A TUTOR to ASTRONOMY AND GEOGRAPHY; OR, An easy and Speedy way to Understand the Use of both the GLOBES, Celestial and Terrestrial. Laid down in so plain a manner that a mean Capacity may at the first Reading understand it▪ and with a little Practise, grow expert in those Divine Sciences. Translated from the first Part of GULIELMUS BLAEU, Institutio Astronomica. Published by J. M. Whereunto is annexed the Ancient Poetical Stories of the several Constellations in Heaven. LONDON, Printed for Joseph Moxon, and are to be sold at his Shop, at the sign of Atlas, in Cornhill; where you may also have Globes of all sizes; 1654. THE PUBLISHER To the Reader. courteous Reader, THis Book of the Use of the Globe being commended by many able Mathematicians, for the best that is extant of this Nature; but being in the latin Tongue, and therefore reserved only for scholars; I was by some of them advised to get it Translated into English, and make it public; not only to deep Wits, but to mean Capacities: Therefore( I hope) if the translator have used somewhat a more plain and familiar style in our Vulgar Tongue, then the Author hath done in that Elegant Language; that neither the Author will be offended at it, or the Buyer complain thereof. Some( but few) alterations I judged fitting to be made in this Translation; and that because there falls out some difference between our Authors own Globes, which he treats of, and the Globes that I have given forth this last year; of which Globes I indeed desire particularly to inform you; they being the latest done of any, and to the accomplishing of which, I have not only had the help of all, or most of the best of other Globes, Maps, plaits, and Sea-Draughts of New Discoveries, both of our Authors and other mens, that were then extant, for the Terrestrial Globe; but also the Advice and Directions of divers learned and able Mathematicians, both in England and Holland, for Tables and Calculations both of Lines and Stars for the Celestial; upon which Globe I have placed every star that was observed by Tycho Brahe, one degree of longitude farther in the ecliptic, then they are on any other Globes; so that whereas on other Globes the places of the stars were correspondent with their places in Heaven 52. yeers ago when Tycho observed them; and therefore according to his rule, want about 44. min. of their true places in Heaven at this time, I have set every star one degree farther in the ecliptic, and rectified them on the Globe according to the true place they will have in Heaven in the year 1671. Also on the Terrestrial Globes we begin not our Longitude at one and the same Place; Our Author begins his at Pico in Teneriffa, an iceland of the Canaries; but mine begins at the Isle Gratiosa, one of the Isles of Azores, which is 10. deg. Westward of Teneriffa; so that any place which shall have 20. deg. of Longitude on my Globes, must be accounted to have but 10. on our Authors; if 30. but 20. &c. Therefore to avoid trouble, I have in this Book name the Long. of Places as they are on my own Globes, viz. from the Azores; and was the more induced thereto, because our other English Globes and Maps reckon their Longitude from them; yet( with Stevinus) I could wish that some particular place were universally pitched upon by all Geographers; whether it were Pico, which he pleads for, or Gratiosa, or other places, that others pled for; for indeed▪ to many that are but merely skilled in the Cosmographical part of Globes and Maps, this particular thing is matter of great Confusion; for ptolemy began the Long. at the Fortunate Islands,( which M. Hues, p. 4. c. 1. in his Treatise of Globes, proves to be the Islands now called Cabo Verde, and not those now called the Canary Islands) because in his time they were the furthest Places of the discovered World, towards the setting of the Sun. Others begun at Corvus and Flora, because under that Meridian the Compass hath no variation, but as most men affirm, respect duly the North and South. Yet others say, it hath its just Position under the Meridian of S. Michaels, and therefore they begin their longitude there. Others again contradict that, and say it is between the Islands of Flores and Fayal that the Compass hath no variation; and therefore they begin their longitude there. In sum, We find that every one begins the longitude where it best liketh him; for the Spanjards of late traveling much into the West Indies, have placed their first Meridian or beginning of Longitude at Toledo, in those parts; and( contrary to all others) account it Westwards. Therefore seeing such diversity in all Nations, and as yet an Uniformity at home, I choose rather to concur with our own Countrymen, in a matter of so small moment, then follow the examples of some Strangers: Yet such as desire to see what Stevinus pleads for Pico in Teneriffa, may peruse our latin Author, fol. 15. which in this Translation is purposely omitted; not in dis-rrspect either to our Author or Stevinus, but because I thought it impertinent to our purpose, in regard( as I said before) I desire chiefly to inform you of our English Globes, which have not their beginning of longitude at that place. One word more about the Longitude, and that is this. Although we have Tables showing the Longitude and Latitude of many eminent Cities, Capes, Rivers, &c. according to which Tables most other Globes and Maps agree: yet do not all places upon my new Terrestrial Globe agree with those Tables: Therefore in a question of any given longitude, let it not puzzle you if you find not the longitude agree with your Tables; for the Error is in them, and not on the Globe: For later Observations, and newer Discoveries hath much rectified the Cosmographical Description of the Earth, both in Longitude and Latitude; for that on most Globes, Maps, and Tables, divers places( especially in the West-Indies) differ 5, 6. yea 7. degrees of longitude, both from my new Terrestrial Globe, and from the Globe which our Author treats of, and also from a very large Map our Author hath lately given forth. Another thing I desire thee to take notice of, and that is this, Whereas in all questions that have a given time, our Author follows the New Style used in Holland, I have altered the date to the Old Style used in England. The last( and scarce worth naming) is a difference in the Plain of the Horizon, which difference I having spoken of in the Chapter of the Horizon, I shall pass by in this place. I know not of any other alterations that are made from our Author, unless either in Printing or Translating, some small erratas may have passed by; which if in this Edition thou takest pains to amend with thy Pen, and shalt acquaint me therewith, I shall be very thankful to thee, and careful to see it mended in the next. At the latter end of the Book I have annexed a small Collection out of D. Hood, which declares the reasons why such strange Figures and Forms are placed in Heaven; and withal, the Poetical Stories of every Constellation. I have not published the Use of the Copernican Sphere, which is the Second Part of this Book; because for the present I am unfurnished with Engraved Plates, and other Appurtenances that belong to the making them; but so soon as I can have them perfected, which I hope will be very shortly, I shall then present thee with it: In the mean time, I desire thee to judge civilly of my first Undertakings; So shall I be obliged to gratify thee with other things of this Nature, and encouraged to press forward, for the Honour of our English Nation. JOS. MOXON. To his Ingenious Friend, M. JOSEPH MOXON, Upon his New GLOBES. THe more I look, the more I do desire To view thy Globes,& must thy skill admire. This I am sure, thy Pains and Care was great, So was thy Charge, ere thou them didst complete: For which all England debtors are to Thee, And must extol thy Ingenuity. A Tutor TO ASTRONOMY AND GEOGRAPHY. CHAP. I. Of the Circles about the Globes, and on their Superficies, and of them common to both. I. What a Globe is. A Globe( according to the definition of Mathematicians) is a round Body, contained under one surface; in the middle or Center whereof is a point, from whence all strait lines drawn to the circumference are alike equal. The World being the fabric and Workmanship of the most omnipotent and infinite God is exhibited and held forth to our view by Astronomers, by two Globes of this kind, under a small, but proper shape; just as some stately edisice may be represented by the Master-builder by some type or draft thereof: I say, under a proper shape; not only because the Globe resembles the Heaven and Earth in their roundness, but chiefly because in one of the Globes, the Firmament, with the fixed stars therein contained, are lively represented to our view, in their true situation and Order, with the difference of their apparent Magnitudes; and in the other, the Earth, with all its Territories, Regions, Islands, and Seas; all which, that they might more diligently and exquisitely( as it were) set forth and hold out to our view, they have with great industry, invented divers greater and lesser Circles, some without the Globes, and others upon the surface of the Globe itself; the greater Circles are such as have the same Center as the Sphere itself, and encompassing the same about in the middle, divide both it and themselves into two equal parts; the lesser Circles are such as have a different Center from that of the Sphere, and divide the same into two unequal parts. But because neither the difference of these Circles, nor their use either in the Celestial or Terrestrial Globe can be well understood without some fore-knowledge both of them and their use, we shall therefore describe them severally; and first, those that are common to both Globes, which are without the same, and not drawn on the Globe itself, and then those that are drawn on the surface of each Globe; and these according to their several proprieties in relation to each Globe distinctly. SECT. II. Of the Axis, and the Poles. THrough the Center of each Globe is drawn an Axis, like to that Axis which we imagine to be in the world; whose ends extending themselves beyond the surface of the Globe in two opposite points, are called Poles; of which one shows the North, called the Artick; the other the South, and is called the antarctic Pole. SECT. III. Of the brazen Meridian which is about the Globe. EVery Globe is hung or fastened in a brazen circled; whose two Poles be directly opposite to one another: and are placed in a strait line with the Eastern side of the circled, the more commodiously to turn it about, without any sensible inclining either to the one or the other side of the circled: and that side directly answering to the Axis and the Poles, cuts the Globe in two equal parts. This circled is called Meridian, from Medidian, which is as much as medius dies; or high noon because the Sun coming to this circled, makes it Noon. It is divided into four Quadrants, and each of those into 90. deg. which on one side of the Axis are numbered from the Aequator to the Poles, by 10, 20, 30, &c. to 90. on the other side from the Poles; that the numbers of 90. meet in the middle between both Poles, to wit, in the equinoctial line. Note. Because I shall often use these terms, of, at, or under the Meridian, I would be understood of its Eastern side, which agrees with the middle of the Axis, the graduations being on that side. SECT. IV. Of the wooden Horizon about the Globe EVery Globe with its brass Meridian is placed in a wooden frame, bearing up a wide wooden circled, with four Banisters; whose supreme Superficies is attributed to divers uses. And here I must crave leave to digress from the Author, because the orisons of those Globes he treateth of, differs from the orisons of the English Globes; and therefore I shall( for the benefit of our own Country men) insist particularly on them; it being no detraction from the worth of the Author, since only the manner, and not the matter is altered: For as himself upon the same occasion saith, If we respect the use, it matters not much. First, the outward circled is divided into four equal parts, answering to the four corners of the World, East, West, North, South; and each of these is subdivided into eight equal parts, so that the whole circumference is divided into 32. equal parts, which Mariners call the 32. points of the Compass. Next to the utmost circled, are set down the ancient Greek and latin names of the Winds, which( according to their account) were but twelve in number. Then follows in a wide Row, twelve unequal divisions; in each division is the name of a month in Capital letters; which Moneths are divided into so many days, as Astronomers have allotted to each particular month, and marked with Arithmetical figures, 1, 2, 3, 4, and so forward, to the Moneths end; before which figures stand the names of such Festival days, as are celebrated by the Church of Rome: so that the twelve Moneths are divided into three hundred sixty and five days, which is the number of days accounted to a common year, and this Row is called The calendar of the new Style: The first seven letters of the Alphabet are inserted for distinction of the week-days, because of the diversity of the Dominical letter. Then succeeds the calendar of the old Style used by us here in England. And last of all, a circled, in which the twelve signs are encompassed; each of which twelve signs are divided into thirty equal parts, which are called Degrees; and each Degree into sixty Minutes; and each Minute into sixty Seconds; and each Second into sixty Thirds; and each Third into sixty Fourths; and so on infinitely if you please. Now on the orisons of those Globes that our Author treateth of, the calendar, and also the twelve signs are placed in the utmost circled of the wooden Horizon; next to them the Winds, and afterwards a circled divided into three hundred and sixty Degrees. In the inner edge of the wooden Horizon are made two Notches,[ just at the points or line of North and South; yet so, as that the East( or divided side of the Meridian) cut the Horizon exactly into two Semicircles,] into which two Notches the brazen Meridian is let, and according to the direct extension of the North and South, descendeth even to that profundity, that one half of the Meridian is precisely extant above the Plain of the wooden circled or Horizon; the other is depressed under it. The first represents to us the upper Hemisphere of the Heaven, conspicuous to out view, the other the lower Hemisphere, that is below us. That wooden circled is called {αβγδ}, as it were a visible Terminator, in the likeness of the true Horizon, which distinguisheth the apparent Hemisphere from the latent. In the lower Basis there is a wooden Foot or Bed, with a notch in it, in which the Meridian resteth, that thereby the Meridian and Globe may be lifted up, and depressed, steadily without any tottering, to divers heights of the Pole, as occasion requires. SECT. V. Of the Hour-Circle. ABout each Pole a small circled is fixed to the brazen Meridian, commonly called the Hour-Circle, which is likewise made of Brass, divided on its upper part in twenty four hours, according to the hours of the Natural Day; and so placed that the two hours of 12. at noon and night, are just over the Eastern edge of the Meridian; but the Center itself being the Axis of the world, hath a brazen Index fastened thereto, which pointeth to all the parts of the Hour-Circle, as oft as the Globe is turned round upon its one Poles in the Meridian; and the Globe remaining without motion, it may most easily be applied to any hour whatsoever. SECT. VI. Of the Points Zenith and Nadir. THe Meridian that appears above the Horizon, contains twice ninety Degrees: If therefore you count upwards from the points of North and South where the Meridian and Horizon intersect each other ninety Degrees, the point of termination will be every way equi-distant from the Horizon, and answering to the point of Heaven directly over our heads, which is called by Astronomers( by that Arabian word) Zenith; its opposite ( viz.) that point of Heaven directly lying under our feet, placed every way equi-distant from the Horizon, is name Nadir: They are likewise called the Poles of the Horizon, because the Horizon at the distance of a Quadrant, may be described from them as from Poles. SECT. VII. Of the Quadrant of Altitude. TO the point Zenith is annexed a thin brazen Bow, fitted to a brass Nut, with a Scrue, to be removed as the alteration of Latitude may require; whose Center is the Zenith: upon which Center it may be turned about, and applied to all the parts of the Horizon: It is divided into ninety Degrees, to be numbered from the Horizon upwards, towards the Zenith; It is vulgarly called the Vertical circled, and the Quadrant of Altitude. SECT. VIII. Of the Box and Compass. IN the Basis of the Globe on the South part under the Meridian, is sometime placed a Compass, serving to direct the Globe toward the four Cardinal points of the world; so that the Horizon of the Globe may agree with the Horizon of the world, and the Meridian to Meridian; and the rest of the Circles on the Globe, to those imagined in the Heaven. CHAP. II. Concerning the Circles in the Celestial Globe. SECT. I. Of the equinoctial. ABout both the Globes, as well the Celestial as Terrestrial, is drawn a great circled, in the middle, distant from both Poles the space of a Quadrant: In the Celestial Globe it is called the equinoctial circled, by the Greek {αβγδ}, as much as Aequidialis; because we observe, when the Sun comes to this circled, the days and nights are equal throughout the whole world; and for this cause,( and its equalizing all apparent irregular motion) it is called Aequator; and is divided( as all other Circles are) into three hundred and sixty Degrees. SECT. II. Of the ecliptic line and the zodiac. THere is drawn upon the Globes another great circled, a slope or obliqne to the equinoctial, and cuts it in two opposite points; and doth as well divide the equinoctial, at it is divided by the same, into two equal parts or Semi-circles; one Semi-circle declines from the equinoctial Northwards 23. deg. 31. min. the other as much toward the South, dividing the Globe into two Hemispheres: that which declines towards the North it called the North part; and that which declines towards the South, the South part of the ecliptic line, being derived from {αβγδ}, to want light; because in and about it happen all the defects and Eclipses both of Sun and Moon: It is also called the way of the Sun; because the Sun goes always under it, passing through it all in his Annual course: sometime without any distinction it is called the zodiac; by reason of that great agreement it hath therewith: They agree in this, that they have the same Axis and Polts; and only differ, that the ecliptic is a Line without Latitude, in the middle of the zodiac; but the zodiac is a circled, or rather girdle, which hath almost twenty Degrees of Latitude, viz. on each side of the ecliptic line almost ten, under which, the Planets ever finish their Motions; wandring sometimes Northerly, and sometimes Southerly from the true ecliptic line. But because there is no need to draw the zodiac, with its Latitude on the Globe, therefore the ecliptic line is only described. SECT. III. Of the Poles and Axis of the ecliptic. AS the Poles of the world are distant from the equinoctial every way ninety Degrees, and are therefore called the Poles of the Aequator; so the two Poles of the ecliptic are distant from it as much; namely, on every side, a Quadrant of a circled; one of which is as far distant from the North Pole, and the other from the South, as is the greatest Declination of the ecliptic from the equinoctial, viz. twenty three degrees, thirty one minutes: that toward the North, is called the North; that towards the South, the South Pole of the ecliptic; from one of the said Poles to the other, there is a streight line imagined to pass through the plain of the ecliptic at right angles, as the Axis of the World through the plain of the equinoctial, and is called the Axis of the ecliptic or zodiac. SECT. IV. Of the division of the ecliptic. OF the two points of intersection where the ecliptic and equinoctial cut each other, one is called the Spring Vernal, the other the Autumnal equinox; but of the two points of the ecliptic, the farthest distant from the Aequator towards the North, is called the Summer Solstice: the Southern is called the Winter Solstice; because the Sun when it comes to these points, seems to stand, and ceases declining from the Aequator to either Pole of the World. The ecliptic is divided into twelve equal parts, which are called the 12. signs, or 12. Houses, and have their names from their Neighbouring Constellations. They begin at the Vernal equinox, and tend from the West, into the East; expressed by these names and Characters in the Globe. Aries, Taurus, geminy, Cancer, lo, ♈ ♉ ♊ ♋ ♌ Virgo, Libra, scorpion, Sagittarius, ♍ ♎ ♏ ♐ Capricornus, Aquarius, Pisces. ♑ ♒ ♓ The three first signs ♈, ♉, ♊, begin at the Vernal equinox, and ascend from the equinoctial Northwards, even to the Summer Solstice. The three following, ♋, ♌, ♍, begin at Cancer, and descend again to the equinoctial, even to the Autumnal equinox. The three next, ♎, ♏, ♐, begin at Libra, and descend into the South, even to the Winter Solstice. The three last, ♑, ♒, ♓, begin at Capricorn, and tend again to the Aequator, and end in the Vernal equinox, or beginning of ♈. Every sign is divided into thirty Degrees, that the whole ecliptic( as all other Circles) may contain three hundred and sixty Degrees. SECT. V. Of the Circles of Longitude. IN the Celestial Globe are described twelve Semi-circles, from one Pole of the zodiac to the other, passing through the beginning of all the 12. signs, and make six great Circles. The first passeth through the Head of ♈,& ♎, and sheweth the beginning of the Longitude of those signs. The second through the head of ♉ and ♏; and so of all the rest; dividing the surface of the Globe into twelve equal parts, which are widest in the ecliptic, and do lessen by little and little, as they approach toward the Poles of the zodiac, and at length wholly terminate therein. The entire Superficies of any of these parts, derives its name from the sign comprehended in the ecliptic, between each Semi-circle: as for example: The Superficies lying between the two Semi-circles, drawn through the beginning of Aries and Taurus, comprehending the sign of Aries in the ecliptic, is also called the sign of Aries; and all the Stars and Planets, and other Points of Heaven, between those two Semi-circles on both sides of the ecliptic to the Poles, are said to be in Aries, and so of the rest. SECT. VI. Of the colours. TWo great Circles( called colours) do intersect one anothers right Angles in the Poles of the World; one called the equinoctial colour, passeth through the Heads of Aries and Libra; the other, called the Solstitial colour, through the Head of Cancer and Capricorn; and each Pole of the zodiac, and by this means divide the ecliptic into four equal Parts or Quadrants, called by the four Cardinal points of Aries, Cancer, Libra, Capricorn: through which when the Sun passeth in its Annual Motion, it makes the variation of the seasons of the year; as Spring, Summer, autumn, Winter: and the Aequator, and all its parallel Circles, do the colours divide into four Quadrants, because they pass through their Poles. SECT. VII. Of the lesser Circles, tropic, and Polar. THe tropics are two lesser Circles, parallel to the Aequator, the one receding from it to the North, the other to the South, so far as the ecliptic is distant from the Aequator, which is 23. Degrees, 31. Minutes; dividing the Globe into two unequal parts. They are described( by the daily Motion of the Heaven) by the points of the extreme digression of the ecliptic from the Aequator, in the beginning of Cancer in the North, and Capricorn in the South. The Boreal is called the tropic of Cancer; the Austral the tropic of Capricorn; because the Sun being come to these Circles, beginneth its( {αβγδ}, that is) conversion toward the equinoctial. Of the same distance from the Poles of the world( as are the tropics from the equinoctial) there are two lesser Circles, called Polar circles; which are described by the Diurnal Revolution of the Poles of the ecliptic. That which is drawn about the Boreal Pole, is called the arctic circled, {αβγδ}, from the Bear, a Neighbour Star; the other about the Austral Pole, is called antarctic, as being opposite to the arctic. SECT. VIII. Of the circled of Position. sometime a Brazen Semi-circle is affixed to the Celestial Globe, in the common intersections of the Meridian and Horizon to the North and South, in that manner that about their extremities upon two Poles, it is movable as well from the Oriental as Occidental part of the Globe, and may be turned upward and downward, as need requires; from the Horizon to the Meridian, and from the Meridian to the Horizon. This Semi-circle doth refer( being constituted for a certain Elevation) to the beginnings of the twelve Celestial Houses, which the Astrologers use to distinguish by six Circles of Positions, as is evident among them. CHAP. III. Concerning the Circles on the Terrestrial Globe. SECT. I. Of the Aequator. AS in the Celestial Globe, in the middle between the two Poles, is drawn the equinoctial circled; so in the Terrestrial Globe is drawn a great circled between the Boreal and Austral Poles, dividing the Sphere of the Earth into two Hemispheres, the Northern and Southern; which Stevinus calls Mediatorem, or Emmesocyclum, but we the Terrestrial Aequator. This circled was distinguished by another name from the Celestial equinox, being manifestly different therefrom, in that it remains under it immovable, the other being turned about with the Heaven in twenty four hours; so that the beginning of one, meets with the beginning of the other but once within that time, as in the use appears: But because the word Emmesocycle, or Mediator, is not so usual as aequator, we give the same to the Terrestrial as to the Celestial, with this difference only calling it the Terrestrial aequator. SECT. II. Of the Meridians and Parallels. THe aequator( as other Circles) is divided into 360. Degrees; through every Degree( either in dead, or in imagination) is drawn a Semi-circle, which tends from one Pole to the other. These Circles are called Meridians, or Circles of Longitude in the earth; from both sides of the Aequator parallel with it, are drawn( either in truth or imagination) 90. Circles, distant from one another the space of one Degree, even to the Poles, called Parallels, or Equi-distants, or Circles of Latitude: But lest the places of Cities or Regions should be much obscured in the Globe, we ordinarily describe both the Meridians and Parallels by the decades of Degrees in the Aequator or Meridian. SECT. III. Of the ecliptic, tropics, arctic and antarctic Circles. THough the ecliptic, tropics, arctic, and antarctic Circles, do properly belong to the Celestial Globe, yet they are usually drawn in the Terrestrial Globe; because they are not a little profitable to our Understanding: CHAP. IV. Of the various distribution of Regions. SECT. I. Of Distribution according to Longitude and Latitude. GEographers, that they might express Regions, Islands, and Seas in their proper scite and proportion, have divided them by a certain measure into length and breadth. The The Length. Longitude of any place, is the arch of the Terrestrial Aequator, comprehended between two semi-meridians, traduced from one Pole to another: and is numbered from the West into the East, till it return to the same Semi-circle, through 360. Degrees. The The breadth. Latitude is the arch of the same Semi-meridian, between the Aequator and the place given, and is double: Northern in the places which are beyond the Aequator in the North; Austral in the places which are situated toward the South. Note, Note. that although in the English Globes the beginning of Longitude or first Meridian, is placed at the Easterly point of I. Gratiosa; yet divers Geographers both in their Globes and Maps differ from them in that particular: For some begin their Longitude at Pico in Teneriffa, an iceland of the Canaries; Others at the Easterly point of S. Michaels, and S. Maries; Others at Corvus and Flora; and others where they think best: But the reason why I in the new Globes placed it at the I. Gratiosa, was; because I was loth to differ( in that particular) from those Globes formerly set forth by M. William Sanderson; deeming it unfitting, and a prejudice to young Artists, to puzzle them with diversity of Longitudes, especially among our English Globes, since the labour was all one, and the place as convenient and useful for it, as any other about the Globe. Therefore that you may make those Terrestrial Globes, and Geographical Tables, made for another beginning of longitude, agree with those made for this; account the number of Degrees that the first Meridian stands more East or West then this; and for so many Degrees as it stands more Eastward, so many Degrees must you add to the Longitude, and it gives you the true Longitude according to this Position; But if the first Meridian stand more Westward, then you must cast away the number of Degrees that is contained between those two Meridians: Take an example of each. Rome according to our Position is situate in 41. Degrees of Longitude; but with them that begin their Longitude at Pico, but 31. therefore Pico being ten degrees to the Eastward of Gratiosa, you must add ten Degrees to 31. and it makes 41. the Longitude of Rome. They that begin their Longitude at Corvae and Flores, have Rome situate in about 47. Degrees of Longitude; therefore Corvae being Westward of Gratiosa, about six Degrees, you must cast away six Degrees, and there remains 41. the Longitude of Rome: And so of all other. SECT. II. Of the distribution of the Earth by Zones. ANcient Geographers divided the Globe of the Earth into Zones, Climates, and Parallels; as the Heaven is divided by four Circles( the tropic of Cancer and Capricorn, the arctic and antarctic Circles) into five parts; so the Globe of the Earth by the same Circles( subject to the Heavenly, and Analogical in every part) have they divided into five portions, which they termed Zones, or Girdles. The first Zone is comprehended between both the tropics, the Aequator passing through its middle. The second between the tropic of Cancer, and the arctic circled. The third between the tropic of Capricorn, and antarctic circled. The fourth is included in the arctic circled in the North. The fift in the antarctic circled in the South. Three of these Zones the Ancients accounted inhabitable; one comprehended between both the tropics; because the Sun passing over the heads of those that lived there, sent forth its Beams perpendicularly upon the Earth, exciting( as they believed) intolerable heat; and for this reason they called it the Torrid Zone. The two other at the Boreal and Austral Pole, they name Frigid Zones, because it is there always exceeding could; the Sun only glancing upon the earth with its most obliqne Beams; not darting it in such a rectitude as to occasion any heat. The other two( as well that bounded by the arctic circled, and tropic of Cancer, as that within the antarctic circled, and tropic of Capricorn) they name Temperate Zones; and did account[ them only] Habitable. But Experience( by the long Navigations of Spanjards, Lusitanians, and others) shows, that not only the Torrid Zone is inhabited of several People and Nations, and abounds in several kinds of Animals and Fruits; but that likewise the Frigid Zones are not in many places destitute of Inhabitants. Further, the Ancients distinguished the Inhabitants of the Zones, from the diversity of the shadows of Bodies; as into Periscii, Heteroscii, and Amphiscii. The Inhabitants of the Frigid Zone, are called by them {αβγδ}; because the shadows of Bodies are turned round in the space of 24. hours, when the Sun is circumvolved in its daily motion over their Horizon, not setting. The Inhabitants of the Temperate Zones they called {αβγδ}; because the Meridian shadows in one part of the world, bend toward either Pole; toward the Boreal, among those which dwell within the tropic of Cancer, and arctic circled; toward the Austral, among those which live within the tropic of Capricorn, and antarctic circled. Finally, those which inhabit the Torrid Zone between each tropic, they called {αβγδ}; because the Meridian shadows in divers times of the year, do fall both into the North, and South; in regard the Sun goes from both sides of their Zenith: For the shadows when the Sun is in Boreal signs, tend to the South; but when in Austral, to the North. Because of the different scite of opposite habitations, the Ancients have divided the Inhabitants of the Earth into Periaeci, Antaeci, and Antipodes. The Periaeci are those which dwell under the same Parallel, and Meridian, but in divers Semi-circles of the Meridian. Antaeci are those which live under the same Semi-meridian, but in several Parallels; one being Boreal, as much as the other is Austral. The Antipodes are those which dwell in opposite Parallels, and divers Semi-circles of the Meridian; that is, are opposed e Diametro, and have feet directly obverse to feet. With the Periaeci we communicate in the seasons of the year; as Spring, Summer, Autumn, Winter, and the temperateness of the air, the increase and decrease of days and nights, and inhabit the same Zone: We differ in this, that it is Noon with us, when Mid-night with them, & 'vice versa. With the Antaeci and us is common, Mid-day, and Mid-night, but we differ in the seasons of the year; for our Summer, is their Winter; and our longest days, are their shortest: Both of us possess the temperate Zones, but of a different condition and denomination. The Antipodes have all things happen contrary to us; as the Seasons of the year, Days and Nights; For when the Sun in the Summer makes our longest Day, it makes their shortest Night in Winter. We have the same Horizon with them, but opposite; and as oft as the Sun, Moon, and Stars rise with us, they set with them, & contra. SECT. III. Of Climates and Parallels. ACcording to the various increasments of the longest Day, the Ancients have divided the Earth from the Aequator towards the North and South into Climates and Parallels: They call that space of Earth a Climate, that is comprehended in two Circles parallel to the Aequator; so that from one to the other, the length of the greatest day may increase half an hour. Those they call Parallels, among which the longest day is increased a quarter of an hour; so that every Climate comprehends in it two Parallels. From both sides of the Aequator they number seven Climates, and denominate them from the most famous City, River, iceland, or Mountain through which the middle Parallel of the Climate is drawn. The first Boreal is extended through Meroes, an iceland of Nile, and is called {αβγδ}. The second through see, a City of Egypt; and is called {αβγδ}. The third through Alexandria, the Metropolis of Egypt; called {αβγδ}. The fourth through Rhodes, an iceland of the Mediterranean; called {αβγδ}. The fift through Rome; called {αβγδ}. The sixth through Boristhenes, a River of Sarmatia; called {αβγδ}. The seventh through the Riphean Mountains of Sarmatia; called {αβγδ}. Those Climates which are as much on the other side of the Aequator toward the South, are expressed by the same names, with the addition of this word {αβγδ}, contra; as {αβγδ}, &c. Some to these seven add two more, some again add five, and modern Geographers extend them to twenty three. Some conceive this kind of division to be useless; first, Because of that great inequality which they have among themselves. The first comprehending in its latitude 127. leagues. The ninth about 34. leagues. The last▪ which is the 23d, scarce one. Secondly, because the Longitude of the greatest days, are as soon found as the number of Climates. But if the Terrestrial Globe be at all divided into Climates, it may be done in a greater equality, by dividing each Hemisphere of the Earth on both sides of the Aequator into nine Climates of equal Latitude among themselves, by every decade of the Degrees of the Meridian, in this manner: The first Boreal Climate will begin at the Aequator, and end in the latitude of 10. degrees, and may be called Ethiopicum, because it transites the middle of Ethiopia; the second will end in the latitude of 20. degrees and is called Arabicum; because it contains a great part of Arabia foelix: the third in the latitude of 30. degrees called Egyptiacum: the fourth in the latitude of 40. degrees called Syriacum: the fift extends to the 50. degree, called Gallicum, or Italicum: the sixth, to the 60. degree, called Germanicum, or Britannicum: the seventh to the 70. degree, called Suecicum; the eighth to the 80. degree called Glaciale Boreum: the ninth even to the Pole, called Boreal, or Polare Boreum; and seven of these are habitable, the other two inhabitable; The Parallels proceed in the same manner, the number being duplicated, from the other side of the Equator, there will be made the like partition of the Climates; The first will begin at the Equator, and end in the Austral latitude of 10. degrees, and may be name Brasilianum, because sailing begond the Equator, to the West, basil is the first principal place; and is for the most part situate under this climate: The second is name Peruanum, from the region of Peru, which it comprehends; extending in latitude to 20. degrees. The third is called Paragua●cum, from that Region, extending to the latitude of 30. degrees. The fourth to the 40. degree Chiliacum, from the Kingdom of Chile. The fift to the 50. degree of latitude, Silvestre, because this tract of America is inhabited by wild and savage men: The sixth to the 60. degree Magellanicum: The seventh to the 70. degree Incognitum: The eighth to the 80. degree, Glaciale Austrinum: The ninth to the Pole, Polare Austrinum. The scite of any place will be known thus by its degrees of Latitude; as for example, Rome, Venice, and Lutetia, are situate within 40. or 50. degrees of latitude, and therefore in the fift climate; Amsterdam, and London, within 50. and 60. degrees of Latitude, and are in the sixth climate: Goa in the East-Indies in the second. The iceland of Zeilan, and Guinea, in the first, and so in the rest. CHAP. V. Of the difference, denomination, and distribution of the stars. SECT. I. Of the difference of the stars. THe ancient Astronomers, who first sought out the motions of the Heavens and Celestial Bodies, met with Stars of a double kind in the heaven, Planets errants and Fixed Stars. Inerrantes. The errants, in Greek {αβγδ}, are five, Saturn, Jupiter, Mars, Venus, Mercury,( to which if we add the Sun and Moon, they make up the Septenary number) so called, not because they are moved in an uncertain course, order, and measure; but because by their proper and different motions, either they never agree among themselves, and keep their destinated distances, or observe not the same motion and order with the fixed: The Inerrantes, or fixed stars, are not so called, because they are without motion( for according to this Hypothesis of the world we see them daily in the space of 24. hours circumvolve the earth) but because they ever keep among themselves the same distances, without any mutation; and have the like motion; These are wont to be described in the celestial Globe, the other because of their various and mutable motion, cannot be represented therein. Further as some stars seem to superate others in clarity and apparent magnitude, so by reason of their divers light they are divided into six magnitudes. The greatest and most fulgent are called stars of the first magnitude; those a little less, of the second; lesser again, of the third; fourth, and fift; The least of all, of the sixth; beside some obscure and nebulous ones: as they are all expressed in the Celestial Globe by divers characters. The Planets are discerned from the fixed stars in the heaven, thus; The fixed( especially the air being serene) always sparkle with a rapid vibration of light: The Planets,( as the Moon) sand forth immovable beams, not subject to any vibration: unless you will except Mercury, Venus, or Ma●●; who some time we perceive to sparkle forth; But that is not perpetual, nor do they sparkle with such a rapid iteration as the fixed, and therefore equal in show with the fixed stars of the first magnitude, or for the most part greater: yet are they easily discerned from them. SECT. II. Of the denomination of the stars. THe Ancients have left in their writings the number of one thousand twenty and two stars, observed by them, as well in the Boreal as Austral Hemisphere of Heaven; and that they might be the better discerned from one another, by various names they did comprehend them under forty eight Images, which are called Constellations: twelve of the chief of which constitute the zodiac: twenty and one fill the Boreal Hemisphere of Heaven: fifteen the Austral; whose names follow. XII. signs of the zodiac. 