domini. 1592. A brief Treatise for the ready use of the Sphere: Lately made and finished in most ample large manner. By Robert Tanner Gentleman, practitioner in Astronomy and Physic. In the which Globe or Sphere, there is added many strange Conclusions, as well Celestial as terrestial, the like heretofore never devised by any. Necessary not only to those that follwe the Art of Navigation: But also to the furtherance of such as be desirous to have skill in the Mathematical Disciplines. Thou O Lord in the beginning hast laid the foundations of the earth: and the heavens are the works of thy hands. Psalm. 102. ver. 25. To the most high, mighty & renowned Princess, and most dread redoubted Sovereign Lady ELIZABETH, by the grace of God Queen of England, France, and Ireland, Defendresse of the faith. MOST Excellent, gracious, and sacred Sovereign, I was moved to take in hand to compile out unto your Highness (so well as my simple learning would serve me) a brief Treatise for the ready use of the Sphere or Globe: A work, by your poor obedient subject, with great pains, labour, and study, made and invented: with sundry additions and forms, not heretofore devised by any: no less pleasant than profitable for the benefit of your highness Commonweal, to the studious in the Mathematical Sciences, and to the furtherance of travelers in the Art of Navigation, and to all other your highness subjects that are desirous of the knowledge of the beautiful frame of the Celestial Orbs with their quantities, distances, courses, and strange intricate miraculous motions of the resplendent Globes of the Sun, Moon, Planets, and Stars fixed. And where it is a thing grafted in Nature, and natural through custom (right renowned Princess) by manifold sundry means, either by the faculties of the mind, the qualities of the body, or the gifts of fortune, for men that are led on by inward affection, to seek the friendship of those whom they affectionate, or rather inwardly love: wherein every man is so liberal, as the gifts of the mind, body, or fortune will afford him. Wherein, although I am not so far endued with any of them, that thereby I may deserve any thing at all: and although the gifts of my mind are unperfect, if they be placed against such an object, (as without assentation be it spoken) your majesties Royal self is; yet weighing with myself, the bountiful goodness of your highness nature to resemble a royal and fruitful Tree, which the more it is loaden, the more it declineth: and the natural gentleness and royal clemency of your majesties courtesy, wherewith your Highness is wont to receive favourably, to conceive and judge royally, of whatsoever your Majesty perceiveth, either to be overslipped by negligence, let pass by infirmity, or inserted by ignorance. And considering likewise the Proverb: Candidae Musarum ianuae, the doors of the learned are free from envy: I purposed by these small fruits of my skill, to make attempt if I could win any favourable acceptance, within the clemency of your highness favourable protection. Persuading myself, that I might safely commit my rude work to the presence of your Royal Majesty, who will wisely wink at my wants, and honourably construe the good meaning of my mind. And the more willing was I led on to seal it, and as my faithful allegiance bindeth me like a dutiful and obedient subject, to choose out your highness most royal worthiness above all other Princes, under the Orbs of the Heavens, to present this small work of mine: because your Majesty can learnedly judge of that which the ignorant can not comprehend. The only name of your highness royal sacred Majesty, shall be unto me a sure target of steel, to beat back the glancing strokes of unskilful tongues: who when they can not find out, by natural reason, the quantity and quality of superior bodies, will utterly condemn the rules of Arts, and quite overthrow all evident demonstrations: against whom (because they deny principles) there is no reasoning nor disputing at all. If I should stand upon terms of Art, and go about to unlock the closet of Astronomy unto your Highness, whom I know sufficient of your royal self to wade through the deepest floods and swiftest streams contained in the Mathematics: your Majesty might justly say, Sus docet Mineruam; & I might rather discover that I want, than your highness want that which I set down. It is better therefore for me to be silent, considering with what a wise, learned, royal Princess I have to deal, than by needless words to open mine own defects: humbly craving pardon of your Majesty for this my bold enterprise hoping that your Highness will not mislike this simple signifying of my bounden duty. For like as the mite of the poor widow mentioned in the holy Scriptures, which she gave in all her penury, is accounted a greater gift than those huge sums that great men laid out of their great store: So this my rude Edition of my simple h●ndy work, if it may be accepted into your highness tution, it shall encourage me hereafter to practise works of greater importance; and (as it is my bounden duty) always to pray to the Almighty God to bless and keep your Majesty in health, tranquillity & peace, So my daily prayer is to the same God, to bless and defend your Highness from all your enemies, and to reign and live over us Nestor's years. Your majesties most humble subject, Robert Tanner. And now to begin how to erect the Sphere or Globe. But first, the definition what a Sphere is, with his parts, are to be known and found out. A Sphere is a massy body, enclosed with one platform; and in the middle of it there is a prick: from which, all lines drawn to the said platform, are equal each to other, and that prick is the Centre of the Globe, and so saith Enclid. The axle-tree is a right line (which moveth not) and passeth through the Centre of the Globe, at which ends are imagined the Poles of the world; one is named the North Pole, the other the South. The North Pole is called, Pole artic and the other Pole in the the South, Antarctic: the South Pole is never seen of us in this our Country, but is evermore under our Horizonte. The North Pole is always seen of us whereas we dwell, and these stars be opposed the one right against the other. The Meridian is a great Circle passing over our heads, in which Circle when the Sun is, he maketh the middle of the day and the middle of the night. And also, in this Circle is showed the Latitudes of all places, by the height of the Poles, in every several Latitude. The horizon what it is. The Horizonte is a Circle, which goeth along by the edge of the ground, and parteth the part of the world which we see, from that part which we see not; and when the Sun riseth, than he is in our Horizonte, and so is he when he is going down as low as we can see him. Also it divideth the whole Sphere of the world into two equal parts, in such sort, that half of the Sphere is ever above the ground, and half always