A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.

The Second Book. Shewing the Practical Use of the GLOBES. Applying them to the Solution of Astronomical and Geographical Problems. (Book 2)

PRAEFACE.

Some Advertisements in Choosing and Using the GLOBES.

1. SEE the Papers be well and neat∣ly pasted on the Globes: which you may know, if the Lines and Circles discribed thereon meet ex∣actly, and continue all the way even and whole: the lines not swerving out or in, and the Cir∣cles not breaking into several Ar∣ches; nor the Papers either come short, or lap over one the other.

2. See that the Culler be transparent, and ly not too thick on the Globe; lest it hide the superficial Descriptions.

3. See the Globe hang evenly between the Meridian and Horizon, not inclining more to one side then the other.

4. See the Globe swim as close to the Meridian and Ho∣rizon

as conveniently it may; lest you be too much puzzeld to find against what point of the Globe any degree of the Ho∣rizon or Meridian is.

5. See the Equinoctal line be one with the Horizon, when the Globe is set in a Parallel Sphear.

6. See the Equinoctal line cut the East and West point of the Horizon, when the Globe is set to an Oblique Sphear.

7. See the Degrees marked with 90. and 00, hang exa∣ctly over the Equinoctial line of the Globe.

8. See that exactly half the Meridian be above the Ho∣rizon, and half under the Horizon: which you may know if you bring any of the Decimal Divisions to the North Side of the Horizon, and find their Complement to 90. inth South.

9. See that when the Quadrant of Altitude is placed at the Zenith, the Beginning of the Graduations reach just to the superficies of the Horizon.

10. See that while the Index of the Hour Circle (by the motion of the Globe) passes from one hour to the other, 15. degrees of the Equator pass through the Meridian.

11. If you have a Circle of Position, see the Graduations agree with those of the Horizon.

12. See that your wooden Horizons be made substantial and strong; for (besides the Inconveniences that thin wood is subject unto, in respect of warping and shrinking) I have had few Globes come to mending that have not had either broken Horizons, or some other notorious fault, occasioned through the sleightness of the Horizons.

In the Using the Globes.

KEep the East side of the Horizon alwaies towards you, unless your Proposition requires the turning of it: which East side you may know by the Word East, placed on the outmost verge thereof. For then have you the gradu∣ated

side of the Meridian alwaies towards you; the Qua∣drant of altitude before you, and the Globe divided exactly into two equal parts.

So oft as I name to, at, of, or under the Meridian, or Horizon, I mean the East side of the Meridian, and Super∣ficies of the Horizon: because the East side of the Meridian passes through the North and South points, both of the Globe and Horizon; and agrees just with the middle of the Axis: And the Superficies of the Horizon divideth the Globe exa∣ctly into two equal parts.

It you happen to use the Globes on the South side the E∣quator, you must draw the wyers out of either Pole, and change them to the contrary Poles; putting the longest wy∣er into the South Pole. And because on the other side the Equator the South Pole is elevated, therefore you must ele∣vate the South Pole of the Globe above the Horizon; ac∣cording to the South Latitude of your Place; as shall be shewed hereafter.

In the working some Problems it will be required that you turn the Globe to look on the West side thereof: which turning will be apt to jog the Ball, so as the degree that was at the Horizon or Meridian, will be moved away, and there∣by the Position of the Globe altered. To avoid which incon∣venince you may make use of a Quill, thrusting the Feather end between the Ball and the Brazen Meridian, and so wedge it up, without wronging the Globe at all, till your Proposi∣tion be answered.

PROBLEME I.

To find the Longitude and Latitude of Places, on the Terrestrial Globe.

SEek the Place on the Terrestrial Globe, whose Longitude and Latitude you would know, and bring that Place to the

Brazen Meridian; and see how many degrees of the Equator is cut by the Meridian, from the first general Meridian, (which on my Globes pass through Gratiosa, one of the Isles of the Azores,) for that number of degrees is the Longitude of the Place.

Example.

I desire to know the Longitude of London, and close to the name London I find a smal mark 0 thus, (which smal mark is in some Globes and Maps adorned with the Picture of a Stee∣ple, &c.) therefore I do not bring the word London to the Me∣ridian, but that smal mark; for that alwaies represents the the Town or Citty sought for: And keeping the Globe steddy in this Position, I examine how many degrees of the Equa∣tor are contained between the Brazen Meridian, and the first ge∣neral Meridian; which I find to be 24. deg. 00. min. There∣fore I say the Longitude of London is 24. degrees 00. min.

For the Latitude.

See on the Brazen Meridian how many degrees are contained between the Equator and the mark for London; which in this Example is 51½: therefore I say London hath 51½ degrees North Latitude.

PROBLEME II.

The Longitude and Latitude being know, to Rectifie the Globe fit for use.

1. WHen you rectifie the Globe to any particular Lati∣tude you must move the Brazen Meridian through the notches of the Horizon till the same number of degrees accounted on the Meridian from the Pole (about which the Hour-Circle is) towards the North point in the Horizon (if in North Latitude, and toward the South if in South Latitude) come just to the edge of the Horizon.

Example.

By the former Proposition I found the Latitude of London to be

51½ degrees North Latitude: therefore I count 51½ degrees from the Pole downwards towards my right hand, and turn the Meridian through the notches of the Horizon till those 51½ de∣grees comes exactly to the uppermost edge of the North point in the Horizon; and then is the Meridian rectified to the Latitude of London.

2. Next rectifie the Quadrant of altitude, after this manner, Screw the edge of the Nut that is even with the gradua∣ted edge of the thin Plate, to 51½ degrees of the Brazen Meri∣dian, accounted from the Equinoctial on the Southern side the Horizon, which is just the Zenith of London: and then is your Quadrant Rectified.

3. Bring the degree of the Ecliptick the Sun is in that day, to the Meridian: which you shall learn to know by the next Pro∣bleme, and then turn the Index of the Hour Circle to the hour 12. on the South side the Hour Circle, and then is your Hour Circle also rectified fit to use, for that Day.

4. Lastly If you will rectifie the Globe to correspond in all re∣spects with the Position and Scituation of the Sphear, you must set the four Quarters of the Horizon. viz. East, West, North, and South, agreeable with the four quarters of the World; which you may do by the Needle in the bottom of the Horizon; for you must turn the Globe so long till the Needle point just to the Flower de luce. Next you must set the Plain of the wooden Horizon parallel to the Horizon of the World; which you may try by setting a common Level on the four Quaters of the Hori∣zon. And then positing the degree of the Ecliptick the Sun is in, to the Height above, or depth below the Horizon, the Sun hath in Heaven, (as by the 11th Probleme) your Globe is made Cor∣respondent in all points with the frame of the Sphear, for that particular Time, and Latitude.

PROBLEME III.

To find the Place of the Sun in the Ecliptick, the Day of the Moneth being first known.

SEek the Day of the Moneth in the Circle of Moneths upon the Horizon, and right against it in the Circle of Signes is the degree of the Ecliptick the Sun is in.

Example.

Imagine the Day to be given is May 10. therefore I seek on the Horizon in the Circle of Moneths, for May, and find the Moneths divided into so many parts as there is Daies in the Mo∣neth; which parts are marked with Arithmetical figures, from the beginning of the Moneth to the end, and denote the number of the Day of the Moneth that each Division represents: there∣fore among the Divisions I seek for 10, and directly against it in the Circle of Signes, I find ♉ 29. degrees. Therefore I say May 10. the Suns Place is in 29. degrees of ♉.

But note, that if it be Leap Year, instead of the 10. of May you must take the 11. of May: because February having in a Leap Year 29. Daies, the 29. of February must be reckoned for the first of March, and the first of March for the second of March; the second of March for the third of March; and so throughout the year.

The Leap Year is caused by the six od hours more then 365. daies that are assigned to every common Year: so that in a Re∣volution of 4. Years, one Day is gained, which is added to Fe∣bruary; and therefore February hath every fourth or Leap Year 29. Daies.

PROBLEME IIII.

To find the Day of the Moneth, the Place of the Sun being given.

AS in the last Probleme it was your task to find on the Horizon the Day of the Moneth first, so now you must first seek the Signe and degree the Sun is in, and against it in the Circle of Moneths you shall see the Day of the Moneth: As against ♉ 29. you have May 10.

PROBLEME V.

The Place of the Sun given, to find its Declination.

HAving by the third Probleme found the Suns Place on the Plain of the Horizon, you must seek the same degree in

the Ecliptick, on the Globe; then bring that degree to the Brazen Meridian; and the number of degrees intercepted between the Equinoctial and the degree just-over the degree of the Eclip∣tick the Sun is in, is the Declination of the Sun for that Day: and bears its Denomination of North or South, according to its Position either on the North or South side the Equinoctial.

Example.

By the third Probleme aforesaid, of May 10. I find ♉ 29. the Suns Place; Therefore I seek in the Ecliptick Line on the Globe for ♉ 29. and bring it to the East side of the Brazen Meridian, which is the graduated side; and over ♉ 29. I find on the Brazen Meridian 20. deg. 5. min. (numbred from the Equinoctial:) and because ♉ is on the North side the Equinoctial, therefore I say, The Sun hath May 10. North Declination 20. degrees 5. min.

PROBLEME VI.

The Place of the Sun given, to find its Meridian Altitude.

THe Globe rectified, Bring the degree of the Sun to the Meridian, (or which is all one, the degree of the Ecliptick the Sun is in;) and the number of degrees contained be∣tween the Horizon and the Suns Place in the Meridian, is the number of degrees that the Sun is Elevated above the Ho∣rizon at Noon, or (which is all one) the Meridian Altitude of the Sun.

Example.

To know what Meridian Altitude the Sun hath here at Lon∣don, May 10. I bring the Suns Place (found by the third Pro∣bleme) to the Meridian, and count on the Meridian the number of degrees contained between the Horizon and the degree just over the Suns Place; which in this Example I find to be 58½▪ Therefore I say the Suns Meridian Altitude May 10. is here at London 58½ degrees.

PROBL. VII.

The Suns Place given, to find the Hour of Sun Rising, and the length of the Night and Day.

THe Globe and Hour Index rectified, Seek the degree the Sun is in on the Globe, and bring that degree to the East∣ern Side of the Horizon; and the Index of the Hour Circle will point at the Hour of Sun Rising.

Example.

To know the Hour of Sun Rising here at London, May 10. The Suns Place (as before) is ♉ 29. Therefore the Globe being rectified (as before) I seek ♉ 29. degrees on the Globe, and bring that degree to the East Side of the Horizon; and look∣ing on the Index of the Hour Circle, I find it point at 4. a clock and ⅙ part of an hour more towards 5; therefore I say May 10. the Sun rises here at London at ⅙ (which is 12. mi∣nutes) after 4 a clock in the Morning.

If you double 4 hours 12. minutes, it gives you the length of the Night, 8 hours 24. minutes. And if you substract the length of the Night 8. hours 24. minutes, from 24. hours, the length of Day and Night; it leaves the length of the Day 15. hours 36. minutes.

PROB. VIII.

To find the Hour of Sun Set.

TUrn the Place of the Sun to the West side of the Horizon, and the Index of the Hour Circle shews on the Hour-Cir∣cle the hour of Sun set; which on the 10th of May aforesaid, is 〈◊〉〈◊〉 parts of an hour after 〈◊〉〈◊〉 7. a clock at Night, Viz. the Sun Sets at 48. minutes past 7. a clock.

PROB. IX.

To find how long it is Twilight in the Morning, and Evening.

TWilight is that promiscuous and doubtfull light which ap∣pears before the Rising of the Sun in the Morning, and con∣tinues after the setting of the Sun in the Evening: It is made by the extension of the Suns beams into the Vapours of the Air, when the Sun is less then 18. deg. below the Horizon: for the Sun ere it Rises, and after it Sets, shoots forth its Beams through the Air, and so illuminates the Vapours of the Air; which il∣lumination does by degrees enlighten the Horizon, and spreads through the Zenith, even into the West, ere the Sun Rises; and also continues above the Horizon, afte•• the Sun sets.

Now though it be Twilight when the Sun is 18. degrees be∣low the Horizon; yet the duration of Twilight (is alterable both in respect of Time) and Place: for at such Time at the Sun is farthest distant from any Place, the Twilight shall be greater, then when it is neerest. And in respect of Place, All Places that have great Latitude from the Equator, have longer Twilight than those that are neerer to the Equator: for as Authors say, under the Equator there is no Twilight; when again in ma∣ny Climes both Northward and Southward, the Nights are indeed no Nights but only (as it were) a little over-spread with a cloudy Shade; and is either increased or diminished ac∣cording to the ••autation of Meo••erological Causes.

Therefore to know the beginning of Twilight in the Morning here at London, May 10; you must (having the Globe re∣ctified) turn the degree of the Ecliptick which is opposite to the Place of the Sun till it be elevated 18. degrees in the Quadrant of Altitude above the Horizon in the West; So shall the Index of the Hour-Circle point at the Hour that Twilight begins: Then subtract the Hour and Minute that Twilight begins from the Hour and Minute of Sun Rising, if in the Morning, or substract the Hour of Sun sett from the Hour of Twilight, if at Night; and the remainder is the length of Twilight.

Example.

The Globe Quadrant and Hour-Index being rectified, as be∣fore;

and the Suns place given, ♉ 29. I seek the opposite degree on the Globe, after this manner▪ I bring ♉ 29. to the Meridian, and observe what degree of the Ecliptik the opposite part of the Meridian cuts; and because I find it cuts ♏ 29. therefore I say ♏ 29. is opposite to ♉ 29. Having found the opposite de∣gree, I bring it into the West, and also the Quadrant of Alti∣tude, and joyn ♏ 29. to 18. degrees (accounted upwards on the Quadrant) so shall ♉ 29. be depressed 18. degrees in the East Side the Horizon: Then looking what Hour the Hour-In∣dex points at in the Hour-Circle, I find it to be, 1. Hor. 8. Min. which shews that Twilight begins at 8. Minutes past 1. a clock in the Morning.

And if you substract 1. Hour 8. Minutes, from 4. Hours 11. Minutes, the time of Sun Rising, found by the 7th. Probleme, it leaves 3. Hours 3. Minutes for the length of Twilight: And if you double 1. Hour 8. Minutes, the beginning of Twilight, it makes 2. Hours 16. Minutes for the intermission of Time between Twilight in the Evening, and Twilight in the Morning. So that May 10. absolute Night is but 2. Hours 16. Minutes long, here at London.

The reason why you bring the degree opposite to the Suns Place to the West, is, because the Quadrant containing but 90. degrees will reach no lower then the Horizon; but this Probleme requires it to reach 18. degrees beneath it: therefore by this help, you have the Proposition Answered, as well as if the Qua∣drant did actually reach 18. degrees below the Horizon. This shift you may have occasion to make in some other Problemes.

If you would know when Twilight ends after Sun set; you shall find it by bringing the degree of the Ecliptick opposite to the Place of the Sun to 18. degrees of the Quadrant of Altitude, on the East side the Horizon; for then shall the Index of the Hour-Circle point at 10. Hours 52. Minutes: which shews that it continues Twilight till 52. Minutes past 10. a clock at Night, May 10. here at London.

PROB. X.

The Suns Place given, to find its Amplitude; And also to know upon what point of the Compass it Riseth.