1. Aries, besides others in the horns and tail, it hath a bright star in the front. 2. Taurus hath the Pleiades, and a bright star in the Southern eye, called by the Romans, Palilicium, by the Arabians, Aldebaran; which for its excellence is commonly called, oculus Tauri. 3. geminy, show two bright ones in their heads. 4. Cancer, consists of little stars, and hath a nebulous one in the middle of the breast, called Presaepe. 5. lo, is adorned with divers fulgent stars in the neck and loins, but two more eminent then the rest, one in the breast, called Cor Leonis, Regulus, and Basiliscus; the other in the tail, which is name, Cauda Leonis. 6. Virgo, hath a most glittering star in the left hand, called Spica Virginis. 7. Libra, hath two more bright then the rest, which are called Lunces. 8. Scorpius, hath various bright stars, one eminent in the middle, called Cor Scorpii, or Antares. 9. Sagittarius, hath none eminent, except in his Bow and Arrow. 10. Capricornus, hath two in his tail more splendid then the rest. 11. Aquarius, in the end of the water, shows a bright star, called Fomahant. 12. Pisces, consists of many small stars, with a line connecting them. XXI. signs of the Northern Hemisphere. 1. Ursa Minor, beside others, hath three well known to Mariners, one in the extremity of the tail, called the North, or Pole star; because it is very near to the arctic Pole; two in the anterior part of the body, which Englishmen call the Guards. 2. Ursa mayor, hath lucid and eminent stars, called Plaustrum; four of these consisting in a body of a quadrant form; come in stead of a Chariot the three others in the tail, for the horses. 3. Draco, in his head are two bright stars. 4. Cepheus, without any notable stars. 5. Bootes Bubulcus, or Vociferator, between whose legs is a great and known star, called Arcturus. 6. Corona borealis, hath a bright star of the same name. 7. Hercules, hath a known star in the head. 8. Lyra, vulture cadens, hath a star of the name of great light and clarity. 9. Cygnus, besides, others, hath a notable one in the tail. 10. Cassiopaea, shines brightly, with five disposed stars. 11. Perseus, hath a bright star in the right side and head of Medusa. 12. Erichtonius, or Auriga, hath a most fulgent star in the left shoulder, which is called Hircus, or Capella. 13. Opiuchus, or Serpentarius. 14. Serpens Opiuchi. 15. Telum, or Sagitta. 16. Aquila, vulture volans; beside others, it hath a bright one in the shoulder. 17. Delphinus, in the form of a ring. 18. Equiculus, the section of a horse, {αβγδ}. 19. Pegasus, hath bright stars in the wings and breast. 20. Andromeda, hath a bright one in the head which with those three of Pegasus, make a just Triangle. 21. Triangulum, or Deltoton. The XV. signs of the Southern Hemisphere. 1. Cesus, or Balena, hath an indifferent lucid star in the tail. 2. Orion, enameled with many excellent stars, two of the chief are in the shoulder; three in the middle, which they call trees Reges; By us, Orions Girdle. one in the right knee▪ and the brightest in the left foot, called Rigel. 3. Eridanus, fluvius, by some Nilus; in the extreme part is a bright star, called by the Arabians Acarnar; but to us inconspicuous. 4. Lepus, hath 4. little ones in the ears. 5. Canis mayor, hath a most splendent star called Sirius; and is the greatest and brightest of all in the heaven. 6. Canicula, or Canis Minor; hath a bright star, called protion, or ante Canis. 7. Argo navis, in whose stern is a fulgent star, called Canopus. 8. Hydra hath a bright star in the breast, called Cor Hydrae. 9. Crater; imposed on the Hydra. 10. Corvus, imposed also upon the Hydra, and hath two meanly bright stars, in a straight line with the Spica Virginis. 11. Centaurus hath among other fair stars, four in the last feet, making a across; which the Spaniards and Lusitanians in their Navigations name, And we the Crosiers. El Cruzero. 12. Lupus seu fera, contiguous to the Centaurus. 13. Ara, or Thuribulum. 14. Corona australis, or Notia. 15. Piscis austrinus, or Notius, in whose mouth is Fomahant. That incomparable Scrutatour of the heavens and stars, Tycho brach, the Atlas of our age, hath corrected the canons of the fixed stars, which he could perceive in the Danish Horizon; far beyond the constitution of the Ancients; and hath enriched them with a notable accession of the fixed stars. The stars about the Southern Pole. In the part of heaven near the southern Pole, which was not manifest either to the ancient Egyptians or Grecians, nor Tycho brach; Fredericus Houtmanus living in the Isle Sumatra, hath took notice of many stars which he reduceth into 13. constellations; The 1. of which is name Phoenix. 2. Columba. 3. Musca. 4. Piscis volans. 5. chameleon. 6. Triangulum australe. 7. Apis Indica. 8. Pavo. 9. Indus. 10. Grus. 11. Toucan or Pic● Indica. 12. Hydrus. 13. Piscis, which the Spaniards call Dorado, as you may see in our Celestial Globes. Beside the stars contained in the Canons of Astronomers, in the Constellations themselves, or thereabout, appear in a winter night( the air being clear) an innumerable number of very little stars( because at that season the air is not at all illustrated with any light from the sun, as it is in the summer, and therefore the deceivableness is greater) but in the summer, they are altogether invisible. Of the Via Lactea; or milky Way. In the Sphere of the fixed stars, is an apparent broad and clear tract, compassing the heaven like a girdle, of a pale or milky colour▪ therefore called the milky way; by the greek {αβγδ}: This via Lactea, is in one place clearer whiter, and wider then in another; and in one place single, in another double: It tends from auriga towards the South, by geminy, Canis mayor, Argo; it returns back in to the North, by scorpion, Sagittarius, Opiuchus, Aquila, Cygnus, Cassiopaea, Perseus; until it come to Auriga; as you may see in the celestial Globe, where it is expressed in its proper scite. This Lactean whiteness and clearness, ariseth from a great number of little stars, constipated in that part of heaven; flying so swiftly from the sight of our eyes, that we can perceive nothing but a confused light: this the Tubus Diopticus( more lately found out) doth evidently demonstrate to us: by the benefit of which( little stars otherwise inconspicuous to our eyes) are there clearly discerned: About the Southern Pole are seen two white spots, like little clouds, coloured like the via Lactea▪ one of which is triple the latitude of the other; some Mariners call them Nubeculae Magellani. SECT. III. Of the distribution of the stars according to longitude and latitude. AS the Regions of the Earth in the Terrestrial Globe are placed according to their longitude, by the degrees of the Aequator, and according to their latitude, by the degrees of the Meridians from the Aequator to the Poles of the earth; so in like manner are the stars placed in the Celestial Globe in their proper longitude, according to the degrees of the ecliptic, and latitude, according to the degrees of the circles of longitude from the ecliptic towards its Poles. The longitude therefore of stars is the arch of the ecliptic comprehended in two Semicircles of longitude( that is which are drawn through the Poles to the ecliptic) one of which transits the head of some of the twelve signs a● the beginning of longitude, the other the very body of the star, &c. The longitudes is numbered from sign to sign, even, to the 30. degree in every one; or from the Semi-circle of longitude which transits the head of Aries, going through the whole circuit of the ecliptic even to the 360. degree. The latitude of stars is the arch of the Semi-circle of longitude drawn through the star; comprehended between the middle of the star and the ecliptic line, and is of a two fold account, viz. North latitude, and South latitude; North in those stars which go from the ecliptic into the North; South in those which incline to the South. CHAP. VI. Of the proper motion of the Sphere of fixed stars about the Axis of the zodiac. THe Sphere of fixed stars( called the eighth in respect of the seven Planetary orbs that it encompasseth) is turned by a double motion; the first called Diurnus, is made from the East, through the South, into the West, about the Axis of the world, and is finished in the space of 24. hours and taketh and carries about with it all the Planetary Spheres. Ptolomey is of opinion, that this is done by the motion of the ninth: some again by the tenth; others the seventh; which used to be called the primum mobile: Although Artists concur not in the number, yet in the mean time they agree, that the primum mobile is the cause of this motion, called Diurnus. The other motion of the fixed stars called Secundus, and Planetarum proprius, is made into the contrary angle of the world, from the West into the East upon the Axis and Poles of the ecliptic; and according to the opinion of Tycho brach, it absolves its course in 25412. yeers: after which period of years, all the fixed stars return to the places in which they at first were posited. But because this proper motion of the fixed stars is made upon the Poles of the ecliptic, hence it will First easily be understood that they are not subject to any mutation of latitude, but only longitude; as making out in every hundred years 1. degree 25. minutes, or a whole degree in 70. yeers and 215. days. Secondly it discovers the difference of the signs of the zodiac, and Dodecatemories, or places of the ecliptic; that is, why the images in the Celestial Globe, which constitute the zodiac, agree not with the Dodecatemories,( or their proper places) but Aries will go into the Dodecatemory, or place of Taurus; Taurus into the place of geminy, &c. The cause of this, is this second and proper motion of the fixed stars; by reason of which, the stars and images change their seats and places, the Dodecatemories remaining without mutation of place; as may be made manifest by comparing the observations of divers times: For about 2000. years ago, when the egyptian and graecian Astronomers were intent upon the observation of the stars, the first star in the horns of Aries was about the beginning of ♈( or the true Equinoctial colour) from which it is now receded Eastward 28. degrees, so that as on the images( at that time agreeing with the Dodecatemories of the ecliptic) they imposed also names on the signs of the zodiac from the neighbour Constellations. CHAP. VII. Concerning the motion of the Sun in the ecliptic. ALthough the Sun, and Moon and other Planets, with the eighth Sphere, are according to this Hypothesis carried about by the Primum mobile, out of the East into the West; yet every one( as the Sphere of fixed stars) hath a proper and particuliar motion to itself from the West into the East; And this the Sun absolves through the 12. signs of the zodiac▪ under the ecliptic, in a Tropical or Natural year( which is 365. days 5. hours and about 49. minutes;) and its daily motion goes near one degree, from the tenth day of March, to the 2. of June. Being Spring it passeth through Aries, Taurus, and geminy, to the Summer Solstice; from the 2. of June, to the 2. of September being Summer, it runs through Cancer, lo, and Virgo, to the Autumnal Equinox; From this time to the 2. of December, being Autumn, it passeth through Libra, scorpion, and Sagittarius, till it come to the Hyemal Solstice; the other three Capricorn, Aquarius, and Pisces, it goes through in the Winter; from December the 2. to March the 10th. till it come to the Vernal Equinox in the beginning of Aries; And hence it is clear, that the Sun transits the Equinox twice in a year; declining from it once this way, another that way. The beginnings of Cancer, and Capricorn, are called Solstices, because the Sun being( as it were) imoveable, there seem to observe its stations: yet it must not be understood of its motion through the ecliptic, but in respect of its declination from the Aequator: for part of the ecliptic viz. some degrees before and after the beginnings of Cancer and Capricorn, are almost parallel to the Aequator; so that the Sun when it transits these parts, varies little or nothing its declination, and may be therefore judged as it were immovable. The proper motion of the Sun through the ecliptic may be illustrated by this simile: set a little To represent the Sun. fly upon the Globe, so that it may go along the ecliptic line, from the West into the East; and so turn the Globe about its Axis, from the East into the West; and as oft as the Globe shall go about, the fly may go the contrary way one Or a very small matter more or less. degree; so that the Globe turning 365. times upon its Axis, from the East to the West, the fly in the mean time goeth from the West into the East through all the signs of the zodiac. Concerning the courses of the other Planets which cannot be represented in the Globe, we shall not stand to dispute; only in general acquaint you, that Saturn, being next to the fixed stars, absolves his course in the space of 30. years; Jupiter, 12. Mars, 2. Venus and Mercury( the constant Concomitants of the Sun) in 1. year; but the moon in 27. days: And all these Planets go not as the Sun, always under the ecliptic; but go now into the North, then into the South; as the way of their proper latitude requires. CHAP. VIII. Of the Horizon. THe Horizon is the circled circumscribed to our eye( as the Center,) terminating our sight of the heaven on every side; whence it is called Finitor, or Terminator visus; by the Greeks {αβγδ} and is to be considered three ways; Mathematically, Naturally, and Apparently. The Mathemathical Horizon( comprehended by the intellect rather then the eyes) divides the heaven precisely into two equal parts; the Apparent, and Latent; whose Poles are the Zenith, and Nadir, and whose Center is the same with the world; But that circular superficies which comes commonly under the name of Horizon, which runs round the Heaven, according to our sight of the earth, and divideth it into two parts, is rather to be took according to the sense of the thing, then the truth: For to speak properly, and Mathematically, this circled divides not the heaven into equal parts, because it doth not transite the Center of the world, and because the distance of the superficies of the earth from the Center,( that is the semi-diameter of the earth) is not so much, that it can any way hinder( all impediments, as hills, trees, mountaines, &c. being removed) the conspection of the very same mediety of the Heaven( for he that looks from a mountain sees more then the half of Heaven) therefore this visible circled is taken for the Horizon: And to distinguish it from the Mathematical is called diagram the Natural Horizon. Further, that the distance of the superficies of the earth from the Center, hath no sensible proportion to the amplitude of heaven, may be thus shown. In this invidiam the lesser circled described about a the Center, is the Globe of the earth: a b its Semidiameter or the distance of the superficies b to the Center a: the greater circled d f g is the Sphere of the fixed stars, distant from the Center of the earth according to Alpharganus and others at least 22612. Semidiameters of the earth, therefore a g the Semidiameter of the Mathematical Horizon drawn through the Center of the earth consists of 22612. such parts as a b the Semidiameter of the earth is one: but if from b the superficies of the earth, be drawn b e the Semidiameter of the Natural Horizon, parallel with a g: The arch g e of the difference of both orisons will not be in the circled d f g greater then 9 seconds, that is the 400. part of a degree; which quantity is accounted incomprehensible, as those which have but saluted Geometry at the threshold, are not ignorant of. The Apparent or Visible Horizon, is that space of the earth or sea, which may be beholded and seen by our eyes every way round, which extends not from the eye much further then two common leagues: For because the superficies of the earth( in plain places and at sea) is round, the eye elevated over it cannot comprehended more space then the recte cut asunder, which goes forth from the ey to the contact of the Globe on every side; as is known to all that are but meanly exercised in the optic discipline. The end of the first Book. LIB. II. ARGUMENT I. Of the setting and rising of Celestial Bodies, and other things thereto pertaining. Consisting of fifty three problems: as followeth. problem I. Of the various positions of the Sphere. ALthough the word Sphere and Globe denote almost the same thing; yet by a Sphere is commonly understood a round system, not close on every side, and firm, but consisting of such Circles wrought in it, as are imagined in the heaven; and is used by us in this description for the Celestial Globe, to distinguish it from the Terrestrial. But the heaven or the Sphere itself in respect of the Horizon is looked on by the inhabitants of the earth under a triple constitution: viz. Sphaera recta Or a Right Sphere. Sphaera Parallela Or a Parallel Sphere. and between these the Sphaera Obliqua, Or obliqne Sphere. it is called the direct Sphere, when both the Poles of the world ly upon the Horizon; and the equinoctial circled is farthest remote from it passing through the Zenith, according to the following invidiam; And in the position of this kind of Sphere, all the Celestial Bodies, Sun, Moon, Planets, and Fixed stars by the daily turning about of the heaven, directly ascend above and descend below the Horizon, because the Circles which they make in the first motion are cut by it at right angles. The constitution of such a Sphere is shown by the Globe thus, turn the brazen Meridian in the notch of the wooden Horizon, until the Poles or the extremities of the Axis touch the Horizon towards the North and South, and the equinoctial will transite the Zenith to the greatest remoteness from the Horizon; and if you turn the Globe thus placed, there will appear to your sight. 1. All the Circles stars and signs in the Globe which will ascend directly diagram to the East above the Horizon, and descend directly into the West beneath it. 2. All the stars or signs( whither they be near to the Aequator, or far of) which ascend together over the Horizon, will together likewise pass through the Meridian and be hide under the Horizon. 3. All these will spend as much time above the Horizon as they will do under it; because the Circles which they make by the turning of the Globe, are cut by the Horizon into two equal parts: And hence it is manifest, that the Sun as well in the Aequator as out of it,( towards the North or South more or less constituted,) by the daily motion of the heaven, stayeth an equal time both above and below the Horizon; and so the days are without any variation ever equal with the nights: This happens to those that dwell directly under the Aequator, without any latitude towards either Pole of the world; as the Inhabitants of the island of S. Thomas about Africa; some of the Moluccaes: and places that have the same scite in the earth. A Parallel Sphere is, when one Pole of the world is elevated above the Horizon to the Zenith; the other depressed as low as the Nadir, and the equinoctial line is joined with the Horizon, as appears in the following scheame. Therefore the stars by the turning of the heaven, neither get above the Horizon, nor go below it, but move with it always in a Parallel manner: This appears diagram thus. Turn the Globe with the brazen Meridian, so that one Pole may be in the Zenith, distant every way from the Horizon, 90. degrees; the other in the Nadir, and the equinoctial line about the Horizon: Then if you turn about the Globe, you will see. 1. All the stars, Circles, and other parts of the Globe, neither ascend above, nor descend beneath the Horizon, but be turned with it Parallelly. 2. The North Pole being elevated, as long as the Sun passeth through the Northern signs of the zodiac( from March 10. to September 12.) it goes about above the Horizon, and never sets, and so makes a constant day of six moneths; and on the contrary from September 12. to March 10.) while it goes through the Southern signs, it daily runs round beneath the Horizon, but never riseth, and so makes six moneths a continual night; this happens in those places of the earth that have 90. degrees of latitude, which is under each Pole, or in the points of the true North and South. By the obliqne Sphere is understood such a constitution of the heaven in which the Axis of the world( being neither direct nor Parallel to the Horizon) is inclined obliquely towards both sides of the Horizon; as in the scheame adjoined: Therefore all the Celestial diagram Bodies have obliqne and unequal Ascensions and Descensions towards the Horizon; and this position of the Sphere is shown by the Globe, when the Axis doth not lye on the Horizon, nor is directly elevated, but inclines obliquely North or South towards the Horizon: whence it comes to pass, that so much as one of the Poles is elevated above the Horizon on the one side, so much the other is depressed under the Horizon on the other side. From such constitution of the Globe. 1. The Aequator, and the other Circles, with the the signs and stars, will obliquely ascend above the Horizon, and descend again under it, not directly, as in the direct Sphere; nor Parallelly, as in the Parallel Sphere. 2. All the lines Parallel to the Aequator on both sides( even those which are made through the turning of the Sphere, by the Sun, stars, or other signs) you will see divided by the Horizon into unequal parts; so that of those which decline from the Aequator towards the elevated Pole, the greater part will be extant above the Horizon, the lesser obscured under it; but of those that tend towards the depressed Pole, the greater part remain under the Horizon; the lesser extant( by the turning of the Sphere) above; Hence, one may see, that when the Sun is out of the Aequator in a sign tending to the elevated Pole, it makes a great deal more of its course above the Horizon then under it, and remaines longer above the earth, making the days longer then the nights; on the contrary, when it enters the signs tending towards the depressed Pole, it spends less time above then under the Horizon, and consequently is not so long above the earth as under it, thereby making the days shorter then the nights: it is likewise manifest, that by how much the more either Pole is elevated above the Horizon, by so much the more unequally are the Circles cut; and thence is it, that there ariseth that difference that there is between the days and nights. 3. When the Sun is in the Aequator, it stays the same time above and beneath the Horizon, and so doth precisely measure out the day and the night; because the Equinoctial and Horizon( the greatest Circles) do cut one another into equal parts; so that one part of the Aequator is always extant above it, the other, latent under it; though the Pole be more or less elevated or depressed. 4. All the stars about the elevated Pole, comprehended within the circled, described in the Intersection of the Meridian and Horizon. interval of the elevation of the Pole, never set: and contrarily the other stars about the depressed Pole incirculated between the Pole and the intersection of the Meridian and opposite part of the Horizon, never rise; but those posited in the Between the two forementioned Circles of Intersection. intermediate places, rise and fall: excepting those which are in the foresaid Circles themselves, which neither set nor rise, but only move round the edge of the Horizon; such a position of the Sphere have all the Inhabitants of the earth, under whatsoever degree of latitude they dwell from the sides of the Aequator, whither Northern or Southern, until they come to the Poles themselves, where the Sphere is Parallel, as we have already said. problem II. That the elevation of the Pole is equal to the latitude of places; and does with the altitude of the Aequator make 90. degrees. FRom the constitution of the obliqne Sphere, among others, these two are worth our animadversion; first, that the altitude of the Pole is equal to the distance of the Zenith, from the Aequator; or( which is all one) to the latitude of places. 2. That the altitude of the Aequator and the Pole, make together 90. degrees, and then one being deducted from 90. degrees, the residue shows the altitude of the other. The first may be thus demonstrated by the Globe; join both Poles to the Horizon, as in the direct Sphere; and they will be without any elevation; and then the Zenith falls in the Aequator. Remove hence either of the Poles from the Horizon( for example) 10. degrees, and the Aequator will descend contrarily from the Zenith so many degrees towards the Horizon: and by how much higher the Pole is elevated so much will the Aequator be declined from the Zenith; hence it appears, that the altitude of the Pole is always equal to the distance of the Zenith, from the Aequator: or to the latitude of places in the Terrestrial Globe: The second may be known by the Globe the same way; When the Pole is elevated above the Horizon 20. degrees, the Equinoctial recedes so much from the Zenith: and is distant from the Horizon 70. degrees, the sum of which numbers added together is 90. degrees, if the Pole should be elevated 60. degrees, the Aequator declines so many degrees from the Zenith, and is above the Horizon 30. degrees; which with the 60. make 90. degrees, and so in the rest. It may be Mathematically demonstrated thus; in diagram the scheme adjoined, the Meridian is a e p d, the Horizon a g d, the Equinoctial g e, the elevated Pole p; z the Zenith, e z p the quadrant of the circled from the Aequator through the Zenith to the Pole z p d, the quadrant from the Zenith through the Pole to the Horizon: I say according to the first p d, that the elevation of the Pole is equal e z to the distance of the Aequator from the Zenith; for because the quadrants e p and z d are equal among themselves, if from both should be drawn the common arch z p, there yet remains the compliment of the two quadrants p d and e z. According to the second( I say) that e a the elevation of the Aequator, and the arch p d the elevation of the Pole, make together 90. degrees: For because the Semi-circle of the Meridian a e z p d contains twice 90. degrees, if the quadrant e z p( from the Aequator to the Pole 90. degrees) should be subducted from the Semi-circle a e z p d, the remaining arches, to wit, a e( the elevation of the Aequator) and p d( the altitude of the Pole) will make together 90. degrees; And if you subduct the altitude of one from 90. degrees, that which remaines is the elevation of the other. problem III. To find out the Longitude and Latitude of places on the Terrestrial Globe. FOr example, we will take Rome( a city of Italy) and Bantam( an island of Java in the East-Jndies) one of which is Northern the other Southern from the Aequator; for the first, turn the Globe till Rome be in the Meridian and( thrusting a quill or some such thing between the Globe and brazen Meridian, or between the Globe, and the wooden Horizon: you may make it stand there without moving to the East or West) see what degree of the Aequator touches the Meridian, and what degree of the Meridian is at Rome, and you will find the 41. degree of the Aequator to be under the Meridian for the longitude of Rome, and the 42. degree of the Meridian from the Aequator towards the North, shows the latitude thereof. For the latter to find the Longitude and Latitude of the City Bantam, turn the Globe till Bantam come to the Meridian, and you shall find for the Longitude the 140 ½. degree of the Aequator, for the latitude 6●. degree of the Meridian from the Aequator Southward; which is called South Latitude. problem IV. The Longitude and Latitude being given, how to find out any place on the Terrestrial Globe. FOr example; The city Limae in Peru, is known to lie in 300 ⅔. degrees of Longitude, and 12 l⅓. degrees of South Latitude, turn the Globe till you find 300 ⅔. degrees of the Aequator be under the Meridian, and then number Southward in the Meridian 12. degrees,( the known Latitude) and at the degree on the Globe you will find the true place of the City Limae. problem V. To find the distance of places by the Terrestrial Globe. FOr example, to know the distance between Amsterdam and Constantinople: take your compass and set one foot to Amsterdam, the other to Constantinople, and then applying your Compasses to the Aequator, count the number of degrees between the two feet, which you shall find 21, multiply them by 15.( because every degrees is 15. German miles) and there will be 315. German miles, which is the distance of the said cities; If you multiply the same degrees of distance by 20. you will find 420. French miles, if by 60. there will be 1260. Italian or English miles; and so on according to the miles used among other nations. Otherwise bring to the Meridian one of the Cities, as Amsterdam, and with the Quadrant of Altitude, cut Constantinople; then number the degrees in the Quadrant of Altitude between the two Cities and you will find 21. as before. problem VI. To rectify the Globes for any Latitude so as that it may correspond with the true situation of the world, on any place of the Earth. FIrst set the Globes on a table so that the upper superficies of the Horizon may be parallel with the true Horizon. Secondly erect the Pole so many degrees above the Horizon as the Latitude of the place contains: as at Amsterdam 52 l⅓. degrees, because that City hath 52 ½. North Latitude. Thirdly turn the Globes until the brazen Meridians agree with the lines of the North, and South in the Mariners compass,( placed in the basis of the Horizon) so that the Northern Pole may respect the North, and the Southern the South; this being done, the Axis of the Globes will agree with the Axis of the world, and all the parts on the wooden orisons( as East, West, North and South and other parts) with the places of the true Horizon. Fourthly apply the place proposed to the Terrestrial Meridian, and the scite of the Terrestrial Globe will be every way correspondent to the scite of the earth, and will show how all Regions are situated in respect of that place. If you turn the Celestial Globe from the East into the West, you will see how, and in what parts of the Horizon, the celestial bodies rise and set: which are always above the Horizon, and set not; which, always under, and never rise. problem VII. A certain plaece being given, how to find how other places are situate from it according to the angle of position. WE will take for an example the city Amsterdam, and see which way Alexandria in Egypt lieth from it; First lift the North Pole of the earth above the Horizon( according to the Latitude of Amsterdam) 52 ●/ 2. degrees, and bring Amsterdam to the Meridian; then screw the Quadrant of Altitude to the Zenith, and bring it through Alexandria, and see where it toucheth the Horizon, which you will find to be in 61. degrees from the South toward the East;( that is the part a little more Easterly then what is called in the mariners compass South East and by East) in which point of the compass Alexandria is placed in respect of Amsterdam. But if with the same diligence you number in the Quadrant of Altitude, the degrees between the Zenith,( that is Amsterdam) and Alexandria, you will have the shortest distance between both Cities, according to the greatest circled. If one place below the Horizon be distant above 90. degrees from the other, so as the Quadrant of Altitude can not reach it, as the City Limae in Peru is, do thus, Amsterdam▪ being under the Meridian, look whither Limae be more Eastward or Westward, and you shall find it in the West under the Horizon, then turn the Globe Eastward till Limae touch the Horizon: and( the Globe being fastened) you must at the opposite part of the Horizon( in a Diametrical line) make a mark on the Globe with a coal or a piece of chalk: then turn it to its former situation, that Amsterdam may be at the Meridian, and the mark will be elevated so much from the Easterly side of the Meridian above the Horizon, as is Limae below it, from the Westward side; This done apply the Quadrant of Altitude to the mark, and see where it touches the Horizon, and you will find 10. degrees from the East towards the North. Therefore in respect of Amsterdam, Limae is situated so many degrees in the opposite part of the Horizon, from the West into the South. If you seek the distance of Cities, number the degrees of the Quadrant of Altitude from the Horizon upward, even to the mark, which is here 8. to these add 90. degrees, the total length of the vertical, and you will have 98. degrees, which if you multiply by 15. you will have 1470. german miles for the distance between Amsterdam and Limae. problem VIII. How to find out the Periaeci, Antaeci, and Antipodes, in the Terrestrial Globe. BRing the place of your habitation to the Meridian, then fasten the Globe; and so many degrees as it is from the Aequator Northward, number so many degrees in the Meridian from the Aequator Southward; and you will have the place of your Antaeci. Hence turn the Globe into the East or West till 180. degrees of the Aequator are past the Meridian, then fasten it again, and the place of the Periaeci will be in that degree of the Meridian in which your habitation first stood: and the place of the Antipodes, from the Aequator Southward in the degree of the Meridian your Antaeci was in. Or you may find them out another way, Turn the Globe Eastward or Westward till the place of your habitation touch the Horizon, and note the intercepted degree; If it be in the Northern part Westward from the Meridian, then you must count so many degrees in the Southern part from the Meridian Eastward: and there will be the place of your Antipodes. problem IX. How to find out the place of the Sun in the ecliptic at any time of the year. THis may be done with the calendar in the Horizon by the column of every day in the year, thus, upon the 5. of May I would know in what degree of the zodiac the Sun is, therefore in the Horizon I look for the 5. day of May, and against it I find the 25. deg. of Taurus; which sought in the Globe shows the true place of the Sun upon the day proposed. So do with all the days of the year: but take notice that in the Bissextile the day following the 28. of February then the 29. is to be given to the first of March, the first of March to the second, &c. But we can not affirm that what is held forth in this Practical part is wholly exact for it is always exposed to some small error. Therefore that you may know the exact place of the Sun, you must look for the Suns motion in the Ephemerides which is for this end calculated by Artists. problem X. How to find the Declination of the Sun. THe Declination is the Suns recedement from the equinoctial line, and is two-fold, Northern and Southern: Northern when the Sun is in signs Northward from the equinoctial; Southern when in signs Southward from the Equinoctial: therefore that we may know how far it is declined Northward or Southward, on any day propounded, we will take for example April 22. and Nov. 2. and first seek in the 8. Probl. the Suns place in the ecliptic the two and twentieth of April and you will find it in the 12. deg. of Taurus a Northern sign, apply this to the Meridian and count in it the number of degrees from the Aequator, and you will find 15 ½. deg. for the Northern Declination of the Sun that day: by the same problem the Suns place is found, Nov. 2. to be in the 19. deg. of scorpion, a Southern sign, join it therefore to the Meridian, and number the degrees of the Meridian from the place of the Sun to the equinoctial, and you will have 17 ½. deg. for the Southern Declination of the Sun that day. But the Suns Declination may be found out with more certainty by Astronomical Tables made for that purpose. problem XI. To find the Declination of any Star. THe Declination of the stars( as of the Sun) is two fold North and South, North in those which decline from the Aequator into the North, and South in those which decline from the Aequator into the South: which that you may learn by the Celestial Globe, join the star( whose Declination you examine) to the Meridian, and in the Meridian number the degrees from the Aequator Northward or Southward, until you come to the star, and the number of the degrees is the Declination sought for. Example I. I would know the Declination of the star in the left eye of Taurus called Aldebaran, therefore I turn the Globe till the star come to the Meridian, and numbering from the Aequator to the place of the star Northward, I find its North Declination 15 ¾. deg. Example II. If you would know the Declination of the star in the left foot of Orion, called Rigel, bring it to the Meridian and numbering from the Aequator Southward you find its South Declination 8 ⅔. deg. and so in others. The difference of the Declination of the Sun and stars consists chiefly in this, the Sun doth very swiftly vary its Declination, by reason of its speedy motion through the ecliptic, by which it goes every month through a whole sign of the zodiac, but the variation of the Declination of the fixed stars scarce becomes sensible in a long tract of time, because of their exceeding slow motion about the Poles of ●●e zodiac; yet in time it doth happen that some declining not very far into the North from the Aequator transfer themselves by their proper motion into the South, and contrarily others that have but small South declination do an length become Northern. But because it is difficult to know the declination of the fixed stars, and the Sun, exactly by the Globe, we have added a Table of the Declination of certain stars, according to the accurate observations of Tyeho brach; calculated for the years 1635. and 1650. A Table of the Declination of 76. principal Stars: distinguished into 5. columns. The first of which comprehends the names of the stars. The second their Declination to the year 1635. The third their Declination to the year 1650. The fourth by the letters N. S. shows whither the Declination be North or South. The fifth denotes the visible magnitude of the stars. In the XII. signs of the zodiac. ARIES. Declinat. an. 1635. Declinat. an. 1650.   Magni●ude. deg: min: deg: min:   The bright Star in the head 21. 43 21. 48 N 3 TAURUS.         The Southern eye Aldebaran 15. 43 15. 46 N 1 In the extremity of the Northern horn 28. 15 28. 16 N 2 In the extremity of the Southern horn 20. 53 20. 54 N 3 geminy.         The brightest in the feet 16. 40 16. 39 N 3 In the Northern head, Castor 32. 37 32. 36 N 2 In the Southern head, Pollux 28. 51 28. 49 N 2 CANCER.         The cloudy star in the breast called Praesepe 20. 55 20. 53 N   lo.         The lions heart, Regulus 13. 41 13. 39 N 1 The midst and brightest in the neck 21. 40 21. 36 N 2 The brightest in the back 22. 32 22. 26 N 2 The lions tail 16. 36 16. 32 N 1 VIRGO.         In the Northern wing, Vindemiatrix 12. 57 12. 53 N 3 The virgins girdle 5. 26 5. 20 N 3 Spica Virginis 9. 12 9. 17 S 1 LIBRA.         In the Southern Scale 14. 28 14. 32 S 2 In the Northern Scale 7. 58 8. 2 S 2 SCORPIUS.         The Scorpions heart, Antares 25. 32 25. 34 S 1 SAGITTARIUS.         The most Oriental in the head 21. 32 21. 32 S 4 CAPRICORNUS.         The more Northern of the 2. in the horns 13. 34 13. 32 S 4 AqUARIUS.         The left shoulder 7. 6 7. 2 S 3 The right shoulder 2. 3 1. 59 S 3 The last in the effusion of the water, Fomahant 31. 28 31. 24 S 1 PISCES.         In the fore part of the head of the Southern fish 1. 18 1. 23 N 4 In the Northern signs.         URSA MINOR.         The Polar star, Alcuraba 87. 21 87. 26 N 2 The bright one in the shoulder 75. 43 75. 39 S 2 URSA MAIOR.         The more Northern of the antecedent ones in the Plaustrum 63. 43 63. 38 N 2 The more Southern 58. 20 58. 15 N 2 The Northern of those following in the same Square 59. 4 58. 58 N 3 The Southern of the same 55. 45 55. 40 N 2 The first of the 3. in the tail called Horses 57. 59 57. 54 N 2 The middle 56. 52 56. 47 N 2 The last of the tail 51. 11 51. 6 N 2 DRACO.         The brightest in the head 51. 36 51. 36 N 3 CEPHEUS.         The bright one in the Girdle 68. 58 69. 3 N 3 BOOTES.         The left shoulder 39. 53 39. 43 N 3 The bright one in the hem of the garment, Arcturus 51. 8 11. 4 N 1 The Northern Crown.         The bright one in the Crown 27. 59 27. 55 N 2 HERCULES.         That in the head 14. 52 14. 51 N 3 vulture CADENS.         