under the earth. This Circle hath great use in the heavenly motions, that by it we judge the risings & settings of the Sun and Moon, and all other Stars; And in this Horizonte you shall find noted, the names of the winds, which the Mariners useth, by the 32. points of the Compass. The next Circle is noted, the degrees which every day in the month doth contain: that is to say, the first day one degree; the second day two degrees; and so forth as they succeed in order, to a point like a little star, where the last day of every month endeth. The next Circle showeth, what day of the month the Sun entereth into any of the twelve signs, telling every day one degree, to thirty degrees, & so they succeed through ever one of the twelve signs, monthly. This Horizonte is divided into four quarters, East, West, South, and North, every quarter of the world containeth 90. degrees: and the whole compass thereof, is 360. degrees. The next Circle is Motus trepedationis, a starry firmament, whose motion is slow, from the West to the East, that every hundredth year (by the observation of divers Astronomers) moveth but one degree. The Zodiac, is a great broad and slope or shoring Circle, in the which are depictured the twelve signs and fixed stars, in the midst whereof, is the Ecliptic line, from which the Sun never swerveth. Then followeth the two Colluers, and the Equinoctial Circle, parting the Sphere in the very midst, betwixt the two Poles: by reason whereof, there are two Latitudes, the one is North and the other South. The North Latitude is contained betwixt the Equinoctial and the North Pole; the South Latitude, is betwixt the Equinoctial and the South Pole: either of these two spaces containeth in breadth 90. degrees. A Degree is one part of a Circle being divided into 360. parts, and 360. degrees, is the very Longitude of the Earth: and at the furthest Meridian in the West, beginning with one degree, and so proceed Eastward, unto 180. degrees of the Equinoctial, & from thence go forward to the West, where you come again to 360. degrees, which is the last degree of Longitude. Next followeth the two tropical Circles. That is to say, the North tropic is Cancer, and is the return of the the Sun in Summer declining, back again towards the Equinoctial, the days being then at the longest, and the nights at the shortest with us, and then beginneth the days to shorten again. The Winter Tropic (saith Proclus) is the most Southerliest Circle of all them that the Sun doth describe, by the revolution of the world, in the which when the Sun is, he maketh his winterlie turn, and then is the longest night in all the year and shortest day with us. Parallels. The Parallel lines are described by the wires in the Globe, and a Parallel of the longest day, is a space of the Earth: by this is known the increase of the day to be a quarter of an hour, going from the Equinoctial towards any of the Pole stars. A Climate containeth two Parallels, in which spaces the day increaseth by half an hour: Of these Parallels are made 24. Climates, between the Equinoctial and the tropic of Cancer. Then followeth the artic Circle, and the Antarctic Circle. The artic Circle is the North Circle: and the contrary Circle in the South, is called the Antarctic Circle: by the which Greeke composition, as you would say, contrary or against the Arctic Circle, & it well may be called the South Circle. But now here how Proclus defineth them. The Arctic Circle is the greatest of all those Circles which do always appear, and toucheth the Horizonte in one only point, and is altogether above the Earth, and all the stars that be within this Circle neither rise nor set, but are seen to run round about the Pole all the night. The Antarctic Circle is equal & equidistant to the artic Circle & toucheth the Horizonte in one only point, ' and is all under the ground, & all the stars that be in it, are evermore out of our sight. Then is there two other smaller Circles, called Poller Circles, or Pole Circles: in this Circle about the Antarctic Pole, is divided certain degrees to take the Altitude of the North star, this star is in the extremity, or end of the tail of the less Bear, being a constellation, commonly called the Horn: for this North star (of the most notablest stars above the Pole) is nearest unto it, & shall therefore show a less Circle than any other, and so shall his Altitude differ little from the Altitude of the Pole. This star hath declination 85. degrees, and 51. minutes, and the complement of ninety (which are four degrees and nine minutes) is his distance from the Pole. And although the Mariners hold opinion, that it is not distant more than three degrees & a half, yet to the judgement of those persons that hath knowledge in Astronomy, more credit ought to be given to the Astronomer than to the Mariner, for as much as the Astronomer doth know the place of the stars, with their Longitudes, Latitudes, declinations, and right ascensions, more perfectly and precisely than doth the Mariners: for they account not only by degrees, but also by minutes and seconds; therefore whosoever will precisely know it, let him take the highest Altitude of the North star, which is his being over the Pole, and the less Altitude, which is his being under the Pole: then take away the less from the more, and the half of that remaineth, shallbe the distance of that star, from the Pole of the world. And likewise by this experience may be known the Altitude of the Pole, and what all the other stars that go not down under the Horizonte, be distant from it, joining the greater Altitude with the less: and that shall amount thereof, divided by the half, shall be the Altitude of the Pole; and taking away this Altitude of the Pole, from the greater Altitude of the Star, or the less from the Altitude of the Pole, the rest that remaineth, shall be the distance of the star from the Pole. And as the Pole is invisible, it can not be seen or known when the North star is higher & lower, except it be by the mean of some other mark. And for this is considered, the position of the former Guards or Watch, being one of the two stars called the Guards, which are in the mouth of the Horn: the Mariners have noted eight positions, from the former Guard star to the North star, which answereth to the eight principal winds; and as the Guard is to the North star, according to the placing of these positions, so it shall be higher and lower from the Pole. Let us here put the common Rules which the Mariners use, to compile with those that are of opinion of three degrees and a half. And for the opinion of Astronomers, (which is the distance of 4. degrees & 9 minutes) I have in my Sphere or Globe annexed to my Dial in the North end, a Circular or Figure with a movable Horn; Upon the uttermost Margin of the Dial, is noted the eight winds of the eight positions, and also the other points belonging to the Mariner's Compass, and putting the Guards and the