The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

THE AUTHOR TO HIS Fourth Book.

MY New-rigg'd Ship, Strike now thy Sails, Let slip thine Anchor, the Wind fails; And Sea-men oft in Calms do fear That foul and boist'rous Weather's near. If a robustious Storm should rise, And bluster from censorious Eyes; Although the swelling Waves be rough, And proud, thy Harbour's safe enough. Rest, rest a while, till Ebbing Tides Shall make thee stanch, and breme thy Sides: When VVinds shall serve, hoise up thy Sail, And fly before a Prosp'rous Gale; That all the Coasters may resort, And bid thee Welcome to thy PORT.

THE Compleat Sea-Artist; OR THE ART OF NAVIGATION. The Fourth Book. CHAP. I. Of Sailing by the Plain Chard, and the Ʋncertainties thereof; And of Navigation.

THE Art of Navigation, is a Knowledge by certain Rules for to Steer a Ship through the Sea, from the one Place to the other; and may not improperly be divided into two parts, namely, the Common, and also the Great Navigation.

The Common Navigation requireth the Use of no Instru∣ments but the Compass and Sounding-Lead, as chiefly consist∣ing in Practice and Experience, in Knowledge of Lands and Points, how they lie in Distance and Course one from the other, and how they are known at Sea, in knowledge of Depths and Shoulds and varieties of Grounds, the Course and Setting of Tides, upon what Point of the Compass the Moon maketh High-water in each several place, and the like; which must be reckoned partly by the Information of skilful Pilots, but far better by a Man's own Practice and Experience.

The Great Navigation useth, besides the foresaid Common Practice, divers other Artificial Instruments and Rules, which they must take out of Astronomy and Cosmo∣graphy. It is therefore needful, that every Pilot and Officer, that takes charge of any Ship or Vessel in the Practice of the Great Navigation, be first and chiefly well in∣structed in the principal Points of the foresaid Arts; that is, that he know the Order and understand the Division of the Sphere of the World, and the Motions of the Heavens, especially the Eighth, Fourth, and First; Together with the contriving or Making and Use of Instruments, as I have shewn briefly in the Second Book. Know this, Without this Knowledge it is impossible to perform great Voyages (not before at∣tempted) over the Sea. In regard such Knowledge may be attained to, by good In∣struction, we have set forth the same in this Treatise, for the benefit of all such young

Sea-faring Men, as are desirous to be Sea-Artists or Navigators, so clearly and plainly as the brevity of the same could suffer to be done.

The Defects and Imperfections of this Art are many; partly in the Skill or Theo∣rick, partly in the Practick.

After a long Voyage, the Ship supposed to be near the Shore, the Commander or Master requires from their Mates an Account of their Judgement how the Land or Cape bears from them, the Course and Distance of it when they see it: He that comes nearest the Shore, is supposed to have kept the best Reckoning. I have known some that have not been scarce able to number and make five Figures, have gone neerest the Shore than the best Artist in the Ship; but they have been wonderfully mistaken, to my knowledge, in other Voyages. I went a Voyage to Barbadoes in the Rainbow, and took our Reckoning from Lundy, in the Mouth of Severn; and in the Ship were 12 Practitioners and Keepers of Account; eleven of them kept it by the Plain Chart, and my self made use of Mercator and Mr. Wright's Projection. When we came in the Latitude (which was 400 Leagues from the Shore) every Man was ready to give his best Judgement of his Distance off the Shore: But they all fell wonderfully short of the truth; for he that should have had the best Reckoning, was 300 Leagues short, and most of all the rest was 268 and 250 Leagues; and he that was account∣ed an excellent Artist aboard the Ship, was 240. But by the Reckoning kept by Mercator's Chart, which wanted but three Leagues short of the Island. In the same Ship, going from thence to Virginia, they also fell short, by the same way of Account by the Plain Chart, 90 Leagues the nearest; and those that were advised to keep it by Mercator, found it come but 4 or 5 Leagues short of the Cape of Virginia: But coming from thence home, they got their Credit mended; they came all within 30, 20, and 10 Leagues of the Shore.

So I say, If the Course and Distance had been first agreed upon from the Place they were bound to, to be just the same, unto the Cape or Land they first descried; If men differ then, there is something in that, in respect of the uncertainty of the Longitude: A bad Reckoning may prove better than a good.

But we find that there is near 180 Leagues difference Error, between the Meridian of Barbadoes and Lundy, and much more in the Distance; and in some Charts about 620 Leagues Errour, in the Distance between Cape Fortuna, the South Cape of Anian Fretum, to Cape Hondo by the River Depiscadores; and these Errors may be ascribed partly to the uncertainty of the Longitude, and partly unto the Plain Chart, and Sailing by it, which makes some Places nearer than they are, and other Places far more distant than they are, and scituated much out of their true Course or Rhomb.

Secondly, Men many times commit great Errors in bad Steerage, and careless look∣ing to the Compass; for I have known many Seamen when their trike or turn have been out, and the Log hove, they have told the Master or his Mate, they have Steered ½ a Point a Weather the Course; besides, the Points of the Needle or Wyres being touched by the Load-stone, are subject to be drawn aside by the Guns in the Steerage, or any Iron neer it, and liable to Variation, and doth not shew the true North and South, which ought continually to be observed by a good Meridian, or as some call it an Azimuth-Compass, which is the proper Name. Such a one you have described, by which I Survey Land with, as is shewn in the following Treatise; so the Variation ought to be carefully allowed.

* 1.1Besides, on Land there is great difference in the same Country and Places, as Dial∣lists well know, by taking often the Declination of several Walls; as also Mr. Gunter's Observations at Limehouse, for the finding of the Variation, found it ½ a Degree more, and other Places of the same Ground less; and Moetius saith, he hath found a De∣gree or two difference. This difference at Land must needs shew the uncertainty we have at Sea. Besides, many times the Ship is carried away by unknown Currents, which when they be discovered by their Ripplings, as also some by reason of Trade-Winds, we set them in our Journal; as also if we meet with any Soundings, as there is in divers Places 100 Leagues off the Land or Islands, to my knowledge, I would advise all Learners to be careful to put down all such remarkable things as neer as he can, their Latitude and Longitude. So I believe did Moetius, to remember the Current that set between Brasilia and Angola, in the opposite Coasts of Africa, where he in∣stanceth,

That an able Master bound to St. Helen's, in 16 Degrees of South-Latitude, in the mid-way betwixt both Coasts, and being in the Parallel of Latitude thereof, steered East, was notwithstanding carried by the unknown Motion of an unknown Current 800 Miles Westward, and yet stemmed the Current with a fair Wind, and at last made the Coasts of Brasilia.

From the 10 of April to the 15 of July, the Current sets near North-West. From the 15 of July to the 12 of October, there is no Current perceivable. From the 12 of October to the 13 of January, it sets South-West; And from the 13 of January to the 12 of April, it seems to have no Motion perceivable. Again,

Currents is a means of great mistake in keeping of a Reckoning; for Captain Luke Fox in his North-West Discoveries, and the rest, complained fearfully of the fast Lands of Ice upon those Coasts, that so alters the Current, that in some Places they cannot make good their Course they steer upon, by three Points; especially in Davis his Streights, where steering East-by-South, they scarce could make good South-East-by-South, which is four Points of the Compass, and the Error at least 70 Leagues.

I have also perceived a good Current to set to the Eastward, E. S. E. about the Western Islands, and the Madera's, in several Voyages I have made to the West-Indies; but more especially I have observed it in my last Voyage to Barbadoes. I went out of England in Company with Captain Jeremy Blackman, in the Eagle bound to the East-Indies, and a Dutch Ship in his Company, and one of Plymouth for the Isle of May: So we kept company together as far as the Madera's, but intended never to see it that Voyage; for we reckoned our selves 25 Leagues, and some more, to the West∣ward of the Meridian of the Maderas: But being in the Latitude near about we had espied the Land; and being becalmed, drove with the Current by the Eastern end of the Island, betwixt Porto Sancto, and the Desarts or Rocks that lie off from that end. I compared Reckoning with most aboard each Ship that kept Account, and found some 30 Leagues to the Westward of the Island; and thereby in five Voyages made before that way, knew by Experience there is a Current sets strongly near about it E. S. E. Besides, several Ships of London and the West-Country have mist it, after much labour and trouble to find it. Snellius instanceth, That one of good repute, sailing out of Holland twice, mist it and came home. I shall not here trouble you with more Instances, nor multiply needless Questions, nor strive to branch them out in their several Varieties; but give you those which are most useful and necessary: And then if my time will permit, I will shew you some Arts which will as much delight you to learn, and this as briefly as I can.

As for the first and most useful Questions in Navigation, is this;* 1.2 By the know∣ledge of the Rhomb or Course you sailed upon, and the distance of Miles or Leagues that you sailed thereon, to know your difference of Latitude and Longitude (that is, how much you are Northerly or Southerly in respect of Latitude, or Easterly or Wester∣ly in respect of Longitude.) This is the most ordinary manner of keeping of Account by most Masters and Mates, of the Ships Way, which is called the Dead Reckoning. And to keep this Account, first you see, That the knowledge of the Rhomb they sail∣ed is always supposed to be had of the Log-board, supposing the Compass by which we steer, either doth or should shew the same exactly; and so you have the Distan∣ces in Miles and Leagues, put down every half Watch upon the Log-board, with the Course sailed, and Winds By or Large: Therefore we will come to the first Que∣stion, and Resolve it by the Traverse-Table following, and also by the Traverse-Scale in the Fifth Chapter of the Second Book. I have shewed by the Sinical Quadrant alrea∣dy, in the Sixth Chapter of the Second Book: And we will resolve it also by the Arti∣ficial Sines and Tangents on the Ruler, and the Tables.

But know this, I never knew any Course steered at Sea, nearer than to half a Point; for there is no Halfs nor Quarters marked on the Compass.

The First Proposition. Questions of Sailing by the Plain, Ordinary Sea-Chart.

I. Sailing 57 Leagues upon the first Rhomb, How much shall I alter my Parallel of Latitude?

THe Angle that any Point makes with the Meridian, we call the Rhomb; but the Angle that it makes with any Parallel, is called the Complement of the Rhomb. Unto every Point of the Compass there answers 11 deg. 15 min. therefore the fifth Rhomb from the Meridian makes Angles therewith of 56 deg. 15 min. namely, S. W. b. W. S. E. b. E. N. W. b. W. N. E. b. E. whose Complement 33 deg. 45 min. is the Angle of the same Rhomb with every Parallel.

Now admit I sail from A to D, S. W. b. W. 57 Leagues, I demand the difference of Latitude EA.

[illustration] geometrical diagram

First, by the following Traverse-Table, at the Head of the Table, over every Co∣lumn, is put the Figure of Halfs, Quarters, and whole Rhombs; and in one of the Columns over head is N. S. and at the foot E. W. and so is numbred at the Head, from the left hand to the right. N. S. stands for Northing. Then the Rhombs are reckon∣ed at the bottom, from the right hand back again; The Margent of the Tables shews the Leagues sailed; and over E. W. or under E. W. shews how much you have sailed East or West from the Meridi∣an. N. S. shews North or South from the Latitude. As in this Example, The di∣stance sailed is 57 Leagues on the fifth Rhomb; therefore under

3 Rhomb.
N S	W E
47 39	31 67
E W	N S
5 Rhomb.

Distance Sailed, in the Side, I enter with 57 Leagues, and in the Common Angle or Line of Meeting, I find 31. 67/100 over N. S. in the Foot; and in the next Column, over E. W. is 47. 39, as you see in the Table in the Side: So that the Difference of Lati∣tude is 31 Leagues and 67/100 Parts of a League. And if it were required to find the Departure, you see it to be 47 Leagues and 39/100 Parts. This is very plain and easie, you need no farther Precept.

By the Traverse-Scale.

EXtend the Compasses in the Line of Numbers from 100 to 57, the same Distance will reach from 5 Points to 31, and about 7/10 in the Line of Numbers.

By the Artificial Sines and Numbers on the Ruler.

EXtend the Compasses from 100 in the Line of Numbers, to 57, as before; the same Distance will reach from the Sine-Complement of the Rhomb, to the Diffe∣rence of Latitude, which is the same way as by the Traverse-Scale.

By the Tables of Artificial Sines and Numbers, by the Fourth Case of Plain Triangles.

As the Radius, which is the Sine of 90 deg. or Angle at E	1000000
Is to the Distance run 57 Leagues AD	175587
So is the Sine Complement of the Rhomb at D 33 deg. 45 min.	974473
To the Difference of Latitude required AE 31 Leag. 7/••••	150060

In like manner you may find the Difference of Latitude for any Distance run upon any Point of the Compass: But remember to add the second and third Numbers together, and from it to substract the first or uppermost.

II. Sailing 57 Leagues upon the first Rhomb, How far am I de∣parted from the Meridian of the Place from whence I came?

By the Traverse-Table.

THis Question was answered in the last Example, and found over E. W. to be 47 Leagues and 39/100, as you may see in the small Table in the foregoing Side. In the like manner you may find the Difference of Latitude and departure from the Me∣ridian, for any Distance run upon any Point of the Compass, which is the Use of that Table.

By the Traverse-Scale.

EXtend the Compasses from 100 in the Line of Numbers, to the Distance run 57 Leagues; so is the Sine of the Rhomb; that is, put one Point of the Compass on 5 Points, in the Line of East and West of the Scale, and the other will reach to the Departure from the Meridian 47 Leagues 39/100 Parts.

By the Tables of Sines and Numbers, by the Fourth Case of Plain Triangles.

As the Radius or Sine of 90. deg. at E	1000000
Is to the Distance run 57 Leagues AD	175587
So is the Sine of the Rhomb 56 deg. 15 min. A	991084
To the Departure from the Meridian to 47 39/100 ED	166671

By the Artificial Lines on the Ruler.

EXtend the Compasses from 90 deg. to 57; the same Distance will reach from 56 deg. 15 min. to 47 39/100 Leagues.

Or, Extend the Compasses from 90, to 56 deg. 15 min. the same Distance will reach from 57 Leagues, to 47 39/100, as before.

III. Sailing upon the fifth Rhomb, until I alter my Latitude 1 deg. 35 min. I demand how far I have Sailed?

AS sailing from A to C, S. W. b. W. till the Difference of Latitude be 31 Leagues 67/100, I demand the Distance run AC.

[illustration] geometrical diagram

First, By the Traverse-Table, Look in the Foot of the Table for the fifth Rhomb, and over N. S. in that Column, look for 31 Leagues 67/100, and in the Common Angle of Meeting, to the left hand, under Distance Sailed, you will find Distance Sailed 57 Leagues AC required.

By the Line of Sines and Numbers.

EXtend the Compasses from the Complement-Sine 33 deg. 45, to 31 67/100 the Diffe∣rence of Latitude; the same Extent will reach from 90 deg. to 57 Leagues.

Or, Extend the Compasses from 33 deg. 45 min. to 90; the same Distance will reach from 31 67/100 Leagues, to 57 Leagues, the Distance AC, as before.

Say by the second Case in Plain Triangles,

As the Sine-Complement of the Rhomb, 33 deg. 45	9,744739
Is to the Difference of Latitude 31 67/100 Leagues	3500648
So is the Sine of 90 deg. Radius	10000000
To the Distance run AC 57 67/100 Leagues	3755909

IV. Sailing upon the fifth Rhomb, until I have altered my Latitude 31 67/100, or 1 deg. 35 min. How much am I departed from my first Meridian?

AS sailing from A to C, S. W. b. W. till the Difference of Latitude AB be 31 67/100 Leagues, I require BC my departure from my Meridian.

By the Traverse-Table.

AS in the last Case, find 31 67/100 Leagues over the fifth Rhomb, in the Foot, and in the next Column to the left hand, over E. W. is 47 39/100 Leagues, the Departure required.

By the Line of Sines and Numbers.

EXtend the Compasses from the Complement-Sine of the Rhomb, to 33 deg. 45, to 31 67/100 Leagues; the same Distance will reach from 56 deg. 15 min. the Sine of the Rhomb, to 47 39/100 Leagues, the Departure from the Meridian.

By the fourth Case of Plain Triangles.

As the Sine of 90 deg.	10000000
To the Difference of Latitude AB 31 67/100	2501059
So is the Tangent of the Rhomb 56 deg. 15	10175107
To the Departure from the Meridian 47 39/100 Leagues	2676166

In the like manner, by the Departure from the Meridian, you may find the Diffe∣rence of Latitude.

V. Sailing upon some Rhomb between the South and the West 57 Leagues, and finding I have altered my Latitude 1 deg. 35 m. I demand upon what Point I have sailed.

SUppose I had sailed from A to C (being a Rhomb between the West and South) 57 Leagues, and then find the Difference of Latitude 31 67/100 Leagues, I demand the Angle BAC.

By the Traverse-Table.

NUmber 57 Leagues in the Column of Distance Sailed, and in that Line or Com∣mon Angle of Meeting, you must find the Difference of Latitude 31 67/100 Leagues, at the Foot of the Table in the fifth Rhomb, which was required.

By the Line of Sines and Numbers on the Scale.

EXtend the Compasses from the Distance run 57 Leagues, to the Sine of 90; the same Distance will reach from the Difference of Latitude, to the Sine-Comple∣ment of the Rhomb 33 deg. 45 min.

By the fifth Case of Plain Triangles.

OR, Open the Compasses from 57 Leagues the Distance, to 31 67/100 the Difference of Latitude; the same Distance will reach from the Sine of 90, to the Sine of 33 deg. 45 min. the Sine-Compl. Rhomb.

As the Distance on the Rhomb AC 57 Leagues	2755874
Is to the Difference of Latitude 31 7/10 Leagues AB	2501059
So is the Sine of 90 deg. B	10000000
To the Compl. Sine of the Rhomb at C 33 d. 45 m. the Sum	12501059
The first Number substract	2755874
The Sine of the Angle	9745185

The Sine-Complement of the Rhomb is C 33 deg. 45, substracted from 90 degrees, there remains the Angle of the Rhomb at A 56 deg. 15 min. which is five Points, namely, S. W. b. W. We neglect some part of a Minute, which is not to be regarded.

VI. Sailing upon some Rhomb between the South and the West 57 Leagues, and finding I have altered my Latitude 1 deg. 35 min. I demand my Departure from my first Meridian.

By the Traverse-Table.

NUmber 57 Leagues in the Column of Distance Sailed, and in that Line or Angle of Meeting find 31 67/100 Leagues, and in the Column to the left hand you will have 47 39/100 the Departure from the Meridian.

By the Sixth Case of Plain Triangles.

Distance run AC 57 Leagues	Sum 88 Leagues	2947923
Diff. of Lat. AB 31 67/100 Leagues	Remain 26 7/10 Leagues	2424881
		5372804
Departure from the Meridian BC 47 ⅔ Leagues	2681402

This is thus done. To the Distance run, add the Difference of Latitude, and also substract it from the same, noting the Sum and Remainder; then add together the Lo∣garithm of this Sum and Remain, and half that is the Logarithm of the Distance from the first Meridian.

By the Line of Numbers.

EXtend the Compasses from the Distance 57 Leagues, to 31 ⅔ the Difference of La∣titude; the same Distance will reach from 88 the Sum, to the Departure, as be∣fore, 47 ⅔ Leagues.

Or, Extend the Compasses from 57, to the Sum 88 ⅔ Leagues; the same Distance will reach from 31 ⅔, to 47 ⅔, as before, which is the Departure required.

All things that have been done by the Artificial Sines and Numbers, are done by the Traverse-Scale, or Artificial Points, Halfs, and Quarters, and Tangent-Rhombs, with the Line of Numbers in the Traverse-Table; and this agreeing very well in Leagues and 100 Part of a League.

CHAP. II. What must be observed by all that keep Account of a Ship's Way at Sea; And to find the true Point of the Ship at any time, according to the Plain Chart.

I Might have further inlarged and multiplied Questions, but that I think these sufficient for any Use at present; and therefore I will be brief, and come to the most material Business, (viz)

The whole Practice of the Art of Navigation, in keeping of a right Reckoning, consists chiefly of three Members or Branches.

First, Well experienced in Judgment, in estimating the Ship's Way in her Course upon every shift of Wind; allowing for Leeward-way, and Currents.

Secondly, In duly estimating the Course or Point of the Compass on which the Ship hath made her way good; allowing for Currents, and the Variation of the Com∣pass.

Thirdly, The diligent taking all Opportunities of due observing the Latitude.

The Reckoning arising out of the two first Branches, we call our Dead Reckoning; and of these Branches there ought to be such an Harmony and Concent, that any

two being given, as you see by the Work before-going, a third Conclusion may thence be raised with Truth.

As, Having the Course and Distance, to find the Latitude of the Ship's Place.

Or, By the Course and Difference of Latitude, to find the Distance:

Or, By the Difference of Latitude and Distance, to find the Course.

But in the midst of so many Uncertainties that daily occur in the Practice of Na∣vigation, a joynt Consent in the th••ee Particulars, is hardly to be expected; and when an Error ariseth, the sole Remedy to be trusted to, is the Observation of the Latitude, or the known Soundings when a Ship is near Land: and how to rectifie the Reckoning by the observed Latitude, we shall shew.

I would advise all Sea-men to yield unto Truth in this particular, That about 24 of the common English Sea-Leagues, are to be allowed to vary a Degree of Latitude, Sailing due North or South, under the Meridian; otherwise they put themselves to many Uncertainties in their Accounts.

First, In Sailing directly North or South, where there is no Current, finding their Reckoning to fall short of the observed Latitude, they take it to be an Errour in their Judgement, in concluding the Ship's Way by estimation or guess to be too little.

And secondly, If there be a Current that helps set them forward, that there is a neer agreement between the observed and the Dead Latitude, they conclude there is no such Current.

Or lastly, If they stem the Current, they conclude it to be much swifter than in truth it is: And thus one Error commonly begets another. But supposing a Confor∣mity to the Truth, we shall prescribe four Rules for correcting a Single Course.

THE LOG-BOARD.

SS 1666.
Hours.	Course.	Knots.	Half Knots.	Fathom.	By or large.
2	S. E. b. S.	7	½	2	L
4	S. S. W.	6	½		L
6	E. b. N.	9			L
8	N. b. E. ½ E.	8			L
10	N. N. W. ½ W.	7	½		L
12	W. N. W.	9			L
2	S. E. b. S.	8	½	2	L
4	S. S. W.	7	½		L
6	S. W. b. S.	6			L
8	S. W.	9			L
10	S. E.	8	½	3	B
12	S. E.	9			B

But first of all it is most necessary to shew how we do keep our Reckonings at Sea, by the Log-board, and also by our Journal-Book.

The first Column is for Time.

The second for the Ship's Course.

The third for the Knots.

The fourth for the Half Knots.

The fifth for the Fathoms.

The sixth is to put down the Sailing Large; that is, to make her Way good on the Point she Sails, signified by L; and Sailing By the Wind, signi∣fied by B; that is, to give al∣lowance to your Course ac∣cording to the Lee-way you have made (by taking in or having out more Sail, or by Currents or Variation) those several Distances

Our English or Italian Mile by which we reckon at Sea, contains 1000 Paces, and each Pace 5 Foot, and every Foot 12 Inches; the 120 part of that Mile is 41 ⅔ Feet, and so much is the space between the Knots upon the Log-line: so many

Knots as the Ship runs in half a Minute, so many Miles she Saileth in an Hour; or so many Leagues and so many Miles she runneth in a Watch, which is four Hours, the time in which half the Company belonging to the Ship watcheth at once by turns.

EXAMPLE.

Nine Knots in half a Minute, is nine Miles in an Hour, which is nine Leagues and nine Miles in a Watch, which is 12 Leagues or 36 Miles in all. Every Noon, after the Master Mates having observed the Sun's Altitude, or every Day at Noon, they take the Reckoning from the Log-board, and double the Knots run, and then di∣vide the Product, which is the number of Miles run, by three; the Quotient is the Leagues run since the former Noon. Or else add up the Knots, and multiply them by 2, and divide by 3, you have the same: But be sure it is all upon Course. We throw the Log every two Hours, and we never express the Course nearer than ½ a Point of the Compass.

Mr. Norwood gives full satisfaction in his Seaman's Practice, by his own experience, That in our ordinary Practice at Sea, we cannot, if we will yield Truth the Con∣quest, allow less than 360000 of our English Feet to vary one Degree of Latitude upon the Earth, in sailing North or South under any Meridian. According to this Measure, there will be in a Degree 68 2/11 of Miles of our Statute-measure, each Mile 5280 Feet; and by the common Sea-measure, 5000 Feet to a Mile, there will be 72 Miles or 24 Leagues in a Degree, which we will take for truth.

Now if you would have shewn the Miles of a true Degree, allowing 60 to a De∣gree, the Miles must be enlarged proportionally, and the distance between every one of the Knots must be 50 Foot; as many of these as run out in half a Minute, so many Miles or Minutes the Ship saileth in an Hour; and for every Foot more, you most allow the 10 part of a Mile. And so, if you will work the old way by Leagues, you must reduce them by Arithmetick into a Degree, and 100 parts of a Degree; or Miles or Minutes may serve. For I have seen no Chart that the Meridian is divided into more parts than 6 times 10, which is 60 Minutes; or Mercator's Chart 20 times 3, which is 60: So the small Divisions on the Dutch Mercator's Charts, every 3 is a Mile or Minute, which is near enough for any use at Sea; and these Degrees are not above ½ an Inch upon the Aequator.

Sailing East or West berween any two Places, and using a Log-line that hath a Knot at every 7 Fathoms, and to reduce it into such Miles 60 to a Degree, each con∣taining 6000 Feet, the Proportion in Number of these two is this, As 6 to 5; for 6 Knots of 7 Fathoms makes 5 of 8 2/6 Fathom, or 50 Feet. Admit a Man keeps a Reckoning of his Ship by a Log-line of 7 Fathoms, and by it find the distance of two Places 1524 Miles, or 508 Leagues, and would know the distance by a Log-line of 50 Feet to a Knot, or 6000 Feet to a Mile: Say then by the Rule of Proportion, As 6 is to 5: So is 1524 to 1720 Miles, whereof 60 Miles make a Degree or 20 Leagues.

Next we will work the Courses of the Log-board, and by it find the difference of Latitude, and departure from the first Meridian.

A Ship being in the Latitude of 47 deg. 30 min. North, and Longitude 00 degrees, the first Course of the Log-board is S. E. b. S. 16 Miles, and S. S. W. 13 Miles, E. b. N. 18 Miles, and N. b. E. ½ E. 16 Miles, N. N. W. ½ W. 15 Miles, and W. N. W. 18 Miles, and S. E. b. S. 18 Miles, and S. S. W. 15 Miles, 8. W. b. S. 12 Miles, and S. W. 18 Miles, S. E. 18 Miles by the Wind, the Wind at W. S. W. and E. S. E. The Ship made two Points Leard-way on the two last Courses.

I demand the Difference of Latitude, and departure from the Meridian the last 24 Hours, and the Latitude I am in.

There are several ways to work Traverses; but the most necessary and readiest is by the Traverse-Scale, and the following Table; the first is to the 10 part of a League, and the Table to the 100 part of a League or Mile. We shall work the for∣mer Traverse by the Tables following, and you at leisure may work it by the Tra∣v••••se-Scale, and find the neer agreement of both without any sensible Error.

		North.	South.	East.	West.
Course by Com∣pass.	Miles sailed.	Miles. 100.	Miles. 100.	Miles. 100.	Miles. 100.
S. E. b. S.	16		13 30	08 89
S. S. W.	13		12 01		04 97
E. b. N.	18	03 51		17 65
N. b. E. ½ E.	16	15 31		04 64
N. b. W. ½ W.	15	13 23			07 07
W. N. W.	18	06 89			16 63
S. E. b. S.	18		14 97	10 00
S. S. W.	15		13 86		05 74
S. W. b. S.	12		09 98		06 67
S. W: W. S. W.	18		06 89		16 63
S. E: E. S E.	18		06 89	16 63
Sum of all		38 94	77 90	57 81	57 61
Substract least			38 94	57 61
Remains differ. Latitude.		38 96	00 20
11 Differ. South and East.	The Latitude the Ship is in is 46 d. 49 m.
The Course made is South almost.

You must put down the Courses made good upon each Point of the Compass, and the number of Miles or Leagues you find sailed on them by the Log-board; in such manner as I have done in this Table: then accord∣ing to the Rhombs, look in the Table following for the Point, Half, or Quarter sailed, and the Distance in Miles or Leagues, in the right hand or left hand Column; and count the four Points and Quarters in the head of the Table, and the four next the East and West, from the left hand to the right hand, in the foot of the Table.

Put down in four Columns N. S. E. VV. and under put what answers each Point.