The brightest called Lyra 38. 29 38. 30 N 1 CYGNUS.         That in the breast 39. 7 39. 10 N 3 The bright one in the tail 44. 1 44. 3 N 1 CASSIOPEA.         That in the breast 54. 33 54. 38 N 3 In the hippe 58. 45 58. 50 N 3 In the leg 58. 18 58. 24 N 3 The bright one in the buttock 57. 9 57. 15 N 3 PERSEUS.         The bright one on his side 48. 29 48. 32 N 2 the Northern and bright one in the head of Medusa, Algol 39. 30 39. 34 N 3 AURIGA.         The bright one in the left shoulder, Capella 45. 34 45. 35 N 1 That in the right shoulder 44. 51 44. 52 N 2 SERPENTARIUS or Ophiuchus.         In the head 12. 53 12. 52 N 3 The antecedent in the left hand 2. 44 2. 46 N 3 In the left knee 9. 44 9. 46 N 3 In the right knee 15. 11 15. 12 N 3 The bright one in the serpents head 7. 39 7. 36 N 3 AqUILA.         In the tail 13. 23 13. 24 N 3 The bright one in the shoulder 7. 58 8. 0 N 2 PEGASUS.         In the mouth 8. 13 8. 18 N 3 The bright one in the leg, Scheat 26. 7 26. 12 N 3 In the shoulder, Marcab 13. 16 13. 21 N 2 In the extremity of the wing 13. 9 13. 15 N 2 ANDROMEDA.         In the head 27. 5 27. 11 N 2 In the girdle 33. 43 33. 48 N 2 In the Southern foot 40. 33 40. 38 N 2 In the Southern signs.         coetus.         The bright star in the mouth 2. 37 2. 41 N 2 The Northern in the tail 10. 50 10. 44 N 3 The Southern in the tail 20. 1 19. 55 N 3 ORION.         The left foot, Rigel 8. 40 8. 38 N 1 The left shoulder 5. 58 5. 59 N 2 The antecedent in his Girdle 0. 36 0. 35 S 2 The middle 1. 27 1. 26 S 2 The following and last 2. 10 2. 9 S 2 The right shoulder 7. 17 7. 18 N 2 CANIS MAIOR.         The most splendid in the mouth, Sirius 16. 12 16. 13 S 1 CANIS MINOR.         In the hinder leg, a bright one called protion 6. 8 6. 6 N 2 HYDRA.         The Hydraes heart 7. 5 7. 9 S 2 From this Table the Declinations of years may be taken, if you use the difference of the Declinations according to year. As if I would know the Declinanation of the Polar-star for the year 1639. I take the Declination of the year 1635. 87. deg. 21. min. and the Declination for 1650. which is 87. deg. 26. min. The difference of these numbers being proportionated to the year 1639. the Declination is 87. deg. 22 ½. min. The Declination in 15. years being 1 min. the Declination in 4 years is 1 l⅓ which added to the number of the year 1635. makes it just 87. deg. 22 l⅓. min. problem XII. Of the Altitude of the Sun and Stars; and how they may be known. BY the Altitude of the Sun Stars or or other points of heaven, is to be diagram understood their distance from the Horizon toward the Zenith; which by divers Instruments as Quadrants Astrolabes and the Jacobs staff, may be observed. By the Quadrant you must proceed thus: The right side A B, in the invidiam is placed on the level parallel to the Horizon, but the Circular side K D H is turned towards the Sun, and the Index F C is lifted up and down until the Sun pierce through the slits of the sights, and then the extremity of the Index F shows the degrees of the Altitude of the Sun, to be numbered in the arch from H upwards into D and F. Otherwise, thus: The strait side diagram of the Quadrant A B is placed parallel to the Horizon, and the circular side averse from the Sun: The Sun therefore passing through each sight, the Index show the arch of the altitude of the Sun to be numbered downward from B to C. Or thus: diagram We use the movable Quadrant with the fixed sights placed on either side as A B, and the thread with the perpendicular C hanging out of the center, we turn the Quadrant up-wards and down-wards until the Sun pass through the former sight into the hindermost, and then the thread shows the arch of the Altiude of the Sun to be numbered from E to C. If the altitude of a Star is to be took, instead of the irradiation of the Sun, we comprehend the Star by an ocular aspect, through the sights, and the Index or thread, as before, shows the altitude sought for: but at Sea where one may freely behold the Horizon, we use the Jacobs staff to take the altitude of the Sun or Stars; thus, joining the end of the staff to the eye, we move the Transum to and fro, till the eye perceive the Horizon, through the lower term and through its upper the center of the Sun or star, and then we take the degrees noted in the Index, and cut off from the Transum, for the altitude sought for. problem XIII. To find out the altitude of the Pole, by the stars about the Pole. SHould the Pole not be the Mathematical but visible point, its altitude might be found the same way that the Suns or stars are by the Quadrant Astrolabe or Jacobs staff: but because it cannot be seen, other means must be used that the altitude may be obtained: Therefore take by the 12 problem the altitude of any star about the Pole provided it sets not so often as it goes beneath the Pole, and join it to the Meridian according to your observation, either above or beneath the Pole, and from the star number downward in the Meridian the degrees of the altitude observed, and bring that degree to the Horizon; and then the Pole in the Globe will be elevated so many degrees above the Horizon as is the Pole of the Heaven in the place of your habitation. Example. I. I take the Star called dub in the back of Ursa mayor, the Northern of the two hindermost wheels of the Plaustrum Majores, being very low under the Pole; whose altitude above the Horizon I admit to be 12. deg. Therefore that Star I join to the Meridian under the Pole of the Globe, and numbering downward from that Star 12. deg. I bring those 12. degrees to the Horizon, which being done I number again from the Pole downward to the Horizon, and I find 38. degrees of the Meridian and 17. min. for the altitude of the Pole at the place in which the observation was made. Example. II. I allow the same Star to be above the Pole, and to have the altitude above the Horizon of 66. deg. 30. min. Therefore I join the Star to the Meridian above the Pole in the North, and number from thence downward in the Meridian 66½. deg. which I bring to the Horizon; and then numbering from the Pole to the Horizon, I find the intercepted deg. of the Meridian to be to 40. and 13. min. therefore I say the altitude of the Pole was so much in the place of the observation. Yet this may bee with more facility wrought by numbers, thus, Seek in the 11. problem for the Declination of the Star observed, as here it is the Northern of the last wheels of the Plaustrum, and you will find 63. deg. 43. min. The compliment of which to 90 deg.( or the distance of the Star from the Pole) is 26. deg. 17 min. which added to the altitude 12. degrees( observed in the first Example) you shall have as before the altitude of the Pole 38. deg. 17. min. or subtract the Declination and its compliment to 90. from the altitude observed in the last Example; and you will find the same altitude of the Pole 40. deg. 13. min. problem XIV. To find the altitude of the Pole by the Stars near the Equinoctial. FIrst observe the highest altitude of any Star; and then seek the Star observed in the Globe and bring it to the Meridian, then count the numbers of the degrees of the Stars altitude in the Meridian, from the Star downward, and bring that number to the Horizon, and the Pole of the Globe will be of the same altitude as the Pole of heaven is. Example. I. I imagine the Meridian altitude of the Star in the South eye of Taurus, called the bulls ey, or Aldebaran, to be 50. deg. turning the Globe I bring the Star to the Meridian, and move the Meridian through the notch of Horizon, till there be 50 deg. between the Star and the Horizon, and then the Pole of the Globe is so much above the Horizon as is the Pole of the world, to wit 55. deg. 43. min. Example. II. I allow the Meridian altitude of Sirius( a Star in the great Dogs chaps) to be 20. deg. then I bring the Star to the Meridian, and count downward from it 20 deg. which 20th. degree in the Meridian I bring to the Horizon, and I find the North-pole above the Horizon 53. deg. 48. min. but these are as easily done by numbers, thus Example. I. Seek in the 2. problem the Declination of Aldebaran, and you will find it 15. deg. 43. min. Northward from the Equinoctial▪ subtract that from the altitude observed, 50. deg.( because the Star is so many deg. higher then the Equinoctial) and there will remain 34. deg. 17. min. for the Meridian altitude of the Equator, and if you subduct the Meridian altitude of the Equator from 90. deg. there will rest 55. deg. 43. min. for the elevation of the Pole, according to the 2. problem. Otherwise add the Declination( 15. deg. 43. min.) to the compliment of the altitude observed 40. deg. the sum makes 55. deg. 43. min. for the distance between the Equinox and the Zenith, which his equal to the altitude of the Pole. Example. II. Look for the Declination of Syrius the brightest star in Canis mayor by the 2 problem and you will find it 16. deg. 12. min. add those to the altitude observed of 20. deg. because the star declines so much from the Equinoctial Southward, and you will have for the altitude of the Equinoctial 36. deg. 12. min. which being substracted from 90. deg. there remain 53. deg. 48. min. for the altitude of the Pole. Otherwise subtract the Declination of 16 deg. 12. min. from the compliment of the given altitude( 70. deg.) and there will remain 53. deg. 48. min. for the distance between the Zenith and the Equinoctial, which is equal to the altitude of the Pole. problem XV. How to find the altitude of the Pole by the Sun. FIrst take the Meridian altitude of the Sun, then by the 9. problem seek its place in the zodiac, and bring it to the Meridian in the South, and number in the Meridian downward the Altitude observed, and apply that number to the Horizon, and the Pole of the Globe will be elevated as the Pole of heaven. Example. I. april 22. The Meridian altitude of the Sun is observed to be 48. deg. and its place found by the 9. problem to be in the 12. deg. of Taurus, I bring it to the South part of the Meridian, and numbering downward the observed altitude of 48. deg. I bring that term of the numeration to the Horizon, and find the Pole, in the North to be elevated 57. deg. ●0. min. This practise by the Sun, and the Stars near the Equator may be absolved by numbers, thus: the Sun being as before in a Northern sign, I find on the 22. of april by the 10. problem, its North declination 15. deg. 30. min. which I deduct from the observed altitude of 48. deg. and there remains 32. deg. 30. min. for the altitude of the Equator; which 32. deg. 30. min. subtract from 90. and there rests 57. deg. 30. min. for the altitude of the Pole. Example II. Now the Sun being in a Southern sign, I find its Meridian altitude 18. deg. and its Declination by the 10. problem 17. deg. 11. min. which I add together, and there will be 35. deg. 15. min. for the altitude of the Equator: the compliment of which to 90. deg. is 54. deg. 45. min. which is the altitude of the Pole. Otherwise: If the North Declination 15. deg. 30. min. be added to the compliment of the observed altitude, which is 42. deg. there are 57. deg. 30. min for the distance of the Zenith from the Equator, which by the 2. Prob. is equal to the altitude o the Pole. Or if we deduct the South Declination of 17. deg. 15. min. from 72. the compliment of the observed altitude,( 18. deg.) we shall find 54. deg. 45. min. for the distance between the Zenith and Equator; which is equal to the altitude of the Pole. This manner of working is used when both the Sun and Equinoctial decline from the Zenith; towards either North or South: but in those parts of the Earth whose Zenith it between the Equinoctial and the Sun, the compliment of the Declination of the Sun to 90. deg. is substracted from the altitude found out, and the residue is the very altitude of the Pole: If the Sun be North from the Zenith, the North-pole is elevated; if South the South-pole: which appears by the Globe, if the Poles are depressed until the Zenith be placed in the middle between the Equinoctial and the place of the Sun. problem XVI. How to find out the altitude of the Pole, by the beams of the Sun. LET the Globe be placed by the sixth Problem parallel with the Horizon, so as that the four corners( viz. East West North and South) of the Horizon may agree with the four corners of the World; then to the degree of the ecliptic the Sun is in that day, fasten with a little wax some small perpendicular, as the Spherick Gnomon, or a pin, but you must fasten it so as that it may cut the superficies of the Globe on every side at right Angles; that is, that the top of the perpendicular decline not more to one side of the Globe then to the other: then bring the degree of the ecliptic the Sun is in to the Meridian; and waiting till full noon viz. that the Sun in the heaven be full in the South which you shall know by the shadow, for then it will not be on either side of the Meridian, but directly under it: turn the Globe through the notch of the Horizon, upwards or downward till the Spherick Gnomon or perpendicular project no shadow on any side of it, but seems to stand as it were upon the very shadow itself; and then the Pole of the Globe will be elevated so many degrees as is the Pole of the world in the heaven itself. problem XVII. How the Suns Declination may be found by its beams, with its place in the ecliptic. HAving by the last problem found the altitude of the Pole, you are to take care that the Globe be not moved from its former situation, but that the Horizon and corners of it respond with the Horizon and corners of the World, as in the last problem: then at full Noon you must place the Spherick Gnomon or perpendicular, upon that degree of the brazen Meridian that the Sun can give no side-waies shadow to, but that the shadow may be just under the perpendicular; and the degree of the Meridian the perpendicular is at is the degree of the Suns declination, whether Northward or Southward from the Equinoctial: but you must be sure the perpendicular cut the superficies of the Globe on every side at right Angles, when you make this operation. Then turn the Globe till some degree of the ecliptic lie directly under the observed degree of the Meridian; and that will be the place of the Sun in the ecliptic for the day proposed. Note. From the 12. of June to the 12. of December the descending signs of the zodiac are to be used in this problem; which are Cancer, lo, Virgo, Libra, scorpion, Sagittarius, from the 12. of December to the 12. of June, the ascending signs Capricorn, Aquarius, Pisces, Aquarius, Pisces, Aries, Taurus, geminy. problem XVIII. To find in what part of the Horizon the Sun and stars ascend and descend. TUrn the Globe( rectified for the altitude of the Pole of your place) until the deg. in which the Sun is at the time proposed touch the Horizon on the East side, and that is the place in which the Sun rises; or in the West side, and that shows the place in which the Sun sets. The like way is to be observed for the fixed stars. An Example for the Sun. I would know May 15. in what part of the Horizon the Sun rises and sets at Amsterdam: therefore I elevate the Pole for the altitude of that City 52. deg. 23. min. and by the 9. problem I find the Sun that day in the 4. deg. of geminy: then I seek that degree upon the Globe, and bring it to the East side of the Horizon, and I find it decline from the true East 32. degrees towards the North; which is the place of the Commonly called the Suns Amplitude. Suns rising: and because it wanteth somewhat of the point called northeast and by East; therefore I say the Sun riseth a little more Eastward then is the point called northeast and by East, aforesaid. Now to find the place of the Suns setting, apply the same deg. of the ecliptic to the West-side of the Horizon,& you shal find the sun sets 32. deg. from the West, Northward: it being a little more Westward then the point called North-West and by West. An Example of the Stars. I would know in what corner of the World( as to Amsterdam) the bright star in the left foot of Orion called Rigel rises and sets: Therefore the Globe being rectified as before, I join the Star to the East side of the Horizon, and it points at 14. deg. 18. min. from the East, Southward; which being somewhat to the Southward, of East and by South, therefore that star rises between the points called East and by South, and East-South-East. Then turning the Star to the West side of the Horizon, I find it set 14. deg. 18. min. from the West towards the South. problem XIX. Of the various ascensions and descensions of the Sun, and Stars, and how they may be found. BY the ascensions of the Sun Stars or other points of heaven, is understood the Equinoctial degree( numbered from the head of Aries) with which they ascend above the Horizon: By the descension the degree of the Equator with which they descend beneath the Horizon: each is twofold, Direct, and obliqne. Right Ascension. The Right ascension of the Sun, Stars or any other point, is the degree of the Equator with which it riseth in a direct sphere and is always equal to the direct descension for by the 1. problem all the signs of heaven which in a direct sphere ascend together above the Horizon, do apply themselves also together to the Meridian, and descend together beneath the Horizon. And these ascensions and descensions are ever uniform, because the disposition of the direct sphere is onely one. Now to find the Right ascension, bring the point proposed to the Meridian, and the number of degrees cut by the Meridian in the Equinoctial, from the beginning of Aries to the degree cut, will be the Right Ascension and Descension of that sign. For example. I. In the Sun. I would know the right ascension of the Sun June 27. when its place in the ecliptic is by the 9. problem the 15. deg. of Cancer. Therefore I bring that degree to the Meridian, then looking in the Equinoctial line, I find 106. deg. 17. min.( numbering from the beginning of Aries, or Vernal section) cut by the Meridian; and so much therefore is the Right Ascension of the Sun, for the day proposed. An Example in the Stars. To know the Right Ascension of Arcturus( a bright Star in the hem of Bootes garment,) I apply the Star to the Meridian, and find 209. deg. of the Equator 48. min. to be under it for its Right Ascension. obliqne Ascension. The obliqne Ascension of any point, is the deg. of the Equinoctial ascending with it above the Horizon, in the obliqne sphere. The obliqne Descension is the deg. of the Equator which descends with any point proposed, beneath the Horizon in the obliqne sphere: These Ascensions and Descensions are various, and changed according to the latitudes of the places of the earth, as the Axis of the World is inclined more or less from the Zenith to the Horizon. Therefore that you may find the obliqne ascension, rectify the Pole of the Globe to the altitude of the Pole of your place, and apply the point whose ascension is sought for, to the East side of the Horizon; and the deg. of the Equator intersected by the Horizon will be the obliqne ascension of the point sought for: And if you desire to have the the obliqne descension bring it to West, side of the Horizon, and the degree of the Equator cut by the Horizon in the West, shows the obliqne descension thereof: An Example in the Sun. On June 27. when the Sun is in the 15. deg. of ♋. I would know its obliqne ascension and descension at Amsterdam, whose latitude is 52. deg. 23. min. Therefore elevating the Pole of the Globe to that altitude, I turn the 15. deg. of Cancer to the East side of the Horizon, and I find 76. deg. 15. min. of the Equator cut by the Horizon, which is the obliqne ascension of the Sun at the day proposed: Then turning the place of the Sun to the West side of the Horizon, I find 136. deg. 19. min. of the Equinoctial to descend with it; and so much is the obliqne descension of the Sun. An Example in the Stars. The obliqne ascension of Arcturus is to be found for the City of Amsterdam: Therefore the Pole being elevated for the North altitude of 52. deg. 32. min. I join the Star to the East side of the Hoizon, and with it I find the Horizon cut 179. deg. 42. min. of the Equinoctial; therefore I say the obliqne ascension of Arcturus is 179. degrees 42. min. Then I turn the Globe till the Star touch the Horizon in the West, and with it I find 239. deg. 29. min. of the Equator descend, which is the obliqne descension of Arcturus. The like is to be observed in all other stars, or points in the heaven. A Table of the Right Ascensions of the chief fixed Stars: for the years 1635. and 1650. In the XII. signs of the zodiac. ARIES. 1635. 1650. M●gnitude. deg: min. deg: min: The bright Star in the head 26. 43 36. 55 3 TAURUS.       The Southern eye Aldebaran 63. 47 64. 0 1 In the extremity of the Northern horn 75. 50 76. 4 2 In the extremity of the Southern horn 78. 58 79. 11 3 geminy.       The brightest in the feet 94. 9 94. 22 2 In the Northern head, Castor 107. 45 108. 1 2 In the Southern head, Pollux 110. 46 111. 0 2 CANCER.       The cloudy star in the breast called Praesepe 124. 51 125. 4 Neb lo.       The lions heart, Regulus 147. 14 147. 27 1 The midst and brightest in the neck 149.55 150. 8 2 The brightest in the back 163. 40 163. 53 2 The lions tail 172. 37 172. 59 1 VIRGO.       In the Northern wing, Vindemiatrix 191. 3 191. 14 3 The virgins girdle 189. 20 189. 32 3 Spica Virginis 196.32 196.44 1 LIBRA.       In the Southern Scale 217. 43 217. 56 2 In the Northern Scale 224. 22 224. 35 2 SCORPIUS.       The Scorpions heart, Antares 241. 50 242. 4 1 SAGITTARIUS.       The most Oriental in the head 282. 4 228. 17 3 CAPRICORNUS.       The more Northern of the 2. in the horns 299. 27 299. 39 3 AqUARIUS.       The left shoulder 318. 5 318. 17 3 The right shoulder 326. 47 326. 59 3 The last in the effusion of the water, Fomahant 339. 17 339. 28 1 PISCES.       In the fore part of the head of the Southern fish 344. 36 344. 47 4 In the Northern signs.       URSA MINOR.       The Polar star, Alcuraba 7. 10 7. 47 3 The bright one in the shoulder 222. 52 222. 58 2 URSA MAIOR.       The more Northern of the antecedent ones in the Plaustrum 160. 12 160. 27 2 The more Southern 159. 46 160. 1 2 The Northern of those following in the same Square 179. 18 179. 30 3 The Southern of the same 173. 32 173. 44 2 The first of the 3. in the tail, called Horses 189. 25 189. 35 2 The middle 197. 16 197. 25 2 The last of the tail 203. 16 203. 25 2 DRACO.       The brightest in the head 267. 4 267. 9 3 CEPHEUS.       The bright one in the Girdle 320. 54 320. 57 3 BOOTES.       The left shoulder 214. 24 214. 33 3 The bright one in the hem of the garment, Arcturus 209. 48 209. 59   The Northern Crown.       The bright one in the Crown 229. 49 229. 58 2 HERCULES.       That in the head 254. 30 254. 40 3 vulture CADENS.       The brightest called Lyra 276. 9 276. 17 1 CYGNUS.       That in the breast 302. 20 302. 28 3 The bright one in the tail 307. 15 307. 23 1 CASSIOPEA.       That in the breast 5. 4 5. 17 3 In the hippe 8. 51 9. 4 3 In the leg 15. 36 15. 50 3 The bright one in the buttock 357. 31 357. 42 3 PERSEUS.       The bright one on his side 44. 33 44. 46 2 The Northern and bright one in the head of Medusa, Algol 41. 12 41. 25 3 AURIGA.       The bright one in the left shoulder, Capella 72. 25 72. 44 1 That in the right shoulder 83. 20 83. 37 2 SERPENTARIUS or Ophiuchus.       In the head 259. 30 259. 40 3 The antecedent in the left hand 238. 54 239. 2 3 In the left knee 244. 18 244. 30 3 In the right knee 252. 7 252. 15 3 The bright one in the serpents head 231. 38 231. 50 2 AqUILA.       In the tail 282. 13 282. 24 3 The bright one in the shoulder 293. 16 293. 28 2 PEGASUS.       In the mouth 321. 37 321. 49 3 The bright one in the leg, Scheat 341. 34 341. 45 3 In the shoulder, Marcab 341. 41 341. 52 2 In the extremity of the wing 358. 40 358. 52 2 ANDROMEDA.       In the head 357. 26 357. 37 2 In the girdle 12. 19 12. 32 2 In the Southern foot 25. 26 25. 40 2 In the Southern signs.       coetus.       The bright star in the mouth 40. 51 41. 2 2 The Northern in the tail 0. 16 0. 28 3 The Southern in the tail 6. 18 6. 26 3 ORION.       The left foot, Rigel 74. 18 74. 20 1 The left shoulder 76. 26 76. 38 2 The antecedent in his Girdle 78. 25 78. 36 3 The middle 79. 28 79. 39 3 The following and last 80, 35 80. 48 3 The right shoulder 83. 55 84. 7 2 CANIS MAIOR.       The most splendid in the mouth, Sirius 97. 16 97. 26 1 CANIS MINOR.       In the hinder leg, a bright one called protion 110. 5 110. 17 2 HYDRA.       The Hydraes heart 137. 27 137. 48 2 The Right ascensions of the intermediate years may be easily collected from this table, by allowing a proportionable space according to the year given: as for example, I would know the Right Ascension of Arcturus 1642. Therefore because the Right ascension 1635. is 209. deg. 48. min. and in 1650. 209. deg. 59. min. the difference in 15. years is 11. min. The year 1642. exceeds the year 1635. 7. yeares, therefore by the rule of proportion if 15. years give 11. min. then 7. gives 2/ 15. min. add these to the Right Ascension of 1635. and you will have the Right Ascension of Arcturus 1642. 209. deg. 53. 2/ 15. min. and so for any other star. problem XX. To find what degree of the ecliptic ascends with any star above the Horizon, in a direct Sphere. THis operation is very like that by which we find the Right Ascension, and hath this difference onely, that the zodiac is used in stead of the Aequator. As for example, I join Arcturus to the Meridian, and find 2. deg. of scorpion, come to the Meridian with it, therefore doth Arcturus ascend and descend in a direct Sphere. problem XXI. To find what degree of the zodiac rises or sets with any star, in an obliqne Sphere. rectify the Globe for the Altitude of the Pole of your place, and apply the proposed star to the East side of the Horizon, and you shall see what degree of the zodiac rises with the star: Then turn the star to the West side of the Horizon, and you may see what degree of the zodiac sets with it. problem XXII. How to know the hour of the rising and setting of the Sun, in any Latitude, every day of the year. choose a place of known latitude, as Amsterdam,( which city may serve in stead of all,) and inquire what hour the Sun riseth and sets on the 20. of july: first rectify, the Globe for the Altitude of the Pole at Amsterdam, and bring lo 7. deg.( the place of the Sun) to the Meridian,) then bring the Horary Index to the 12. hour, and turn the Globe till that degree touch the Horizon in the East, and the Index will point at 17▪ min. past 4. a clock, for the rising of the Sun: or turn the Globe till the place of the Sun touch the Horizon in the West, and the Index will show the 7. hour 43 min. after noon, for the setting of the Sun the day proposed. Because the equinoctial contains 360. deg. which always in a natural day of 24. houres pass through the Meridian, to wit, every hour 15. deg. and in every minute of time the fourth part of a degree. Therefore in all problems, by the benefit thereof, the time may be found with more certainty then by the Index of the Horary circled, after this manner; in stead of an example let the problem proposed be taken to find the hour of the setting and rising of the Sun, on july 20. Apply the place of the Sun( which is the 7. deg. of lo) to the East side of the Horizon, and note the degree of the Aequator which is cut by the Meridian and you shall find 13. deg. 33. min. from the beginning of Aries, then turn the Globe till the place of the Sun touch the Meridian; and see in the Aequator what degree is under the Meridian, and you shall find 129. deg. 15. min. so that from the rising of the Sun till noon 115. deg. 42. min. of the Aequator shall pass through the Meridian; which 115. divide by 15.( because 15. deg. make one hour) and you will have 7. hours, and the remaining degrees, which are 10. deg. 52 min. multiply by 4.( because every degree is 4. minutes of time) and there will more-over arise 43. horary minutes: reduct these 7. houres 43. min. from 12. the fore-going mid-night and there will remain 4. houres 17. min. for the time of the rising of the Sun. Now to find the hour of Sun-set join the Suns place to the Meridian, and you shall see 129. deg. 15. min. of the Equinoctial under it. Then turn the Globe till the place of the Sun touch the Horizon in the West, and you shall see the Meridian cut 244. deg. 57. min. so that in the mean time 115. deg. 42. min. of the Aequator passes through the Meridian; divide these by 15. and multiply the remainder by 4. and there will be as before 7. houres 43. min. for the time that the Sun sets after noon. To find the same otherwise by the obliqne Ascensions. The Ascentional difference( that is the remainder of one that is substracted from the other, be it either the Right Ascension from the obliqne, or the obliqne from the Right) reduced into hours, must have 6. hours added to it, if the Sun be Northerly from the Aequator; but if Southerly from the Aequator, it must be substracted from 6. and that shows the time between noon, and the rising or setting of the Sun. For an example of both, we will take july 20. and October 26. On the 20. of july the Sun being in the 7. deg. of lo, its Right Ascension is found by the 19. problem to be 129. deg. 25. min. its obliqne 103. deg. 33. min. the difference between both is 25. deg. 52. min. which makes by the foresaid rule 1. hour 43. min. and that being added to 6. houres( because the Sun is North from the Aequator) gives 7. houres 43. min. for the time of the Suns rising that day before noon, and setting after noon. On the 26. of Octob. the Sun is found by the 9. problem to be in the 13. deg. of scorpion, and its Right Ascension by the 19. problem 220. deg. 32. min. the obliqne Ascension 199. deg. 1. min. the Ascensional difference is 21. deg. 31. min. which makes one hour 26. min. which being deducted from 6. houres, because the Sun is Southerly from the Equinoctial there remains 4. houres 34. min. for the time which the Sun rises that day before noon, and sets after noon. problem XXIII. To know the length of days and nights, at any place and time. THat may be sufficiently understood by the former problem, for if the time from noon to the setting of the Sun 7. houres 43. min. should be doubled or added to the space of time between the rising of the Sun and noon, there are 15. houres 26. min. for the length of the day which being deducted from 24. houres, there remain 8. houres 34. min. for the length of the night. Otherwise. Bring the degree the Sun is in( as here it is in lo 7.) to the East side of the Horizon, and the Index to the 12. hour towards the South, and turn the Globe till the degree of the Sun touch the Horizon in the West, and count the hours from the 12. in the South to the Index; and you shall find 15. hour 26. min. which is the length of that day; and the remainder of 24. is the length of the night. Or bring the place of the Sun to the West side of the Horizon, and the Index to the 12. hour, then turn the Globe till the degree of the Sun come to the East, and the Index will show 8. hour 34. min. as before, for the length of the night. problem XXIV. To find the hour of the rising or setting of the Stars, at any Place or Time. FOr Example: I would know the hour of the rising and setting of Sirius at Amsterdam, on December 16. Therefore I apply the place of the Sun to the Meridian( which by the 9. Probl. is in Capricorn 5.) and the Index to the 12. hour, Southwards, then I bring the star to the East side of the Horizon, and the Index points at 7. hour 40. min. after noon, which shows the time that that star rises that day: and if the Globe be turned till that star come to the West side of the Horizon, the Index will show the time of the setting of that star, which will be 4. hour 35. min. after mid-night. You may note that from the time of the rising of this star, it remains 8. hoar. 55. min. above the Horizon, and continues 15. hoar. 5. min. under it. The like also you may observe in other stars, if you do but consider the time of their rising or setting, be they either inconspicuous in the day or obvious in the night. problem XXV. To find what Stars never rise nor set, in any given Latitude: and also those which touch the Horizon descending, or those which daily do transit the Zenith. ELevate either of the Poles of the Celestial Globe above the Horizon, according to the Latitude of the place propounded; then turning the Globe, you shall see about the elevated Pole what stars be always above the Horizon, and which by descending, only touch it: and about the depressed Pole, you shall see by the turning of the Globe, which stars never ascend above the Horizon, and which at their rising only touch the very edge of it: you may also see what stars about the Zenith pass through, and what stars swerve either to this side or that, according to the variety of Declination. problem XXVI. The Latitude given to find the space of time between the rising or setting of any two stars. FOr example, if you would know how long Spica Virginis riseth after the bulls eye or Aldebaran, at Amsterdam, the Globe being set to the elevation, bring Aldebaran, to the East-side of the Horizon, and the Index to the 12. hour then turn the Globe till Spica Virginis comes to the East side of the Horizon, and the Index, will show 11. houres 4. min. for the time that Spica Virginis rises after Aldebaran. If you will know the time between their setting: bring Aldebaran to the West side of the Horizon, and the Index to the 12. hour, then turn the Globe till Spica Virginis likewise touch the Horizon in the West, and the Index will show 6. houres 37. min. for the time that Spica Virginis, setteth after Aldebaran, or the bulls eye. To find it otherwise by the obliqne Ascensions and Descensions. subtract the obliqne Ascension of Aldebaran, which by the 19. problem is 42. deg. 36. min. from the obliqne Ascension of Spica Virginis 208. deg. 44. min. and there will remain 166. degrees 8. min. divide them by 15. and you shall have 11. houres 4. min. for the time between the rising of Spica Virginis, and Aldebaran. That you may know the time between their setting, subtract the obliqne Descension of Aldebaran which is 85. deg. 16. min. from the obliqne Descension of Spica Virginis, which is 184. deg. 28. min. and there will remain 99. deg 12. min. which divided by 15. make 6. hours and almost 37. min. which is the time that Spica Virginis sets after Aldebaran. Note If it happen or that there be more deg. of the obliqne Ascension or Descension of the first star, then of the second or following star,( which alway happens when the Vernal section comes between them both,) then you must add the compliment of the greater number to 360. to the lesser Number, or add 360. deg.( the whole circled) to the lesser Number, and subtract the greater number from the total sum, and that which remains dividing it by 15.( according to the 22. problem) reduce into hours, and you shall have the time sought for. Example. To know the difference of time between the rising of the bright star in the Eagle,( called vulture) and Aldebaran, you must by the 19. problem know the obliqne Ascension of vulture, which is 282. deg. 52. min. and the obliqne Ascension of Aldebaran, which is 4. deg. 36. min. the number of the first star is the greater( because the beginning of Aries is between both) so that it cannot be substracted from the lesser, therefore add the compliment of the greater to 360. deg.( that is 77. deg. 8. min.) to 42. deg. 36. min. the lesser sum, and it will make 119. deg. 44. min. or add 360. deg. or the whole circled to the lesser 42. deg. 36. min. and they produce 402. deg. 36. min. from which, if you subtract the greater number 282. degrees 52. min. there will remain 119. degrees 44. min. as above. Lastly divide them by 15. and they will bring forth 7. hours 54. min. for the time between the rising of vulture and Aldebaran. problem XXVII. To find the beginning and ending of Nights, and Dayes, at all places and times, and also the beginning and end of Twilight. THe day begins when the Sun ascends above the Horizon, and the day ends, and night begins when it descends under the Horizon; and yet darkness does not presently follow the setting of the Sun in the evening, nor continue till the rising of the Sun in the morning; but it is light in the morning somewhat before Sun rising, and in the evening somewhat after Sun setting. The cause where of is, that the Sun in the morning, lying under the Horizon, casteth forth his beams into the air; now the vapours which environ our visible Horizon, forth-with produce or cause some whiteness and clearness; and this we call Break of day, or morning Twilight: which clearness continually increasing, at length spreads itself through the Zenith, even unto the West: but the time from which the Sun beginneth so to enlighten the air in the morning or forsake it at night is when it is 18. degrees under the Horizon, according to the verticle circled: If it be more then 18. deg. it is quiter dark through the whole air, without any certain or doubtful light. In those places therefore where the Sun in Summer cannot descend to that depth under the Horizon, it is hardly night, but always twilight. nevertheless it is to be understood that it is not at all times and in all places twilight when the Sun is 18. degrees under the Horizon, because the various, temperature and height of the air causes twilight to begin and end sooner or later then they are wont; as you may understand by those Authors which do fully handle this matter. That we may know when this light in the morning, which we call dawning or break of day, begins to spread into the air at any time of the year; we will take this Example to find at what hour it is at Amsterdam September 25. Therefore elevate the North Pole of the Globe to the height of the Pole of Amsterdam, and bring the place of the Sun( which that day is in the 12. of Libra, to the Meridian, and the Index to the 12. hour on the South side: then turn the Globe into the East until the opposite degree of the ecliptic( which is here the 12. of Aries) be in the West elevated above the Horizon 18. deg. of the Quadrant of Altitude, and then the place of the Sun in the East will be depressed 18. deg. beneath the Horizon; and( the Globe remaning unmoved, you shall see that) the Index shows the 4. hour 26. min. in the morning,( that is, after mid-night,) for the beginning of break of day. Then turn the Globe, until the 12. degree of Aries be again elevated 18. degrees of the quadrant of Altitude above the Horizon in the East, and the Index will show the 7. hour 34. min. after noon, for the time that twilight ends at night. problem XXVIII. To find out the threefold rising or setting of the Stars or signs, with the Sun, according to the description of Ancient Poets. ANcient Poets, and rustic writers describe the Seasons of the year, as Spring, Summer, Autumn, and Winter, by 3. divers rising and setting of the signs and stars, which they call Cosmick, Acronick, and Heliack. A Cosmical or morning rising, of a sign or star, is, when together with the Sun it climbeth above the Horizon. A Cosmical or morning setting when a sign or star setteth ( ex adverso) with the rising Sun. An Acronyck rising, which is both chronic and Vespertine, is when a star or some sign riseth opposite to the setting Sun. An Acronyck or Vespertine, is when together with the Sun a sign or stars descends below the Horizon. From which it is manifest, that the signs and all parts of the zodiac, which set Acronically, rise Cosmically; and on the contrary, that they that rise Chronically set Cosmically, according to this verse: Cosmice descendit signum quod Chronice surgit. Chronice descendit signum quod Cosmice surgit. Which nevertheless is much different in fixed stars, for the stars whose latitude is North from the ecliptic, and which rise Cosmically, that is, when they rise with the Sun in an obliqne Sphere,( whose Northern Pole is elevated more then the circled of the greatest Declination, of the Sun from the Aequator,) set not together with the Sun, Chronically, but long after the Sun. And on the contrary, those which are South from the ecliptic( in such a position of the Sphere,) set before the Sun. But where the South Pole of the world is elevated so much above the Horizon, the courses or the former disposition of the stars are at some time of the year changed, and some sign of the zodiac riseth Cosmically and setteth Chronically: we will take for example, the beginning of lo: therefore seek in the calendar of the Horizon the beginning of lo, and you shall find against it the 13. day of July at which time the sun entereth that sign, and riseth which it Cosmically, and setteth Chronically. If you seek the Chronical rising, and Cosmical setting of this sign; take the place of the ecliptic opposite to it,( which is the beginning of Aquarius, on the Horizontal calendar) and you shall find against it the 10. day of January, all which time the sun entering the beginning of Aquarius, causeth the beginning of lo, then to rise Chronically and set Cosmically. If you would seek the same in a fixed star( at Amsterdam) the example shall be Arcturus. The Globe being set to the elevation of the Pole 52. deg. 23. min. join the star to the East side of the Horizon, and see what degree of the ecliptic touches the Horizon: And you shall find 30. degrees of Virgo, with which the star riseth Cosmically. But the time when the sun doth enter the degree, is had by the precedent problems, and is the 12. day of September. The opposite degree of the ecliptic, to wit, 30, of Pisces, is found to be possessed by the sun the 5. of March, which denotes the time when Arcturus riseth Acronically at Amsterdam. To know the Acronical setting of this star, bring it to the West side of the Horizon, and look what degree of the ecliptic touches the Horizon there, and it will be the 5. of Capricornus, which the sun possesseth the 16. of December; at which time the star setteth Chronically, The 5. degree of Cancer is opposite, which the sun is found to be in( by the precedent problems) on the 16. of June, when the star setteth Cosmically. The Heliack rising of a star( which may rather be called an apparition) is, when a star which was inconspicuous before,( by reason of its nearness to the Sun)( whose brightness suffers it not to be seen) getteth out of the Suns beams, by the retiring of the sun in the ecliptic, and is discovered to sight. But this apparition of stars is made sooner in some stars then in others, because of their various magnitudes: stars of the first bigness are discovered( by common account) when the sun is hidden 12. deg. of the Vertical circled under the Horizon; of the second bigness when the Sun is 13. deg. under the Horizon; of the third when 14. deg. of the fourth when 15. and so to 16. 