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 Third BOOK, Being the Practical Use of the GLOBES. Applyed to the Solution of Problemes In the Art of NAVIGATION. (Book 3)

PRAEFACE.

BEcause the Art of Navigation consists aswell in the knowledge of Astronomical and Geographical Problemes, as in Problemes meerly Nautical; Therefore I must desire the Artist to seek in the last Book such Problemes as are only Astronomical or Geographi∣cal. For my Designe is here to collect such Problemes as are only used in the Art of Navigation, some few particulars ex∣cepted, as for finding Latitude, Longitude, Course; Di∣stance, &c. Which though they are handled in than Book, yet for their exceeding Vtility in the Art of Navigation, and for that what there is given, cannot alwayes be had to work by; therefore in this Book I have mentioned divers other Observations, which being made or had, you may by the Rules proper for each Observation find what shall be pro∣posed.

PROB. I.

The Suns Amplitude and Difference of Ascension gi∣ven, to find the Heigth of the Pole, and Declination of the Sun.

ELevate the Pole so many degrees as the Difference of the Suns Ascension is, and screw the Quadrant of Altitude to the Zenith, and bring the first point of ♈ to the Me∣ridian, then number on the Quadrant of Altitude up∣wards the complement to 90. of the Suns Amplitude, and move the Quadrant of Altitude till that number of degrees cuts the E∣quator; So shall the Quadrant cut in the Horizon the degree of the Pole Elevation; and in the Equator the degree of the Suns Declination.

Example.

The difference of Ascension is 27. degrees 7. minutes. There∣fore I Elevate the Pole 27. degrees 7. minutes above the Hori∣zon, and screw the Quadrant of Altitude to 27. degrees 7. mi∣nutes, which is in the Zenith: then I bring the first point of ♈ to the Meridian, and number on the Quadrant of Altitude up∣wards 56. degrees 40. minutes, the Complement of the Suns Amplitude, and bring that degree to the Equator; then I see in what degree of the Horizon the Quadrant cuts the Horizon, and find 51 ½, which is the Elevation of the Pole: then looking in what degree of the Equator the Quadrant of Altitude cuts the Equator, I find 20 degrees, 5 min. which is the Declination of the Sun at the same Time.

PROB. II.

The Suns Declination and Amplitude given, to find the Poles Elevation.

ELevate the Pole so many degrees as the Complement of the Suns Amplitude is; and screw the Quadrant of Altitude

in the Zenith, and bring the first point of ♈ to the Meridian: Then count on the Quadrant of Altitude to the Degree of the Suns Declination, and bring that degree to the Equinoctial; and the degree of the Equinoctial cut by that degree of the Quadrant of Altitude, is the degree of the Poles Elevation.

Example.

The Suns Amplitude is 33. degrees 20. minutes, his Decli∣nation is 20 degrees 5 minutes, his Complement of Amplitude to 90. is 56 degrees 7 minutes. Therefore I Elevate the Pole 56. degrees 7 minutes above the Horizon, and screw the Quadrant of Altitude to 56 degrees 7 minutes which is in the Zenith: Then I bring the first point of ♈ to the Meridian, and number on the Quadrant of Altitude upwards 20. deg. 5 min. for the Suns Declination, this 20^th degree 5 minutes, I bring to the Equi∣noctial, and find it cut there 51 ½. degrees, for the Heigth of the Pole.

PROB. III.

The Suns Declination and Hour at East given, to find the Heigth of the Pole.

ELevate the Pole so many degrees as the Suns Declination is, and screw the Quadrant of Altitude in the Zenith: Then convert the Hours or minutes past 6. given into degrees; by allowing 15 degrees for every Hour of Time, and for every minute of Time 15 minutes of a Degree; and number those degrees or minutes in the Horizon from the East Southwards; so shall the Degree of the Quadrant of Alti∣tude cut by the Equator be the Complement of the heigth of the Pole.

Example.