As for Example. The first Course sailed is three Points from the Meridian; namely, S. E. b. S. under that Column I count 16 Miles in the side, and find against it 13 30/100 Miles Southing, and 89/100 Miles Easting. I put it down in the Ta∣ble in its place, 13. 30 under South, 8. 89 under East. In the like manner you must do by the rest. Likewise the last Course sailed S. E. but by reason of 2 Points Leeward-way, it is but E. S. E. that is, 6 from the South; therefore I reckon them in the Foot of the Table, and right against 18 I find 06. 89 Southward, and 16. 63 Eastward, which you may put down as I have done in the Table. In the like manner you must do if your Course were North or VVesting. This is so plain it needs no far∣ther Precept.

Then add up the Sums in each Column, and substract the lesser out of the greater, the Remainer is the Difference of Latitude and Departure: As I find that the Ship hath gone but 38 96/100 Miles to the Southward, and the Latitude she now is in is 46 deg. 49 min. and the Eastward but 20 parts of 100 of a Mile: Therefore her Course is neer South she made good the last 24 Hours.

CHAP. III. A Formal and Exact Way of Setting down and Perfecting a Sea-Reckoning.* 1.3

THis being the most necessary Rule in this Art of Navigation, How to keep an Exact Reckoning; Although the Course and Distance cannot be so truly and certainly known, as the Latitude may be; yet we must endeavour in these also to come as neer the truth as may be; the rather, for that some Reckonings must necessarily depend wholly upon them. Therefore we come now to shew an Orderly and Exact way of Framing and Keeping a Reckoning at Sea; for which purpose I have inserted this Table following, which sheweth how much a Ship is more Nor∣therly or Southerly, and how much Easterly or VVesterly, by sailing upon any Point

or Quarter-point of the Compass, any distance or number of Miles or Leagues propo∣sed.

Mr. Norwood many Years since laid the ground of making this Table, after this Proportion, [As Radius is in Proportion to Distance run: So is the Sine-Complement of the Rhomb, to the Distance of North or South: And so is the Sine of the Rhomb to the Distance of East or West] as you may see by the first and second Case of Plain Triangles.

Therefore for every Point and Quarter-point from the Meridian, there are four Columns: In the first thereof is set down the number of Leagues or Miles run or sailed upon that Point or Quarter-point of the Compass; The second sheweth how much you have altered the Latitude, that is, how much you are more Southerly or Northerly, by running so far upon that Point or Quarter-point; The third sheweth how much you are more Easterly or Westerly, by running or sailing that Course and Distance, as you have been before directed.

Note this, The Numbers set in the first Column from 1 to 10, are also to be un∣derstood from 10 to 100, or from 100 to 1000: and the Figure of the fourth place answers to the Figure in the first.

Course	Distance.	Southing.	Westing.
South	100	995	98
½ Po. W.	70	697	68
	3	29	3
Leagues.	173	1721	168

As, Suppose a Ship sails away South ½ a Point Westerly 173 Leagues or Miles; we set down this Number thus. Look into thefirst Column for the ½ Point, or ½ the first Rhomb from the Meridian against 10 is sometimes made use of, and understood to be 100. I find in the second Column against it 995 (or you may have the same Number at 100 towards the Foot of the Table, omitting the last Figure) and then in the third Column you may see 98; also against 70, or 7, there is 697, and in the second 68; and in the third against three in the first Column is 29, in the second is 2 and 9/100, which is almost 3/10; therefore I put down 3.

These summed up as in the Table, shews that the Ship sailing upon the first half Point from the Meridian, as namely, S. ½ W. is to the Southwards of the Place she de∣parted 172 1/10 Leagues or Miles, and to the Westward 16 Leagues and 8/10. If you desire more Exactness, you may use all the Places for the greatest Number, which is 100, (viz.)

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table. The 1 Points Quarter.
Dist. in Leagues or Miles sail'd.	2 deg.	49 m.	5 deg.	38 m.	8 deg.	26 m.	11 deg.	15 m.	Dist. in Leagues or Miles sail'd.
0 Point ¼	0 Point ½	0 Point ¾	1 Point.
N S	E W	N S	E W	N S	E W	N S	E W
1	01 00	00 05	01 00	00 10	00 98	00 14	00 98	00 20	1
2	02 00	00 10	01 99	00 20	01 97	00 29	01 96	00 39	2
3	03 00	00 15	02 98	00 29	02 96	00 44	02 94	00 58	3
4	04 00	00 20	03 98	00 39	03 95	00 58	03 92	00 78	4
5	04 09	00 25	04 97	00 49	04 94	00 73	04 90	00 93	5
6	05 09	00 29	05 97	00 59	05 93	00 88	05 88	01 17	6
7	06 09	00 34	06 97	00 69	06 92	01 02	06 86	01 37	7
8	07 09	00 39	07 96	00 78	07 91	01 17	07 85	01 56	8
9	08 09	00 44	08 96	00 88	08 90	01 32	08 83	01 76	9
10	09 09	00 49	09 95	00 98	09 89	01 46	09 81	01 95	10
11	10 98	00 54	10 95	01 08	10 88	01 61	10 79	02 15	11
12	11 98	00 59	11 94	01 18	11 87	01 76	11 77	02 34	12
13	12 98	00 63	12 94	01 27	12 86	01 91	12 75	02 54	13
14	13 98	00 68	13 93	01 37	13 85	02 05	13 73	02 73	14
15	14 98	00 73	14 93	01 47	14 84	02 20	14 71	02 19	15
16	15 98	00 78	15 92	01 57	15 83	02 34	15 69	03 12	16
17	16 98	00 83	16 92	01 67	16 82	02 49	16 67	03 32	17
18	17 97	00 88	17 91	01 76	17 80	02 64	17 65	03 51	18
19	18 97	00 93	18 91	01 86	18 79	02 79	18 64	03 71	19
20	19 97	00 98	19 90	01 96	19 78	02 93	19 62	03 90	20
21	20 97	01 03	20 90	02 06	20 77	03 08	20 60	04 10	21
22	21 97	01 08	21 98	02 16	21 76	03 22	21 58	04 29	22
23	22 97	01 13	22 89	02 25	22 75	03 37	22 56	04 49	23
24	23 97	01 17	23 88	02 35	23 74	03 52	23 54	04 68	24
25	24 97	01 22	24 88	02 45	24 73	03 66	24 52	04 88	25
26	25 96	01 27	25 87	02 55	25 71	03 81	25 50	05 07	26
27	26 96	01 32	26 87	02 65	26 70	03 96	26 48	05 27	27
28	27 96	01 32	27 86	02 75	27 69	04 10	27 46	05 46	28
29	28 96	01 42	28 86	02 84	28 68	04 25	28 44	05 66	29
30	29 96	01 47	29 86	02 94	29 67	04 40	29 42	05 85	30
31	30 96	01 52	30 85	03 04	30 66	04 55	30 40	06 05	31
32	31 96	01 57	31 85	03 14	31 65	04 69	31 38	06 24	32
33	32 96	01 61	32 84	03 23	32 64	04 84	32 37	06 44	33
34	33 95	01 66	33 84	03 33	33 63	04 98	33 35	06 63	34
35	34 95	01 71	34 83	03 43	34 62	05 13	34 33	06 83	35
36	35 95	01 75	35 83	03 53	35 61	05 28	30 31	07 02	36
37	36 95	01 81	36 82	03 63	36 60	05 42	36 29	07 22	37
38	37 95	01 86	37 82	03 73	37 59	05 57	37 27	07 41	38
39	38 95	01 91	38 81	03 82	38 58	05 72	38 25	07 6••	39
40	39 95	01 96	39 81	03 92	39 57	05 87	39 23	07 80	40
41	40 95	02 01	40 80	04 02	40 55	06 02	40 21	08 00	41
42	41 95	02 06	41 80	04 12	41 54	06 16	41 19	08 19	42
43	42 95	02 11	42 79	04 21	42 15	06 31	42 17	08 39	43
44	43 94	02 15	43 79	04 31	43 52	06 45	43 15	08 58	44
45	44 94	02 20	44 78	04 41	44 51	06 60	44 14	08 78	45
46	45 94	02 25	45 78	04 51	45 60	06 75	45 12	08 77	46
47	46 94	02 30	46 77	04 61	46 49	06 89	46 10	09 17	47
48	47 94	02 35	47 77	04 70	47 48	07 04	47 08	09 36	48
49	48 94	02 40	48 76	04 80	48 47	07 20	48 06	09 56	49
50	49 94	02 45	49 76	04 90	49 46	07 33	49 04	09 75	50
51	50 93	02 50	50 75	05 00	50 44	07 48	50 02	09 95	51
52	51 93	02 55	51 75	05 10	51 43	07 63	51 00	10 14	52
53	52 93	02 60	52 74	05 20	52 42	07 77	51 98	10 34	53
54	53 93	02 65	53 74	05 29	53 41	07 92	52 96	10 53	54
55	54 93	02 70	54 73	05 39	54 40	08 07	53 94	10 73	55
56	55 93	02 75	55 73	05 49	55 30	08 21	54 92	10 92	56
57	56 93	02 79	56 72	05 59	56 38	08 36	55 90	11 12	57
58	57 93	02 84	57 72	05 68	57 37	08 51	56 89	11 31	58
59	58 92	02 89	58 71	05 78	58 36	08 65	57 87	11 51	59
60	59 92	02 94	59 71	05 88	59 35	08 80	58 85	11 70	60
70	69 91	03 43	69 66	06 86	69 24	10 27	68 65	13 65	70
80	79 90	03 92	79 61	07 84	79 13	11 73	78 46	15 60	80
90	89 89	04 41	89 56	08 82	89 02	13 20	88 27	17 55	90
100	99 87	04 90	99 51	09 80	98 91	14 67	98 08	19 50	100
200	199 76	09 80	199 02	19 60	197 82	29 34	196 16	39 00	200
	E W	N S	E W	N S	E W	N S	E W	N S
	7 Point ¾	7 Point ½	7 Point ¼	7 Point.
	87 deg.	11 m.	84 deg.	22 m	81 deg.	34 m.	78 deg.	45 m.
The 7 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table, The 2 Points Quarter.
Dist. in Leagues or Miles sail'd.	14 deg.	04 m.	16 deg.	52 m.	19 deg.	41 m.	22 deg.	30 m.	Dist. in Leagues or Miles sail'd.
1 Point ¼	1 Point ½	1 Point ¾	2 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 97	00 24	00 96	00 29	00 94	00 33	00 92	00 38	1
2	01 94	00 48	01 91	00 58	01 88	00 67	01 85	00 76	2
3	02 91	00 72	02 87	00 87	02 82	01 01	02 77	01 75	3
4	03 88	00 97	03 83	01 16	03 77	01 34	03 70	01 53	4
5	04 85	01 21	04 78	01 45	04 71	01 68	04 62	01 91	5
6	05 82	01 45	05 74	01 74	05 65	02 02	05 54	02 30	6
7	06 79	01 70	06 70	02 03	06 59	02 35	06 47	02 68	7
8	07 76	01 94	07 66	02 32	07 53	02 70	07 39	03 16	8
9	08 73	02 18	08 61	02 61	08 47	03 03	08 31	03 44	9
10	09 70	02 43	09 57	02 90	09 41	03 37	09 24	03 83	10
11	10 67	02 67	10 53	03 19	10 36	03 71	10 16	04 21	11
12	11 64	02 91	11 48	03 48	11 30	04 04	11 09	04 59	12
13	12 61	03 15	12 44	03 77	12 24	04 36	12 01	04 97	13
14	13 58	03 40	13 40	04 06	13 18	04 72	12 93	05 36	14
15	14 55	03 64	14 35	04 35	14 12	05 05	13 86	05 74	15
16	15 52	03 88	15 31	04 64	15 06	05 39	14 78	06 12	16
17	16 49	04 13	16 27	04 93	16 00	05 73	15 71	06 51	17
18	17 46	04 37	17 22	05 22	16 95	06 06	16 63	06 89	18
19	18 43	04 61	18 18	05 51	17 89	06 40	17 55	07 27	19
20	19 40	04 86	19 14	05 81	18 83	06 74	18 48	07 65	20
21	20 37	05 10	20 10	06 10	19 77	07 08	19 40	08 04	21
22	21 34	05 34	21 05	06 39	20 71	07 41	20 32	08 42	22
23	22 34	05 48	22 01	06 68	21 66	07 75	21 25	08 80	23
24	23 28	05 83	22 97	06 97	22 60	08 08	22 17	09 18	24
25	24 25	06 07	23 91	07 26	23 54	08 42	23 10	09 57	25
26	25 22	06 31	24 88	07 55	24 48	08 76	24 02	09 95	26
27	26 19	06 56	25 84	07 84	25 42	09 10	24 94	10 33	27
28	27 16	06 80	26 79	08 13	26 36	09 43	25 87	10 71	28
29	28 13	07 04	27 75	08 42	27 30	09 77	26 79	11 10	29
30	29 10	07 28	28 71	08 71	28 25	10 11	27 72	11 48	30
31	30 07	07 53	29 66	09 00	29 19	10 44	28 64	11 86	31
32	31 04	07 77	30 62	09 29	30 13	10 74	29 56	12 25	32
33	32 01	08 01	31 58	09 58	31 07	11 12	30 49	12 63	33
34	32 98	08 26	32 54	09 87	32 01	11 45	31 44	13 01	34
35	33 95	08 50	33 49	10 16	32 95	11 79	32 34	13 39	35
36	34 92	08 74	34 45	10 45	33 89	12 13	33 26	13 78	36
37	35 80	08 99	35 41	10 74	34 84	12 47	34 18	14 16	37
38	36 26	09 23	36 36	11 03	35 78	12 80	35 11	14 54	38
39	37 83	09 47	37 32	11 32	36 72	13 14	36 03	14 92	39
40	38 80	09 71	38 28	11 61	37 66	13 48	36 96	15 31	40
41	39 77	09 96	39 23	11 90	38 60	13 81	37 88	15 69	41
42	40 74	10 20	40 19	12 19	39 34	14 15	38 80	16 07	42
43	41 71	10 44	41 15	12 48	40 49	14 49	39 73	16 45	43
44	42 68	10 69	42 12	12 77	41 43	14 72	40 65	16 84	44
45	43 65	10 63	43 06	13 06	42 37	15 16	41 57	17 22	45
46	44 62	11 17	44 62	13 35	43 41	15 50	42 50	17 60	46
47	45 59	11 42	44 98	13 64	44 25	15 83	43 42	17 99	47
48	46 56	11 66	45 95	13 93	45 19	16 17	44 35	18 37	48
49	47 33	11 90	46 89	14 22	46 13	16 37	45 27	18 75	49
50	48 50	12 14	47 85	14 51	47 08	16 85	46 19	19 13	50
51	49 47	12 39	48 80	14 80	48 01	17 18	47 12	19 52	51
52	50 44	12 63	49 76	15 09	48 96	17 31	48 04	19 89	52
53	51 41	12 87	50 72	15 38	49 90	17 85	48 97	20 28	53
54	52 38	13 12	51 67	15 67	50 84	18 19	49 89	20 66	54
55	53 35	13 36	52 63	15 96	51 78	18 53	58 01		55
56	54 32	13 60	53 59	16 26	52 73	18 87	51 73	21 15	56
57	55 29	13 85	54 55	16 55	53 67	19 20	52 66	21 43	57
58	56 26	14 09	55 50	16 84	54 61	19 54	53 58	22 81	58
59	57 23	14 33	56 46	17 23	55 55	19 87	54 21	22 20	59
60	58 20	14 57	57 42	17 42	56 49	20 21	55 43	22 58	60
70	67 90	17 00	66 90	20 31	65 90	23 58	64 67	26 78	70
80	77 60	19 43	76 55	23 22	75 32	26 95	73 91	30 61	80
90	87 30	21 86	86 10	26 12	84 73	30 39	83 14	34 44	90
100	97 00	24 29	95 69	29 02	94 15	33 68	92 38	38 26	100.
200	194 00	48 58	191 38	58 04	188 30	67 36	184 76	76 52	200
	E W	N S	E W	N S	E W	N S	E W	N S
	6 Points ¾	6 Points ½	6 Points ¼	6 Points.
	75 deg. 56 m.	73 deg. 7 m	70 deg. 19 m.	67 deg. 30 m.
The 6 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat, and Departure from the Meridian.

The Traverse-Table, The 3 Points Quarter.
Dist. in Leagues or Miles sail'd	25 deg. 19 m.	28 deg. 07 m.	30 deg. 56 m.	33 deg. 45 m.	Dist. in Leagues or Miles sail'd.
2 Points ¼	2 Points ½	2 Points ¾	3 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 90	00 43	00 88	00 47	00 86	00 51	00 83	00 56	1
2	01 81	00 85	01 76	00 94	01 71	01 03	01 66	01 55	2
3	02 71	01 28	02 65	01 41	02 57	01 54	02 49	01 67	3
4	03 61	01 71	03 53	01 89	03 43	02 06	03 32	02 22	4
5	04 52	02 14	04 41	02 36	04 29	02 57	04 16	02 78	5
6	05 42	02 56	05 29	02 83	05 15	03 08	04 99	03 33	6
7	06 33	02 99	06 17	03 30	06 00	03 60	05 82	03 89	7
8	07 23	03 42	07 05	03 77	06 86	04 11	06 65	04 44	8
9	08 14	03 85	07 94	04 24	07 72	04 63	07 48	05 00	9
10	09 04	04 28	08 82	04 71	08 58	05 14	08 31	05 55	10
11	09 94	04 70	09 70	05 18	09 44	05 66	09 15	06 11	11
12	10 85	05 13	10 58	05 66	10 29	06 17	09 98	06 67	12
13	11 75	05 56	11 46	06 13	11 15	06 68	10 81	07 22	13
14	12 66	05 99	12 35	06 60	12 00	07 20	11 64	07 78	14
15	13 56	06 41	13 23	07 07	12 87	07 71	12 47	08 33	15
16	14 46	06 84	14 11	07 54	13 72	08 23	13 30	08 89	16
17	15 37	07 27	14 99	08 01	14 58	08 74	14 13	09 44	17
18	16 27	07 70	15 87	08 48	15 44	09 25	14 97	10 00	18
19	17 18	08 12	16 76	08 96	16 30	09 77	15 80	10 56	19
20	18 08	08 55	17 64	09 43	17 16	10 28	16 63	11 11	20
21	18 98	08 98	18 52	09 90	18 01	10 80	17 46	11 67	21
22	19 89	09 41	19 40	10 37	18 87	11 31	18 29	12 22	22
23	20 79	09 83	20 28	10 84	19 73	11 82	19 12	12 78	23
24	21 60	10 26	21 17	11 31	20 59	12 34	19 95	13 33	24
25	22 60	10 69	22 05	11 78	21 44	12 85	20 79	13 89	25
26	23 50	11 12	22 93	12 26	22 30	13 57	21 62	14 44	26
27	24 41	11 54	23 81	12 73	23 16	13 88	22 45	15 15	27
28	25 31	11 97	24 69	13 20	24 02	14 39	23 28	15 56	28
29	26 22	12 40	25 58	13 67	24 87	14 91	24 11	16 11	29
30	27 12	12 83	26 46	14 14	25 73	15 42	24 94	16 67	30
31	28 02	13 25	27 34	14 61	26 59	15 94	25 78	17 22	31
32	28 93	13 68	28 22	15 08	27 45	16 45	26 61	17 78	32
33	29 83	14 11	29 10	15 56	28 31	16 97	27 44	18 33	33
34	30 74	14 54	29 98	16 03	29 16	17 48	28 27	18 89	34
35	31 64	14 96	30 87	16 50	30 02	17 99	29 10	19 44	35
36	32 54	15 39	31 75	16 97	30 88	18 51	29 93	20 00	36
37	33 45	15 82	32 63	17 44	31 74	19 02	30 76	20 56	37
38	34 35	16 25	33 57	17 91	32 59	19 54	31 60	21 11	38
39	35 26	16 68	34 40	18 38	33 45	20 05	32 43	21 67	39
40	36 16	17 10	35 28	18 86	34 31	20 56	33 26	22 22	40
41	37 06	17 53	36 16	19 34	35 17	21 08	34 09	22 78	41
42	37 67	17 96	37 04	19 81	36 02	21 59	34 92	23 34	42
43	38 87	18 38	37 92	20 27	36 88	22 11	35 75	23 89	43
44	39 78	18 81	38 80	20 74	37 74	22 62	36 58	24 44	44
45	40 68	19 24	39 69	21 21	38 60	23 14	37 42	25 00	45
46	41 51	19 67	40 57	21 68	39 46	23 65	38 25	25 56	46
47	42 49	20 09	41 41	22 16	40 31	24 16	39 08	26 11	47
48	43 39	20 52	42 43	22 63	41 17	24 68	39 91	26 67	48
49	44 30	20 95	43 21	23 10	42 03	25 19	40 74	27 22	49
50	45 20	21 38	44 10	23 57	42 89	25 71	41 57	27 78	50
51	46 10	21 61	44 98	24 04	43 74	26 22	42 40	28 33	51
52	47 01	22 23	45 86	24 51	44 60	26 73	43 24	28 89	52
53	47 91	22 66	46 74	24 98	45 46	27 25	44 07	29 44	53
54	48 82	23 08	47 62	25 46	46 32	27 76	44 90	30 00	54
55	49 72	23 52	48 51	25 93	47 17	28 28	45 73	30 56	55
56	50 62	23 94	49 39	26 40	48 03	28 79	46 56	31 11	56
57	51 53	24 37	50 27	26 87	48 89	29 30	47 39	31 67	57
58	52 43	24 79	51 15	27 34	49 75	29 82	48 22	32 22	58
59	53 33	25 23	52 03	27 81	50 61	30 33	49 06	32 78	59
60	54 24	25 65	52 91	28 28	51 46	30 84	49 89	33 33	60
70	63 27	29 92	61 73	32 99	60 04	35 98	58 22	38 88	70
80	72 31	34 20	70 55	37 71	68 61	41 12	66 51	44 44	80
90	81 35	38 47	79 37	42 43	77 19	46 26	74 83	50 00	90
100	90 39	42 75	88 19	47 13	85 77	51 41	83 14	55 55	100
200	180 78	85 50	176 38	94 26	171 54	102 82	166 28	111 11	200
	E W	N S	E W	N S	E W	N S	E W	N S
	5 Points ¾	5 Points ½	5 Points ¼	5 Points.
	64 deg. 41 m	61. deg. 52 m	59 deg. 4 m.	56 deg. 15 m
The 5 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table, The 4 Points Quarter.
Dist. in Leagues or Miles sail'd.	36 deg. 34 m.	39 deg. 22 m.	42 deg. 11 m.	45 deg. 00 m.	Dist. in Leagues or Miles sail'd.
3 Points ¼	3 Points ½	3 Points ¾	4 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 80	00 60	00 77	00 63	00 74	00 67	00 71	00 71	1
2	01 61	01 19	01 55	01 27	01 48	01 34	01 41	01 41	2
3	02 41	01 41	02 32	01 90	02 22	02 01	02 12	02 12	3
4	03 21	02 38	03 09	02 54	02 96	02 69	02 83	02 83	4
5	04 02	02 98	03 86	03 17	03 70	03 36	03 54	03 54	5
6	04 82	03 57	04 64	03 81	04 44	04 03	04 24	04 24	6
7	05 62	04 17	05 41	04 44	05 18	04 78	04 95	04 95	7
8	06 43	04 76	06 18	05 07	05 93	05 37	05 66	05 66	8
9	07 23	05 36	06 96	05 71	06 67	06 04	06 36	06 36	9
10	08 03	05 96	07 73	06 34	07 41	06 72	07 07	07 07	10
11	08 83	06 55	08 50	06 98	08 15	07 39	07 78	07 78	11
12	09 64	07 15	09 28	07 61	08 89	08 06	08 49	08 49	12
13	10 44	07 74	10 05	08 25	09 63	08 73	09 19	09 19	13
14	11 24	08 34	10 82	08 88	10 37	09 40	09 90	09 90	14
15	12 05	08 94	11 60	09 52	11 11	10 07	10 61	10 61	15
16	12 85	09 53	12 37	10 15	11 85	10 74	11 31	11 31	16
17	13 66	10 13	13 14	10 78	12 70	11 42	12 02	12 02	17
18	14 46	10 72	13 91	11 42	13 34	12 09	12 73	12 73	18
19	15 26	11 32	14 69	12 04	14 08	12 76	13 44	13 44	19
20	16 06	11 91	15 46	12 69	14 82	13 43	14 14	14 14	20
21	16 87	12 51	16 23	13 32	15 56	14 10	14 85	14 85	21
22	17 67	13 11	17 01	13 96	16 30	14 77	15 56	15 56	2••
23	18 47	13 70	17 78	14 59	17 04	15 45	16 26	16 26	23
24	19 28	14 30	18 55	15 22	17 78	16 12	16 97	16 97	24
25	20 08	14 89	19 32	15 86	18 52	16 79	17 68	17 68	25
26	20 88	15 49	20 10	16 49	19 26	17 46	18 38	18 38	26
27	21 69	16 08	20 87	17 13	20 00	18 13	19 09	18 09	27
28	22 49	16 68	21 64	17 76	20 75	18 77	19 80	19 80	28
29	23 29	17 27	22 42	18 40	21 49	19 44	20 51	20 51	29
30	24 10	17 87	23 19	19 03	22 23	20 12	21 21	21 21	30
31	24 90	18 47	23 96	19 67	22 97	20 82	21 92	21 92	31
32	25 70	19 06	24 74	20 30	23 71	21 49	22 63	22 63	32
33	26 51	19 66	25 51	20 93	24 45	22 16	23 33	23 33	33
34	27 31	20 25	26 28	21 57	25 19	22 83	24 04	24 04	34
35	28 11	20 85	27 06	22 20	25 93	23 50	24 75	24 75	35
36	28 91	21 46	27 83	22 84	26 67	24 17	25 46	25 46	36
37	29 72	22 04	28 60	23 47	27 41	24 85	26 16	26 16	37
38	30 52	22 64	29 37	24 11	28 16	25 52	26 87	26 87	38
39	31 33	23 23	30 15	24 74	28 90	26 19	27 56	27 56	39
40	32 13	23 83	30 92	25 38	29 64	26 86	28 28	28 28	40
41	32 93	24 42	31 69	26 01	30 38	27 53	28 99	28 99	41
42	33 73	25 02	32 47	26 64	31 12	28 21	29 10	29 10	42
43	34 54	25 61	33 24	27 28	31 86	28 88	30 41	30 41	43
44	35 34	26 21	34 01	27 91	32 60	29 55	31 11	31 11	44
45	36 14	26 81	34 78	28 55	33 34	30 22	31 82	31 82	45
46	36 94	27 40	35 56	29 18	34 08	30 89	32 53	32 53	46
47	37 75	28 00	36 33	29 82	34 82	31 56	33 23	33 23	47
48	38 55	28 59	37 10	30 45	35 57	32 23	33 94	33 94	48
49	39 36	29 19	37 88	31 08	36 31	32 91	34 65	34 65	49
50	40 17	29 78	38 65	31 72	37 05	33 58	35 35	35 35	50
51	40 96	30 38	39 42	32 35	37 79	34 25	36 06	36 06	51
52	41 77	30 98	40 20	32 99	38 53	34 92	36 77	36 77	52
53	42 57	31 57	40 97	33 62	39 27	35 59	37 48	37 48	53
54	43 37	32 17	41 74	34 26	40 01	36 26	38 14	38 14	54
55	44 18	32 76	42 52	34 86	40 75	36 94	38 89	38 89	55
56	44 98	33 36	43 29	35 53	41 49	37 61	39 60	39 60	56
57	45 78	33 96	44 06	36 16	42 23	38 28	40 30	40 30	57
58	46 59	34 55	44 83	36 79	43 07	38 95	41 01	41 01	58
59	47 39	35 15	45 61	37 43	43 72	39 62	41 72	41 72	59
60	48 19	35 74	46 38	38 06	44 45	40 29	42 43	42 43	60
70	56 22	41 69	44 11	44 41	51 85	47 00	49 49	49 49	70
80	64 25	47 65	61 84	50 75	59 26	53 72	56 56	56 56	80
90	72 28	53 61	69 57	57 09	66 67	60 44	63 63	63 63	90
100	80 32	59 56	77 30	63 43	74 08	67 15	70 71	70 71	100
200	160 64	119 12	154 60	126 86	148 16	134 30	141 41	141 41	200
	E W	N S	E W	N S	E W	N S	E W	N S
	4 Points ¾	4 Points ½	4 Points ¼	4 Points.
	53 deg. 26 m.	50 deg. 37 m	47 deg. 49 m.	45 deg. 00 m.
The 4. Points Quarters.