THe Globe &c. rectified: Bring the Suns Place to the East Side the Horizon; and the number of degrees intercepted

between the East point of the Horizon and the Suns Place, is the number of degrees of Amplitude that the Sun hath at its Ri∣sing; and bears its denomination either of North or South, accord∣ing to its inclination to either point in the Horizon.

Or, if you would know upon what point of the Compass the Sun Rises, Look but in the Circle of Winds; and against the Place of the Sun you have the name of the point of the Compass upon which the Sun Riseth.

Examples of both.

May 10. the Suns Place is ♉ 29. There••••re ^• the Globe being rectified; I bring ♉ 29. to the East side the Horizon, and find it touch against 33, degrees 20. Minutes from the East point to∣wards the North: Therefore I say the Sun hath North Ampli∣tude 33, degrees 20. Minutes.

And to know upon what point of the Compass the Sun rises; I keep the Globe to its Position, and look in the Circle of Winds, in the outmost verge of the Horizon, and find the Suns Place against the Wind named North East and by East; Therefore I say May 10. here at London the Sun riseth upon the North East and by East point of the Compass.

PROBL. XI.

The Hour of the Day given, to find the Heigth of the Sun.

THe Globe &c. Rectified. Turn about the Globe till the Index of the Hour-Circle point (in the Hour-Cir∣cle) to the Hour of the Day: Then bring the Qua∣drant of Altitude to the Suns Place in the Ecliptick, and the degree on the Quadrant which touches the Suns Place, shall be the number of degrees of the Suns Altitude.

Example.

May 10. here at London; At 53. Minutes past 8. a clock in the Morning, I would know the Heigth of the Sun above the Ho∣rizon. Therefore I turn about the Globe till the Index of the

Hour-Circle come to 53: Minutes past 8. a clock (which is almost 9.) in the Hour-Circle: And keeping the Globe to this Posi∣tion, I bring the Quadrant of Altitude to the Suns place, viz. 〈◊〉〈◊〉 29. (found by the third Probleme) and because the Suns Place touches upon 40. degrees of the Quadrant, therefore I say May 10. 53. Minutes past 8. a clock in the Morning, here at London, The Sun is just 40. degrees above the Horizon; or which is all one, hath 40. degrees of Altitude.

PROB. XII.

The Altitude 〈◊〉〈◊〉 Sun, and Day of the Moneth given, to find the Hour of the Day.

AN Hour is the 24th. part of a Day and a Night, or the space of time that 15. degrees of the Equator takes up in * 1.1 passing through the Meridian; for the whole Equator which contains 360. degrees, passes through the Meri∣dian in 24. Hours, therefore 15. degrees which is the 24th. part of 360, pass through in one Hour. These Hours are Vulgarly divided into halfs, quarters, and half quarters; but Mathemati∣cally into Minutes, Seconds. Thirds, Fourths, &c. A Minute is the 60th. part of an Hour, so that 60, minutes make an Hour, 30, half an Hour, 15. a quarter of an Hour: A Second is the 60th * 1.2 part of a Minute: a third is the 60th part of a Second: a Fourth is the 60th part of a Third: and so you may run on to Fifths, Sixths, Sevenths, &c. if you please. 12. of these Hours make a Day, and 12. more make a Night: so that Day and Night con∣tain 24. hours as aforesaid▪ which are Volgarly numbred from Noon with 1, 2, 3, to 12, at Night▪ and then begin again with 1, 2, 3, till 12 at Noon: But by Astronomers they are Numbred from Noon with 1, 2, 3, &c. to 12. at Night; and so forward to 13, 14, 15, till 24; which is just full Noon the next Day. Yet in this Treatise I shall mention the Hours as they are Vulgarly co••••ted, viz. from 〈◊〉〈◊〉. after noon, to 12. at Night, and call the Hours after Midnight by 1, 2, 3, 4, &c. in the Morning, to 12. at Noon again, the next Day. But to the operation.

The Globe, &c. Rectified, Bring the Place of the Son to the Number of degrees of Altitude accounted upon the Quadrant of

Altitude, and the Hour-Index shall point at the Hour in the Hour-Circle: yet herein respect must be had to the Fore or After noons Elevation; as shall be shewed in the next Pro∣bleme.

Example.

May 10. The Sun is elevated 40. degrees above the Horizon, here at London: Therefore having found the Place of the Sun, by the third Probleme, to be ••29. I move the Globe and Quadrant till I can joyn the 29. degree of 〈◊〉〈◊〉 to the 40. deg, upon the Quadrant of Altitude; and then looking on the Hour-Circle, I find the Index point at 53. Minutes past 8. a clock, for the Fore noon Elevation; and at 3. hours 7. Minutes for the After noons Elevation. Therefore if it be Fore-noon, I say, It is 53. Minutes past 8. a clock in the Morning. But if it be After noon I say, It is 7. Minutes past 3. a clock in the After noon.

PROB. XIII.

How to know whether it be Before or After Noon.

HAving made one Observation, you must make a Second a little while after the First; and if the Sun increase in Alti∣tude, it is Before Noon: but if it decrease in Altitude, it is After Noon.

Example.

The Sun was at 8. hor. 53. Min. elevated 40. degr. above the Horizon: A little while after (suppose for examples sake aquar∣ter of an hour,) viz. at 9. hor. 8. Min. I observe again the heigth of the Sun, and find it 42. degrees high; so that the Altitude is increased 2. degrees; Therefore I say, It is Fore-Noon: But if the Sun had decreased in Altitude, I should have said it had been After-Noon.

How to take Altitudes by the Quadrant, Astrolabe, and Cross-staff.

There are divers Instruments whereby Altitudes may be taken: but the most in use are the Quadrant, Astrolabe, and Cross-staff. A Quadrant is an Instrument comprehen∣ded between two Straight lines making a Right Angle, and an

Arch discribed upon the Right Angle, as on the Center, con∣taining 90. degrees, which is a quarter of a Circle: and therefore the Instrument is called a Quadrant. See this Figure.

[illustration]

A prepresents the Center; upon which is fastned a Plumb-line, A B the one side, A C the other side, upon which the Sights are placed: B C the Arch or Quadrant, which is divided into 90. equal parts, and numbred from B to C. D one Sight, E the other Sight: F the Plumbet fastned to the Plumb-line.

When by this Instrument you would observe the heigth of the Sun, you must turn the Center A to the Sun, and let the beams thereof dart in at the hole in the first Sight D, through the hole in the second Sight E; so shall the Plumb-line ly upon the degree in the Limb, of the Suns Elevation: As if the plumb-line ly upon the 20th degree, then shall the Alti∣tude be 20. degrees; if on 25. the Altitude shall be 25. degrees: and so for any number of Degrees the thred or Plumb-line lies on, the same number of Degrees is the Altitude of the Sun.

But if it be a Star whose Altitude you would observe; you must hold up the Quadrant, and joyn the Limb to your Cheek bone, and turn the Center towards the Star: then winking with one Ey, look through the holes of the Sights with the other Ey, till you can see the Star through those holes; so shall the Plumb-line (as before in the Sun) hang upon the degree in the Limb of the Stars Elevation.

Another sort of Quadrants is made with a moveable Index, as is represented in this Figure.

[illustration]

A is the Center, A Band A C the two sides, B C the Limb, D E two Sights fixed upon a moveable Index or Label; F G two other Sights, for observing the Horizon.

When by this Quadrant you would observe an Altitude, the side B A must be parallel to the Horizon, and the Index must be mo∣ved till the Object (be it either the Sun Moon or any Star) be seen through the holes or slitts of the Sights placed on the Index; for then the Arch D B shall be the Elevation required. You

may know when the side B A is parallel to the Horizon, by ob∣serving the parting of Heaven from the Earth through the Sights on the Side B A.

To take Altitudes by the Astrolabe.

The Astrolabe is a round Instrument, flat on either side, upon one of the flats or Plains is discribed a Circle as B C D E, divided into 360, equal parts or degrees, numbred from the line of Level B A C, with 10, 20, 30, &c. to 90. in the Per∣pendicular D C. Upon the perpendicular is fastned a Ring as F, so as the Instrument hanging by it, the line of Level may hang pa∣rallel to the Horizon. Upon the Center is a moveable Label or Ruler, as G H, whereupon is placed two Sights as I K.

[illustration]

If you desire further instructions for making this Instrument, you may peruse M^r Wright in his Division of the whole Art

of Navigation, annexed to his Correction of Errors: where he also shews the use of it at large; which in brief is as follows.

You must hold the Astrolabe by the Ring in your left hand, and turning your right side to the Sun, lift up the Label with your right hand, till the beams of the Sun entring by the hole of the uppermost Vane or Sight, doth also pierce through the hole in the nethermost Vane of Sight; and the deg. and part of deg. that the Label lies on is the height of the Sun above the Horizon.

But if it be a Star you would observe; you must use the A∣strolabe as you were directed to use the Quadrant, holding it up to your Cheek bone, and looking through the Sights, &c.

To take Altitudes by the Cross-staff.

This Instrument consists of a Staf about a yard long, and three quarters of an inch square: Upon it is fitted a Vane, (or sometimes two, or three,) so as it may slide pretty stiff upon the Staff, and stand at any of the Divisions it is set to.

[illustration]

The making is taught by M^r Wright, aforesaid: But the use is as follows.

You must put that end of the Cross-staff which is next 90. degrees to your Cheek bone, upon the outter corner of your Ey, and holding it there steddy, you must move the Vane till you see the Horizon joyned with the lower end thereof, and the Sun or Star with the higher end; then the degree and part of degree which the Vane cutteth upon the Staff, is the height of the Sun or Star.

Some of these waies for taking Altitudes have been formerly taught by others, that have treated upon the Use of Globes: and therefore because some would be apt to think this Treatise un∣compleat if I did not shew these waies also, I have thought fit to insert them: Yet the same things may be performed by the Globe alone, without troubling your self with multiplicity of In∣struments; if your Globe be made with a hollow Axis; for then if the Globe stand Horizontal, you shall by Observing the Object through the Axis have the degree of Elevation, noted by the superficies of the Horizon.

PROB. XIV.

To observe with the Globe the Altitude of the Sun.

PLace the Globe so that the upper plain of the Horizon may stand parallel to the Plain of the Horizon of your Place; as was taught by the Second Probleme; then turn the North Pole towards the Sun, and place it higher or lower, by moving the Meridian through the notches of the Horizon, till the beams of the Sun pierce quite through the Axis of the Globe: So shall the arch of the Meridian com∣prehended between the Pole and the Horizon, be the number of Degrees that the Sun is elevated above the Ho∣rizon.

Example.

March 20. just at noon, here at London, I would observe the Meridian Altitude of the Sun. Therefore placing the Ho∣rizon Horizontal, as by the Second Probleme: I turn the North

Pole towards the Sun, and move it with the Meridian upwards or downwards, either to this side or that, till I can fit it to such a Position that the Sun Beams may dart quite through the Axis of the Globe; which when it does, I look on the Meri∣dian and find 42. degrees 25. min. comprehended between the Pole and the superficies of the Horizon; Therefore I say the Meridian Altitude of the Sun March 20. here at London, is 42. degrees 25. min.

PROB. XV.

To find the Elevation of the Pole, by the Meridian Alti∣tude of the Sun, and Day of the Moneth given.

THe Day of the Moneth is March 20. By the 4th Prob. you may find the place of the Sun to be ♈ 10. Therefore bring the Place of the Sun to the Meridian, and elevate it above the Horizon the same number of degrees it hath in Hea∣ven; so shall the arch of the Meridian comprehended between the Pole and the Horizon, be the elevation of the Pole, in your Place.

Otherwise.

The Day of the Moneth given is March 20. so that by the fourth Prob. you have the Suns Place ♈ 10; and by the fifth, the Declination of the Sun 3. 55. North: therefore the Declination being North, and you on the North side the Equator; you must substract 3. 55. from the Meridian Altitude 42. 25. and there remains 38, 30. for the heighth of the Equinoctial above the Horizon; but if your Declination had been South, you must have added 3 55. to the Meridian Altitude, and the Sum would have been the Elevation of the Equinoctial. Having the Elevation of the Equinoctial, you may easily have the Elevation of the Pole; for the one is alwaies the Complement of the other to 90. Thus the Height of the Equinoctial 38. 30. subtracted from 90. leaves 51. 30. for the Elevation of the Pole, here at London. And thus it follows, that the Latitude of any Place from the Equinoctial, is alwaies equal to the Elevation of the

Pole: for between the Zenith and the Equinoctial is contained the Complement of the Heighth of the Equinoctial above the Horizon to 90.

PROB. XVI.

To take the Altitude of any Star above the Horizon; by the Globe.

THe Horizon of the Globe set parallel to the Horizon of the World, as before: Turn the North Pole towards the Star, and when you can see the Star through the Axis, the Northern notch of the Horizon will cut the degree of Eleva∣tion on the Meridian.

Example.

April 19. at 11. a clock at Night, I would observe the Alti∣tude of Spica Virgo: Therefore I set the Horizon parallel to the Horizon of the World, as by the Second Probleme, and turn the Northern Pole till it point towards the Star: Then looking in at the South Pole of the Globe through the Axis, I shall see the Star, and have on the Meridian the Question resolved. But if it point not exactly, then I move the North Pole upwards or downwards, either to the right hand, or to the left, according as I may find occasion, till I can see the Star through the Axis: and then the edge of the notch in the Horizon cuts 28. degrees 57. min. on the Brazen Meridian. Therefore I say April 19. at 11. a clock at Night, here at London, the Altitude of Spica 〈◊〉〈◊〉 is 30. degrees above the Horizon.

PROB. XVII.

By the Meridian Altitude of any Star given, to find the Height of the Pole.

JOyn the Star to the Meridian, and place it to the Altitude observed; so shall the number of degrees intercepted be∣tween the Pole and the Horizon, be the Elevation of the Pole.

Example.

Spica Virgo is observed to have 28. degrees 57. min Meri∣dian Altitude; therefore I bring Spica Virgo to the Meridian, and raise it or depress it higher or lower as I find occasion, till it is just 28. degrees 57. min. above the Horizon: Then I count the number of degrees between the Pole and the Horizon, and find them 51½. Therefore I say the Elevation of the Pole is here at London 51½. Yet note, If the Star whose Altitude you observe have fewer number of degrees of Declination from the Pole, then the Elevation of the Pole, you may be apt to mistake in its coming to the Meridian; for those Stars never set; and there∣fore are twice Visible in the Meridian in 24. hours, once above the Pole, and once under the Pole.

If your Star have greater Altitude then the North Star, it is above the Pole; but if it have less, it is below the Pole: so that if you know but whether it be above or below, it is enough; for so you may accordingly raise it to the Altitude on the Me∣ridian it hath in Heaven, and joyn it to the Meridian either above or beneath the Pole, as the Star is placed in Heaven: and then the arch of the Meridian comprehended between the Pole and the Horizon, is the Elevation of the Pole, as aforesaid.

Otherwise.

Having the Meridian Altitude of the Star, you must find its Declination by the 27. Probleme: and if the Declination be South, and you on the North side the Equator, you must ad the Declination to the Meridian Altitude, and the sum of both makes the Altitude of the Equinoctial: But if the Declination be North, and you on the North side the Equator, you must substract the Declination from the Meridian Altitude, (as was taught by the 15. Prob. in the Example of the Sun) and the remainder is the Altitude of the Equinoctial Then (as was taught by the 15 Probleme aforesaid) substract the Altitude of the Equinoctial from 90, the Remainder is the Elevation of the Pole in your Place.