North star in every of the Winds, it shall be the distance that the North star is higher and lower than the Pole, as by the third appeareth in the cutting of the degrees in the Pole Circle, when the Horn is moved too and fro. common Rules after the Mariners account, but not after the Astronomers account, as may appear in the Rules next before. THE former Guard being in the East, the North star is one degree and a half under the Pole. The Guard being in the north-east, the North star is three degrees and a half under the Pole. The Guard being in the North, the star is three degrees under the Pole. The Guard being in the Northwest, the star is half a degree under the Pole. The Guard in the West, the star is one degree and a half above the Pole. The Guard in the south-west, the star is three degrees and a half above the Pole. The Guard in the Southeast, the said North star is half a degree above the Pole. And thus in the Dial and the Circle about the same, may you see the North star, in what part it is of the degrees, high or low, from the Pole: not only by the Mariners Rule, but also by the Astronomers Rule. And being thus known, how much the North star is under & above the Pole, let us take the Altitude thereof. And that of it that is under the Pole, let us join to his height, and as much of it as is above, let us take away, and that shall rise thereof, shall be the Altitude of the Pole above the Horizonte. Thus much for brevity sake, I have borrowed and collected out of Martin Cortese, and other good Authors, these few notes, for the use of the Guards, fixed in the North end of my Sphere or Globe. And now I am to entreat of the inward part of the Celestial Globe, and also of the terrestial Globe; and to begin with the lowest first. The terrestial Globe hath depictured upon it, a Map or Cart of the description of all the Earth, and the chiefest Regions, Cities, and Towns under Europe, Africa, Asia, and America: And in this Globe is contained two Elements, that is to say, Earth and Water. The Earth is lowest of all Elements, black, ponderous, round, environed and enclosed with the other three; she is called the Mother of fruits, the root of all plants, the nurse of living Creatures, the foundation of buildings, the Sepulchre of the dead, the Centre of the beautiful frame of the world, the matter and substance of man's body, and the Receptackle of heavenly influence: she is also garnished with fragrant flowers, with beautiful colours of Man, Beast, and Fowl, inhabited, and comfortably quickened by the nourishing beams of the Sun, Moon, Planets, and fixed stars. The Earth in comparison to the whole world, is but a prick or mote, the whole compass thereof, is 360. degrees, & every degree is 60. miles: and ye multiply 360. degrees by 60. it yieldeth 21600. miles about the same. The next Circle above the terrestial Globe, is the Element of Air: and the next Region above the Air, is the Element of Fire: and there are the four Elements, described in this Sphere or Globe. Then ensueth the Spheres of the 7. Planets: that is to say, the first is the Sphere of the Moon: the second is the Sphere of Mercury: the third is the Sphere of Venus: the fourth is the Sphere of sol: the fift is the Sphere of Mars: the sixth is the Sphere of Jupiter: the seventh is the Sphere of Saturnus: the eight is the Sphere of the starry Firmament; and every one of these Spheres doth carry his sign and Character upon him. And according to the common account, the Earth is 39 times so much as the Moon. But the Sphere of the Moon is far bigger than the Globe of the Moon, & the semidiamiter of her Sphere, is 33. times ½. longer than the earths semidiamiter, & the miles of the semidiamiter of her Sphere is 115278. and the miles of her Sphere in compass, containeth 724604. 4/ 7. The semidiamiter of the Sphere of Mercury, is 64. times so long as the earths semidiamiter: the miles of the semidiamiter, contains 220500. 2/ 33. And the miles of his Sphere in compass, containeth 1386000. 4/ 231. The semidiamiter of the Sphere of Venus, is 167. times so long as the earths semidiamiter: the miles of the semidiamiter, containeth 573872. 3/ 11. the miles of the Sphere in compass, containeth 3607200. The semidiamiter of the Sphere of the Sun, is 1120. times so long as the earths semidiamiter: the miles of the semidiamiter, containeth 3848367. 3/12 the miles of his Sphere in compass, containeth 34189737. 1/ 7. The semidiamiter of the Sphere of Mars, is 1220. times so long as the earths semidiamiter: the miles of the semidiamiter, containeth 4192363. 7/ 11. the miles of the Sphere in compass, containeth 26352000. The semidiamiter of the Sphere of Jupiter, is 8876. times as long as the Earth's semidiamiter: the miles that the semidiamiter containeth, is 30501163. 7/ 11. the miles of the Sphere in compass, containeth 191721600. The semidiamiter of the Sphere of Saturn, is 14405. times so long as the earths semidiamiter: the miles that this semidiamiter containeth, is 4950318. 2/ 11. the miles of this Sphere in compass, containeth 311148000. The semidiamiter of the eight Sphere, is 20110. times so long as the earths semidiamiter: the miles that this semidiamiter containeth, is 69105272. 11/8: the miles of this Sphere in compass, containeth 434376000. In this Armill or Ring Sphere, are wonderful conclusions to be learned, very strange and marvelous to the simple & ignorant persons, void of this knowledge, no less profitable than commendable to them, and to the skilful & wise; for the use thereof is very apt and ready in teaching, and is more easy for young learners, than the Solid or Massy Globe. And this is a marvelous excellency in knowledge, to be able so certainly to judge of things absent, as if they were present, to be able to tell what hour of the day it is in all parts of the Earth, and when the Sun riseth and setteth in all places under heaven: for the hours of the day are divers in divers Regions; so is the shadows that the Sun causeth in their Dial's, and all other shadows doth disagree many ways, not only from our shadows, but also, one of them from another. Again, the times of the year are not alike through all the world, but when it is Summer to us, it is winter to some other, and when it is spring-time with us, it is Summer in another Country; and when it is Harvest with us, other people have Summer: so when it is winter with us, some Nations have Summer, yea, when Spring time beginneth with us, it is Harvest in some Countries, and in other Countries it is Midsummer at the same time: but when it is Midsummer with us, it is Harvest no where in the world, but middle Winter it is then in two divers parts of the world. And those people whose Zenith is within 23. degrees and a half of any of the Poles, have their shadows running round about them: and the nearer they dwell under the Pole, the longer is their day, and therefore doth their shadows run the oftener about them; for where the day