As for Example.

	100	9951	980
S. ½ West.	70	6966	686
	3	299	29
Leagues.	17:3	172:16	16:95

Beforegoing, if you take all the Numbers in the Table, they will stand as here appear∣eth, where the Southerly Distance is 172 16/100 Leagues, and the Westerly is 16 95/100 Leagues.

But I hold it more convenient to omit the last Figure to the right hand, and so take the Tenths, as in the second Example; and then in all things it will agree with the Tra∣verse-Scale, on which if you extend the Compasses from 100 to 73, the same Distance will reach from the first ½ Point next the Line of Numbers, to 172 1/10; and from the half Point of the Westing, to 16 9/10 Leagues, as before.

As also, If you extend the Compasses from 172 1/10 the Difference of Latitude, or from 72 1/10 to 6 8/10, which stands for 16 8/10 on this or the like occasion, and apply this Distance from 4 Points on the Tangent-Line of the Scale, and the other Point of the Compasses will reach to ½ Point, which is from the South Westerly, as before.

Now for the Point and ½ Points reckoned at the Bottom, it is thus.

Admit a Ship fails 57 Leagues or Miles North-West and by West, or the 5th Rhomb from the Meridian; I would know how much I am to the VVestward, and how much to the Southward.

Distance	3 Rhomb.	3
	N S	E W
57	474	317
Sailed	E W	N S
	5 Rhomb.	5

Therefore look in the bottom of the Ta∣ble for the 5th Rhomb, and in the Side for 57 Leagues or Miles; and in the Line of Meeting over the fifth Rhomb you have 47.39 or 47 4/10 for the Westing, and 31.67 or 31 7/10 almost for the Northing.

Now had you been to find the Northing and Westing of the third Rhomb from the Meridian, as N. W. b. N. to 57 Leagues di∣stance, the Northing would be 47 4/10, and the Westing 31 7/10, as you see signified by the Letters N. S. and E. W. at the head of the Table, and North N. S. under E. W. at the foot of the Table. This is so plain, it needs no further Precept.

Or by the Traverse-Scale, Extend the Compasses in the Line of Numbers from 10 or 100, to 57 Leagues; the same Distance will reach from 3 Points in the next Line, with 5 Points of the Easting and Westing, to 47.4 Leagues or Miles; that Distance will reach from 5 Points in the Line of N. and S. to 31.7 Leagues, as before.

And the Compasses extended from 47 4/10, to 31 1/10 on the Line of Numbers; the same Distance will reach from 4 Points in the Tangent-Line, to 5 Points from the Meridian, or 3 Points if the Case so required, as if it had been N. W. b. N. The like do in all such Questions.

Likewise by the Traverse-Scale, Let the Course be given N. W. b. W. and Departure 47 4/10, To find the Distance and Difference of Latitude.

Extend the Compasses from 5 Points in the Line of E. W. of the Scale, to the De∣parture; the same Distance will reach from 10 or 100 in the Line of Numbers, to 57 the Distance; And also from 5 Points in the Line of N. S. to 31 7/10 the Diffe∣rence of Latitude. I make this plain by the Scale, by reason the Compasses and the Scale, are more portable than the Book and Table.

A larger Example I will give you of the Tables and Traverse-Scale together, whereby you may perceive, That the Artificial Numbers, Points, and Quarters agree in all things with the Table; nay, I hold the Scale the best of the two, for the ready allowing for Variation, and for Currents, which is done by removing the Compasses from one Point or Distance to another. Now let the Question be this,

Suppose a Ship sail from the Island of Lundy, in Latitude 51 deg. 22 min. North, and Longitude 25 deg. 52 min. to the Island of Barbadoes, in Latitude 13 deg. 10 min. North, and Longitude 332 deg. 57 min. By the Plain-Chart, Difference of Latitude is 764 Leagues, and Longitude 1059 Leagues, and I sail these several Courses, (viz.) S. S. W. ½ W. from A to B 400 Leagues, S. W. b. S. ½ W. 125 Leagues, and S. W. 180 Leagues, and S. W. b. W. ½ Westerly 190 Leagues, W. S. W. 146 Leagues, and W. b. S. 159 Leagues, and South 8 Leagues 7 7/10: All these Courses and Distances I set down as followeth. In the first Column is expressed the Days of the Month, and Distance sailing upon each Course; The second, the Day of the VVeek; The third, the Course sailed; The fourth, the Distance from the Meridian; The fifth, the Place and Point of each Course by Letters; The sixth, the Distance sailed; The se∣venth, eighth, ninth, and tenth, the Northing, Southing, Easting, and VVesting, which is the Difference of Latitude and Departure from the Meridian in Leagues 1/10 Parts; The eleventh Column is the Latitude; The twelfth, the Longitude; The thir∣teenth, the Variation of the Compass.

Da. Month.	Da. Week.	Course sailed.	Distance from the Meridi∣an.	The Places.	Dist. sailed.	North∣ing.	South∣ing.	East∣ing.	West∣ing.	Latitud. D••gr. Min.	Longit. Degr. Min.	Variati∣on.
* 1.421	f	S. W. ¾ W.	S.W. 54 d. 12 m.	From A to K.	1306 Leagu.	764 Leagues	704 Leagu.	1058 Leag.	1058 Leag.	51 22	25 52	Easterly 5 m.
13 10	332 57
* 1.52	2	S. S. W. ½ W.	S. W. 2 Po. ½	From A to B.	200 200	Current sets E. S. E.	176 4/10 176 4		94 3/10 94 3	33 44	16 26	Cur. sets by estim. E. S. E.
6	G	S. W. b. S. ½ W.	S. W. 3 Po. ½	From B to C.	100 20 5		773 155 39		634 127 32	28 28	12 28	Variat. 00 m.
10	d	S. W. S. W. ¼ W.	S. W. 4 Points. S W. 3 ¾	From C to D.	100 80 12		707 566 87		707 566 80	22 06	5 42	Variat. 00 m.
15	b	S. W. by W. ½ W.	S. W. 5 Po. ½	From D to E.	100 90		471 424		882 794	17 38	35 19	Westerly 2 degr.
19	f	W. S. W.	S. W. 6 Points.	From E to F.	100 40 6		383 153 23		924 370 55	15 50	350 24	Westerly 4 degr.
24	d	W. by S.	S. W. 7 Points.	From F to G.	100 50 9		195 98 38		981 490 92	13 11	342 46	Westerly 5 degr.
		The Course made good.	S. W. 48 d. 34 m.		1212 3/10		763 8/10		862	13 11	342 46

This done, add up the South Column, which Sum is 763 8/10 Leagues; which redu∣ced into Degrees,* 1.6 by dividing by 20 and multiplying the odd Leagues under 20 by 3, and adding the Minutes in the Tenths, you will find the Difference of Lati∣tude in Degrees to be 38 deg. 11 min. which substracted from 51 deg. 22 min. there re∣mains 13 deg. 11 min. the Latitude of Barbadoes.

* 1.7Add up the Sums of the West Column, which is 862 Leagues; that converted in∣to Degrees, is 43 deg. 6 min. Substract that from the Longitude of the Island of Lun∣dy; if you cannot, add to it 360 deg. So 25 deg. 52 min. added to 360 deg. makes 385 deg. 52 min. Then the Difference of Longitude substracted from it, 43 deg. 6 m. there remains 342 deg. 46 min. the Longitude the Ship is in.

You must note, The Degrees are such that 60 Miles or min. makes a Degree of Longitude or Latitude, or of a Great Circle.

Note, The day we set sail, we put down the day of the Month and VVeek, the di∣rect Course to the Port we are bound to, and the Place marked with two Letters, as

in this Table A for Lundy and K for Barbadoes; and also under Distance, the number of Leagues upon a straight Course; and under Northing and Southing, the Difference of Latitude in Leagues and Tenth Parts; and under Latitude, the Latitude of the two Places; and under Longitude, the Longitude of the two Places, and also the Va∣riation of the Compass from whence we set out first: which you may see all plain in the head of the Table, in the Common Angle of Meeting with the 21 of April.

And remember, You have the Latitude and Longitude given you; therefore by it you must find the direct Rhomb and Distance, as you have been shewed by the second and sixth Case of Plain Triangles.

Now if you would set down this Reckoning on the Plain Chart severally, you must extend your Compasses from one of the Parallels of Longitude, to the Latitude you are in; as also take off so many Leagues of the Meridian Line, as your Departure hath been, reckoning 5 Degrees for 100 Leagues, and every Degree for 20 Leagues.

As for Example.

Suppose we would set down the first Distance of South and West, Extend your Compasses from the Parallel of 40 deg. to your Latitude you are in 33 deg. 44 min. And also extend another pair of Compasses on the Aequinoctial, if there is one divided; if not, on the Meridian, which is all one; and take off 16 deg. 26 min. by one of the Parallels of the Meridian: or take off 188 Leagues 6/10, which is 9 deg. 26 min. the Difference to the Westward from your first Meridian; and so let the Compasses of the Difference of Latitude run upon the Parallel of 40 deg. and the other Compasses with 188 6/10 or 9 deg. 26 min. on one of the Parallels of North and South, until they meet in the Point B: (And so add the Meridian-difference of the second Place to the first; and the Difference of Latitude of the second Place, substract from the first,* 1.8 by reason you are going from the North Pole toward the South or Aequator.) As for your De∣grees of Longitude, you must know where you begin the first Meridian; and as you go to the Westward substract the Difference of Degrees of Meridians, and as you sail to the Eastward add the Difference of Degrees, and you have the Longitude in Degrees where you are.

So that this may suffice for a President, to lay down on your Draught or Blank Chart the Point of the Place of the Ship, by the Meridian-distance and Difference of Latitude; and as you have been directed, so are the Points C, D, E, F, G set down, So that you need not pester the Chart with Rhomb-lines, as formerly; but take the Difference between the Latitude and Meridian-distance off the Line of Numbers, and apply that Distance to the Tangent-line of Rhombs on the Traverse-Scale, and that will presently shew you the Point or Rhomb between any two Places assigned.

The drawing of the Plain Sea-Chart, and the way of sailing thereby, is the most easie and plainest of all others: And though it be fit to use only in Places neer the Aequinoctial, or in short Voyages, yet it will serve for a good Introduction to the other kinds of Sailing. Therefore we shall not lose our labour; for in all kinds of Sailing the same Work must be observed with some caution.

[illustration] sea-chart

The Plaine Sea Chart.

folio 156

First make the Square ASTB, of what length and breadth you please, and divide each Side into as many equal Parts as your occasion requires; and then: draw straight Lines through these Parts, crossing one the other at Right Angles, so making many lit∣tle Geometrical Squares, each of which may contain one Degree: but I have made this, by reason of its largeness; to contain 10 Degrees. Note, That the Degrees of the Meridian at the Aequinoctial are all of equal distance to the Poles, which is a gross Error, which shall be shewn in the following Discourse. So that you may make the Meridian-Line in your Chart 25 deg. 52 min. to the Westward of the Meridian of Lundy: Or you may divide the two Sides into Degrees as far as you think fit, and every Degree into 60 Parts, which is the old way; and I know most Mariners will not be directed a new way of dividing the Degrees each of them into 10 Parts; so each Part will contain about 2 Leagues; and that division of double Leagues is near enough for the Mariners use. You may suppose each of these Parts to be sub∣divided into 10; so every Degree will contain 100 Parts, which is a very ready way if you keep your Account by Arithmetick, by Decimals or 10 Parts. This is so plain, it needs no further Precept; therefore we will proceed to the use of it.

Now your several Courses and Traverse-Points are laid down on your Chart, from

Lundy at A, to B the first, second to C, third to D, fourth to E, fifth to F, the sixth to to G, which is the Point the Ship is in when you cast up this Reckoning.

764	00
763	08
000	02

1058

862

196 Leagues short of Barbadoes at G.

Now to know how far you are short of the Island by the Plain Chart, substract the Sum of the South Column 763 8/10 from the Difference of Latitude 764 Leagues, and you will find you are but 2/10 parts of a League to the Northward of your given Latitude, which is not to be regarded; and also substract the Sum of the West Column, from the Difference of Longitude, and the Remainer is 197 Leagues, which you are short at G of the Barbadoes; and being in the Latitude of 13 deg. 11 min. the Island bears off you due West at K: So that you should sail 197 Leagues on that Point West, before you should be arrived at your Port by the Plain Chart.

But by the true Sea-Chart you are arrived at G, which is the Island of Barbadoes:* 1.9 For the true Meridian-distance is but 865 Leagues betw••••n Lundy and Barbado••s, and the Plain Chart makes it 1059 Leagues; and the true Course from Lundy to Barba∣does is but 48 deg. 34 min. which is S. W. a little above a quarter of a Point Westerly; and the Plain Chart makes it 54 deg. 12 min. S. W. which is above ¾ of a Point; And the true Distance is but 1152 Leagues, and by the Plain Chart it is 1366 Leagues. By this you may plainly perceive, that no Island, nor Cape, or Head-Land, can be truly laid down in the Plain Chart in its true scituation, but near the Aequinoctial only, and near about the same may be used without sensible Error, because there only the Meridians and Parallels are equal; but on this side or beyond the Aequino∣ctial, there is Error committed proportionally to the Difference of the Meridian and Parallel; that is, The true Difference of Longitude found out by the Plain Chart, hath the same proportion to the true Difference of Longitude, that the Parallel hath to the Meridian. But most Mariners will not be drawn from this plain easie way of Sailing, notwithstanding the have it plainly demonstrated to them by us: But those that take the true way of Sailing, find the Credit and Benefit of it, to the shame of those that are so obstinate, conceited, and grounded in Ignorance.

B••t in the following Discourse I will use my endeavour to make things so plain, that if the Ingenious Mariner will but spend half an hours time at the setting forth of his Voyage, to find by direction his true Course and Distance, and Meridian-di∣stance, and put it at the Head of his Journal, as you see in the Table, he shall use his Plain Sailing, all the rest of his Voyage; and he shall have direction how to use it by the Chart made according to the Globe. But something more of this way, accord∣ing to my Promise.

CHAP. IV. How to Correct the Account, when the Dead Latitude differs from the Observed Latitude.

WE are come now to make good what was promised in the second Chapter, to prescribe four Precepts for correcting a Single Course.

I shall be brief, in regard Mr. Collins, in pag. 22. of his Mariner's Scale new Plained, hath imitated Moetius a Hollander, a Latin Author, in these Exam∣ples; but good Rules, the oftner writ, the more they get.

The First EXAMPLE.

IF a Ship sail under the Meridian, if the Difference of Latitude be less by Esti∣mation, than it is by Observation, the Ship's Place must be corrected and enlar∣ged under the Meridian; and the Error is to be imputed either to the Judgment in estimating the Distance run, in making it too little; or if the said Distance be estima∣ted by a sound experienced Judgment, it is to be supposed you stem some Current.

Admit a Ship sail from A, in the Latitude of 36 deg. directly South, 70 Leagues, or 3 deg. 30 min. and by Estimation is at B, but by Observation he is in Latitude 32 deg. The Reckoning rectified, the Ship's Place is in the Point C; but if the Difference of Latitude be more by Estimation, than it is by Observation, the Judgment may err, in supposing the Distance run to be too much. In this Case, the Distance is to be shortned, and the Correction must be made according to the Latitude observed under the Meridian.

Admit a Ship sail South from A, in the Latitude 36 deg. untill she have altered her Latitude 3 deg. 30 min. by Estimation being at B, in Latitude 32 deg. 30 min. and if the observed Latitude be 33 deg. 00 min. the Ship's Place corrected is at C, and not at B.

RULE II.

SUpposing no Current, If the Dead Latitude differ from the Observed Latitude, the Error is in misjudging the Distance run, which is to be made longer or shorter, as the Case requires.

Admit a Ship sail from A, S. S. E. ¾ Easterly 70 Leagues, and is by Estimation at P in the Latitude of 33 deg. but if the observed Latitude be 32 deg. 30 min. ad∣mit at B, then a Line drawn through B, parallel to NA, crosseth the Line of the Ship's Course at Q, which is the Corrected Point where the Ship is: So that the Di∣stance is inlarged 10 Leagues 4/10, the whole Distance AQ is 82 Leagues 4/10.

[illustration] geometrical diagram

The same manner, If the Ship had sailed 94 Leagues on the same Course, and by Estimation were at the Point R, in the Pa∣rallel of 32 deg. and by Observa∣tion the Latitude were found to be 32 deg. 30 min. In this Case the Ship's Distance is to be short∣ned, by drawing the foresaid Line BQ parallel to NA; and it will cross the Line of the Ships Course at Q, the Corrected Point where the Ship is.

By the Traverse-Scale.

EXtend the Compasses from 100, to 94; the same Di∣stance will reach from 2 ¾ Points, to 82 4/10 Leagues in the Line of Numbers.

RULE III.

SUppose there is some Current, and you can depend upon the Observed Difference of Latitude, and Log-distance, as both true; then the Error may be imputed to the Rhomb, which alters by reason of the supposed Current.

Especially when you sail in Rhombs near the East and West; for then if the Dead Latitude differ from the Observed Latitude, the Error is to be imputed either wholly to the Rhomb, or partly to the Rhomb, partly to the Distance.

If wholly to the Rhomb, then retain the observed Difference of Latitude, and Di∣stance by Observation, and thereby find the Departure from the Meridian, by draw∣ing a new Rhomb-line.

But if your Judgment would allot the Error partly to the Rhomb, partly to the

Distance, keep the observed Difference of Latitude: And for the Departure from the Meridian, let it be the same as was by the Dead Reckoning.

Suppose a Ship sail East by South ½ a Point Southerly 72 Leagues, from the Latitude of 36 deg. from A to M, and by Dead Reckoning should be in the Latitude of 35 deg. If the Observed Latitude be 35 deg. 20 min. which is at S; In this Case, if the Error be wholly imputed to the Distance, the Line SX being drawn parallel to NA, would cut off or shorten the Distance as much as the Measure MX, which is 26 Leagues; which because it seems absurd and improbable, is not to be admitted of: Wherefore imputing the Error to the Rhomb only, place one Foot of the Extent AM in S, and with the other cross the Line NA at L; and so is AL the Departure from the Meri∣dian required; whereby the Rhomb-line, if it were drawn, will be ordered to pass through F the Cross.

By the Traverse-Scale.

IF you extend the Compasses from 100, to 72 the Distance; the same Extent will reach from the Difference of Latitude by Observation, to the true Rhomb, which is almost East by South: and if you apply that Distance to one Point on the Line N. S. of the Scale, the other will reach to the Departure required 70 6/10 Leagues.— Which is far better than the other way.

The Fourth PRECEPT, CASE, or EXAMPLE.

IF a Ship sail East or West, and the Dead and Observed Latitude doth agree, the Reckoning cannot be corrected; but if they differ, the Error will be partly in the Rhomb, and partly in the Distance: In such a Case keep the Meridian-distance, and the Difference of Latitude is the Distance you are gone to the Northward or South∣ward of the East and West.

By the Traverse-Scale.

EXtend the Compasses from 100, to the Distance sailed; the same Extent will reach from the Difference of Latitude by Observation, to the true Course: So that you may in a moment do all these Questions and Cases by the Traverse-Scale, and Line of Numbers and Artificial Points and Quarters thereon. If you have but the perfect Use of it, I know there is no Instrument whatsoever more ready to resolve any useful Question, and correct your Reckoning.

Lastly, If by frequent Observation you find the Ship is still carried from the East or West, either Northward or Southward, you may conclude some Current to be the cause thereof: Keep the Distance by Dead Reckoning and Observation, and the Diffe∣rence is the Distance from the Parallel.

We will not multiply too many Examples, but rather advise the Ingenious to make use of such as his need shall require; for understanding what hath been said, will be advantageous to the Practitioner.

CHAP. V. How to allow for known Currents, in Estimating the Ship's Course and Distance.

THis Subject hath been largely handled by Mr. Norwood, at the end of his Sea-mans Practice; and by Mr. Philips, in his Advancement of Navigation, page 54, to 64. As also how to find them out by comparing the Reckoning homeward with the Reckoning outward, which was kept betwixt two Places: There∣fore

I shall be brief, and demonstrate by Scale and Compass, what they have done by Tables.

First, This is easie to be understood, If you sail against a Current, if it be swifter than the Ship's way, you fall a Stern; but if it be slower, you get on head so much as is the Difference between the Way of the Ship, and the Race of the Current.

EXAMPLE.

* 1.10If a Ship sail 8 Miles South in an Hour, by Log or Estimation, against a Current that sets North 3 Miles in an Hour, that substracted from 8, leaves 5 Mile an Hour the Ship goes a head South: But if the Ship's way were 3 Mile an Hour South, against a Current that sets 8 Mile an Hour North, the Ship would fall 5 Miles an Hour a Stern.

* 1.11Admit a Ship runs East 4 Miles an Hour, and the Current runs also 3 Miles an Hour, What is the true Motion of the Ship? Answer, 7 Miles an Hour a Head.

Admit a Ship cross a Current that sets North East-by-North 4 Miles an Hour; the Ship sails in a Watch, or 4 Hours, 9 Leagues East-by North, and in two Watches more she sails 13 Leagues E. N. E. by the Compass.

Now it is required what Course and Distance the Ship hath made good from the first place of setting out from A.

[illustration] geometrical diagram

First draw the Right Line AL, then with the Chord of 60 Deg. describe the Quadrant on it; to be sure take 90 deg. off the Line of Chords, and lay it from N to O; then draw the North Line AP; then set off the Ship's first Course one Point from the East from N to G, and draw the Line AG, and from A to B lay off the first Distance 9 Leagues: Then prick off the Course of the Cur∣rent, being 5 Points from N to F, and draw the Line AF, being the Course N. E. b. N. of the Current. And because the Cur∣rent in 4 Hours sets 5 ⅓ Leagues forward in its own Race, there∣fore draw the Line BC, parallel to AF, that is, take the nearest Distance from B to AF, and sweep a small Arch, and from B to the upper Edge of the Arch, draw the Line BC thereon, put from B to C 5 ⅓ the Currents Motion, and draw the Line AC, which shews the Course the Ship hath made good the first Watch.

Now for the second Course, draw CH parallel to the Line AL, and with the Ra∣dius or Chord of 60 deg. upon C as a Center, draw the Arch HZ, whereon prick 22 deg. 30 min. or 2 Points for E. N. E. for the Ship's second Course from the East; and draw CZ, whereon prick down the Distance sailed 13 Leagues from C to D; then draw DW parallel to AF, as you did BC; then because the Current sets 10 ⅔ in two Watches, therefore prick down 10 ⅔ Leagues from D to W, and draw the Line AW; which being measured upon the same Scale of an Inch divided into 10 parts, shews the Ship's direct Distance is 35 6/10 Leagues; whereas if there had been no Cur∣rent, the direct Distance had been AR 22 2/10 Leagues: Then measure the Arch NE, and you will find it 35 deg. which is a little above 3 Points from the East. So the Point the Ship hath made good is North-East-by-East a little Northerly; whereas if there had been no Current, the Course had been NS, that is, East and by North ¾ of a Point Northerly, and had been at R, but now the Ship is at W, therefore di∣stant from it equal to RW 15 6/10 Leagues. The prick'd Lines are the Courses and Arches without a Current.

This is a good way to work these Questions: If you have no Compasses, draw on a Slat or Quadrant to work Traverses by; if you have, that way is the soonest done by them after the same manner. Some will expect, that knows me, some other sort of Questions, (besides these most useful beforegoing:) For them, and their leisure-time, I have inserted these six Questions following.

QUESTION I. A Ship Sails 40 Leagues more than her Difference of Latitude, and is departed from the Meridian 80 Leagues, I demand her Diffe∣rence of Latitude.

[illustration] geometrical diagram

MAke a Right-Angled Trian∣gle, so that the Base FG be equal to her Difference 40 Leagues, and the Perpendicular GH equal to her Departure 80 Leagues: Then continue the Base FG, and find the Center point E unto H and F, so it will be E, and G 60 Leagues for the Diffe∣rence of Latitude sought.

Arithmetically.

Square GH 80, you have 6400,* 1.12 which divide by GF 40, the Quotient is 160; from whence substract GF 40, there remains 120; the half is 60, for the Difference of Latitude sought.

QUEST. II. A Ship Sails 20 Leagues more than her Difference of Latitude, and but 10 Leagues more than her Departure from the Meridian, I demand her Distance Sailed.

[illustration] geometrical diagram

[illustration] geometrical diagram

IN the Triangle ABC, you have EB 20 Leagues more than the Difference of Latitude AC; and AD, 10 Leagues more than the De∣parture from the Meridian BC.

First, with the double of ei∣ther Number, which here I take, the double of EB 20, w^ch is 40 Leagu. and lay from F unto G; then I take the other Number AD 10, and add it thereunto, as GH. Now on the midst of FH, as at K, making it the Cen∣ter, I describe the Semicircle HIF: Then on G erect the Perpendicular which cuts the Yrch in I; then measuring

GI, it will be equal to DE 20 Leagues, which added to the two former Numbers 20 and 10, you have in all 50 Leagues for the Distance sailed, required.* 1.13

Anabically: 2 AD:X:EB = DEq 400, whose V q is 20, 〈 math 〉〈 math 〉 (20 the Root.

QUEST. III. Two Ships Sail from one Port; The first Ship Sails directly South, the second Ship Sails W. S. W. more than the first by 35 Leagues, and then were asunder 76 Leagues; The Question is, How ma∣ny Leagues each Ship Sailed.

FIrst draw the Meridian-line AB, and from A draw a W. S. W. Course as AC continued, and from C lay down the 35 Leagues unto D. Now draw the Chord-line of 6 Points, as BC; then take 76 Leagues, and lay it from D to cut the Chord-line in E. Lastly, from E you must draw a Parallel Meridian, which will cut the Rhomb-line in F; so measuring EF, you shall have 45 68/100 Leagues, that the first Ship sailed directly South: So the second Ship sailed 35 Leagues more, therefore must Sail in all 80 68/100 Leagues, which is the Distance required.

[illustration] geometrical diagram

By the Artificial Tables of Sines and Numbers.

As the Side ED	76 Leagues co: ar.	811919
To the Sine of the Angle ECD 56 deg. 15 min	991985
So is the Side CD	35 Leagues	154407
To the Sine of the Angle CED 22 deg. 31 min.	958311

which substract from 56 deg: 15 min. you have the Angle at D 33 deg. 44 min.

Then,

As the Sine of the Angle at F 67 deg. 30 min. co. ar.	003438
Is to his opposite Side	ED 76 Leagues add	188081
So the Sine of the Angle at D 33 deg. 45 min. add	974455
To his opposite Side	FE 45 ••8/100 Leagues	165974

So the South Ship Sailed 45 68/100 Leagues; and the other W. S. W. 80 68/100 Leagues.

QUEST. IV. Two Ships Sailed from one Port: The first Sails S. S. W. a certain Distance; then altering her Course, she Sails due West 92 Leagues: The second Ship Sailing 120 Leagues, meets with the first Ship. I demand the second Ship's Course and Rhomb, and how many Leagues the first Ship Sailed S. S. W.

DRaw the first Ship's Rhomb from A unto E, being S. S. W. then lay her Distance sailed West 92 Leagues from A unto C, and from C draw a S. S. W. Course, as CD continued: Next take 120 Leagues, and lay it from A, so that it shall cut the continued Line in D: so drawing AD, you shall have the second Ship's Rhomb, near W. S. W. Lastly, measuring CD equal to AB, you shall find it to be 49 ½ Leagues that the first Ship sailed S. S. W.

[illustration] geometrical diagram

For the Course,

As the Side AD	120 Leagues,	co: ar.	792082
Is to the Sine of the Angle at B 67 deg. 30 min.	996562
So is the Sine of the Side BD 92 Leagues	196379
To the Sine of the Angle BAD 45 deg. 6 min.	985023

Unto which add the Angle FAB 22 deg. 30 min. you have the second Ship's Rhomb 67 deg. 36 min. being near W. S. W. whose Complement is the Angle ADB 22 deg. 24 min.

For the Distance,

As the Angle	BAD 45 deg. 6 min. co. ar.	014976
Is to the Side	BD 92 Leagues	196379
So is the Angle	ABD 22 deg. 24 min.	958101
To the Side AB 49 5/10 Leagues required	169456

QUEST. V. Two Ships Sail from one Port 7 Points asunder: The one Sails in the S. W. Quadrant, and departs from the Meridian 57 Leagues; and the other Sailed in the S. E. Quadrant, and was departed from the Meridian but 25 Leagues, and then are both fallen into one Latitude; I demand the Rhomb or Courses of each Ship.