The Suns Declination is 20 deg. 5 min. Therefore I Elevate the Pole 20 degrees 5 minutes, and also screw the Quadrant of Altitude to ••0 degrees 5 minutes which is in the Zenith: the Hour the Sun comes to be at East is 8 a clock 53 minutes, that is, 1 Hour 7 minutes after 6. Therefore I convert 1 Hour 7 mi∣nutes

into Degrees, as before, and it gives 16 degrees 50 mi∣nutes; which number of degrees and minutes I count from the East point Southwards, and thither I bring the Quadrant of Al∣titude: Then I look in what degree of the Quadrant of Alti∣tude, the Equator cuts, and find 38 ½, which is the Complement of the Poles Heigth, viz. 51 ½ degrees for the Heigth of the Pole.

In this Probleme the Declination of the Sun and Elevation of the Pole bears the same Denomination of either North or South, for when the Declination and the Elevation are different the Sun cannot come to the East point.

PROB. IIII.

The Declination of the Sun and his Altitude at East gi∣ven, to find the Heigth of the Pole.

ELevate the Pole to the Complement of the Suns Altitude, and screw the Quadrant of Altitude to the Zenith: Then bring the Equinoctial point ♈ to the Meridian, and number on the Quadrant of Altitude the degrees of the Suns Declination, and bring that degree to the Equinoctial, and note the degree it cuts; for its Complement to 90 is the Heigth of the Pole.

Example.

May 10. The Suns Declination is 20 degrees 5 minutes; His Altitude at East is 25 degrees 55 minutes here at London: I en∣quire the Heigth of the Pole. Therefore I substract 20. 5 min. from ••0 the remains is 69 deg. 55 min. for its Complement; wherefore I bring 69 deg. 55 min. of the Meridian to the Horizon; and to 69 deg. 55 min. which is in the Zenith, I screw the Quadrant of Alti∣tude then I bring ♈ to the Meridian, and count on the Quadran: of Altitude upwards 20 deg. 5 min, and move it about the Equi∣noctial till those 20 deg. 5 min. touch the Equinoctial, which I find to be in 38 ½ degrees, Therefore I substract those 38 ½ from 90, and the remains is 51 ½ degrees, Therefore I say the Pole here at London is Elevated 51 ½ degrees.

The Declination and the Elevation is alwaies the same, either North or South, for when they alter their Denomina ions the Sun at East can have no Altitude, neither can it indeed reach the

East point: and therefore in this example, because the Declina∣tion of the Sun is North, it is the North Pole that is Elevated here at London.

To perform the same otherwise, with a pair of Compasses.

Take off with your Compasses from the Equator or Qua∣drant of Altitude the number of degrees of Altitude observed, and place one foot at the beginning of ♈ on the inner edge of the Horizon, and extend the other directly upwards towards the Ze∣nith: Then move the Brazen Meridian through the notches of the Horizon till the other point of your Compasses (respecting the Zenith) reach the Parallel of the Suns Declination: So shall the number of degrees on the Meridian be the number of degrees that the Pole is Elevated above the Horizon; and is ei∣ther North or South according as the Suns Declination is: as before.

This may yet otherwise be performed with the Quadrant of Altitude, by taking the Nut off the Meridian, and laying the edge of its Index (specified in Chap. 1. Sect. 6. of the first Book) exactly on the East line of the Horizon: for when that lies straight between the point of East on the outer Verge of the Ho∣rizon, and the beginning of ♈ in the inner Verge of the Horizon, then shall the upper end of the Quadrant of Altitude point di∣rectly to the Zenith: and if then you turn the Meridian through the notches of the Horizon till the Suns Altitude on the Qua∣drant of Altitude cut the Parallel of Declination, you will have on the Meridian the heigth of the Pole: as before.

PROB. V.

By the Suns Declination and Azimuth at 6. of the Clock given, to find the Heigth of the Pole, and Almicantar at 6.

ELevate the Pole so many degrees as the Suns Azimuth is at 6. and screw the Quadrant of Altitude in the Zenith, and bring the first point of ♈ to the Meridian: Then number on the Quadrant of Altitude upwards the Complement of the Suns Declination, and bring that degree to the Equator: So shall the

degree of the Horizon cut by the Quadrant of Altitude be the Complement of the Poles Elevation; and the degree of the Equa∣tor cut by the Quadrant of Altitude shall be the Almicantar of the Sun at 6. of the clock.

Example.