Example.

By the last Probleme the Meridian Altitude of Spica Virgo was 28 degrees 57 min, and the Declination of Spica by the 27th Probleme is found 9. degrees 33. min. South: therefore because the Declination is South, I ad 9. degrees 33. min. to the Meridian Altitude, which makes 38. deg. 30. min. for the Ele∣vation of the Equinoctial: which 38. deg. 30. min. substracted from 90. leaves 51. degrees 30. min. for the Elevation of the Pole here at London.

PROB. XVIII.

Another way to find the Height of the Pole by the Globe; if the Place of the Sun be given: and also to find the Hour of the Day, and Azimuth, and Almican∣tar of the Sun.

THis must be performed by help of a Spherick Gnomon, (as Blaew calls it,) which is a small Pin or Needle fix∣ed perpendicularly into a smal Basis with an hollow concave bottom, that it may stand upon the convexity of the Globe. Therefore the Horizon of the Globe being set parallel to the Horizon of the World, (as by the Second Pro∣bleme) the Spherick Gnomon must be set exactly upon the Place of the Sun; and then turning the Globe about (upon its Axis) either from East to West, or contrarily from West, to East; or else by the Meridian, through the notches of the Horizon, till the Spherick Gnomon cast no shadow on any side thereof; you have on the Meridian in the North point of the Horizon the number of degrees that the Pole is elevated above the Ho∣rizon.

Example.

Imagine the four Quarters of the Horizon of the Globe cor∣respond with the four Quarters of the Horizon of the World; and the Plain of the Horizon of the Globe is parallel to the Plain of the Horizon of the World: The Suns Place is ♉ 29¼,

which I find on the Globe, and place the Spherick Gnomon thereon; Then at a guess I move the Globe both on its Axis, and by the Meridian, (as neer as I can) so as the Spherick Gnomon may cast no shadow; yet if it do, and the shadow fall to∣wards the North Pole; then I elevate the North Pole more, till the shadow fals just in the middle of it self: but if the shadow fall downwards, towards the South Pole, then I depress the North Pole: If the shadow fall on the East side, I turn the Globe on its Axis more to the West; and if the shadow fall to the West, I turn the Globe more into the East: and the degree of the Meridian which the North point of the Horizon touches, is the degree of the Poles Elevation: which in this Example is 51½. the Latitude of the City of London.

By this Operation you have also given the Hour of the Day in the Hour-Circle, if you keep the Globe unmoved: and the Azimuth, and Almicantar, if you apply but the Quadrant of Altitude to the Place of the Sun, as by the 22, and 23. Problemes.

PROB. XIX.

To observe by the Globe the Distance of two Stars.

YOu must pitch upon two Stars in the Meridian; and ob∣serve the Altitude of one of them first, and afterwards the Altitude of the other: Then substract the lesser Altitude from the greater, and the remainder shall be the distance re∣quired.

Example.

March 7. at 11. a clock at Night here at London, I see in the Meridian the two Stars in the foremost Wheels of the Waggon, in the Constellation of the Great Bear, called by Sea-men the Pointers, (because they alwaies point towards the Pole-Star.) Therefore to observe the distance between these two Stars, I first observe (as by the last Probleme) the Altitude of the most Northern to be 77. degree 59. minutes, and set down that number of Degrees and minutes with a Pen and Ink on a Paper, or with a peece of Chalk or a Pencil on a Board: and afterwards I observe the Altitude of the other Star which is un∣der

it, as I did the first, to be 83. deg. 21. min. and set that number of degrees and minutes also down, under the other number of degrees and minutes: Then by substracting the lesser from the greater, I find the remainder to be 5. degrees 22. min. which is the distance of the two Stars in the Great Bear, called the Pointers.

PROB. XX.

How you may learn to give a guess at the number of degrees that any two Stars are distant from one another; or the number of degrees of Altitude the Sun or any Star is elevated above the Horizon: only by looking up to Heaven, without any Instru∣ment.

BEtween the Zenith and the Horizon is comprehended an Arch of a Circle containing 90. degrees; so that if you see any Star in or neer the Zenith, you may know that Star is 90. or neer 90. degrees high; and by so much as you may conceive it wants of the Zenith, so much you may guess it wants of 90. degrees above the Horizon. By this Rule you may guess at an Arch of Heaven containing 90. degrees, or at an Arch of Heaven containing 45. degrees; if by your ima∣gination you divide the whole Arch into two equal parts, for then shall each of them contain 45. degrees; And if by your imagination you divide the Arch of 90. into 3. equal parts, each division shall contain an Arch of 30. degrees, &c. But this way is a little too rude for guessing at Stars elevated but few degrees, or for Stars distant but few degrees from one another. Therefore that you may learn to guess more precisely at Distances in Hea∣ven, you may either with a Quadrant, Astrolabe, or the Globe; find the exact distance of any two known Stars that are but few degrees asunder, and by a little revolving the distance of those Stars in your fancy, you may at length so imprint their distance in your memory, that you may readily guess the distance of other Stars by the distance of them.

Example.

You may find either by the Globe, Quadrant, or As••rotabe,

(for they all agree) 3. degrees comprehended between the first Star in Orions Girdle, and the last; therefore by a little 〈◊〉〈◊〉∣nating upon that distance, you may imprint it in your fancy for 3. degrees, and so make it applicable to other Stars, either of the same distance, or more, or less: And the Pointers (by the last Probleme) are distant from one another 5. degrees and almost an half: These are alwaies above our Horizon, and therefore may alwaies stand as a Scale for five and an half degrees; So that by these for 5½ degrees, and those in Orions Girdle for 3. degrees, and others observed, either of greater or lesser distance, you may according to your own Judgement shape a guess, if not exactly, yet pretty neer the matter of Truth, when you come to other Stars. Thus you may exercise your fancy upon Stars found to be 10. or 15. degrees asunder, or more, or less; and with a few experiments of this nature enure your Judgement to guess di∣stances, and enable your memory to retain your Judgement.

This way of guessing will be exact enough for finding the Hour of the Night by the Stars, for most common Uses; or the Hour of the Day, by guessing at the Altitude of the Sun; if after you have guessed at the Altitude, you shall work as was taught by Prob. 12. for the Hour of the Day: and as shall be taught in the next Probleme, for the Hour of the Night.

PROB. XXI.

The Day of the Moneth, and Altitude of any Star given, to find the Hour of the Night.

THe Globe, Quadrant, and Hour Index rectified: Bring the Star on the Globe to the same number of Degrees on the Quadrant of Altitude that it hath in Heaven: So shall the Index of the Hour-Circle point in the Hour-Circle at the Hour of the Night.

Example.

March 10. the Altitude of Arcturus is 35. degrees above the Horizon, here at London: Therefore having the Globe,

Quadrant and Hour Index rectified, I bring Arcturus on the Globe to 35. degrees on the Quadrant of Altitude: And then looking in the Hour-Circle, I find the Index point at 10. a clock; which is the Hour of the Night.

PROB. XXII.

The Place of the Sun, and Hour of the Day given, to find its Azimuth in any Latitude assigned.

THe Globe, &c. rectified to your Latitude: Turn the Globe till the Index of the Hour-Circle come to the given hour; and bring the Quadrant of Altitude to the Place of the Sun: so shall the number of degrees contained between the East point of the Horizon and the degree cut by the Quadrant of Altitude on the Horizon, be the number of degrees of the Suns Azimuth, at that time.

Example.

May 10. at 53. minutes past 8. a clock in the Morning, I would know the Azimuth of the Sun: Therefore (the Globe being first rectified) I turn about the Globe till the Index of the Hour-Circle point to 53. minutes past 8. a clock, or which is all one, within half a quarter of an hour of 9; then I move the Quadrant of Altitude to the degree the Sun is in that Day, and there let it remain till I see how many degrees is contained be∣tween the North point and the Quadrant; which in this Ex∣ample is 108. deg. 25. min. And because this distance from the North, exceeds 90. degrees; therefore I substract 90. de∣grees from the whole, and the remains is 18. degrees 25. min. for the Azimuthal distance of the Sun from the East point towards the South. But if it had wanted of 90. degrees from the North point, then should the Complement of 90. have been the Azimuthal distance of the Sun from the East point.

PROB. XXIII.

The Place of the Sun, and hour of the Day given, to find the Almicantar of the Sun.

THe Almicantars of the Sun is upon the matter the same thing with the Altitude of the Sun: only with this di∣stinction. The Almicantars are Circles parallel to the Horizon, discribed by the degree of the Quadrant of Altitude upon the Zenith as its Center, by turning the Qua∣drant round about the Globe till it comes again to its first Place: But the Altitude is an Arch of the Vertical Circle, comprehen∣ded between the Horizon and any point of the Globe assigned. Their agreement consists in this; When the Sun or any Star ha•••• any known Almicantar, they are said to have the same number of degrees of Altitude; As if the Sun be in the 20th Almican∣tar; he hath 20 degrees of Altitude; if in the 30th Almicantar, he hath 30. degrees of Altitude, &c. Now because the Opera∣tion is the same for finding the Altitude and Almicantar, I shall refer you to the 11th Probleme; which shews you how to find the Altitude or Heighth; and by consequence the Almicantar.

PROB. XXIV.

The Place of the Sun given, to find what Hour it comes to the East, or West, and what Almicantar it then shall have.

THe Globe, Quadrant, and Hour Index rectified, Bring the Quadrant of Altitude to the East point in the Horizon, if you would know what hour it comes to the East; or to the West point, if you would know what hour it comes to the West: Then turn about the Globe till the place of the Sun come to the Quadrant of Altitude; and the Index of the Hour Circle shall point at the hour of the Day: which on the Day aforesaid will be 7. hor. 7 min. in the Morning, that the Sun commeth to the East, and 4 hor. 53. min. after noon, that the Sun commeth to the West. And if you then count the number of degrees from

the Horizon upwards on the Quadrant of Altitude, it will shew you the Almicantar of the Sun for that time; which will both Morning and Evening be 15, deg. 30. min. as was taught you by the last Probleme.

PROB. XXV.

To know at any time what a clock it is in any other Part of the Earth.

THe difference of Time is reckoned by the access and pro∣gress of the Sun: for the Sun gradually circumvolving the Earth in 24. hours, doth by reason of the Earths rotundity en∣lighten but half 〈…〉〈…〉 at one and the same moment of Time; as shall be shewed hereafter: so that hereby it comes to pass, that when with us here in England it is 6. a clock in the Morning, with those that have 90. degrees of Longitude to the Westward of us, it is yet Midnight: with those that have 180. degrees of Longitude from us, it is Evening; And with those that have 90. degrees of Longitude to the Eastwards, it is Noon. So that those to the Eastward have their Day begin sooner then ours: But to the Westward their Day begins after ours. Therefore that you may know what Hour it is in any Place of the Earth, of what distance soever it be, you must first Bring the Place of your own Habitation to the Meridian, and the Index of the Hour Circle to 12. on the Hour Circle; Then bring the other Place to the Meridian, and the Arch of the Hour Circle comprehended between the hour 12. and the In∣dex, is the difference in Time between the two Places.

Example.

London in England, and Surat in the East Indies: First I bring London to the Meridian, and turn the Index of the Hour-Circle to 12; then I turn the Globe Westward, because London ••s Westward of Surat, till Surat come to the Meridian; and see at what Hour the Index of the Hour Circle points, which in this Example is 5. hor. 54. minutes: And because Surat lies to the Eastward of us so many degrees, therefore as was said before,

their Day begins so much before ours: So that when here at London it is 6. a clock in the Morning, at Surat it will be 11. a clock 54. minutes; when with us it is 12. a clock, with them it will be 5 a clock 54. minutes afternoon.

If you would know the difference of Time between London and Jamaica; Working as before, you may find 5. hor. 15. min. But Jamaica is to the West of London; therefore their Day begins 5. hor. 15. min. after ours: so that when with us it is Noon, with them it will be but three quarters of an hour past 6. a clock in the Morning: and when with them it is Noon, with us it will be one quarter past 5. a clock after Noon, &c.

Or you may yet otherwise know the difference of Time, if you divide the number of Degrees of the Equinoctial that pass through the Meridian while the Globe is moved from the first Place to the second, by 15. so shall the product give you the dif∣ference of hours and minutes between the two Places: as you will find if you try either of these Examples, or any other.

PROB. XXVI.

To find the Right Ascension of the Sun, or Stars.

THe Right Ascension of any point on the Globe is found by bringing the point proposed to the Meridian, and counting the number of degrees comprehended between the Vernal Colure, and the Meridian.

Example, for the Sun.

June 1. I would know the Right Ascension of the Sun: His Place found, as by the third Probleme, is ♊ 20. Therefore I bring ♊ 20. to the Meridian; and then the Meridian cuts the Equinoctial in 79. degrees 15. minutes, accounted from the Ver∣nal point ♈: Therefore I say the Right Ascension of the Sun June 1. is 79. deg. 15. Minutes.

Example, for a Star.

I take Capella, alias Hircus, the Goat on Auriga's sholder,

and bring it to the Meridian; and find the Meridian cut the Equinoctial (counting as before from the Vernel point ♈) in 73. degrees 58. minutes: Therefore I say, the Right Ascension of Hircus is 73. degrees 58. min. Do the like for any other point of the Globe proposed.

PROB. XXVII.

To find the Declination of the Sun, or Stars.

THe Declination of any point on the Globe is found by bringing the point proposed to the Meridian, and counting the number of degrees comprehended on the Meridian between the Equinoctial and the point proposed: and bears its Denomi∣nation of North or South, according as it is scituate on the North or South side the Equinoctial.

Example, for the Sun.

June 1. I would know the Declination of the Sun. His Place found, as before, i•• ♊ 20. Therefore I bring ♊ 20. to the Me∣ridian; and find 23. degrees 8. min. comprehended on the Me∣ridian between the Equinoctial and ♊ 20. and because ♊ is on the North side the Equinoctial; Therefore I say, June 1. The Sun hath North Declination 23. degrees 8. minutes.

Example, for a Star.

I take Hircus aforesaid, and bring it to the Meridian, and find 45. degrees 40. minutes comprehended on the Meridian between the Equinoctial and the Star Hircus. And because Hircus is on the North side the Equinoctial; Therefore I say, Hircus hath North Declination 45. degrees 40. min. Do the like for any other point on the Globe proposed.

But Note, The Right Ascension and Declination of the Sun al∣ters dayly; for in twelve Moneths he runs through every degree of Right Ascension, and in three Moneths to his greatest Decli∣nation: But the Right Ascension and Declination of the Stars is scarce perceiveable for some Years: Yet have they also an alter∣ation of Right Ascension and Declination: For, those Stars

that have but few degrees of Right Ascension, will in process of Time have many; and those Stars between the Tropick that have North Declination, will in length of Time have South De∣clination; and the contrary (as shall be more fully shewed hereafter:) For, the Stars moving upon the Poles of the Eclip∣tick go forwards in Longitude one whole Degree in 70½ Years (as hath been shewed before, Book 1. Chap. 3. Sect. 3.) and so alter both their Right Ascension, and Declination; as may be seen by this following Table of Right Ascensions and Declina∣tions of 100. of the most eminent fixed Stars, Calculated by Tycho Brahe, for the Years 1600. and 1670. which I have in∣serted; partly, because by it you may see the differences of their Right Ascensions and Declinations in 70½ Years; and partly to Accomodate those that may have occasion to know their Right Ascensions and Declinations neerer than the Globe can shew them.