17. 18. degrees. The Heliack setting of a star( which may be called more truly a hiding) is made when a star which before was conspicuous& shining( by reason of his sufficient distance from the Sun, is by the Suns moving and approach in the ecliptic darkened, nor doth appear larger though the air be fair and clear. To find out the Heliack rising of any star,( as of Arcturus) in the North latititude of 52 l⅓.( the Globe being so elevated) turn Arcturus to the East side of the Horizon, and fix the Quadrant of altitude to the Zenith, and by it examine what degree of the ecliptic is elevated 12. deg. above the Horizon( because Arcturus is a star of the first magnitude) and you shall find the 11. deg. of Aries; and the 11. deg. of Libra opposite to it despressed under the Horizon 12. deg. is the place of the Sun, with which the star riseth Heliacally. Then seek it( viz. Libra 11.) in the Horizon, and you shall have September 24. against it, for the required time of the year. You shall find the Heliack setting for the place given, if you join Arcturus to the West side of the Horizon, and seek out what degree of the ecliptic that( by the Quadrant of altitude) is elevated 12. deg. above the East side of the Horizon, which will be the 10. of geminy. Therefore we say that degree of Sagittarius, which is 12. deg. under the Horizon is the place of the Sun, with which the star setteth Heliacally, and this happens the 12. of December, according to the precedent problems. problem XXIX. Concerning the Azimuth of the Sun and Stars, and how it may be found out. AS in a terrestrial Globe the Meridians are drawn from one Pole to another, by the degrees of the Aequator; so the Vertical Circles, called by the Arabians Azimuth, are drawn from the Zenith to the Nadir, by the degrees of the Horizon. They are described by the Quadrant of altitude on the Globe thus; fix one end to the Zenith, and the other may be applied to all the parts of the Horizon, and the edge of the Quadrant of altitude describes an Azimuth Line. The Azimuth of the Sun or stars, is the arch of the Horizon comprehended between the Meridian and that Vertical circled which is extended out of the Zenith through the Center of the Sun or Star, even into the Horizon,( where all Azimuths are numbered) and is twofold, Easterly and Westerly: The Eastern Azimuth, which is numbered from the Meridian in the South towards the East, even to the Meridian in the North by 180. degrees. The Western which is numbered from the Meridian in the South towards the West, until it is gotten to the Meridian in the North, which likewise makes 180. degrees. To find out the Azimuth of the Sun or any star by the Globe, you must know first either the hour of the day, or the height of the Sun or star above the Horizon. Therefore to find the Azimuth of the Sun when the hour is given: we will propose at Amsterdam the 16. of May at eight a clock before noon; now the Globe being set to the elevation of that Pole, join the place of the Sun( which is 5. degrees of geminy) to the Meridian, and the Index to the 12. hour then turn the Globe into the East, until the Index point at the 8. hour( or by the 22. Probl. until 60. deg. of the Aequator pass through the Meridian) there stay the Globe, and bring the Quadrant of altitude to the 5. deg. of geminy, and note the degree that it cuts into the Horizon, and you shall have the required Azimuth 79. degrees 36. min. from the South towards the East. That you may find the same day at the 11th. hour after noon, the Azimuth of vulture, the bright star in Aquila, turn the Globe into the West, until the Index points at the 11. hour at night; and bring the Quadrant of altitude to the star on the East side, and that shows on the Horizon 83. degrees 11. min.( from the South Eastward,) for the Azimuth of that star at the time propounded. To find the Azimuth of any known altitude, the example shall be the 10. day of August, the altitude of the Sun above the Horizon at Amsterdam before noon, was observed to be 20. deg. The Globe being set to the elevation of the Pole at Amsterdam, turn the place of the Sun for that day to the East( which by the 9. problem is in the 27. deg. of lo,) and bring the Quadrant of altitude to that degree; viz. the 27. of lo; and then the Quadrant will show in the Horizon 77. deg. 16. min. from the South towards the East. For the Azimuth of the Sun at the time propounded, the same way of working must be observed in fixed stars: as for example. In the same latitude the star in the heart of lo, called Regulus, is observed to be in the West, at the altitude of 25. degrees, above the Horizon, therefore join that star to the 25. deg. upwards of the Quadrant of Altitude, and that will show 79. deg. 47. min. in the Horizon from the South into the West, for the Azimuth of that star at the altitude observed. problem XXX. Concerning Almicantaraths, or Circles of Altitude, and how they may be found. THe Circles of Altitudes called Almacantars are the lesser Circles drawn by Imagination about the Zenith( as if that were the Pole or Center) and are parallel with the Horizon; ascending upwards, and cut the Azimuth Circles every where( as the Parallels do the Meridians in the Terrestrial Globe) at right angles. These are described( in the Celestial Globe) by every point of the Quadrant of Altitude, if it be fixed to the Zenith, and be turned upon its own Center round about the Horizon. But that it may be found in which of these Circles the Sun or star is, that is, how high it is above the Horizon, you must either know the time of the day, or else observe the true Azimuth. The time being known, for Example, at Amsterdam the 21. of April, at 9. a clock in the morning, the Almicantur or Altitude of the Sun above the Horizon, may be found thus; the Pole being erected to that Altitude, join the place of the Sun,( which on that day is in the 11. deg. of Taurus) to the Meridian, and the Index to the 12th hour at noon; then turn the Globe to the East until the Index point at the 9. hour before noon,( or till 35. deg. of the Aequator pass through the Meridian,) and bring the Quadrant of altitude to the place of the Sun, and on it number upwards from the Horizon to the place of the Sun, and you shall find 38. deg. 54. min. for the height of the Sun or Almicantarath circled, which the Sun toucheth at the time given. Proceed so likewise in the stars; for Example, seek the altitude of the Bright star in the Harp, above the Horizon at Amsterdam, on the same day, at 11. hours after noon; the place of the Sun being applied to the Meridian, and the Index to the 12. hour) turn the Globe into the West till the Index show the the 11. hour at night( or may pass 11. times 15.( that is 165.) deg. of the Aequator through the Meridian) then bring the Quadrant of altitude to the foresaid star, and on it number from the Horizon upwards to the star, and you shall have 39. deg. 27. min. for its altitude at the hour given. Likewise by the known Azimuth( which may be found by the Mariners compass, or other Instruments for that purpose) to find the Almicantarath of the Sun or stars, you must proceed thus. Bring the place of the Sun( the 21. of April, observed to be in the point South East, that is in the Azimuth of 45. deg. from the South into the East) to the Horizon, and also bring the lower end of the Quadrant of altitude to the Horizon at 45. deg. from the South into the East,( to wit the Azimuth observed,) and turn the Globe so long till the place of the Sun, which is the 11. deg. of Taurus, touch the place of altitude; and on that number from the Horizon upwards, and you shall find 44. deg. 47. min. for the altitude of the Sun, or Almicantarath circled which it toucheth that day, in that part of the Horizon. For fixed stars, Take the bright star in the Eagle,( observed to be in the point East South East) that is, in 67. deg. and ½. from the South into the East) Therefore bring the Quadrant of altitude to the Horizon, so many degrees distant from the South Eastward, and join the star to the Quadrant of altitude, and you shall find it elevated above the Horizon in the Verticle circled 26. deg. 3. min. for the Almicantarath of the star. problem XXXI. To rectify the Celestial Globe at any time, to the situation of the heaven. THis is performed either by the altitude of the Sun by day, or of the stars by night, or by the known hour: that it may be done by day by the altitude of the Sun, propound April 21. before noon, and imagine the altitude of the Sun at Amsterdam to be 10. deg. above the Horizon; the Globe being posited by the 6. problem, according to the four corners of the World, and the Pole being elevated to the height of Amsterdam, bring the place of the Sun,( which is in the 11. deg. of Taurus) to the 10. deg.( upwards) of the Quadrant of altitude Eastward, and the situation of the Globe will be like the situation of heaven, in every respect. By the Azimuth of the Sun. The 8. July before noon, the Sun( at Amsterdam) is observed to be in the point East South East, that is, 67. deg. ½. from the South into the East. The Globe being set as before, bring the lower end of the Quadrant of Altitude to that degree of the Horizon which is distant 67. deg. ½. from the South towards the East; then turn the place of the Sun( which is the 15 deg. of Cancer,) to the Quadrant of Altitude; and you shall have the situation of the Globe correspond in every respect with the position of heaven. You may perform the same by night by the Altitude of the stars, Example, the height of Aldebaran in the East part of the heaven, is 25. degrees, bring that star Eastward to the 25. degree of the Quadrant of Altitude, above the Horizon, and the Position of the Globe will be the same with the Position of heaven. By the Azimuth of the stars, proceed thus: admit the same star is observed to be 60. deg from the South towards the East; therefore bring the Quadrant of Altitude to the 60. deg. in the Horizon, counting from the South towards the East, and turn the Globe till the star is joined to the Quadrant of Altitude; and the Globe and Heaven will be both in one posture. The certain hour as well by night as by day, being known, will perform the same proposition, after this manner: we will propose the 26. of October, at 9. of the clock at night, therefore apply the place of the Sun( which is the 13. deg. of scorpion) to the Meridian, and the Index of hours to the 12. at noon; then turn the Globe Westward, till the Index point at the 9. hour afternoon, and you shall have the position of the Globe agree with the position of heaven, and the stars and all points in Heaven placed on the Globe, as they are in the Heaven itself. problem XXXII. How you may know the stars in Heaven, by the use of the Celestial Globe. IF you would know any star in the Heaven, as for example, the bright star in the great Dog, called Syrius; you may perceive it above the Horizon between the East& South point, therefore place the Globe by the foregoing problem, according to the situation of Heaven, which you may do either by the benefit of the Azimuth, or else by the altitude of the star, and so fix it: what stars soever of the Globe you desire to know in Heaven,( whether it be the Bright-star in the lesser dog, or Cor Leonis, or the heads of geminy, all which are to be seen at the same time in the Eastern hemisphere of the heaven) you must apply to the Quadrant of altitude, and look in the Horizon what Azimuth it hath, and in the Quadrant of altitude what height it has above the Horizon: both which you must keep in mind; then erect the Index in the Astrolabe, or Quadrant, or( where you have a free Horizon) The Transversary of the Jacobs staff to the altitude found, and turning your face to the Azimuth of the star) by the help of the Instrument, you shall meet with it, and easily discern it( when it comes in view) from others. If you know no star: set the Globe by the foregoing problem to the position of Heaven, that day and hour wherein you desire to know the stars.( For example: at Amsterdam the 13. of December, at 9. of the clock at night,) the hour being come, look round about you for the brightest, and most eminent stars; and you shall find near the Meridian, among others, three bright stars in a strait line near one another, the more Eastward of which is lower then the other: then look what stars are near to the Meridian in the Globe, in such a position, and you shall find them to be in the girdle of Orion. But that you may be surer of it, observe the altitude of one of the three above the Horizon, suppose the middle-most, and you shall find it near 36. deg. number therefore 36. deg. in the South part of the Meridian, of upwards from the Horizon, and you shall find in the end of the number, the middle-most of the propounded stars. Look a little higher in the Heaven, and you shall see two great and bright stars, further distant from one another; one whereof is more Eastward, the other more Westward: which when you have sought in the Globe, you shall find them placed on each shoulder of Orion. About the same distance below the Girdle as the two stars in Orions shoulder are above his Girdle, you shall find likewise two bright stars in the Heaven, having a little more distance between themselves, then the two in the shoulders have; finding these in the Globe, you shall discern the Eastern to be in the right knee of Orion, the Western shining in the lest foot called Rigel. At the same time a shining star is discerned in the Heaven, near about 18. deg. distant from the South, and elevated almost 20. deg. above the Horizon toward the East. Therefore that you may know what star it is, bring the Quadrant of altitude to the Horizon about 18. deg. from the South towards the East;& on it number almost 20. deg. upward, and you shall meet with one called Syrius, one of the greatest and most shining stars in the Heaven, whereby you may be sure you know it. Some of the chief fixed stars being known, it is easy to find out others by them; and that two ways; fi●st by the figures and forms which they make: secondly, by their distance from one another. By forms, because some are placed in a strait line, some in a quadrangle, some in a triangle, and others in some other figure. The three Bright stars in the Eagle make a strait Line, and direct that sight almost into the Bright star of the Harp. The stars in the face of the Bull, called Hyades, whereof the chief is Aldebaran, make the form of a Bee hive or pontifical Crown. The three greater in Pegasus, together with the head of Andromeda make a very great quadrangle. The 5. bright ones in the Swan make a great cross. Four in the Dolphin make an oblong circled. And the North Crown makes almost a whole circled. Stars are known by their distances after this manner. See on the Globe by the Quadrant of altitude how many degrees the unknown star is distant from the known, for example: search how many degrees the bright star of the Harp is distant from vulture, the brightest star in the Eagle; and you shall find 34 deg 12. min. then fit the Transversary on the Iacobs staff, to the observed distance of 34. deg. 12. min. and the end of the Index being joined to your Eye, direct one end of the Transversary towards the most Easterly of the three stars in the Eagle, the other towards the most Northerly, for the drawing of a strait line, which the three foresaid stars in the Eagle make, which strait line being extended will point to the forementioned bright star in the Harp, and thereby thou mayst know that the star that stands in a strait line with the three in the Eagle, is the bright star in the Harp. Do thus in other stars. problem XXXIII. How to find out the Longitude and Latitude of the Stars on the Celestial Globe. THe longitude of the stars be the succession of the signs of the zodiac, and are of single account: but the latitude by the description of the first part of the 5. Chapter, is of a double account, viz. Northern, and Southern: Those are Northern, which remain in the North hemisphere of Heaven; and those are Southern that are in the South hemisphere. To find out the longitude and latitude of stars in the Northern hemisphere; Erect the North-pole 66. deg. and ½. above the Horizon, then that will be distant from the Zenith 23. deg. and ½. which is the greatest Declination of the ecliptic from the equinoctial. Then turn the Globe till the beginning of Capricorn be in the Meridian towards the South; and the beginning of Cancer will be in the Meridian towards the North; the beginning of Aries will be in the East, Libra in the West, the North-pole of the ecliptic in the Zenith at the Meridian, and the ecliptic line will be all one with the Horizon; and all the stars of the Northern Hemesphear will be above the Horizon. But if then you fix the Quadrant of altitude to the Zenith, and bring it to any star, it will show its longitude( which is to be numbered in the ecliptic) by its lower end: and if you number upwards to the star, you shall have the degrees of North latitude. Example I. The Globe being rectified as before' bring the Quadrant of Altitude to the star in the head of Andromeda; and its lower end in the ecliptic show 9. deg. 7. min. of Aries for the longitude of the star; and by numbering in the Quadrant upwards, even to the star, you shall find 25. deg. 42. min. for its North Latitude. To find out the longitude and latitude of stars in the Southern Hemisphere of Heaven, elevate the South Pole above the Horizon 66. deg. and ½. and turn the Globe till the beginning of Cancer be in the Meridian on the North-side, then will the beginning of Capricorn be at the South, the beginning of Aries, at the West, of Libra at the East; the South Pole of the ecliptic in the Zenith under the Meridian, and the ecliptic will be all one with the Horizon; and all the stars which are in the South Hemisphere will be above the Horizon. If then you apply the Quadrant of Altitude( fixed to the Zenith) to any star, it will show by the lower end in the ecliptic, the longitude of that star, and by numbering upwards; you shall have the South latitude. Example II. The Globe being set as aforesaid, join the Quadrant to Sirius, the bright star in the mouth of the great Dog, and it will show by its lower end 8. deg. 36. min. of Cancer, for the longitude of that star; and by numbering upwards even to the star, its South latitude will appear to be 39. deg. 30. min. Work after the same manner in all other stars. problem XXXIV. How by the altitude of the Sun, to find out its Azimuth, and hour of the day. THe altitude of the Sun being took, and the Globe being set to the latitude of your place; join the place of the Sun to the Meridian, and the Index to the 12. hour; then turn the Globe to the East( if it be in the forenoon, or to the West, if in the afternoon) until the place of the Sun come to that degree on the Quadrant of altitude( by numbering from the Horizon upwards) that your observed altitude of the Sun was: and the Index of the hour circled will show the hour of the day; and the Quadrant of altitude will show the Azimuth of the Sun, in the Horizon, at that time. Example. The 27. day of June in the morning, the observed height of the Sun is 22. deg. above the Horizon, at Amsterdam: The Globe being erected to the Elevation of the Pole 52. deg. 23. min. join the place of the Sun to the Meridian, which that day is in the 15. deg. of Cancer, and the Index to the 12. hour; then turn the Globe into the East, and bring the 22. degrees of the Quadrant of alti●ude to the place of the Sun; and the Globe in this posture will show two things: first, That the Index points directly to the 6. hour 28. min. after midnight, showing the time of observation: secondly, That the Quadrant of altitude outs 99. deg. 2. min. in the Horizon, from the South into the East, for the Azimuth of the Sun. problem XXXV. The Azimuth of the Sun being known, to find out its Altitude, and the hour of the day. FOr example, at Amsterdam, the 16. day of May, the Sun is observed to be in the point East South East, that is, 67. deg. ½. from the South into the East; This being known, you may find its Altitude above the Horizon, and the hour of the day: thus, the Globe being rectified as before, apply the place of the Sun( which is the 5. deg. of geminy) to the Meridian, and the Index to the 12. hour, and the lower end of the Quadrant to the 22 ½. deg. of the Horizon, from the East towards the South; then turn the Globe Eastward till the place of the Sun come to the Quadrant, and you shall find two things▪ to wit 42. deg. 23. min. of the Quadrant for the height of the Sun; and 8. hours 52. min. pointed at by the Index, for the inquired time. problem XXXVI. How to find at any time the Suns Altitude, Azimuth, and the hour of the Day. FIrst, set the Globe by the 6. problem correspondent to the situation of the world, and apply the place of the Sun to the Meridian, and the Index to the 12. hour, then set up a Spherical Gnomon in the place the Sun is in,( or a needle fastened with a little wax) so as that it cut the superficies of the Globe on every side at Right Angles; then turn the Globe into the East, if before noon or into the West, if after noon( which by the shadow of the Meridian is easily to discern) until the Gnomon point directly towards the Sun, which will be when the needle casts forth no shadow from it, either one way or the other. Then( the Globe being fixed to that position) bring the Quadrant of Altitude to the place of the Sun, and the Globe will show you three things at once: for first, the Index will show the hour in the hour circled: Secondly, the end of the Quadrant, cutting the Horizon, will show the Azimuth of the Sun: and thirdly, the degrees in the Quadrant( numbered upwards from the Horizon) will show the height of the Sun above the Horizon. problem XXXVII. From the known altitude of the stars to find their Azimuth and hour of night. FOr example, at Amsterdam the 29. January at night, the star in the Hart of the Lion called Regulus, may be observed, in the altitude of 30. deg. above the Horizon from the South towards the East. The Globe therefore being set to the elevation of the Pole at Amsterdam, and the place of the Sun being joined to the Meridian( being that day in the 10. deg. of Aquarius) and the Index to the 12. hour: Turn the Globe, till the star comes to the 30. deg. of the Quadrant, and the lower end of it will show in the Horizon 72. deg. 26. min. from the South towards the East; and the Index the 11. hour 21. min. of the night in the Hour-Circle for the time sought for. problem XXXVIII. To find out by the known Azimuth of the stars, their Altitude and the hour of night. FOr example, the 19. of January at night, the bright star in the lesser Dog is observed at Amsterdam, to be in the point called South East: its height above the Horizon being sought, as also the hour of night: set the Globe to the height of the Pole of that City, and join ●he place of the Sun( which is the 10. of Aquarius) to the Meridian, the Index to the 12. hour, and the Quadrant of Altitude in the Horizon, to the 45. deg. from the South towards the East, that is South East: then turn the Globe, till the star touch the Quadrant; and numbering upwards from the Horizon in the Quadrant, you shall find 35. deg. 22. min. for the height of that star: and the Index will point at 10. hours 30. min. past noon, for the hour of the night. problem XXXIX. To find out the hour of night, by 2. stars, placed in one and the same Azimuth. THe 26. of May at night, the bright star in the Harp, and the bright star of the vulture, are observed at Amsterdam in one and the same Azimuth. Now the hour of the night may be known by them stars, thus; rectify the Globe, place of the Sun,( which is in the first of geminy) and the Index of hours as is often taught before; and turn the Globe and Quadrant to and from, all the edge of the Quadrant touch both the stars at once; and the Index will show 1. hour 23. min after mid-night. Or the stars being applied to the Quadrant,( as before) see what degree of the Aequator is in the middle of Heaven, and you shall find 263. deg. 5. min. from which subtract the Right Ascension of the Sun, which on that day( by the 19. problem) is 63. deg. 2. min. and there will rest 200. deg. 43. min. which being divided by 15. produce 13. hour. 23. min. for the time since noon of the foresaid day: that is, 1. hour 23. min. after mid-night as before. problem XL. To find out the hour of night by the rising and setting of the Stars; or by their approach to the Meridian, as well in the South as in the North. THe practise of this problem is very like to the practise of the two foregoing. For the Pole, the place of the Sun, and Index being set as before, and the propounded star being brought to the East or West Horizon, and the Meridian to the South or North, the Index will show the hour of night that the propounded star comes either to the East or West, or to the Meridian, as aforesaid, on the day propounded. The hour is found likewise without the Index, by the Ascension of the Sun, or stars, after this manner: if you observe a star in the South, subtract the Right Ascension of the Sun from the Right Ascension of the Star, and divide the residue by 15. and you shall have the hour required. If you see a star in the North, subtract the right Ascension of the Sun from the right Ascension of the star, or the Right Ascension of the star from the Right Ascension of the Sun, and divide the remaining degrees by 15. into hours and minutes; and if the Sun comes sooner to the Meridian then the star, the hour found produceth the time after mid-night; but if the Sun follow the star, or the star come to the Meridian before the Sun, the hour found out sheweth the time before mid-night. We will declare these by the following examples. Example I. When a Star is in the South. The 1. of May at night Spica Virginis is observed in the very Meridian: from hence I desire to know what hour of night it is. The right ascension of the Sun( by the 19. Prob.) on that day is 38. deg. 33. min. and of Spica Virginis 196. deg. 36. min. therefore the former being deducted out of this, there will remain 15. deg. 3. min. which divided by 15. yield 10. hours 32. min. afternoon for the time required. Example II. When a Star is in the North, the Sun going before it. The 19. of July at night, the more Northward star in the hinder wheels of the greater Plaustrum( called dub) is observed to be in the very North: I seek from hence the hour of night, by substracting the Right Ascension of the Sun,( which on that day is 128. deg. 32. min.) from the Right Ascension of the star 160. deg 17. min.( for because it is greater then the Right Ascension of the Sun, it argueth that the Sun went before the star,) and by dividing the remaining 31. deg. 45. min. by 15. I have 2. hours 17. min. after mid-night, for the time desired. Example III. When the Sun followeth the Stars. The same star dub, is seen in the North the 10. of September, and I desiring to know by it the hour of the night, deduct the Right Ascension of the star 160. deg. 17. min. from the Right Ascension of the Sun 178. deg. 2. min.( which in this case exceedeth that; from which it appeareth that the Sun followeth the star,) and the remaining 17. deg. 45. min. being divided by 15. produce 1. hour 11. min. for the time before mid-night, which being substracted from 12. there will remain 10. hours 49. min. for the time since the foregoing noon. Note. If it happen that the beginning of Aries( from which the numeration of Ascensions begin) should come between the Right Ascension of the Sun and Star, those things should be observed, which are spoken before to the example, and noted in the 26. problem. problem XLI. How to find the Azimuth of the Sun and Stars, and their height or Almucantarath at any time. THis problem is( as it were) contrary to the 37. and 38. For as by them the hour is found out from the known height and Azimuth; so by this, the height and Azimuth is found by the known hour, and that after this manner. If you would know how high the Sun is above the Horizon, the 21. of May, at 9. a clock before noon, join the place of the Sun( which on that day is in the 11. deg. of Taurus) to the Meridian, and the Index to the 12. hour, and turn the Globe toward the East, till the Index shows the 9. hour before noon; or( if you desire to work by a greater circled) till 45. deg. of the Equinoctial transit the Meridian by the 22. problem. Then ( keeping the Globe steadfast) bring the Quadrant to the place of the Sun, and the lower end of it will cut 60. deg. 42. min. of the Horizon, numbered from the South towards East, for the Azimuth of the Sun: and the number of degrees in the Quadrant between the Horizon and the place of the Sun being. 38. deg. 41. min. is the Altitude of the Sun at the time required. The same way of working, is to be observed with the fixed stars. problem XLII. To know at any time, what a clock it is in any place. BEcause the Sun doth accomplish his Diurnal motion about the earth in 24. hours, it is certain that it is mid-night, with those which live under our Meridian, in the opposite hemisphere of the earth, when with us it is mid-day: and likewise that it is noon with those which live in the middle between us,( that is 90. deg. of longitude distant from us Eastward,) when with us it is 6. a clock in the morning, and that it is noon with those which are so many degrees of the Aequator Westward, when with us it is 6. a clock at night. That it may be known how much every place of the earth by itself should differ from the place given, in hours and minutes of hours; join the place given on the Terestrial Globe to the Meridian, and the Index to the 12. hour: then turn the Globe, till the other place comes also to the Meridian; and the Index will show the horary distance sought for between both places. Or by the 3. problem seek the difference of longitude, and divide it by 15. and the Quotient will show the difference of time as before. If the place proposed be East from your habitation, the Sun comes to the Meridian so much sooner; but if West, so much later. And if you would know what a clock it is at any strange place of the earth, you may know by this example. When it is 2. of the clock afternoon at Amsterdam, I would know what a clock it is at Bantam, a City in the Isle of Java in the East-Indies: Therefore I bring Amsterdam to the Meridian, and the Index to the 12. hour, and turn the Globe until Bantam come to the Meridian; the Index will show the 9. hour 12. min. afternoon, for the time which was past noon that very moment in Bantam. If you would know what a clock it is at Lima, in the Region of Peru, at that moment( the Index being set as before) bring Lima to the Meridian, and that will show the 7. hour. 56. min. from midnight, which is the hour at that time, in the propounded City. problem XLIII. To find out the hour of our habitation by the Sun or Stars, rising or setting in other Regions, or elevated a certain Altitude above the Horizon. INquire by the 22. and 24. problem what hour the Sun or star, or other Celestial sign ascends above the Horizon, or descends beneath it in the place propounded. Then by the fore-going problem, seek the difference of time between the said place and your habitation; and if it be situate to the East, add the difference of Time to the found hour; if to the West, subtract from it, and you shall have the hour of your place that the Sun or star ascend above the Horizon in the other place, or descends beneath it. That you may know the hour of your habitation, when the Sun or star hath a certain altitude above the Horizon in a different place: seek by the 24. Probl. what a clock it is in the said different place, then seek the difference of Time between the two places, and that being found you may by the fore-going problem perform the rest, as before. problem XLIIII. To find the Italian hours by the Sun. IN France, Belgia, England and else where, twice 12. hours and numbered between the time {αβγδ}, by beginning from noon, and ending at noon the day following. In Italy( and as in times past at Athens) 24. houres are counted successively in a natural day, by beginning ●heir first hour at Sun-set( whether in Summer, when the days are longer, or in Winter when they are shorter) and so counting forward 2, 3, 4, &c. to 12. 13, 14, &c. to 24. till Sun-set again the day following. These hours are found out on the Globe by the Sun three ways. 1. By the known Altitude, 2. By the observed Azimuth, 3. By the rays of the Sun. I. By the altitude of the Sun. Suppose( for example) that you demand to know the hour, numbered after the Italian manner, at Amsterdam, on the 20. day of July after noon, when the Sun is elevated 30. deg. above the Horizon: Therefore the Globe being elevated to the latitude of Amsterdam, join the place of the Sun that day,( which is in the 7. deg. of lo,) to the West side of the Horizon, and the Index to the 12. hour towards the South; Then turn the Globe till the place of the Sun in the West come to the 30. degree of the Quadrant of Altitude numbered upwards from the Horizon; and the Index will show in the Horary circled( if you begin to number from the Southermost 12. hour) 20. hours 35. min. for the time of day in Italian hours. II. By the Azimuth of the Sun: The place of the Sun being applied to the West, and the Index to the 12. hour at noon, bring the Quadrant to the observed Azimuth, either Eastward or Westward from the Meridian, as observation sheweth; and turn the Globe till the place of the Sun be under the Quadrant, and the Index will show in the Horary circled the Italian hour of the day, to be numbered from the 12. at noon. III. By the rays of the Sun. The place of the Sun being brought to the West, on the day of observation, and the Index applied to the 12. hour; turn the Globe till the place of the Sun ascend above the Horizon, either in the East or the West; there place a spherick Gnomon or needle fixed with a little wax, and turn it to the Sun, till it doth cast forth from itself no shadow on the other side, and the Index will show the hour sought for, to be numbered from the Southermost 12. hour as before. problem XLV. To find out the Italian hours in the night by the stars. THat is performed two ways, to wit, either by their Altitude, or by their Azimuth. I. By their altitude: the Globe being set to the elevation of the Pole, and the place of the Sun being applied to the West side of the Horizon, and the Index applied to the 12. hour at noon; turn the Globe till the star propounded come to such a degree of the Quadrant as you observed, and the Index will show the hour sought for, numbering from the Southermost 12. hour. II. By their Azimuth: the Globe and place of the Sun and Index, being set as before, and the Quadrant brought to the known Azimuth, turn the Globe till the star come to the Quadrant, and the Index will show in the Horary circled, the Italian hour sought for; to be numbered from the Southermost 12. hour. problem XLVI. To know at any time how many hour are past since the rising of the Sun. AT Norimberg and in other places of Germany, the hours are numbered( as in times past with the Chaldeane, and Babylonians) from the rising of the Sun, by 1. 2. 3. and so successively to 24. until they come to the rising of the Sun again the next day. The difference between the finding out of these, and the Italian hours, is this; instead of applying the place of the Sun to the West side of the Horizon, we bring it to the East: and use the same way of working both in Sun and stars, which we have used in the fore-going problem. problem XLVII. To find out the unequal hours, which are called Planetary hours; as well by day as by night. IN times past with the Jews, Greeks, and ancient romans, were used hours differing from these hours as we use at this time: for our hours as well by day as by night, are always of an equal length throughout the year; to wit, 24. parts of a Natural day, numbering from mid-night to mid-night; but their hours were always unequal, for they divided the day, how great soever it was, into 12. hours; reckoning from the rising to the setting of the Sun; and the night, from the setting to the rising of the Sun. But such daies( in all regions that are far from the Aequator towards the Poles of the world) are always unequal, as well the fore going as following day; likewise these hours are always unequal, by reason of the difference which happens between those dayes: Mention is made of such hours in ancient Histories, and Holy Writ, the 20. Chap. of Matth. the 11. of John, and in some other places. To find out the quantity of an unequal hour every day or night of the year, do thus; bring the place of the Sun that day to the East side of the Horizon, and see what degree of the Aequator is cut by it( that is, how much the obliqne▪ Ascension of the Sun is) and keep that in your mind; from hence bring the place of the Sun to the Meridian, and see what degree of the Aequator the East side of the Horizon cuts, and count the number of degrees between the former degree of the Aequator which you bore in mind, and it; which number of degrees divide by 6. because 6. unequal hours are precisely accomplished from the rising of the Sun till noon, and the quotient will show how many degrees of the Aequator pass through the Meridian, for every unequal hour of the day. Example. The 20. of July I desire to know the quantity of an unequal hour, in the City of Amsterdam. The Globe therefore being rectified to the latitude of that place, I join the place of the Sun that day,( which is in the 7. deg. of lo) to the East side of the Horizon, and I find 103. deg. 33. min. of the Aequator ascending with it; afterwards I apply the place of the Sun to the Meridian, and find 219. deg. 25. min. of the Aequator ascend above the Horizon; so that from the rising of the Sun to its arrival to the Meridian, it hath ascended above the Horizon( or past through the Meridian) 115. deg. 22. min. of the Aequator: which being divided by 6. 