The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

SECT. I. Solving many questions, relating to the Sun in our Elevation. (Book 1)

Operation I. To set the Globe level or parallel to the Horizon.

I Begin here, because 'tis what we first suppose done in most* 1.1 Operations, especially in the nice ones, nor is the perform∣ance difficult, for we have nothing to do, but to place the String and Plumet exactly upon the South side of the Meridian or 12 a Clock hour Circle, and if it hangs just over the little Star on the Pedestal, then the Plane where the Globe stands is Horizontal and Level; otherwise 'tis faulty as much as the Plummet varies from being Perpendicular to the said Star; for the Star (you must suppose) is engraved by the Globe-maker there, where he found the Plumet to hang upon his Placing the Globe truly level.

Let therefore the String and Plumet be always long enough* 1.2 to touch almost the Pedestal, for thereby you may better per∣ceive any Error; and remember also that in case the said Pe∣destal (to be less cumbersom) be not as big as the Diameter of the Globe, then there is to be under it a little wooden Ruler, which being drawn out, and markt with a Star will serve for this and several other uses as you will see anon.

There is another way speculatively true, tho perchance* 1.3 not so exact in practice, which is thus perform'd. Place your Globe on your Plane with the String lying on the Meridian as before, and if the Extuberancy or swelling of the Globe just touches and bears up the String at the Horizontal Circle, then

the Plane is Level, or Parallel to the Horizon, otherwise it differs as many degrees, as are between the point, where the said String touches the Globe, and its Horizon.

The reason of this is, That seeing the greatest and most extu∣berant* 1.4 Circle on a Globe is that which lies 90 degrees from its Pole, the Horizon becomes here the greatest and most extube∣rant one that can be described from the Zenith, therefore the Globe being on a Level which makes its Zenith to correspond with the Zenith in the Heavens, the String cannot fall short of the Horizon, because it must rest on the most extuberant Circle that occurs; nor can it touch below it, because the Plum∣met drawing the said String perpendicular from the greatest extuberancy, hinders its bending, and consequently its inclina∣tion to any part of the Globe beneath the Horizon. Now if the Plane be not level, then the Zenith of the Globe and Hea∣vens not corresponding, another Circle or part of the Globe, in∣stead of the Horizon must have the greatest extuberancy and this Circle, being 90 Degrees from the point of the Globe, (which lies directly under our Zenith) it must differ from the Horizon of the Globe, as many Degrees as its Zenith differs from that in the Heavens; therefore the way prescribed is at least speculatively true.

Operation II. To find the Suns Almucantar, or Height.

THere are three distinct ways of performing this indepen∣dent of the following Operations, and each of great use; for the first gives you the Suns height in an instant if he shines. The second if you have the least glimps of him, or can guess at his place in a Cloud. The third, if you know the hour by any good Watch, Pendulum or the like, whether we see the Heavens or no.

I. As for the first way, 'tis this; your Globe being level,* 1.5 move it 'till the shade of the Pin in the Zenith falls directly upon

the Meridian, and then the shade of the Extuberancy (i. e. that made by the swelling or bellying out of the Globe) will touch the true degree in the Quadrant of Altitude reckoning from the Ze∣nith to it. And thus you will find not only the Sun's height, sooner perchance than by any ordinary Quadrant, but will still have it before your eyes as long as you please, nothing being to be fur∣ther done, but to move sometimes the Globe that the shade of the said Pin may still concur with the Meridian. But if your Globe be fix'd, (or that for some particular reason, you have no mind to stir it at all, draw your string from the Zenith, through the shade of its Pin, i. e. lay the string in the Plane of the Sun, and then if you mount your Bead till it reaches the nearest part of the shade of Extuberancy, it will (by bring∣ing it to the Meridian or Quadrant of Altitude) lye on the true Degree, reckoning (as before) from the Zenith to it.