A Table of the Right Ascensions and Declinations of 100. Select fixed Stars; Calculated by Tycho Brahe, for the Years 1600, and 1670. As also their Difference of Right Ascensions and Declinations, in 70. Years.

	1600		Differentia.	1900
Names of the Stars.	R. Asc.	Declin.		R. As.	Decl.	R. Asc.	Declin.
Scedir, in Casssopeae.	4 36	54 21	N	1 22	34 S	5 58	54 55
The Pole Star.	5 47	87 9½	N	3 59	34 S	9 46	87 43½
Southern in the whales tail.	5 51	20 12	S	1 17	34 N	7 8	19 38
Cassiopeae's Belly.	8 21	58 33	N	1 27	34 S	9 48	59 7
Girdle Andromeda.	11 50	33 32	N	1 23	33 S	13 13	34 5
Knee of Cassiopeae.	15 3	58 7	N	1 35	33 S	16 38	58 40
1. in ♈ horn.	22 56	17 19	N	1 23	31 S	24 19	17 50
Whales belly.	22 59	12 16	S	1 15	31 N	24 14	11 45
2. in ♈ horn.	23 10	18 50	N	1 22	31 S	24 32	19 31
South foot of Andromeda.	24 55	40 23	N	1 29	30 S	26 24	40 53

In the Knot in the line ♓.	25 22	0 50	N	1 18	30 S	26 40	1 20
* Star in ♈ head.	26 23	21 33	N	1 25	30 S	27 38	22 3
* In the wtales jaw.	40 25	2 29	N	1 15	25 S	41 40	2 54
Caput Medusae	40 38	39 22	N	1 37	25 S	42 15	39 47
* In Persons side.	44 2	48 22	N	1 28	21 S	45 30	48 43
* In the Pletades.	50 57	22 49	N	1 29	21 S	52 26	23 10
In the Nostrils of ♉.	59 16	14 37	N	1 25	17 S	60 41	14 54
North Ey of ♉.	61 21	18 14	N	1 24	17 S	62 45	18 31
Aldebaran.	63 16	15 38	N	1 26½	15 S	64 43	15 53
Hircus, Capella.	71 49	45 30	N	1 49	10 S	73 38	45 40
* Orions foot, Rigel.	73 51	8 43	S	1 15	9½ S	75 7	8 33½
North Horn ♉.	75 16	28 12	N	1 37	8 S	76 53	28 20
Orions left sholder.	75 58	5 55	N	1 19	3 S	77 17	6 3
Belly of the Hare	77 48	71 6	S	1 5	7 N	78 53	20 59
1. In Orions Girdle	77 58	〈◊〉〈◊〉 39	S	1 17	7 N	79 15	0 32
Uppermost in Orions face	78 21	9 36	N	1 22	7 S	79 41	0 43
South Horn ♉.	78 26	20 51	N	1 31	7 S	79 57	20 58
2. In Orions Girdle.	79 1	1 30	S	1 17	6 N	80 18	1 24
Last in Orions Girdle.	80 10	2 12	S	1 16	5 N	81 26	2 7
Auriga's right Sholder.	82 40	44 50	N	1 55	4 S	84 35	44 54
Orions right Sholder.	83 26	7 16	N	1 22	4 S	84 48	7 20
* Foot ♊.	93 38	16 40	N	1 28	2 N	95 6	16 38
Great Dog Sirius.	96 53	16 11	S	1 7	4 S	98 0	16 15
Head of Castor, the first Twin.	107 9	32 41	N	1 44	11 N	108 53	32 30
The little Dog, Procyon.	109 37	6 12	N	1 20	12 N	110 57	6 0
Head Pollux, second Twin.	110 13	28 55	N	1 34	12 N	111 47	28 43
* In the Stern of the	117 39	23 11	S	1 4	15 S	118 43	23 26
Praesepe ♋	124 20	21 2	N	1 28	19 N	125 48	20 43
Northern Asse ♋ Ship.	124 58	22 51	N	1 30	20 N	126 28	22 31
Southern Asse ♋	125 27	19 35	N	1 27	20 N	126 54	19 15
The Heart of Hydra.	137 1	6 57	S	1 15	25 S	138 16	7 22
South of 3. in neck ♌	146 22	18 42	N	1 28	28 N	147 50	18 14
Lions Heart, Basiliscus.	146 45½	13 53½	N	1 53½	28½ N	148 8	13 25
North of 3. in neck ♌	148 33	25 23	N	1 23	29 N	150 1	24 54
Middle of 3. in neck ♌	140 〈◊〉〈◊〉	21 50	N	1 50	29 N	150 51	21 21

First lowest in 〈◊〉〈◊〉 Vrsa Ma••.	159 12	58 31	N	1 37	32 N	160 49	57 59
First upper in □ Dubbe	159 37	63 54	N	1 41	32 N	161 18	63 22
* back ♌.	163 10	22 43	N	1 27	34 N	164 37	22 9
Lions tail.	172 9	16 49	N	1 19	34 N	173 28	16 15
following lowest in □ Ursa Major.	173 3	55 57	N	1 23	34 N	174 26	55 23
Uppermost following in □.	178 50	59 15	N	1 20	34 N	180 10	58 41
Girdle 〈◊〉〈◊〉.	188 53	5 37	N	1 18	34 N	190 11	5 3
Rump Ursa Major, Aliot.	189 1	58 10	N	1 19	33 N	190 10	57 37
Vindemiatrix, ♍.	190 36	13 8	N	1 17	33 N	191 53	12 35
Spica ♍.	196 4	9 1	S	1 19½	32½ S	197 23½	9 33½
Middle tail Ursa Major.	196 54	57 3	N	1 3	32 N	197 57	56 31
End Tail Urs. Major.	202 54	51 22	N	1 2	31 N	203 56	50 51
Arcturus.	209 23½	21 18½	N	1 11	29½ N	210 34½	20 49
Left Sholder of Bootes.	214 2	40 3	N	1 2	27 N	215 4	39 36
South Scale ♎.	217 14½	14 18	S	1 23	27 S	218 37½	14 45
North Scale ♎.	223 54½	7 50	S	1 21½	24 S	225 16	8 14
* Northern Crown.	229 26	28 6	N	1 5	21 N	230 31	27 45
* Serpents neck.	231 12	7 46	N	1 15	21 N	232 27	7 25
Northern of 3. * in front ♍.	235 34	18 38	S	1 28	19 S	237 2	18 57
Lest hand Ophiucus.	238 25	2 37	S	••1 23	18 S	239 48	2 55
Heart 〈◊〉〈◊〉. Antares,	241 18	25 26	S	1 32	16 S	242 50	25 42
Right Shold▪ Hercules.	243 15	22 27	N	1 5	15 N	244 20	22 12
Left knee of Ophiucus.	243 49	9 39	S	1 23	15 S	245 12	9 54
Right knee of Ophiucus.	251 50	15 7	S	••0 50	10 S	252 40	15 17
Head of Hercules.	254 6	14 55	N	1 8	8 N	255 14	14 47
Left Sholder of Hercules.	254 40	25 22	N	0 52	8 N	255 32	25 14
Head of Ophiucus.	259 5	12 56	N	1 11	7 N	260 16	12 49
Right Sholder of Ophiucus.	260 56	4 49	N	1 13	5 N	262 9	4 44
* head of the Dragon.	266 52	51 37	N	0 35	2 N	267 27	51 35
* Lyrae.	275 52	38 28	N	••0 50	4 S	276 42	38 32
Most Eastern in Head ♐.	281 32	21 35	S	1 31	8 N	283 3	21 27
Vultures tail.	281 47	13 20	N	1 13	8 S	283 0	13 28
In the Swans Beak.	288 40	27 10	N	1 1	11 S	289 41	27 21
* in Vulture.	292 49	7 54	N	1 17	13 S	294 6	8 7
In the Swans North wing.	293 10	44 12	N	0 48	14 N	293 58	44 26

Upper horn ♑.	289 57	13 40	S	1 25	16 N	300 22	13 24
Lower horn ♑.	299 39	15 57	S	1 27	17 N	301 6	15 40
In the Swans breast.	302 1½	39 1	N	0 53½	18 S	302 55	39 19
Left hand of ♒.	306 32	10 53	S	1 16	19 N	307 48	10 34
Swans Tail.	306 57	43 53½	N	0 51½	20½S	307 49	44 14
In the Swans South wing	307 31	32 30	N	1 0	21 S	308 31	32 51
Left Sholder ♒.	317 37	7 15	S	1 21	26 N	318 58	6 49
1. In tail ♑.	319 28	18 21	S	1 26	26 N	320 54	17 55
In Cepheus Girdle.	320 46	68 50	N	0 22	26 S	321 8	69 16
In Pegasus mouth.	321 10	8 5	N	1 18	26 S	322 28	8 31
2. in tail ♑.	321 16	17 51	S	1 25	27 N	322 41	17 24
Right Sholder of ♒.	326 19	2 13	S	1 20	29 N	327 39	1 44
Fomahant, ♒.	338 46	31 39	S	1 25	31 N	340 11	31 8
Scheat. P••gasus.	241 9	25 56	N	1 12	32 S	342 11	26 28
Marchab, Pegasus.	341 15	13 5	N	1 15	32 S	342 30	13 37
Mouth of Southern fi••h.	344 9	1 7	N	1 17	33 S	345 26	1 40
Head of Andromeda.	356 59	26 54	N	1 17	34 S	358 16	27 28
* Cassiopeae's chair.	357 5	56 58	N	1 15	34 S	358 20	57 32
End of Pegasus wing. (tail.	358 14	12 58	N	1 16	34 S	359 30	13 32
Northern in the wh••les	359 49	11 1	S	1 18	34 S	1 7	10 27

The Vse of this Table.

The first Collumne on the left hand is the names of the Stars. The Second Collumne shews the degrees and minutes of Right Ascension, for the Year 1600. The third the Declination for the same Year. The fourth shews whether the Declination be North or South; N stands for North, S for South. The fifth shews the difference in degrees and minutes of Right Ascension of the Stars, between the Years 1600▪ and 1670. The sixth shews the Difference of Declination; and whether it be North, or South. The seventh shews the Right Ascension in degrees and minutes, for the Year 1670. The eighth shews the D••clination in degrees and minutes for the same Year.

By this Table you may perceive the fixed Stars increase in Right Ascension, till they come to the Vernal Colure; from

whence the number of their Right Ascension is reckoned: and by the Collumne of their Difference of Right Ascension, you may see how much they increase in 70. Years▪ And if you would know how much they increase for any other number of Years, you must find what proportion they have to 70, and the same proportion the Difference of the Right Ascension of the Stars will have to the Difference in the Table.

Example.

I would know the Difference of Right Ascension the Pole-Star will have in 35. Years. I find in the fifth Collumne the Difference of Right Ascension of the Pole Star to be 3. degrees 59. min. Therefore by the Rule of Proportion. I say, If 70. Years give 3. degrees 59. min. 35. Years shall give 1. degree 59½▪ min: and so proportionably for any other number of Years.

Though this Rule serves for finding the Difference of Right Ascension of any Star; Yet it will not serve for finding the Difference of any Stars Declination. For the Stars on the North side the Equinoctial between the Hyemnal and Solsticial Colures, and on the South side the Equinoctial between the Solsticial and Hyemnal Colures, increase in Declination. But the Stars on the South side the Equinoctial between the Hyem∣nal and Solsticial Colures, and on the North side the Equino∣ctial between the Solsticial and Hyemnal Colures, Decrease in Declination: as you may yet more plainly see by the Globe, if you bring 66½ deg. of the Meridian to the North side of the Ho∣rizon, and screw the Quadrant of Altitude to 66½ degrees in the Zenith, and Declination of the Pole of the Ecliptick; and bring the Hyemnal Colure to the Meridian; for so shall the Pole of the Ecliptick be joyned with the center of the Quadrant of Altitude, and the Ecliptick with the Horizon; and all the Circles that the several degrees on the Quadrant make in a Re∣volution from West to East upon the Poles of the Ecliptick, re∣present the great Revolution of every Star that each degree on the Quadrant cuts. And thus demonstratively will be represen∣ted the progress of the fixed Stars through every degree of Lon∣gitude, and by consequence the alteration of their Right Ascen∣sion, and Declination. For, Imagining that degree of the Qua∣dra••t

of Altitude to be the Star, which just reaches the Star; you may by turning about the Quadrant, see how Obliquely the Star (or the degree representing the Star) either moves about, or cuts the Equinectial, and all Circles parallel to the Equinoctial; and thereby observe it sometimes to incline in mo∣tion to, and other times to decline in motion from the Equi∣noctial. But how long time it will be ••re the Star inclines to, or declines from the Equinoctial, you may know by finding the distance of Longitude in degrees it hath from either the Solsticial or Hy••mnal Colure; and with respecting the forego∣ing Rules in its Position, you may by the Table in Book 1, Chap. 3. Sect. 3. satifie your self.

Example.

The most Northerly Star in the Girdle of Orion doth yet de∣crease in Declination. But I would know how long it shall de∣crease; Therefore by the 32. Probleme, I find the Longitude of that Star to be for the Year 1670. 77. deg. 51. min. which subducted out of 90, (the distance of the Solsticial Colure from the Equinoctial,) leaves 12. 9, for the distance of that Star from the Solsticial Colure. Therefore by the Table aforesaid, I find what number of Years answers to the motion of 12. deg. 9. min. And because I cannot find exactly the same number of degrees and minutes in the Table, I take the number neerest to it; which is 14. degrees 10. minutes, and that is the motion of the Ecliptick in 1000. Years. But because this 14. degrees 10. minutes is 2. degrees 1. minute too much, I seek 2. degrees, 1. min. in the Table, and the number of Years against it I would subduct from the number of Years against 14, deg, 10. min. and the remainder would be the number of Years required: But 2. deg. 1. min. I cannot find neither, therefore I must take the number of degrees and minutes neerest to it, which is 2. deg. 50. min. and that yeelds 200. Years; which subducted out of 1000. leaves 800. Years. But because this is also too much by the motion of 49. min. Therefore I seek for 49. min. in the Table, and subduct the number of Years against it from 800, and the remainder would be the number of Years required. But 49. min. is not in the Table neither, Therefore I take the neerest to it, which is 51. min. and that yeelds 60. Years; which sub∣ducted out of 800. leaves 740. But this is likewise too much by

the motion of two min. Therefore I seek 2. min. in the Table, but cannot find it neerer then 2½, and against it I find 3. Years, which 3. Years I subduct out of 740, and the Remainder is 737. the number in Years required. You may if you please for exactness, subduct for the ½ min. 8. Moneths; so have you 736, Years 4. Moneths, for the Time that the most Northerly Star in the Girdle of Orion will decrease in Declination after the Year 1670. which will be till An. Dom. ••406. after which time it will increase in Declination for 12706. Years together, till it come to have 47. degrees 8. min. of Declination: at which time it will be in or very neer the place of the most Southerly Star of the Southern Crown; and that Star in its place.

And thus the Pole Star is now found to increase in Declina∣tion, and will yet this 421 Years: after which time it will de∣crease in Declination for 12706 Years together, till it come to be within 42. degrees 42. minutes of the Equinoctial, in the void space now between Draco and Lyra; at which time Lyra will be almost as neer the Pole, as the Pole Star now is; and then the most proper to be the Northern Pole Star: And the last Star in the Stalk of the Doves mouth will be then very neer the Southern Pole, and therefore most fit to be the Sou∣thern Pole-Star.