19. deg. and almost 19. min. of the Aequator are allowed, for the length of an unequal hour, which exceeds the equal hour 4. deg. and almost 19. min. that is, 17. minutes of time and a little more. So much as the unequal hour exceeds the equal by day, so much by night it is lesser then the equal, therefore if 17. min. should be substracted from the equal hour, 60. min. there would remain 43. min. for the length of the unequal hour by night, at the time propounded. If you will know the unequal hour of the day, by the given Azimuth, or by the observed altitude of the Sun above the Horizon; you must first bring the Quadrant to the degree of the Azimuth in the Horizon, and then join the place of the Sun to the given Azimuth, or altitude observed; then if it be before noon, see how many degrees of the Aequator are contained between the obliqne Ascension of the Sun( before known) and the point of the Aequator which then is at the Horizon in the East, or if it be afternoon, how many degrees of the Aequator are between the obliqne Descension of the Sun, and the point of the Aequator; that is at the Horizon in the West, and divide them by so many degrees as every unequal hour of the day contains; and the quotient will show how many unequal hours are past since the rising of the Sun. Example. The foresaid 20. of July before noon, the Altitude of the Sun is observed at Amsterdam to be 40. degrees; now I would know how many unequal hours, are past since the rising of the Sun. The Pole of the Globe being elevated for the latitude of Amsterdam 52. deg. 23. min. I join the place of the Sun( which is the 7. of lo) to the East side of the Horizon, and I find 103. deg. 33. min. of the Aequator ascend with it,( which is the obliqne Ascension) then I turn the Globe till the place of the Sun touch the 40. deg. of the Quadrant, and see in the East what degree of the Aequator is cut by the Horizon, and I find 171. deg. 51. min. now the difference between 103. degrees 33. min. and 171. deg. 51. min. is, by substracting the lesser number from the greater, 68. deg. 18. min. so that the fore-going point of the Aequator, which shewed the obliqne Ascension of the Sun, is ascended above the Horizon 68. deg. 18. min. of the Aequator; and because by the foregoing Example, in that day every unequal hour of the day is found to contain 19. deg. 19. min. of the Aequator, therefore numbering in the Aequator, from the Horizon upwards, I find how often so many degrees the first point of the Aequator viz. the obliqne Ascension, shall have ascended above the Horizon; which in this Example I find is three times 19. deg. 19. min. and that there yet remain 10. deg. 27. min. which I reduce to minutes of unequal hours, according to the Rule, after this manner: If 19. deg. 19. min. of the Aequator make one unequal hour, how much does 10. degrees 27. min. make? Answer, 32. min. So that at that time there is 3. unequal hours 32. min. past since the rising of the Sun. We use the same way of working when an unequal hour is to be found by the Azimuth, or rays of the Sun, which may be understood by what we said in the 35. and 36. problem, for the finding out of the unequal hours. Otherwise by Numbers. For example, the 27. day of June, I desire to know how many unequal hours are past, at 3. a clock afternoon. By the 23. problem, the artificial day is 16. equal hours; which being divided by 12. it yieldeth 1. equal hour and 20. min. for the length of an unequal hour. Therefore I say by the common rule, If one equal hour and 20. min. give one unequal hour, what does 3. unequal hours give? Answer, They produce 2. unequal hours and 15. min. which being added to the 6. unequal hours before noon, 8. unequal hours and 15. min. are found for the number of unequal hours, since the rising of the Sun. These unequal hours are otherwise called Planetary hours, because the Ancients have ascribed to every Planet one of these hours, wherein it is to rule; ●o that the first hour( beginning from the rising of the Sun) that Planet reigns from which the Day hath its Denomination,( for every day in the week bears the name of one of the 7. Planets) the second hour the Planet next succeeding in order, and so forward, so that, if when you desire to know what Planet rules at any hour of the day or night, you need only observe their following order; in this round Figure annexed: ♄ Saturne, ♃ Jupiter, ♂ Mars, ☉ Sol, ♀ Venus, ☿ Mercury, ☽ Luna. ♄ Saturday. ♃ Thursday. ♂ Tuesday. ☉ Sunday. ♀ friday. ☿ Wednesday. ☽ monday. Therefore that you may know what Planet ruleth at the hour given; seek the day of the week in the round Figure, and to it is annexed the Planet that ruleth the first hour of the day: then count from that towards your right hand in the circled forewards, one place for one hour, two places for two hours, &c. till you have counted to the number of Planetary hours, and there you will see the Character of the Planet that ruleth that hour. Example. I desire to know, what Planet shall rule the 10. Planetary hour on Tuesday, therefore I begin first with Mars, who ruleth the first hour in that day, secondly I pass to Sol, thirdly to Venus, fourthly to Mercury, fifthly to Luna, and then to Saturn, and so forward, till I come to the tenth, and there I find Mercury; which shows that Mercury is the Planet that rules the 10. Planetary hour of Tuesday. Likewise I desire to know what Planet rules the fifth nocturnal Planetary hour of monday; that is the 17. Planetary hour from the fore-going rising of the Sun, therefore beginning at the first hour of monday I find Luna, and numbering round about ●o the 17. I end in Jupiter, which I say is Lord of the fifth Nocturnal Planetary hour of monday. The same proceedings is to be observed in all other hours. problem XLVIII. The time given to find( by the Terrestrial Globe) in the Zenith of what place of the earth the Sun is. FOr example, we inquire in the Zenith of what place of the earth the Sun is the 11. of May, when it is half an hour past 6. a clock in the morning at Amsterdam, or 5 ½. hours before noon. Therefore bring Amsterdam to the Meridian, and apply the Index, to the 12. hour, and turn the Globe into the West, because when it is before noon, the Sun is Eastward from Amsterdam) till the Index pass through 5. hours and ½. then number the Declination of the Sun that day( which by the 10. problem is 21. degrees Northward) in the Meridian from the Aequator to the North; and make a mark there which will happen in the North latitude of 21. deg. and will be distant in the longitude from Amsterdam 82. deg. and ½. not far from the City Suratta in the East-Indies; which is the place directly over which the Sun is at the time given. problem XLIX. To find in what place of the earth the Sun touches the Horizon, when it rises in the morning, or sets in the evening. SEek first by the foregoing problem in the Zenith, of what place of the earth the Sun is, whether by day or by night, which being found( as for example: for the place we will take Suratta, which hath about 21. deg. North latitude; and for the time the time aforesaid in the last problem) apply the place to the Meridian, and elevate the North Pole to the latitude given; and the place will be every way equi-distant from the Horizon; that is, directly under the Zenith, this being done, you will find all parts that are cut by the Horizon, have also the Sun in their Horizon; and they, which inhabit Eastward from the Meridian, see it descend to the West under the Horizon; they which inhabit Westward, see it elevated in the East above the Horizon. They which live under the Meridian in the North, have the Sun very low under the Horizon, and yet immediately arising with them; but they which are under the Meridian in the South, have it very high above the Horizon, and yet immediately setting. All Countries therefore that are above the Horizon, have the Sun also conspicuous above it, and have light Countries; and all that are under the Horizon, have the Sun inconspicuous under the Horizon, and are in darkness. If you turn the Globe so posited, you shall see all Countries about the Artick Pole, included in the interval arch of the circled of the elevation of the Pole 21. deg. cannot descend under the Horizon, and by consequence, the Sun staying there continually, they have always day: and contrarily you shall see the Countries included in such an arch about the antarctic, cannot climb above the Horizon, and therefore the Sun always lying hide, they have continual night. problem L. To find in what places of the earth the Sun touches the Horizon, rising or setting, at any time by the ray●● of the Sun. BEcause the wooden Horizon by reason of its Latitude may hinder the rays of the Sun, therefore it is necessary in this problem, that you take the Terrestrial Globe out of it▪ and hang it by a thread fastened to the Zenith of the Place that you inquire after, in such a manner, as that the rays of the Sun may have a free access to the body of the Globe: then fasten one thread to the extremity of the North, and another to the extremity of the South side of the Meridian, and with those two threads you may fasten the Globe, so as that its Meridian may respect the true Meridian, and its Poles the true Poles of Heaven; then bring the place inquired after, to he Meridian, and the Globe will be posited in all respects correspondent with the earth itself, not only Pole to Pole, or Meridian to Meridian, but the Regions on the Globe, to the Regions on the earth: this being done, and the Sun shining on the Globe, you may with great delight perceive the several Observations following. I How the counterfeit Globe like the true one will have one Hemisphere inlighted, and the other shadowed, and as it were in darkness. II. That it is day at that time in all Regions situated in the enlightened Hemisphere, and night at the same time in all places situated in the shadowed Hemisphere. III. If in the middle of the enlightened Hemisphere a needle be fixed with a little wax perpendicular to the superficies of the Globe, so that it project no shadow on any side, it will show that the Sun is in the very Zenith of that place, and directly over the heads of the inhabitants of that place. IV. Draw a Meridian line on the Globe from one Pole to the other, through the middle of the enlightened Hemisphere, and in all places situate under that line, it is noon. In those places also which are situate to the East, it is afternoon, because they have the Sun Westward; but in those places which are situate to the West, it is morning, because they have the Sun Eastward. V. The ●nhabitants of all places, which are between the enlightened and shadowed part of the Globe, do behold the Sun in the Horizon; and those which are East from the circled drawn through the middle of the enlightened Hemisphere, do see it setting; others which are distant from that circled Westward, do discern-the Sun rising. VI. If the light doth comprehend or exceed either of the Poles( which comes to pass, when the Sun passes through the Northern signs of the zodiac, about the Artick Pole; acomplishing the same through Southern signs, about the antarctic Pole) the places comprehended by the interval circled, described by the excess of the Suns light above the Pole, have the Sun at that time not setting, but continual day. And contrarily, the places comprehended by the interval circled, described by the distance of the Suns light from the opposite Pole, discern not the Sun rising, but have continual night. VII. If you let the Globe hang steadyly, and wait a little while, you may see on the West side of the Globe at what place it grows day, and how it creeps on by little and little, and contrarily you may see on the East side at what places it grows night and how by degrees it grows darker and darker. problem LI. To find in how many places, as well in the same, as in the different Longitude the Sun is in one and the same line at one height above the Horizon. BY the 48. problem, join that place over whose Zenith the Sun is to the Meridian, for example; Surrat in the Indies,( under the North latitude, of 21. degrees) and fix the Quadrant to it then turn it through the Horizon, and you will find all places subjected to the Suns degrees, have the Sun in the same altitude above the Horizon; because they see it equidistant from their Zenith. For example, those places which are situate under that circled which the eightieth degrees of Quadrant describes, by the Circumvolution thereof observe the Sun together at that time also elevated 80. deg. above the Horizon. But they who are under the circled from the 70. deg. of the Quadrant, likewise see the Sun in height 70. degrees. And so from one degree to another or lesser parts of the Quadrant, if you please. Therefore because all places, as well of longitude, as of another under the circled( whether more or less) from the Suns place as it were in the described Center of the Zenith, observe the Sun at the same time, so high above the Horizon; it is to be noted, in all latitudes( of 10, 20, 30, degrees or more or less) equally Northwards or Southwards from Surat, that the Sun at noon on that day, is of an equal altitude, as in the latitude of 20. and 22. degrees; so likewise is it in the latitude of 15. and 27. deg. 5. and 37. and also in the 10. Southern degrees, and 52. North degrees; this only being the difference, that the more Southern places see the Suns place from the Zenith to the North, but the more Northern places see the Sun from the Zenith to the South. But because the Sun seems alike elevated above the Horizon in divers latitudes, which either cursively, or together on both sides, are North or Southward from the Aequator; it not only happens at noon when the Sun is under the Meridian, but at some other hours of the day. For Example. If you desire to know under what latitude the Sun is the 30. of May at 9. in the morning, that is, 3. hours before noon, the longitude being alike, the Sun is observed to have the same Altitude as at Amsterdam: join that City to the Meridian, and the Index to the 12. hour, and turn the Globe towards the West, till the Index show the 3. hour( or for the 3. hours pass through the Meridian 45. deg. of the Aequator) and then reckon the Suns Declination that day, which is 21. deg of the Meridian from the Aequator towards the North, and mark the end of the number, which will be in the Suns place, then turn the Globe about, till Amsterdam stand under the Meridian again, and there fix it. This being done, apply the lower end of the Quadrant to the very Eastern point in the Horizon, and press down the upper end in the Meridian, until its edge marked with deg. cut the said mark, or the Sun, and the upper end of the Quadrant will show in the Meridian 30. deg. 58. min. from the Aequator to the North; but because the latitude of Amsterdam is 52. deg. 23. min. Northward, the foresaid place in the Meridian differs 21. deg. 25. min. from the Zenith of Amsterdam. Therefore count so many degrees from the Quadrant in the Meridian, towards the South, and the end of your numbering will fall upon 9. deg. 33. min. of latitude, for the place to which the Sun at that time hath a like altitude above the Horizon with Amsterdam. Otherwise. The same may be found out after this manner, place one foot of your Compasses to the mark, and the other to the City of Amsterdam Northwards; and afterwards turn it to the South under the Meridian; and look which deg. of latitude it touches, there you shall find as before 9. deg. 33. minutes. Therefore those two places( like two Zeniths or points of the Quadrant) are equidistant from the foresaid mark, which denotes the Sun; and by consequence, the Sun in those two places hath an equal altitude above the Horizon. But because the Quadrant applied to the East, and drawn through the place of the Sun as is said, doth from thence perpendicularly apply towards the Meridian( as the Meridian out of the Pole happens upon the Aequator) therefore from hence it appears, that not onely the foresaid two places at one& the same time have the Sun of one nearness to their Zenith; but also al other places which are under the same Meridian, whither nearer to, or further from the Quadrant, for the Quadrant having this application to the latitude of 30. deg. 58. min. the places 1. deg. more Northward or Sou●hward from it, that is, which have the latitude ●1. deg. 58. min. and 29. deg. 58. min. may see the Sun of an equal nearness to their Zenith: neither is it otherwise with places which are 10. deg. from the Quadrant either Northward or Southward, as they which have the latitude of 40. deg. 58. min. and 20. deg. 58. min. the same observation must be used by those places which are 40 deg. South, or North; to wit, under the South latitude of 9. deg. 2. minutes, and under the Northern latitude of 70. 58. min. for these behold the Sun under one and the same distance from the Zenith, and by consequence are equally elevated above the Horizon. From hence you may note, how much they err which hope that they can find out the elevation of the Pole at all hours of the day, by the altitude of the Sun above the Horizon. Moreover it is manifest, that it is impossible to find out the hour of the day, unless you first know the true elevation of the Pole. problem LII. To place the Planets on the Celestial Globe, and to know them thereby in the Heaven. ALthough Planets cannot be expressed and shown on Globes, for any long time( as you may see by reasons therefore given and set down in the fifth Chap. of the first Book) yet may they on them be notified to a certain moment of time precisely given. Therefore you must first know the place in Heaven of such Planets, at your given time; and then transfer them to the same place upon the Globe. But that we may show it more plainly, we will make use of an example: The time being given, as admit it were December 29. 1634. at 10. a clock at night at Amsterdam, I would place the Planets on the Globe, according to their places in Heaven: Therefore I look in some Ephemerides( suppose those which are published by Mr. David Origanus to the longitude of the City of frankford at other,) and mark what longitude and latitude the Planets have at the noon of that day, and I find them of this disposition.   Longitude. Latitude. Of the Sun 18. 24. ♑ 0. 0. Of the Moon 12. 10. ♉ 3. 12. N. Of Saturn 17. 4. ♐ 1. 46. N. Of Jupiter 22. 34. ♊ 1. 2. S. Of Mars 27. 37. ♍ 2. 38. N. Of Venus 19. 12. ♐ 1. 14. N. Of Mercury 2. 33. ♒ 0. 6. N. But at noon the following day, of this disposition.   Longitude. Latitude. Of the Sun 19. 25. ♑ 0. 0. Of the Moon 24. 55. ♉ 3. 58. N. Of Saturn 17. 11. ♐ 1. 46. N. Of Jupiter 22. 28. ♊ 1. 1. S. Of Mars 27. 52. ♍ 2. 40. N. Of Venus 20. 27. ♐ 1. 11. N. Of Mercury 2. 42. ♒ 0. 21. N. But because Amsterdam is about 10. deg. more Westward then Frankford, to whose longitude the Ephemerides are calculated; it is noted by the 42. Prob. if when it is 10. a clock at night at Amsterdam, then it is 10. and 40. min. at frankford. Therefore if I inquire what was the disposition of the Planets in Heaven according to the longitude of Frankford at that time I shall also have their disposition at Amsterdam, precisely to the 10. hour. We will try that according to the Moon, that it may be an example in others. The 29. of December at noon, the Moon at frankford is in the longitude of 12. deg 10. min. of Taurus, but at noon the day following, in the longitude of 24. deg. 55. min. of the same sign: The difference is 12. deg. 45. min. in longitude, which the Moon passeth through in the space of 24. hours. Therefore I say, by the common rule, if the Moons motion be 12. deg. 45. min. in 24. hours, how many degrees will be her motion in 10. hours and 40. min? you shall find it to be 5. deg. 40. min. add those to the longitude of the Moon on the 29. of December, and you shall have 17. deg. 50. min. of Taurus for the longitude of the Moon to the time propounded. The latitude of the Moon to the 29. December is 3. deg. 12. min. To the 30. 3. deg. 58. min. both Northward from the ecliptic, the difference is 46. min. therefore I say again, if the latitude of the Moon be increased 46. min. in 24. hours, how much will it be increased in 10. hours and 40. min? the product will be 20. min. which being added to 3. deg. 12. min.( because the latitude is increasing) 3. deg. 32. min. is the product for the Northern latitude of the Moon, to the time given. Follow the same manner of working in all the other Planets, and you shall find their situation and constitution in heaven the foresaid 29. of December at 10. of the clock at night at Amsterdam, to be thus.   Longitude. Latitude Of the Sun 18. 51. ♑ 0. 0. Of the Moon 17. 50. ♉ 3. 32. N. Of Saturn 17. 7. ♐ 1. 46. N. Of Jupiter 22. 32. ♊ 1. 2. S. Of Mars 27. 43. ♍ 9. 39. N. Of Venus 19. 45. ♐ 1. 13. N. Of Mercury 7. 37. ♒ 0. 12. N. Therefore that you may transfer these their places on the Globe, place it so( by the 33. problem) that the ecliptic may agree with the Horizon, and its North Pole with the Zenith; and the Quadrant being fixed to the Zenith fasten the Globe to its station, and note the Planets which have North latitude, and then place the Planets on the Globe to the time given, after this manner. Join the lower end of the Quadrant to the longitude of the Moon in the 17. deg. 50. min. of Taurus, and number in the Quadrant upwards 3. deg. 32. min. for the Northern latitude,( according to the Table) and make a mark there on the Celestial Globe, which will show the same place among the fixed stars, where the Moon is then posited: for the place of Saturn, join the end of the Quadrant to the 17. deg. 7. min. of Sagitarius, and number upwards 1. deg. 46. min. for the Northern latitude, and likewise set a mark on the Globe, and that will show the place of Saturn among the fixed stars, at the time propounded. Do thus in like manner in Mars, Venus, and Mercury. But that you may place Jupiter in the Globe, which hath a Southern latitude, turn it so, that the Southern Pole of the ecliptic may agree with the Zenith; then join the Quadrant,( let down from the Zenith) to the ecliptic in the 22. deg. and 32. min. of geminy, and in that number upwards. 1. deg. 2. min. make there a mark for the true place of Jupiter: also make another mark at the 18. deg. 51. min. of Capricorn, for the place of the Sun in the ecliptic: and that being performed, in the last place, turn the Globe▪ and rectify it to the situation of Heaven for the hour given( by the 31. Prob.) and all the Planets in the Globe will be placed among the fixed stars, as they are in the very Heaven. Use the same way of working to any time given; and you may easily know them by the 32. problem. problem LIII. To erect a Figure of the 12. Houses of Heaven by the Celestial Globe. AStrologers( who treat of the powers and influences that the Heavenly bodies have upon the earthly, and conceive that they can foretell future events by the face of Heaven,) divide the whole Heaven into 12. parts, which they call Houses. This division is made by the six great Circles,( as it were) passing through two points opposite to one another, as the two Poles in Heaven are; to wit, the common intersections of the Horizon and Meridian, towards the North and South. The chief of them are the Meridian, and Horizon, which always divide the Heaven into four Parts: the other four are thus shown; by the circled of Position two Quadrants of the Equinoctial being above the Horizon, are each of them divided into 3. equal parts; to which divisions, the circled of Position( whose ends as the Poles) are fastened to the two intersections of the Horizon and Meridian) is lifted up, and by this reason, each of the Quadrants of Heaven above the Horizon is divided into 3. parts( which are called Houses) between the Horizon and Meridian, so that both the Quadrants above the Horizon, make six Houses; and the parts opposite to them make the 6. remaining Houses under the Horizon. By these Circles the equinoctial is divided into 12. equal parts, and the ecliptic into so many unequal parts: But the greatest account is had of the unequal parts, for they are particularly marked, as the bounds and marks of the beginning of each House. As for the order of numbering the Houses, you must take the beginning from the East, and reckon downward beneath the Horizon, so that the first six are always under the Horizon, and the other 6. above it. Four of them are of greater account then the rest: The first, which is called the Horoscope, or Ascendant, which taketh its beginning from the East side of the Horizon: The fourth, from the Meridian under the Horizon in the bottom of heaven: The 7. from the West side of the Horizon: The 10. from the Meridian in the top or middle of heaven. For when the Celestial bodies apply themselves to those, they have a greater power and operation. These twelve Houses are represented by the following Figure of 12. Triangles. The Figure of the 12. Houses of Heaven. Wee will give you this example following, that wee may show you how the Houses of Heaven are described to a time propounded. The Celestial Figure shall be described as the heavens were posited in Holland, in the year 1571. the 2●. day of November at 6. of the clock at night under the elevation of the Pole 52. deg. 50. minutes. First seek by the preceding problem, the true places of the Planets to the time given; you shall find them as they are in the following Table, which afterwards you may transfer to the Globe. A Table of the Longitude and Latitude of the Planets for the 29. of November, at 6. of the Clock at night, in the year 1571.   Longitude. Latitude. Of Saturn 12. 14. ♏ 2. 7. N Of Jupiter 16. 45. ♓ 1. 27. S Of Mars 29. 5. ♍ 1. 42. N Of the Sun 27. 17. ♐ 0. 0. Of Venus 26. 17. ♏ 0. 19. N Of Mercury 5. 9. ♐ 0. 52. N Of the Moon 28. 18. ♍ 4. 0. N Elevate the North Pole 52. deg. 50. min. and join the place of the Sun( which is in the 27. deg. 17. min. of Sagittarius) to the Meridian; and the Index to the 12. hour at noon; then turn the Globe, till the Index points at the 6. hour,( or for more certanty by the 26. problem) till 90. deg. of the equinoctial pass through the Meridian, towards the West.( beginning from the Right Ascension of the Sun at 267. deg. 2. min.) this being done, fix the Globe, and fasten the circled of Position to its Poles, for the West side of the Globe. Then looking in the equinoctial, you shall find at the intersection of the Horizon, on the West side, 267. deg. 2. min. which is called the obliqne Descension of the seventh House. From hence reckon upwards in the equinoctial the third part of the Quadrant comprehended between the Meridian and Horizon, which is 30. deg. even to the 297. deg. 2. min. of the equinoctial; for so much is the obliqne Descension of the 8. House. By numbering from hence the third part of the Quadrant, or 30. deg. more, even to the 327. deg. 2. min. you shall have the obliqne Descension of the 8. House, and the circled of Position being brought to it, will intersect 20. deg. 10. min. of Pisces; for the beginning or cusp of that House: the 26. deg. 46. min. of Pisces possesseth the Meridian for the beginning or cusp of th● 10. House. Afterwards apply the circled of position to the Meridian on the East side of the Globe, and from thence number in the equinoctial the 3. part of the Quadrant or 30. deg. and you shall have the obliqne Ascension of the 11. House, 27. deg. 2. min. apply to this the circled of position, and that will cut the ecliptic in the 9. deg. 20. min. of Taurus, for the beginning of the 11. House. From the obliqne Ascension of the 11. House number 30. deg. of the equinoctial, and you will come to the 57. deg. 2. min. for the obliqne Ascension of the 12. House; to which degree bring the circled of Position, and it will show in the ecliptic that the 12. House begins at the 27. deg. 9. min. of geminy, and 25. deg. 28. min. of Cancer possesseth the Horizon, which is the beginning of the first House. The 6. Houses of Heaven, which are above the Horizon, being found in this manner, the other 6. also beneath the Horizon are known by the Opposition of the former signs; for the whole circled of position,( because it is one of the greatest Circles) divides the ecliptic( always in two Opposite places) into two equal parts. Therefore for the beginning of the 7. House, you shall find in the Horizon towards the West, 25. deg. 28. min. of Capricorn; for the beginning of the 4. House under the Horizon in the Meridian 26. deg. 46. min. of Virgo, and so in the rest; as is to be seen in this Table. The 6. Houses found above the Horizon are these. 8-14. 20 ♒ The 6. other Opposite to the former under the Horizon. 2-14. 20 ♌ 9-2. 10 ♓ 3-2. 10 ♍ 10. 26. 46 ♓ 4-26. 46 ♍ 11-9. 10 ♉ 5-9. 10 ♏ 12-27. 9 ♊ 6-27. 9 ♐ 1-25. 28 ♋ 7-25. 28 ♑ Lastly, consider in which Houses the Planets are found. You shall find the Moon and Mars to possess the 4. House; Venus, Mercury and Saturn the 5. House; the Sun the 6. all being under the Horizon: but Jupiter to be placed in the 9. above the Horizon. All these are noted in one Scheme, as here follows; for the face of Heaven at the time and place aforesaid, as thus. In the year 1571. the 29. Nov. at 6. afternoon D. A. M. was born, the Sun possessing the 27. deg. 27. min. ♐ LIB. III. Concerning Sun-Dyals. Of the necessity and use of Sun-Dyals. AMong the manifold delights which arise from the use of Globes, the description of Sun-Dyals is none of the least: For wee passing through the greatest part of our lives in workemanships, Merchandise, and meetings at certain times, can scarcely want the use of dials, since by them certain hours and set times are propounded to us; according to which, wee dispose, ordain, and perform our labours, rest, actions, meetings, &c. This so great profit being observed by the Ancients, they have found out divers and subtle inventions, by which they have taught us to discern and observe times and hours, as well Nocturnal as Diurnal. But among all those, none is found out which can satisfy their desire with more certainty and less cost then Sun-Dyals, described on the plane superficies of immovable bodies. And although these may be described divers ways, as well by lines as by numbers and instruments; yet there is not given an easier or clearer demonstration, then that which is performed by Astronomical Globes: which wee have determined at this time to unfold more at large. Of the variety of Sun-Dyals. THere are two sorts of Sun-dyals, that is to say, Pendent and Fixed: Pendent are they which being hung by the hands and turned to the Sun or stars, show the hours of the day and night; and those are such, in which we either use Or sight. Pinnacids, to transmit the rays of the Sun; or an ocular beholding, to observe some Celestial Star, as are Astrolabes Cylinders, Astronomical rings, Universal dials, and the like; those are fixed which are neither hung nor moved, but are made on an immovable plane, and show the hours of the day by the shadow of a fixed style. Of these there are also two sorts, to wit, those which are made either on a plane surface, or on a Spherical, being either Concave or Connex. It is not my mind to describe here all kind of dials, and how many ways they may be made; for that would require a large volume: but onely how some of the most eminent may be described on a plane surface by help of the Globes, which may serve as a foundation to all others of this nature; and which being well understood, every one exercised in Arethmetick and Geometry, shall easily understand, not onely in what manner these may be made, but also how all others may be made as well by lines as numbers, according to his own desire. Sun-Dyals on plain superficies are divers, and are distinguished by their names, according to the Celestial Circles with which their planes are Parallel. Among these are Horizontal dials, which being placed level, are Parallel to the Horizon; and whose upper face do directly behold the Zenith. Direct upright dials are such as are Parallel to the Azimuth of East and West, which passeth through the Zenith and terminates in the Horizon at the said points, and are twofold, Northern and Southern. Upright Decliners are such as swerve from the North or South towards the East or West, and are Parallel to that Verticle circled or Azimuth which descends from the Zenith to the Horizon beyond the points of East and West; as are all upright walls that decline from the South or North towards the Coasts of South West, South East, North East, and North West. Reclining and Inclining, plains are likewise of two sorts; namely Direct or declining. Direct Incliners are such whose under faces lean forward, towards the South or North, the upper faces whereof are said to Recline or lean backward. Declining Reclin●rs are such which swerving from the South or North, towards the East or West lean backward from the Zenith like the roofs of Houses, situated towards any of the said Coasts of the World; the edge of whose walls swerve more or less from the true North or South points. Declining Incliners are such as swerve from the North or South towards the East or West, and stoop forward contrary to the Recliners, like the inside of the roof of a House the face or Wall whereof standing more or less from the South or North towards the East or West. equinoctial dials are twofold, and are drawn on a plain Parallel to the equinoctial; having two faces, the one above, and the other beneath; the upper most looks up towards the North Pole, and the under most towards the South. Meridional dials are such whose flats or faces lie directly Parallel to the Meridian of the place; and are commonly called East and West dials. Polar dials are likewise twofold, as having two faces; and are such whose planes are Parallel to the Axis of the World, as also to a circled imagined to pass through both Poles intersecting the equinoctial and Horizon at the points of East and West; the upper face respects that part of the equinoctial that is above the Horizon, and the under face the lower half of the equinoctial that is under the Horizon. The problems follow. problem LIV. To find the true North or South. WHen we desire to draw a Sun-Dyal on an Horizontal plane, or to set up a direct erect dial, it is necessary that first of all we know the true North and South, that so we may place the dial to its true situation. How to find the same by the Globe, we will show you divers ways, as follows. I. By the rising and setting of the Sun. Secondly by his Azimuth to any Altitude given. Thirdly, by the greatest distance of those stars that are near the Pole from the North, either towards the East or West, and move round, having their revolutions from the Zenith towards the North. Fourthly, by the Azimuth of other stars to any Altitude given, like as by the Sun in the same case. 1. Do thus by the rising or setting of the Sun. ON a smooth board( Parallel to the Horizon) draw a circled, and divide it by two Diameters, crossing one another at right angles, into four Quadrants, and each of them into 90. deg. at the ends of the Diameters writ the names of East, West, North, and South, then set up a strait pin in the Center, or a style of brass or Iron, perpendicular to the board, and by the 18. problem, see in what degree of the Horizon the Sun rises or sets on the day given; for example, at Amsterdam the 15. of May, you shall find the Sun rises in the morning 36. deg. from the East towards the North, and sets at night so many degrees from the West towards the North: Then having the Board ready, just when in the morning the Sun rises, turn it about, till the shadow of the style falls upon so many deg. from the West towards the South, as the Sun rises from the East towards the North: then the line of the South and North upon the board will agree with the true Meridian line in Heaven. 2. By the Azimuth of the Sun. SEek by the 34. problem the Azimuth of the Sun by help of its Altitude, for the day given; for Example, the 27. day of June in the morning, the Sun being 22. degrees, high, you shall find he will be 9. deg. 2. min. from the East towards the North; Then at that very instant, turn the foresaid Board, till the shadow of the style falls directly on 9. deg. 2. min. from the West towards the South, and the Meridian line of the board will agree with the Meridian line of the World. 3. By the greatest distance of those stars that are near the Meridian from the Pole. TAke for Example the bright star in the square or foot of the lesser Bear, being one of those which Mariners call the Guards; the Globe being set to the Latitude of Amsterdam, turn it round, and bring the Quadrant of Altitude so near the Pole, that the star may touch the same at its greatest distance towards the East; and then observe in what Azimuth the Quadrant of Altitude intersects the Horizon, and you will find it to be 24. deg. from the North towards the East; this being done, place a board with a perpendicular style or wire erected in its verge or limb, 24. deg. from the North towards the East of the board with a style in the Center; then turning the board about( when the said star hath its greatest distance from the Pole) bring the said Perpendicular and style into a right line with the star, by your sight. Otherwise, place a style or sight in the board just against the Azimuth of the star, 24. deg. from the South towards the West, and turn the board about, bringing the style in the Center, the said sight, or perpendicular, and the star into one right line, and then will the Meridian line of the board agree with the true Meridian of the World. 4. By the Azimuth of a Star to any Altitude given. THis is done the same way as by the Sun, the difference being only, that instead of the Sun-beams, you are to place a sight or perpendicular so many degrees from the West towards the South or North, as the star is found to be from the East, towards the North or South; then turn the board about, till you bring the style in the Center, the said sight or perpendicular, and the star into a right line; and then will the Meridian line of the board agree with the true Meridian of the World. problem LV. To find out the Declination, Reclination, and Inclination of any plain. WHen you are to draw any dial that is not just Horizontal, it will first be necessary to know whether the plain be erect, or whether it inclines or reclines; and how much it declines or swerves from the North or South, towards the East or West. diagram That you may find whether it be upright, or how much it inclines; make a square Table, and in it a quadrant divided into 90. deg. with a perpendicular, as is to be seen in the Figure. If the wall incline towards the Horizon, Apply the side of the Quadrat A B to it; but if it recline, the side C D: and the Plummet will show the quantity of inclination in the Arch B E. To find how much it declines from the South( if the plane be upright, or that the Inclination, and reclination be but small) fix an Iron or brass style on it at right angles, and tarry till the shadow of the style cast itself directly downward, which you may perceive by help of a plumb-line or of the other style; at the same moment take the Altitude of the Sun, and there-with by the 34. problem find his Azimuth, which is as much as the wall declines from the South; But if the time be in the morning, the declination is towards the East; if in the afternoon, towards the West. Otherwise. If a wall be upright, observe when the Sun is in the same strait line or Azimuth with it; that is, when it touches it wi●h his rays; then observe the Altitude of the Sun at the same moment, and thereby find his Azimuth; then the Declination of the wall differs from the Azimuth of the Sun 90. deg. after this manner: If the observation be made before noon, and the Sun be towards the East part of the wall, by how much the Azimuth of the Sun then exceeds 90. deg. by so much the wall also declines from the South towards the East; or as much as it wants of 90. deg. so much the wall declines, from the South towards the West. If the observation be made in the after noon, and the Sun be posited towards the West part of the wall; by how much the Azimuth of the Sun in this case exceeds 90. deg. by so much the wall also declines from the South towards the West, or so much as it lacks of 90. deg. so much the wall declines from the South towards the East. If the wall recline, draw on it a strait line Parallel to the Horizon; but if it incline, draw a strait line Parallel to the Horizon by help of the board or Quadrant, at the distance of two foot, or more, as occasion serves, from the Wall, upon some Horizontal plane; then hold up a thread and plummet, and observe when the shadow of it on the reclining wall fals upon the foresaid line Parallel to the Horizon; or on an inclining wall, upon the line drawn Parallel there-to on the Horizontal plane or board: at the same time take the altitude of the Sun, and thereby find his Azimuth, the Declination of the same wall will differ from the Azimuth of the Sun 90. deg. precisely, as in the foresaid upright walls. problem LVI. To describe an Horizontal dial. ON the plane whereon an Horizontal dial is to be made, draw a circled( as large as you think fit) as in the Figure A B C D; divide it by two Diameters crossing themselves at right diagram angles, so that one of the Diameters A E C lie towards the South and North; and the other D B towards the East and West, and they will divide the circled into 4. Quadrants; two of which on either side of the line E C, as C D and C B, divide into 90. deg. and every degree into so many lesser parts as they can admit of; the line E C being placed North, will express the 12. hour; E D towards the West, the 6. in the morning; E B towards the East the 6. at night. To find the other hours; set the Globe to the Latitude of that place where the dial is to be made, for Example, to the Altitude of the Pole at Amsterdam 52 l⅓. deg. then bring either of the great Circles called colours to the Meridian, and set the Index to the 12. hour; then turn the Globe towards the West, till the Index show the first hour after noon, and look in what place the colour cuts the Horizon, and you shall find 11. deg. 59. min. from the North towards the West; set off the same on the plane or dial on the East side from C towards D and B, and on it make marks for the first hour after noon, and the 11. before noon. Then turn the Globe towards the West, till the Index shows the second hour, and see as before how many deg. of the Horizon are comprised between the Meridian and the colour toward the North; and you shall find 24. degrees 34. min. again number them from C towards D for the hour of 2. in the after noon, and from C towards B for the 10. hour before noon. Use the same way of working for the other hours, and you shall find 38. deg. 23. min. contained between the Meridian and the foresaid colours to the North, for the third hour after noon, and the ninth before noon; for the fourth after noon, and eighth before noon 53. deg. 55. min. for the fift after noon, and seventh before noon 71. deg. 21. min. for seven at night, and five in the morning 108. 