The Reason of the Operation is this; The Sun when he rises* 1.6 brushes the Zenith and Nadir of the Globe with his Rayes, for he illuminates alwayes (within some few Minutes) just half of it, therefore when he gets (v. g.) a Degree higher, he must needs illuminate a Degree beyond the Zenith, and so proporti∣onably from time to time, or else he would sensibly illuminate more or less of the Globe at one moment than at another, which* 1.7 is absurd. Now since the Sun in truth illuminates more than an Hemispere, the Reader must remember that Ptolomy rec∣kons this excess (take one time with another) to be about 26 minutes, and Tycho something less, therefore substract 13 mi∣nutes (or half the said Excess) from what the shade of Extube∣rancy mark's, and you have his Height with all ordinary Exact∣ness: but should you chance at any time to doubt how far the said Shade of Extuberancy (which is not so discernable as that* 1.8 made by a Gnomon) just reaches, erect then a piece of stick, straw, quill, &c. or, if you please, rest your Finger on the Globe, between the Sun and the point in dispute, and where the shade of your Finger, straw, stick or quill is lost, that will be the true Term of the shade.

As for the Second Way (for both the former we reckon but* 1.9 one) turn the Meridian of your Globe to the Sun as before, or because we suppose him not to shine out-right, direct by your Eye the said Meridian, so that it lye in the same Plain with him, and this you may do in a manner as well (if you have the

least glimps of him, or can by any accident guess whereabouts he is) as if you had the fore-mentioned help of the Pin's shade in the Zenith. Having thus done, Take your String in both hands, and cross with it (as exactly as you can at right Angles) that part of the Meridian next your body, whether it happens to be the Quad. of Alt. or that of Proportion, then putting your Face close to it, and moving your Ey lower and low∣er, till by reason of the Extuberancy you can but just see the Sun, or his supposed place in Heaven, do but bring your String (held as before) to this point, viz. bring your String towards you till it just takes away the Sun or his supposed place from your Ey, and the degree in the Meridian on which it then lies will be (counting from the Zenith) the Height re∣quired; for so far his raies would reach did he shine out-right.

The third way is when we know the Hour by any Watch, Pendulum,* 1.10 &c. thus, Find among the Aequin. or Diurnal Parallels that belonging to the present Day, which we will suppose Apr. 10. and drawing your string from the Zenith over that Point in the said Parallel, where 'tis cut by the Hour given, i. e. by the morning 9 a Clock Circle, move your Bead to the said Point, and the distance from the Bead to the Horizon will be the required Height, viz. about 36 degrees, as you'l find if you bring the Bead to the Meridian and count the degrees between it and the Horizon.

The Suns Height may be also known by its Azimuth, as by Operat. 5.* 1.11 Having therefore by any of the aforesaid waies his Height, 'twill (upon any doubt) soon appear whether it be Fore or Afternoon, for as long as ever he increases in Degrees, i. e. mounts higher and higher above the Ho∣rizon, it wants of Noon, whereas if he falls or declines, 'tis after Noon.

OPERAT. III. To Compose the Globe, either by a Meridian Line, or without it, to the site of the World.

IF you have a Merid. line drawn, viz. a Line lying exactly North and South, place the Globe * 1.12 level with its Merid. directly over it, i. e. place so the little Notch in the Pedestal (markt S) that it cover the South∣ern extremity of the said line, and the Notch N the Northern, and then the Poles and Circles on the Globe will (without sensible error) corre∣spond with those in Heaven, and each painted Region or Countrey on it, will be turn'd towards the real one which it represents.

But if you have no line drawn, Know the day of the Moneth, and you have two quick waies to do this Operation without any forreign helps.

The Globe having in it smal pin-holes, on the several intersections of* 1.13 the Merid. with the aforesaid Diurnal Parallels, or (to be exacter) on each point of the Merid. which an imaginary Parallel of each fifth day would cut; for tho' we are to suppose Parallels for every day throughout

the year, yet there being no sensible difference in the Sun from 5 daies to 5 days, such holes will be abundantly sufficient; nay the aforesaid ones from ten Dayes to ten Days, may very well serve the turn in any ordinary Operation: I say, the Globe having holes in its Meridian at this distance, put the Zenith Pin, or, if you think better a Needle, in the Hole, which most agrees with the true day of the Month, and then exposing your Globe level to the Sun, do but move it till the shade of the said Needle or Pin falls directly along the Diurnal Parallel where 'tis placed; or, if it be not placed in any of the said Parallels, move the Globe till the shade falls parallel to the next Diurnal Parallel, and 'twill be as truly Compos'd as before, supposing you know (as we have already * 1.14 taught you) whether it be Forenoon or Afternoon when you operate; for, as in the Morning the Stiles of Dials cast their shades Westward, and in the Afternoon Eastward, so must your Needle or Pin do when the Globe is Compos'd.