PROB. XXVIII.

The Place of the Sun or any Star given, to find the Right Descension, and the Oblique Ascension, and the Oblique Descension.

BRing the Place of the Sun or the Star to the Meridian un∣der the Horizon, and the degree of the Equator that comes to the Meridian with it is the Degree of Right Descension.

For the Oblique Ascension.

Bring the Place of the Sun or the Star to the East side the Horizon, and the degree of the Equator cut by the Horizon, is the Degree of Oblique Ascension of the Sun or Star.

For the Oblique Descension.

Bring the Place of the Sun or Star to the West side the Hori∣zon, and the degree of the Equinoctial cut by the Horizon is the Degree of Oblique Descension. They need no Examples.

PROB. XXIX.

Any Place on the Terrestrial Globe being given, to find its Antipodes.

BRing the given Place to the Meridian, so may you (as by the first Probleme) see its Longitude and Latitude; then turn about the Globe till 180. degrees of the Equator pass through the Meridian; and keeping the Globe to this Po∣sition, number on the Meridian 180. degrees from the Latitude of the given Place: and the point just under that degree is the Antipodes.

Example.

I would find the Antipodes of Cuida Real, an Inland Town of the West Indies, which lies upon the River Parana, an Arm of Rio de la Plata: Therefore I bring Cuida Real to the Me∣ridian, and find (as by the first Probleme) its Latitude 23. 50: South; and its Longitude 333. degrees: Then I turn about the Globe till 180. degrees of the Equator pass through the Me∣ridian; and keeping the Globe to that position, I number so many degrees North Latitude as Parana hath South, viz. 23, 50, and just under that degree I find Lamoo, a Town lying upon the Coast of China, in the Province of Quancij: Therefore I say Lamoo is just the Antipodes of Cuida Real.

Another way.

Bring the given Place to the North or South point of the Ho∣rizon, and the point of the Globe denoted by the opposite point of the Horizon, is the Antipodes of the given Place.

PROB. XXX.

To find the Perecij of any given Place, by the Terrestrial Globe.

BRing your Place to that side the Meridian which is in the South notch of the Horizon, and follow the Parallel of that Place on the Globe till you come to that side the Meridian which is in the Northern notch of the Horizon; and that is the Perecij of your Place.

PROB. XXXI.

To find the Antecij of any given Place, upon the Terrestrial Globe.

BRing your Place to the Meridian, and find its Latitude by the first Probleme; If it have North Latitude, count the same number of degrees on the Meridian from the Equator Southwards; But if it have South Latitude, count the same number of degrees from the Equator Northwards: and the point of the Globe directly under that number of degrees is the Antecij of your Place.

PROB. XXXII.

To find the Longitude and Latitude of the Stars, by the Coelestial Globe.

THe Quadrant of Altitude will reach but 90. degrees, as was said Prob. 9. Therefore if the Star you enquire after be on the North side the Ecliptick, you must elevate the North Pole 66½ degrees above the North side the Horizon: If on the South side the Ecliptick, you must elevate the South Nole 66½ degrees above the South side the Horizon: Then bring the Solsticial Colure to the Meridian on the North side the Horizon, and screw the Quadrant of altitude to the Zenith, which will be in 23½ degrees from the Pole of the World: So shall the Eclip∣tick ly in the Horizon, and the Pole of the Ecliptick also ly under the Center of the Quadrant of Altitude (as was

shewed Prob. 27.) Now to find the Longitude of any Star, do thus Turn the Quadrant of Altitude about till the graduated edge of it ly on the Star; and the degree in the Ecliptick that the Quadrant touches is the Longitude of that Star.

Example, for a Star on the North side the Ecliptick.

I would know the Longitude of Marchab, a bright Star in the wing of Pegasus: I find it on the North side the Ecliptick, Therefore I elevate the North Pole, and placing ♋ on the North side the Meridian, I screw the Quadrant of Altitude to the Zenith, as aforesaid: Then laying the edge of the Quadrant of Altitude upon that Star, I find that the end of it reaches in the Ecliptick to ♓ 18. 56. Therefore I say, the Longitude of Marchab is ♓. 18. 56.

For the Latitude of a Star.

The Degree of the Quadrant of Altitude that touches the Star is the Latitude of the Star.

Example.

The Globe and Quadrant posited as before, I find 19. deg. 26. min. (accounted upwards on the Quadrant) to touch Marchab aforesaid: Therefore I say, the Latitude of Marchab is 19. deg. 26. min.

And thus by elevating the South Pole and placing the Globe and Quadrant of Altitude as aforesaid, I shall find Canicula have 15. degrees 57. min. South Latitude, and 21. degr. 18. min in ♋, Longitude.

PROB. XXXIII.

To find the Distance between any two Places, on the Ter∣restrial Globe.

THis may be performed either with the Quadrant of Al∣titude, or with a pair of Compasses: with the Qua∣drant of Altitude, 〈◊〉〈◊〉: Lay the lower end thereof to one Place, and see what degree reaches the other Place, for

that is the number of degrees between the two Places. If you multiply that number of Degrees by 60 the Product shall be the number of English Miles between the two Places.

Example.

I would know the distance between London and the most Easterly point of Jama••ca; I lay the lower end of the Quadrant of Altitude to Jamaica, and extending the other end towards London, I find 68½. deg. comprehended between them: Therefore I say 68½ is the number of degrees comprehended between Lon∣don and Jamaica.

If you would find the Distance between them with your Compasses, you must pitch one foot of your Compasses in the East point of Jamaica, and open your Compasses till the other foot reach London; and keeping your Compasses at that Di∣stance apply the feet to the Equinoctial line, and you wil find 68½ degree comprehended between them: as before.

If you multiply 68½. by 60, is it gives 4110. English miles.

If you multiply it by 20, it gives 1370. English Leagues.

If you multiply it by 17½, it gives 1199. Spanish Leagues.

If you multiply it by 15, it gives 1054 Dutch Leagues.

PROB. XXXIV.

To find by the Terrestrial Globe upon what point of the Compass any two Places are scituate one from another.

FInd the two Places on the Terrestrial Globe, and see what ••umb passes through them; for that is the point of the Compass they bear upon.

Example.

Bristol and Bermudas are the Places: I examine what Rhumb passes through them both: and because I find no Rhumb to pass immediately through them both, Therefore I take that Rhumb which runs most Parallel to both the Places; which in this Example is the tenth Rhumb counted from the North towards the left hand; and is called as you may see by this following

Figure West South West; Therefore I say Bermudos lies scituate from Bristol West South West; and by contraries Bristol lies cituate from Bermudas East North East.

[illustration]

PROB. XXXV.

To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars.

WHen any Star Rises with the Sun, it is said to Rise Cosmically.

And when any Star Sets when the Sun Rises, it is sa••d to Set Cosmically.

To find these, Rectifie the Globe to the Latitude of your

Place, and bring the Place of the Sun to the East side the Ho∣rizon; and the Stars then cut by the Eastern Semi-Circle of the Horizon, Rise Cosmically; and those Stars cut by the Western Semi-Circle of the Horizon, Set Cosmically.

Example.

Novemb. 9. I would know what Stars Rise and Set Cosmi∣cally▪ here at London. The Suns Place found, as by the third Probleme is 〈◊〉〈◊〉 27. Therefore I bring 〈◊〉〈◊〉 27. to the East side the Horizon, and in the Eastern Semi-Circle I find Rising with the Sun the right Wing of Cygnus, the Star in the end of A∣quila's tail, Serpentarius and Centaurus: Therefore these Con∣stellations are said to the Cosmically. In the Western Semi-Circle of the Horizon I find Setting Andromeda, the Triangle, Tau∣rus, Orion, (anis Major, and Argo Navis; Therefore I say, these Constellations Set Cosmically.

PROB. XXXVI.

To find by the Coelestial Globe the Acronical Rising and Setting of the Stars.

THe Stars that Rise when the Sun Sets, are said to Rise A∣cronically. And,

The Stars that Set with the Sun, are said to Set Acronically.

To find these, Rectifie the Globe to the Latitude of your Place, and bring the Place of the Sun to the West side the Hori∣zon; and the Stars then cut by the Eastern Semi-Circle of the Horizon, Rise Acronically: And those Stars cut by the Western Semi-Circle of the Horizon, Set Acronically.

Example.

November 9. I would know what Stars Rise and Set Acro∣nically here at London. The Suns Place as before, is 〈◊〉〈◊〉 27. Therefore I bring 〈◊〉〈◊〉 27. to the West side the Horizon; and in the Eastern Semi-Circle I find Rising the Southern Fi••h, Foma∣hant, Ce••us, Taurus, Auriga, and the Feather in Castor's Cap. Therefore these Constellations are said to Rise Acronically. In

the Western Semi-Circle of the Horizon I find Setting the Lyons tail, Virgo, Scorpio, and Sagittarius, Therefore I say, these Con∣stellations Set Acronically.

PROB. XXXVII.

To find by the Coelestial Globe the Heliacal Rising, and Setting of the Stars.

WHen a Star formerly in the Suns Beams gets out of the Suns Beams it is said to Rise Heliacally. And.

When a Star formerly out of the Suns Beams, gets into the Suns Beams, it is said to set Heliacally.

A Star is said to be in the Suns Beams, when it is made in∣conspicuous by reason of its neerness to the Suns Light. The Bigger Stars are discernable more neer the Suns Light, then the Lesser are: For, Stars of the first Magnitude may (accor∣ding to the received Rules of ancient Authors) be seen when the Sun is but 12. degrees below the Horizon but Stars of Second Magnitude cannot be seen unless the Sun be 13. degrees below the Horizon: Stars of the third Magnitude require the Sun to be 14. degrees below the Horizon ere they can be seen; of the fourth Magni••ude 15. degrees. of the fifth Magnitude 16. de∣grees of the sixth Magnitude 17 degrees; the Nebulous ones 18. degrees. Yet this Rule is not so certain but that either clear or cloudy weather may alter it. Read more of this subject in M^r Palmer on the Plamsphear. Book 4. Chap. 20

Now to find the Time that any Star shall Rise Heliacally. Do thus Rectifie the Globe and Quadrant of Altitude to your Latitude. Then bring the given Star to the East side the Horizon, and turn the Quadrant of Altitude into the West side, and see what degree of the Ecliptick is elevated so many degrees above the Horizon as the Magnitude of the Star you enquire after re∣quires, according to the foregoing Rules; for the opposite degree of the Ecliptick is the degree the Sun shall be in when that Star Rises Heliacally. Having the degree of the Ecliptick the Sun is in, you may find the Day of the Moneth, by the 4th Pro∣bleme.

Example.

I would know when Cor Leonis shall Rise Heliacally here at London: Therefore I Rectifie the Globe and Quadrant of Altitude for London, and bring Cor Leonis to the East side the Horizon, and turn the Quadrant of Altitude into the West; and because Cor Leonis is a Star of the first Magnitude, therefore I see what degree of the Ecliptick is elevated in the West side the Horizon 12. degrees on the Quadrant of Altitude, and find ♓ 9. deg. Now the degree of the Ecliptick opposite to ♓ 9. is 〈◊〉〈◊〉 9. Therefore I say, when the Sun comes to 〈◊〉〈◊〉 9. degrees (which by the 4th Probleme I find is August. 23.) Cor Leonis shall Rise Heliacally.

For the Heliacal Setting.

The Globe, &c. Rectified, as before: Bring the Star to the West side the Horizon, Then see what degree of the Ecliptick is elevated on the Quadrant of Altitude so many degrees as the Stars Magnitude requires; for when the Sun comes to the oppo∣site degree of the Ecliptick that Star shall set Heliacally.

Example.

I would know when Bilanx a Star in the Beam of the Scales, will Set Heliacally here at London. The Globe and Qua∣drant Rectified, I bring Bilanx to the West side the Horizon, and turn the Quadrant of Altitude into the East; Then I exa∣mine what degree of the Ecliptick is elevated 13. degrees of the Quadrant of Altitude (because Bilanx is a Star of the second Magnitude) and find ♉ 4½. opposite to ♉ 4½. is 〈◊〉〈◊〉 4½. Therefore I say, When the Sun comes to 〈◊〉〈◊〉 4½. (which by Probleme 4. will be October 18) Bilanx shall set Heliacally.

PROB. XXXVIII.

To find the Diurnal and Nocturnal Arch of the Sun, or Stars, in any given Latitude.

THe Semi-Diurnal Arch is the number of degrees of the E∣quator that passes through the Meridian whiles the Sun or

any Star is ascending above the East side the Horizon to the Me∣ridian. To know the number of degrees it contains, Rectifie the Globe to the given Latitude, and bring the Place of the Sun or Star to the East side the Horizon, and note what number of de∣grees of the Equinoctial is then cut by the Meridian: Then re∣move the Place of the Sun or Star to the Meridian, and see again what number of degrees of the Equinoctial is then cut by the Meridian, and substract the former from the latter, and the remainder shall be the number of degrees of the Sun or Stars Semi-Diurnal Arch. But Note, If the Equinoctial point ♈ pass through the Meridian while the Sun or Star is turned from the East side the Horizon to the Meridian, then you must substract the number of degrees of the Equinoctial cut by the Meridian when the Sun or Star is at the East side the Horizon from 360. degrees, and to the remainder ad the num¦ber of degrees of the Equinoctial that comes to the Meridian with the Place of the Sun or Star, and the Sum of them both is the number of degrees of the Sun or Stars Semi-diurnal Arch; which being doubled is the number of degrees of the whole Di∣urnal Arch: and which being substracted from 360, given the Nocturnal Arch.

Example, of the Sun.

Having Rectified the Globe, I would May 10. know the Diurnal Arch of the Sun: His Place found by Prob. 3. is 8 29. Therefore I bring ♉ 29. to the Fast side the Horizon, and find then at the Meridian 299. degrees 30. min. of the Equi∣noctial; then I turn the Place of the Sun to the Meridian, and find 56. deg. 30. min. of the Equinoctial come to the Meridian with it. Here the Equinoctial point ♈ passes through the Me∣ridian while the Sun moves between the Horizon and the Meri∣dian; Therefore as aforesaid, I substract the first number of degrees and minutes viz. 299. deg. 30. min. from 360. degrees, and there remains 60▪ degr. 30. min. for the number of degrees and minutes contained between the degree of the Equinoctial at the Meridian and the Equinoctial point ♈; and to this 60. deg. 30. min. I ad the second number of degrees and minutes, viz. 56. deg. 30. min. the number of degrees and minutes between the point ♈ and the deg. of the Equinoctial at the Meridian, and they make together 117. degrees, for the Suns Semi diurnal

Arch; By doubling of which, you have 234. degrees, for the Suns Diurnal Arch; And by substracting 234. (the Diurnal Arch) from 360. you have 126. degrees, for the Suns Noctur∣nal Arch.

Example, for a Star.

I take Sirius, a bright Star in the Great Dogs mouth. The Globe rectified, as before; I bring Sirius to the East side the Hori∣zon, and find then 29. degrees 30 minutes of the Equinoctial at the Meridian, then I turn Sirius to the Meridian and find 97. degrees 38 minutes of the Equinoctial come to the Meridian with it: Therefore I substract the first number viz. 29. degrees 30. minutes, from the second, 97. 38, and the remains is 68. de∣grees 8 minutes, for the Semi-diurnal Arch of Sir••us.