39. For eighth at night, and four in the morning 126. deg. 5. min. number all these arches from C towards D and B: and make marks in the circled, and afterwards draw through them strait lines out of the Center of the said circled E, which will be the true hour lines. The Index of the dial is to be drawn from the Center of the circled towards the Pole, Parallel to the Axis of the world, wherefore number in either Quadrant from C towards D or B, the elevation of the Pole 52. deg. 23. min. make a mark there, and through it from the Center of the circled draw a strait line, as E F and from the end of this, draw another perpendicular to the line of the 12. hour E C, as is F G, the Triangle E F G made of brass, or other matter, and erected perpedicularly over the line E C, its obliqne side E F will point toward the Pole, and will be Parallel to the Axis of the world, and by its shadow, shows the hour of the day. problem LVII. To describe a Direct Erect South dial. UPon the Plane given, draw a Semi-Circle, as in the following Figure B C D; so that the line D A B be Parallel to the Horizon: and divide it by the perpendicular A C( which shows the hour of 12.) into two Quadrants, and each of those into 90. deg. then set the Globe to the Latitude of the place which we( for Examples sake) take to be 52. deg. 23. min.) and the Quadrant of Altitude being fixed to the Zenith, bring the lower end thereof to the Horizon in the very point of West, and one of the colours to the Meridian, diagram and set the Index to the 12 hour; then turn the Globe towards the West, till the Index shows the first hour, or till 15. deg. of the equinoctial be passed through the Meridian; and look where the colour cuts the Quadrant of Altitude, and you shall find 9. deg. 17. min. from the Zenith downward; number these in the Quadrant of the plane from C towards B for the first hour after noon, and towards D for the eleventh before noon, and set marks thereto: Then turn the Globe further towards the West▪ till the Index shows the second hour, and see where the colour cuts the Quadrant of Altitude, and you shall find 19. deg. 25. min. from the Zenith downward: number those again from C towards B for the second hour after noon; and towards D for the tenth before noon; and set marks thereto; Do the like for the rest of the hour lines, and you shall find 31. deg. 24. min for the third after noon, and ninth before noon 46. deg. 36. min. for the fourth after noon and eight before noon 66. deg. 18. min. for the fift after noon and seventh before noon. Number these Arches as the foregoing, from C towards B for afternoon hours, from C towards D for the fore noon hours, and make a mark at every one, through which to the end draw strait lines out of the Center A, and they will show the hours: But A D will show the sixth hour in the morning, and A B the sixth at night. To place the Cock or style; Count the Latitude of the place from B or D, as here 52. deg. 23. min. there make a mark, and draw the right line A E through it, from the Center A, and another from C making a right angle with the line A E to A F: then of some solid matter, make a Triangle A E F, and erect it perpendicular to the plane upon the line A C, and the side A F will point unto the Pole Parallel to the Axis of the world, and its shadow will show the hours. problem LVIII. To draw a direct erect North dial. THe delineation or draft of the hour lines as well in direct erect North as South dials, is one and the the same; the difference being onely in the placing of the dial. If a direct erect South dial be turned towards the North, upside down, and the hour lines, 4, 5, 7, 8 be drawn through the Center to the opposite part of the Plane, and the numbers changed, so as 8 be put for 4, and 7 for 5, and 5 for 7, and 4 for 8, as may be seen in the following Figure; there will be drawn a direct upright North dial. diagram problem LIX. To make upright direct dials out of the Horizontal. IN the drawing of dials, we may observe, that a direct upright Plane, is Parallel to the Horizontal; and in respect of the Sphere, is one and the same with this Caution, that they differ 90 degrees of Latitude under the same Meridian; as for example, an upright dial to the North Latitude of 52. degrees, is the same with a Horizontal dial to the South Latitude of 38. degrees, and for as much as Horizontal dials for the same Latitudes( as well to the Southward as to the Northward of the equinoctial, as to the draft of the hour lines) are like each to other; it hence follows, that if a Horizontal dial be made to the Latitude of 38. degrees, without respect of North or South Latitude; the same( so far as concerns the hour lines) is like unto an upright dial made for the Latitude of 52. degrees. Also an Horizontal dial to the Latitude of 60. degrees, is like unto an upright dial made for the Latitude of 30. degrees, and so for others. From whence it further follows, that an Horizontal and an upright direct dial for the Latitude of 45. deg. are both one and the same, only with this difference, that the numbers which in Horizontal dials( made for a North Latitude) were to be accounted from the right hand towards the left, are now to be transposed or changed, and reckoned from the left hand towards the right; and so the contrary, &c. problem LX. To draw upright dials declining from the South. TO draw upright dials declining from the South, for example, at Amsterdam, to draw a dial on a wall which declines 35. deg. from the South towards the West; draw on the Wall or plane, a line Parallel to the Horizon; as in the following Figure, D A B and diagram upon the Center A, draw a Semi-Circle B C D, and divide it by the perpendicular A C,( showing the twelfth hour) into two Quadrants, and each of them into 90. deg. and set the Globe to the Latitude of Amsterdam, bringing the colour to the Meridian; the Index of the hour circled to twelve, and the lower end of the Quadrant of Altitude( being screwed to the Zenith;) to the Horizon 35. deg. from the West towards the North, so many deg. as the wall declines from the South towards the West: then turn the Globe West, till 15. deg. of the Aequator pass under the Meridian; or till the Index shows the first hour after noon: and then observe where the colour cuts the Quadrant of Altitude, and you shall find 9. deg. 52. min. from the Zenith; number those in one Quadrant from C to B, and set a mark thereto; from whence through A, draw a strait line, which will show the hour of one in the after-noon. Then turn the Globe again till 15. deg. more of the Aequator pass under the Meridian towards the West, or till the Index come to the second hour after noon, and look in what place the colour cuts the Quadrant of Altitude, and you shall find 18. deg. 3. min. Likewise number then from C towards B, and set a mark at the end thereof, through which from A draw a line which will show the second hour after noon. Proceed after the same manner for the other hours after noon, and you shall find that the colour cuts the Quadrant of Altitude in the 25. deg. 37. min. from the Zenith downward for the third hour; for the fourth hour in 33. deg. 37. min. for the fifth in 42. deg. 10. min. for the sixth in 53. deg. 20. min. and for the seventh in 68. deg. 57. min. number these arches as the two foregoing from C towards B, and from the Center A draw strait lines through those marks, and you shall have all the after noon hour lines, which a plane or dial of this kind can admit of. To find the fore noon hours, remove the Quadrant of Altitude to the Eastern side of the Meridian, and bring the lower end of it in the Horizon so many degrees from the East towards the South, as the wall declines from the South towards the West, to wit 35. degrees: again, bring the colour to the Meridian, and the Index to the 12. hour. Then turn the Globe to the East, till 15. deg. of the Aequator are past under the Meridian, or till the Index shows the 11. hour before noon, and observe where the colour cuts the Quadrant of Altitude, and you shall have 13. deg. 12. min. number those in the Quadrant from C towards D, and from A draw a strait line, which will show the 11. hour. Then turn the Globe further until 15. degrees more of the Aequator have passed through the Meridian, or till the Index shows the 10. hour before noon, and observe where the colour cuts the Quadrant of Altitude, and you shall find 32. deg. 20. min. from the Zenith downward. Proceed so for the rest of the hours, and you shall find for the 9. hour 58. deg. 54. min. for the 8. hour 88. deg. 12. min. number those as you did the 11. hour from C towards D, and through these arks draw strait lines from the Center A, and so all the hours which such a dial can receive will be described. In such dials declining from the Meridian, the style ought not to be placed over the hour line of 12. nor at the same Altitude as in a direct erect dial, but over another line and at another Altitude. That you may find that line( commonly called the substylar) over which the style hangs in its nearest distance to the Plane, and how much it is to be elevated above the same; turn the Globe till you make the colour cut the Horizon in the quantity of the Planes Declination, counted from the South towards the West, namely 35. degrees, and there hold it: then will the colour and the Quadrant of Altitude in its former position cut each other at right angles, being 90. degrees asunder on both sides of the Horizon. Then observe these two things, namely how many degrees of the Quadrant of Altitude are contained between the Zenith and the colour; and how many degrees in the colour are contained between the Quadrant of altitude and the Pole: you shall find, for the first on the Quadrant of altitude between the Zenith and the colour, 23. deg. 51. min. and so much is the distance between the substylary line and the hour of 12. Then number in one Quadrant from C towards B 23, deg. 51. min. and out of A through the said arch draw the strait line A E; which will be the substylar, over which the style ought directly to hang. For the second, set a mark at the arch,( because the colour is not graduated where the Quadrant of Altitude makes the intersection) and turn the Globe till you bring the mark under the Meridian; and you shall find 30. deg. between it and the Pole, for the elevation of the style: Wherefore from the substylar A E, number 30. deg. towards B, even unto H; and through H draw a strait line from A, which is A F; and an other at right angles from the substylar, which is E F; then the Triangle as A E F, erected upon the line A E; A F will show with obliqne or upper side the hours, and will likewise point towards the Pole. Between dials of this sort declining to the West, and others declining towards the East, this onely is the difference; that those which are prescribed to be made here,( by the Quadrant of Altitude or other Circles) towards the West, then ought to be accomplished towards the East: or that the afternoon hour lines( which here exceed the other in number) and in these fall from the 12. hour towards the West, are to be changed into fore-noon hours;( which then exceed those in number) and to be placed from the hour line of 12. to the East: and likewise the fore-noon hours are to be changed into afternoon hours, on each side. problem LXI. To draw upright dials declining from the North. THe draft of the hour lines on such Planes which have like Declination either from the South, or from the North, is one and the same; the difference is onely, that the one is to be changed into the other; and the hour lines into their compliments to 12. For example; If in a dial declining from the South, Westward 35. deg.( such an end as we described above,) we shall change the upper side with the lower, and turn the same 35. deg. from the North into the East, and draw the hour lines through the Center to the opposite side, and change the numbers; so that we place 4 against 8, and 5 against 7, and 7 right against 5; and so for the rest; we shall have a dial described for the same position or cost of the World. problem LXII. To draw upright declining dials out of the Horizontal. AS a direct upright dial and the Horizontal under the same Meridian, being distant 90. degrees by the 59. problem are Parallel and a like, so also the upright Decliner and Horizontal dial under the same Azimuth 90. degrees, asunder are Parallel, and like each other, save only in time. If then in stead of drawing an upright Decliner, you make an Horizontal dial for some place under the same, Azimuth 90. degrees asunder, the Case will be the same, and the difference will be only in the time. For example, admit you were to draw an upright dial at Amsterdam, which declines from the South; Westwards 30. deg. and that by help of a Horizontal dial; first, find out in what part of the earth the upper face of the Horizontal dial may be Parallel( and how much they differ in time) after this manner. To the upright Decliner above said, set the Terrestrial Globe to the Latitude of Amsterdam 52. deg. 23. min. and bring the City itself to the Meridian, then reckon in the Horizon on the South side, from the Meridian towards the West, the Declination given of the plane proposed 30. deg. and thereto set a mark, which above the place where the surface of the Horizontal dial is Parallel to the upright Decliner given at Amsterdam; then turn the Globe to the East, till you bring the said mark under the Meridian, and you shall see that it is distant from the Aequator into the Southwards 31. deg. 55. min. and that 36. deg 55. min. of the Aequator( as much as the difference of the longitude of either place) have passed through the Meridian; which by the 42. problem being turned into time, make two hours, 24⅓. min. for the time wherein the Sun comes later to the Meridian of that place, then at Amsterdam: And so it is found, that an Horizontal dial made for the South latitude of 31. deg. 55. min. and anticipating by two hours 24⅓. min. in the time, is the same with an upright dial made to the North latitude of 52. deg. 23. min. declining 30. deg. from the South into the West. To make an Horizontal dial of this sort, draw a line upon the Plane, Parallel to the Horizon, as in the following Figure D A B, and upon the Center A, draw the Semi-Circle D C B, which divide into two Quadrants by the perpendicular line A C( which becomes the hour line of 12.) and likewise divide each of those Quadrants into 90. degrees, then set one of the Poles of the Globe to the Latitude aforesaid, namely 31. deg. 55. min. and bring either of the colours to the Meridian; and then turn the Globe to the West, till 36. deg. 5. min. of the Aequator( for two hours 24⅓. min. of time) have passed under the Meridian, and there hold it, observing diagram where the colours cuts the Horizon towards the North, and you shall find 21. deg. 4. min. from the North towards the West; set a mark to that place of the Horizon for the hour of 12. and reckon in one of the Quadrants drawn upon the plane, so many degrees from the Perpendicular line A C towards B, and through the end of the said arch out of the Center A, draw the strait line A G, which represents the Meridian line for the South Latitude of 31. deg. 55. min. and in this case will be the substylar line, over which the style must hang. To find the fore noon hours, the Globe( hitherto being unmoved) set the Index of the hour circled to the hour of 12. and then turn the Globe to the East, till 15. deg. of the Aequator pass through the Meridian, or till the Index shows the 11. hour; and look where the colours cuts the Horizon, and you shall find 12. deg. 9. min. from the hour of 12. and from the Meridian 33. deg. 13. min. then reckon in the Semi-Circle from C towards D, 12. deg. 9. min. or from the sub-stylar E A, 33. deg. 13. min.( for the effect is the same) and through the end of the said arch from the Center A, draw a strait line, which will represent the 11. hour, then turn the Globe more to the East, until 15. deg. more of the Aequator pass under the Meridian, or till the Index shows the 10. hour, and observe where the colour cuts the Horizon, and you shall find from the 12. hour marked in the Horizon, 28. deg. 57. min. and from the Meridian 50. deg. 1. min. Do the same for the rest of the fore noon hours, and you shall find for the 9. hour that the colour cuts the Horizon 52. deg. 24. min. distant from the hour of 12. and 73. deg. 28. min. from the Meridian; for the 8. hour, 80. deg. 20. min. from the hour of 12. and from the Meridian 101. deg. 24. min. Reckon these arches in the Semi-Circle on the plane, the former from the perpendicular A C, or the latter from the sub-stylar A E, and draw strait lines through each of them from the Center A, and thus will the forenoon hours be delineated or drawn. Now to find the afternoon hours, bring the colour as before, to the distance of 36. deg. 5. min. of the Aequator from the Meridian, and 21. deg. 4. min. from the Meridian to the West in the Horizon; where the 12. hour was marked, and set the Index to the hour of 12. in the hour circled: this being performed, turn the Globe into the West, till 15. deg. of the Aequator pass under the Meridian, or till the Index shows the first hour afternoon; and the colour will cut the Horizon 9. deg. 31. min. from the 12. hour towards the East; and 11. deg. 31. min. from the Meridian towards the West; then reckon in the Quadrant of the plane, either from C the 12. hour to B 9. deg. 33. min. or from the sub-stylar A C to C 11. deg. 31. min. and through the end of either of the arches from the Center A draw a line, which will be the hour line of one in the after noon; then turn the Globe further to the West, till 15. deg. more of the Aequator pass under the Meridian, or till the Index shows the second hour after noon, and you shall perceive that the colour cuts the Horizon at 17. deg. 50. min. from the 12. hour Eastward, and 3. deg. 14. min. from the Meridian Westward: Then number again in the Quadrant from C to B 17. deg. 50. min. or from the sub-stylar to C 3. deg. 14. min. and out of the Center A draw a strait line for the hour line of 2. in the after noon. Use the same manner of working for all the rest of the after noon hours, and you shall find the colour to cut the Horizon for the hour line of 3. 25. deg. 48. min. from the 12. hour, and 4. deg. 44. min. from the Meridian, for the hour line of 4. 34. deg. 16. min. from the 12. hour, and 13. deg. 12. min. from the Meridian. For the hour line of 5. 44. deg. 12. min. from the 12. hour, and 35. deg 58. min. from the Meridian: For the hour line of 6. 57. deg. 2. min. from the 12. hour, and 35. deg. 58. min. from the Meridian: For the hour line of 7. 74. deg. 58. min. from the 12. hour, and 53. deg. 54. min. from the Meridian; all towards the East. Number these arches as you did the first from C, or from the sub-stylar towards B, as the latter, and from the Center A draw the hour lines, viz. as many as such a Plane can admit of. Then for the height of the style, number from the sub-stylar towards B or D 31. deg. 55. min. as much as was the South Latitude aforesaid; and from the Center A through the end of the said arch, draw a strait line, as here E F, and another at right angles to the line A E, namely E F; so will these three lines make a trigon, namely A F E which must be raised perpendicularly over the sub-stylar line A E, and the side A F will show the hours, and will point towards the Poles of the World. problem LXIII. To make direct Reclining, or Inclining dials. BEtween direct Reclining or Inclining dials, and direct upright dials, the difference is no other in the manner of making but the latitude of the places where they stand. For how much the direct reclining dial leans backward, also how much the direct incliner stoops forward, so much it differs in the height of its style from the direct erect dial. For Example: A Plain that stands directly South in the Latitude of 50. deg. reclining 10. deg. is no other then an upright direct dial for the Latitude of 60. deg. Likewise in the Latitude of 50. deg. a Plane inclining 10. deg. differs not from a direct upright dial to elevation of the Pole or Latitude of 40. deg. It therefore an upright direct dial be made for the Latitude of 40. deg.( by the 57. Proposition) the same is also a direct recliner for the Latitude of 30. deg. and a direct incliner to the Latitude of 50. deg. the arch of Re/ Inclination being 10. degrees. problem LXIV. To draw Declining Reclining dials. FOr Example, admit a dial were to be made at Amsterdam, on a Plane, declining 24. deg. from the South Westwards, and reclining 10. deg. In the first place draw on it a line Parallel to the the Horizon, as here D A B, and on the Center A draw the Semi-Circle D C B, which divide into two Quadrants by the perpendicular diagram line A C, and each of those Quadrants into 90. deg. Then set the Pole of the Globe to the Latitude of Amsterdam, 52. deg. 23. min. and bring the colour to the Meridian, and the Index to the hour of 12. and the Quadrant of Altitude on the North side 24. deg. from the Meridian towards the East, namely so much as is the Declination of the Plane from the South towards the West. Then get a thin Semi-Circle of smooth brass, or of any other bending solid matter, like the Quadrant of Altitude, and divide the same into 180. degrees, and bring one end thereof to the Horizon at 24. deg. from the East towards the South, the other so many deg. from the West towards the North, but fasten the middle of it at the distance of 10. deg. from the Zenith, being as much as the flat or Plane whereon the dial is to be made doth recline downward toward the Horizon on the North side: which being done, observe in what place the brass Meridian cuts the Semi-Circle, and you shall find at 4. deg. 25. min. distant from the Zenith; reckon these on the Plane from C to B, and through the end of the said arch from the Center A, draw a strait line, which will be for the hour line of 12. To find the after noon hours, turn the Globe Westwards, till 15. deg. of the Aequator pass under the Meridian, or till the Index shows the hour of 1. in the after noon; and mark where the colour cuts the Semi-Circle, and you shall find 11. deg. 12. min. number these from C to B▪ and draw a strait line from the Center A through the end of the said arch, and the said line will represent the hour of 1. in the after noon. Do the like for the rest of the after noon hours, and you shall find the colour will cut the Semi-Circle in 17. deg. 23. min. from the Zenith for the hour of 2. and for the hour of 3. at 23. deg. 50. min. for the hour of 4. in 31. deg. 16. min. for the hour of 5. in 41. deg. 5. min. for the hour of 6. in the 55. deg. 52. min. and lastly for the hour of 7. in 80. deg. 23. min. Reckon these arches severally in the Quadrant from C towards B, and draw strait lines through them from the Center A, so shall you find all the after noon hours. Then to find the fore noon hours, bring the colour again to the Meridian, and the Index to the hour of 12. and turn the Globe Eastward, till 15. deg. of the Aequator pass under the Meridian, or till the Index point out the hour of 11.( which is all one,) then the colour will cut the Semi-Circle in 3. deg. 55. min. on the East side of the Azimuth of the plane; and working after the same manner for all the rest of the hours, you shall find that the colour cuts the Semi-Circle for the hour of 10. in 15. deg. 39. min. by numbering from the middle thereof; For the hour of 9. in 34. deg. 29. min. for the hour of 8. in 64. deg. 43. min. Reckon these arches from C towards D, and out of the Center A draw strait lines through them, and you shall have all the fore noon hours described. In like manner all the hour lines will be drawn which such a plane is capable of. Then know where and how high the style of such a dial is to be placed: let the brass Semi-Circle remain as aforesaid, and turn the Quadrant of altitude to the other side of the Globe, placing the lower end thereof 24. d. from the South towards the West, being as much as is the Declination of the Plane, then turn the Globe till the colour cuts the Quadrant of Altitude 10. degrees above the Horizon, being as much as is the Reclination of the Plane; Then the Globe remaining steadfast, the colour will cut the Semi-Circle at right angles. This being done observe two things; namely, first how many degrees are contained between the middle of the Semi-Circle and the colour; secondly, how many degrees are contained in the colour between the Semi-Circle and the Pole; and you shall find for the first 15. deg. 48. min. But if the colour be not divided into degrees, set a mark at the place where it and the Semi-Circle cut each other, and turn the Globe till you bring the colour under the Meridian, and you shall find for the second arch 24. deg. 18. min. between that mark and the Pole. Count the former number 15. deg. 48. min. from the perpendicular A C towards B, and through the end of the same from the Center A draw a strait line for the sub-stylar as A E; and reckon the latter arch 24. deg. 18. min. from the sub-stylar towards B even unto H, and through H draw a strait line from the Center A, which is A F, and another strait line from the line A F, as here E F: the trigon A E F made by these three lines being raised perpendicularly over the sub-stylar A E, the slope side A F, will point to the Pole, and the shadow of that side will show the hour of the day. The manner of finding the hour lines for a Reclining Plane Declining towards the East, is one and the same; but only that the Quadrant of altitude in the former example which was placed in the Horizon from the North towards the East, and from the South towards the West, is to be placed in this contrary; namely, from the North towards the West, and from the South towards the East: in like manner the Semi-Circle in stead of being placed there from the East towards the South, and from the West towards the North, is in this case to be placed in the Horizon, from the East towards the North, and from the West towards the South. Also the hour of 12. and the style of the dial is to be drawn on the other side of the perpendicular line A C. problem LXV. To draw Declining Inclining dials. FOr Example; suppose a Sun-Dyal were to be drawn on a wall, which in the latitude of 52. deg. 23. min. doth decline 30. deg. from the South towards the East, and inclines 20. degrees to the Horizon; first draw on it( as in the foregoing problem) a Semi-Circle divided by a perpendicular line into two Quadrants; and then the Globe being set to the latitude given, bring the lower end of the Quadrant of Altitude to the Horizon 30. deg. from the South towards the East, as much as is the Declination given; and set one end of the Semi-Circle( as aforesaid) in the Horizon to the distance of 30. deg. from the East towards the North, and the other at the distance of so many degrees from the West to the South, and the middle in the Azimuth of the plane to the distance of 20. deg. from the Zenith downward towards the South, as much as is the Inclination given, and then will it represent some circled in the heavens, to which the upper face of the wall is supposed Parallel; this being done, the Meridian will cut the Semi-Circle in the 11. deg. 10. min. from the middle of it towards the West, number these degrees on the wall from the perpendicular A C to B, and draw a strait line out of the Center A through the end of the said arch, which will represent the hour line of 12. To find the other hours, turn the Globe to the East for the forenoon hours, to the West for the afternoon hours, till for every hour 15. deg. of the Aequator pass under the Meridian; and observe where the colour cuts the Semi-Circle; and you shall find at 2. deg. 41. min. towards the East for the hour of 11. and at 15. deg. 6. min. for the hour of 10. at 26. deg. 4. min. for the hour of 9. at 38. deg. 22. min. for the hour of 8. at 50. deg. 28. min. for the hour of 7. at 63. deg. 53. min. for the hour of 6. at 79. deg. 1. min. for the hour of 5. At 27. deg. 2. min. towards the West for the hour of one in the after noon, at 45. deg. 1. min. for the hour of two at 64. deg. 22. min. for the hour of three, at 83. deg. 38. min. for the hour of four. Number all those arches for the forenoon hours from C towards D, and for the afternoon hours from C towards B, and through the ends of every of them from the Center A, draw strait lines, and all the horary lines which such a plane is capable of, will be described according to the following Figure. To find the place of the style and its elevation; retain the Semi-Circle in the same situation, and place the lower diagram end of the Quadrant of Altitude on the other side of the Globe at 30. deg. of the Horizon( being so much as is the Declination of the Plane) from the North to the West: Then turn the Globe till the colour cuts the Quadrant of Altitude at 20. deg. above the Horizon, being an arch equal to the inclination of the Plane, and there hold it, then will the colour cut the Semi-Circle at right angles. Then as in the former problem observe these two things: First how many degrees of the Semi-Circle are comprehended between the middle thereof and the colour, secondly how many degrees of the colour are contained between the Semi-Circle and the Pole; and you shall find for the first 28. deg. 26. min. which number from C towards D, and out of the Center A, draw the strait line A G, for the sub-stylar: for the second, you shall find 50. deg. 9. min. number those from the line A G, towards B into H, and from A to H, draw the strait line A F, and an other strait line from F, which may fall square-wise on the line A G, as here E F, these three lines will make such a trigon as is here represented by A E F, which being raised perpendicularly over the sub-stylar A E, the slope side thereof A F,( as in the former example) will point towards the Poles, and the shadow of it will show the hours. problem LXVI. To draw Northern dials declining, which likewise recline or incline. LIke as upright dials declining from the South into the East or West, by the 60. problem, being inverted, become upright dials declining from the North into the West or East, the case being the same for dials that decline, which also recline or incline. For example; a dial made by the 64. problem to the declination of 24. deg. from the South into the West, and reclining 10. degrees, if it be turned upward so that it may decline 24. deg. from the North into the East, and incline 10. deg. towards the Horizon, in stead of reclining so much from the Zenith, and then draw the hour lines( by the 61. problem) quiter through the Center to the Opposite side, and change the numbers into their compliments, it will become a North dial declining inclining, such as was proposed. In like manner, if a dial made by the 65. problem for the Declination of 30. deg. from the South into the East, and inclining 30. degrees be so changed that in heaven it decline 30. degrees from the North into the West, and reclines 20. degrees, and the hour lines drawn quiter through the Center; the numbers being changed into their compliments; the dial will be made to that cost of the world desired. problem LXVII. To draw declining reclining dials by help of an Horizontal. UPright and Horizontal dials lying under the same Azimuth, at the distance of 90. degrees( by the 62. problem) are alike, saving only in time: the like is to be undetflood not onely of upright direct dials there described, but also of all manner of decliners, that likewise recline or incline. Now to know in what place a Plane that declines and reclines shall become a Horizontal Plane( as in the 64. problem,) take for example at Amsterdam, a Plane that declines 24. degrees from the South into the West, and reclines 10. degrees; set the Globe to the Latitude of Amsterdam, as hath line been often repeated, and bring the colour to the Meridian; placing the Quadrant of Altitude in the Horizon 24. degrees from the South towards the West( as much is the Declination of the Plane) and count thereon 10. degrees upwards, as much is the reclination of the Plane, and thereto set a mark upon the Globe for the place sought for; then turning the Globe, bring the said mark to the Meridian, and you shall see that it fals on 24. degrees 18, minutes of South Latitude, and is situate more Westwardly, in difference of Longitude( as appears by the passing of the equinoctial under the Meridian) 26. deg. 4. min. which make 1. hour 44 1/ 15. minutes of time that the Sun comes later unto the Meridian of that place, then at Amsterdam. Then draw( by the 62. problem) a Horizontal dial, differing 1. hour 44 1/ 15. minutes in time, and you shall find that the colour will cut the Horizon towards the North at 11. degrees 23. minutes for the hour of 12. and in 4. deg. 36. min. for the hour of 1. in the afternoon, and in 19. degrees 43. min. for the hour of 11. in the morning, and in 31. deg. 27. min. for the hour of 10. and at 50. deg. 11. min. for the hour of 9. and in 80. deg. 31. min. from the Meridian to the West for the hour of 8. And for the rest of the afternoon hours, namely for the hour of 2. in 1. deg. 37. min. for the hour of 3. in 8. deg. 2. min. for the hour of 4. in 15. deg. 28. min. for the hour of 5. in 25. deg. 17. min. for the hour of 6. in 40. deg. 4. min. for the hour of 7. in 64. deg. 35. min. from the Meridian to the East. Number the first arch in the following Figure from the line A E G( which represents the Meridian, or the hour line of 12. in the foresaid Southern latitude) towards D, and the rest of those arches towards B; and thereto from the Center A draw strait lines, and all the hour lines will be finished. Moreover set off 24 deg. 18. minutes from the line A E, as much is the foresaid South latitude to H, and from the Center A through the point H draw the line A F, and another out of F squire wise to A E; the trigon made by these three lines namely A F E is to be raised perpendicularly at right angles to the Plane, and the slope side A F will represent the style. But because in all declining reclining dials the hour line of 12, cannot be perpendicular, but is to stand Eastwards upon such Planes as decline Westward, and on the contrary diagram Westward upon such as decline Eastward, we must therefore find out in this example, how far the same ought to be placed Eastward, in manner following. Lift up the Aequator above the Horizon 24. deg. as much as is the Declination of the Plane, and bring the Quadrant of Altitude( being fastened to the Zenith) the lower end thereof to 10. deg. in the Horizon, reckoned from the East or West towards the South,( for so much is the inclination of the plane,) and look how many degrees of the Quadrant of Altitude are contained between the Horizon and the equinoctial, and you shall find 4. deg. 25. min. number these from the hour line of 12. towards the West, and out of the Center A draw the line A C; then turn the plane till A E be perpendicular; and the hour lines will be drawn in their true situation: and the style A F will point towards the Poles, and show the hour of the day. problem LXVIII. To make declining inclining dials, by help of the Horizontal. THat you may know in what place of the earth a Plane at Amsterdam, that declines from the South into the East 30. degrees, and inclines 20 degrees to the Horizon( as in the 62. problem) may be like a Horizontal; raise the Pole of the Globe to the latitude given, and bring the colour to the Meridian; But because the Zenith of the place to be sought for, fals under the Horizon from the South towards the East, place the Quadrant of Altitude opposite to the cost of Declination in the Horizon 30. degrees from the North towards the West, and thereon count an arch of 20. degrees equal to the Declination of the plane set, and at it set a mark upon the Globe; and so you shall find a place differing 180. degrees in longitude so much to the Northward, as the place sought is Southward from the Aequator. Then turn the Globe into the West, till that mark pass under the Meridian towards the North and return the same above the Horizon, whereby you shall observe two things. First that the mark is under the Meridian 50. deg. 9. min. to the Northward of the equinoctial, which shows the place to be so much Southwardly of the same: Secondly, that in turning the Globe round, 227. degrees of the equinoctial have past under the Meridian, from which if the Semi-Circle of 180. degrees be subducted, there will remain 47. deg. 9. min. for the difference of longitude, which makes 3. hours 8 3/ 20. minutes of time that the Sun comes sooner to the Meridian there then at Amsterdam. Therefore draw a Horizontal dial by the 62. problem, for the South latitude of 50. deg. 9. min. which will show the time later by 3. hours 8 3/ 20. minutes; and you shall find that the colour will cut the Horizon on the North side at 39. deg. 36. min. from the Meridian Eastwardly, for the hour of 12. and for the hour of 1. in the afternoon at 55. deg. 28. min. for the hour of 2. at 73. deg. 27. min. for the hour of 3. at 92. deg. 48. min. for the hour of 4. at 111. deg. 54. min. for the hour of 11. before noon at 25. deg. 45. min. for the hour of 10. at 13. deg. 20. min. for the hour of 9. in 1. deg. 39. min. from the Meridian towards the West. For the hour of 8. in 9. deg. 56. min for the hour of 7. in 22. deg. 2. min. for the hour of 6. in 35. deg. 27. min. for the hour of 5. at 50. deg. 41. min. from the Meridian towards the East. Among these arches reckon all those which tend from the Meridian towards the East, from the line A E G( which represents the Meridian or hour line of 12. for the Latitude of the place aforesaid, diagram and in this dial the substylar line) towards B; the rest towards D, and through the ends of every arch out of the Center A, draw strait lines, so will all the hour lines be finished that such a plane can admit of. Moreover draw a strait line distant from the substylar A E G, as much as the arch of the South latitude was found to be, namely 50. degrees 9. minutes to wit the line A F; and another from F perpendicular to A G, which is F E, then set up the trigon A F E perpendicularly over the substylar line; so will it by the shadow of its upper edge A F show the hour of the day in declining planes that inclines, contrary to those that recline. I mean in those whose Declination is Westward, the hour line of 12. doth always fall to the Westward of the perpendicular line; But those that decline towards the East, the hour line of 12. doth always fall on the other side of the perpendicular line, in like manner towards the East: now to find in this dial how many degrees, the same is distant from the perpendicular line towards the East, raise the equinoctial on the South side of the Globe 30. deg. above the Horizon, namely as much as is the Declination of the plane and the upper end of the Quadrant of altitude being fastened to the Zenith, bring the lower end to 20. degrees on the Horizon counted from the East towards the South, as much is the inclination of the plane, and observe how many degrees of the Quadrant of altitude are contained between the Horizon, and the equinoctial, and you shall find 11▪ deg. 10. min. reckon the same from the hour line of 12. Westward, and through the limits of the said arch draw a line from the Center A, namely A C: then turn the Plane, till you make A C to be perpendicular to the Horizon, and the hour lines will be drawn in their true situation: The