is but 24. hours long, there the shadows runneth but once about: and where it is half a year long, there it runneth about 103. times, and in all other mean places accordingly; so that those people that have these shadows thus running about them, under the North Pole. Then they that dwell under the South Pole have no shadows at all, for it is continual darkness with them: and yet do they not want light although they lack the Sun, but only half a month together, when the Moon is in that half of the Zodiac which is out of their horizon. And though the Sun and Moon be out of their sight, ye see with us, that we have a light before Sun rising, and after the Sun setting: so have they such a light by the beams of the Sun, 50. days continually, after they have lost the sight of the Sun, and so have they like light 50. days together before the Sun doth rise to them. And when the Sun is at the highest with us, it is at the lowest with divers other Nations, namely, to all them that dwell under the Equinoctial directly, or South from it; And therefore all those Nations have Midwinter when we have Midsummer. Now followeth, how to erect the Sphere. First, for the use of the same, you must place and set your Sphere level, that it may stand upright, and by the needle in the compass in the foot thereof, let it be placed due North and South, then shall the Arctic Circle stand North and the Antarctic South. The next Rule, is to find out the elevation of the Pole of the heaven, in that place where you mind to observe the Sphere for, & this being known, then turn your Meridian Circle, and rectify the Pole of the Sphere, so many degrees above his horizon, as the Pole of the heaven is elevated, in the place where you will observe the same. Then mark the degree of any sign that the Sun is in that day, whose quantity you desire to know: set that degree just in the Horizonte towards the East, and mark what degree of the Equinoctial is in the Horizonte at the same time: then turn the Sphere Westward, till the degree of the Sun be just in the Horizonte again in the West part, and mark then what degree of the Equinoctial doth light on the horizon in the East part, accounting truly how many degrees be betwixt those two degrees, which you have marked, and that Ark of the Equinoctial, is called the Ark of that day: which you may easily turn into hours, accounting 15. degrees to an hour, and for every degree less than 15. accounting 4. minutes of an hour. Example. I set the Globe to the elevation of 52. degrees, and consider the place of the Sun, the 14. day of August, and find it to be by the Ephemerideses, in the first beginning of Virgo, therefore do I set the beginning of Virgo in the very Horizonte, and then do I see with it, the 137. degree of Equinoctial in the same Horizonte, which I do mark; afterward I turn the Sphere till the place of the Sun, be in the horizon on the West part, & then in the East part I mark the place of the Equinoctial, which is 347. degrees, now abating 137. out of 347. there resteth the whole day Ark, which is 210. degrees, which maketh 14. hours: wherefore I conclude, that the night is but 10. hours, and both those times maketh just 24. hours. another way to find the same, more easier. Example. For London, the Pole of heaven being raised there, 51. degrees and 34. minutes. Turn your Meridian Circle 51. degrees & 34. minutes, them the Pole of your Sphere is elevated to the Latitude of London, thus being finished. The next Rule, to know the day of the month you will practise on. That is to be found out in the Horizonte Circle of the Sphere, where you shall find also, what degree the Sun occupieth in the sign that day. Then turn the Circle of the Sun, that the middle body of the Sun be brought right against the said degree, in the Zodiac: then turn the whole Globe about Westward, till the body of the Sun be right under the Meridian Circle, and there let him stay, till you have removed the index of the hourly Circle or Dial, precisely on 12. of the clock at noon: then turn & bring the Globe back again, to the East part of the Horizonte, where you first found out what degree of the sign the Sun was in that day; Then look upon the Dial, on the North part of the Sphere or Globe, & ye shall find what hour the Sun riseth: this being done, bring him back again Westward, toward the Meridian Circle, & it noteth the place of the elevation of the Sun every hour, till he be at his full height under the Meridian Circle, than it is said to be in the very noon steed, for that place where you use the Sphere for, then turn the Globe or Sphere from the Meridian Circle, westward, and it showeth the number of hours which he falleth from the Meridian height, till the time that he setteth under the Horizonte, and the index in the Dial, will tell you the hour that he setteth under the Horizonte that day. So thus having regard to the former instructions, will tell you the time of the length of the days & nights, in all places of the world, throughout the whole year; Provided always, that ye erect and set the degrees of the Meridian Circle, to the Latitude of the said place, where you mean to make your observation. Yet by the way, I will give you a Rule touching the suns motion, in his Eccentric Circle. The Eccentric Circle in the Sphere or Globe, being narrower on the one side than on the other, and hath his Centre distant or divided from the Centre of the world, and is described in the heaven of the Sun, imagining a line from the Centre of the Excentricke to the Centre of the Sun, making a complete revolution at the proper motion of the Sun. In the other heavens, imagining a line from the Centre of his Eccentric, to the Centre of the epicyle. The epicyle, is a Circle or little Roundle, fixed in the depth of the Eccentric: in which, the Planet is fixed, and near to his Centre is moved Circulerlie. The Auge, is a point in the circumference of the Eccentric, nearest unto the Firmament: or it may be said, that the Auge is a point farthest distant from the Earth. Aux, in the Greek tongue is as much to say, as the greatest Longitude or greatest elevation from the Earth. The opposite of the Auge, is an other point in the circumference of the Eccentric, nearest unto the Earth, and farthest distant from the Firmament. And you must here note and understand, the Sun is not moved Regularly in the Zodiac, making so much by his proper motion in one day, as in the other, because his Regular motion is in respect of the Centre of his own proper Sphere, or orb wherein he is moved, whose Centre is distant without the Centre of the world, towards the parts of Cancer: so that the greater part of his orb Eccentric, is toward the septentrional part, where the Sun passing by the septentrional signs, is more distant from the Earth, and hath more to go of his orb Excentricke, than being in the South signs: for, passing by the North signs, he tarrieth 9 days more, to describe the half of the