His Nocturnal Arch you may find as before.

PROB. XXXIX.

To find the Azimuth and Almicantar of any Star.

THis Probleme is like the 22, and 23. Problemes, which shew the finding the Azimuth and Almicantar of the Sun; only, whereas there you were directed to bring the degree of the Sun to the Quadrant of Alti∣tude, you must now bring the Star proposed to the Quadrant of Altitude; and by the Directions in those Problemes the resolu∣tion will be found.

PROB. XL.

To find the Hour of the Night, by observing two known Stars in one Azimuth, or Almicantar.

REctifie the Globe Quadrant and Hour Index. Then find the two known Stars on the Globe; and if the two Stars be in one Azimuth, turn about the Globe and Quadrant of Altitude till you can fit the two Stars to ly under the graduated edge of the Quadrant of Altitude: so shall the Index of the Hour-Circle p••int at th•• Hour of the Night. If

the two Stars be in one Almicantar, Turn the Globe forward or backward till the two Stars come to such a Position that by moving the Quadrant of Altitude, the same degree on it will ly on both the Stars; so shall the Index of the Hour-Circle point at the Hour of the Night.

PROB. XLI.

The Hour given that any Star in Heaven comes to the Me∣ridian, to know thereby the Place of the Sun, and by con∣sequence the Day of the Moneth, though it were lost.

BRing the Star proposed to the Meridian, and turn the In∣dex of the Hour-Circle to the Hour given, Then turn a∣bout the Globe till the Index point at the Hour of 12, for Noon; and the Place of the Sun in the Ecliptick shall be cut by the Meridian.

Example.

March 7. at 11, aclock at Night the Pointers come to the Meridian of London. Therefore I place the Pointers on the Cae∣lestial Globe under the Meridian, and turn the Index of the Hour-Circle to 11. past Noon, afterwards I turn back the Globe till the Index point to 12. at Noon; Then looking in the Eclip∣tick, I find the Meridian cuts it in ♓ 26. 45. minutes; Therefore I say, when the Pointers come to the Meridian at 11. a clock at Night, the Place of the Sun is ♓ 26. 45. Having thus the Place of the Sun, I may find the Day of the Moneth by the fourth Probleme; and so either know the Day that the Pointers come to the Meridian at 11. a clock at Night, or at any other Hour given.

The Day of the Moneth might also be found by the Declina∣tion and the Quarter of the Ecliptick the Sun is in, given: For the Meridian will cut the degree of the Suns Place in the Eclip∣tick in the Parallel of Declination: So that having respect to the Quarter of the Ecliptick, you'le find the Suns Place; and having the Suns Place, you may as aforesaid find the Day of the Moneth.

PROB. XLII.

The Day of the Moneth given, to find in the Circle of Let∣ters on the Plain of the Horizon, the Day of the Week.

THe seven Daies of the Week were by the Idolatry of the ancient Roman Heathenish Times Dedicated to the Ho∣nour of seven of their Gods, which we call Planets. The first is the most eminent, and therefore doubtless by them set in the first Place, called Dia Solis, or the Suns Day: The second Dia Lu∣na, the Moons Day: The third Dia Martis, the Day of Mars: by us called Tuesday: The fourth Dia Mercurius, Mercuries Day: by us called Wednesday; from Woden, an Idol the Saxons Worshipt, to whose Honour they Dedicated that Day, and is by all those Germain Nations still called Wodensdagh: The fifth Dia Jovis, Jupiter or Joves Day: which doubtless the Saxons (from whom probably we receive it) called Donder-dagh, be∣cause Jupiter is the God of Thunder; and we either by corrup∣tion or for shortness, or both, call it Thursday: The sixth Dia Veneris, the Day of Venus: but the Saxons transferring her Honour to another of their Goddesses named Fria, called it Fri∣dagh: and we from them call it Fryday: The seventh is Dia Saturnis, Saturus Day.

The same Day of the Moneth in other Years happens not on the same Day of the Week, therefore the Dominical Letter for one Year is not the same it is the next: Now because you can∣not come to the knowledge of the Day of the Week unless you first know the Sundaies Letter, therefore have I in Prob. 5•• inser∣ted a Table of M^r Palmers, by which you may find the Domini∣cal or Sundaies Letter for ever; and having the Dominical Letter you may in the Circle of Letters on the Horizon find it neer the day of that Moneth, and count that for Sunday, the next under it for Monday, the next under that for Tuesday, and so in order, till you come to the Day of the Moneth.

Example.

I would know what Day of the Week June 1. Anno 1658. Old Style, falls on; I find by the Table aforesaid the Dominical

Letter is C, then I look in the Calender of Old Style for June 1. and against it I find Letter E, which because it is the second Let∣ter in order from C, therefore it is the second Day in order from Sunday, which is Tuesday.

PROB. XLIII.

The Azimuth of any Star given, to find its Hour in any given Latitude.

THe Hour of a Star is the number of Hours that a Star is distant from the Meridian. To find which, Rectifie the Globe and Quadrant of Altitude, and bring the Star proposed to the Meridian, and the Index of the Hour-Circle to 12. Then place the lower end of the Quadrant of Altitude to the given A∣zimuth in the Horizon, and turn the Globe till the Star come to the graduated edge of the Quadrant of Altitude; so shall the Index of the Hour-Circle point at the Hour of the Star. Only this caution you must take; If the Star were turned from the Meri∣dian towards the Eastern side of the Horizon, you must substract the number of Hours the Index points at from 12. and the re∣mainder shall be the Hour of the Star. But if the Star were turn∣ed from the Meridian towards the West side the Horizon, the Hour the Index points at is (without more adoe) the Hour of the Star.

PROB. XLIV.

How you may learn to know all the Stars in Heaven, by the Coelestial Globe.

REctifie the Globe, Quadrant, Hour-Index and Horizon, as by Prob. 2. Then turn about the Globe till the In∣dex of the Hour-Circle point at the Hour of the Night on the Hour-Circle. Then if every Star on the Globe had a hole in the midst, and your Ey were placed in the Center of the Globe; you might by keeping your Ey in the Center and look∣ing through any Star on the Globe see its Ma••ch in Heaven: that is, the same Star in Heaven which that Star on the Globe repre∣sents: for from the Center of the Globe there proceeds a straight

line through the Star on the Globe, even to the same Star in Hea∣ven. Therefore those Stars that are in the Zenith in Heaven, will then be in the Zenith on the Globe; those that are in the East in Heaven, will be in the East on the Globe; those in the West in Heaven, in the West on the Globe; and those Stars that are in any Altitude in Heaven, will at the same time have the same Altitude on the Globe; So that if you see any Star in Heaven whose Name you desire to know, you need but observe its Azimuth and Altitude, and in the same Azimuth and Alti∣tude on the Globe, you may find the same Star: and if it be an eminent Star, you will find its Name adjoyned to it.

Example.

December 10. at half an hour past 9. a clock at Night, here at London, I see two bright Stars at a pretty distance one from ano∣ther in the South; I desire to know the Names of them; There∣fore having the Globe rectified to the Latitude of London, and the Quadrant of Altitude screwed to the Zenith, the Hour-Index also Rectified, and the Horizon posited Horizontally, as by Prob. 2. I observe the Altitude of those Stars in Heaven, (either with a Quadrant, Astrolabe, Cross-staff, or the Globe it self, as hath been shewed Prob. 13, 16.) to be, the one 78. degrees, the o∣ther 42, degrees above the Horizon. Therefore having their Altitudes, I count the same number of degrees as for the first 78. upon the Quadrant of Altitude upwards, and turn it into the South, under the Meridian, and see what Star is under 78. de∣grees, for that is the same Star on the Globe which I saw in Heaven. Now at the first examination of the Globe you may see that that Star is placed in the Ey of that After time which is called Caput Medusa, and indeed, that being the only Star of Note in that Constellation, bears the Name of the whole Con∣stellation. The other Stars about it you may easily know by their Scituation. As, Seeing two little Stars to the Westwards of that Star in Heaven, you may see on the Globe that the hithermost is in the other Ey of Caput Medusa, and the furthermost in the Hair or Snakes of the same Asterisme. Looking a little to the Southwards of those Stars in Heaven, you may see two other smal Stars a little below those in the Eyes; Therefore to know those also, you may look on the Globe, and see that there is one on the

Nose, and another Starre in the Cheek of Caput Medusa

In like manner for the second Star in the Meridian, which is 42 degrees above the Horizon: If you move the Quadrant of Altitude (as before) to the South or Meridian, and count 42 de∣grees upon the Quadrant of Altitude, you will find a Star of the second Magnitude in the Mouth of the Whale: Therefore you may say, that Star in Heaven is in the Mouth of the Whale: and because close to it on the Globe is written Menkar, Therefore you may know the name of that Star in Heaven is Menkar.

In the South East and by South 56 degrees above the Hori∣zon, I ••ee a very bright Star in Heaven; therefore I bring the Quadrant of Altitude to the South East and by South point in the Horizon, and find under 56 degrees of the Quadrant of Alti∣tude a great Star, to which is prefixed the name Occulus Tau∣rus; Therefore I say, the name of that Star in Heaven is Oc∣culus Taurus.

In the South East in Heaven you may see three bright Stars ly directly in a straight line from one another, the middlemost whereof is 25. degrees or thereabouts above the Horizon, there∣fore bring the Quadrant of Altitude to the South East point of the Horizon, and about 25 degrees above the Horizon you will see the same great Stars on the Globe, in the Girdle of Orion: There∣fore those Stars are called Orions Girdle.

At the same time South East and by East you have about 10 degrees above the Horizon the brightest Star in Heaven, called Sirius, in the Mouth of the Great Dog; Canicula a bright Star in the Little Dog East and by South, about 25 degrees above the Horizon: Cor Leonis just Rising East North East: you have also at the same time on the East side the Horizon, the Twins, Auriga, the Great Bear; and divers other Stars, eminent both for their splendor and Magnitude.

In the West side the Horizon you have South West and by West about 4 degrees above the Horizon a bright Star in the Right Leg of Aquarius: and all along to the Southwards in Cetus the Whale, you have other eminent bright Stars: More upwards towards the Zenith you have a bright Star in the Line of the two Fishes: Higher yet, you have the first Star in ♈, an eminent Star, because the first in all Catalogues that we have cognizance of; and therefore probably in the Equinoctial Colure when the Stars were first reduced into Constellations: yet more

neer the Zenith you have a bright Star in the Left Leg of An∣dromeda: From thence towards the North, you find other very eminent bright Stars in Cassiopea, Cepheus, Ursa Minor, in the Tail whereof is the Pole Star: and Draco: Hecules: where you turn back, to Lyra, Cygnus, Pegasus, the Dolphin, &c. all which, or any other, you may easily know by their Altitude a∣bove the Horizon, and the point of the Compass they bear upon.

Thus knowing some of the most eminent Fixed Stars, you may by the Figure of the rest come to the knowledge of them also. For Example, Looking towards the North North East in Heaven, you may see seven bright Stars constituted in this Figure; There∣fore looking towards the same Quarter on the Globe, you may (without taking their Altitude) see the same Stars lying in the same Figure in the hinder parts of the Great Bear; from whence you may con∣clude, that those Stars in Heaven are scitu∣ate in the hinder parts of the Asterisme called Ursa Major.

[illustration]

Yet nevertheless you may see some Stars of Note in Heaven, which you shall not find on the Globe, and those in or neer about the Ecliptick: They are called Planets, and cannot be placed on the Globe, unless it be for a particular Time, with Black Lead, or some such thing that may be rubbed out again: Because they having a continual motion alwaies alter their Places. Of those there are five in number, besides the Sun and Moon, which are also Planets, though they shew not like Stars. These five are called Saturn, Jupiter, Mars, Venus, Mercury; yet Mecury is very rarely seen: because he never Rising above an Hour before the Sun, or Setting above a Hour after, for the most part hath his light so overspread with the dazelling Beams of the glittering Sun, that sometimes when he is seen he seems rather to be a More in the Suns Beams, then a Body en∣dowed with so much brightness as Stars and Planets seem to be.

Now there are divers waies (by some of which you may at all times) know those Planets from the Fixed Stars: as first, Their not twinkling, for therein they differ from fixed Stars; be∣cause they most commonly do twinkle, but Planets never; unless it be ♂ Mars; and yet he twinkles but very seldom neither.

Secondly, They appear of a considerable Magnitude, as ♃

sometimes appears greater ly far then a Star of the first Magni∣tude; and ☿ many times bigger then he. They are both glitter∣ing Stars, of a bright Silver collure; but ♀ most radient, especially when she is in her Perigeon. ♂ appears like a Star of the second Magnitude; and is of a Copperish colloure. ♄ shewes like a Star of the third Magnitude, and is of a Leaden Collour; and he (of all the others,) is most difficult to be known from a fixed Star; partly because of his minority, and partly because of the slowness of his motion. ☿ is very seldom seen (as aforesaid) unless it be in a Morning when he Rises before the Sun, or in an Evening when he Sets after the Sun: He is of a Pale Whitish Collour, like Quick silver, and appears like a Star of the third Magnitude. He may be known by the Company he keeps, for he is never above 29. degrees distant from the Sun.

Thirdly, The Planets may be known from fixed Stars by their Azimuths and Altitudes observed: (as hath been taught before) for if when you have taken the Azimuth and Altitude of the Star in Heaven you doubt to be a Planet, and you find not on the Globe in the same Azimuth and Altitude a Star appearing to be of the same Magnitude that that in Heaven appears to be, you may conclude that that in Heaven is a Planet. Yet notwithstanding it may happen that a Planet may be in the same degree of Longitude and Latitude in the Zodiack that some eminent fixed Star is in; as in the degree and minute of Longitude and La∣titude that Cor Leonis, or the Bulls Ey, or Scorpions heart is in, and so may eclipse that Star, by being placed between us and it: But that happens very seldom and rarely; but if you doubt it▪ you may apply your self to some other of the precedent and subse∣quent Rules here set down for knowing Planets from fixed Stars.

The fourth way is by shifting their Places; for the Planets having a continual motion, do continually alter their Places: as ♂ moves about half a degree in a day: ♀ a whole degree; but ♃ and ♄ move very slowly; ♃ not moving above 5. mi∣nutes, and ♄ seldom above 2. minutes. Yet by their motions alone the Planets may be known to be Planets, if you will precisely ob∣serve their distance from any known fixed Star in or near the E∣cliptick as on this Night, and the next Night after observe whether they retain the same distance they had the Night before; which if they do, then are they fixed Stars; but if they do not then are they Planets: yet this Ca••••on is to be given you in this Rule also,

That the Planets sometimes are said to be Stationary, as not al∣tering 1. minute in Place, forwards, or backwards in 6. or 7. daies together. Therefore, if you find cause to doubt whether your Star be a Planet, or a fixed Star, you may for the help of your understanding confer with some of the former Rules, unless you are willing to wait 8 or 9 daies longer, and so by observation of its motion resolve your self, Or,

Fifthly, you may apply your self to an Ephemeris for that Year, and see if on that day you find any Planet in the degree and minute of the Zodiack you see the Star you question in Heaven; and if there be no Planet in that degree of the Zodiack, you may conclude it is no Planet, but a fixed Star.

PROB. XLV.