FIrst draw an East and West Line continued; and making choice of a Point at D, upon D erect a Perpendicular, which will be a Meridian-line, as DA continued. Now from D lay down the West Ship's Departure DB 57 Leagues; also the East Ships Departure 25 Leagues DC: so their whole Distance will be CB 82 Leagues. Now upon the Point at B, or else as here at C, draw an Angle of the Complement of 7 Points, or one Point, which is W. b. N. as CF the prickt Line; but if their Courses had been more than 8 Points, then you must lay it to the Southward of the West Line.

[illustration] geometrical diagram

Now from the midst between B and C, at E, draw another Meridian-line, until it cut the former Rhomb-line CF in the Point G: So taking the Distance from the Point G unto C, lay the same from G until it cut the Meridian-line in the Point A, which is the Place and Port you Sailed from.* 1.14 Lastly, From A you shall draw their Rhombs or Courses, as AB, which is 4 ½ from H to N from the South, Westwards; and the Eastward Ships Course is AC 2 ½ Point from P to N, from the South, Eastward.

As the Sum of their Departures CB 82 Leagues	191381
To the Difference of their Departure SB 52 Leagues	150515
So is the Sine of the Sum of their Courses CAB 78 deg. 45 min.	999080
To the Sine of the Difference of their Courses, Sum	1149595
SAB 22 deg. 30 min. the Sum	958214

Now 22 deg. 30 min. added to 78 deg. 45 min. the half is 50 deg. 37 min. ½; that is 4 Points ½ or S. W. ½ W. for the one Ships Course Sailed from A to B: and 22 deg. 30 min. substracted from 78 deg. 45 min. the half is 28 deg. 07 min. ½; that is, 2 Points and ½ S. S. E. ½ a Point Easterly, for the other Ship's Course.

QUEST. VI. From the Port at A I Sail S. S. W. unto B, and from B I Sail N. W. b. W. unto C, and from C I Sailed unto my first Port at A, E. b. N. Now having Sailed in all 120 Leagues, I would know how many Leagues I have Sailed upon each Point.

FIrst draw AB a S. S. VV. Course, at any convenient distance; then from B draw a N. VV b. VV. Course, and from A draw the opposite Course of E. b. N. which is VVest by South, which will cut BC in C; so continue the Sides of the Tri∣angle AB unto E, and AC unto F. Then lay BC from B unto D, and AC from D unto E. Then take 120 Leagues, and lay the same from A unto F: Next draw the Line EF, and from D and B draw Parallels thereunto, which will cut AF in G and H. Lastly, measuring AH, you shall have 33 ⅔ Leagues that you have Sailed S. S. VV. And measuring HG, you shall have 39 Leagues 6/10 parts that you have Sailed N. VV. b. VV. Also measuring GF, you shall have 46 ¾ Leagues near, that you have Sailed E. b. N. which makes in all near 120 Leagues.

[illustration] geometrical diagram

Arithmetically, By the Table of Natural Sines in the Sea-mans Kalendar.

First, Add up all the Sines of the Angles together, Which is

deg.	min.
45	00	7071
56	15	8314
78	45	9790
		25175

Then by the Rule of Three,

As 25194, to 120 Leagues: So	45	00	To the Distan∣ces sailed	S. S. W. 33 68/106 AB.
56	15	N. W. b. W. 39 60/100 Leag.
78	45	E. b. N. 46 72/100 CA.

I might have added several other Questions of this nature, but I hold these sufficient; for those that understand how these are done, may do any of the like nature: But the way of demonstrating and laying of them down, as you see in the Figures, I ne∣ver saw before of any other Mans Work. Therefore now we will come to the true way of Sailing, and Use of the true Sea-Chart.

CHAP. VII. The Disagreement betwixt the Ordinary Sea-Chart, and the Globe; And the Agreement betwixt the Globe and the True Sea-Chart, made after Mercator's Way, or Mr. Edward Wright's Projection.

THe Meridians in the ordinary Sea-Chart are Right Lines, all parallel one to another, and consequently do never meet; yet they cut the Aequinoctial, and all Circles of Latitude, or Parallels thereunto, at Right Angles, as in the Terrestrial Globe: But herein it differeth from the Globe, for that here all the Parallels to the Aequinoctial being lesser Circles, are made equal to the Aequinoctial it self, being a great Circle; and consequently, the Degrees of those Parallels, or lesser Circles, are equal to the Degrees of the Aequinoctial, or any other great Circle, which is meerly false, and contrary to the nature of the Globe, as shall be plainly demon∣strated.

The Meridians in the Terrestrial Globe do all meet in the Poles of the World, cut∣ting the Aequinoctial, and consequently all Circles of Latitude, or Parallels to the Aequator, at right Spherical Angles: so that all such Parallels do grow lesser to∣ward either Pole, decreasing from the Aequinoctial Line.

As for Example, 360 Degrees, or the whole Circle in the Parallel of 60 Degrees, is but 180 Degrees of the Aequinoctial; and so of the rest: Whereas in the ordina∣ry Chart, that Parallel and all others are made equal one to another, and to the Aequinoctial Circle, as we have said before.

The Meridians in a Map of Mercator or Mr. Wright's Projection, are Right Lines, all Parallel one to another, and cross the Aequinoctial, and all Circles of La∣titude, at Right Angles, as in the ordinary Sea-Chart: But in this, though the Cir∣cles of Latitude are all equal to the Aequinoctial, and one to another, both wholly, and in their Parts and Degrees; yet they keep the same proportion one to the other, and to the Meridian it self, by reason of the inlarging thereof, as the same Parallels in the Globe do. Wherein it differeth from the ordinary Sea-Chart, for in that the Degrees of great and lesser Circles of Latitude are equal; and in this, though the Degrees of the Circles of Latitude are equal, yet are the Degrees of the Meridian un∣equal, being inlarged from the Aequinoctial towards either Pole, to retain the same proportion as they do in the Globe it self; for as two Degrees of the Parallel of 60 Degrees, is but one Degree of the Aequinoctial, or any Great Circle upon the Globe, so here two Degrees of the Aequinoctial, or of any Circle of Latitude, is but equal to one Degree of the Meridian, betwixt the Parallel of 59 ½ and 60 ½ and so forth of the rest.

Now for the making of this Table of Latitudes, or Meridional Parts, it is by an addition of Secants; for the Parallels of Latitude are less than the Aequator or Me∣ridian,* 1.15 in such proportion as the Radius is to the Secant of the Parallel.

For Example. The Parallel of 60 Degrees is less than the Aequator; and con∣sequently, each Degree of this Parallel of 60 Degrees is less than a Degree of the Aequator or Meridian, in such proportion as 100000 Radius, hath to 200000 the Secant of 60 Degrees.

Now how Mr. Gunter and Mr. Norwood's Tables are made, which are true Meridi∣onal Parts, is by the help of Mr. Edward Wright's Tables of Latitude. Mr. Gunter's is an Abridgment, consisting of the Quotient of every sixth Number, divided by 6, and two Figures cut off.

As for Example. In the Tables of Latitude for 40 Degrees, the Number is 〈 math 〉〈 math 〉

deg.	parts.
(43:	712

That divided by 6, the Quotient is 43 deg. 712 parts of the Aequator, to make 40 Degrees of the Meridian. And Mr. Norwood's Tables of Meridional parts, is an Abridgment of Mr. Wright's Table of Latitudes; namely,

every sixth Number cutting off four Figures to the right hand, as for 40 Degrees: as before the Number is 2622/7559 in regard it wants but a little of ••••000 cut off, we make the Meridional parts 2623, as you will find by his Table. So this Table sheweth how many Parts every Degree, and every Tenth part of a Degree of Latitude in this Chart, is from the Aequinoctial; namely, of such Parts, as a Degree of the Aequator containeth 60. And this which I here exhibit, and call a Table of Meridional Parts, is also an Abridgment of the Table of Latitudes of Mr. Wright's, namely, the first Numbers, omitting al∣ways the three last Figures.

As for Example▪ All the Numbers are for 40 deg. 26. 227. 559; omit the three last, and divide the rest by 3, and in the Quotient is 8742, the Meridional parts for 40 Degrees; and so of the rest: So that this Table sheweth how many Parts every Degree, and every Tenth part of a League, and every Tenth Minute of Lati∣tude in this Chart. is from the Aequinoctial to the Poles; namely, of such Parts as a Degree of the Aequinoctial contains 20 Leagues. This is large enough for our Uses at Sea, and as ready, being in Leagues, by cutting off the last Figure, which is a Tenth: For I could never see any Draught or Plat made according to Mr. Wright's Projection, excepting his own in his Book, that is divided into more Parts than 6; for all the Mercator's or Dutch Charts as I have ••een, are divided into 6 times 10, which is 60 Minutes: But he that desires a larger Table, may make use of Mr. Wright's Tables of Latitudes.

The Use of this Table shall partly appear in the Problems following, and may be illustrated after this manner.

PROBLEM I. How to find by the following Tables what Meridional Parts are con∣tained in any Difference of Latitude.

YOu must take the Meridional Parts answering to each Latitude, and substract the lesser from the greater; so the Remainer is the Number of Meridional parts contained in the Difference of Latitude proposed.

As, Let one Latitude be 51 deg. 20 min.	12002	Meridional Parts.
And the other Latitude be 13 deg. 10 min.	2657
	9345

The Meridional Parts contained in the Difference of Latitude are 934 5/10 Leag.

The Degrees are over the Parts, and the Minutes are on each side under the De∣grees; and in the Common Angle of Meeting or Line with the Minutes, is the Me∣ridional Parts you desire.

PROBL. II. The Latitudes of two Places being given, and Difference of Longi∣tude of both Places, To find the Rhomb and Distance.

TO the intent the Application may be the more evident, our Examples shall be of two Places before-expressed on the Plain Chart.* 1.16

Suppose the Latitude of the Island of Lundy in the Mouth of Seavern, to be at A, 51 deg. 22 min. and the Latitude of Barbadoes 13 deg. 10 min. at B, and the Diffe∣rence of Longitude 52 deg. 55 min. CD, that the Barbadoes is to the VVestward of the Island of Lundy; The Course and Distance from the one Place to the other is de∣manded.* 1.17

First you may demonstrate the Question by the Scale. Draw the Right Line AC for the Meridian; and in regard the Difference of Latitude is 38 deg. 12 min. con∣vert them into Leagues, by multiplying them by 20, the Number that goes to a De∣gree,

[illustration] geometrical diagram

and the odd Minutes divide by 3, and the Difference in Leagues will be 764; which lay from A to B,* 1.18 for the Common Difference of Latitude. Then take the Diffe∣rence of the two Latitudes inlarged, 934 5/10 Leagues, and lay from A to C; then draw the two Parallel Lines, as BE and CD. Then 52 deg. 55 min. the Difference of Lon∣gitude, converted into Leagues, as before-directed, is 1058 ••/3, which lay from C to D, and draw the Line AD, which is the true Course from A to D, and the Distance according to the True Chart inlarged: Therefore AE is the true Rhomb-line and Di∣stance found out, produced by the former Work. And as D is the true Point by Mercator's Chart of Barbadoes, so is E the true Point of the same Place of Barbadoes by the Plain Chart; and AE the true Distance, BAE the true Course. And as CD is the true Longitude by the Globe, so is BE the true Meridian-distance between Lun∣dy and Barbadoes.* 1.19 You may work afterwards by the Rules of the Plain Chart; and you need not work Mercator's way any more, without you have a Mercator's True Chart; and to work by that, you shall be directed in the following Discourse. There∣fore to work by the Plain Rules all the Voyage after, measure AE, and you will have 1157 Leagues for the Distance; and for the Course take GH, and apply it to the Points on the Scale, and you will find the true Course S. VV. a little more than a Quarter VVesterly, which is all one Course with the True Sea-Chart; but the Di∣stance inlarged is 1408 Leagues AD. Now by the Plain Sea-Chart the Course is BAF, S. W. above ¾ of a Point VVesterly; and the Distance is AF 1306 Leagues: So that the Plain Chart sheweth the Distance more than it is by 149 Leagues, and the Course more VVesterly by half a Point, and the Meridian-distance too much by 194 Leagues, which is a gross Error; and in such Distances grosly are these Men mistaken, that use a Plain Chart.

A Table of Meridional Parts to the 10 part of a League, and for every 10 Mi∣nutes of Latitude from the Aequinoctial to the Poles.

Minutes.	DEGREES.	Minutes.
0	1	2	3	4	5	6	7	8	9
Le. 1/10	Le. 1/10	Le. 1/10	Le. 1/10	Le.1/10	Le. 1/10	Le. 1/10	Le. 1/10	Le. 1/10	Le. 1/10
0	00	200	400	600	801	1001	1202	1403	1605	1807	0
10	33	233	433	634	834	1035	1236	1437	1639	1841	10
20	67	267	467	667	867	1068	1269	1471	1673	1875	20
30	100	300	500	700	901	1102	1303	1504	1706	1909	30
40	133	333	534	734	934	1135	1336	1538	1740	1943	40
50	167	367	567	767	968	1109	1370	1571	1774	1976	50
M.	10	11	12	13	14	15	16	17	18	19	M.
0	2010	2214	2418	2623	2828	3035	3242	3451	3661	3827	0
10	2044	2248	2452	2657	2863	3069	3277	3486	3696	3907	10
20	2078	2282	2486	2691	2897	3104	3312	3521	3731	3942	20
30	2112	2316	2520	2725	2931	3138	3347	3556	3766	3977	30
40	2164	2350	2554	2760	2966	3173	3381	3591	3801	4013	40
50	2180	2384	2588	2794	3000	3208	3416	3626	3836	4048	50
M.	20	21	22	23	24	25	26	27	28	29	M.
0	4084	4297	4512	4729	4947	5167	5388	5612	5837	6065	0
10	4119	4333	4548	4765	4983	5203	5425	5648	5875	6103	10
20	4155	4369	4584	4801	5020	5240	5462	5686	5913	6141	20
30	4196	4405	4620	4838	5056	5277	5500	5724	5951	6179	30
40	4226	4440	4656	4874	5090	5314	5537	5761	5989	6218	40
50	4262	4476	4692	4910	5130	5351	5574	5799	6027	6256	50
M.	30	31	32	33	34	35	36	37	38	39	M.
0	6294	6527	6761	6998	7238	7481	7726	7975	8277	8483	0
10	6333	6565	6800	7038	7278	7521	7768	8017	8270	8526	10
20	6371	6604	6840	7078	7319	7562	7809	8059	8312	8569	20
30	6410	6644	6879	7118	7359	7603	7850	8101	8355	8612	30
40	6449	6683	6919	7158	7400	7644	7892	8143	8397	8655	40
50	6488	6722	6938	7198	7440	7685	7934	8185	8440	8699	50
M.	40	41	42	43	44	45	46	47	48	49	M.
0	8742	9005	9272	9543	9819	10100	10385	10675	10971	11273	0
10	8786	9049	9317	9589	9865	10147	10433	10724	11021	11324	10
20	8829	9093	9362	9635	9912	10194	10481	10773	11071	11375	20
30	8873	9138	9407	9681	9959	10241	10530	10823	11121	11426	30
40	8917	9182	9452	9727	10005	10289	10578	10872	11172	11478	40
50	8961	9227	9498	9773	10052	10337	10626	10922	11222	11529	50
M.	50	51	52	53	54	55	56	57	58	59	M.
0	11581	11896	12217	12545	12881	13226	13581	13941	14313	14696	0
10	11633	11949	12271	12600	12938	13284	13640	14004	14377	14761	10
20	11685	12002	12325	12656	12995	13342	13700	14063	14440	14826	20
30	11737	12055	12380	12712	13052	13401	13759	14121	14504	14892	30
40	11790	12109	12435	12768	13110	13460	13820	14188	14568	14958	40
50	11842	12163	12490	12825	13168	13520	13881	14251	14632	15024	50
M	60	61	62	63	64	65	66	67	68	69	M.
0	15091	15497	15917	16350	16798	17263	17745	18246	18769	19315	0
10	15158	15586	15988	16423	16874	17342	17827	18332	18858	19408	10
20	15225	15635	16059	16497	16951	17421	17920	18448	18948	19502	20
30	15293	15705	16131	16572	17028	17501	17993	18505	19035	19597	30
40	15300	15775	16204	16647	17106	17582	18077	18592	19130	19693	40
50	15428	15846	16277	16722	17184	17662	18161	18680	19222	19789	50
M.	70	71	72	73	74	75	76	77	78	79	M
0	19886	20485	21116	21781	22485	23234	24033	24890	25815	26819	0
10	19984	20588	21224	21896	22607	23368	24172	25039	25976	26995	10
20	20083	20692	21333	22011	22730	23495	24312	25190	26140	27173	20
30	20183	20796	21444	22128	22854	23628	24455	25344	26306	27354	30
40	20283	20901	21555	22246	23979	23762	24598	25499	26474	27530	40
50	20384	21008	21668	22365	23106	23897	24743	25656	26645	27727	50
M.	80	81	82	83	84	85	86	87	88	89	M
0	27917	29130	30484	32019	33789	35881	38441	41740	46387	54331	0
10	28110	29345	30726	32296	34112	36270	38929	42395	47385	56420	10
20	28307	29564	30974	32579	34445	36673	39439	43090	48477	58977	20
30	28507	29787	31226	32870	34788	37096	39973	43830	49684	62274	30
40	28711	30015	31484	33168	35141	37523	40532	44621	51034	66920	40
50	28919	30247	31748	33474	35505	37973	41120	45970	52564	74863	50

By the Tables.

ADmit a Ship is at A, in Latitude 51 deg. 22 min. North, as is Lundy, and sails, or is to sail to E, in Latitude 13 deg. 10 min. according to the Plain Chart corrected, which is Barbadoes; or by Mercator's Chart, Barbadoes is in the Point D, and the Difference of Longitude is 1058 Leagues, which is 52 deg. 55 min.. First find the Difference of Latitude inlarged, as is before-directed in the first Problem, and found to be 934 5/10 Leagues.

Now you have given AB the Difference of Latitude 38 deg. 12 min. inlarged from B to C, and CD the Difference of Longitude 52 deg. 55 min. whereby the Angles and Hypothenusal shall be found by the Fourth and Fifth Case of Plain Triangles.

But because in this kind of Projection, the Degrees of Longitude and Latitude are not equal (except in Places near the Aequinoctial) the Degrees of Latitude at every Parallel, exceeding the Degrees of Longitude, in such proportion as the Aequinoctial exceeds that Parallel; therefore these Differences of Longitude and Latitude must be expressed by some one common measure; and for that purpose serves the foregoing Table, which sheweth how many Equal Parts are from the Aequinoctial, in every Degree of Latitude, to the Poles; namely, of such Equal Parts as a Degree of Lon∣gitude contains 20 Leagues.

Wherefore, as before-directed, multiplying 52 deg. by 20, and dividing the odd Minutes, being 55, by 3, it will be 18 ⅓ Leagues; added to the former Sum, makes 1058 ⅓ Leagues, for the Meridional parts contained in the Difference of Longitude. Also by the last Problem, I find the Meridional parts contained in the Difference of Latitude to be 934 5/10 Leagues: So that AC is 934 5/10 Parts, and CD 1058 ⅓ of such Parts.

Therefore, By the Second Case of Plain Triangles.

As the Difference of Latitude inlarged AC is 934 5/10 parts	297057
Is in proportion to the Radius 90 deg.	10
So is the Difference of Longitude in such Parts CD 1058 ⅓	1302448
To the Tangent of the Rhomb at A 48 deg. 33 min.	1005391

Extend the Compasses from 934 5/10 Leagues the inlarged Latitude, to 1058 ⅓ Leagues; the same Distance will reach from the Radius to the Tangent of the Course 48 deg. 33 min. which is the Course from Lundy to Barbadoes, S. W. a little above a quarter of a Point Westerly.

By the Fifth Case of Plain Triangles.

As the Sine-Complement of the Rhomb at D 41 deg. 27 min.	982083
To the Difference of Latitude AB 764 Leagues	288309
So is the Radius o 90 deg.	10
To the Distance AE 1154 2/10 Leagues	306226

Extend the Compasses from the Complement-Sine of the Rhomb 41 deg. 27 min. to the Sine of 90 deg. the same Extent will reach from the true Difference of Latitude 764 Leagues, to the Distance AE 1157 Leagues, which is required.

PROBL. III. The Latitude of two Places, and their Distance given; To find the true Course and Point, or Place you are in, by Mercator's Chart.

ADmit I sail from the Island of Lundy, in the Latitude 51 deg. 22 min. in the Southwest Quarter of the Compass, 1154 2/10 Leagues; and then find my self in the Latitude of 13 deg. 10 min. I would know what Point of the Compass I have sailed upon, and my Difference of Longitude to the Westward.

The Difference of Latitude AB is 38 deg. 12 min. which reduced into Leagues is 764 Leagues.

As the Distance sailed 1154 2/10 Leagues AE	306226
Is in proportion to the Radius 90 deg.	10
So is the true Difference of Latitude 764 Leagues AB	288309
To the Sine-Complement of the Rhomb 41 deg. 27 min. at D	982083

that is, S. W. ¼ W. or Southwest 3 deg. 33 min. Westerly, the Course that the Ship hath sailed upon.

Extend the Compasses from 1154 Leagues the Distance, to the Sine of 90; the same Distance will reach from the Difference of Latitude 764 Leagues, to 41 deg. 27 min. the Co-sine of the Rhomb: The Sine is 48 deg. 33 min. that is, 4 Points and above a Quarter from the South Westward from the Meridian.

Secondly, For the Difference of Longitude.

Find by the First Problem the Difference of Latitude inlarged, as is there dire∣cted, 934 5/10 Leagues: Then it is,

As the Radius 90 deg.	10
To the Difference of Latitude in Parts 934 5/10 AC	297057 Inlarged.
So is the Tangent of the Rhomb 48 deg. 33 min. A	1005395
To the Difference of Longitude in Parts 1058 Leagues	302452

Extend the Compasses from the Sine of 90 deg. to the Difference of Latitude inlar∣ged 934 5/10 Leagues; the same Extent will reach from the Tangent of the Course 48 deg. 33 min. to 1058 Leagues: which laid off from C to D, shall be the Point or Place in Mercator's Chart where the Ship is.

Or, 1058 Leagues ⅓ converted into Degrees, by dividing by 20, the Quotient is 52 deg. 55 min. the Difference of Longitude required.

PROBL. IV. Sailing 1154 Leagues upon the 4 ¼ Rhomb from the Meridian, or 48 deg. 33 min. from the South Westerly, I demand the Departure from the Meridian.

As the Radius 90 deg.	10
To the Distance sailed 1154 Leagues AE	306226
So is the Sine of the Rhomb 48 deg. 33 min. at A	987479
To the Departure from the first Meridian 865 Leagues	293705

Extend the Compasses from the Sine of 90 deg. to 48 deg. 33 min. the same Extent will reach from the Distance sailed 1154, to the Meridian Departure 865 Leagues,

BE is the true Meridian Distance, which you may set in the Head of your Journal, to substract your Daily Distance from your first Meridian,

PROBL. V. Both Latitudes and the Meridian Distance of two Places being given, To find the Difference of Longitude, and Course and Distance on the True Sea-Chart.

THis is a most useful Problem, when the Mariner hath cast up his Traverse: Sup∣pose a Ship sail upon the S. W. Quarter of the Compass, from Latitude 51 deg. 22 min. unto Latitude 13 deg. 10 min. and the Departure from the first Meridian to the Westward 865 Leagues.

You must find first the Difference of Latitude inlarged, as is before-directed in the first Problem 934 5/10.

As the true Difference of Latitude AB 764 Leagues	288309
Is to the Meridian-distance or Departure BE 865 Leagues	293701
So is the Difference of Latitude inlarged AC 934 5/10 Leagues	297057
To the Difference of Longitude in Leagues 1058 CD	590758
	302449

By the Line of Numbers.

EXtend the Compasses from AB the true Difference of Latitude 764 Leagues, to BE 865 Leagues Meridian-distance; the same Extent will reach from AC. 934 5/10 Leagues the Difference of Latitude inlarged, to the Difference of Longitude 1058 Leagues; which laid off upon the Parallel-Line from C to D, is the Point and Place of the Ship in Mr. Wright's or Mercator's Chart.

As the true Difference of Latitude 764 Leagues AB	288309
Is to the Meridian-distance 865 Leagues BE	1293701
So is the Radius 90 deg.	10,
To the Tangent of the Course 48 deg. 33 min. at A	1005392

By the Artificial Lines on the Scale.

EXtend the Compasses from AB 764 Leagues, to BE 865; the same Distance will reach from 90 deg. to the Tangent of 48 deg. 33 min. that is, 4 Points and above a Quarter from the South Westward, that is, S. W. ¼ Westerly, the Course the Ship hath kept.

As the Sine of the Course at A, 48 deg. 33 min.	987479
Is to the Radius 90 deg.	10
So is the Departure from the Meridian 865 Leagues	1293701
To the Distance sailed AE 1154 2/10 Leagues	306222

By the Scale.

EXtend the Compasses from the Sine of 48 deg. 33 min. at A, to the Sine of 90 deg. the same Extent will reach from 865 Leagues BE, to 1154 Leagues AE, the Distance sailed.

PROBL. VI. By the Difference of Longitude, and one Latitude, and the Course, To find the other Latitude and Distance run.

SUppose I sail from Lundy, in Latitude 51 deg. 22 min. North Latitude, S. W. 3 deg. 33 min. Westerly, until my Difference of Longitude be 52 deg. 55 min. that

is, from C to D, which is the Place of the Ship in Mercator's Chart; I demand how much I have laid the Pole, and how far I am from Lundy?

As the Tangent of the Rhomb 48 deg. 33 min.	1005395
To the Difference of Longitude CD 1058 Leagues	302448
So is the Radius	10
To the Difference of Latitude in Leagues 934 5/10. AC	297053

By the Artificial Lines on the Scale.

EXtend the Compasses from 48 deg. 33 min. to 1058 in the Line of Numbers; the same Extent will reach from 90 deg. to 934 5/10 Leagues.

Or, Extend the Compasses from 48 deg. 33 min. to 90 deg. the same Distance will reach from 1058 Leagues, to AC 934 5/10 Leagues, as before.

Now the Meridional parts answering the Latitude of 51 deg. 20 min. is 12002;* 1.20 from it substract 934 5/10 here found, and there remains 2657, which Number I look for in the Table, and find it under 13 deg. and in the Line of 10 min. which is the Latitude of the second Place where the Ship is; and the Difference of Latitude is 38 deg. 12 min.

The Distance may be found as before, in the second and fifth Problems.

PROBL. VII. By the Course and Distance, and one Latitude, To find the other La∣titude, and Difference of Longitude.

SUppose I sail S. W. 3 deg. 33 min. Westerly, 1157 Leagues, and by observation find my self in the Latitude of 13 deg. 10 min. I require the Latitude of the Place from whence I came, and the Difference of Longitude between the two Places.

For the Difference of Latitude,

As the Radius B 90 deg.	1000000
To the Distance sailed 1154 Leagues AE	306222
So is the Sine-Complement of the Course E, 41 deg. 27 min.	982083
To the D fference of Latitude 764 Leagues	288315

Extend the Compasses from the Sine of 90 deg. to 1154 Leagues; the same will reach from the Sine of 41 deg. 27 min. to 764 Leagues, which converted into Degrees, is 38 deg. 12 min. the Difference of Latitude; which added to 13 deg. 12 min. the Latitude of the last Place, the Total is 51 deg. 22 min. the Latitude of the first Place required.

The Difference of Longitude is found as before in the third Problem, saying,

As the Radius, To the Difference of Latitude inlarged 934 5/10:

So is the Tangent of 48 d. 33 m. To the Difference of Longitude in Leagues 1058, which is 52 deg. 55 min.

Now to convert the Difference of Longitude found in any Latitude into Leagues, do it after this Example.

Suppose two Places in one Parallel of Latitude, as in the Parallel of 51 deg. 22 min. whose Difference of Longitude is 52 deg. 55 min. I require the Distance of those two Places.

As the Radius	10
Is in proportion to the Compl. Sine of the Latitude 51 d. 22 m.	979573
So is the Difference of Longitude 1058 Leagues	302448
To the Distance in that Latitude 661 Leagues	282092

You must understand, That the Leagues of Longitude in any Parallel of Latitude, are in proportion to the Distance in Leagues, as the Aequinoctial is to that Parallel; or, as the Semidiameter of the one, is to the Semidiameter of the other, as was said in the Seventh Chapter.

CHAP. VIII. How to divide a Particular Sea-Chart, according to Mercator and Mr. Wright's Projection.