But here the Reader must take notice, that in case the shade of the* 1.15 Needle or Pin will by no means fall sensibly parallel, but (as you move the Globe) draws nearer and nearer its being so, till at last it shortens to nothing, then the Sun is exactly South, and consequently your Globe is compos'd, as soon as the shade thus vanishes.

Now, Because the shadow of the Pin is on the Globe an Arch of a Great Circle, this way of Composing the Globe cannot be accounted Ma∣thematically true, For as the Sun approaches each Tropick and the Tro∣picks not Great Circles, it will happen Mornings and Evenings (when the Pin projects long shadows) that the shadow of the Pin will not ly exactly in the Parallel of the Day, but will (more or less) intersect it in the Center or Pin-hole. Therefore tho' the aforesaid way of Composing the Globe be true enough for ordinary uses, yet I shall give you two other waies without exception.

Observe the Concentrics between the North Pole and its Polar Circle,* 1.16 and first you will find that they are equal in number to the Parallels, ei∣ther from the Equator to the Tropick of Cancer, or to those from the said Aequator to Capricorn; for to avoid the confusion of too many Parallels, there are usually but 8 Northern and 8 Southern described on the Globe. 2ly. That they are distant from the Pole as the said Parallels are from the Equator. And 3ly. That they are markt not only with the Daies of the Month of the Northern Parallels, but with those of the Southern also. The Day of the Month then being (for example sake) Apr. 10. Move but the Globe (when level) till the shade of Extuberancy touches the Concen∣tric markt Apr. 10. and 'twill be truly Composed; supposing that the Eastern face of the Globe looks towards the Forenoon or Eastern parts

of Heaven, and the Western face towards the Afternoon. In like manner, If the Day of the Month or Suns Parallel be an imaginary one between any two that are exprest; for to avoid (as I mention'd) the confusion of too many Parallels there are usually but 8 Northern and 8 Southern de∣scribed; I say in like manner, If the Day of the Month, or Suns Parallel happens thus, let the said Shade but touch or fall proportionably between the correspondent Concentrics, and the Globe will be Compos'd, as before.* 1.17

The reason of the Operation is this; The Sun illuminating (as has been said) half the Globe, the Shade of Extuberancy (or in other terms the Con∣fines between the Obscure and Illuminated parts) will be still 90 degrees from the point or place where the Sun is vertical; therefore if the Sun be (v. g.) in the Equator, the aforesaid Shade or Illumination must terminate in the Poles of the World; and when he is in the Parallel of Ap. 10. the Il∣lumination must fall short of the South Pole, and go beyond the North Pole as many degrees as the said Parallel declines from the Equator; But the Concentric of Ap. 10. is by Construction just distant from the Pole those degrees; Ergo when the said shade of Extuberancy or the Illuminati∣on touches this Concentric, the Globe must (if its Eastern face looks to∣wards the Fore-noon part of Heaven or the Western the Afternoon) be il∣luminated as the Earth is, and consequently Compos'd; for its correspond∣ing with the Earth in its site and position is all we mean by Composing.

As for the reason why I mark each Concentric with the 4 opposite Months, whereas the Parallels are markt only with 2 of them, 'tis that the Globe may be Composed by the help of the Northern Concentrics, even when the Sun is in his Southern Declension, it being more convenient and ready for one to cast his Ey on the North Pole than to stoop to the South Pole; about which otherwise there must have been the like number of Concentrics, and markt as the Southern Parallels are; I say this is the rea∣son of thus marking the Concentrics; for since the Sun in its Northern de∣clension illuminates beyond this Pole, he must in his Southern fall propor∣tionably short of it; therefore move the Globe as before (let it be Summer or Winter or any other time of the Year) till the said Illumination or Shade touch the Concentric markt with the day of the Month, and 'twill be still Composed.

The second way I shall defer to Operat. 10. because the intermediate* 1.18 ones conduce much to the facilitating it, as you'l see.