How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in A∣stronomy, and Geography.

TAke the Terrestrial Ball out of the Horizon, and fasten a thred on the Brazen Meridian to the degree of the La∣titude of your Place; by this thred hang the Globe in a place where the Suns Beams may have a free access to it; Then direct the Poles of the Globe to their proper Poles in Heaven, the North Pole to the North, and the South Pole to the South; and with a thred fastned to either Pole, brace the Globe, so, that it do not turn from his position: then bring your Habitation to the Meridian; so shall your Terrestrial Globe be Rectified to correspond in all respects with the Earth it self; even as in Prob. 44. the Celestial Globe doth; the Poles of the Globe, to the Poles of the World; the Meridian of the Globe, to the Meridian of the World; and the several Regi∣ons on the Globe made Correspondent to the same Regions on the Earth: So that with great delight you may behold,

1. How the counterfeit Earth (like the true one) will have one Hemisphear Sun shine light, and the other shadowed, and as it were dark. By the shining Hemisphear you may see that it is Day in all Places that are scituate under it; for on them the Sun doth shine; and that it is Night at the same time in those Places

that are situate in the shadowed Hemisphear; for on them the Sun doth not shine; and therefore they remain in darkness.

2. If in the middle of the enlightned Hemisphear you set a Spherick Gnomon Perpendicularly, it will project no shadow, but shews that the Sun is just in the Zenith of that Place; that is, di∣rectly over the heads of the Inhabitants of that Place: and the point that the Spherick Gnomon stands on, being removed to the Meridian, shews the Declination of the Sun on the Meridian for that Day.

3. If you draw a Meridian line from one Pole to the other, in all Places under that line, it is Noon: in those Places scituate to the West, it is Morning; for with them the Sun is East: and in those Places scituate to the East, it is Evening; for with them the Sun is West.

4: Note the degree of the Equator where the enlightned He∣misphear is parted from the shadowed; for the number of de∣grees of the Equator intercepted between that degree and the Meridian of any Place, converted into Hours (by accounting for every 15. degrees 1. Hour) shews, if the Sun be Eastwards of that Place, how long it will be ere the Sun Rises, Sets, or comes to the Meridian of that Place: or if the Sun be Westward of that Place, how long it is since the Sun Rose, or Set, or was at the Meridian of that Place.

5. The Inhabitants of all Places between the enlightned and shadowed Hemisphear, behold the Sun in the Horizon: Those Westwards of the Meridian Semi-Circle drawn through the mid∣dle of the enlightned Hemisphear behold the Sun Rising: Those in the East, see it Setting.

6. So many degrees as the Sun reaches beyond either the North or South Pole, so many degrees is the Declination of the Sun, either Northwards or Southwards: and in all those Places comprehended in a Circle described at the termination of the Sun-shine, about that Pole, it is alwaies Day, till the Sun decrease in Declination: for the Sun goes not below their Horizon: as you may see by turning the Globe about upon its Axis: and a the opposite Pole at the same distance, the Sun-shine not reach∣ing thither, it will be alwaies Night, till the Sun decrease in Declination: because the Sun Rises not above their Horizon.

7. If you let the Globe hang steddy, you may see on the East side of the Globe, in what Places it grows Night; and on the

West side the Globe how by little and little the Sun encroaches upon it; and therefore there makes it Day.

8. If you make of Paper or Parchment a narrow Girdle, to begirt the Globe just in the Equinoctial, and divide it into 24. e∣qual parts, to represent the 24. hours of Day and Night, and mark it in order with I, II, III, &c. to XII. and then be∣gin again with I, II, III, &c. to the other XII. you may by placing one of the XII^s. upon the Equinoctial under the Meridian of your Place, have a continual Sun-Dyal of it, and the hour of the Day given on it, at once in two places; one by the parting the enlightned Hemisphear from the shadowed on the Eastern side, the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe. Much more might be said on this Probleme: But the Ingenuous Artist may of himself find out diversities of Speculations: therefore I forbear.

PROB. XLVI.

To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is.

THis may be performed by the former Probleme in the Day time, if the Sun shines: but not else. But to find it at all times, do thus. Bring the Place of your Habitation to the Meri∣dian, and the Index of the Hour-Circle to 12; Then turn the Globe Eastwards, if Afternoon, or Westwards, if Before Noon, till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is, either before or After-Noon: so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day.

Example.

May 10 at ¾ of an hour past 4. a clock After Noon▪ I would know in what Place of the Earth the Sun is in the Ze∣nith. My Habitation is London. Therefore I bring London to the Meridian, and the Index of the Hour-Circle to 12. and because it is After Noon: I turn the Globe Eastwards, till the Index passes through 4 hours and 3 quarters, or (which is all one) till 70 degrees 15 minutes of the Equator pass through the Me∣ridian.

Then I find by Prob. 5. the Suns Declination is 20. de∣grees 5. minutes which I find upon the Meridian, and in that Place just under that degree and minute on the Globe, the Sun is in the Zenith: which in this Example is in the North East Cape of Hispaniola.

Having thus found in what Place of the Earth the Sun is in the Zenith. Bring that Place to the Meridian, and Elevate its respective Pole according to its respective Elevation; so shall all Places cut by the Horizon have the Sun in their Horizon: Those to the Eastwards shall have the Sun Setting; those to the Westward shall have it Rising in their Horizon: those at the Intersection of the Meridian and Horizon under the Elevated Pole, have the Sun in their Horizon at lowest, but Rising; those at the Intersection of the Meridian and Horizon under the Depressed Pole, have the Sun in their Horizon at highest, but Setting. Thus in those Countries that are above the Horizon it is Day-light, and in those but 18 degrees below the Horizon, it is Twilight: But in those Countries further below the Horizon it is at that time dark Night: And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial, have the Sun alwaies above the Horizon, till the Sun have less Respective Declination then the Elevated Pole; and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon, till the Sun inclines more towards the Depressed Pole; As you may see by turning about the Globe; for in this position, that portion of the Globe intercepted between the Ele∣vated Pole, and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon: neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole, ascend above the Horizon.

PROB. XLVII.

To find in what different Places of the Earth the Sun hath the same Altitude, at the same time.

FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith, and bring that Place on the

Globe to the Zenith, and on the Meridian [there] screw the Quadrant of Altitude, and turn it about the Horizon, de∣scribing degrees of Almicantars thereby, as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon. Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon; those in the 20^th Almicantar shall have the Sun Elevated 20 degrees above their Horizon; those in the 30^th, 30. degrees &c. So that you may see, when the Sun is in the Zenith of any Place, All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon. But to find in what different Places the Sun hath the same heighth at the same time, as well Before or After Noon, as at Full Noon; and that in Countries that have greater Latitude then the Suns greatest Declination, (and therefore cannot have the Sun in their Zenith,) requires another Operation.

Therefore, Elevate its respective Pole according to your re∣spective Latitude; and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation, and the degree of the Ecliptick the Sun is in represent the Sun: Then bring the Sun to the Meridian, and the Index of the Hour-Circle to 12, and turn the Globe Eastwards, if Before Noon, or Westwards, if After Noon, till the Index point to the Hour of the Day: Then place the lower end of the Quadrant of Altitude to the East point of the Horizon, and move the upper end (by sliding the Nut over the Meridian) till the edge of the Quadrant touch the place of the Sun: Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place, and count the number of remaining degrees on the Meridi∣an, on the contrary side the degree of the Meridian where the up∣per end of the Quadrant of Altitude touches the Meridian, and where that number of degrees ends on the Meridian, in that La∣titude and your Habitations Longitude, hath the Sun the same heighth at the same time.

Example.

May 10. at 53. minutes past 8. a clock in the Morning I

would know in what Place the Sun shall have the same Alti∣tude it shall have at London, London's Latitude found by Prob. 1. is 51½ degrees Northwards: And because the Elevation of the Pole is equal to the Latitude of the Place (as was shewed Prob. 15.) Therefore I Elevate the North Pole 51½ degrees, so shall 51½ degrees on the Meridian be in the Zenith: This 51½ degrees on the Meridian represents London. The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian, and the Hour Index to 12. on the Hour Circle: Then I turn the Globe Eastwards (because it is before Noon) till the Index point at 8. hours 53 minutes on the Hour-Circle, and place the lower end of the Quadrant of Altitude to the East point in the Horizon, and slide the upper end either North or Southwards on the Meridian till the graduated edge cut the degree of the Ecliptick the Sun is in: Then I examine on the Meridian what degree the up∣per end of the Quadrant of Altitude touches; which in this example, I find is 38½ degrees. Therefore I substract 38½ from 51½ Londons Latitude, and there remains 13. Then counting on the Meridian 13. degrees backwards, from the Place where the Quadrant of Altitude touched the Meridian, I come to 25½ on the Meridian, Northwards. Therefore I say, In the North Latitude of 25½ degrees, and in the Longitude of Lon∣don (which is in Africa, in the Kingdom of Numidia) the Sun May 10. at 53. minutes past 8. a clock in the Morning hath the same Altitude above the Horizon it hath here at London.

The Quadrant of Altitude thus applyed to the East point of the Horizon makes right angles with all points on the Meridian, even as all the Meridians proceeding from the Pole, do with the Equator: therefore the Quadrant being applyed both to the East point, and the Suns Place, projects a line to intersect the Me∣ridian Perpendicularly in equal degrees; from which intersection the Sun hath at the same time equal Heighth, be the degrees few or many; for those 5. degrees to the Northwards of this in∣tersection, have the Sun in the same heighth that they 5 degrees to the Southwards have it: and those 10, 20, 30. degrees, more, or less, to the Northwards, have the Sun in the same heighth that they have that are 10, 20. 30. degrees more or less to the Southwards: So that this Prob. may be performed ano∣ther way more easily, with your Compasses, Thus: Having first rectified the Globe, and Hour Index, Turn about the Globe till

the Hour Index point to the Hour of the Day; Then pitch one foot of your Compasses in the Suns Place, and extend the other to the degree of Latitude on the Meridian, which in this exam∣ple is 51½ degrees North; then keeping the first foot of your Compasses on the degree of the Sun, turn about the other foot to the Meridian, and it will fall upon 25½. as before.

Blaew commenting upon this Probleme, takes notice how grosly they ere that think they can find the heighth of the Pole at any Hour of the Day, by the Suns height: because they do not consider that it is impossible to find the Hour of the Day, unless they first know the height of the Pole.

PROB. XLVIII.

To find the length of the Longest and Shortest Artificial Day or Night.

THe Artificial Day is that space of Time which the Sun is above the Horizon of any Place: and the Artifici∣al Night is that space of Time which the Sun is under the Horizon of any Place. They are measured in the Hour Circle, by Hours and Minutes.

There is a constant unequallity of proportion in the Length of these Daies and Nights; which is caused both by the alteration of the Suns Declination, and the difference of the Poles Elevation.

Those that inhabite on the North side the Equator have their longest Day when the Sun enters ♋; and those that inhabite on the South side the Equator, have their longest Day when the Sun enters ♑. But to know how long the longest Day is in any North or South Elevation, Raise the North or South Pole ac∣cording to the Elevation of the Place, and bring ♋ for North Elevation, or ♑ for South Elevation to the Meridian, and the Index of the Hour Circle to 12. Then turn the Globe about till ♋ for North Elevation, or ♑ for South Elevation, come to the West side the Horizon and the number of Hours and mi∣nutes pointed at on the Hour Circle, doubled, is the number of Hours and minutes of the Longest Day.

The length of the Night to that Day is found by substracting the length of the day from 24. for the remainder is the length of the Night.

The shortest Day in that Latitude is the length of the shortest Night, found as before. And the longest Night is of the same length with the longest Day.

Example.

I would know the length of the longest Day at London. There∣fore I Elevate the North Pole 51½ degrees, and bring ♋ to the Meridian, and the Index of the Hour Circle to 12. Then I turn ♋ to the Western side the Horizon, and find the Index point at 8. hours 18. minutes, which being doubled makes 16. hours 36. minutes, for the length of the longest Day here at London.

PROB. XLIX.

To find how much the Pole is Raised, or Depressed, where the longest Day is an Hour longer or shorter then it is in your Habitation.

REctifie the Globe to the Latitude of your Place; and make a prick at that point of the Tropick which is at the Meri∣dian; I mean at the Tropick of ♋, if your Habitation be on the North side the Equator; or ♑, if your Habitation be on the South side the Equator: And if you would know where the longest Day is just an hour longer then it is at your Habitation, turn the Globe to the Westward till 7½ degrees of the Equato•• pass through the Meridian, and make there another prick on the Tropick: Then turn about the Globe till the first prick come to the Horizon; and move the Meridian through the notches of the Horizon till the second prick on the Tropick come to the Ho∣rizon; so shall the arch of the Meridian contained between the Elevation of your Place, and the Degree of the Meridian at the Horizon, be the number of Degrees that the Pole is Elevated higher then it is in your Latitude.

Example.

I would know in what Latitude the longest Day is an Hour longer then it is at London. Therefore I Rectifie the Globe to 51½ deg. and where the Meridian cuts the Tropick of ♋ I make

a prick; then I note what degree of the Equator is at the Meri∣dian, and from that degree on the Equator count 7½ degrees to the Eastwards, and bring those 7½ degrees to the Meridian also; and again where the Meridian cuts the Tropick of ♋ I make ano∣ther prick, so shall 7½ degrees of the Tropick be contained be∣tween those 〈◊〉〈◊〉 pricks. Then I turn the Globe about, till the first prick comes to the Horizon, and (with a Quill thrust be∣tween the Meridian and the Ball) I fasten the Globe in this posi∣tion: Afterwards I move the Meridian through the 〈◊〉〈◊〉 of the Horizon, till the second prick rises up to the Horizon, and then I find 56½ degrees of the Meridian cut by the Superficies of the Horizon: Therefore I say, In the Latitude of 56½ de∣grees, the longest Day is an Hour longer then it is here at Lon∣don.

But if you would know in what Latitude the Dayes are an Hour shorter, you must make your second prick 7½ degrees to the Westwards of the first, and after you have brought the first prick to the Horizon, you must depress the Pole till the se∣cond prick descends to the Horizon: so shall the degree of the Meridian at the Horizon, shew in what Elevation of the Pole the Daies shall be an Hour shorter.

By this Probleme may be found the Alteration of Climates: for (as was said in the Definition of Climates, Book 1. fol. 28.) Climates alter according to the half-hourly increasing of the Longest Day: therefore the Latitude of 56½ degrees having its Daies increased an whole Hour) is distant from the Latitude of London by the space of two Climates.

PROB. L.

The Suns Place given, to find what alteration of Declina∣tion be must have to make the Day an Hour longer, or shorter: And in what number of Da••es it will be.

REctifie the Globe to the Latitude of the Place, and b••ing the Suns place to the East side the Horizon, and note against what degree of the Horizon it is: then bring one of the Colures to intersect the Horizon in that degree of the Horizon, and at the point of Intersection make a prick in the Colure; and observe what degree of the Equator is then at the Meridian: Then turn the Globe Westward, if the Daies shorten; but Eastwards, if

they lengthen, till 7½ degrees of the Equator pass through the Meridian, and where the Horizon intersects the same Colure, make another prick in the Colure: Afterwards bring the Colure to the Meridian, and count the number of degrees between the two pricks, for so many degrees must the Suns Declination alter to lengthen or shorten the Day an Hour.

Example.