* 1.21IF it be a Particular Chart you would make, you must first consider the two L••titudes you would make the Chart for; and out of the foregoing Table of Meridional parts, take the Numbers answering to each Latitude, and substract the lesser out of the greater, and the Remain is the Numbers which you must take for the extreme Parallel of Latitude.

Deg. Min.	Parts. Merid.	Differ.	Parts. Equal
30	13401		1975
20	13342	59	1921
10	13284	58	1863
55 00	13226	58	1805
50	13168	58	1747
40	13110	58	1689
30	13052	58	1631
20	12995	57	1573
10	12938	57	1516
54 00	12882	57	1459
50	12825	57	1402
40	12768	57	1345
30	12712	56	1288
20	12656	56	1232
10	12600	56	1176
53 00	12545	55	1120
50	12490	55	1065
40	12435	55	1010
30	12380	55	955
20	12325	55	900
10	12271	54	846
52 00	12217	54	792
50	12163	54	738
40	12109	54	684
30	12055	54	630
20	12002	53	576
10	11949	53	523
51 00	11896	53	470
50	11843	53	417
40	11790	53	364
30	11737	53	311
20	11685	52	258
10	11633	52	206
50 00	11581	52	154
50	11539	52	102
40	11479	52	51
30	11426	51

As for Example, I would make a Blank Merca∣tor's Chart from the Latitude of 49 deg. 30 min. to 55 deg. 30 min. and for 10 Degrees of Longitude.* 1.22 Look in the Table of Meridional Parts, and for the Latitude of 49 deg. 30 min. you will find the Number answer∣ing thereunto is 11426, and the Numbers for the Lati∣tude of 55 deg. 30 min. is 13401; the least substracted from the greater, the Remainer is 197:5 Equal Parts for the length of the Meridian-Line.* 1.23 Therefore first draw the Line AB, DC for the Meridian-Line, and cross it with two Perpendiculars, as BC and AD: Then di∣vide one of the Parallels of Latitude into 10 Equal parts, as AD, and subdivide each of those Degrees into 20 equal parts or Leagues that makes a Degree of Longitude and Latitude at the Aequator; and suppose each of these 20 Parts to be divided into 10 parts more, so will a Degree be divided into 200 parts: Then take with your Compasses 1975 Equal parts out of the Line AD, and lay from A to B, and from D to C, for the extreme Parallels of Latitude; and through each Degree of Longitude marked with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, draw Meridian-lines parallel to the first Meridian: Then out of the Table of Meridional parts collect the Numbers answering to every 10 Minutes of Latitude, as in the first Column of this Table annexed,* 1.24 the second Column is the Number answering the Minutes of La∣titude in the Table of Meridional parts, which substra∣cted the lesser from the greater, the Remain is the Dif∣ference, as in the third Column 51 deg. for the Diffe∣rence of the two lowermost Numbers: Then add the Numbers together in the fourth Column in this manner; 51 for the first 10 minutes, and 52 added to it, makes 102 for 50 Minutes; and 52 added to 102, makes 154 for the Number of Equal parts you must take out of the Line AD for 30 min. from A to 50 Deg. of Latitude,* 1.25 and lay it on both sides of the Chart, and draw the Parallels of 50 Degrees of Lati∣tude; and so do of the rest, as you see in this Table. And for 51 Degrees the Number is 470; take 470 and lay it upwards from A to 51 Degrees on both sides, and draw the Parallels of 51 Degrees of Lati∣tude; and so do with all the rest.

[illustration] geometrical diagram

A Particular Sea Chart

CHAP. IX. The Projection of the Meridian-Line by Geometry, and how to make a Scale of Leagues for to measure Distances in any Latitude.

THE Projection is the ground-work of Mr. Wright's Table of Latitudes, in his Book called, The Correction of Errors in Navigation, where he sheweth how to make it, and hath also made a Table by the continual addition of the Secants of every Minute, which shews how much you are to lengthen the De∣grees of Latitude in your Chart, that so there may be a true proportion between the

Degrees of Longitude and Latitude in all Places. Which Table I have abridged, and made it more plain and easie, by reducing it into Leagues and Tenth parts, as hath been shewed before. We will here shew you how to do the same by Geometry, and also how to make a Meridian-line answerable to any Line of Longitudes, and a Scale of 100 Leagues to measure any Distance in any Latitude.

First, Make the Quadrant ABC, of what largeness you please, and divide the Limb thereof into 90 Degrees, and number them from B towards C; Then divide the Side of the Quadrant into 5 Equal parts, which are five Degrees of the Aequi∣noctial. Then divide the first Degree from the Center, as AD, into 6 Equal parts, and through them draw Parallel-lines to AC: You may divide each of the other four Degrees from D to B into 20 Equal parts, which are 20 Leagues, which makes a De∣gree of Longitude at the Aequator; and so you may number them as you see, from 10 to 100: So the whole Line AB will be your Radius, and the length of 110 Leagues, or five Degrees and a half of Longitude of your Chart. And because the Degrees of Longitude are to be of one length in all Latitudes, therefore the Degrees of Lati∣tudes must encrease, as the Secants of the Latitudes increase. Therefore if you would know how long one Degree of Latitude must be in the Latitude of 50 Degrees, lay a Ruler on 50 Degrees, and on the Center A, and draw the Line AH. Now the Ra∣dius being AD, the length of one Degree of the Aequator, this Line A h, or h K,

[illustration] geometrical diagram

being both of one length, is the Secant of 50 Degrees to that Radius, and must be the length of one Degree of Latitude in a Chart from 50 Degrees to 51 Degrees, as you may presently try by the former Chart; and so the Line AC which is the Secant of 20 Degrees, is the length of one Degree of the Meridian-line in the Latitude of 20 Degrees; and so for any other Latitude. The six Lines divided in the first Degree AD, are 10 Minutes apiece; and so you have the Secant of every 10 Minutes of Latitude, and their length in every Latitude, for a particular Chart, and for a gene∣ral Chart, which hath in it North and South Latitude.

You may divide the Quadrant's Side AB into 10 Equal parts, and subdivide them into 10 more; so will D ♓ be 10 Degrees of the Aequator, and e ♑ will be

the length and Secant of 10 Degrees in the Latitude of 20 Degrees, and L ♈ the length and Secant of 10 Degrees in the Latitude of 60 Degrees, which is twice the length of one Degree of the Aequator: So that you may presently try the truth of this Proje∣ction, how it agrees with the Globe: Whereas one Degree of Latitude in the Globe, is equal to two Degrees of Longitude in that Latitude of 60 Degrees; so here AL the Secant of 60 Degrees, is twice the length of AD the measure of one Degree of Longitude in the Blank Chart; and L ♈ is twice the length of 10 Degrees D ♓: So every Degree is two of the Aequator in the Latitude of 60 Degrees of a general Chart; and by the Globe, in the Latitude of 75 deg. 30 min. one Degree of Latitude is equal to four Degrees of Longitude. So in the Quadrant, AR is four times the length of A D: and so the Proportion will hold in any other Latitude.

[illustration] geometrical diagram

A Scale of Leagues from the Latitude of 25 Degrees, to the Latitude of 57 Degrees 00 Minutes.

How to make the Scale of Leagues.

THE Quadrant being drawn, as before-directed, take 110 Leagues and lay from A to B, and draw the Line MNB at Right Angles thereunto: and if it be for a particular Chart, as that before-going, draw Lines from the Center through every particular Latitude; as you see in the Quadrant I have done, to make a Scale for the blank Chart before-going, from the Latitude of 49 deg. 30 min. to 55 deg. 30 min. So that if you would know the length of 110 Leagues in the Latitude of 50 Degrees, lay a Ruler upon 50 deg. in the Arch of the Quadrant and the Center, and draw the Line A ♌, and that is the length of 110 Leagues in that Latitude. So that if you draw Parallel-lines to MN, through every 10 Leagues in the Side AB, you will have the length of every 10 Leagues in every Latitude, as you may plainly see in the Quadrant: and so you may do for every League, as you see the little Checkers be∣twixt the Latitude of 20 deg. and 30 deg. for 10 Leagues between Latitude of 50 deg. and 56.

Suppose you would know the length of 40 Leagues in the Latitude of 50 deg. Extend the Compasses from A to K, and that Distance is 40 Leagues in that Latitude: And in like manner work by the rest in any other Latitude.

If you would make this into a Scale, as the Figure YM in N; First in the Qua∣drant extend your Compasses from the Center A, to the Intersections of the Lines drawn through every Degree MNB, and lay them down upon the Side of the extreme Latitude of your Chart, as A, O, P, Q, Y, M, with the small Arches, as you see I have done from M to NY, and that is the length of the Meridian-line of

your Scale or Degree of Latitude MY; therefore draw the Parallel-lines YN and M m for the extreme Parallels of your Scale: Then extend your Compasses from Y in the Quadrant, to each of the Intersections of these small Arches that are drawn from the Intersections on the Tangent-line MN; and from 25 deg. uppermost, lay that Extent downward for the Parallel of 55 deg. of Latitude, as the Line above the lowermost; and so lay down all your Latitudes by these small Arches, in like man∣ner; and so neatly divide the Side of your Scale MY of Deg. of Latitude: Then draw Parallel-lines to all these Degrees, as you see: Then extend the Compasses from the Center of the Quadrant to M, for the length of the lowermost Line of your Scale M m for 110 Leagues. Then extend the Compasses from the Center of the Quadrant to N, which is the length of 110 Leagues in the Latitude of 25 deg. and it is the Di∣stance of the uppermost Line YN of your Scale; and draw N m the outside of your Scale 120 Leagues: So take every 10 Leagues from the Center A, in the Line AM, in Latitude 56 Degrees, and divide the lowermost Line of the Scale; and the like do in the Latitude of 25, for to divide the uppermost Line of the Scale; and draw Lines through each of them, which will divide all the rest of the Parallel-lines in each Latitude into 10 Leagues apiece, and number them as you see I have done; and divide the first 10 Leagues by the Meridian-line of the Scale, into 10 Equal parts below and above, and draw Lines through each of the Divisions: So have you neatly divided your Scale, and every Degree of Latitude thereof, into Leagues, to 100 and 10 odd Leagues; which will measure any Distance in a Chart, made according to the Degrees of Latitude and Longitude in the foregoing Chart.

For to know the Rhomb between any two Places, shall be shewed in the Use of the general Sea-Chart following, by a Protracting Quadrant, and also how to find the Place of any Ship in Mercator's Chart, and to lay down any Traverses.

CHAP. X. The Way of Sailing by a Great Circle.

WE will now shew you the way of Sailing by the Arch of a Great Circle, which is the most true way of Sailing of all others, if a Man is sure to have Winds, that he may, keep neer the Arch that goes over any two Places propounded. But as there is a great deal of uncertainty in having a constant Wind by the Arch, so likewise the Trade-winds many times lye wide of this Arch many Leagues; besides many dangers of Rocks, and Sands, and great Currents, and danger of Pirates; which by keeping near the Arch may lead Men into many incon∣veniences; which may be a greater trouble to a Man, more than by sailing a few Leagues the more, for his best advantage and more security; besides the trouble in that way, of keeping of Accounts, which Men that watch every 4 Hours, cannot al∣low so much time every Noon, not will be perswaded to do it once in three or four Days, in regard Mercator's Char•• comes neer the very truth. Let the Wind, and Sea, and Currents, or Pirates, drive a Ship ever so far wide of the Arch, yet it is all line by that True Chart. If you keep a true Account of the Ship's way, allowing for Variation of the Compass, and Setting of Currents, and having of the Sea, you may at any time have the ••••ue Point where the Ship is, and how to shape a Course the most ready and convenient way to the Port you are bound to: Yet, I say, these Men that are perfect in this way of sailing, may see by their Mercator's Chart the dan∣gers that lie between any two Places, and shun them; and likewise make many Voy∣ages, where the Winds may favour them, sailing by the Arch, and no danger of Rocks or Sands to trouble them, which will prove a great advantage when your Course lies neer East and West; for sailing upon these two Points, Men trust altogether upon their Dead Reckoning (by the two former ways) but by this way you may hol•• your self,* 1.26 by altering your Latitude many Degrees, by which you may often recti••ie your Account.

For Example, Admit you were to sail from Avero on the Coast of Portugal, to the

Bay on the back side of Aquamacke neer Virginia,* 1.27 which lye both neer the Latitude of 40 Degrees; and suppose the Difference of Longitude between these two Places be 70 Degrees: The Distance of the two Places East and West is 53 deg. ½ and some∣thing more; but the Distance in the Arch of a Great Circle is but 52 deg. and a little more, that is, 1 deg. and about ½ less, which is but a little benefit to this, which is the chiefest, That in sailing between two such Places by the Arch of a Great Circle, you will in the first half of the way raise the Pole 5 deg. 41 min. and then in the other half depress the Pole as much; so that in the whole Voyage you will alter your Latitude 11 deg. 22 min. by several Courses; by which you may rectifie your Dead Reckoning, which you cannot do in sailing upon a Parallel of East and West; by which you see it is the best way of sailing, as well as the nearest, especially in such occasions, if the Wind favour you.

Now concerning this way of sailing, Mr. Edward Wright our Noble Countryman did first lay down a way, in his Book of Correction of Errors in Navigation, pag. 63, 64, and 65, by Geometry, which Captain Santanstal did comment upon in his Book called the Navigator, which was only of a Parallel Course; for any other way he said but little or nothing.

Mr. Norwood in his Book of Trigonometry hath added many Problems of sailing by the Arch of a Great Circle; for those that will or can, may by his pains find out all things in this way of sailing: But as they are difficult, and the way unknown to most Sea-men how to calculate; so they are tedious to those of the best skill: There∣fore I commend Mr. Philips his Tables, in his Book called The Advancement of Na∣vigation, and likewise his Plain Figures in his Book of the Geometrical Sea-man. I shall likewise by Geometry, and by Calculation, give you some satisfaction. Either way shall be done with speed, and as exactly as need be required.

The true Distance between two Places in the Arch of a Great Circle contained be∣twixt them, is thus to be found out.

If the two Places have no Latitude (being both under the Aequator, and one of them also no Longitude, the Longitude of the other being less or not more than 180 Degrees, the Longitude is the Distance.

But if the Longitude be greater than 180 Degrees, substract it out of 360 Degr. the Remainer is the Distance.

If two places be in one Meridian, and have the same Longitude both, and but one hath Latitude North or South, the Latitude is the Distance.

But if both Places agreeing in Longitude, have Latitude also of like denomination (that is, both Latitudes Northerly, or both Southerly) then substract the lesser out of the greater, the Remain is the Distance.* 1.28

But if both Places in one Meridian, have one Northerly Latitude, and the other Southerly Latitude, add them together, for the Sum is the Distance in Degrees.

CHAP. XI. How to find the true Distance of Places, one of them having no Latitude: The other having Latitude and Difference of Longitude less than 180 Degrees, To find

• 1 Their Distance in a Great Circle.
• 2 The Direct Position of the First Place from the Second.
• 3 And the Second Place from the First.

The First Scituation.

FIrst, If any two Places being proposed, the one under the Aequinoctial, the other may be in any other Latitude given, either North or South, and the Difference of Longitude of the Places being known; you may find the three things before spoken of in any Question, by the following Directions. We call the

Angle that the Rhomb leading from one Place to another, makes with the Meridians, the Position of these Places: But in regard the Arch of a Great Circle, drawn between two Places, is the most neer distance from the one Place to the other; therefore the Angles which that Arch makes with the Meridian of those Places, we call the An∣gles of Direct Position: or direct way of two Places one from the other.

* 1.29Now in the following Diagram, let A be the Entrance of the great River of Ama∣zones, under the Aequator; AQ the Arch of the Aequator, or Difference of Longi∣tude; and let C represent the Island of Lundy, lying in Latitude 51 deg. 22 min. Northerly, and CQ the Meridian thereof: and suppose the Difference of Longitude AQ to be 41 deg. 22 min.

[illustration] geometrical diagram

How to do these Questions Geographically.

FIrst, With an Arch of 60 Degrees describe the outward Meridian AEECQIF.

Secondly, Draw AEQ the Aequinoctial Line. Thirdly, Take 51 deg. 22 min. of the Line of Chords, and lay it from Q to C; and draw the Line CD through the Center, and the Line EF at Right Angles thereunto. Fourthly, Take off your Scale of ½ Tangents, counting from 90,-41 deg. 22 min. and lay from Q to A, for A re∣presents the River of Amazones. Now draw the Circle CAD through A, the Hori∣zon thereof is EF; then measure FK, and apply it to the Line of ½ Tangents, as before directed: and you will find the Angle of Direct Position to be 48 deg. 25 min. Take that Number out of your Line of ½ Tangents, from 1 Degree forwards towards 90, and lay it from H to L for the Pole, and draw a Line from L through A, it will cut the Line in I; so measuring CI on the Line of Chords, it will be 61 deg. 57 min. for the Distance, which is 1237 ⅓ Leagues and 3712 Miles.

By the Tables.

THen in this Triangle CAQ, Right-Angled at Q, there is required CA the nearest Distance of the two Places in the Arch of a Great Circle; and the Angle ACQ of Direct Position from the Island Lundy to the Amazones: and the Angle

CQO being the Complement of the Angle of the Direct Position of the Island of Lundy.

For the nearest Distance CA,

As Radius, is to Co-sine of Difference of Longitude 41 d. 22 m.	987534
So is Co-sine of the Latitude or Difference 51 deg. 22 min.	979699
To the Co-sine of the Distance 61 deg. 57 min.	967233

which 61 deg. 57 min. converted into Leagues, is 1237 ⅓ as before, the nearest Di∣stance between those two Places.

For the Angle of Direct Position from the Amazones toward Lundy, NAER,

As the Radius, to the Sine of the Differ. of Longitude 41 d. 22 m.	982011
So is the Co-tangent of Difference of Latitude 51 deg. 22 min.	990267
To the Co-tangent of the Angle of Position 27 d. 50 m. NAER	972278

For the Angle of Position ACQ,* 1.30

As Radius 90, is to Co-sine of Differ. of Lat. 51 d. 22 m. QC	989273
So is Co-tangent of Differ. of Longitude 41 deg. 22 m. AQ	1005522
To the Co-tang. of the Angle of Direct Position 48 d. 25 m. ACQ	994795

The same Proportions will hold by the Artificial Lines on the Scale.

And thus you see, he which will sail the nearest way from the Amazones to the Lizard, shall at first shape his Course 27 deg. 50 min. from the Meridian to the Eastward; that is, N. N. E. almost ½ a Point Easterly. Now if the Wind should serve that you might sail this Course, it is to be understood, that in this kind of sail∣ing he is not to continue this Course long; but to shift it, and incline more and more to the Eastward, as often as occasion requires: which how it may be done, shall be shewed in the following Discourse.

PROBL. II. How to find the Great Circle's greatest Latitude N. or S. or Obliquity.

NOte, Without the knowledge of the true Quantity of the Obliquity or Latitude of that Great Circle which will pass directly over the Places propounded, there can be no compleat Demonstration, much less Arithmetical Calculation of things per∣taining thereunto; therefore it is needfull that the true Quantity of each Great Cir∣cle's Obliquity be diligently found to exact certainty: which to do, in some Cases is very easie, and in some again more difficult. Therefore I will propound Rules for the several Scituations following, except those that are scituate under the Aequator, or under the same Meridian.

If one Place be under the Aequator and hath no Latitude, and the other hath any Quantity of Latitude, and the Difference of Longitude being less than 90 deg. as before 41 deg. 22 min. it is easily found, thus:

The greatest Obliquity in the foregoing Diagram is HRV,

As the Sine of the found Distance 61 deg. 57 min.	994573
Is to the Sine of the Latitude 51 deg. 22 min.	1989273
So is the Radius (added to the last Number) To the Sine of the greatest Obliquity 62 d. 16 m.	994700

So 62 deg. 16 min. is the greatest Obliquity or Latitude from the Aequator, of that Great Circle extended over those two Places.

But if the Difference of Longitude be 90 deg. as AEH, and one of the Places have no Latitude, and the other have any Quantity of Latitude; then it is evident to reason, as in the foregoing Diagram may appear, that the second Place is scituate in the very Point of the greatest Obliquity, which is never above 90 Degrees, as HN; and the other Place is in the very Point of Intersection of the said Great Circle with the Aequator: For note, That every Great Circle that passeth over any two Places propounded, cuts the Aequator in two opposite Points 180 deg. from each other, as the Ecliptick Line doth in the two Points of Aries and Libra; and the greatest Obli∣quity of that Circle is 23 deg. 30 min. the Sun's greatest Declination, and never any more.

Now if one Place have no Latitude 00 deg. 00 min. and the other have any Quantity of Latitude, the Difference of Longitude being more than 90 deg. to find the Obliquity of the Great Circle passing over those Places.

As admit one Place Latitude 00 deg. 00 min. and the other 51 deg. 22 min. Diffe∣rence of Longitude 138 deg. 38 min. Distance betwixt them is near 107 deg. There∣fore take the Distance 107 deg. out of 180, and there remains 73 deg. Then,

As the Sine of the Remainer 73 deg.	998251
Is to the Sine of the Latitude 51 deg. 22 min.	989273
So is Radius	10
To the Sine of the greatest Obliquity 54 deg. 25 min.	991022

So that 54 deg. 25 min. is the greatest Obliquity of the Great Circle extended over these two Places. And so you may work for any Questions of this nature.

The second Scituation.

SEcondly, There may be two Places scituated in divers Parallels of Latitude, be∣twixt the Artick and Antartick Poles, that may have one Degree and Minute of Latitude, yet may have several Degrees of Longitude.

[illustration] geometrical diagram

PROBL. III.

Admit there be two Places both in the Latitude of 51 deg. 22 min. and their Difference of Longitude be 52 deg. 55 min.

1. To find the nearest Distance of those two Places.

2. The Direct Position of the one Place from the other.

How to do these Questions Geographically.

TAke off the Line of Chords the Latitude of the Place 51 deg. 22 min. and lay from AE to X, and from Q to C; and take of the ½ Tangents the same Latitude, and lay from K to O; and through these three Points draw the Parallel of Latitude XOC; the Difference of Longitude laid from Q to L, draw the Meridian Circle NLS, the second Place is at R, and first at C the Meridian-circle cuts at R: Therefore draw the Circle from C through R to B, and measure HI on the ½ Tan∣gents, and you will find it 68 deg. 46 min. for the Angle of Direct Position HCI. Now from the ½ Tangents take 68 deg. 46 min. and lay it from the Center K to E, and from E draw through the Point of Intersection at R the prickt Line ERF; and because it cuts the Line in F, therefore measure CF on the Line of Chords, and you will find it 32 deg. 18 min. for the true Great Circles Distance, which is 646 Leagues, or 1938 Miles.

In the Seventh Problem of sailing by Mercator's Chart, yo may see there was re∣quired the Distance of these two Places measured in the Parallel, and found to be 660 5/10: but here is required the nearest Distance in the Arch of a Great Circle: Work thus by the Tables.

For the Distance,

As the Radius, Is to the Sine Comple of the Lat. 38 d. 38 m. RN	979541
So is the Sine of the Differ of Longitude 26 d. 27 m. RFN	964876
To the Sine of half the Distance 16 deg. 09 min. RF	944417

Which doubled is 32 deg. 18 min. and this converted into Leagues and Miles, as be∣fore, is 646 Leagues, and 1938 Miles, the nearest Distance, and less than the Di∣stance measured in a Parallel by Miles 42.

To find the Direct Position,

As Radius 90, Is to the Sine-Compl. of the Lat. 58 d. 38 m. RN	989273
So is the Tangent of ½ the Differ. of Longitude 260 d. 27 m. RNF	969678
To the Co-tangent of the Angle of Position 68 d. 46 m. NRF	958951

Which sheweth, that if you will go the nearest way from C to R, you must not go West, though both be under one Parallel; but must first shape your Course from C from North 68 deg. 46 min Westerly, that is almost W. N. W. and so by little and little inclining to W. b. N. and then W. and W. b. S. and almost W. S. W. as before.

How to find the Obliquity.

TWo Places having Latitude both the same, as 51 deg. 22 min. and towards the same Pole, whether North or South, and Difference of Longitude 52 deg. 55 min. or any number of Degrees under 90: If above 90, take it out of 180, and work with the Remainer the same manner of way.

PROBL. IV.

As Radius 90, To Co-tangent of the Latitudes 51 d. 22 m. RN	990267
So is the Co-sine of ½ the Differ of Longitude 26 d. 27 m. RNF	995197
To the Compl. Tan. of the greatest Obliquity 54 d. 25 m. NF	985464

So that the greatest Obliquity is 54 deg. 25 min. And the same Proportion will hold for any Question of this nature.

We might proceed to frame many Questions touching those two Places; but these being the most material, I leave the rest to your own Practice, to use as much brevity as I may. I might have shewn you the Side and Angles; but in regard they are Sphe∣rical I omit it, and shall demonstrate them at last in Plano: But you may follow these Rules, if you cannot apprehend the Diagram; but some may desire the Tri∣angle, therefore I lay it down.

[illustration] geometrical diagram

In this Triangle CRN, let the two Places be C and R, and let N be the North Pole; then CN or RN either of them are 38 deg. 38 min. the Complement of the Latitude and the Angle CNR is the Difference of Lon∣gitude: There is required CFR the nearest Distance, and the Direct Position of the one to the other, NCR or NRC; for in this Case those two Angles are equal: And seeing NC and NR are equal, therefore let fall the Perpendicular NF, the Triangle NCR is divided into two Right-angled Triangles CNF and RNF, which are every way equal.

The Third Scituation. One Place having North Latitude, and the other Place having South La∣titude, of different Quantities, and the Difference of their Longitudes less than 90. As I omit one Place having North Latitude, as Lundy, 51 deg. 22 min. the other South Latitude, as the Rio de la Plata, 35 deg. 00 min. Difference of Longitude betwixt them 45 deg. 55 min. I demand the Distance, the Angle of Position, and the greatest La∣titude or Obliquity of the Great Circle that passeth over these two Places.

AFter you have described the outward Meridian NESA, take from the Line of Chords the Latitude 51 deg. 22 min. and lay it from E to P, and draw the Line PCO and HCM at Right Angles to P, take off the half Tangent Line the Dif∣ference

[illustration] geometrical diagram

of Longitude 45 deg. 55 min. and lay it from E to F, and draw the Me∣ridian-Circle NFS, whereon lay the Latitude of Rio dela Plata 35 deg. from F to R, by taking 35 out of the Line of Chords, and laying it from E to 35, and the ½ Tangent of FE from C to Pole, and draw the prick'd Line Pole 35, which cuts the Circle NFS in R, the Rio dela Plata: and through R draw the Circle PRO, and measure MN on the half Tangents, you will find the Angle of Position to be RPE 36 deg. 2 min. Then take the half Tangent of 36 deg. 2 min. and lay from C to K, and draw the prick'd Line from K through R, and it will cut the Line at T; therefore measure TP on the Line of Chords, and that is the measure of RP 95 deg. 18 min. for the Distance, or 1906 Leagues, or 5718 Miles: The greatest Latitude or Obliquity is from AE to L; and VLW is the Parallel of 68 deg. 21 min. the greatest Obliquity required,

PROBL. V.

Then by the Tables,

As Radius, To the Co-sine of Differ. of Longitude 45 d. 55 m.	984242
So is the Co-tangent of the greater Latitude 51 deg. 22 min.	990267
To the Tangent of the first Arch 29 deg. 5 min.	974509

The less Latitude 35 deg. and 90 deg. makes 125 deg. Take the first Arch 29 deg. 5 min. therefrom, and there remains 95 deg. 55 min. Take this out of 180 deg. and there remains 84 deg. 5 min. the second Arch: Then

As Co-sine of the first Arch 29 deg. 5 min.	994005
Is to the Co-sine of the second Arch 84 deg. 15 min.	901318
So is the Sine of the greater Latitude 51 deg. 22 min.	989273
Out of	180d	00′
Take	84	42	To the Co-sine of 84 d. 42 m.	890591 Sum
And there remains	95	18	The true Distance 95 d. 18 m.	896586

which was required.

Now to find the Obliquity, Take both their Latitudes as if they were North, or both South, and the Complement of the Difference of Longitude to 180 deg. which here is 134 deg. 05 min. half that is 67 deg. 2 min. 30″: both the Latitudes added to∣gether make 86 deg. 22 min. half that is 43 deg. 11 min. it being too little, I added about 1 deg. 20 min. to the half, to find the mean and true Latitude 44 deg. 31 min. by which I find the Obliquity, as I proved by this Operation.