OPERATION IV. To find the Day of the Month.

THis Operation is also perform'd two ways, as being the Converse of* 1.19 the former; therefore since that requires the knowledge of the Day of the Month, this must require the Globe Compos'd. Having then

Compos'd it by a Meridian line, or otherwise, Consider upon what Ex∣centric, or between which of them the said Shade of Extuberancy or Il∣lumination falls, and that will shew the Day of the Month.

As for the second way, you shall have it when we come to Operat. X.* 1.20 which treats (as we said) of the Second way of Composing the Globe.

OPERATION V. To find the Sun's Azimuth.

THe Sun's Azimuth is an Arch of a great Circle, which passeth through the Zenith and Nadir over his body, so that his Mornings or Afternoons distance (reckon'd by the Degrees of the Horizon) from the Meridian or Southern Cardinal section of the Globe is the thing requir'd; and for performing the Operation there are four several ways.

* 1.21* 1.22 Compose your Globe; Then standing on the illuminated side, or side next the Sun, and fixing your String by its nooze in the Zenith, hold it up by the Plummet-end, and move it along till its Shade falls on the middle of the Fulcrum or supporting Pillar, or (to be more exact) till it covers the Center of the Projection, being the point (you see) directly answering the Nadir; for then the Degree in the Horizon, which the said Shade falls upon, gives from the above mentioned Meridian the requir'd Azimuth. Or else guide your String by winking (or by any other convenient means, which practice will show you) till it concur with the Shade of the Zenith-pin, that is to say, till they both ly in the same Plane; for then the Shade of the String it self (if it hangs strit along the Globe) will cut the Horizon, as before.

* 1.23In case you have onely a glimpse, or faint sight of the Sun, then stand (the Globe being Compos'd) on the obumbrated, or other side of it, and letting your String hang down on that side also, aim or look along it with one by towards the Sun, and role the String gently with your finger backwards or forwards, till it lies exactly in the same Plane as the Sun does, or (if the Clouds suffer you not clearly to see him) till it lies in the Plane of its supposed Place, and the Degree under your String (reckoning the contrary way, that is to say, from the Northern or back part of the Meridian) is the requir'd Azimuth. Therefore (by the by) if the Sun shines out, 'tis but drawing the String through the Shade of the Zenith-pin, and it will (reckoning thus) answer the Question.

* 1.243dly, Having taken the Sun's * 1.25 Height, and having found it to be, sup∣pose 36 deg. bring the String to the Merid. and by the help of the Degr. in the Quad. of Alt. Mount the Bead above the Horizon 36 deg. which Operation we shall frequently call hereafter, Rectifying your Bead to

the Sun's height. I say having taken the Suns height, and Rectifi'd your Bead to it, put your Ring or Noose on the Zenith, and move your String, till your Bead lies exactly on the Parallel of the Day. Which we will alwayes in our Examples, or for the most part at least, suppose to be that of the 10th of April, and the said String will cut the Horizon at 58 Degrees Eastward (or there∣abouts) for his then true Azimuth. And here you may re∣member,* 1.26 That as the Height gives the Azimuth, so the Azi∣muth once known, gives the Height; for your string being on the true Azimuth, if you mount your Bead to the Parallel of the Day, it will show you in the Meridian the requir'd Height.

Fourthly, Supposing that on the 10th of April, the hour gi∣ven* 1.27 be 9 in the Morning, draw your String from the Zenith over the Point where the Parallel of the Day, and the 9 a Clock hour-Circle intersect, and it will fall on the 58 Degree in the Horizon Eastwardly of the Meridian for the then Azimuth.

OPERATION VI. To find the Sun's Declension, Parallel, and Place on the Globe at all times.

BY the Sun's Declension is meant, his Northerly and South∣erly* 1.28 distance from the Aequator, therefore if you know the day of the Moneth to be the 10th of April, you have his Parallel, because 'tis mark'd with the said day: Now since the Colurus Aequinoctiorum, or 6 a clock Hour Circle, is (as we said) gradually divided from the Aequator to the Poles, and that the said Parallel passes almost throu' its 12th Degree, you have his Declension, as also his Place in his Pa∣rallel, if you have his Almucantar, or Azimuth as you will find by the second or following way.