The Suns Azimuth at 6 is 12¾ degrees: Therefore I Elevate the Pole 12¾, and screw the Quadrant of Altitude to 12¾ de∣grees which is in the Zenith: Then I bring the first point of ♈ to the Meridian; The Suns Declination is 20 degrees 5 mi∣nutes. Therefore I number on the Quadrant of Altitude 69 deg. 55 min. which is the Complement of 20 deg. 5 min. to 90. this 69 deg. 55 min. on the Quadrant of Altitude I bring to cut the Equator, and find when 69 deg. 55 min, cuts the Equator, that the Quadrant of Altitude cuts the Horizon, in 38½ deg. which is the Complement of the Poles Elevation: and at the same time the Quadrant of Altitude also cuts the Equator in 15½ degrees which is the Almicantar or Altitude of the Sun at 6. a clock.

PROB. VI.

By the Hour of the Night and a known Star Observed Ri∣sing or Setting, to find the Heigth of the Pole.

REctifie the Hour Index, by Prob. 2. of the former Book; and turn the Globe Westwards till the Hour Index points at the Hour of the Night; fasten the Globe there, and turn the Meridian through the notches of the Horizon till the know•• Star come to the East side the Horizon, if the Star be Rising, 〈◊〉〈◊〉 the West if it be Setting; so shall the degrees of the Poles El••∣vation be cut by the Horizon under the Elevated Pole; and 〈◊〉〈◊〉 North or South according as the Elevated Pole of the Globe 〈◊〉〈◊〉

PROB. VII.

Two Places given in the same Latitude, to find 〈◊〉〈◊〉 Difference of Longitude.

BRing the first Place to the Meridian, and note the number of degrees of the Equinoctial that comes to the Meridan

with it; then Bring the other place to the Meridian and note the number of degrees of the Equator that comes to the Meridian with it: and by substracting the lesser number from the greater you have the difference of Longitude, This needs no Example.

PROB. VIII.

Two Places given in the same Longitude, to find the Dif∣ference of Latitude.

BRing the Places to the Meridian, and the degrees of the Meridian over the two Places is the Latitudes of them both, and by substracting the lesser number of degrees from the greater you will have the difference of Latitude.

PROB. IX.

Course and Distance between two Places given, to find their Difference in Longitude and Latitude.

SEek the Rhumb you have failed upon, as in Prob, 34, of the last Book, and upon that Rhumb make a mark for the Place you departed from; then with your Compasses take off from the Equinoctial the number of Leagues you have failed upon that Rhumb, by allowing a degree for every 20. Leagues and place one foot of your Compasses upon that mark, and where the other foot falls on that Rhumb make a second mark; then by bringing the first mark to the Meridian, you will see on the Meridian the Latitude of that mark, and in the Equa∣tor the Longitude as in Prob. 2. of the last Book: and by bringing the second mark also to the Meridian, you will as before, find the Longitude and Latitude of the second mark also. Then by sub∣stracting the lesser Latitude from the greater Latitude, and the lesser Longitude from the greater Longitude, you will have the difference remaining, both of Longitude and Latitude you are a∣rived into.

PROB. X.

To find how many Miles are contained in a Degree of any Parallel.

EVery Degree of the Equinoctial contains 20. English Leagues and every League 3. English Miles: But in e∣very Parallel to the Equinoctial, the Degrees diminish more and more even to the Pole, where they end in a point. Therefore a Degree in any Parallel cannot contain so many Miles as a De∣gree in the Equinoctial. Now that you may know how many Miles are contained in a Degree of any Parallel to the Equi∣noctial. Do thus, Measure with your Compasses the width of any number of Degrees in any given Parallel; suppose (for Exam∣ples sake) 10. Degrees in the Parallel of 51½; Examine in the E∣quator, how many Degrees of the Equator they will make, and you will find 6⅕. Therefore 1. Degree in the Equator making 60 Miles 6. Degrees makes 360, to which add for the 〈◊〉〈◊〉 part 12 Miles, makes ••72 Miles, to be the Measure of 10 Degrees in the Parallel of 51½. So that by dividing 372. by 10. you have ••7 Miles for the length of a Degree, from East to West in the Parallel of 51½ Degrees.

PROB. XI.