As Radius, To Co-tangent of the Latitude 44 deg. 31 min.	1000732
So is Co-sine of half the Difference of Longitude 67 deg. 2 min.	959158
To the Co-tangent of the Obliquity 68 deg. 21 min.	959890

Now to find whether 68 deg. 21 min. be indeed the true Obliquity, make these Proofs of it.

As Radius, To Co-tangent of Obliquity 68 deg. 21 min.	959890
Take from it the Tangent of the Latitude 51 deg. 22 min.	990267
There remains the Co-sine of Differ. of Longitude 60 deg. 14 min.	969623

Again,

As Radius, To Co-tangent of Obliquity 68 deg. 21 min.	1959890
Take out the Co tangent of the other Latitude 35 deg. 00 min.	1015477
There remains Co-sine of Differ. of Longitude 73 deg. 51 min.	944413

Now both the Longitudes found,* 1.31 73 deg, 51 min. and 60 deg. 14 min. added

together, makes just 134 deg. 05 min. the Difference of Longitude at first propounded betwixt those two Places; which proves, That the greatest Obliquity of the Great Circle that passeth directly over these two Places, the Island Lundy and Rio dela Pla∣ta, so scituate, is 68 deg. 21 min.

Now if it so happen that both the Latitudes be of the same Quantity, as one Place North Latitude 11 deg. 30 min. and the other Place South Latitude 11 deg. 30 m. and the Difference of Longitude betwixt the two Longitudes 55 deg. 48 min. To find the true Great Circles Distance betwixt such Places, first divide the Difference of Lon∣gitude into two equal parts, and then take one Latitude and half the Difference of Longitude, and find the Distance belonging to one Latitude, which doubled, yields the whole Distance betwixt the Places propounded: As Longitude 55 deg. 48 min. halfed is 27 deg. 54 min. and Latitude 11 deg. 54 min. Then work thus.

As Radius, To Co-sine of Differ. of Longitude 27 d. 54 m.	994633
So is the Co-sine of the Latitude 11 deg. 30 min.	999119
To the Co-sine of 30 deg. half the Distance	993752

which doubled is 60 deg. the whole Distance betwixt one Place South Latitude 11 deg. 30 min. and and another North Latitude 11 deg. 30 min. having 55 deg. 48 min. Difference of Longitude. And so work for any two Places so scituate.

Geographical Questions. Two Ships being at Sea, their Difference of Longitude was 53 deg. Now upon a day they observed the Sun being between them; the North Ship found the Sun's Meridian Height 33 deg. and the South Ship 77 deg. the middle Latitude between them was 15 deg. North of the Aequi∣noctial Line: I demand the Angle of Position, and Distance from the North Ship to the South?

* 1.32FIrst add the two Meridian Altitudes Complement together, 33 deg. and 77 deg. Complement 57 and 13, the Sum is 70, the half Sum is 35 deg. the middle La∣titude 15; add the middle Latitude and half Sum together, it makes 50 deg. the

[illustration] geometrical diagram

North Ships Latitude; and substract the middle Latitude from the half Sum, and the Remain is 120 deg. the Latitude of the South Ship. The North Ships Latitude is laid from Q to N 50 deg. the Difference of Longitude QF 53 deg. Through F de∣scribe the Great Circle Meridian PFB, on which lay down the South Ships Latitude 20 deg. as FC, and so draw the Great Circle NCD through the Intersection of the prick'd Line IH, with the Meridian at C; for that is the Latitude of the second Ship: So the Angle of Position is NCQ, whose measure is CG on the half Tangents 48 deg. 58 min. from the South Westwards; and the Distance is NH 48 deg. 22 min. that is, 1683 ⅔ Leagues, or 5051 Miles, the nearest Distance of the two Ships, which was required. How to do it by the Tables, you have been shewed in the last Example.

The Fourth Scituation.

PROBL. VII. The Latitude of two Places being given, together with the Difference of Longitude, To find,

• First, The nearest Distance in the Arch of a Great Circle.
• Secondly, The Direct Position from the first Place to the se∣cond. And,
• Thirdly, From the second Place to the first. And,
• Fourthly, The Circles greatest Obliquity that passeth over those two Places.

ADmit L be the Latitude of Lundy 51 deg. 22 min. and Longitude 25 deg. 52 min. and B is the Latitude of Barbadoes 13 deg. 10 min. and Longitude 332 deg. 57 m. and Difference of Longitude 52 deg. 55 min.

[illustration] geometrical diagram

Lay down first the Latitude 51 deg. 22 min. from Q to L; secondly, the Diffe∣rence of Longitude QF 52 deg. 55 min. and draw the Meridian-circle P through F to S; then lay down the Latitude of Barbadoes from Q to 13, and take of the half

Tangent Line QF 57 deg. 55 min. and lay from C to K, and draw the prick'd Line, and he will cut the Meridian PFS in B, the Latitude of Barbadoes, 13 deg. 10 min. through B draw the Circle LBN, so the Angle of Position is BLQ, whose measure is RO 67 deg. 51 min. that is, W. S. W. 21 min. Westerly; which taken off the Line of half Tangents of your Scale, and laid from C to Pole, and draw the Line from Pole through B, and it will cut the Limb in G: Therefore measure GL on the Line of Chords, you have 57 deg. for the Distance, or 1140 Leagues, or 3420 Miles.

To find the Distance in Questions of this Nature,

1 As the Radius, Is to the Co-sine of the Diff. of Longit. 52 d. 55 m.	978030
So is the Co-tangent of the greater Latitude 51 deg. 22 min.	990267
To the Tangent of the first Arch 25 deg. 44 min.	968297

Take 25 deg. 44 min. from 76 deg. 50 min. the Complement of 13 deg. 10 min. the less Latitude, and the Remain is 51 deg. 6 min. the second Arch.

2 As the Sine of the first Arch 25 d. 44 m.	995464	To find the Distance.
Is to the Co-sine of the second Arch 51 d. 06 m.	979793
So is the Sine of the greater Latitude 51 d. 22 m.	989273
	1969066
To the Co-sine of the Distance 57 d. 00 m.	973602

* 1.33

which is the nearest Distance in the Arch of a Great Circle, by 17 Leagues less than Mercator's Chart by the Rhomb, and less by 166 Leagues than by the Rhomb on the Plain Chart; which confirms this to be the nearest of all ways of Sailing betwixt any two Places.

To find the Angle of Position,

3 As the Sine of the Distance 57 deg. 00 min.	992359
Is to the Sine of the Difference of Longitude 52 deg. 55 min.	990187
So is the Co-sine of the Latitude 13 deg. 10 min.	998843
Add the two last: Substract the first Numbers	1989030
There remains the Sine of the Angle of Direct Position	996681

Which is 67 deg. 51 min. from the South part of the Meridian Westward, as name∣ly, W. S. W, 20 m. Westerly.

Now to know the Distance and Angle of Position, you must put Barbadoes at B, on the West side of the Circle 13 deg. from AE, and draw the Parallel of Latitude 51 deg. 22 min. and lay off the Difference of Longitude from AE to F, and draw the Meridian-circle PFS, and it will cut the Parallel of Latitude in L; therefore from B draw the Circle from L to K: And if you follow your former Directions, BD will be the Measure of BL the Distance found, as before, 57 deg. 00 min. and LBP the Angle of Position, whose Measure is RG 36 deg. 26 min. and the Great Circles greatest Obliquity is CO 54 deg. 40 min. For,

4 As the Sine of the second Arch 51 deg. 6 min.	989111
Is to the Sine of the first Arch 25 deg. 44 min.	963767
So is the Tangent of Difference of Longitude 52 deg. 55 min.	1012157
	1975924
To the Tangent of the Direct Position 36 deg. 26 min.	986813

From B towards L, which is 3 Points, 2 deg. 41 min. from the Meridian, namely, N. E. b. N. 2 deg. 41 min. Easterly, you must sail first from B towards L; but al∣ter your Course, still increasing toward the Eastward, as shall be shewed.

[illustration] geometrical diagram

For the Obliquity, to find that,

5 As Radius, To Co-sine of less Latitude 13 deg. 10 min.	998843
So is the Sine of the Angle of Position 36 deg. 26 min.	977370
To the Co-sine of the greatest Obliquity 54 deg. 40 min.	976213

These are the Scituations of all Places upon the Terrestrial Globe; so that there can∣not be any two Questions, but, in respect of each other, they will be found in one of these four kinds; except they fall in one Meridian, or on the Aequator: and these Directions you have in the Tenth Chapter: Therefore if you will seriously observe these short Directions already given, and as follows, you shall never have your Expe∣ctation deceived.

CHAP. XII. How to describe the Globe in Plano, by the Mathematical Scale.

THese, and all other Questions of this nature, concerning the Resolution of any Spherical Triangle, may very easily be performed by the Globe: But be∣cause the Globe is a chargeable Instrument, and so every one cannot have it, therefore several Men, have for several Uses, invented several ways to Project the Globe upon a Plain, as Mr. Gunter hath them in his Book of the Sector. The fittest for this purpose will be that of Gemma Frisius, which is most used in the Great Maps of the World, the Projection whereof is as followeth.

First, By the Chord of 60 deg. describe the Circle AENES, and by the Chord of 90 deg. divide it into four parts, as AEE a Cross Diameter for the Aequator, and NS for the great Meridian: Then by taking off every 10 deg. of the Chord, you may divide each Quadrant into 90 deg. and number them as in the Figure: Then if you take off your Line of ½ Tangents in your Scale every 10 deg. and 5 deg. and lay them from the Center C on the four Sides of the Quadrants, as you see the Figure, and number them as they are in the Figure; so shall you divide the Diameters into his parts AEE the Aequinoctial, NS the Meridian, which are half Tangents. You may do it also with∣out

the Scale, by your Ruler, if you stop one end of your Ruler at N, and turn the other end about to the several Degrees in the lower Semicircle ESAE: And also if you keep one end of your Ruler fixed in the Point AE, and lay the other end about to the se∣veral Degrees in the Semicircle NES; so have you the Meridian-diam ter divided into half Tangents likewise.

Now you have divided the Diameters, they must guide you in the drawing of the Meridians from Pole N to Pole S, which are perfect Circles; as likewise are the Parallels of Latitude.* 1.34 You may find the Centers in the Diameter AE, if you extend the Compasses from the first Degree on the half Tangents, to the Secants of every 10 Degrees, and with that Distance put one Point at 10 deg. in the Semidiameter AEC, and in EC will the other Point be the Center of the Meridian of the first 10 deg. from AE: and do the like from E in the same manner, for any other Degree. To draw the Meridian of 50 deg. Longitude, take the Secant of 50 deg. off the Scale, and one Point will stand in the Semidiameter AEC, at 50 deg. and the other will stand in the Center at East, and likewise at West for 50 deg. on the other side: And so do for the rest; and so you may find the Center of any Circle whatsoever, upon the Cross Semidiameter belonging to it, which you must continue beyond the Great Cir∣cle,* 1.35 where the Center will be in many Questions. For the Parallels of Latitude, it is thus: Take the Complement-number of Degrees off your Line of Tangents, put one Point in the Degree of Latitude, the other will stand in the Center.

[illustration] geometrical diagram

The GLOBE in PLANO. The Globe in Plaino.

For Example. If you will draw the Parallel of Latitude for 60 deg. take off the Tangent-line of your Scale 30 deg. the Compl. of 60 Latitude, and the other will fall upon V the Center of the Parallel of 60 deg. in the Semidiameter NS continued be∣yond the Circle.

So, Take the Tangent of 40 deg. and it will draw the Parallel of 50 deg. whose Center is at ♓: and so do in drawing all Parallels of Latitude. You may draw them also by making several Trials, until your three Points be in a Circle, and also draw the Parallels of Latitude: with the same Distance find their Centers; but if you can, by the Scale is the surest way.

The Four Scituations that are in the Globe.

The First Scituation.

AE is a Point of Intersection for the Mouth of the River of Amazones, Z Lundy, CRV the Obliquity 62 deg. 16 min. E the other Point of Intersection with the Aequa∣tor, NRV the measure of the Angle of Position. which applied to the Aequator from AE inwards, shews you 27 deg 50 min. from Amazones to Lundy. Now if you will know the Distance in such Questions, measure it in the Meridian that agrees with the Angle of Position; as namely, for this Distance AEZ, you must measure from N in the Meridian-line of 27 deg. 50 min. and you will find it 61 deg. 57 min. And so do for to measure any other Distance.

The Second Scituation.

I is the first Places Latitude, ♈ is the Difference of Longitude 52 deg. 55 min. ♈ is likewise the second Places Latitude; and ♍ H is the measure of the Angle of Position, which measured in the Semidiameter AEC, will be found 68 deg. 46 min. In that Meridian measure l r the Distance, and you will find it from N towards C, to reach 32 deg. 18 min. Remember to measure the Distances from the Poles in the same Meri∣dian, of the Number of Degrees of the Angle of Position: The greatest Obliquity of that Circle N r l is at W 54 deg. 25 min. Intersection of the Aequator at Y, W is a Meridian of greatest Obliquity.

The Third Scituation.

L is the first Places Latitude 51 deg. 22 min. North; E p is the Difference of Lon∣gitude 45 deg. 55 min. R is the second Places Latitude, or Rio de Plata, ▵ the greatest Olliquity 68 deg. 22 min. m n the Measure of the Angle of Direct Position: applied to EC will be found 36 deg. 02 min. in that Meridian: from the Pole measure the Di∣stance LR, and you will find it 95 deg. 18 min. P the Intersection of the Great Circle, passing over the two Places in the Aequator.

The Fourth Scituation.

The first Latitude is at L Lundy 51 deg. 22 min. Difference of Longitude counted from E 52 deg. 55 min. that Meridian will cut the Latitude of Barbadoes 13 deg. 10 min. at b: M ♓ the Measure of the Angle of Direct Position 67 deg. 51 min. and b L measured in that Meridian is 57 deg. 00 min. the Distance. Now to know the Angle of Position from Barbadoes, being Westward from Lundy, set it on the West side of the Figure, as at B; and likewise if the first Place be to the Eastward, put his Latitude to the East side of the Meridian.

Now to know the Angle of Position from Barbadoes, and Distance, and Obliquity, B □ O is the Arch of the Great Circle that passeth over these two Places; □ is Lundy, q h is the Measure of the Angle of Position 36 deg. 26 min. B □ measured in that

Line, you will find the Distance 57 deg. O is the greatest Obliquity 54 deg. 40 min. NO ☉ S a Meridian of the greatest Obliquity: d is the Intersection with the Aequator.

CHAP. XIII. By Arithmetick how to Calculate exactly for any Degrees and Minutes of Obliquity; What Degree and Minute of Latitude the Great Circle shall pass through for any Degree and Minute of Longitude, from the Point of Obliquity, or of its Intersection with the Aequinoctial.

NOte these Rules well, for they serve for all Questions of this nature, what Difference of Longitude soever any Point or Place hath from the Meridian of its next Obliquity, which is ever 90 deg. or less; the Complement thereof to 90 deg. is the Difference of Longitude of that Point or Place, from the Meridian of that Great Circle's next Intersection with the Aequator.

The first sort of RULES are these.

By the Latitude of two Places, the Difference of Longitude betwixt them, and the Obliquity of the Great Circle passing directly over both Places given; To find the Difference of Longitude of each Place from the Meridian of the greatest Obliquity.

Let this be our Example. Lundy in North Latitude 51 deg. 22 min. and Barbadoes in North Latitude 13 deg. 10 min. and Difference of Longitude 52 deg. 55 min. and the greatest Obliquity 54 deg. 40 min. Work first with the less Latitude, to find the Difference of Longitude from the Meridian of Obliquity of both Places.

RULE I.

Thus, As Radius, and Co-tangent of Obliquity 54 deg. 40 min.	1, 985059
Take from it the Co-tangent of less Latitude 13 deg. 10 min.	1, 063090
There remains the Co-sine of Differ. of Longitude 80 d. 27 m.	921969

The Difference of Longitude of the second Place from the Meridian of the greatest Obliquity. And by reason the Difference of Longitude from the Obliquity is more than the Difference of Longitude betwixt the two Places, therefore substract the Dif∣ference of Longitude 52 deg. 55 min. from 80 deg. 27 min. and there remains the Dif∣ference of the first Place from the Meridian of Obliquity 27 deg. 32 min. and the first Place is betwixt the second Place and the Meridian of Obliquity. But if the Difference of Longitude from Obliquity had been less than the Difference of Longitude betwixt the two Places, then substract the Longitude from the Difference of Longitude betwixt the two Places, and the Remain had been the Difference of Longitude from the Meridian of Obliquity, to the first Place.

The Use of these Rules are,

1. To find where to place the Meridian of the greatest Obliquity betwixt any two Places, in a blank Chart, or Mercator's Chart or Plat, to trace out the Voyage, as we find that it is 80 deg. 27 min. the Difference of Longitude of the second Place from the Meridian of Obliquity, and 27 deg. 32 min. from the first.

2. You see you find the Difference of Longitude betwixt the Obliquity and any La∣titude propounded, by the last Rule.

3. By the Obliquity of the Great Circle, and the Difference of Longitude from the Obliquity, to find the true Latitude.

RULE II.

As Radius, To Co-tangent of Obliquity 54 deg. 40 min.	1985059
Take from it Co-sine of Differ. of Longitude 80 deg. 27 min.	921086
There remain Co-tangent of the Latitude 13 deg. 10 min.	1063073

And so likewise if you work with 27 deg. 32 min. by the same Rule, you will find the other Latitude 51 deg. 22 min. and by it find from any Place through what Lati∣tude the Great Circle passeth every 10 deg. or 5 deg. or more or less Quantity of Longi∣tude from the Obliquity; and thereby find the Latitude, to make marks in every Meri∣dian; and so trace to out the Great Circle Arch, in your Mercator, or Mr. Wright's Plat or Blank Chart.

As thus, for 2 deg. 28 min. of Longitude more, added to 27 deg. 32 min. makes 30 deg. 00 min.

RULE III.

As Radius, To Co-tangent of Obliquity 54 deg. 40 min.	1985059
Take from it the Co-sine of Differ. of Long. from Obliq. 30 d. 00	993753
There remains the Co-tangent of the Latitude 50 deg. 41 min.	991306

And by the same Rule I made this

Differ. of Longit from Obliq. Lundy	Latitude from Lundy.
Deg. Min.	Deg. Min.
27 32	51 22
30 00	50 41
35 00	49 07
40 00	47 13
45 00	44 56
50 00	42 12
55 00	38 58
60 00	35 12
65 00	30 48
70 00	25 46
75 00	20 03
80 27	13 10	Barbadoes.

Table, of an Arch of a Great Circle, ex∣tended from Latitude 51 deg. 22 min. to Latitude 13 deg. 10 min. Difference of Longitude 52 deg. 55 min. setting the Point of the greatest Obliquity upon a Meridian-line, that so it might be the better protracted on Mercator's Chart: This is, for every 15 deg. Difference of Longitude, these are the Latitudes the Great Circle will pass through; so that you see there is 52 deg. 55 min. added by 5 to the Difference of Longitude of the first Place from the Meridian of Ob∣liquity, which makes 80 deg. 27 min. the Difference of Obliquity of the second Place, which was the Difference of Longitude from Obliquity at first found. In like manner work for any other Place.

CHAP. XIV. How by the Scale of Tangents to make a Part of the Globe in Plano, where∣by you may trace out the Latitudes to every Degree of Longitude; or eve∣ry 5 or 10 Degrees, as neer as you will desire, without Calculation.

BY the Line of Tangents on the side of your Mathematical Scale, you may make the following Projection, which was made by Mr. Philips in his Geo∣metrical Seaman, pag. 5. by Tables and Geometry: But here you may save that labour, if you have a Scale with a Line of Tangents on it.

First, Consider of what length your Tangent or Side of your Quadrant must be, and accordingly set off your Radius from A towards D, as I have done, by taking off 77 deg. of the Tangent-line of my Scale, and set it from A the Pole to D, for 13 deg,* 1.36 on the North side of the Aequator, or 13 deg. of North Latitude, which is the Com∣plement

of 77 to 90 deg. Then make the other side of the same length, and draw the Quadrant ADE, the Radius is always a Tangent of 45 deg. Then with your Com∣passes take off the Line of Tangents the several Degrees, and draw the Arches or Parallels of Latitude, as you see I have done in the Figure. Thirdly, divide the Limb of the Arch DE into 90 deg. and through every 5 or 10 deg. draw Lines of Longitude, or Meridian-lines. The Arches of Latitude must be numbred as in the Fi∣gure; but the Lines of Longitude you may number from either side, as occasion re∣quires.

You may, if you will, when occasion requires, divide a Circle into four Qua∣drants, and draw the Lines of Longitude from the Center; and you may make this as large or as little as you will, by the Tables of Natural Tangents in the Second Book, as you have been there shewed how to lengthen or shorten your Radius: You may number the whole Circle of Longitude into 360 deg.

[illustration] geometrical diagram

The Blank Quadrant, being thus made, will serve for many Examples; especially if you make it upon a Slat Stone, that you may wipe the Arch, that is lightly drawn by a Slat Pen betwixt any two Places, off at pleasure.

You may set down therein the two Places you are to sail between, according to their Latitudes and Longitudes; and then only by your Ruler draw a streight Line from the one Place to the other, which will represent the Great Circle which passeth between the two Places, and will cross those Degrees of Longitude and Latitude, which you must sail by exactly. You may do it by the Difference of Longitude only, if you will, as shall be shewed in this Example, for proof thereof.

Of a Voyage from Lundy, in Latitude 51 deg. 22 min. and Barbadoes, in Longitude 332 deg. 27 min. Difference 52 deg. 55 min. and Latitude 13 deg. 10 min. To find by what Longitude and Latitudes the Arch of a Great Circle drawn between those two Places doth pass.

First, Let the Line AD represent the Meridian of the Island of Lundy,* 1.37 marked out by L for its Latitude 51 deg. 22 min. and the Longitude thereof 25 deg. 52 min. at D, which is set down according to its Longitude and Latitude. Then from D in the Limb or Arch of the Quadrant, count the Difference of Longitude 52 deg. 55 min. and this is the Meridian of the Island of Barbadoes, on which you must mark out the Latitude 13 deg. 10 min. at B; lay a Ruler from the first Latitude L to the second at B, and draw the streight Line LB, which representeth the Arch of a Great Circle between the two Places; and if you guide your Eye along in this Line, you may rea∣dily and truly perceive by what Longitudes and Latitudes you should sail: For where this Line crosseth the Arches of Latitude and the Lines of Longitude, that shews the true Longitude and Latitude of the Arch, accord∣ing to your desire.

Differ. of Longit. substract	Differ of Longit. from Obliqu.	Latitude	Differ of Longit. added.
D. M.	D. M.	D. M.	D. M.
52 55	27 32	51 22	00 00
2 28	30 00	50 41	02 28
5 00	35 00	49 07	07 28
5 00	40 00	47 13	12 28
5 00	45 00	44 56	17 28
5 00	50 00	42 12	22 28
5 00	55 00	38 58	27 28
5 00	60 00	35 12	32 28
5 00	15 00	30 48	37 28
5 00	70 00	2•• 46	42 28
5 00	75 00	10 30	47 28
5 27	80 27	13 10	52 55
52 55		Barbad.

Now the truth hereof will more evidently appear, if you compare the Latitudes and Longitudes which this Line intersecteth, with this Table, as before, Cal∣culated by me for every •• deg. of Longitude. You may see by the Figure, that the Line BL in the Points a, b, c, d, e, F, g, h, i, k, L, doth cross the Parallel of Latitude, as you see in the fourth Column of this Table, at the same number of Degrees from the first Me∣ridian, as you see in the fifth Calu••n. The first Column is the Number of Degrees of Longitude, the second is the Difference sub∣stracted, the third is the Degrees of Longi∣tude from the Meridian of the greatest Ob∣liquity, the fourth and fifth are, as before, Latitude and Longitude added, for the Dif∣ference of Longitude from Lundy. For Example: I would know what Degree of Latitude 47 deg. 28 min. of Longitude from the first Meridian doth cross; and I see by the Figure it is at ••0 deg. of Longitude, which the Table sheweth is 20 deg. ••0 m. of Latitude, and so of the rest, 75 deg. from Meridian of Obliquity, and Longitude 338 deg. 24 min.

And so in like manner you may lay down upon the former Quadrant any two Places, howsoever scituated, by their Longitude and Latitude, of Difference of Longi∣tude, in the manner as you have been shewed in the last Example.

CHAP. XV.

RULE IV. By the Latitude, and Difference of Longitude from the Obliquity, to find the true Great Circle's Distance.

As Radius 90, To Co-sine of the Latitude 51 deg. 22 min.	979541
So is the Sine of the Difference of Longitude 27 deg. 32 min.	966489
To the Sine of the Distance 16 deg. 47 min.	946030

* 1.38

So that 16 deg. 47 min. is the Great Circle's Distance from the Point of the greatest Ob∣liquity of that Great Circle.

RULE V. By the Obliquity of the Great Circle, to find the true Latitude to any Quantity of a Great Circle's Distance, from the Point of his greatest Obliquity.

As Radius, To Sine of greatest Obliquity 54 deg. 40 min.	991158
So is Co-sine of the Distance from Obliquity 16 deg. 47 min.	998109
To the Sine of the true Latitude 51 deg. 22 min.	989267

Again,

As Radius, To Sine of greatest Obliquity 54 deg. 40 min.	991158
So is Co-sine of Distance from Obliquity 73 deg. 47 min.	944602
To Sine of true Latitude of Barbadoes 13 deg. 10 min.	935760

RULE VI. By the Great Circle's Distance from the Point of Obliquity, and the Latitude given; To find the Difference of Longitude betwixt the Place and the Meridian of greatest Obliquity.

As Radius, To the Sine of Distance from Obliquity 16 d. 47 m.	946052
Take from it the Co-sine of the Latitude 51 deg. 22 min.	979541
Remaine the Sine of Difference of Longitude 27 deg. 33 min.	966511

By these four last Rules you may be confirmed of the truth of the former Work, of ••••acing of the Great Circle by Longitude, Latitude, and Distance, from the Point of its greatest Obliquity.

This is worth your Observation, That the Complement to 90 Degrees of the Great Circle's Distance of a Place from the Point of the Great Circle's Obliquity, is always the Great Circle's Distance from the Point wherein that Circle intersecteth the Aqui∣noctial.

The second sort of RULES;

Whereby to find what Rhomb you are to sail upon, that you may keep in or neer the Arch of a Great Circle, extended from one Place to another.

RULE VII. By the Difference of Longitude from the Obliquity, and Latitude given; To find the Great Circle's Distance from the Point and Me∣ridian of greatest Obliquity.

As Radius, To the Sine of Difference of Longitude from Ob∣liquity 80 deg. 27 min.	999393
So is Co-sine of the Latitude 13 deg. 10 min.	998843
To the Sine of the Great Circle's Distance from Obliq. 73 d. 47 m.	998236

So that if you take out 16 deg. 47 min. in the Distances of Obliquity before found out of 73 deg. 47 min. the Remain will be the true Distance of the two Places 57 deg. as was found in the second Rule of the fourth Scituation. But if the Point of greatest Obliquity had been betwixt the two Places, you must have added them together, and the same had been the Distance of the two Places.

RULE VIII. By the Great Circle's Distance from the Obliquity, and the Latitude given; To find the Rhomb.

As Radius 90 d. and Tang. of Great Circles Distance 16 d. 47 m.	947943
Take out the Co-tangent of the Latitude 51 deg. 22 min.	990267
There remains the Co-sine of the Rhomb 67 deg. 50 min.	957676

Having therefore in the four Scituations, before-going, been directed how to find the Distance betwixt the two Places, by the Arch of a Great Circle, and the greatest Obli∣quity of any Circle, you may by the first Rule of Chap. 13. find the Difference of Longitude of each Place, from the Point of the Great Circle's greatest Obliquity; and then by the fourth and seventh Rules of Chap. 15. find the Great Circle's Distance to the Obliquity, and by the eighth Rule find the Rhomb to be sailed on, from either Place towards the other.

RULE IX. To find how far a Man should sail upon a Rhomb, before he change his Course a Point Half a Point, or a Quarter of a Point.

You may try this by your Protracting Quadrant, on your Blank Plat or Chart, made according to Mr Wright's or Mercator's Projection; where the Voyage is truly and carefully traced out as before.

Or you may Arithmetically try every Point, or Quarter of a Point, or Half Point, as you see cause, by these Rules.

Having found by the eighth Rule the Rhomb was 67 deg. 50 min. add to it a Quarter of a Point, or 2 deg. 29 min. it makes 70 deg. 19 min. W. N. W. ¼ W. and Latitude 49 deg. 07 min. and Difference of Latitude 2 deg. 15 min. and it is required the Di∣stance.