If now you know not the day of the Moneth, Take the Sun's* 1.29 * 1.30 Almucantar and † 1.31 Azimuth by some of the foregoing wayes, and Rectifying your Bead to the Height, draw your String from the Zenith on the Horizon, according to the Azimuth

found, and your Bead will lie on his true Place, and con∣sequently show his Declension and Parallel; for, as his Declen∣sion is (as we said) his Distance from the Aequator, so his Pa∣rallel is a Circle described from the Pole according to his De∣clination. And pray observe well this second Way; for tho' it* 1.32 be not extremely necessary in Relation to the Sun, yet it is of singular use, when you come to the Moon and Stars, whose De∣clensions depend not on the day of the Moneth.

OPERATION VII. To find the Sun's Bearing, i. e. in what part of the Heavens he lies, according to the Points of the Compass.

HAving found by the foregoing Operation (on the 10th of April.) the Sun's true Place in his Parallel to be, suppose there where the 9 a Clock Hour Circle cuts it, say over this Point your String, from the Zenith, and 'twill fall at the Horizon a little beyond the Character of SEbE for his Bearing according to the Points of the Compass.

OPERATION VIII. To find when the Sun comes to true East or West, or any other Bearing.

HAving found the Parallel of the Day (viz. that of the 10th of April) and put your String over the Zenith, bring it straight to the East point, that is to say, to the point of the Globe where the Horizon and 6 a clock Circle intersect, and you will find the said String to cut the said Parallel about 20 minutes before 7 in the Morning, which is the exact time of the Sun's then coming to full East. Now if the String be laid on the Western Intersection, 'twill cut the said Parallel at 20 minutes or thereabouts after 5 in the Evening, for the time of the Sun's

coming to full West. In like manner, if you would know, when he come's (v. g.) to S. W. you are only to draw your String (as before) over that Bearing, and you will find by the Intersection of your said string and Parallel, that at a quarter past 2 of the Clock in the Afternoon, or thereabouts he will have that Bear∣ing.

OPERATION IX. To find what Signs and Degrees of it the Sun is in, at any time.

SEEK out the Parallel of the Day (viz. that of the 10th of April) and you will find it to cross the Ecliptic in two pla∣ces, to wit at the first of Taurus, and the first of Leo; Now be∣cause in April the Sun is still Ascending, that is to say, the Dayes encrease, you may conclude that the first of Taurus is his then true place in the Ecliptick; for were he in Leo he would descend toward the Aequator, and consequently shorten the Dayes.

OPERATION X. To find the hour of the Day by the Sun, together with a second way of composing the Globe, and finding the Globe, and finding the Day of the Moneth.

MANY are the wayes to perform this Operation as to the Hour, But now wee'l insist on four only, each of which has some peculiar Propriety belonging to it; for the First gives us the Hour by the help of the Natural Stile; the Second by an Artificial one; the Third without any Stile at all; and the Fourth (together with the said hour) the Contemplation of se∣veral pleasing Operations at a time, and among the rest this of Composing the Globe by the Shade.

I. Having * 1.33 Compos'd your Globe, (and thus wee'l suppose it* 1.34 in each of the following wayes) look among the Hour Circles (which are, as we said, distinguish'd near the Polar Circles, with

little Roman Figures) and the shade of the North-Pole, or A∣xis of the World (which we may justly call the Natural Stile,) will, during the Sun's Northern Latitude, as well as the shade of the South Pole in his Southern, shew you the Hour. And thus you may find it for a while by the Ordinary Globes, in Circu∣lo Horario, when they are once set or Compos'd, which I won∣der none, of those who writ of their Uses take notice of; I say for a while, for it will only serve your Turn there from March to September.

II. Your String hanging by one End on the North Pole, hold* 1.35 it straight by the other, some little distance from the Globe, and moving it on the Noose, till its shade touch, or cover, the Apex of the South-Pole, 'twill show you (among the aforesaid Polar Roman Figures) the true Hour, even to a minute; for the Sha∣dow of the String (which we call an Artificial Stile, because 'tis Independent and Forrein to the Globe) cutting at that In∣stant the Aequator, and Polar Circles, gives you in each place the Degrees of the hours, and consequently the minutes, since the 4th part of a Degree is an exact minute in time.