Zodiac, than the other half toward the South part. And for this cause, the Sun is more swifter in his motion (in the Zodiac) one time, than another: for his motion in one day in the South signs, shall be greater than it is in one day in the North signs. And further it followeth, that the said unequal moving of the Sun obliquite of the Zodiac, certain days of winter, with their nights, are longer, than certain other of Summer, with their nights: that is to say, that the day natural in the winter, doth surmount that in the Summer, because the right ascension which answereth to one days motion of the Sun, being in the South, is greater than the ascension for one days moving, being in the North signs. Next followeth the placing of the other six Planets, in their true order in the Sphere. These six Planets, having each of them several Spheres, and their motions also several, and unlike in time to any other: and therefore they are called wandering stars. These are carried round about the world, by the violence of the first mover, in 24. hours, that is, every day once; yet they keep their places in their Sphere, and have their proper motions from West towards East. The Moon, with her heaven or Sphere, by her proper motion, giveth her turn from the West to the East, in 27. days and 7. hours, with 45. minutes. Venus, Mercury, and the Sun, in a year, which is the space of 365. days, with 5. hours and 49. minutes. Mars, in two years. Jupiter, in 12. years. Saturn, in 30. years. The eight heaven, which is the Firmament or starry heaven, by his own proper motion is moved by the ninth heaven, upon the beginning of Aries and Libra, and upon these two points, accomplisheth his Revolution in seven thousand years. This motion is called Motus trepedationis, (that is to say) the trembling motion, of Access or recess. To rectify the 6. Planets, to go in their due courses about the Sphere. Example. Saturn, who is the slowest in motion of all the 7. Planets, the 30. day of june, 1592. he is found by the Ephemerideses at noon, in his middle motion, to occupy the 16. degree, & 36. minutes of Cancer: then I turn the Sphere of Saturn, that the body or middle part of his star or Character, be just under the same degree in the sign noted in the Zodiac, then moving or turning the whole Globe about, from East to the West, showeth not only the hours of his rising and setting, with his Longitudes & Latitudes, but also, what part of the heavens he occupieth, every hour of the day & night, as by the Dial it appeareth in the Globe, if it be set according to the true place of the Sun. Likewise, jupiter is to be sought out, what degree of the sign he occupieth the same day at noon, & observe his Sphere in the same order. Mars, the like; The Sun, I have showed you the order before. Then Venus followeth, and Mercury, to be ordered and set each of them in their several Spheres, then shall appear every one of them in their several courses, every moment of the day: as by the example of Saturn before is showed. Now to the Sphere of the Moon, whose motion in her Sphere is nearest to the Earth; the observation of her, followeth. The Moon, swifter in course than any of the other Planets, maketh her revolution through the twelve signs, twelve times in a year oftener than the Sun. And she is to be placed in like wise, according to the former Rules, in the sign she is in at noon, that day and hour which you will observe the Globe or Sphere for, and for every hour after, add to her 30. minutes: and (without any great error) she noteth unto you, her rising and setting, the hour and place of the heaven, every day and hour where she is: the change, quarters, and full Moon, the ebbs and floods, every hour throughout all the whole day and month: and so consequently throughout the whole year, without any great error; Also, the depriving of her light by the Earth, in time of her Eclipses. To find out by the Instrument in the Dial, the age of the Moon, with her change, quarters, and full: her aspects with the Sun: the ebbs & floods, and other necessary Rules, appertaining to the Art of Navigation. etc. Mark at the Conjunction of the Sun and Moon, (it is said) the change of the Moon, is when the Sun and she meeteth together, and then the Moon taketh her light of the Sun: and when she is run in her course, 24. hours after the change, it is said that she is a day old; then turn the index of the Moon to the figure of 1. And when she is two days old, turn the index of the Moon to the figure of 2. and so proceed, till she come to the figure of 7. and then it is said to be in the first quarter of the Moon: then at the figure of 15. she is in opposition with the Sun, than it is said to be a full Moon: then she gathereth every day in her decrease, towards the Sun. And when she is 7. days past the full, than she hath lost half her roundness of her light, and is said to be last quarter; and so gathereth every day, nearer and nearer the Sun, till she be deprived quite from her light, and then it is said to be at change again, and a new Moon: and after her change, than her light gins to increase again, every 24. hours, 48. minutes; which yieldeth in 15. days, 12 hours. And so much she is just of the Sun, at the time of the full Moon. And if you will mark the distances, betwixt the index of the Sun, which points the hours in the Dial, and in the index of the Moon: you shall find always what distance the Sun and Moon are a sunder; this is called amongst the Marrines, the shifting of the Sun and the Moon, & hereby they shall know their ebbs and floods, as appeareth in the uttermost part of the Dial: and also, the 32. points of the Compass showeth the same. Another Rule for the hour of the two stars aforesaid, called the Guards, and of some, called Charles Wayne, or Charles Cart: likning four stars to four wheels, and the other three stars to three Oxen. And the first stars I take for my purpose, and declare at every months end, at what hour they are full West, and the hours that they are West and by North, and Northwest, and Northwest and by North, and full North; and so round about 24. hours. Example. JANVARY. From the 2. day of January, to the 17. they are north-east, at 5. at night: so you must turn the former Guard, that the third going from the same to the North star, may fall just upon the North north-east point of the Compass, at 5. of the clock at night: and then turn the Globe round about, and it noteth every hour, and every point in the Compass, that coast where they are situated, and also, what hour they rise and set under the Pole. And by this example put, you may proceed throughout every month in the year, according to the times of their being, and every hour in the same. As at 6. of the clock at night, they are north-east and by North. at 7. north-east. at 8. East and by North. at 9 Full East. at 10. East and by South. at 11. Southeast. at midnight, Southeast and by South. at 1. Southeast. at 2. Southeast