style A F will point towards the Poles, and with its shadow will show the hours of the day. problem LXIX. To make equinoctial Sun-Dyals. TO draw the hour lines on such planes as are Parallel to the equinoctial, whereof the upper face looks towards the North Pole, and the other towards the South Pole; place one of the Poles of the Globe in the Zenith, that the Aequator may fall into the Horizon, and be Parallel thereto, and bring the colour to the Meridian; then turning the Globe, it appears that as often as 15. deg. of the Aequator( for every hour of time) pass by the Meridian, so often also doth the colour pass over 15. deg. in the Horizon: Then choosing some place on the board( whereon the dial is to be made) for a Center, draw thereupon a circled, as in the following Figure B C D E; divide the same into 24. equal parts and through the same draw strait lines to the Center, whereon set up a style every way perpendicular to the board; and so will the dial be finished, these kind of dials which may be made both upon the upper and under side of the Board or Plane, being placed under the Pole, are Parallel to the Horizon; and under the equinoctial are perpendicular thereto, some of the hour lines pointing up towards the Zenith: but being placed in some intermediate Latitude, diagram the hour line of 12. is placed just under the Meridian, and the Plane itself is to be elevated above the Horizon, equal to the height of the equinoctial; then will the styles point to the Poles of the World( as being Parallel to the Axis) and the upper face of the dial shows the hour of the day when the Sun is in Northern signs; and on the contrary, the under face when in Southern. problem LXX. To make direct East and West dials which lie in the Plane of the Meridian. THere is no difference between East and West dials, but only in the hour lines; the forenoon hours in the East dial are drawn after the same manner as the afternoon hours in the West dial; which is thus: Draw a strait line, as A I D, elevated above the Horizontal line A C, to the same altitude with the equinoctial, for example at Amsterdam 37. deg. 37. min. which is shown by the arch C H, and in the said line choose a point, as at I; and through the same draw another line, which may cut the former A D at right angles, as E I 6, which will point unto the Poles, and be Parallel to the Axis of the World, and will in both dials become the hour line of 6. Again, through the point I, draw an other strait line( namely L K) Parallel to the Horizontal line, A C, and will represent the Horizon: in the line I E upon the Center E describe the Semi-Circle F I G, making the Diameter thereof F E G, Parallel to A D; divide it into 12. equal parts; then from the Center E through the marks of the divisions, draw strait lines, even unto the equinoctial A I D; and through the points of Intersection or Contingence, draw other strait lines at right angles to the line A I D, which will be the hour lines sought. A West dial. diagram An East dial. diagram The forenoon hours in East dials are reckoned downward as 4, 5, 6, 7, 8, 9, 10, 11, and in the West dials the afternoon hours are numbered upwards, as 1, 2, 3, 4, 5, 6, 7, 8, the length of the style must be equal to the Semi-Diameter I E of the circled, and erect it in the point I, at right angles to the Plane, and the shadow of the very top of it will show the hour of the day. Or make an Index like P Q as long as you please, and place the same upon two styles as O P, and Q R, which must be both of the same length as E I, and at a like distance from I, being raised perpendicularly over the line E I, so that the style may cross the equinoctial line at right angles, and be Parallel to the Axis of the World, and also to the hour lines; and the shadow of it will show the hours planily, as in other dials. problem LXXI. To draw Polar dials. THe manner of drawing the hour lines on Polar dials, is the very same, as on Meridional or East and West dials; For as those hour lines are drawn on the said dials in reference to the equinoctial, fo are these to the Meridian, being also Parallel to the Axis of the World. The difference is onely, in numbering the hour lines and that these are drawn at right angles to the Horizontal, and not obliquely, as those were; as may be better seen in the following Figure. diagram In which E F represent the equinoctial line Parallel to the Horizon; and C A a perpendicular line, crossing the same at right angles, in the point C, and is likewise the hour line of 12. in which( upon the Center A) draw the Semi-Circle D C B, and divide it into 12. equal parts, and through the divisions from A, draw occult lines to the equinoctial line, and where they cut the same, make marks; and through those marks draw the hour lines perpendicular to the aforesaid equinoctial line, so will they all be Parallel each to other. The style must be made( as in other dials) as long as the Radius of the circled A C, and be set up in the Center C, perpendicularly to the face of the dial; the upper end whereof( by its shadow) will show the hour of the day: or you may make a plate or rod as G H, and set it upon two styles as H L, and G K, equal in length to C A, and both of them placed at the like distance from the Center C perpendicular to the plane and equinoctial line, and Parallel to the Axis of the World; the shadow whereof will show the hours, as in all other dials. LIB. IV. Of the Points of the Mariners compass, called RUMBS: Of the use of Rumbs in Navigation. BEfore we come to the problems themselves, we will premise these few things, for the better understanding thereof. The difference between journeys on shore and Voyages at Sea is very great: For all Land journeys and distances are conceived to lie directly from one place to another, according to the draft of some great circled of the Sphere, which is supposed to cut all the Meridians between both places, at divers angles; but of Sea Voyages which are performed by sailing, some are strait, some circular, but the greatest part crooked and Winding like an Helix, or Spiral line, according to the Way or Rumb of the Mariners compass. strait Voyages are such as when we sail towards the North or South, under the Meridian; or East and West, under the equinoctial: Circular, as when we sail East or West, without the equinoctial, under some Parallel, cutting all the Meridians at right angles: Spiral or bending Courses are such, as when we sail upon some other point of the compass, and departing from the equinoctial either Northwards or Southwards, approach nearer and nearer to one of the Poles. And this happens, because a Ship being steered by the compass( the needle whereof being touched by the Loadstone, by virtue thereof, always points towards the North) upon some certain point or Rumb, either towards the South, North, East, or West, describes( as it were) crooked bending or Spiral lines, which always intersect and across the Meridians, how many soever they are imagined to be, at the same obliqne angles; These kind of Courses to distinguish them from direct sailing under the Meridian, equinoctial, or Parallels, are called Rumbs, name as follows, beginning at the North; the first Eastward, is called North and by East; the second N N E; the third, N E by N; the fourth N E; and so for the rest, which we shal not here repeat; But he that desires fully to understand their nature and use, with the manner of drawing them on the Terrestrial Globe, let him peruse the works of Petrus Nonius, Edward Wright, but chiefly of Simon Stevinius, in quarto libro Geographiae: We shal only here handle their use in Navigation, so far as concerns the Terrestrial Globe. problem LXXII. The Latitude of two places having the same Latitude, together with the difference of their Longitudes being given, to find their Rumb and distance. FOr example, the scape S. Vincent in Spain, and the Isle of S. mary, both which places are under the latitude of 37. degrees, the difference of their longitude being 15 ⅙. degrees let it be required to find their Rumb and distance. For as much as both their latitudes are alike, by the common rule, they must need● lie East and West from each other. To find their distance, open the Compasses to so small an extent, that the strait line which is comprehended between their feet, may not sensibly differ from the Circularness of the space to be measured; viz. to so small a distance, that being set on the Globe( though Circular) may there likewise seem to be strait: for example, to 10. or 20. miles more or less, as the Circularity of the Rumb to be measured seems to require ( for all the Rumbs and Parallels are more Circular about the Pole then near the equinoctial) but in this case, extend them to 10. German miles, and observe how many times the same is contained in a Rumb, Parallel to the Aequator from scape S. Vincent to the iceland of S. mary, and you shall find 18 1/ 10. times, which being multiplied by 10, produceth their distance in German miles, namely 181. and are so many English Leagues. problem LXXIII. The Latitude of two places lying under the same Parallel, together with their distance being given, to find their Rumb and difference of Longitude. FOr example, admit the distance between scape S. Vincent and the iceland of S. mary be 181 ½. German miles, being both in the Latitude of 37. degrees, and let it be required to find their Rumb and difference of Longitude. Seing the Latitude of both places is the same, we may( as in the former problem) conclude they lie East and West from each other; Then to find their difference of Longitude, first bring the one place, and then the other to the Meridian, and observe how many degrees of the equinoctial pass under the same, and you shall find 15. degrees 10. minutes, and so much is the difference of Longitude between these two places. problem LXXIV. The Latitudes of two places being given, which differ in Latitude, together with their Rumb; to find their difference of Longitude and distance. FOr example, the Latitude of the iceland de Sal( being one of those near scape Verde) is 16 ¾. degrees, and the Latitude of the Lizard at the Lands end of England, is 50. degrees, and they bear from each other North North East, and South South West; let it be required to find the difference of Longitude between these two places, and their distance, upon the Terrestrial Globe. Seek out the Rumb given, and bring it to the Meridian, under the Latitude of the iceland de Sal; namely, 16 ¾, degrees, and observe what degree of the equinoctial is under the Meridian; Then, turn the Globe more Westward( because the Lizard is more Eastwardly) and bring the same Rumb to the Meridian under the Latitude of the Lizard, namely 50. degrees; and again observe what degree of the equinoctial is under the Meridian, and reckon what arch is comprehended between both observations, and you shall find 16. degrees 58. minutes for their difference of Longitude. To find their distance, open the Compasses to so small an extent, that the Circularity of their Rumb comprised between them, may seem to differ but little from a strait line; namely to 20. German miles, or English Leagues or thereabouts, and remove them, measuring strait in their Rumb from 16 ¾. d. of Latitude, till you come to the Latitude of 50. deg. and you shall find this distance comprised 27. times between both places for their true distance; which being multiplied by 20. produces 540. German miles, or English leagues. problem LXXV. The Latitudes and Longitudes of two places being given, to find their Rumb and distance. FOr example, the Latitude of the Lizard at the Lands end of England, is 50. degrees, and of the East side of the iceland of S. mary, is 37. degrees, the difference of their Longitude being 18. deg. 2. min. let it be required to find their Rumb and distance. If you find a Rumb that passeth through both the places given, that is the Rumb sought; but this happens but seldom; let us therefore take it for granted, that there passeth no one Rumb through both these places. In this case, turn the Globe till you bring some Rumb or other; namely, that which is nearest the truth to the Meridian, under the Latitude of the more Westwardly place, namely of the iceland of S. mary 37. deg. Then turn the Globe Eastward( because the other place is Eastwardly) till 18. degrees, 2. min. of the equinoctial have passed under the Meridian( being an arch equal to the difference of Longitude) and if the Rumb you took at adventure, cut the Meridian under the Latitude of the second place the Lizard, it is the same sought for; If not, try others more Northwardly or Eastwardly, as occasion requires working as before, till you find the true one, or that which comes nearest the truth; which in this example you will find to be the 4. from the Meridian, namely North East. To find their distance, measure in the Rumb of North East how many German miles or English leagues are contained between both Latitudes, in the manner abovesaid, and you shall find two hundred seventy five. problem LXXVI. The Latitudes and distances of two places being given, to find their Rumb, and difference of Longitude. FOr example, let the more Westwardly place be the iceland of S. mary, under the Latitude of 37. degrees; and the Eastwardly place, the Lizard, under the Latitude of 50. degrees, being 275. German miles or English leagues distant from each other; And let it be required to find their Rumb and difference of Longitude. To find the Rumb, make choice( as in the former problem) of any which you guess may come nearest the truth, and bring it to the Meridian, under the Latitude of the iceland of S. mary, making a mark at the place of Intersection; Then measure in the said Rumb( after the manner of the 72. problem) with the Compasses, the distance of the said places, and bring the point or period of the same to the Meridian; and if it fals under the Latitude of the Lizard, namely, 50. degrees; the Rumb choose at adventure, is the true one sought; but if it fals on a lesser Latitude; choose some other Rumb that is more Northwardly; and if on a greater, more Eastwardly; and repeat the same kind of work, till you find some Rumb wherein the number of miles may end nearest the Latitude given, which in this case is the fourth Rumb; namely North East: The same manner of working will serve to find the difference of Longitude, which in this example is 18. degrees 2. min. problem LXXVII. The Rumb and difference of Longitude of two places, together with the Latitude of one of those places being given; to find their distance, and the Latitude of the other place. FOr example, let the two places be as before, the iceland of S. mary, and the Lizard; bearing from each other South West, and North East; the difference of their Longitude being 18. degrees 2. minutes, and the Latitude of S. Maries iceland 37. degrees; and let it be required to find the Latitude of the Lizard, and the distance between both places. First to find the Latitude of the Lizard, the second place, because the Rumb is North East, set a mark upon such a Rumb on the Terrestrial Globe, under the Latitude of S. Maries iceland, namely 37. degrees; and turn the Globe till you bring the said mark to the Meridian, and observe the intersection thereof with the equinoctial; Then turn the Globe Westward, till 18. degrees 2. min. of the equinoctial pass under the Meridian, and observe where the said fourth Rumb cuts the Meridian; and you shall find at 50. degrees, from the equinoctial Northward, for the Latitude of the Lizard sought. Secondly, make a mark upon the said section, and measure in the Rumb the distance between both marks,( as in the 72. problem,) and you shall find 275. German miles. problem LXXVIII. The Rumb and distance of two places being given, together with the Latitude of one of those places, to find the Latitude of the other place, and their difference of Longitude. FOr example, the distance between S. Maries iceland and the Lizard is 275. German miles, in the Rumb of North East and South West, and the Latitude of S. Maries iceland is 37. degrees; It is required to find the Latitude of the Lizard, and the difference of Longitude between both places. First to find the Latitude of the Lizard, bring the fourth Rumb to the Meridian under the Latitude of S. Maries iceland, namely 37. degrees, and set a mark thereto; then measure with your Compasses( as in 72. problem) the distance given 275. German miles, and at the end thereof make another mark, this being done, search in the Meridian the Latitude of the second mark, and you shall find 50. degrees, which is the Latitude of the Lizard sought, then search the difference of Longitude between both marks( by the 74. problem) which you shall find to be 18. degrees 2. minutes. problem LXXIX. To find the Declination of the Magnetick Needle, which they call the variation of the Mariners compass. EXperience shows, that the Magnetick Needle in the same place, doth always show and point towards the same cost of the World, but not the like in all places; for in some places it points directly North; in other places it declines from the North into the East; and in other places it varies from the North to the West. But although this variation of the Needle is not of very great moment in short Voyages, as from hence into Swedeland, Russia, France, Spain, or other bordering places; and therefore in these Voyages is commonly neglected, especially seeing some Sea Charts are in a manner fitted to the variation: notwithstanding it is not to be neglected in greater Voyages through the vast Ocean, but ought diligently to be observed and considered; seeing that ships are steered by the Mariners compass, as their only guide, and accomplish their Voyages according to the guidance thereof; which by reason of the hidden virtue of the Magnetick Needle, from the true North divers ways, sometimes Eastward otherwhiles Westward, swerves even to the difference of two Rumbs or points of the compass, from the true North; from whence it is manifest, that Ships steered by the guidance of the said Magnetick Needle, may err also so much from the intended Voyage. How much this Declination of the Magnetick Needle is in divers places of the earth, and which way it swerves from the true North, we will pass by as impertinent, and not serving to our purpose; and shall only show how the same may be observed by the Globe. To effect this, observe by such a compass which hath the Magnetick Needle placed directly towards the North, under the flower de luke, in what amplitude or degrees of the compass the Sun rises in the morning, or sets at night; and find by the 18. problem the true Amplitude of the Suns rising or setting for the day given. Then if the rising or setting of the Sun in the compass and Globe agree together, the Needle shows the true North, without any variation: But as much as the same rising in the compass is more Northward, then his true amplitude, so much the Needle varies from the North Eastward, and as much as it is more Southward, so much the Needle declines from the North Westward: Contrarily in the setting, as much as the Sun sets more Northwards then the true amplitude, so much the Needle declines into the West, and as much as it is Southwards, so much the Needle swerves into the East. An Example, by the rising of the Sun. The 10. of May under the Northern latitude of 40. deg. I observe the same to rise by such a compass whose Needle lies directly under the flower de luke 37. deg. from the East Northwards; but by the 19. problem, I find that it ought to rise in such latitude, 26. deg. 37. min. from the East Northwards; therefore because the difference here is 10. deg. 23. min. that the Sun by the compass rises more Northwardly then the truth; by consequence the point of East, points so much from the true East Southwards, also the Needle and flower de luke varies so many degrees and minutes, from the North Eastwards. Another Example by the Amplitude of the Sun at his setting. For the same day and latitude, I find that the Sun by the Globe sets at night 26. deg. 37. min. from the West Northwards. But observing the Sun by the compass, I find that he sets only 16. deg. 14. min. from the West Northward; difference is 10. deg. 23. min. that the Rumb or point of West in the compass points nearer to the North then the truth, therefore also the Needle varies so much from the North Eastward. The variation of the Needle, also may be found at any time, of the day by the height of the Sun; for example the 27. of June in the North latitude of 52. deg. 23. min. the Sun being 22. deg. high, I find( by the 34. problem) that the Sun is in the Azimuth of 9. deg. 2. min. from the East Northwards, but observing by the compass, I find that he is only 4. deg. from the East, Northward: so that the difference here is 5. deg. 2. min. that the Sun by the compass appears more Eastwards then the truth; or( which is the same) I see that the East Rumb is too near to the North by 5. deg. 2. min. and by consequence the Needle varies so much from the North Westward. You may use the same manner of work, in the afternoon for any height of the Sun, but such observations as are made when the Sun is at a good distance from the Meridian, are the most exact. FINIS. Here follows the Ancient Stories of the several STARS, and CONSTELLATIONS. showing by Poetical reasons why they were placed in Heaven. Collected from Dr HOOD. And first, Of the Northern Constellations. 1. URSA MINOR. This Constellation hath the pre-eminence, because it is nearest of all the rest unto the North Pole; And is called of the Greeks {αβγδ}; whereupon the Pole is called the Pole arctic, for that it is near unto that Constellation. It is also called Helice minor, because of the small revolution which it maketh round about the Pole: or rather of Elice, a Town in Arcadia, wherein calisto the great Bear, and mother to the less, was br●d. It is called Cynosura, because this Constellation, though it carry the name of a Bear, yet it hath the tail of a Dog. Last of all, it is termed Phoenice, because that Thales, who first gave the name to this Constellation, was a Phoenicean: And therefore the Phoenicians being taught how to use it in their Navigations, did call it by the name of the country wherein Thales was born. It consisteth of 7. stars, which the latins call Septemiriones; because by their continual motion, those seven stars do as it were wear the heavens. The Spanjards call them all Bosina, that is, an Horn; because they may be very well brought into that form, whereof that which is in the end of the tail, is called the Pole-Star, by reason of the neareness thereof unto the Pole of the world: for it is distant( according to the opinion of most) from the true Pole, but 23. deg. 30. min. the Arabians call it Alrukaba: And of the Scythians it is said to be an Iron nail, and is worshipped by them as a God. The two stars that are in the shoulders of the Bear, are called Guards, of the Spanish word Guardare, which is to behold; because they are diligently to be looked unto, in regard of the singular use which they have in Navigation. The reason why this Constellation was brought into the Heavens, is diversely set down, and first in this manner. Saturn having received of the Oracle that one of his sons should banish him out of his Kingdom, determined with himself to kill all the men children that he should beget: whereupon he gave command to Ops his wife, being then great, that she should show him the child so soon as ever it was born: But she bringing forth Jupiter, and being greatly delighted with his hair, gave the child unto two nymphs of Crete, dwelling in the mount Dicte; whereof this was one, and was called Cynosura; the other was Helice. Jupiter, after that( according to the Oracle) he had bereft his Father of the Kingdom, in recompense of their pains and courtesy, translated them both into the Heavens, and made of them two Constellations; the Lesser Bear, and the Greater Bear. Other some say, that it was Arcas, the son of calisto; and they tell the tale on this manner. calisto a nymph of singular beauty, daughter to Lycaon King of Arcadia, induced by the great desire she had of hunting, became a follower of the Goddess Diana. After this, Jupiter being enamoured with her beauty, and out of hope, by reason of her profession, to win her love in his own person, counterfeited the shape of Diana, lay with calisto, and got her with child; of whom was born a son, which was called Arcas. Diana, or rather Juno, being very much offended here-with, turned calisto into a Bear. Arcas her son at the Age of fifteen, hunting in the woods, by chance lighted upon his mother in the shape of a Bear: who knowing her son Arcas, stood still, that he might come near unto her, and not be afraid: but he fearing the shape of so cruel a Beast, bent his bow of purpose to have slain her: Whereupon Jupiter to prevent the mischief, translated them both into Heaven, and of them made two several Constellations: unto the lesser Bear, there belongs but one star unformed. 2. URSA MAIOR, the Greater Bear, called also of the Greeks Arctos, and Helice, consisteth of 27. stars: Among the which, those seven that are in the hinder part and tail of the Bear, are most observed; the latins call them Plaustrum; and of our men they are called Charles wain; because the stars do stand in such sort, that the three which are in the tail resemble the Horses, and the other four which are in the flank of the Bear, stand( after a manner) like the Wheels of a wagon, or Chariot; and they are supposed by some to be greater then the Sun. The reason of the Translation of this Constellation into the Heaven, is at large set down in the other Constellation, and therefore needs not here to be repeated. This Constellation was first invented by Nauplius the Father of Palamedes the Greek, and in great use among the Grecians; and this is to be noted both in this and the former Constellation, that they never set under the Horizon in any part of Europe: which though it fall out by reason of their situation in the Heavens; yet the Poets say, that it came to pass through the displeasure and hatred of Juno; who for that she was by calisto made a Cukquean, and they notwithstanding( as she took it) in despite of her, were translated into Heaven, requested her brother Neptune, that he would never suffer those stars to set within his Kingdom: To which request Neptune condescended: so that in all Europe they never come near unto the Sea, or touch the Horizon. If any one marvel, that( seeing she hath the form of a Bear) she should have a tail so long; Imagine that Jupiter fearing to come too nigh unto her teeth, laid hold on her tail, and thereby drew her up into heaven; so that she of her self being very weighty, and the distance from the Earth to the Heaven very great, there was great likelihood that her tail must stretch. The unformed stars belonging to this Constellation are eight. 3. DRACO, the Dragon, of some name the Serpent, of others the Snake, by the Arabians, Aben; and by Junctinus Florentinus, Vrago; because he windeth his tail round about the ecliptic Pole; it containeth 31. stars. This was the Dragon that kept the Golden apple in the Orchard of the Hesperides,( now thought to be the Islands of scape de Verde) and for his diligence and watchfulness, was afterwards translated into heaven: Yet others say, that he came into Heaven by this occasion; when Minerva withstood the giants fighting against the Gods; they to terrify her, threw at her a mighty Dragon; but she catching him in her hands, threw him presently up into Heaven, and placed him there as a memorial of that her resistance. Others would have it to be the Serpent Python, whom Apollo slay after the Deluge. 4. CEPHEUS containeth in him 11. stars, and hath two unformed. This was a King of the Aethiopians, and Husband unto Cassiopeia, and father of Andromeda, whom Perseus married. He was taken up into Heaven, with his wife and daughter, for the good deserts of Perseus his son in law; that he and his whole stock might be had in remembrance for ever. The star which is in his right shoulder, is called by the Arabians, Alderahiemin; i.e. his right Arm. 5. BOOTES, the driver of the Oxen( for so I suppose the name to signify, rather then an Herdsman; for he hath not his name because he hath the care of any cattle, but only because he is supposed to drive Charles his Wain, which is drawn by 3. Oxen) he is also called Arctophilax, the keeper of the Bear, as though the care of her were committed unto him. This Constellation consisteth of 22. stars. Some will have Bootes to be Arcas, the son of her who before was turned into the Great Bear; and they tell the tale thus. Lycaon the father of calisto, receiving Jupiter into his house as a guest, took Arcas his daughters son, and cut him in pieces; and among other services, set him before Jupiter to be eaten: for by this means he thought to prove if his guest were a God, as he pretended to be. Jupiter perceiving this heinous fact, overthrew the table, fired the house with lightning, and turned Lycaon into a Wolf: but gathering, and setting together again the limbs of the child, he committed him to a Nymph of Aetolia to be kept: Arcas afterwards coming to mans estate, and hunting in the woods, lighted at unawares upon his mother, transformed by Juno into the shape of a Bear, whom he pursued into the Temple of Jupiter Lycaeus, whereunto by the law of the Arcadians it was death for any man to come. For as much therefore as they must of likelihood be both slain, calisto by her son, and he by the law; Jupiter to avoid this mischief, of mere pity took them both up into heaven. Unto this Constellation belongeth but one star unformed, and it is between the legs of Bootes, and by the Grecians it is called Arcturus, because of all the stars near the great Bear name Arctos, this star is first seen near her tail in the evening. The Poetical invention is thus. Icarus the father of Erigone, having received of the God Bacchus a flagon of wine, to declare how good it was for mortal men, traveled therewith into the Territories of Athens, and there began to carovie with certain shepherds: they being greatly delighted with the pleasantness of the wine, being a new kind of liquour, began to draw so hard at it, that ere they left off, they were past one and thirty; and in the end, were fain to lay their heads to rest. But coming unto themselves again, and finding their brains scarce in good temper, they killed Icarus, thinking indeed that he had either poisoned them, or at the least wise made their brains intoxicate. Erigone was ready to die for grief, and so was Mera her little dog. But Jupiter to alloy their grief, placed her father in heaven between the legs of Arctophilax. 6. CORONA BOREA, the Northern garland, consisteth of eight stars; yet Ovid saith, that it hath nine. This was the Garland that Venus gave unto Ariadne, when she was married unto Bacchus in the Isle Naxus, after that Theseus had forsaken her: which Garland, Bacchus placed in the Heaven as a token of his love. Novidius will have it to be the Crown of the Virgin Mary. 7. ENGONASIS: This Constellation hath the name, because it is expressed under the shape of a man kneeling upon the one knee, and is therefore by the latins called Ingeniculum. It containeth 29. stars, and wanteth a proper name, because of the great diversity of opinions concerning the same. For some will have it to be Hercules, that mighty conqueror, who for his 12. labours was thought worthy to be placed in the heaven, and nigh unto the Dragon whom he overcame. Others tell the tale thus: That when the Tytans fought against the Gods, they for fear of the giants, ran all unto the one side of the heaven: whereupon the Heaven was ready to have fallen, had not Hercules, together with Atlas set his neck unto it, and stayed the fall: and for this desert, he was placed in the Heaven. 8. LYRA, the Harp, it containeth 10. stars, whereof thus goeth the Fable. The River Nilus swelling above his banks, overflowed the Country of egypt; after the fall whereof, there were left in the fields divers kinds of living things, and amongst the rest a Tortoise; Mercury, after the flesh thereof was consumed, the sinews still remaining, found the same, and striking it, he made it yield a certains sound: whereupon he made an Harp like unto it, having 3. strings, and gave it unto Orpheus the son of Cassiopea. This Harp was of such excellent sound, that Trees, Stones, Fowls, and wild Beasts are said to follow the sound thereof. After such time therefore that Orpheus was slain by the women of Thrace, the Muses by the good leave of Jupiter, and at the request of Apollo, placed this Harp in Heaven. Novidius will have it to be the Harp of David, whereby he pacified the evil spirit of Saul. This Constellation was afterwards called vulture Cadens, the falling gripe: and Falco, the Falcon; or Tympanum, the Timbrel. 9. OLOR, or Cygnus, the Swan, called of the Caldaeans Adigege: it hath 17. stars: of this Constellation the Poets Fable in this manner. Jupiter being overtaken with the love of Leda, the wife of Tyndarus King of Oebalia, and knowing no honester way to accomplish his desire, procured Venus to turn herself into an Eagle, and himself he turned into the shape of a Swan: Flying therefore from the Eagle, as from his natural enemy that earnestly pursued him, he lighted of purpose in the lap of Leda, and, as it were for his more safety, crept into her bosom. The woman not knowing who it was under that shape, but holding( as she thought) the Swan fast in her arms, fell a sleep: In the mean while Jupiter enjoyed his pleasure; and having obtained that he came for, betook him again unto his wings; and in memorial of his purpose attained under that form, he placed the Swan among the stars. Ovid calleth this Constellation Milvius, the Kite, and telleth the tale thus. The Earth being greatly offended with Jupiter, because he had driven Saturn his father out of his Kingdom, brought forth a monstrous Bull, which in his hinder parts was like a Serpent; and was afterwards called the Fatal Bull; because the Destinies had thus decreed, that whosoever could slay him, and offer up his entrails upon an Altar, should overcome the eternal Gods. Briareus that mighty giant, and ancient enemy of the Gods, overcame the Bull, and was ready to have offered up his entrails according to the decree of the Destinies: But Jupiter fearing the event commanded the Fowls of the Air to snatch them away: which although to their power, they endeavoured, yet there was none of them found so forward and apt to that action as the Kite, and for that cause he was accordingly rewarded with a place in Heaven. Some call this Constellation {αβγδ}, that is, the bide: others call it vulture volans, the Flying gripe: It is also called Gallina, the Hen. Unto this Constellation do belong two unformed stars. 10. CASSIOPEIA, She consisteth of 13. stars. This was the wife of Cepheus, and mother of Andromeda, whom Perseus married, and for his sake was translated into Heaven, as some writ. Others say that her beauty being singular, she waxed so proud, that she preferred herself before the nereids, which were the Nymphs of the Sea: for which cause, unto her disgrace and the example of all others, that in pride of their hearts would advance themselves above their betters, she was placed in the Heaven with her head as it were downward, so that in the revolution of the Heavens, she seemeth to be carried head-long. 11. PERSEUS, he hath 26. stars. This was the son of Jupiter, whom he in the likeness of a Golden shower begot upon Danaë, the daughter of Acrisius. This Perseus coming unto mans estate, and being furnished with the sword, hat, and wings of his brother Mercury, and the shield of his sister Minerva, was sent by his foster father Polidectes, to kill the Monster Medusa, whom he slay; and cutting off her head, carried it away with him: But as he was hastening homeward, flying in the air, he espied Andromeda the daughter of Cepheus and Cassiopeia, for the pride of her mother, board with a chain unto a rock, by the sea side, there to be devoured by a Whale: Perseus taking notice and pity of the case, undertook to fight with the Monster, upon condition that Andromeda might be his wife; to be short, he delivered Andromeda, married her, and returning homeward unto the Isle Seriphus, he found there his Grand-father Acrisius, whom by mischance, and unadvisedly, he slay with a quoit,( or as Ovid reporteth, with the terrible sight of the horrible head of Medusa, not knowing that it was his Grandfather: but afterward understanding whom he had slain, he pined away through extreme sorrow: whereupon Jupiter his Father pitying his grief, took him up into Heaven, and there placed him in that form wherein he overcame Medusa, with the sword in one hand, and the head of Medusa in the other, and the wings of Mercury at his heels. This Constellation, because of the unluckiness thereof, is called by Astrologers Cacodemon,( i.e.) unlucky, and unfortunate. For( as they say) they have observed it, that whatsoever is born under this Constellation, having an evil aspect, shall be strike with sword, or loose his head. Novidius saith, that it is David with goliath his head in the one hand, and his sword in the other. The unformed stars belonging unto this Constellation, are three. 12. AURIGA, the wagoner, or Carter: he consisteth of 14 stars; the Arabians call him Alaiot; the Greeks Heniochus, i.e. a man holding a bridle in his hand, and so is he pictured. Eratostenes affirmeth him to be Ericthonius, King of Athens, the son of vulcan: who having most deformed feet, devised first the use of the waggon or Chariot, and joined horses together to draw the same, to the end that he sitting therein, might the better conceal his deformities. For which invention, Jupiter translated him into the Heavens. In this Constellation there are two other particular Constellations to be noted; whereof the one consisteth but of one star alone, which is in the left shoulder of Auriga, and is called Hircus, or Capra, the Goat; the Arabians call it Alhaiot: The other consisteth of two little stars a little beneath the other, standing as it were in the hand of Auriga; this Constellation is called Haedi, the Kids. The tale is thus Saturn( as you heard before) had received of the Oracle, that one of his sons should put him out of his Kingdom, whereupon he determined to devour them all: Ops by stealth conveyed away Jupiter, and sent him to Melissus King of Crete to be nourished: Melissus having two daughters, Amalthaea and Melissa, committed Jupiter unto their Nursery. Amalthaea had a Goat that gave suck unto two Kids, so that by the milk of this Goat, she nourished Jupiter very well. To requited this her care and courtesy, Jupiter( after he had put his father out of his Kingdom) translated her Goat and her two Kids into Heaven; and in remembrance of the Nurse, the Goat is called Caprá Amalthaea. Novidius saith, That when Christ was born, and his birth made manifest by the Angels unto the Shepherds, one of them brought with him for a Present, a Goat and two young Kids; which in token of his good will, were placed in Heaven. 13. OPHIUCHUS, or SERPENTARIUS, That is, the Serpent-bearer. This Constellation hath no proper name, but is thus entitled, because he holdeth a Serpent in his hands. It containeth 24. stars. Some say that it is Hercules, and report the tale on this manner. Juno being a great enemy to Hercules, sent two snakes to kill him, as he lay sleeping in his Cradle: but Hercules being a lusty child( for Jupiter had spent two daies in begetting him) without much ado, strangled them both: In memorial of so strange an event, Jupiter placed him in the heavens, with a Serpent in his hands. 14. SERPENS, the Serpent of Ophiuchus, which consisteth of 18. stars. Some say that it is one of the Serpents that should have slain Hercules in his Cradle. Novidius saith, it is the Viper that bit Paul by the hand. Others deliver the tale in these words; Glaucus the son of Minos King of Crete, was by misfortune drowned in a Barrel of Honey. Minos his father craved the help of Aesculapius the physician: And that he might be driven perforce to help the child, he shut him up in a secret place, together with the dead carcase; while Aesculapius stood in a great maze with himself what were best to be done, upon a sudden there came a Serpent creeping towards him; the which Serpent he slay with the staff which he had in his hand. After this there came another Serpent in, bringing in his mouth a certain herb, which he laid upon the head of the dead Serpent, whereby he restored him unto life again. Aesculapius using the same herb, wrought the same effect upon Glaucus. Whereupon( after that) Aesculapius( whom some affirm to be Ophiuchus) was placed in the heaven, and the Serpent with him. 15. SAGITTA, or Telum; the Arrow or Dart. This was that Arrow wherewith Hercules slay the Eagle or gripe that fed upon the liver of Promotheus, being tied with chains to the top of the mount Caucasus; and in memorial of that dead, was translated into Heaven. Others will have it to be one of those Arrows which Hercules at his death gave unto Phylectetes, upon which the Destiny of Troy did depend. The whole Constellation containeth five stars. 