III. Look where the shade of Extuberancy cut's on the Ae∣quator,* 1.36 and the great Roman Figures, (which are there for that purpose) will give you without a Stile or more adoe the exact hour, on what side soever of the Globe, you stand; for you must remember that the Extuberancy casts on the Aequator two shades, the one still Preceding or going before the Sun, and the other Following him. Now if this shade be dubious, your Finger (as I show'd you * 1.37 before) will help you, it being the constant Remedy on all Occasions of this Nature.

IV. As now you find the Hour by your String hanging on* 1.38 the Pole, so this Fourth way is to show it you, in case it had hung on the Zenith; nor have you more to do than to hold it by the end as before, and to move it on its Noose 'till its shade concurrs and agrees with that of the Pin in the Zenith, or for more Assurance till the Strings shade fall's so on the upper part of the Pillar or Fulcrum that it would cover the very Nadir, were it not hid, and then where the said String it self, or its shade cuts the Parallel of the Day, there will be the true hour, according to the Roman Figures of the Polar Circles.

This way I would have you well observe for from hence I shall* 1.39 hereafter lead you to the Contemplation (as I hinted before) of several pleasing and useful * 1.40 Operations at one glance or view; and to give you a little Taste at present, I will here shew you the Second way of Composing the Globe by the shade.

Having for Expedition's sake, turned the North-pole of the Globe, as near as you can guess to that of the World, Hold up your String with one hand to the Sun in the manner now pre∣scribed; That is to say, 'till the String hanging from the Ze∣nith) casts its shade on the Nadir, then move the Globe with your other hand, and making by a proportionable motion of the String its shade to pass still throu' the said two points, observe when it cuts the Parallel of the day at the like hour with that, which the shade of the illuminated Pole indicates, and your Globe will be composed; or, to express this in fewer words, Move thus the Globe, till the shade of the string and the shade of the illumi∣nated Pole agree in the Hour. Nay fixing your String in the Zenith as before, and fastning a Thred on the North-pole, do but hold up both to the Sun till the shade of the String passes the Nadir, and that of the Thred the South Pole, if any body then moves your Globe about till the two shades (passing still throu' the foresaid Points) intersect on the Parallel of the Day,* 1.41 you have your intent; for the Sun being you see in the Planes of the Thred and String▪ he must be in their Intersection. i. e. in the Parallel of the Day; but 'tis impossible for him (as we * 1.42 show'd you) to be in the plane of that Parallel, on the true side of the Meridian, except the Globe be Compos'd, for the corresponding Circles of the Globe and Heavens can never else agree; there∣fore the Operation is true; and if so, let the Globe be but on a* 1.43 Meridian Line, or any way else Compos'd, and the Agreement of the hour in both places, or the Intersection of these two shades shews the Sun's Parallel and consequently the Day of the moneth.

So much then for this second way of composing the Globe, and finding the Day of the Month, which first came into my thoughts by reflecting on the Projection of that great man Mr. Oughtred, who would have bin the Wonder of this Age, had he bin as ambitious and forward, as he was throughly learned.

OPERATION XI. To find the Hour of the Day when the Sun shines not.

TO perform this Operation, we must suppose you know either the Suns Almucantar, Azimuth or Bearing; and by the way you may find these, tho he * 1.44 shine's not; I say you must suppose either his Almucantar, Azimuth, or Bearing, for they giving you his Place in his Parallel, the next Hour Cir∣cle to his said place shews you the time of the Day; for if (v. g.) in the forenoon on the 10th of April.) you know that the Sun is 36 degrees high, Rectify your Bead but to that height, and mo∣ving the String from the Zenith your said Bead will touch the Parallel of the Day at 9 of the Clock. In like manner if you know the morning Azimuth to be suppose, 58 degrees, draw your String from the Zenith over the said Degrees in the Horizon, and 'twill also cut the Parallel of the day at 9. Or, if the Sun's Bearing be (for Example) a little more than SEbE the laying of your String from the Zenith on that Character in the Horizon shows you on the Parallel of the day that 'tis 9 as before.