and by South. at 3. Full South. at 4. south-west and by South. at 5. south-west. at 6. south-west and by South. at 7. south-west. From the 17. to the last, they are north-east and by North at 5. at night. at 6. north-east. at 7. East and by North, at 8. Full East. at 9 East and by South. at 10. Southeast at 11. Southeast and by South at midnight, South Southeast at 1. Southeast and by South at 2. Full South at 3. south-west and by South at 4. south-west, at 5. south-west and by South at 6. south-west at 7. West and by South. From the last to the 15. of February, they are north-east at 5. at after noon. at 6. East and by North at 7. Full East. at 8. East and by South at 9 Southeast at 10. Southeast and by South at 11. Southeast at midnight, South Southeast and by South. at 1. Full South at 2. South south-west and by South. at 3. south-west at 4. south-west and by South at 5. south-west at 6. West and by South at 7. Full West FEBRVARY. The hours of the two stars of Charles Wayne. From the 15. to the 1. of March, they are full East, at 6. at after noon. at 7. East and by South. at 8. Southeast at 9 Southeast and by south at 10. Southeast at 11. Southeast and by south at midnight, full South at 1. south-west and by south at 2. south-west at 3. south-west and by south at 4. south-west at 5. West and by South at 6. Full West. From the 1. of March to the 16. of March, they are East and by South, at 6. at after noon. at 7. Southeast at 8. Southeast and by south at 9 Southeast at 10. Southeast and by south at 11. Full South at midnight, South south-west and by south. at 1. South south-west at 2. south-west and by south at 3. south-west at 4. West and by South at 5. Full West at 6. West and by North MARCH. The hours of the two stars of Charles Wayne. From the 16. to the 1. of April, they are Southeast and by south, at 7. at after noon. at 8. South Southeast at 9 South southeast & by south at 10. Full South at 11. South south-west & by south at midnight, south-west at 1. south-west and by south at 2. south-west at 3. West and by South at 4. Full West at 5. West and by North From the 1. of April, to the 16. they are South Southeast, at 7. at after noon. at 8. South southeast & by south at 9 Full South. at 10. South south-west & by south at 11. South south-west at 12. south-west and by south at 1. south-west at 2. West and by south at 3. Full West at 4. West and by North at 5. Northwest APRIL. The hours of the two stars of Charles Wayne. From the 16. of April to the 2. of May, they are full South, at 8. at after noon. at 9 South south-west & by south at 10. South south-west at 11. south-west and by south at midnight, south-west. at 1. West and by South at 2. Full West. at 3. West and by North at 4. Northwest From the 2. of May to the 18. they are South south-west and by South, at 8. at after noon. at 9 South south-west at 10. south-west and by South at 11. south-west at midnight, West and by South at 1. Full West. at 2. West and by North at 3. Northwest at 4. Northwest and by North. MAY. The hours of the two stars of Charles Wayne. From the 18. of May to the 2. of June. they are south-west and by South, at 9 at after noon. at 10. south-west at 11. West and by South at midnight, Full West at 1. West and by North at 2. Northwest at 3. Northwest and by North From the 2. day of June, to the 18. they are south-west, at nine at after noon. at 10. West and by south at 11. Full West at 12. West and by north at 1. Northwest at 2. Northwest and by north at 3. Northwest JUNE. The hours of the two stars of Charles Wayne. From the 18. of june, to the 4. of july, they are West and by South, at at 9 at after noon. at 10. Full West at 11. West and by north at midnight, Northwest at 1. Northwest and by north at 2. North northwest at 3. North northwest & by north From the 4. of july to the 20. they are full West at 9 at after noon. at 10. West and by north at 11. Northwest at midnight, Northwest and by north. at 1. North northwest at 2. North northwest and by north. at 3. Full North JULY. The hours of the two stars of Charles Wayne. From the 20. of july, to the 4. of August, they are full West, at 8. at night. at 9 West and by north at 10. Northwest at 11. Northwest and by north at midnight, Northwest at 1. North northwest and by north. at 2. Full North at 3. North North-east & by north From the 4. of August to the 20. they are West and by north, at 8. at after noon. at 9 Northwest at 10. Northwest and by north at 11. Northwest at midnight, Northwest and by north. at 1. Full North at 2. North north-east and by north. at 3. North north-east at 4. north-east and by north AUGUST. The hours of the two stars of Charles Wayne. From the 20. of August, to the 4. of September, they are Northwest, at 8. at after noon. at 9 Northwest and by north at 10. North northwest at 11. North northwest and by north. at midnight, full north at 1. North North-east & by north at 2. North north-east at 3. north-east and by north at 4. north-east From the 4. of September to the 19 they are Northwest at 8. at after noon. at 9 North northwest at 10. North northwest and by north. at 11. Full north at midnight, North north-east and by north at 1. North north-east at 2. north-east and by north at 3. north-east at 4. East and by north SEPTEMBER. The hours of the two flarres of Charles Wayne. From the 19 of September to the 5. of October, they are Northwest and by north, at 7. at after noon. at 8. North northwest at 9 North northwest & by north at 10. Full north at 11. North North-east & by north at midnight, north-east at 1. north-east and by north at 2. north-east at 3. East and by north at 4. Full East at 5. East and by South From the 5. of October to the 20. they are North northwest, at 7. at after noon. at 8. North northwest and by north. at 9 Full north at 10. North North-east & by north at 11. North north-east at midnight, north-east & by north at 1. north-east at 2. East and by north at 3. Full East at 4. East and by South at 5. Southeast OCTOBER. The hours of the two stars of Charles Wayne. From the 20 of October, to the 3. of November, they are North north west at 6 at after noon. at 7. North northwest and by north at 8. Full north at 9, North North-east & by north at 10, North north-east at 11, North-east and by north at midnight, north-east at 1, East and by north at 2, Full East at 3, East and by South at 4, Southeast at 5, Southeast and by south at 6, South southeast From the 3▪ of November, to the 18, they are North northwest & by north, at 6, at after noon. at 7, Full North at 8, North North-east & by north at 9, North north east at 10, North east and by north at 11, north-east at midnight, East and by north at 1, Full East at 2, East and by South at 3, Southeast at 4, Southeast and by south at 5. Southeast at 6, South southeast & by south NOVEMBER. The hours of the two stars of Charles Wayne. From the 18. to the 3, of December, they are full North, at 6, at after noon. at 7, North