The Suns Place is ♉ 10. I would know how much he must alter his Declination before the Day is an Hour longer here at London. Therefore I rectifie the Globe to the Latitude of London, and bring ♉ 10. to the East side the Horizon, and find it against 24½ degrees from the East point: therefore I bring one of the Colures to this 24½ degrees, and close by the edge of the Horizon I make a prick with black lead, in the Colure: then keeping the Globe in this position, I look what degree of the E∣quator is then at the Meridian, and find 250¼, and because the Daies lengthen, I turn the Globe Eastwards, till 7½ degrees from the foresaid 250¼ pass through the Meridian: then keeping the Globe in this position I make another prick in the Colure, and bringing this Colure to the Meridian, I find a little more then 5 degrees of the Meridian contained between the two pricks: therefore I say, when the Sun is in ♉ 10. degrees, he must alter his Declination a little more then 5 degrees, to make the Day an Hour longer.

Now to know in what number of Daies he shall alter this Declination, you must find the Declination of the two pricks on the Colure as you found the Suns Declination by Prob. 5. and the Arch of the Ecliptick that passes through the Meridian while the Globe is turned from the first pricks Declination to the second pricks Declination, is the number of Ecliptical de∣grees that the Sun is to pass while he alters this Declination: and the degree of the Ecliptick then at the Meridian is (with respect had to the Quarter of the Year) the place the Sun shall have when its Declination shall be altered so much as to make the Day an Hour longer

Thushaving the Suns first place given, and its second place found▪ you may by finding those two places on the Plain of the Horizon, also find the number of Daies comprehended between them, as you are taught by the fourth Probleme.

This Probleme thus wrought for different Times of the Year, will shew the falacy of that Vulgar Rule which makes the Day to be lengthned or shortned an Hour in every Fifteen Daies: when as the lengthning or shortning of Daies keeps no such equality of proportion: for when the Sun is neer the Equinoctial points the Daies lengthen or shorten very fast: but when he is neer the Tropical points, very slowly.

PROB. LI.

Of the Difference of Civil and Natural Daies, commonly called the Equation of Civil Daies. And how it may be found by the Globe.

THe Civil Day is that space of Time containing just 24. Hours, reckoned from 12 a clock on one Day to 12 a clock the next Day; in which space of Time the E∣quinoctial makes upon the Poles of the World a Di∣urnal Revolution. The Natural Day is that space of Time wherein the Sun moveth from the Meridian of any Place to the same Meridian again. These Daies are at one time of the Year longer then at another; and at all Times longer then the Civil Daies. There is but smal discrepancy between them, yet some there is, made by a two-fold Cause. For first, The Suns Appa∣rent motion is different from his true motion; He being much slower in his Apogeum then he is in his Perigeum: For when the Sun is in his Apogeum he scarce moves 58 minutes from West to East in a Civil Day, but when he is in his Perigeum he moves above 61 minutes in a Civil Day: and therefore increases his Right Ascension more in equal Time.

The second Cause is the difference of Right Ascensions answe∣rable to equal parts of the Ecliptick: for about ♋ and ♑ the diffe∣rences of Right Ascensions are far greater then about ♈ and ♎: for about ♈ and ♎ the Right Ascension of 10. degrees is but 9. degrees 11. minutes; but about ♋ and ♑ the Right Ascension of 10 degrees will be found to be 10. degrees 53. minutes, as by the Globe will appear.

But because of the smalness of the Globes graduation▪ you can∣not actually distinguish to parts neer enough for the solution of this Probleme, if you should enquire the difference in length of two single Daies; it will be requisite to take some number of

Daies together; Suppose 20. Therefore find by Prob. 3. the Places of the Sun for the beginning and ending of those Daies you would compare; and find the Right Ascensions answerable to each place in the Ecliptick; and also the differences of Right Ascensions answerable to the Suns motion in each number of Daies: Then compare the differences of Right Ascensions toge∣ther; and by substracting the lesser from the greater, you will have the number of degrees and minutes of the Equator that have passed through the Meridian more in one number of Daies then in the other number of Daies: which degrees of the Equa∣tor converted into Time, is the number of minutes that the one number of Daies is longer then the other number of Daies.

Example.

I would know what difference of Time there is in the length of the first 20. Daies of December, and the first 20, Daies of March. I find by Prob. 3. the Suns place December 1, is 〈◊〉〈◊〉 19. 45. at the end of 20 Daies. viz. on the 21 Day his place is 〈◊〉〈◊〉 10. 11. The Suns place March 1. is ♓ 21. 16. at the 20. Daies end, viz. March 21, his place is ♈ 11. 3.

I find by Prob. 26. the Right Ascension answerable to	♐ 19. 45	is	258. 10.
♑ 10. 11	280. 25.
♓ 21. 16	352. 00.
♈ 11. 3	9. 40.

and the difference of Right Ascensions contained between the first Day in each Moneth, and the 21 of the same Moneth, by substracting the lesser from the greater is for

258. 10.	And for	352. 00.
280. 25.	9. 40.
22. 15	17. 40.

But note, because the Vernal Colure, where the degrees of Right Ascension begin and end their account, is intercepted is the Arch of the Suns motion from the first to the 21. of March, therefore instead of substracting the lesser number of degrees of Right Ascension from the greater, viz. 9. 40 from 35. 2. I do for finding the difference of the Right Ascensional arch of the Suns motion in those 20 Daies, sustract the foresaid 352 degrees from 360, and the remains is 8. which is the difference of Right As∣cension from ♓ 21, 16. to the Equinoctial Colure: to which 8

adding 9 degrees 40 minutes, the Right Ascension from the E∣quinoctial Colure. to ♈ 11. 3. it makes 17 degrees 40. minutes for the difference of Right Ascensions between ♓ 21, 16. and ♈ 11. 3 Then I find the difference of this Difference of Right Ascension, by substracting the less from the greater, viz. 17. 40. from 22. 15. and the remains is 4. degrees 35. minutes, for the number of degrees and minutes of the Equator that pass through the Meridian in the first 20 Daies in the Moneth of December more then in the first 20 Daies of the Moneth of March: which 4. degrees 35. minutes converted into Time, gives 19. minutes, that is, a quarter of an Hour and 4 minutes that the first 20 Daies of December aforesaid, are longer then the first 20 Daies of March.

PROB. LII.

How to find the Hour of the Night, when the Moon shines on a Sun Dyal, by help of the Globe.

REctifie the Globe, and find by Prob. 54. or an Ephemeris, the Moons place at Noon: Bring it to the Meridian, and the Index of the Hour Circle to 12. and turn about the Globe till the Index of the Hour Circle points to the same Hour the shade of the Moon falls on, on the Sun Dyal. Then by Prob. 3. find the Suns place at Noon, and see how many degrees of Right Ascension are contained between the Suns place and the degree of the Equator at the Meridian, when the Index of the Hour Cir∣cle is brought to the Hour the Moon shines on in the Sun Dyal; for those number of degrees converted into Time, shall be the Time from Noon, or the Hour of the Night. Only note, Respect must be had to the motion of the Moon from West to East, for so swift is her mean motion, that it is accounted to be above 12. degrees in 24. Hours; that is 6 degrees in 12 Hours, 3 degrees in 6 Hours, &c. and this also converted into Time, as aforesaid, you must add proportionably to the Time found from Noon; and the sum shall give you the true Hour of the Night.

Example.

Here at London, I desired to know the Hour of the Night Ja∣nuary 6. this present Year 1658. The Moons place found by

an Ephemeris, or for want of an Ephemeris, by Prob. 54. is in ♊ 21. degree 22, minutes; Therefore I rectified the Globe to Lon∣dons Latitude, and brought ♊ 21. 22. minutes to the Meridian, and the Index of the Hour Circle to 12. then by Prob. 3. I found the Suns place in ♑ 26. degrees 46. minutes, and by Prob. 26. I found his Right Ascension to be 300 degrees; Then I turned about the Globe, till the Index of the Hour Circle pointed at 10 Hours, and at the degree of the Equator at the Meridian I made a prick; then I counted the number of degrees of the Equater contained between the foresaid 300 deg. and this prick and found them 111¼ degrees which converted into Time, by allowing 15 degrees for an Hour, gives 7 hours, 25 minutes, Time from Noon: which if the Moons motion were not to be considered, should be the immediate Hour of the Night: But by the Rule a∣foresaid, the Moons motion from West to East, in 7 hours 25 mi∣nutes is 3 degrees 42 minutes, and this 3 degrees 42 minutes be∣ing converted into Time, is 14 minutes more, which being added to 7 hours 25 minutes: make 7 hours 39 minutes, for the true Hour of the Night.

PROB. LIII.

To find the Dominical Letter, the Prime, Epact, Easter Day, and the rest of the Moveable Feasts, for ever.

THough these Problemes cannot be performed by the Globe, because of the several changes, and irregular accounts that their Rules are framed upon, yet because they are of frequent and Vulgar use, and for that the so∣lution of many other Questions will have dependency on the knowledge these; Therefore I have thought fit here to inserte this Table of M^r Palmers, by which you may find them All.

I shall not insist upon the Reasons of the several changes of Letters, and Numbers, Himself having already very learnedly handled that subject, in his Book of the Catholick Planisphear, Book 1. Chapter 11. (to which I refer you) Neither shall I need to give you any other Instructions for finding what is here proposed, then what himself hath given in his fourth Book, Chap∣ter 66, and part of 67. Therefore take it as he there delivers it.

An Example, shall serve here instead of a Rule. For the Year 1657. I would know all these: wherefore I seek the Year 1657. in the Table of the Suns Cycle, and over against it, I find 14. for the Year of the Cycle of the Sun, and D for the Dominical Letter. And note here, that every Leap-year hath 2 Dominical Letters (as 1660, hath A G) and the first (viz. A) serveth that Year till February 25, and the second (G) for the rest of the Year. And note that these Letters go alwayes backwards when you count forwards (as B A, then G F, &c. not F G, and, then A B) as you may see by the Table.

Then in the Table of the Cycle of the Moon, I have for the Year 1657. the Prime 5. the Epact 25. Those had, I go to the Table for Easter, and seek there in the first rank the Prime 5, and

[illustration]

under it in the middle rank stands E; that is not my Dominical Letter; therefore I seek not backward, but alwayes forward in the middle rank, till I come to my Dominical Letter D. and under it I find in the third rank March 29. upon which Easter day falls this Year 1657. The rest of the moveable Feasts may be had by their distances from Easter, which are alwayes the same. One∣ly for Advent Sunday, remember that the next Sunday after November 26 is Advent Sunday. Read Book 1. 11. and that will sufficiently instruct you with this Example.

To find the Age of the Moon.

Remember first that the Epact begins with March, which must be here accounted the first Moneth: Then if you add to the Epact the number of the Moneth current, and the number of the day of the Moneth current, the sum or the excess above 30, is the Moons age.

Example. January 20. 1656. According to the accompt of the Church of England, (who begin the Year with March 25. which was the Equinoctial day about Christ time) the Epact is 14. January is the 11^th Moneth, and the 20^th day is proposed; now add 14. 11. and 20. together, they make 45. out of which I take 30. and there remains 15, the Moons age.

PROB. LIV.

The Age of the Moon given, to find her place in the Eclip∣tick according to her mean motion.

THis Probleme may be performed exact enough for Com∣mon uses by the Globe, but in regard it only shews the Moons place in the Ecliptick according to her meat motion, it will often fail you some few degrees of her true Place. The work is thus,

First set figures to every twelth degree of the Equinoctial, ac∣counted from the Equinoctial Colure, marking them with 1, 2, 3, 4. &c. to 30 which will end where you began viz. at the E∣quinoctial Colure again: so shall the Equinoctial be divided into 30 equal parts, representing the 30 Dayes of the Moons Age These figures (to distinguish them from the degrees of the Equator) were best be writ with Red Ink.

When you would enquire the Moons Place, Elevate the North Pole 90 degrees, that is, in the Zenith, so shall the Equator ly in the Horizon: Then bring the Equinoctial Colure against the Day of the Moneth in the Horizon, so shall the Moons Age written in Red figures, stand against the Signe and degree in the Horizon that the Moon is in at that Time.

Example.

September 28. 1658. I would know the Moons place in the Ecliptick, she being then 12 Daies old. Therefore I Elevate the North Pole 90 degrees above the Horizon, and turn the Globe about till the Equinoctial Colure come to September 28. in the Circle of Daies on the Horizon; then looking against what Signe and degree of the Ecliptick Circle in the Horizon the 12^th division in Red figures stands, I find ♓ 9. which is the Signe and degree the Moon is in, according to her mean Motion.

This Probleme may be applyed to many Uses: for, having the Moons Place you may find the Time of her Rising, Southing, Setting, and Shining &c. by working with her, as you were taught to work with the Sun, in several fore-going Problemes, proper to each purpose.

PROB. LV.

Having the Longitude and Latitude, or Right Ascension and Declination of any Planet, or Comet, to place it on the Globe, to correspond with its place in Heaven.

PLanets and Comets cannot be placed on the Globe so as their places will long retain correspondence with their places in Heaven; Because as was said Chap. 44. they have a continual motion from West to East upon the Poles of the Ecliptick: yet never-the-less you may by having their Longitude and Latitude, or Right Ascension and Declinati∣on, for any set Time, place a Mark for them on the Globe, either with Ink if your Globe be Varnisht, for then you may with a wet finger wipe it off again; or with Black-lead, if it be not Var∣nisht, and then you may rub it out again with a little White

Bread: which Mark for that Time, will as effectually serve you to work by, as any of the Fixed Stars placed on the Globe will do.

Therefore if the Longitude and Latitude of any Planet, or Comet, be given; Do thus, Elevate the North Pole, if the La∣titude given be North; but if the Latitude given be South, E∣levate the South Pole 66 ½ degrees; and place the Pole of the Ecliptick in the Zenith, and over it screw the Quadrant of Alti∣tude: so shall the Ecliptickly in the Horizon; and the Qua∣drant of Altitude being turned about the Horizon shall pass through all the Degrees of Longitude: Then find the point of given Longitude in the Ecliptick, and bring it to the Quadrant of Altitude, and hold it there: Then count upwards on the Quadrant of Altitude the number of degrees and minutes of gi∣ven Latitude, and at the point where the number ends, close to the Quadrant of Altitude, make a smal Prick, and that Prick shall represent the Planet or Comet you were to place on the Globe.

If it be the Right Ascension and Declination of a Planet or Comet that is given; you must find the degree and minute of Right Ascension on the Equinoctial, and bring it to the Meridian, and keep the Globe there steddy; then find the degree and mi∣nute of Declination on the Meridian, and under that degree and minute on the Globe make a Prick, and that Prick shall repre∣sent the Planet, or Comet, as aforesaid,

If it be ♄ or ♃ that this Prick is to represent, it may stand on the Globe sometimes a Week or a Fortnight, without much difference from the Planets place in Heaven. But if the Prick were to represent the other Planets, you must (in regard of their swift motion) alter it very often, especially for the Moon; for so swift is her motion, that in every two Hours she alters about a degree in Longitude.

Having thus placed this Mark on the Globe, you may find out the Time of its several Positions, and Aspects, if you work by it as you are directed to work by the Sun, in the several re∣spective Problemes throughout this Book.

The End of the Second Book.

Notes

• * 1.1

  An Hour defi∣ned.
• * 1.2

  Minutes, Se∣conds, and Thirds, &c. defined.