OPERATION XII. To know when the Sun rises and sets.

FIND the Parallel of the Day (to wit that of the 10th of April) and where it cuts the Horizon on the East-side of the Globe, there the Suns place at his Rising will be so that the time of the day appears by the next Hour Circle to be a ve∣ry little past 5 in the morning; and if you cast your eye in the Intersection of the said Circle on the West, you'l find the hour to be almost 7 in the Evening.

This being so, here follow's a very pleasant and useful Opera∣tion,* 1.45 as a Corallary, viz. How to find at what time of the year, and at what Declension the Sun rises or sets, an Hour, or any other space of time, either early or later, than it does at the pro∣posing of the Question: for, if you observe but what Parallel in∣tersects

with the Horizon, on the 4 a Clock morning hour-circle which is an hour earlier than when it rises on the 10. of April, you will find it an Imaginary Parallel, which the next real or mark't one shews to be the Parallel, for the 14. of May and 12. of July, and consequently by the Devisions of the Aequinocti∣al Colure that the then Declension is about 21 Degrees. In like manner you must have look't on the West side of the Globe if you would have had the time of the Sun's setting an hour later than 7; and thus you are still to operate when any other space of time is required.

OPERATION XIII. To find the Sun's Amplitude, Ortive or Occasive.

BY the Sun's Amplitude we mean his distance in the Horizon from the true East and West Points at his Rising or Setting; so that this Operation is also a Corollary from the former; for, knowing (on the said 10. of April) the point or place where he Rises, you will find the Ortive Amplitude to be Northward from East about 18 Degrees, and (on the other side of the Globe) the Occasive Amplitude, to be Northward as much from the West.

OPERATION XIV. To find the length of the Day and Night.

DOuble the hour of the Sun's Setting, (which on the 10. of April happens, as we said, about 7 at night) and the Product (to wit near 14 hours) will be the length of the Day; or double (5) the hour of his Rising, and the Product (10 hours) gives the length of the Night. Nay, if you do but consider how the Parallel of the Day is cut by the Horizon, you have the whole business represented to the life at one view, even as it hap∣pens in the very Heavens themselves; for that part of the said Parallel above the Horizon, being devided to your hand by the Hour-circles, into almost 14 hours, shews the Days length, and consequently that part under the Horizon (shewing a little more than 10 hours,) gives the length of the Night.

OPERATION XV. To find the beginning and end of the Crepusculum.

BY the Crepesculum is understood the Twilight which ap∣pears before the Sun's Rising, and continues after his Set∣ting; for as soon as the Sun comes within 18 Degrees of the Ho∣rizon (according to the Opinion of the antient Astronomers) or within 16. Deg. according to that of Tycho, and some Modern ones) his Rays are reflected from the Atmosphere or circumam∣bient vapours, and consequently illuminates, so that this light still encreases, by how much the Sun approaches the said Hori∣zon, and decreases as it recedes. Now to find it, you are to bring the String hanging on the Zenith to the Meridian, and making the Bead (if you follow the latter Hypothesis) to stand by the help of the Quadrant of Depression) at 16 De∣grees under the Horizon, move it on the East side of the Globe along the Parallel of the Day (i. e. that of the 10. of April) till it just touches the said Parallel, under the Horizon, and there will be the true point of the Morning Crepusculum, which the adjacent Hour-circle tells you begins about 3 in the morning; In like manner if you move your Bead on the West or Evening∣side of the Globe▪ you will find it to end neer 9.

OPERATION XVI. To find the Sun's Depression at any time of the Night.

BY Depression we mean, how many Degrees the Sun is then under the Horizon, which is easily perform'd if you know the hour of the night, by the Moon, Stars, Clock, or the like; for, finding (as hath been * 1.46 shown you) what part or point of his Parallel the Sun is then in; i.e. where the Hour-Circle (cor∣responding to the time of the night) and Parallel of the Day intersect, draw the String from the Zenith over it, and moving your Bead to it, bring the said Bead to the Merid. or Quadr. of Depression, and then by the help of the Degrees there (reckoning

from the Horizon to the Bead) you have before you the requi∣red Depression.

OPERATION XVII. To find the Sun's Right Ascension.