North-east & by north at 8, North north-east at 9, north-east and by north at 10. north-east at 11. East and by North, at midnight, Full East. at 1. East and by South. at 2. Southeast at 3. Southeast and by South at 4. Southeast at 5. South Southeast and by South. at 6. Full South at 7. South southwest and by South From the 3. of December, to the 17, they are full North, at 5, at after noon. at 6. North north-east & by north at 7. North north-east. at 8. north-east and by north at 9 north-east at 10. East and by North. at 11. Full East. at midnight, East and by South. at 1. Southeast. at 2. Southeast and by South. at 3. South Southeast. at 4. South Southeast & by south at 5. Full South at 6. South south-west & by south at 7. South south-west DECEMBER. The hours of the two stars of Charles Wayne. From the 17. of Decmber, to the 1. of January, they are full North, at 4. at night. at 5. North North-east & by north at 6. North north-east at 7. north-east and by north at 8. north-east at 9 East and by North at 10. Full East. at 11. East and by South at midnight, Southeast at 1. Southeast and by south at 2. South Southeast at 3. South southeast & by south at 4. Full South. at 5. South south-west & by south at 6. South south-west at 7. south-west and by South From the 1. of January to the 16. they are North north-east at 5. at after noon. at 6. north-east and by north at 7. north-east at 8. East and by north at 9 Full East at 10. East and by South. at 11. Southeast at midnight, Southeast & by south at 1. South Southeast at 2. South southeast & by south at 3. Full South at 4. South southwest and by South. at 5. South south-west at 6. south-west and by south at 7. south-west. A ready note in few words, for the difference of hours, according to the distan●● miles, from East to West under the Equinoctial. FIRST, you shall understand, that 15. miles difference from East toward West, doth make the Sun rising, the noonstead, and Sun setting, to be later by one minute of an hour: & so 30. miles, 2. minutes: 120. miles, 8. minutes: 225. miles, 15. minutes: which is a quarter of an hour. And he that is ready in account of Arithmetic, may find it out by the Rule of proportion. As for Example. London hath Latitude 51, degree and 30. minutes, or there about, I travail East-wards from London 2000 miles; My desire is, to know the difference of their Longitudes, and the time of their noon steeds, for when it is 12. of the clock with us at London, 2000 miles Eastward from London, is then but 2. of the clock and 13. minutes at after noon. And 2000 miles West from London, it was then with them, but 10. of the clock and 13. minutes in the fore noon: the difference of these 3. places, one from the other, is to be found by the Rules in Arithmetic, as followeth. If 15. miles in Longitude, Eastward from London give one minute of time, what giveth 2000 miles. miles, 15. 1. minute of time. miles, 2000 133. (5. I work it in this manner, dividing 2000 miles by 15 miles, and it yieldeth 133. times 15. miles, and 1. third part of 15. miles, to be divided into 15 parts. Now, allow to every 15. miles, one minute of time, (as you have heard me say before) and reduce them into hours, in this manner as followeth. 60. minutes maketh a degree of the Equinoctial; so then divide 133. by 60. minutes of time, & the Cotient will be 2. and 13. will remain: that is, 2. hours and 13. minutes difference, between that place & London. And in this wise may you work by the Rules in Arithmetic, to find the West Longitude from London. There be some persons that make a great obscurity, in finding out the Longitudes in sailing East and West; a thing once known, & of no great importance, as ready to be found out as the Latitudes. A little Brief (therefore) I will give you, to understand the same skill. Let the Mariner, Sailor, or other persons, provide him a perfect Watch, or Clock, artificially made by a Clock-maker. Let him set the same by the hour of the day in that place you are in, and to come by the true place of the Sun, your Astrolob quadrant cross staff, or other Instrument, will serve you to take the height of the Sun, & to find out the true hour in every several Latitude, with the help of the Rules before. And the true hour being found of the day in this manner, set your Clock or Watch. Then travel either by Sea or Land, and when you are 40. miles, or 60. more or less, distant of the place you went from, then look to your Clock or Watch, how many hours have passed since you set on your journey: then take your Quadrant or orther Instrument, & take the height of the Sun in that place you are in; and if the time of the day taken with your Instrument, do agree with your clock, be you sure your place is North or South, from the place you came from, and therefore have the same Longitude and Meridian line; But if the time differ, subtract the one out of the other, and the difference turn in degrees and minutes of the Equinoctial: and 15. minutes of the Equinoctial, maketh one minute of time, according unto the Rules going before, you may thus know the Longitudes, difference of hours, and times, betwixt any two places East or West ward. The Latitudes are easily found out by the Altitudes of the North or South Poles, and also, by the Meridian height of the Sun at noon. Example. I find the Sun to possess the 1. minute of Geminie: his height in the Meridian line at noon with us here at London, is 54, degrees and 10, minutes, and his declination is 15, degrees and 40, minutes: now I subtract the declination out of the suns height, & there remaineth 39, degrees and 30, minutes, this I take from 90, degrees, and I find the place in height 51, degrees and 30, minutes; And this you must bear in memory, that if the Sun have South declination, you must add it to the said Altitude: then adding or substracting that number from 90, degrees, there shall remain the true elevation of the Pole. Always bear this in memory, if the Sun be on the South side of the Equinoctial line, it is called South declination; if on the North side, North delination; And this hath a most singular use in the Art of Navigation, and by it you may find out the height of the Pole in all places where you travel. ¶ Hear followeth the Degrees, called Putei, Fortune, Lucidi, Tenebrosi, Vacui, Masculini, and Feminei, Fumosi and Azamene, in all the 12. Signs of the Zodiac. By this letter p. is meant Putie: for. signifieth Fortune: and a. Azamene: this letter l. berokeneth Lucidi: t. Tenebrosi: this letter v. noteth Vacui: and m. Masculini: this letter f. signifieth Feminei: and this syllable fu. noteth Fumosi. Aries. Degrees, 1, t. m. 2, t. m. 3, t. m. 4, l. m. 5, l. m. p. 6, l. m. 7, l. m. 8, l. m. 9, t. f. 10, t. f. 11, t. m. p. 12, t. m. 13, t. m. 14, t. m. 15, t. m. 16, t. f. p. 17, l. f. 18, l. f. 19, l. f. for. 20, l. f. 21, v. f. 22, v. f. 23, v. m. p. 24, v. m. 25, l. m. 26, l. m. 27, l. m. 28, l. m. 29, l. m. p. 30, v. m. Taurus' Degrees, 