The Rhumb you have sailed upon, and the Latitudes you de••arted from, and are arived to, given, to find the Difference of Longitude, and the number of Leagues you have Sailed.

FIrst seek the Rhumb you have sailed on, and pass it through the Meridian till it cuts in the Meridian the La∣titude you departed from; and keeping the Globe there sted••y make a mark close by the Meridian, under that Latitude and in that Rhumb on the Globe, and note in the E∣quinoctial the degree of Longitude at the Meridian: then pass that Rhumb through the Meridian again, till it cuts in the Meridian the Latitude you are arived to; and in that Rhumb and Latitude make on the Globe another mark, and examine in the Equinoctial

the Longitude of the second mark; for the difference between the first and second mark, is the difference of Longitude. Then o∣pen your Compasses to one Degree of the Equinoctial, and by measuring along in the Rhumb count how many times that Di∣stance is contained between the two points in that Rhumb: for so many times 20. Leagues is the Distance you have sailed.

Example.

I sail upon the North West Rhumb from the Latitude of 1••▪ degrees, into the Latitude of 30. degrees 40. minutes. There∣fore I find the North West Rhumb▪ and turn the Globe through the Meridian till this Rhumb cut the Meridian in the first Lati∣tude, viz. in 10. degrees and directly under 10. degrees upon the Rhumb I make a prick, and also find 10 degrees 3 minutes, of the Equator at the Meridian, for the Longitude of the First Place. Then I turn the Globe again through the Meridian, till the same Rhumb cut the Meridian in the second Latitude. viz in 30 degrees 40 minutes, and directly under those 30 degrees 40 minutes upon the same Rhumb, I make another prick, which re∣presents the Place I am arrived to: I examine the Longitude of this prick, as before, and find it 32 degrees 10 minutes. Therefore I substract the first Longitude, viz. 10 degrees 3 mi∣nutes from the second Longitude, viz. 32 degrees 10 minutes, and there remains 22 degrees 7 minutes, for the Difference of Longitude.

Then for examining the Distance I open my Compasses to 1. degree on the Equinoctial and measure upon the Rhumb how oft that Distance is contained between the two pricks, and find 29¼, that is, 29 degrees 15 minutes, which multiplyed by 2••. gives 585, for the number of Leagues failed upon that R••umb.

The reason why I open the Compasses no wider then to 1 de∣gree, is because the Rhumbs being Circular or 〈◊〉〈◊〉 lines the distance on them may be measured more exactly by often count∣ing that 1 degree in them the•• if the 〈◊〉〈◊〉 had bin op••red to many degrees. Thus if the Compasses had been opened wide enough to reach between the two pricks aforesaid. I should not have had above 583 Leagues for the distance between the two Places: neither is there indeed more great Circle distance between them; But I sailed upon a Rhumb, that is, I follow••d

the Course of a Circular winding line, and so fetcht a Compass about to come to these two pricks; and therefore I have in truth sailed 585. Leagues. For the segment of a Rhumb between two Places is alwaies greater then a straight line drawn betwixt them; yea sometimes by half or more in Places neer either Pole.

Note, If you be not very curious in opening your Compasses to this smal distance, you may in oft turning them about upon the Rhumb commit error in your measuring: therefore when you have taken the Distance of one degree, try if you neither gain or loose any thing in measuring 10, or 20. degrees of the Equi∣noctial by them: for then your Compasses are opened to a width exact enough for your purpose.

PROB. XII.

The Longitudes and Latitudes of two Places given, to find Course, and Great Circle distance between them.

FInd on the Globe the Longitudes and Latitudes given, and make pricks to either Longitude and Latitude: If any Rhumb pass from one place to the other, that is (without more a doe) the Rhumb sought. But if no Rhumb pass through; Take the Rhumb that runs most Parallel to the two pricks: for that shall be the Rhumb or the neerest Rhumb that these two pricks Bear on. An Example of this, see in Prob. 34. of the Last Book: And the Great Circle Distance between these two pricks, you may find as by Prob, 33. of the same Book.

PROB. XIII.

The Latitude you departed from, and the Latitude you are arrived to, and the number of Leagues you have sailed given, to find the Rhumb you have sailed on, and diffe∣rence of Longitude.