THE Right Ascension is that Point or Degree of the Aequa∣tor cut by the Meridian, or Hour Circle that runs through the Sun's place in the Ecliptic; and this Degree is called the Right Ascension, because in the Position termed by Astronomers and Geographers the Right Sphere, (which together with the Oblique and Parallel Spheres, shall be farther explained in the * 1.47 Geo∣graphical Section) it rises or Ascends with the Sun.

To find then the Sun's Right Ascension (a thing often of great Use) you are only to take the String (hanging from the Pole) and lay it on the Degree of the Ecliptic possest then by the Sun, that is to say upon the 1st. of ♉ (for the 10. of April is still our Example) and the Degree of the Aequator cut by the said String is the required Right Ascension, which counting from ♈ or East Point (as you must always do) happens to be 28 Degrees, or thereabouts.

OPERATION XVIII. To find the Ascensional Difference.

AS for the Ascensional Difference (i. e. the Difference be∣tween the Right and Oblique Ascensions) we have it here before our Eyes at a View, as being that portion of the Day's Parallel which lyes between the Sun's Rising or Setting, and the 6 a Clock Hour Circle, so that if he rises on the 10. of April at almost 5. and sets near 7. we may conclude that the Ascensio∣nal Difference is about 14. Degrees, for 15. make an hour. But if you will be exact, then lay the String from the Pole on the Point where the Sun rises or sets, and when it cuts the Aequa∣tor, count there the Degrees from the said String to the 6 a Clock Circle, and all is done. Thus then you see, that when we

know the Ascensional Difference we have the time of the Suns Rising and Setting, for it is but adding it to 6 a Clock, if the Sun be in his Northern Declension, or substracting it in his Southern.

The END of the first Section.

Notes

• * 1.1

  The first way.
• * 1.2

  A Memoran∣dum.
• * 1.3

  The second way.
• * 1.4

  The Reason and Demon∣stration of the Operation.
• * 1.5

  The first way.
• * 1.6

  The Reason and Domon∣stration of the operation.
• * 1.7

  How much the Sun illu∣minates more than half the Earth.
• * 1.8

  How to know the terms of the shade of Extuberancy when the sun shines faintly.
• * 1.9

  The second Way.
• * 1.10

  The Third way.
• * 1.11

  To know at any time whether it be Forenoon or After∣noon.
• * 1.12

  Operat. 1. pag. 4.
• * 1.13

  A way to Compose the Globe by the Sun.
• * 1.14

  Operat. 2. pag. 7.
• * 1.15

  A Memo∣randum.
• * 1.16

  The first way of Com∣posing the Globe.
• * 1.17

  The Demon∣stration.
• * 1.18

  The 2d way vid. Op. 10.
• * 1.19

  The 1. way.
• * 1.20

  The Second way. vid. Op. 10.
• * 1.21

  The first way.
• * 1.22

  Operat. 3. pag. 8.
• * 1.23

  The second way.
• * 1.24

  The Third way.
• * 1.25

  vid. Oper. 2. pag. 5.
• * 1.26

  A Memoran∣dum.
• * 1.27

  The 4th. way.
• * 1.28

  The first way.
• * 1.29

  The 2. way.
• * 1.30

  Op. 2. pag. 6.
• † 1.31

  Op. 5. pag. 10
• * 1.32

  A Memoran∣dum.
• * 1.33

  Op. 3. pag. 8.
• * 1.34

  The 1st. way.
• * 1.35

  The 2. way.
• * 1.36

  The 3d. way.
• * 1.37

  2. pag. 6.
• * 1.38

  The 4th. way.
• * 1.39

  A Memoran∣dum.
• * 1.40

  vid. the particulars in the conclusion or last Chap∣ter. The 2d. way of composing the Globe by the shade.
• * 1.41

  Demonstrati∣on.
• * 1.42

  Op. 3. pag. 8
• * 1.43

  The 3d. way of finding the day of the month.
• * 1.44

  Op. 2. pag. 6 & Op. 5. pag. 10.
• * 1.45

  To find when, and at what declension, the Sun rises or sets earlier or later, accord-
• * 1.46

  Op. 6. pag. 11.
• * 1.47

  Vid. Oper. 13. Sect. 2.