As Radius 90 deg. To Sine of Difference of Latitude 2 d. 15 m.	859394
Take out the Co-sine of the Rhomb 70 deg. 19 min.	952739
There remains the Sine of the Distance 06 deg. 42 min.	906655

Therefore 06 deg. 42 min. is 134 Leagues, may be sailed W.N.W. ¼ Westerly, from the Latitude 51 deg. 22 min. to Latitude 49 deg. 07 min.

RULE X. By the Great Circle's Distance, and the Difference of Latitude given; To find the Rhomb.

As Radius, To Sine of Difference of Latitude 2 deg. 15 min.	859394
Take out the Sine of the Distance 6 deg. 42 min.	906655
There remains the Co-sine of the Rhomb 70 deg. 19 min.	952739

RULE XI. By the Rhomb, and Distance upon it given, To find the Difference of Latitude.

As Radius, To Co-sine of the Rhomb 70 deg. 19 min.	952739
So is Sine of the Distance 06 deg. 42 min.	906655
To the Sine of Difference of. Latitude 2 deg. 15 min.	859394

Which 2 deg. 15 min. taken from the first Latitude 51 deg. 22 min. there remains the Latitude 49 deg. 07 min. which are good Proofs:

RULE XII. By the Obliquity of the Great Circle, and the Latitude given; To find the Difference of Longitude from the Meridian of Obliquity.

As Radius 90, To Co-tangent of Obliquity 54 deg. 40 min.	985059
Take out the Co-tangent of the Latitude 49 deg. 07 min.	993737
There remains Co-sine of Difference of Longitude 35 deg. 00 m	991322

35 deg. 00 min. is the Difference of Longitude from the Meridian of Obliquity. You you may also try it by the Difference of Longitude in the fifth Column, 7 deg. 28 min. in the foregoing Table, added to 27 deg. 32 min. makes 35 deg. as before.

RULE XIII. By the Latitude, and Difference of Longitude from the Obliquity given; To find the Great Circles Distance from the Meridian of Obliquity.

As Radius, To Co-sine of the Latitude 49 deg. 07 min.	981592
So is the Sine of the Difference of Longitude 35 deg. 00 min.	975859
To the Sine of the Distance 22 deg. 05 min.	957451

Which is the Distance from the Meridian of the greatest Obliquity: Then you may proceed to the Rhomb next to be failed on.

Now if you add 2 deg. 49 min. to the former Rhomb 70 deg. 19 min. it makes 73 deg. 8 min. that is W. S. W. half a Point Westerly, and the Difference of Latitude 4 deg. 11 min. which you may find by the foregoing Tables, or thus by the ninth Rule.

RULE XIV.

As Radius, Is to Co-sine of Difference of Latitude 4 deg. 11 m.	886301
Take out the Co-sine of the Rhomb 73 deg. 08 min.	946261
There remains the Sine of the Distance 14 deg. 34 min.	940040

Which 14 deg. 34 min. converted into Leagues is 291 Leagues ⅓ the Distance you may sail W. S. W. ½ a Point Westerly, from Latitude 49 deg. 07 min. to Latitude 44 deg. 56 min. and the Difference of Longitude is 10 deg. as you may see by the former Table, by the Latitude 44 deg. 56 min. is 17 deg. 28 min. and the Difference of Longitude from Obliquity is 45 deg. 00 min. and the Longitudes according to my Globes made by Hon∣dius 8 deg. 24 min. and so work until you have calculated the Distance for every ¼ Point, or rather half Point, because ¼ of a Point cannot be well steered upon. It is no matter if you do not exactly keep the Arch of a Great Circle, for the Reasons be∣fore given: but as neer to it as you may conveniently, as Mr. Norwood hath sufficiently answered in his ninth Problem of Sailing by a Great Circle.

But let me advise you to get into your Latitude short of the Place you are bound to, for fear of mistakes in your Reckoning, and so over-shoot your Port to a greater disgrace, than the credit of Great Circle Sailing will bring you; and then to know what Distance you are to sail in that Parallel of Latitude.

RULE XV. By the Latitude, and Difference of Longitude given: To find the Di∣stance upon a Course of East or West.

As Radius, Is to Co-sine of the Latitude 13 deg. 10 min.	998843
So is the Sine of Difference of Longitude 5 deg. 00 min.	894029
To the Sine of the true Distance 4 deg. 52 min. which is 97 Leagues ⅓.	892872

After you have made some progress in your Voyage, you may make use of these most excellent Rules, whereby a Mariner may make his Conclusion most certain.

RULE XVI. By the Difference of Latitude, and Rhomb sailed on; To find the Distance. You have it in the Fourteenth Rule before-going.

.

RULE XVII. By the Latitude, and Distance sailed upon an East or West Course, To find the Difference of Longitude; as 20 Leagues sailed in Latitude 51 deg. 22 min.

As Radius, To Sine of the Distance 1 deg. 00 min.	1824185
Take away Co-sine of the Latitude 51 deg. 22 min.	979541
Remains the Sine of Difference of Longitude 1 deg. 36 min.	844644

Therefore sailing 20 Leagues East or West in the Parallel of 51 deg. 22 min. the Difference of Longitude made is 1 deg. 36 min. which is a good Rule when you are in the Latitude of the Place you are bound to. In the first Rule you have how for to find the Difference of Longitude from Obliquity, Chap. 13. and likewise in Rule 12. where the Difference of Longitude is 35 deg. substract it from 27 deg. 32 min. and the Remain will be the Difference of Longitude of two Places, one in Latitude 51 d. 22 min. the other 49 deg. 07 min. as you have been directed before.

So that what hath been written will satisfie any ingenious Spirit, to make use of these Rules in these four Scituations; and these four will answer any thing required, in all sorts of Great Circle sailing. I shall now make the blank Mercator Plat; and trace out the Arch of a Great Circle; and likewise shew how by Latitude and Longi∣tude to find the Place of any Ship in Mercator's Chart.

CHAP. XVI. How to make the most true Sea-Chart, and the Ʋse thereof in Mercator's and Great Circle Sailing, called a General Chart.

FOr the manner of the Division, Let the Aequator be drawn and divided, and crossed with Parallel-Meridians, as before directed; only one Degree of Longitude in the Particular Chart before-going, is 10 deg. of the Aequator of this General Chart. You have been directed how to make the Meridian-line off the Scale which is for a General Chart; and the same Rule makes this. Look in the Table of Meridional parts, and you will find the Difference between the Aequator and 40 deg. of Latitude in the Meridian-line to be 874, 2 which is 874 Leagues and 2/10; that divided by 20 is 43 deg. 42 min. 2/10 of the Aequator, therefore take out of a Scale of Equal parts, answerable to each Degree of the Aequator, divided into 20, which you must reckon 200 Parts, take 874 Parts, and that Distance will reach from the Aequator to 40 deg. of Latitude. Always remember in a General Chart to omit the last Figure in the Table, which is Tenths, 2/10 in this.

And for 50 deg. take 1158 such Equal parts, which is 57 deg. 54 min. will reach from the Aequator at Ae, to 50 deg. of Latitude in the Meridian-line: And so do for any other Degree or Minute of Latitude, until you have made the Chart, as I have done the Figure following.

* 1.39You may divide the Meridian-line by the Projection in the Quadrant, making the side thereof answerable to 5 Degrees of the Aequator of the Chart, as in this.

Suppose you would know the Distance betwixt 40 deg. and 50 deg. of Latitude, in the Meridian-line of a Chart.—Take the middle of 10 deg. which is 45 deg. out of that Latitude in the Quadrant, and it will reach from 40 to 50 deg. of Latitude in the Chart, which you may soon try. And so work for any other Latitude.

* 1.40You have also there a Scale of Leagues for every Parallel of Latitude, to measure any Distances in the Chart; for every Degree is 200 Leagues in this Chart, as you may soon apprehend, without more words, by the former Directions.

* 1.41The Protracting Quadrant (you may see the Figure following) shews you all at one sight, without more words, how to make it by dividing it into eight Points, and each Point into four Quarters, and an Arch within into 90 deg. and a Libal or Index to be rivetted to the Center, and a Hole drilled through the Rivet, to put a Pin through the Center of the Quadrant upon any Place assigned, and let him square by the Pa∣rallel-Meridians and Parallels of Latitude; so laying the Index over the second Place, the Limb of the Quadrant will shew you the Point of the Compass, and what Angle it makes with the Meridian, or bearing of the first Place from the second, as we have shewn by divers Arithmetical Rules, for your more certain and exact direction, how to keep your Reckoning upon your Mercator's Chart, or Blank; and to know first and afterwards what Rhomb you are to sail upon, keeping in or neer the Arch of a Great Circle; and to know what Longitude and Latitude you are in, after some pro∣gress made in your Voyage.

You shall have here also the way how you shall trace out the Arch of a Great Cir∣cle betwixt the Places in a Blank or Mercator's Plat, and how to prick down upon your Chart any Distances of Longitude and Latitude.

Before in the third Rule of Chap. 13. you have the way how to calculate for any Degree and Minute of Obliquity, and any number of Degrees of Longitude; what Degrees and Minutes of Latitude the Great Circle shall pass through, by the same Rules I have calculated, for every 10 Degrees of Longitude, reckoning from the greatest

[illustration] geometrical diagram

A Generall Sea Chart According to Mercator.

The Index

Fasten this in with a Rivet to the Centor of the Quadrant A that it may turne upon it with a hole through the Rivet.

A Scale of equall parts for the deviding the Meridian Line by the Table of Meridionall parts.

Obliquity, to the Intersection of the Great Circle with the Aequator, viz.

Greatest Obliquity G 54 deg. 40 min.

For Deg. Lat.	10	20	30	40	50	60	70	80:27	For 90 deg. Longit.
54 d. 15 m.	52:58	50:41	47:13	42:12	35:12	25:46	13:10	For 00 deg. Latitude.

In this following Mercator's Plat, G standeth at 54 deg. 40 min. of North La∣titude, and AE just 90 deg. of Longitude Westward, and AEN 90 deg. Eastward from G, being the two opposite Points in the Aequator, 180 deg. from each Point of In∣tersection AEAE.

In every Meridian betwixt G and AE, on both sides a Meridian drawn at every 10 deg. of Longitude in the Chart, make a mark at Latitude found in the Table, by the Meridian-line of the Chart; and having so marked every Meridian betwixt G and AE, then by these marks ye may draw Arches from one to another: but it will suffice to draw Right Lines from Mark to Mark, as from G the greatest Obliquity of the Great Circle, to the next Meridian on each side, and likewise to the next, until you come down to the Aequator at AE. on both sides; so have you pourtrayed on this Mercator Plat a Great Circle Arch from Lundy to Barbadoes, one being in North Latitude 51 deg. 22 min. at L, the other at B in North Latitude 13 deg. 10 min. with Difference of Longitude 52 deg. 55 min. from C unto L, to C under B.

Note, To make a perfect Circle: the Latitudes of the Arch are the same on the South side of the Aequator, as you have found them on the North side. You might have marked out only so much of the Great Circle from the first Latitude, as you see I have done from the side of the Meridian-line, and Latitude of Lundy 51 deg. 22 min. at l, to Latitude 13 deg. 10 min. at B, by the Difference of Longitude in the last Column of the Table in Chap. 13. and Difference you will find of Longitude is 52 deg. 55 min. by the former Direction: The Figure makes all plain in the Chart or Blank.

Two Places in one Latitude, as in the second Scituation Latitude 51 deg. 22 min. as in the following Chart, one at H, and the other Place at L in the same Latitude, and Difference of Longitude 52 deg. 55 min. the neerest Distance is not upon a Parallel di∣rectly from H to L, but from H to sail from 51 deg. 22 min. by G the greatest Obli∣quity, in Latitude 54 deg. 40 min. W. N. W. almost, then W. b. N. and W. b. S: W. S. W. the other half from G to L, which is the neerest Distance by 42 Miles; for the Distance by the Parallel is 660 5/10 Leagues, but by the Arch of a Great Circle is but 646 Leagues: And one would not think but the Parallel were the neerest, to look in the Plat: but he that knows the Globe, conceives that by the Arch that goes neerer the Poles, cross the Meridians, to be the neerer; therefore the Arch must be the neerest way. And sailing into several Latitudes, you have the benefit to correct your Dead Reckoning, which you cannot so well do by keeping a Parallel of East and West. These Directions may be sufficient for any Questions you will have any way in Great Circle Sailing.

But he that will take the pains, may find great delight in this sort of Practice: Yet I must conclude, That although it is the neerest way, it is not the convenientest way for Seamen, for several Reasons best known to them that keep an Account of the Ships way, which I could lay down here; but in regard it is needless, I leave every one to his mind, and shall shew you the way how I did keep my Account at Sea, by the Plain Chart and Mercator's Chart; and how to measure Distances in Mercator's Chart, in any Parallel also: which, if you have a better way, publish it, that others may gain benefit by it; for you will not hurt me any way; but rather I desire, that all the Nauigators in England did exceed me (for His Majestie's sake, whose Subjects we are) and hope that the Neighbour-Nations will once know, That the English Mariners are not less known in Art, than by their Courage, which the Dutch know by dear-bought Experience.

CHAP. XVII. How to keep a Sea-Journal, that so every Sea-man, Navigator, and Mari∣ner, may not be ashamed to shew their Account to any Artist, and by it benefit themselves and others.

I Would not have any ingenious Sea-Artist, that hath a long time kept Account of a Ship's way, and hath been Commander or Mate many years, to think I pre∣scribe him Rules, and to perswade him out of his beaten Path (No, I think that a hard matter.) But we prescribe Rules for those that are but new Learners, that so they may have a perfect Method and Way of keeping Account of a Ships way at Sea; that if the Master should perceive an Ingenious Practicioner aboard, and by exami∣ning his Journal find him able, might at his return home give him encouragement, by speaking in his behalf to other Men to make him a Mate; and that is the way to encourage Artists: But I confess the greatest Dunces have commonly the best Imploy∣ments, and many abler men before the Mast: which is great pity, that the deserving Men had not their right. But what shall I say? There is such an aversment in Fate. Therefore I shall proceed to our Journal. I conceive it will be fit to have a Book in Folio, that a sheet of Paper makes but two Leafs, and to keep the left side of your Book void, that you may write all the Passages of the Voyage; that is to say, when you set Sail, with what Wind, and what Ships are in company with you, and how far you keep company; what Storms, and how the Wind was: and likewise put down the time that you come by any misfortune, of cracking or breaking a Mast or Yard, or if any Men should die; and also what Damage you receive by any Storm, and the like Occurrences, as you shall think requisite; and what Currents and Variation you meet with. But before all this, put down the Title of the Voyage, over the left-hand Page, in these or such like Words, viz.

A JOURNAL of our Intended VOYAGE by God's Assistance from Kingrode-Port Bristol in Latitude 51 deg. 30 min. to the Island of Madara in Latitude 32 deg. 10 min. and from thence to Barbadoes in Latitude 13 deg. 10 min.

The right side of your Book throughout may be divided into 13 Columns, by Lines, as you may see in the following Example.

In the first must be expressed the day of the Month, in the second the Letter of the Week-day that Year; put it once in the top of the Page: In the third Column the Months; make him large enough to put down the Latitudes you make by Observa∣tion of the Sun or Stars, and Currents, and how they set: In the fourth, the Course steered by the Compass: In the fifth, the Variation of the Compass, if there be any; or else the Variation by Currents, if there be any. Set down the Angle of the Rhomb, it made with the Meridian in the sixth Column; and in the seventh, the Distance sailed in Leagues or Miles: In the eighth, ninth, tenth, and eleventh Columns, set down the Northing, Southing, Easting, and Westing: In the twelfth, the Latitude by Dead Reckoning; and in the thirteenth Column, the Difference of Longitude from the first Meridian, according to Mercator's Chart, or the Arch of a Great Circle, or a Polar Chart or Globe.

1666.	Month Days.	Week Days.	A Journal of our Intended Voyage, by God's Assistance, in the Good Ship the Eliz. of B. S. S. Commander, from Kingrode in Latitude 51 d. 30 m. to Madara in Latitude 32 d. 30 m. and from thence to Barbadoes, in Latitude 13 d. 10 m.
March	25	a	Set sail out of Kingroad, in Company with the John bound to Cales, and Ann•• bound to Virginia; the Wind at E. N. E. thick rainy Weather.

The Journal of our Intended Voyage, by God's Assistance, in the C. (of B.) S. S. Comman∣der, from Lundy, in Latitude 51 d. 20 m. to the Island of Madara, in Latitude 32 d. 30 m. Angle of Position, or Course S. S. W. 1 d. W. Distance 411 Leagues, Meridian Distance 167 Leagues, Difference of Longitude 11 d. 16 m. from Madara to Barbadoes, in Latitude 13 d. 10 m. Angle of Position or Course S. W. 61 d. 14 m. Distance 798 Leagues, Meridian Distance 698 Leagues, Difference of Longitude 41 d. 40 m.
		51 deg. 20 min.	Course	5 East	Degr. from the Merid. SW 25d. SW 61 d. 14 m.	Distan.	Diff. La	Diff. La.	M. dep.	M. dep.	51 d. 20′	diff. Lo.
		32 deg. 30 min.	SSW	Variation.	411	377	377	167	167	32 d. 30′	11d. 16′
		13 deg 10 min.	SWbW half W		798	387 lea.	387 lea.	698	698	13 d. 10′	41 d. 40
		Latitude by Ob∣servation.	Course by Compass.	Variation of Compass.	Degrees from the Meridian.	Dist. sailed.	North.	South.	East.	West.	Lat. By dead R.	Diff. of Longit.
		Degr. Min.	Points.	Degrees.	Degrees.	Leag. 10	Lea. 100	Lea. 100	Lea. 100	Lea. 100	D. M.	D. M.
26	a	Set sa••l March 25.	S b W half W	5 deg 30 min. E	SW 22 d. 30 m.	48		44 35		18 37	49 07
27	b		S b W half W	5 deg. 30 min. E	SW 22 d. 30 m.	49		45 27		18 75	46 51
28	c	44 deg. 31 min.	S b W half W	5 deg. 30 min. E	SW 22 d. 30 m.	51		47 12		19 52	44 30
28			Add up the Numbers, the sum is 148		136 74		56 64		04 14
29	d		SSW	2 deg. 45 min. E	SW 25 d. 15 m.	43		38 87		18 38	42 34
30	e	40 deg. 27 min.	SSW	1 degree East	SW 22 d. 30 m	46		42 50		17 60	40 26
31	f	38 deg. 30 min.	SSW	0 degr. East	SW 22 d. 30 m.	39		36 03		14 92	38 38
			Add up the Numbers, the sum is 128		117 40		50 90
			Correction by Observation 2 9		2 70		01 10	8
			The sum corrected is 130 9		120 10		52 00	38 30	07 43
			Difference of Latitude, Depart. from first Merid. 278		256 84		108 64
1	G	April, a Current sets E b S.	SW b S	11 d. 30 m. Cur.	SW 22 d. 30 m.	43		43 42		17 99	36 17
2	a	SW b S	11 d. 30 m. Cur.	SW 22 d. 30 m.	45		41 57		17 22	34 12
3	d	32 deg. 30 min.	SW b S	11 d. 30 m. Cur.	SW 22 d. 30 m.	42		38 80		16 07	32 19
		Set to th'Eastward by the Current in 3 days 22 Leagues and almost a half E b S by estimat.	Add up the Numbers, the sum is 134		123 79		51 28
		Correction by Observation 3 9	3 66		1 50		11
		The sum corrected is 131		120 13		49 78	32 30	10 46
4	c	Madara Island bears West distant. 8.58				8 58
		Difference of Latitude, Depart. from first Merid. 418		376 97		167 00	32 30	11 16
24	v	Set sail April 23. from Madara.	SW b S	5 d. 30 m. East by Current.	SW 28 d. 30 m.	36		31 75		16 97	30 55
25	c		SW b S	2 d. 45 m. East	SW 30 d. 45 m	46		39 46		23 65	28 57
26	d	27 deg. 43 min.	SW b S		SW 33 d. 45 m.	30		24 94		16 67	27 42
27	e	25 deg. 54 min.	SW		SW 45 degr.	51		36 06		36 06	25 55
28	f	23 deg. 47 min.	SW		SW 45 degr.	60		42 43		42 43	23 48
29	G	22 deg. 40 min.	SW		SW 45 degr.	28		19 80		19 80	22 47
			Numbers added, the sum is 151		194 44		155 58
			Correction by Observation 3		2 30		1 90	7
			Sum corrected is 154		196 74		157 48	22 40
29			Difference of Latitude, Depart. from first Merid. 572		573 71		324 48		20 47
30	a		SW b W	00 degr.	SW 56 d. 15 m.	45		25 00		37 42	21 25
1	b	May	SW b W	00 degr.	SW 56 d. 15 m.	47		26 11		39 08	20 07
2	c	18 deg. 57 min.	SW b W	00 degr.	SW 56 d. 15 m.	43		23 89		35 75	18 56
3	d		SW b W	00 degr.	SW 56 d. 15 m.	44		24 44		36 58	17 43
4	e	16 deg. 50 min.	SW b W	00 degr.	SW 56 d. 15 m.	39		21 67		32 43	16 37
			Add up the Numbers, the sum is 218		121 11		181 26
			Correction by Observation 7 8	4 33		6 50		13
			Sum corrected is 210 2		116 78		174 76	16 50
4			Difference of Latitude, Depart. from first Merid. 782 2		690 49		499 24		31 06
5	e	16 deg. 14 min.	WSW half W	5 degr. West	SW 67 d. 30 m.	31		11 86		26 64	16 15
6	G	14 deg. 03 min.	WSW half W	5 d. 30 m. West	SW 67 d. 30 m.	46		17 60		42 50	15 22
7	a		WSW half W	5 d. 30 m. West	SW 67 d. 30 m.	33		12 63		30 49	14 44
8	b	14 deg. 03 min.	WSW half W	5 d. 30 m. West	SW 67 d. 30 m.	30		11 48		27 72	14 09
			Add up the Numbers, the sum is 140		53 57		127 35
			Correction by Observation 5 2		2 00		4 80	6
			Sum corrected is 145 2		55 57		132 15	14 03
8			Difference of Latitude, Depart. from first Merid. 927 4		746 6		631 39		38 50
9	c	13 deg. 48 min.	W b S half W	5 degr. half	SW 84 d. 20 m.	55		5 39		54 73	13 47
10	d		W b S half W	2 degr. 50 min.	SW 87 d. 11 m.	60		2 94		59 92	13 39
11	e	13 deg. 10 min.	W b S half W	00 deg. 00 min.	SW 78 d. 30 m:	51		9 95		50 02	13 09
		Ship is in Lat. Bar∣badoes 69 lea. Ea.	Add up the Numbers, the sum is 166		18 28		164 67
11		Difference of Latitude, Depart. from first Merid. 1092		764 34		796 06		48 41
12	e	13 deg. 00 min.	West	5 d. 30′ Cur. sets	SW 84 d. 22 m.	39		3 80		38 60	12 59
13		The Current set S.	W b N	S. 2 d. 45′ Cur.	SW 81 d. 30 m.	26	81			25 71	13 10
13	G	13 deg. 11 min.	Difference of Latitude, Depart. from Lundy 1163		764 33		860 37	13 10	52 39
13		Barbadoes Island bears West distant of Leag. 5

Place this between folio 202. and folio 203.

Let this be our Example.

We will frame a Reckoning between the three Places before-mentioned, from Lun∣dy to Madara, from thence to Barbadoes, whose Distance in their Rhombs, and Diffe∣rence of Latitude, and Meridian-distance, I have put over in the head of the left-hand page, as you may see, answers to the words under. And in truth, I have found these Distances very near the truth; In two Voyages I differ but two Leagues, and that I was short. I worked it first out of a Mercator-Chart, and in Plain Sailing took the Product of that Work for my Distance, and Meridian-distance, and Course, as you have been already shewn in the first Question in Mercator-Sailing.

You see by the left-hand Page that we set sail the 25th day; but we entred it not in the right-hand Page until the 26th day at Noon: for it is to be understood,* 1.42 That since her setting sail March 25. to Noon of the 26th day, the Ship steers away and makes her Way good on the S. b. W. ½ W. Point of the Compass; but the Varia∣tion being 5 deg. ½ or half a Point to the Eastward, as you see in the fifth Column, therefore the Point she hath made good upon is only S. W. 22 deg. 30 min. as is ex∣pressed in the sixth Column: Upon this Rhomb she sails 48 Leagues, as in the seventh Column appears: And answerable thereunto I find in the Traverse-Table before-going, the Southing to be 44 35/1••0 Leagues, or by the Traverse-Scale 44 4/10. Leagues; and the Westing 18 37/100 Leagues by the Traverse-Scale 18 4/10 Leagues, as here in the ninth and eleventh Column appears by the Figures plainly set down. The Figures to the left hand signifie Leagues in this Journal, or Miles; and the two Figures to the right hand sig∣nifie the 100 part of a League: The Southing being 44 35/100 Leagues, which is 2 deg. 13 min. nearest; if that be substracted from the Latitude from whence you came, Lundy 51 deg. 20 min. it makes the Latitude the Ship is in at Noon to be 49 deg. 07 min. as appears in the twelfth Column. In the same manner, the second entrance, being the 27th of March, sheweth, that from the 26th day at Noon, to the 27th day at Noon, she made her way good upon the S. b. W. ½ W. Point of the Compass; but the Variation being 5 deg ½ Easterly, therefore the Angle of the Rhomb which the true Meridian was from the South to the Westward S. W. 22 deg. 30 min. and sailing 49 Leagues, the Southing is 45 27/100 Leagues, and the Westing 18 75/100 Leagues: So the La∣titude is now 46 deg. 51 min. So the third Entrance is the 28th day, the Course and Variation the same as before, and the Distance 51 Leagues; the Southing 47 12/100 Leagues, the Westing 19 52/100 Leagues: So the Latitude now is 44 deg. 30 min. You must understand the like manner of working of all the rest. What hath been said of a Reckoning may suffice; but it is of very good use to set down the Longitude in the last Column, and a Rule how to convert the Easting and Westing, that is, the Leagues or Miles in the East and West Column, into Degrees and Minutes of Longitude. I will give you this General Rule, that you may do it neer enough, without any sensible Error, on your Mercator Chart, or Polar Chart or Globe, provided these Rhombs differ not much one from another; by which Rule I found the Longitude for every Sum in the Journal. Say then,

As the Difference of Latitude,

To the Departure from the Meridian:

So is the Difference of Latitude in Meridional parts,

To the Difference of Longitude in Leagues or Miles.

The Difference of Latitude in the South Column summ'd up (as you must do as often as you have any notable Difference betwixt your observed Latitude and Dead Latitude) is 136 74/100 Leagues; omit the last Figure to the right hand 4/100, and then it will be 136 7/10.

The Departure from the Meridian in the West Column is 56. 64; omit the last Figure, it is 566: So you put them down.* 1.43

The Meridional parts for the Latitude 51 deg. 22 min. is	12002
The Meridional parts for the Latitude 44 deg. 30 min. is	9959
The Difference of Latitude in Meridional parts is	2043

Say then,

* 1.44As the Sum of the South Column, or Difference of Latitude 1367	313576
Is to the Sum of the West, or Departure from the Meridian 566	275281
So is the Difference of Latitude in Meridional parts 2043	331026
	606307
To the Difference of Longitude in Leagues 84 6/10	292731

Which reduced into Degrees is 4 deg. 14 min. for the 28th of March. So still you must remember to take the Sum of Difference of Latitude and Departure from the first Meridian. There are several other Rules you may see laid down before, for a Paral∣lel-Course of East and West, and other Rules to find the Longitude; as occasion re∣quires, you may make use of them: But this Rule saves you trouble, and comes neer enough in sailing several Courses.

* 1.45But let us proceed with our Journal. I observed the Meridian Altitude of the Sun the third day at Noon, that is from 30 at Noon to 31. I find my Latitude by obser∣vation 38 deg. 30 min. which, by Dead Reckoning it, is but 38 deg. 38 min. so the Dif∣ference is 8 min. Southerly; but being assured of a good Observation, I correct the Dead Reckoning thereby, by this Rule of Proportion, saying,

As the Sum of the North Column corrected is 1201	307954
To the Sum of the East Column corrected 520	271600
So is the aforesaid Increasing Southerly 27	143136
	414736
To the Increasing Westerly 1 17/100 Leagues	106782

* 1.46

Which is 1 League 1/10, and something more, not to be taken notice of. This Rule of Proportion Mr. Norwood hath laid down in page 111. of his Seaman's Practice, in the Description of his Journal in Miles, from Barmoodoes or Summer Islands to the Li∣zard; which method I do in many things follow, but not all: But this Rule that I propose is by the Traverse-Scale, which I hold best, which is thus.