MAke a prick on the Globe in the Latitude you departed from: then open your Compasses to the number of Leagues you have sailed, by taking for every 20. Leagues 1. degree of the Equator, half a degree for

10 Leagues, a quarter of a Degree for 5 Leagues, and so propor∣tionably for any other number of Leagues: Place one foot of your Compasses in the prick made for the Latitude you departed from, and extend the other towards the Latitude you are arived to, and discribe an occult Arch; Turn the Globe till this occult Arch come to the Latitude on the Meridian, and where the Latitude cuts this occult arch make another prick to represent the Latitude you are arived to; so shall the Rhumb passing through those two pricks (or that is most Parallel to those two pricks) be as in the last Prob. the Course or the Rhumb those two pricks Bears on.

The difference of Longitude you may find as by Prob. 11.

PROB. XIV.

To find by the Globe the Variation of the Needle; com∣monly called the Variation of the Compass.

OBserve by a Compass whose wyer is placed just under the Flower deluce, what point of the Compass the Sun Rises or Sets on, Morning, or Evening: Then exa∣mine by Prob: 10. of the second Book, what degree of the Horizon the Sun Rises or Sets on by the Globe also; and if the Rising or Setting be the same, both on the Globe and Com∣pass, there is no Variation in your Place, But if there be difference between the Rising or Setting by the Compass and the Globe, then is there Variation in your Place.

If the point the Sun Rises upon in the Compass be neerer the North point, then the point the Sun Rises upon by the Globe, the Variation is Westwards.

If the point the Sun Sets upon in the Compass be neerer the North then the point it Sets upon by the Globe, the Variation is Eastwards.

If the point the Sun Sets upon in the Compass be further from the North point, then the point the Sun Sets upon by the Globe, the Variation is Westwards.

If the point the Sun Rises upon in the Compass be further from the North point then the point the Sun Rises upon by the Globe, the Variation is Eastwards. And so many degrees as there is between the point of Rising or Setting found by the Compass, and the point of true Rising or Setting found by the Globe, so

many degrees is the Variation from the North towards the East, or West point.

Otherwise, when the Sun hath Altitude.

Having the Altitude of the Sun; find by Prob. 22. of the second Book, its Azimuth: Then examine by a Compass whe∣ther the true Azimuth found by the Globe, agree with the A∣zimuth found by a Nautical Compass: If they agree there is no Variation: But if the Azimuth of the Compass before Noon be neerer the North then the true Azimuth found by the Globe, the Variation is Westwards.

If the Azimuth by the Compass Afternoon be neerer the North, the Variation is Eastwards.

If the Azimuth by the Compass Afternoon be further from the North, the Variation is Westwards,

If the Azimuth by the Compass before Noon be further from the North, the Variation is Eastwards.

And this Variation shall be as aforesaid so many degrees as there is between the Azimuth Observed by the Compass, and the true Azimuth, Observed by the Globe.

PROB. XV.

To keep a Journal by the Globe.

BY some of these foregoing Problemes you may Dayly (when Observations can be made find both the Longitude and Latitude on the Globe of the Places you are arived to, and also the Way the Ship hath made, and make pricks on the Globe in their proper Places for every Da••••s Journey, so truly and 〈◊〉〈◊〉 naturally that if you kept your reckoning aright you may be sure you cannot miss any thing of the truth it self; and that with less trouble and greater advantage, then keeping a Book of every Daies Reckoning.

PROB. XVI.

To Steer in the Night by the Stars.

REctifie the Globe and Hour Index as by Prob. 2. of the last Book, and turn about the Globe till the Index of the Hour Circle points to the Hour of the Day or Night: Then turn the Globe till the Difference of Longitude between the Place you depart from, and the Place you sail to pass through the Meridian and if any Star in the Latitude of the Place you sail To come to the Meridian, or neer the Meridian with the degree of the difference of Longitude, that Star is at that time in or neer the Zenith of that Place you sail to: and by finding the same Star in Heaven, as by Prob, 44. of the last Book you may direct your ship towards that Star, and fail as confidently (saies M^r Blagrave) as if Mercurie were your Guide. But because this Star moves from the Zenith of this Place you must often examine what Star is come to the Zenith, and so often charge the Star you Steer by, as the length of your Voyage may require.