1, f. t. 2, f. t. 3, f. t. for. 4, f. l. 5, f. l. p. 6, m. l. a. 7, m. l. a. 8, m. v. a. 9, m. v. a. 10, m. v. a. 11, m. v. 12, f. v. p. 13, f. l. 14, f. l 15, f. l. for 16, v. f. 17, v. f. 18, v. m 19, v. m 20, v. m 21, l. m. 22, l. f 23, l. f 24, l. f. p 25, l. m. p 26, l. m 27, l. m. for 28, l. m 29, t. m 30, t. m Gemini, Degrees, 1, l. f. 2, l. f. p 3, l. f 4, l. f 5, t. f 6, t. m 7, t. m 8, l. m 9, l. m 10, l. m 11, l. m. for 12, l. m. p 13, v. m 14, v. m 15, v. m 16, v. m. 17, l. f. p 18, l. f. 19, l. f 20, l. f. 21, l. f. 22, l. f, 23, t. m 24, t. m. 25, t. m. 26, t. m. p 27, t. m 28, v. f 29, v. f 30, v. f. p Cancer. Degrees, 1, l. m. for. 2, l. m. for 3, l. f. for 4, l. f. for 5, l. f 6, l. f 7, l. f 8, l. f 9, l. m. a 10, l. m. a 11, l. f. a. 12, l. f. a. p 13, t. m. a 14, t. m. a 15, v. m. a. for 16, v. m 17, v. m. p 18, v. m 19, fu. m 20, fu. m 21, l. m. 22, l. m 23, l. m. p 24, l. f. 25, l. f 26, l. f. p 27, l. f. 28, l. f 29, t. v 30, t. v. p Leo. Degrees, 1, t. m. 2, t. m. for 3, t. m 4, t. m 5, t. m. for 6, t. m. p 7, t. f. for 8, t. f 9, t. m 10, t. m 11, fu. m 12, fu. m. 13, fu. m. p 14, fu. m 15, fu. m. p 16, fu. f. 17. fu. f 18, fu. f. a 19, fu. f. for 20, v. f. fu. 21, v. f. 22, v. f. p 23, v. f. p 24, v. m 25, v. m. a 26, v. m. a 27, l. m. 28, l. m. p 29, l. m 30, l. m Virgo, Degrees 1, f. t. 2, f. t. 3, f. t. for 4. f. t 5, f. t. 6, f. t 7, f. l 8, f. l. p 9, m. v 10, m. v 11, m. l 12, m. l 13, f. l. p 14, f. l. for 15, f. l 16, f. l. p 17, f. fu 18, f. fu. 19, f. fu. 20, fu. for 21, m. fu. p 22, m. fu 23, m. v 24, m. v 25, m. v. p 26, m. v 27, m. v 28, m. t. 29, m. t 30, m. t Libra, Degrees 1, l. m. p▪ 2, l. m. p 3, l, m. for 4, l. m 5, l. m. for 6, t. f 7, t. f. p 8, t. f 9, t. f 10, t. f 11, l. f 12, l. f 13, l. f 14, l. f 15, l. f 16, l. m. 17, l. m 18, l. m 19, t. m 20, t. m. p 21, t. f. for 22, l. f. 23, l. f 24, l. f 25, l. f 26, l. f 27, l. f 28, v. m 29, v. m 30, v. m. p Scorpio, Degrees, 1, t. m. 2, t. m 3, t. m 4, l. m 5, l. f. for 6, l. a. f 7, l. f. for 8, l. f. 9, v. f. p 10, v, f. p 11, v. f 12, v. f 13, v. f 14, v. f 15, l. m 16, l. m 17, l. m 18, l. f. for 19, l. a f 20, l. f. for 21, fu. f 22, fu. f. p 23, v. f. p 24, v. f 25, v. m 26, v. m 27, v. m. p 28, t. m 29, t. a. m 30, t. m. Sagitarius Degrees, 1, l. m. a 2, l. m 3, l. f 4, l. f 5, l. f 6, l. m 7, l. m. a p 8, l. m. a 9, l. m 10, t. m 11, t. m 12, t. m. p 13, l. f. for 14, l. f 15, l. f. p 16, l. f 17, l. f 18, l. f. a 19, l. f. a 20, fu. f. for 21, fu. f. 22, fu▪ f 23, fu. f 24, l. f. p 25, l. m 26, l. m 27, l. m. p 28, l. m 29, l. m 30, l. m. p Capricor. Degrees, 1, t. m 2, t. m. p 3, t. m 4, t. m 5, t. m 6, t. m 7, t. m 8, l. m 9, l. m 10, l m 11, fu. m. 12, fu. f. for 13, fu. f. for 14, fu. f. for 15, fu. f 16, l. f 17, l. f. p 18, l. f 19 l. f 20, t. m. for 21, t. m 22, t. m. p 23, v. m 24, v. m. p 25, v. m 26, t. m. a 27, t m. a 28, t. m. a p 29▪ t. m. a● 30, t. m Aquary. Degrees 1, fu. m. p 2, fu. m 3, fu. m 4, fu. m 5, l. m 6, l. f 7, l. f. for 8, l. f 9, l. f 10, t. f 11, t. f 12, t. f. p 13, t. f 14, l. f 15, l. f 16, l, m. for 17, l. m. for 18, l. m. a 19, l. m. a 20, l. m. for 21, l. m 22, l. f. p. v 23, v. f 24, v. f. p 25, v. f 26, l. m 27, l. m 28, l. f 29, l. f. p 30, l. f Pisces. Degrees 1, t. m 2, t. m 3, t. m 4, t. m. p 5, t. m 6, t. m 7, l. m 8, l. m 9, l. m. p 10, l. m 11, l. f 12, l. f 13, t. f. for 14, t. f 15, t. f 16, t. f. 17, t. f 18, t. f 19, l. f 20, l. f. for 21, l. m 22, l. m 23, v. m 24, v. f. p. 25, v. f 26, l. f 27, l. f. for. p 28, l. f. p 29▪ t. m. 30. t. m. To know the place of the Sun, by the Rule of memory: And to know in what degree the Sun is, without respect of minutes. Bear in memory these numbers that hereafter followeth. 11. 10. 11. 10. 11. 12. 13. 14. 13. 14. 12. 12. The first 10. standeth for January, the second for February, with their signs, & so the rest; And to know in what degree the Sun is, you shall take away the days that are applied to every month, according to the said numbers of the days, for the which you desire to know the place of the Sun, and in them that remain, in so many degrees is the Sun, of the sign into which it entereth that month. And if the days pass of the month, shall be less than the days applied to the same month, you shall join 30. with those days passed of the month, & of the Sun that amounteth, you shall take away the days applied to the said month, and the rest shall be the degrees, in the which the Sun shall be, of the sign of the month past. As for example. month, Degrees, Signs. ja. 11. Aquarius Fe. 10. Pisces. Ma. 11. Aries Ap. 10. Taurus' Mai. 11. Gemini June. 12. Cancer july. 13. Leo Au. 14. Virgo Sep. 13. Libra Octob. 14. Scorpio No. 12. Sagitarius De. 12. Capricornus The 12 day of October, taking away 14, that were applied, remaineth 28. degrees of Scorpio, where the Sun is. Another Example. The sixth of December, which are lesser than 12. which is applied unto it, if we join 6. to 30. which are the days of the month next afore, they make 36. and from them we take away the 12. & there rest 24. degrees is the Sun of the month before, which is Sagitarius. A Rule to know when the Sun entereth into every of the 12. Signs. And that we may in the years to come, know the day, hour, and minute, in the which the Sun entereth into every sign, we will follow this order; upon the day, hours, & minutes, that the Sun entereth into every sign, the year 1545. we must add for every year 5. hours and 49. minutes, which with the 365. days which every year containeth, shallbe the time in the which the Sun accomplisheth his revolution. And because that in the year of the Bebysextile or Leapyere, is added to February, 1. day more to his 28, which we have once in 4. years, from 6. to 6. hours; if we shall take from the Computation, that we have given turning one day backward, as shall be in the year 1548. and upon that remaineth: shall return in the year following of 1549 to add 5, hours 49. minutes, and as much more every other year following shall be a certain Rule for ever. And it is to be noted, that the degrees and minutes which we have touched before, are properly for the city of Cadiz. And if we desire to apply them for other cities or places more Eastward, than for every 15 degrees that they are distant from Cadiz, in Longitude, we must add one hour, And if for the Cities or places more westward in like manner, for every 15. degrees, we must take away one hour, by reason of the course of the Sun, by his rapt moving from the East to the West. For it is certain, that when with us in Cadiz it is 12. hours of the clock to them that are 15. degrees Eastward from us, it is one of the clock: and to them that are from us 15. degrees towards the West, it is 11. of the clock. And thus may you apply it to every several Longitude East or West, giving to every 15. miles, one minute of time according to the other Rules in Arithmetic specified. FINIS. AT LONDON Printed by john Charlwood.