16. AqUILA, the Eagle, which is also called vulture Volans, the flying gripe: It hath in it 9. stars. The Poetical reason of this Constellation, is this; Jupiter transforming himself into the form of an Eagle, took Ganimides the Trojan Boy, whom he greatly loved, up into heaven, and therefore in sign thereof( because by that means he performed his purpose) he placed the figure of the Eagle in the Heaven. There belong unto this Constellation 6. stars( before time) unformed, but now brought into the Constellation of Antinous. But whereupon that name should come, I know not, except it were that some man devised it there, to cury favour with the Emperour Adrian, who loved one Antinous Bithynicus so well, that he builded a Temple in his honour at mantinaea. 17. DELPINUS, the Dolphin: It containeth 10. stars; yet Ovid in his second Book de Fastis, saith that it hath but nine. Neither did the ancient Astronomers attribute unto it any more, according to the number of the Muses; because of all other Fishes, the Dolphin is said to be delighted with music. The tale goeth thus concerning this Constellation. When Neptune the God of the Sea greatly desired to match with Amphitrite, she being very modest and shamefaced, hide her self: whereupon he sent many messengers to seek her out, among whom, the Dolphin by his good hap, did first find her; and persuaded her also to match with Neptune: For which his good and trusty service, Neptune placed him in the Heavens. Others say, that when Bacchus had transformed the Mariners that would have betrayed him, into Dolphins, he placed one of them in Heaven, that it might be a lesson for others to take heed how they carried any one out of his way, contrary both to his desire, and their own promise. Novidius referreth this Constellation unto the Fish which saved Jonas from drowning. 18. EqUICULUS, is the little Horse, and it consisteth of 4. stars. This Constellation is name almost of no Writer, saving Ptolomeus, and Alphonsus, who followeth ptolemy, and therefore no certain tale or History is delivered thereof, by what means it came into Heaven. 19. EqUUS ALATUS, the Winged Horse, or Pegasus, it containeth 20. stars. This Horse was bread of the blood of Medusa, after that Perseus had cut off her head, and was afterward taken and tamed by Bellerophon, whiles he drank of the River Pirene by Corinth, and was used by him in the conquest of Chimera: After which exploit, Bellerophon, being weary of these earthly affairs, endeavoured to fly up into Heaven: But being amazed in his flight, by looking down to the earth, he fell from his horse; Pegasus notwithstanding continuing his course( as they feign) entered into Heaven, and there obtained a place among the other Constellations. 20. ANDROMEDA, She consisteth of 23. stars; but one of them is common both unto her, and Pegasus. This was the daughter of Cepheus and Cass●opeia, and the wife of Perseus: the reason why Minerva, or Jupiter placed her in the Heavens, is before expressed. Novidius referreth this Constellation unto Alexandra the Virgin, whom S. George through the good help of his horse, delivered from the Dragon. 21. TRIANGULUM, the Triangle, called also Deltoton, because it is like the fourth letter of the Greeks Alphabet Δ which they call Delta; it consisteth of four stars. They say it was placed in Heaven by Mercury, that thereby the head of the Ram might be the letter known. Others say, that it was placed there in honour of the Geometricians, among whom, the Triangle is of no small importance. Others affirm, that Ceres in time past requested Jupiter that there might be placed in Heaven some Figure representing the form of sicily, an iceland greatly beloved of Ceres for the fruitfulness thereof: now this iceland being triangular,( at her request) was represented in the Heaven under that form. Thus much concerning the Constellations of the Northern Hemisphere. Now follow the Poetical Stories of the Constellations of the Southern Hemisphere. Secondly, Of the Southern Constellations. 1. coetus, the Whale, it is also called the Lion, or Bear of the Sea. This is that monstrous fish that should have devoured Andromeda, but being overcome by Perseus, was afterwards translated into Heaven by Jupiter, as well for a token of Perseus his manhood, as for the hugeness of the fish it self. This Constellation consisteth of 22. stars. 2. ORION, this hath 38. stars. The Poetical reason of his translation into the Heaven, shall be shown in the Scorpion, amongst the Zodietical Constellations. The Ancient Romans called this Constellation Jugala; because it is most pestiferous unto cattle, and as it were the very cut-throat of them. There are bright stars in his girdle, which we commonly call our Ladies yard, or wand. Novidius, applying this sword of Orion unto Scripture, will have it to be the sword of Saul, afterward called Paul, wherewith he persecuted the members of Christ, which after his conversion was placed in Heaven. In his left shoulder there is a very bright star, which in latin is called Bellatrix, the warrior, in the feminine gender. I cannot find the reason, except it be this; that women born under this Constellation shall have mighty tongues. The reason of the Oxhide which he hath in his hand, may be gathered out of the next story. 3. FLUVIUS, the River; it comprehendeth 34. stars. It is called by some Eridanus, or Padus; and they say that it was placed in Heaven in remembrance of Phaeton, who having set the whole world on fire, by reason of misguiding of his father Phoebus his chariot, was slain by Jupiter with a thunder boult, and tumbling down from Heaven, fell into the river Eridanus, or Padus, which the Italians call Po. Others say, that it is Nylus, and that that Figure was placed in the Heaven, because of the excellency of that river, which by the Divines is called Gihon; and is one of the Rivers of paradise. Others call it flumen Orionis, the flood of Orion; and say, that it was placed there, to betoken the Off-spring from whence Orion came: for the tale is thus reported of him. Jupiter, Neptune, and Mercury, traveling upon the earth in the likeness of men, were requested by Hyreus to take a poor lodging at his house for a night: they being overtaken with the evening, yielded unto his request; Hyreus made them good cheer, killing an ox for their better entertainment: The Gods seeing the good heart of the old man, willed him to demand what he would in recompense of his so friendly cheer. Hyreus and his wife being old, requested the Gods to gratify them with a Son. They to fulfil his desire, called for the hid of the ox that was slain, and having received it, they put it into the earth, and made water into it all three together, and covering it, willed Hyreus within ten moneths after to dig it out of the earth again; which he did, and found therein a manchild; whom he called Ourion, ab Urina, of piss; although afterwards by leaving out the second letter, he was name Orion. At such time therefore as he was placed in Heaven, this flood was joined hard to his heels, and the ox hid wherein the Gods did piss, was set in his left hand, in memorial of his Off-spring. 4. LEPUS, the Hare, which consisteth of 12. stars. This Constellation was placed in Heaven between the legs of Orion, to signify the great delight in hunting which he had in his life time. But others think it was a frivolous thing, to say that so notable a fellow as Orion, would trouble himself with so small and timorous a beast as the Hare, and therefore they tell the tale thus. In times past there was not a Hare left in Isle Leros: a certain youth therefore of that iceland, being very desirous of that kind of beast, brought with him from another country there about, an Hare great with young; which when she had brought forth, they in time became so acceptable unto the other countrymen, that every one almost desired to have and keep a Hare. By reason whereof, the number of them grew to be so great, within a short space after, that the whole iceland became full of Hares, so that their masters were not able to find them meat: whereupon the Hares breaking forth into the fields, devoured their corn. Wherefore the inhabitants being bitten with hunger, joined together with one consent, and( though with much ado) destroyed the Hares. Jupiter therefore placed this Constellation in the Heaven, as well to express the exceeding fearfulness of the beast, as also to teach men this lesson; that there is nothing so much to be desired in this life, but that at one time or an other it bringeth with it more grief then pleasure. Some say, that it was placed in Heaven at the request of Ganimedes, who was greatly delighted with hunting the Hare. 5. CANIS MAIOR, the Great Dog, it consisteth of 18. stars. It is called Sirius Canis, because he causeth a mighty drought by reason of his heat. This is the Constellation that giveth the name unto the Canicular, or Dog-days; whose beginning and end is not alike in all places, but hath a difference according to the Country and time: as in the time of hippocrates the physician, who lived before the time of Christ 400. yeers, the Canicular days began the 13. or 14. July. In the time of Avicenna, the Spaniard, who lived in the year of our Lord 1100. the Canicular days began the 15, 16, or 17. of July. In our Country, they begin about S. James-tide, but we use to account them from the 6. of July, to the 17. of August. Which is the time when the Sun beginneth to come near unto, and to depart from this Constellation. Novidius will have it to be referred to Tobias Dog, which may very well be, because he hath a tail; and Tobias Dog had one; as a certain fellow once concluded: because it is written that Tobias his Dog fawned upon his master, therefore it is to be noted( said he) that he had a tail. The Poets say, that this is the Dog whom Jupiter set to keep Europa, after that he had stolen her away, and conveyed her into Crete, and for his good service was placed in Heaven. Others say, that it was one of Orion his Dogs; There belong unto this Constellation 11. stars unformed. 6. CANIS MINOR; the Lesser Dog; this of the Greeks is called protion, of the latins Ante Canis; it containeth but two stars. Some say, that this also was one of Orions Dogs. Others rather affirm it to be Mera, the Dog of Erigone, or rather of Icarius her father, of whom mention is made in the Constellation of Bootes and Virgo. This Dog of mere love to his master being slain, as is aforesaid, threw himself into the river Anygrus, but was afterward translated into Heaven with Erigone. Among the Poets there is great dissension which of the two should be the Dog of Erigone; some saying one, and some the other, and therefore they do many times take the one for the other. 7. ARGO NAVIS, the Ship Argo, which comprehendeth 41. stars; this is the Ship wherein Jason did fetch the Golden Fleece fron Colchis, which was afterward placed in Heaven as a memorial, not only because of the great Voyage, but also, because( as some will have it) it was the first Ship wherein any man sailed. Their reason why this Ship is not made whole is, that thereby men might be put in mind not to despair, albeit that their Ship miscarry in some part now and then. Some avouch it to be the Ark of Noe. Novidius saith it is the Ship wherein the Apostles were, when Christ appeared unto them walking on the Sea. In one of the Oars of this Ship, there is a great star called Canopus, or Canobus, which the Arabians called Shuel, as it were a bonfire, because of the greatness thereof. It is not seen in Italy, nor in any Country on this side of Italy. Some say that Canobus the master of Menelaus his Ship, was transformed into this star. 8. HYDRA, the Hydre; this hath 25. stars, and two unformed. 9. CRATER, the Cup, or standing piece; this hath seven stars. Some say that this was the cup wherein Tagathon, that is, the chief God, mingled the stuff whereof he made the souls of men. 10. CORVUS, the Crow; this hath seven stars. These 3. Constellations are to be joined together, because they depend upon one History, which is this. Upon a time Apollo made a solemn feast to Jupiter, and wanting water to serve his turn, he delivered a cup to the Crow( the bide wherein he chiefly delighted) and sent him to fetch water therein: The Crow flying towards the River, espied a figtree, fell in hand with the figs, and abode there till they were ripe: In the end, when he had fed his fill of them, and had satisfied his longing, he bethought himself of his errand, and by reason of his long delay, fearing a check, he caught up a snake in his bill, brought it to Apollo, and told him that the snake would not let him fill the Cup with water. Apollo seeing the impudence of the bide, gave him this gift, that as long as the figs were not ripe upon the three, so long he should never drink: and for a memorial of the silly excuse that he made, he placed both the Crow, Cup, and Snake, in Heaven. 11. CENTAURUS, the centaur, which comprehendeth 37. stars. Some say, that this is Typhon, others call him Chiron, the Schoolmaster of those three excellent men, Hercules, Achilles, and Aesculapius; unto Hercules he red Astronomy; he trained up Achilles in music, and Aesculapius in physic: and for his upright life, he was turned into this Constellation. Yet Virgil calleth Sagittarius by the name of Chiron. In the hinder feet of this Constellation, those stars are set which are called the Crosiers, appearing to the Mariners as they sail towards the South Sea, in the form of a cross, whereupon they have their name. The four stars which are in the Garnish of the centaurs Spear, are accounted by Proclus as a peculiar Constellation, and are called by him Thyrsilochus, which was a Spear compassed about with Vine leaves: but they are called by Copernicus and Clavius, and other Astronomers, the stars of his Target. It should seem that they were deceived by the old translation of Ptolomee, wherein Scutum is put for Hasta, i.e. the Target for the Spear, as it is well noted by our Countryman M. R. Record, in his Book entitled the Castle of knowledge. 12. LUPUS, the Wolf, or the beast which the centaur holdeth in his hand, and containeth 19. stars; the Poetical reason is this. Chiron the centaur being a just man, was greatly given to the worship of the Gods: which thing, that it might be notified to all posterity, they placed him by this beast, which he seemeth to stick, and thrust through with his Spear,( as it were) ready to kill for sacrifice. 13. Ara, the Altar, it is also called Lar, or Thuribulum, i.e. a Chimney with the fire, or a Censor. It consisteth of seven stars, and is affirmed of some Poets, to be the Altar whereon the centaur was wont to offer up his sacrifice. But others tell the tale thus. When as the great giants called the Tytans, laboured as much as might be to pull Jupiter out of Heaven, the Gods thought it good to lay their heads together to advice what was best to be done: Their conclusion was, that they should all with one consent join hands together to keep out such fellows: and that this their league might be confirmed, and thoroughly ratified; they caused the Cyclops,( which were workmen of Vulcan) to make them an Altar: about this Altar all the Gods assembled, and there swore, that with one consent they would withstand their enemies; afterwards, having gotten the victory, it pleased them to place this Altar in heaven, as a memorial of their League, and a token of that good which unity doth breed. 14. CORONA AUSTRINA, the South Garland, it hath 13. stars. Some say that it is some trifling Garland which Sagittarius was wont to wear, but he cast it away from him in jest, and therefore it was placed between his legs: others call it the Wheel of Ixion, whereupon he was tormented for that great courtesy he would have offered unto Juno, thinking indeed to have gotten up her belly: but Jupiter seeing the impudence of the man, tumbled him out of Heaven( where by the licence of the Gods he was sometime admitted as a guest) into Hell, there to be continually tormented upon a wheel. The Figure of which wheel was afterwards placed in Heaven, to teach men to take heed how they be so saucy, to make such courteous proffers unto other mens wives. The Greekes call this Constellation by the name of Uraniscus, because of the Figure thereof: For it representeth the palate▪ or roof of the mouth, which they call Uraniscus. 15. The last is PISCIS AUSTRINUS, or Notius, the South Fish, which comprehendeth 11. stars, besides that which is in the mouth thereof, belonging to the water, which runneth from Aquarius, and is called by the Arabians Fomahant. The reason why this Fish was placed in the Heaven, is uncertain: yet some affirm, that the daughter of Venus going into a water to wash her self, was suddenly transformed into a fish; the which fish was afterward translated into Heaven. The unformed stars belonging unto this Constellation are six. Thus much concerning the Constellations of the Northern and Southern Hemispheres; now follow the Poetical Stories of the Zodietical Constellations. Thirdly, Of the Zodietical Constellations. 1. ARIES, the Ram, it is called by the Greekes {αβγδ}, it containeth in it 13. stars, which were brought unto this Constellation by Thyestes, the son of Pelops, and brother of Atreus. This is the Ram upon which Phrixus, and hell his sister, the children of Athamas did sit, when they fled from their step-mother into, over the Sea of Hellespout: which Ram was afterward for his good service, translated into Heaven by Jupiter. Others say, that it was that Ram which brought Bacchus unto the spring of water, when through drought he was likely to have perished in the desert of Lybia. Novidius will have this to be the Ram which Abraham offered up in stead of his son Isaac. The star that is first in the head of the Ram, is that from whence our later Astronomers do account the Longitude of all the rest, and it is distant from the head of Aries, in the tenth Sphere, 27 deg. 53. min. The unformed stars belonging unto this Constellation, are five. 2. TAURUS, the Bull, which consisteth of 23. stars. This was translated into Heaven in memorial of the rape committed by Jupiter and Europa, the daughter of Agenor, King of Sidon; whom Jupiter in the likeness of a white Bull stolen away, and transported into candy. Others say, that it was jo the daughter of Inachus, whom Jupiter loved, and turned into the form of a Cow, to the intent that juno coming upon him at unawares, should not perceive what a part he had played: jupiter afterward in memorial of that crafty conveyance, placed that Figure in Heaven; The reason why the Poets name not certainly whether it be a Cow or a Bull, is, because it wanteth the hinder parts; yet of the most of them it is called a Bull. In the Neck of the Bull there are certain stars standing together in a cluster, which are commonly called the seven Stars; although there can hardly be discerned any more then six. These are reported to be the seven daughters of Atlas, called Atlantiades, whereof six had company with the immortal Gods, but the seventh( whose name was Morope) being married unto sisyphus a mortal man, did therefore withdraw and hid her self, as being ashamed that she was not so fortunate in matching her self as her sisters were. Some say, that that star which is wanting is Electra, the eldest daughter of Atlas, and that therefore it is so dim, because she could not abide to behold the destruction of Troy; but at that time, and ever since, she hide her face. The reason why they were taken up into Heaven, was, their great pity towards their father, whose mishap they bewailed with continual tears. Others say, that whereas they had vowed perpetual virginity, and were in danger to lose it, by reason of Orion, who greatly assailed them, being overtaken with their love; they requested Jupiter to stand their friend; who translated them into stars, and placed them in that part of Heaven. The Poets call them Pleiades, because when they rise with the Sun, the Mariners may commit themselves to the Sea. Others will have them to be termed so a pluendo; because they procure rain. Others give them this name, of the Greek word {αβγδ}, because they be many in number. They be also called Vergiliae, because they rise with the Sun in the Spring time: likewise Athoraiae, because they stand so thick together. Our men call them by the name of the seven Stars, or Brood Hen. The Astronomers note this as a special thing concerning these stars, that when the Moon and these stars do meet together, the eyes are not to be meddled withall, or cured if they be sore: their reason is, because they be of the nature of Mars, and the Moon. Moreover, there be five stars in the face of the Bull, representing the form of the Roman letter V, whereof one( which is the greatest) is called the Bul's Ey. They be called Hyades, and were also the daughters of Atlas, who so long bewailed the death of Hyas their brother, slain by a lion, that they died for sorrow, and were afterward placed in Heaven for a memorial of that great love they bare to their brother. The ancient Romans call the Bul's Ey, Parilicium, or Palelicium; of Pales their goddesse; whose feast they celebrated, after the conjunction of this star and the Sun. The unformed stars belonging unto this Constellation, are eleven. 3. geminy, the Twins; it consisteth of 18. stars. The Poets say they are Castor and Pollux, the sons of Leda, brethren most loving, whom therefore Jupiter translated into Heaven. Some say that the one of them is Apollo, and the other Hercules: but the most affirm the former. The unformed stars of this Constellation are seven, whereof one is called Propus, because it is placed next before the foot of Castor. 4. CANCER, the Crab, it hath 9. stars. This is that Crab which bit Hercules by the heel as he fought with the Serpent Hydra in the Fen Lerna; and for his forward service, was placed in Heaven by Juno, the utter enemy of Hercules. In this Constellation, there are stars much spoken of by the Poets; although they be but small; whereof one is called the Crib, other two are the two Asses, whereof one was the ass of Bacchus the other of Vulcan, whereon they road to battle, when as the giants made war with the Gods, with whose braying and strange noise, the giants were so scared upon the sudden, that they forsook the field, and fled. The Gods getting the victory, in triumphing manner, translated both the Asses, and their manger into Heaven. The unformed stars of this Constellation are four. It is called animal re●rogradum, for when the Sun cometh into his Sign, he maketh Retrogradation. 5. lo, the lion; it hath 27. stars, this is that lion which Hercules overcame in the wood of Nemaea, and was placed in Heaven in remembrance of so notable a dead. Novidius saith, this was one of the lions which were in the den into which Daniel was cast, and was therefore placed in Heaven, because of all other he was most friendly unto Daniel. In the breast of this Constellation is that notable great star, the light whereof is such, as that therefore it is called by Astronomers, {αβγδ}, or Regulus i.e. the Viceroy, or little King among the rest. The unformed stars belonging to the lion are eight; whereof three make the Constellation which is now called Coma Berenices, that is, the hair of Berenice This Constellation was first found out and invented, by Canon the Mathematician, but described by Calimachus the Poet. The occasion of the Story was this, Ptolomeus euergetes having married his sister Berenice, was shortly after, enforced to depart from her, by reason of the warres he had begun in Asia: whereupon Berenice made this vow, that if he returned home again in safety, she would offer up her hair in Venus Temple. ptolemy returned safe, and Berenice, according to her vow, cut off her hair and hung it up. After certain days, the hair was not to be found; whereupon ptolemy the King was greatly displeased: but Canon, to please the humour of the King, and to cury favour with him, persuaded him that Venus had conveyed the hair into Heaven. Canon attributeth seven stars unto it, but ptolemy alotteth it but three because the other be insensible. 6. VIRGO, the Virgin, it hath 26. stars. This is affirmed to be Justice, which among all the Gods sometime living upon the earth, did last of all forsake the same, because of the wickedness that began to multiply therein, and choose this place for her seat in Heaven. Others say, that it was Astraea, the daughter of Astraeus, one of the giants that were called Titans, who fighting against the Gods, Astraea took their parts against her own father, and was therefore after her death commended unto the Heavens, and made one of the 12. signs. Others say, that it was Erigone, the daughter of Icarius, who for that her father was slain by certain drunken men, for very grief thereof did hang herself: but Jupiter taking pitty of the Virgin for her natural affection, translated her into Heaven. In her right wing there is one star of special note, which by the Astronomers is called Vindemeator( i.e.) the gatherer of grapes. This was Ampelos the son of a satire and a Nymph, and greatly beloved of Bacchus, unto whom in token of his love, Bacchus gave a singular fair Vine, planted at the foot of an elm( as the manner was in old time.) But Ampelos in harvest gathering grapes, and taking little heed to his footing, fell down out of the Vine, and broke his neck. Bacchus in memorial of his former affection, translated him into Heaven, and made him one of the principal stars in this Constellation. There is another great star in the hand of the Virgin, called of the latins Spica, of the Greeks Stachus, of the Arabians Azimech( i.e.) the ear of corn: whereby they signify, that when the Sun cometh to this sign, the corn waxeth ripe. Albumazar the Arabian, and Novidius, take this Constellation for the Virgin Mary. The unformed stars in this Constellation, are six. 7. LIBRA, the balance, it containeth 8. stars. Cicero calleth it Jugum the Yoke, and here it is to be noted, that the ancient Astronomers that first set down the number of the Constellations contained in the zodiac, did account but eleven therein, so that the sign which now is called Libra, was heretofore called {αβγδ}, that is to say, the claws of the Scorpion, which possesseth the space of two whole signs. But the latter Astronomers, being desirous to have 12. signs in the zodiac, called those eight whereof the claws of the Scorpion do consist, by the name of Libra; not that there was any Poetical Fiction to induce them thereto but only moved by this reason; because the Sun joining with this Constellation, the day and the night are of an equal length, and are( as it were) equally poised in a pair of balance. Yet( as I remember) some will have this to be the balance wherein Justice, called also Astraea, weighed the deeds of mortal men, and therein presented them unto jupiter. It hath 9. unformed stars appertaining unto it. 8. scorpion, the Scorpion; called of the Arabians, Alatrab; of Cicero, Nepa. It consisteth of 21. stars. The fiction is thus. Orion the son of Hyreus greatly beloved of Diana, was wont to make his boast, that he was able to overcome what beast soever was bread upon the earth: The Earth, being moved with this speech, brought forth the Scorpion, whereby Orion was stung to death. Jupiter thereupon,( at the request of the Earth,) translated both the Scorpion, and Orion into Heaven; to make it a lesson for ever for mortal men, not to trust too much unto their own strength: and to the end he might signify the great enmity between them, he placed them so in the Heaven, that whensoever the one ariseth, the other setteth; and they are never both of them seen together above the Horizon at once. Gulielmus Postellus will have it to be the Serpent which beguiled Eve in Paradise. The unformed stars about this Scorpion are three. 9. SAGITTARIUS, the Archer. It hath thirty one stars. Touching this sign, there are among the Poets many and sundry opinions. Some say that it is Crocus, the son of Eupheme, that was nurse unto the Muses. This Crocus was so forward in learning of the liberal sciences, and in the practise of fears of activity, that the Muses entreated Jupiter, that he might have a place in Heaven. To whose request Jupiter inclining, made him one of the 12. signs: And to the end that he might express the excellent qualities of the man, he made his hinder parts like unto a horse, thereby to signify his singular knowledge in horsemanship: and by his Bow and Arrow, he declared the sharpness of his wit. Whereupon the Astrologers have this conceit, that he that is born under Sagittarius, shall attain to the knowledge of many Artes, and be of prompt wit, and great courage. Virgil affirmeth this to be Chiron the Centaur, who for his singular learning and Justice, was made the Master of Achilles. At which time Hercules coming to visit him( for he had heard both of the worthiness of the Schoolmaster and of the great hopes of the scholar) brought with him his quiver of arrows dipped in the blood of the Serpent Hydra; but Chiron being desirous to see his shafts, and not taking heed of them, being in his hand, let one of them fall upon his foot, and being greatly tormented, not only by the anguish of the poison working in the wound, but much more because he knew himself to be immortal, and his wound not to be recovered by medicine, he was enforced to make request unto the Gods, that he might be taken out of the world, who pitying his case, took him up into Heaven, and made him one of the 12. signs. 10. CAPRICORNUS, the Goat, it consisteth of 28. stars. The Poets say, that this was Pan, the God of the shepherds, of whom they feign in this manner: The Gods having war with the giants, gathered themselves together into egypt, Typhon the giant pursued them thither, whereby the Gods were brought into a quandary, that well was he that by changing his shape might shift for himself. Jupiter turned himself into a Ram: Apollo became a Crow: Bacchus, a Goat: Diana lurked under the form of a Cat: Juno transformed her self into a Cow: Venus, into a Fish: Pan leaping into the river Nilus, turned the upper part of his body, into a Goat, and the lower part into a Fish. Jupiter wondering at his strange device, would needs have that Image and picture translated into Heaven, and made one of the 12. signs. In that the hinder part of this sign is like a Fish, it betokeneth, that the latter part of the month wherein the Sun possesseth this S●gne, inclineth unto rain. 11. AqUARIUS, the Waterman. It hath 42. stars, whereof some make the Figure of the Man: other some, the Water pot; and some, the stream of water that runneth out of the pot. This is feigned to be Ganimedes the Trojan, the son of Tros, and Callirhoe, whom Jupiter did greatly love for his excellent favour and beauty, and by the service of his Eagle carried him up into Heaven, where he made him his Cup-bearer, and called him Aquarius. Others notwithstanding, think it to be Deucalion, the son of Prometheus, whom the Gods translated into Heaven, in remembrance of that mighty deluge which happened in his time, whereby mankind was almost utterly taken away from the face of the earth. The unformed stars belonging unto this sign are three. 12. PISCES, the Fishes: these together with the line that knitteth them together, contain 34. stars. The Poets say that Venus and Cupid her son coming upon a certain time unto the River Euphrates, and sitting upon the bank thereof, upon a sudden espied Typhon the giant, that mighty and fearful enemy of the Gods coming towards them. Upon whose sight▪ they being strike with exceeding fear, leaped into the River, where they were received by two Fishes, and by them saved from drowning. Venus for this good turn, translated them into Heaven. Gulielmus Postellus would have them to be the two Fishes wherewith Christ fed the 5000. men. The unformed stars of this Constellation, are four. Thus have I briefly run over the Poetical reasons of the Constellations: It remains now that I speak of the Milky way. VIA LACTEA, or Circulus Lacteus; by the latins so called; and by the Greekes, Galaxia; and by the English, the Milky way. It is a broad white circled that is seen in the Heaven, in the North Hemisphere, it beginneth at Cancer, on each side the head thereof, and passeth by Auriga, by Perseus, and Cassiopeia, the Swan, and the head of Capricorn, the tail of scorpion, and the feet of Centaur, Argo the Ship, and so unto the head of Cancer. Some in a sporting manner, do call it Watling street; but why they call it so, I cannot tell; except it be in regard of the narrowness that it seemeth to have, or else in respect of that great high way that lieth between Dover and S. Albons, which is called by our men, Watling street. Concerning this circled there are sundry opinions: for there is great difference among some writers, both touching the place, matter and efficient cause thereof. Aristotle dissenteth from all other, both Philosophers and Poets, in the place, matter, and cause of this circled; saying, that it is a Meteor engendered in the air, made of the vapours of the earth, drawn up thither by the heat of the Sun, and there set on fire, but his opinion is of all men confuted. First, touching the place, it cannot be in the air; for whatsoever is in the air, is not seen of all men, at all times, to be under one and the same part of Heaven. If we see it in the South, they that are in the West shall see it under the East side of the Heaven; and they that are in the East, shall see it in the West part of the Heaven; but this circled is of all men seen always under the same part of Heaven, and to be joined with the same stars; therefore it cannot be in the air. Again, for the matter it cannot be made of that which Aristotle nameth, ( i.e.) the vapours of the earth, because of the long continuance of the thing, and that without any alteration: for it is impossible that any meteor made of vapours drawn up from the water, or exhalations from the earth, should last so long; as may be seen in blazing stars; which though they have continued long, as namely, 16. moneths, some more, some less; yet at the length they have vanished away: whereas this circled hath continued from the beginning unto this day. Beside, put case it were made of these exhalations, whence will they infer the uniformity thereof? The Comets do alter diversely, both in the fashion of their blazing, and also in their several quantities; whereas in this circled, there is nothing but the same part, always of one form and of one bigness. In the efficient cause therefore he must needs err: for if it be neither in the Air, nor made of the exhalations of the earth, it cannot be caused by the Sun; for the one is the place, and the other the matter, wherein, and whereupon the Sun sheweth his power. All other,( besides Aristotle) agree in the place, but differ in the efficient cause thereof: and they are either Philosophers or Poets. Both these affirm that it is the Firmament ( i.e.) in the eight Sphere; but they disagree in the cause thereof. Ovid saith, that it is the great Causey, and the high way that leadeth unto the Palace of Jupiter; but he allegeth not the cause of the whiteness; belike he would have us imagine that it is made of white Marble. Others therefore allege these causes: Jupiter having begotten Mercury of Maia the daughter of Atlas, brought the child when he was born, to the breast of Juno lying a sleep; But Juno awaking, threw the child out of her lap, and let the milk run out of her breast in such abundance that( spreading itself about the Heaven) it made that circled which we see. Others say, that it was not Mercury, but Hercules; and that Juno did not let the milk run out of her breast; but that Hercules sucked them so earnestly, that his mouth run over, and so this circled was made. Others say; that Saturn being desirous to devour his children, his wife Ops presented him with a ston wrapped in a clout, instead of his child. This ston stuck so fast in Saturn his throat, as he would have swallowed it, that without doubt he had therewithal been choked, had he not been relieved by his wife, who by pressing the milk out of her breasts, saved his life: the milk that missed his mouth( whereof you must suppose some sufficient quantity) fell on the Heavens and running along, made this circled. And thus you hear the opinion of the Poets; who although in some circumstance they differ, yet do they Jump all in this; that it is in the Firmament, howsoever the causes they allege, are very frivolous. The Philosophers,( and chiefly Democritus) affirm the cause of the thing, to be the exceeding great number of stars in that part of Heaven, whose beams meeting together so confusedly, and not coming distinctly to the ey, causeth us to imagine such a whiteness as is seen. But the best opinion is this, that this Milky way is a part of the Firmament, neither so thin as the other parts thereof are, nor yet so thick as the stars themselves. If it were as thin as the other parts of the Heaven besides the stars, then could it not retain the light, but the light would pass through it and not be seen: If it were as thick as the stars, then would the light be so doubled in it, that it would glister, and shine as the stars themselves do: but being neither so thin as the one, nor so thick as the other, it becometh of that whiteness we see. Dr. HOOD Commenting upon Constellations, saith; The stars are brought into Constellations, for Instructions sake: things cannot be taught without names: to give a name to every star had been troublesone to the Master, and for the scholar; for the Master to device, and for the scholar to remember: and therefore the Astronomers have reduced many stars into one Constellation, that thereby they may tell the better where to seek them; and being sought, how to express them. Now the Astronomers did bring them into these Figures, and not into other, being moved thereto by these three reasons: first these Figures express some properties of the stars that are in them; as those of the Ram to be hot and dry; Andromeda chained, betokeneth imprisonment: the head of Medusa cut off, signifieth the loss of that part: Orion with his terrible and threatening gesture importeth tempest, and terrible effects: The Serpent, the Scorpion, and the Dragon, signify poison: The Bull, insinuateth a melancholy passion: The Bear infereth cruelty, &c. Secondly, the stars,( if not precisely yet after a sort) do represent such a Figure, and therefore that Figure was assigned them: as for example, the Crown, both North, and South; the Scorpion, and the Triangle, represent the Figure which they have. The third cause, was the continuance of the memory of some notable men, who either in regard of their singular pains taken in Astronomy, or in regard of some other notable dead, had well deserved of Man-kind. The first author of every particular Constellation is uncertain; yet are they of great antiquity; we receive them from Ptolome●▪ and he followed the Platonicks; so that their antiquity is great. Moreover we may perceive them to be ancient by the Scriptures; and by the Poets. In the 38. Chapter of Job there is mention made of the Pleiades, Orion, and Arcturus, and Mazzar●th, which some interpret the 12. signs: Job lived in the time of Abraham, as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis. Now besides all this, touching the reason of the invention of these Constellations, the Poets in setting forth those Stories, had this purpose, to make men fall in love with Astronomy. When Demosthenes could not get the people of Athens to hear him in a matter of great moment, and profitable for the Commonwealth, he began to tell them a tale of a fellow that sold an Ass; by the which tale he so brought on the Athenians, that they were both willing to hear his whole Oration▪ and to put in practise that whereto he exhorted them. The like intent had the Poets in these Stories: They saw that Astronomy being for commodity singular in the life of man, was almost of all men utterly neglected: Hereupon they began to set forth that art under these Fictions; that thereby, such as could not be persuaded by commodity, might by the pleasure be induced to take a view of these matters: and thereby at length fall in love with them. For commonly you shall note this, that he that is ready to red the Stories, cannot content himself therewith, but desireth also to know the Constellation, or at leastwise some principal star therein. FINIS.