PROB. XVII.

How to platt on the Globe a New Land, never before Dis∣covered.

THese two following Problemes are 2. Chapters of M^r Wrights, delivered by him as follows.

It may sometimes fall out in new Discoveries, or when your Ship by means of a Tempest is driven out of her right Course, that you shall come to the sight of some Isle, Shoald, or new Land, whereof the Mariner is utterly ignorant: And to make some relation of the same. or to go unto it some o∣ther time, if you desire to set it down on your Globe in the true place, you may do it after this manner: So soon as you have sight thereof, mark it well first with your Compass, observing diligently upon which Point thereof it lieth, And secondly, you must there take the heigth of the Sun, or of the Pole-star, as you were taught Prob. 13. of the second Book, that you may know

in what Point your Ship is, and that point you must call the First Point; which being so done, your Ship may sail on her Course all that day, till the day following, without losing her Way: and the next day mark the Land again, and see upon what Point it li∣eth; and then take your heigth, and with it cast your Point of Traverse once again; and that you may call your second Point. Then take a pair of Compasses, and placing one foot upon the First Point, and the other upon the Rhumb towards which the Land did Bear, when you Cast your First Point: set also one foot of another pair of Compasses in the second Point, and the other foot upon the Rhumb upon which the Land lay when you cast your second Point; and these two Compasses thus opened, you must move by their Rhumbs, till those two feet of both Com∣passes do meet together, which were moved from the foresaid two Points: and where they do so meet together, there may you say is the Land which you Discovered; which Land you may point out with the In lets and Out-lets, or Capes and other Signes, which you saw thereupon. And by the graduation you may see the Latitude thereof; that thereby you may find it, if a any time after you go to seek for it.

PROB. XVIII.

Seeing two known Points or Capes of Land, as you sail 〈◊〉〈◊〉∣long, how to know the distance of your Ship from them▪

PItch one foot of one pair of Compasses upon one of the two foresaid Capes, and the other foot upon the Rhum•• which in this Compass pointeth towards that Cape. 〈◊〉〈◊〉 in like manner shall you do with another pair of Com∣passes, placing one foot thereof upon the other known Cape, 〈◊〉〈◊〉 the other foot upon the Rhumb, which stretcheth towards 〈◊〉〈◊〉 said second Cape; and moving the two Compasses (so opened) by these two Rhumbs off from the Land, the very same Point where the two feet which came from the two Capes do meet, you may affirm to be the very Point where your Ship is. And then measuring by the degrees of the Equinoctial, you may see what distance there is from the said Point to either of the fore∣said Capes, or to any other place, which you think good, for it is a very easie matter, if you know the point where your Ship is,

PROB. XIX.

Of Tides, and how by help of the Globe you may in general judge of them.

DIvide the Equinoctial into 30 equal parts, as was directed in Prob. 54. of the last Book. These 30. equal parts represent the 30. daies of the Moons Age.

Then on the North and South point of the Com∣pass in the outmost Verge of the Horizon, Write with red Ink 12. From the North Eastward, viz. at the Point North and by East, Write 11 ¼. At the next point to that the same way, viz. North North East, Write 10 ½. At the next, viz. North East and by North, Write 9 ¾. And so forward to every point of the Compass; reba∣ting of the last hour ¾ till you come to 12. in the South; where you must begin again to mark that Semi-Circle also in the same order you did the last. In this Circle is then represented the Points of the Compass the Sun and Moon passeth by every Day; and the Figures annexed represent the twice 12. hours of Day and Night.

Having thus prepared your Globe and Horizon, you may by having the Moons Age, and the point of the Compass on which the Moon maketh full Sea at any Place given, find at what Hour of Day or Night it shall be high Tide in the same Place. Thus,

It is a known Rule that a North and South Moon makes high water at Margarate. Therefore Bring the first point of ♈ to the North or South point in the Horizon, and Elevate the North Pole into the Zenith: Then count in the Equinoctial the Daies of the Moons Age numbred in red figures; and the Hour and minutes written in red figures annexed to the names of the Windes) that stands against the Moons Age shall be the Hour of High Tide on that Day or Night at Margarate.

The End of the Third Book,