By the Traverse-Scale.

Extend the Compasses from the Point made good in the last summing up, to the number of Leagues or Miles Difference of Latitude by Observation, and by Dead Rec∣koning, in the Line of Numbers; the same Distance will reach from some Points from the East and West, to the Difference of East or West.

As for Example.

Extend the Compasses from 2 Points and a little more (which was the Sum of the Course made good the 31 of March) unto 2 7/10 Leagues, which is 8 min. or there∣abouts in the Line of Numbers; the same Extent will reach from 6 Points to 1 1/10 Leagues and something more in the Line of Numbers, and that is the increasing Westerly. You may also with the same Extent correct the Distance, if you put one Foot at W or 100 in the Line of Numbers, the other will reach to the Distance 2 9/10 Leagues corre∣cted by Observation, as you see I have done in the Journal. So you see, That understand∣ing perfectly the Use of the Traverse-Scale, you may do the same, and more readily, as Mr. Norwood doth with his Table, to every Degree and Minute of the Quadrant, without sensible Error.

Now this Difference being found, I add therefore and put down in the South Co∣lumn the Difference 2 70/100 Leagues, and the West Column 1 16/100 Leagues, and under Distance 2 9/10 Leagues: Now the same corrected is by observation 130 9/10 Leagues, Distance 120 10/100 Leag. Southing and Westing 52 Leag. 8 min. substracted from the Dead Latitude, make 38 deg. 30 min. the true corrected Latitude according to observa∣tion:

Then I sum up the first Sums of the 28 of March, and this Sum corrected 31 of March together, and you have the Distance 278 Leagues,* 1.47 Difference of Latitude 256 84/100 Leagues, and Departure 108 64/100 Leagues, and by the Rules before-given 256 8/10 Leagues Southing, and 108 6/10 Leagues Westing; and with the Difference in Me∣ridional Leagues 364 7/10 Leag. I find the Difference of Longitude in Leagues 154 ••/10 Leagues, converted into deg. and min. is 7 deg. 43 min.

In like manner, upon the third of April I should be in Latitude 32 deg. 19 min. but by very good observation, I find the Ship in the Latitude 32 deg. 30 min. that is, not so much Southerly by 11 minutes: therefore to correct it by Observation, I put under Distance 3 9/10 Leagues, and in the South Column 3 66/100 Leagues, and in the East 1 50/100 Leagues, and under Dead Latitude 11 min. I substract the corrected Difference of Distance out of the Sum over it, and likewise the corrected Difference in the North Column out of the Sum in the South, and likewise the East out of the West Column, and add the 11 min. to the Dead Latitude, and then you have the Sum corrected; but if there be any Current, you may set it down, and allow for it, and note it down, as is that Example following the first of April to the third, and by your Traverse-Scale presently find how much the Current hath set you to the Eastward.

But if your Course be neer the East and West,* 1.48 it is sufficient to correct it in Lati∣tude only, as in the Example of the 12th and 13th of May; for in that Case the Longitude cannot be corrected but from some further ground. Now to set down this Reckoning upon the Plain Chart, or common Sea-Chart, it is needless and unnecessary: The better way is to set down every one of the Sums as they are corrected by Observa∣tion, in the same manner as you are directed in the latter end of the third Chapter of this Book; and so by the total Sums of the Difference of Latitude and Departure from the first Meridian, or Latitude and Meridian-distance, you may set it down on your Draught or Chart as often as you please with ease.

Now to set off every Sum corrected in Degrees of Latitude and Leagues of Longi∣tude, you have a Scale of Leagues or Miles for that very purpose, and Directions how to do it, in the ninth Chapter of this Book: But if you are desirous to set down your Reckoning in a Mercator or Mr. Wright's Chart, on in the Polar Chart, you have in the 12th and 13th, or last two Columns of your Journal, the substance and principal scope of your Reckoning set down as often as you sum up or correct your Reckoning: name∣ly, your Latitude and Longitude; which whensoever you have a desire to set down in the foresaid Chart, or any other graduated Chart, with Degrees of Longitude and La∣titude, you may readily do it.

As for Example. Suppose I would set down the Plat of the aforesaid Journal from the 25th of March to the 13th of May, I find the Latitude against the 25th of March 51 deg. 20 min. and the Latitude of the Barbadoes 13 deg. 10 min. and the Difference of Longitude 52 deg. 35 min. Therefore in the Latitude of 13 deg. 10 min. I draw or point out an occult Parallel, and reckon 52 deg. 35 min. from the Island Lundy towards the West: I draw by that Longitude an occult Meridian;* 1.49 the Intersection of this Meridian with the foresaid Parallel is the Point representing Bar∣badoes, or the Place of the Ship; and the like is to be understood of any of the other: And so I put down in the General Chart of Mercator the 8 Points of the Ship's Place, 1 a, 2 b, 3 c, 4 d, 5 e, 6 f, 7 g, 8 h, as there you may see. This form of keep∣ing a Reckoning is the most fit and agreeable of all others as I have seen or heard of, to all sorts of Charts, Maps, or the Globe it self, and to all kinds and ways of Sailing whatsoever.

CHAP. XVIII. A Description of the following Table of the Latitude and Longitude of Places, and the way how to find both.

THE ancient Geographers, from Ptolomy's time downward, reckoned the Longitude of Places from the Meridian, which passeth through the Cabo Verde Islands; and others have the beginning at the Canary Islands; and Jodocus Hondius beginneth at the Isle Pico one of the Azores; and Mr. Emery Mulli∣neux doth account the Longitude from the Westermost parts of St. Michael's, another Island of the Azores: who, albeit they differ greatly in respect of the beginning of each of their several Longitudes, they come all to a neer agreement for their Difference of Longitude from any particular Meridian or Place: And for the exact setling of La∣titudes, we have many certain helps; but the Longitude of Meridians hath still wea∣ried the most able Masters of Geography. By Latitude and Longitude the Geographers strive to represent the Parts of the Earth, that they may keep Symmetry and Harmony with the Whole.

Now the Longitude of any Place is defined to be an Arch or Portion of the Aequi∣noctial, intercepted between the Meridian of any Place assigned; as the Meridian that passeth through the Lizard, the most Southern Land of England, or any other Place from whence the Longitude of Places is wont to be determined. Many have en∣deavoured to set down divers ways how to find by observation the Difference of Longitude of Places; but the most certain way of all for this purpose, is confessed by all Learned Writers to be by the Eclipses of the Moon: But now these Eclipses hap∣pen but seldom, and are yet more seldom and in very few places observed by the skilful Artist in this Science; so that (some there are) but very few Longitudes of Pla∣ces designed out by these means.

If you would know how to find out the Longitude of any Place by the Eclipse of the Moon, you must first get some Ephemerides, as the Practick Tables, or Mr. Vincent Wing's Directions in his Harmonicon Coeleste, pag. 150. or any other Learned Mathe∣maticians Calculation, and see what hour such an Eclipse of the Moon shall happen at that Place for which the said Tables were made; then afterwards you must ob∣serve the same Eclipse in that Place whose Longitude you desire to know. Now if the time of the Eclipse agree with that other for which the Tables were made, then you may conclude, that both Places have the same Longitude, and are scituated under the same Meridian. But if the number of the Hours be more than the Place you are in is scituate Eastward, you must therefore substract the less Number out of the greater, and the Remainer must be converted into Degrees and Minutes.

A TABLE OF THE LONGITƲDE and LATITƲDE Of the most Notable Places, That is, HARBOURS, HEAD-LANDS, and ISLANDS OF THE WORLD. Newly Corrected, and Composed after a new manner, by beginning the said Longitude at the Meridian of the most Southern Port of England, the Lizard.

By Capt. SAMUEL STURMY Math.

The Sea-Coast of Newfound-Land, and New-England.

The Places Names.	North Latitude	West Longit.
	D.	M.	D.	M.
Cape Honblanto	52	11	50	14
Belile	51	02	48	44
Cape Bonavista	49	19	47	42
Trinity Bay	48	54	49	04
Bacalao Island	48	40	46	55
Consumption Bay	48	21	47	49
Cape St. Francis	48	01	47	27
Cape Daspaire	47	36	46	03
Cape de Raca	46	27	46	30
Bay Bulls	47	28	47	11
St. John's Harbour	47	47	47	21
Plasantia Bay	47	32	47	41
Cape St. Larinso	47	10	48	59
Island St. Paly	47	36	50	18
Cape Raya	48	05	52	49
Cape Deganica	54	01	53	21
New-Eng. Cape S. Charles	52	48	52	23
Cape Brittan	46	01	52	57
Cape Salila	43	46	55	22
Cape Codde	42	21	61	32
Boston	42	39	64	36
Plymouth	42	07	62	35
Nantucket	41	08	60	17
Martins Tinyard	41	17	61	12

The Sea-Coasts on the main Continent in A∣merica, or West-India.

The Places Names.	Latitud.	Longit.
	D.	M.	D.	M.
Elizabeth Island	41	02	62	04

Bloik Island	40	55	62	36
Long Island	40	45	63	16
Cape May	39	55	64	45
Virginia. Cape Charles	37	47	65	26
Cape Henry	37	01	65	38
Cape Hatcrass	35	49	65	46
Cape Fara	34	06	69	56
Cape de Catocha	21	23	80	37
Cape de Camaron	16	05	76	19
Cape de Gratias	15	31	70	56
Cattergaine	10	24	65	06
Bay Tonto	12	10	62	36
Cape St. Roman	11	55	60	36
Cape Dacodara	11	08	56	38
Cape Trag, or 3 Points	11	17	55	41
Cape Brama	09	21	54	16
Cape Dasbassas	08	20	53	11
Suramo	06	09	50	56
Suranam	05	58	49	52

The West-India Islands.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Defonsseaca Island	12	23	48	30
La Burmuda	32	25	56	00
Behama	27	57	73	06
Teavis	27	27	71	04
Sigvatro	26	18	68	45
Guatro	25	47	68	00
Guamina	25	15	67	53
Tiango	24	33	66	30
Guanahimo	23	50	66	39
Mayagnana	23	05	66	51
Caycoss	22	05	64	31
Amiana	21	40	64	38
Inagua	21	19	67	03
Yamatta	22	32	67	49
Soamia	24	20	68	50
Javaqua	25	10	71	30
Yamia	24	22	70	10
St. John	18	30	60	42
Santa Cruce	17	42	59	18
Anguilla	18	48	57	00
St. Martin	18	35	56	47
St. Bartolama	18	15	56	33
Barbada	17	18	55	39
Antego	16	32	54	52
Dassijada	16	00	54	36
Marigallatita	15	41	55	26
Dominica	15	00	55	05
Mattalina	14	20	54	44
St. Lucia	13	30	54	43
Barbadus	13	10	52	58
Tobago	11	12	53	06
Point Degallaia	10	45	53	31
Gianada	12	10	54	32
St. Vincent	12	50	54	28
Guardadupa	16	00	55	31
Monsariat	16	20	55	41
Maves	17	00	56	27
St. Cristova	17	30	56	45
Island Devas	15	57	57	28
Island Blanco	12	20	56	52
Margaita	11	28	56	37
Turtuga	11	30	57	40
Island Derickilla	12	19	58	01
Boca	12	19	58	53
Island Deavos	12	29	59	22
Bonoga	12	32	60	54
Quissa	12	25	60	39
Moagos	12	20	61	55
East end of Hispaniola	18	47	62	28
Middle of Hispaniola	18	30	64	58
West end of Hispaniola	18	25	68	26
East end of Jamaica	18	00	71	58
Jamaica Harbour	18	15	72	57
West end of Jamaica	18	38	74	57
The East end of Cuba	22	00	75	56
Caimanis	19	41	77	41
Grand Caiman	19	21	78	45
Santavilla	17	28	77	50
Mosquito	14	50	76	04
Guanabo	16	33	81	19
Guanabimo	16	10	83	04
Cozumal	19	25	84	56
Lasalleerauas	22	00	87	58
The Island Delas	23	30	91	58
Abraio	25	50	94	00
Labarmaia	22	55	93	16
Island Dearanas	22	36	93	14
Triango	21	23	93	05
Zarka	20	50	93	00
The Island of Proudanco	13	27	81	16
St. Andrea	12	42	80	57

The Sea-coasts of Brazilia.

The Places Names.	South Latitud.	West Longit.
	D.	M.	D.	M.
The River Amazones	00	00	41	30
The Island of St. Paul	00	55	14	36
The Island of Ascension	07	48	20	06
Cape Blanco	02	25	22	29
Island Rocas	03	42	17	16
Island Farnando	03	40	15	16

Abratho	05	00	17	56
Cape St. Raphall	06	10	19	36
Cape St. Augustin	08	25	18	28
River St. Mignall	09	30	19	01
The River Roall	11	21	20	41
River Gianda	14	49	22	06
Cape de Abeotho	17	52	21	42
St. Harbara	18	11	21	06
Island Ascension	17	19	17	01
Trinidada	19	50	14	24
St. Maria Dagasta	19	38	12	14
Island de Martin	19	00	08	03
Island de Pidos	21	52	05	51
Cape St. Toma	21	47	23	38
Cape Frio	22	52	24	43
Cape St. Maria	35	00	37	11
River de Platta	35	50	45	52
Port St. Juliano	50	00	52	30
The Streights of Ma∣gellane	53	30	56	30
Cape de Sancto Spirito	52	20	58	30
Cape Victoria, West end of the Streights	52	30	65	40
Lima Cape	12	00	80	30
Cape Guya, Cape Blancoo	06	10	85	30
Cape St. Frainsco	01	30	80	30
Cape St. Frances	North.	West
Point de bon matre	07	30	80	00
Nombre de Dios. W. Sea	10	00	77	30
Nova Albion, or New-England, in the South Sea, the back side of it	46	00	162	30
Cape de Fortuna (Aniar. fra.	55	30	170	E 00
Insulae Salamonis	So. Lat.	W. Long.
Nombre de Jesus	05	50	169	30
Tapan Insule	36	N. 00	153	E 00
Cape de Buena Desco	01	S. 00	155	00

The East India Islands.

The Places Names.	South Latitud.	East Longit.
	D.	M.	D.	M.
Hipon Island	06	45	125	20
Bantam, East-India	06	15	115	34
Jamba Islands	01	49	122	25
South end of Sumatra	05	52	125	48
Middle end of Sumatra	01	30	120	49
North end of Sumatra	05	28	116	35
Gomaspala	05	40	116	29
Niobar	07	00	115	04
Island Desombro	08	00	114	44
Island Rusta	09	50	114	33
Quarinibar	11	10	114	44
Ghitra Andomaio	12	00	114	41
Island Dandemajo	13	00	114	39
Island Decocoss	14	30	115	12
Celloan	07	50	98	39
Doda Safia	09	40	93	02
Andaio	11	30	90	51
Garine	10	50	90	56
Moique	09	05	91	29
Cuballa	08	53	91	07
Island de Prosoll	10	23	90	55
Island de Zocha	11	12	90	45
Chorebaman	12	32	87	55
Sucatra	12	18	74	01
Abdelcari	12	12	71	44
Apoluria	09	S. 20	90	50
Adu	05	39	88	50
Degomo	02	40	87	35
Piedros Blanco	06	10	76	55
Diego gratiosa	08	30	78	15
Set Hermanas	03	02	70	25
Domes Caicuhas	03	21	65	24
Island Quellallo	03	40	64	20
De Almiranta	03	57	63	28
Agnalaga	09	00	66	15
Asdore Has	09	05	65	02
John de Nava	09	00	63	26
Cosmobodo	09	40	61	52
Donatall	08	20	59	57
Aignos	09	30	58	18
John de Comoro	09	00	57	20
Pemba	05	09	53	30
Zanziba	06	26	53	35
Mansia	07	50	53	08
John Demiz	10	48	54	24
Comoro	11	20	55	48
Mohalla	12	11	56	25
Foanna	12	09	57	03
Mayatta	12	40	57	55
St. Christopher	14	30	56	03
John de Nova	17	20	55	29
Baslas de India	22	10	55	22
North end of St. Lau∣rence	25	37	60	54
St. Apohima	20	50	65	54
Domscascahas	20	50	66	54
Moroslass	20	10	68	44
Dosgarias	15	20	70	43
St. Branda	17	13	74	44

Englands Forest	20	50	71	14
Diego Roize	20	05	74	54
John de Lisbone	25	24	68	32
Romoras	28	19	81	21

The Sea-coast on the Main Continent in the East India.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Malacca	01	41	116	14
Queda	06	47	117	44
River de Care	10	45	118	54
River Bongale	22	09	121	33
Aicopoir	20	19	112	39
Samnabron	18	30	108	52
Arme Gon	14	35	100	27
Naga Patam	11	21	99	59
Cape Comorin	07	50	97	39
Cochin	09	40	97	29
Callant	10	48	97	27
Mongalar	12	40	97	19
Dodall	17	01	98	55
Goa	14	40	97	01
Chaul	18	10	98	51
Calecut in East India	11	30	92	58
Macao in the K. of Pegu	19	30	112	49
Domon	19	54	99	01
Surrat	21	00	99	36
Dio	20	48	96	57
River Decinda	24	55	95	39
Gudar	24	50	89	28
Cape Muchoaridan	25	32	82	39
Cape Russallgat	22	07	84	39
Cape de Ponto	18	19	79	09
Dofar	17	00	75	04
Cape de Matriaia	15	33	72	39
Adon	13	08	66	56
Cape Guardafuy	11	40	71	24
Cape de Baslos	04	30	65	19
Magadox	02	30	59	24
Molinda	02	S. 42	52	11
Tanga	05	20	52	01
Cape Faslto	08	02	52	24
Dagnada	15	17	53	26
Cape Corintes	23	30	48	51
Cape St. Marin	25	40	46	59
River St. Lussea	28	25	46	09
Bay Doliagoa	33	18	43	59

The Sea-coast from Cape Bone Esprance to Guiney.

The Places Names.	South Latitud.	East Longit.
	D.	M.	D.	M.
Island Desistian	36	57	11	44
Island Degiaiatica	37	56	14	04
Cape Agullas	36	20	33	54
Cape Bonee sprance	35	50	32	54
Cape Sacos	29	40	30	14
Ascention Island	07	48	05	24
St. Elana	16	03	10	08
St. Elana Nova	16	03	19	48
Bassas	17	45	27	35
Cape Lado	10	00	29	23
Cape Padron	06	00	29	04
Cape Lopas	01	00	25	21
Anabona Island	01	22	22	56
Island St. Mathaos	01	40	07	45
Island St. Toma	00	N. 10	23	34
Island Chocos	00	40	23	50
River Gaboan	00	10	27	16
River de Angai	01	00	27	30
Island de Principas	01	50	25	14
Island Defarnanda	03	10	26	06
River Boilin	02	42	27	29
River Decainaronas	04	00	27	09

The Sea-coast from Samsons River to the River of Gambo, Coast Guiney and Barbary.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Old Callabar	04	50	25	15
New Callabar	04	40	23	37
Cape Formossus	04	03	22	52
River Binnin	06	50	22	12
River Dallagoa	07	40	19	49
River de Valta	06	05	16	52
Cape 3 Points	04	10	13	10
River St. Andrass	05	23	08	06
Cape de Palmas	04	40	06	05
River de Casto	05	20	03	48
Cape Mounta	05	23	01	46
Cape Roxo	11	38	6	W. 13
River of Gambo	12	47	2	17
Cape de Verd	14	24	6	57

The Cape de Verd Islands.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Abrolho	00	00	16	16
Vigia	03	10	10	01
St. Paul	01	32	14	56
Rochass	02	30	16	16
Varo	11	12	21	07
Vigia	12	26	19	48
Abrogo	16	36	10	19
Brava	14	49	15	14
Fogo	14	42	14	56
Lantiago	14	52	14	22
Maya	15	00	14	02
Bonanista	15	58	13	49
Sall	17	00	13	26
St. Nicholas	16	30	15	44
St. Lucia	16	50	16	08
St. Tincant	16	55	16	32
St. Antonio	17	07	16	56
Cape Blanco	20	30	9	26
Cape Boyadojo	26	55	2	52
Marquepana	27	22	2	11
Cape Denao	28	52	1	46
Cape Gillam	29	50	1	29
Cape de Garto	30	30	1	25
Cape Cantin	32	27	1	06
Tangiar East Longit.	35	36	1	49

The Sea-Coast on the Main, from Tangiar to Joppa in the Straights.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Wadallo in the Straights	34	57	3	13
Ballis	34	57	3	48
Oran	35	46	7	59
Tanis	36	30	9	18
Sally	36	40	9	48
Argier	36	40	10	54
Tadallis	36	48	11	25
Ragin	36	50	11	44
Gion	36	50	13	30
Gigaria	37	03	14	26
Colla	37	09	15	14
Stora	37	09	15	44
Bona	37	19	16	44
Bozarat	37	30	17	50
Tunis	36	50	17	24
Cape Beun	37	05	18	11
Sussa	36	02	18	07
Britto	35	23	18	41
Chereune	34	56	18	36
Cape Mizarrata	32	18	24	00
Cape de Solli	31	1	25	49
Cape Russutta	32	58	29	26
Cape Roattini	32	18	32	04
Alexandria	30	40	41	28
Michallat	30	30	41	55
Cairo	30	35	41	44
Joppa	31	42	43	39

The Coast from Antiochia to Sagua in the Straights.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
From Antiochia to Sagua	34	54	46	26
Cape Pollapolla	35	35	44	01
Cape Seridioni	35	55	41	24
Cape Decoxman	36	16	36	44
Cape Babarnau	37	58	36	22
Land Miri	39	12	37	05
Incomodio	40	26	40	39
Constantinople	40	56	40	33
Gallippollo	40	20	37	59
Cape Degriffa	40	12	37	11
Cape Pimra	40	26	32	23
Cape St. George	39	28	32	10
Cape Collo	37	40	32	35
Cape Sille	37	15	31	52
Cape Matapan	36	28	30	53
Casteltornis	37	45	30	32
Drugromastra	38	38	30	40
Cape Linga	40	18	29	38
Hirassa	40	57	30	38
Antavara	41	49	30	54
Cattaro	42	21	29	47
Ragussa	42	29	28	57
Stanio	42	57	28	11
Trovor	43	30	27	37
Cape Casta	43	27	26	48
Salconico	44	01	27	24
Zaro	44	05	26	39
Sagua	44	47	25	49

From Cape Fistria to Giblitore.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Cape Fistria	44	40	24	10
Venetia	45	37	22	45
Gorro	44	57	21	35
Giavocha	44	19	21	26
Ancana	43	25	24	29
Angollo	41	31	27	02
Cape St. Massa	39	52	26	53
Gallipoli	40	08	27	04
Cape Callom	38	50	25	40
Cape Sparta-venta	37	46	24	16
Pollicastro	40	08	24	02
Sallarno	40	51	23	32
Napolis	41	08	22	51
Rome	41	50	21	09
Ciritacha	41	46	20	24
Leagueorne	43	28	19	03
Cape Malle	43	51	15	37
Cape Larci	42	58	14	38
Tallone	43	00	14	04
Marsilia	43	12	12	44
Cape Degofrito	41	41	11	18
Cape Pallomallo	40	10	8	39
Cape Martin	38	46	8	20
Allagant	38	20	7	14
Cape Paul	37	28	7	11
Cape Degat	36	47	5	24
Valis	36	49	3	33
Malagoe	36	45	3	07
Giblitore	36	40	2	06

The Islands in the Straights, called the Archipelago.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Sarfanto	36	57	33	39
Sarfo	37	17	33	22
Famania	37	28	33	18
Trava	37	49	34	41
Pipor	39	32	33	51
Lassor	39	58	33	51
Lamo	39	44	33	38
Stripo	39	16	33	51
St. Penaga	38	52	33	03
Andrea	38	12	34	46
Ipsava	38	28	35	11
Mortalin	38	54	35	52
Stavisratta	39	28	35	14
Lamnoss.	39	41	35	49
Embross	40	09	36	09
Palamos	40	14	36	04
Tassa	40	00	35	19

Islands in the Straights.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Sapientia	36	47	30	16
Stouty	37	10	29	43
Zant	37	37	29	38
Cape Sidro	38	15	29	33
Paxa	38	49	29	30
Corfu	39	26	29	26
Faimo	39	44	29	19
Sessino	40	22	29	14
Pianassa	41	52	26	08
Trinite	41	50	25	53
Pollagassa	42	17	26	37
Mallida	42	37	28	03
Corsella	42	35	27	38
Agusta	42	36	27	13
Catssalla	42	40	27	03
Catsso	42	44	26	58
Lissa	43	00	26	33
Buzo	43	02	26	18
St. Androa	43	07	25	58
Poma	43	14	25	48
Island Grosso	44	00	25	36
Saussaga	44	20	25	02
Piper	35	52	22	15
Malta	36	00	21	54
Comino	36	15	21	24
East end of Cyprus	34	48	44	18
Middle of Cyprus	34	18	43	09
West End of Cyprus	34	22	41	47
Rhodes	35	40	37	22
Sivia	36	05	37	17
Gozo	34	37	32	39
East end of Candia	35	04	35	32
Middle of Candia	35	08	33	56
West end of Candia	35	15	32	25
Scarpanta	35	10	36	04
Caros	35	35	35	39
Langa	36	33	36	02
Stampalia	36	11	34	59
Levatta	36	38	34	54
Niza	37	02	34	31
Cavari	36	40	32	16
Palla	36	52	32	09

Cardinals Hats	37	25	32	31
Forlconari	36	59	32	37
Millo	36	40	33	19
Goza	35	41	20	51
Samatto	35	46	19	39
Lampadossa	35	58	19	59
Linossa	36	20	20	05
Pantalaria	36	53	19	35
Kambro	37	10	18	34
Maritimo	37	52	20	02
Massina	38	07	23	21
East end of Sicilia	37	07	23	24
Middle of Sicilia	37	42	22	09
West end of Sicilia	37	52	20	07
Ustica	38	50	20	58
Allicur	38	45	21	47
Fallieur	38	43	22	01
Listallin	38	34	22	32
Lipari	38	40	22	27
Volcana	38	48	22	30
Stromballo	39	03	23	02
Foldemassina	38	20	23	29
Iscia	40	46	21	36
Ponussa	40	40	20	32
Palmarolla	40	50	19	59
Ginnute	41	59	19	48
Gigio	41	58	19	39
Crista	41	55	18	51
Planossa	42	07	18	33
Lilbo	42	31	18	36
Caprera	42	58	18	21
Gargona	43	20	18	28
North end of Corsica	42	55	17	26
Middle of Corsica	42	05	17	07
South end of Corsica	41	20	17	01
Taloro	40	56	17	19
Azanera	41	08	16	22
North end of Sardinia.	41	10	17	25
Middle of Sardinia.	40	06	16	54
South end of Sardinia.	38	56	16	37
The Island of St. Pedra	39	20	16	03
Pallmade follo	39	11	16	05
Sarpentara	39	00	17	18
Callatta	37	57	16	28
Minorke	39	55	12	16
Mayorka	39	38	11	12
Cabrea	39	07	11	05
Collombratta	39	50	08	44
Evissa	39	05	09	57
Formentara	38	44	09	54

The Canary Islands.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Forta Ventura	28	12	06	28
Sanslorrotta	28	51	06	08
Allegranssa	29	11	06	13
Grand Canary	27	43	08	31
Tenarife	28	20	09	28
Gomara	28	09	10	15
Faro	28	05	10	43
Palma	28	58	10	42
Salvagas	30	05	08	57
Dazarts	32	08	09	46
Madara	32	27	11	19
Por. Santo	33	14	10	09

The Western Islands.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Abraoso	37	55	29	46
Vaso	40	30	27	28
Corvo	40	09	24	59
Flauris	39	30	24	55
Fiall	38	49	22	13
Pico	38	30	21	37
St. George	39	00	21	20
Trassara	39	31	20	22
Gratiassa	39	30	21	11
Abrajo	39	52	18	53
Vajo	38	43	18	23
St. Michael	38	00	18	16
Horningo	37	25	17	36
St. Maria	37	00	17	56
Vejo	42	22	18	56
Island Varda	44	48	22	46
Maiden Island	46	30	23	36
Old Brazeel	51	03	09	56

The Sea-coast of Portugal and France, from Cales to Callis.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Cales	36	32	1	24
Cape St. Maria	36	52	0 We.	24
Cape St. Vincent	37	00	1	18
Lisbone	39	08	1	06
Rock of Lisbone	39	00	2	04
Burlings	39	43	2	28
Isles of Boyon	42	22	2	00
Cape Finisterre	43	10	2	55
Cape Corian	43	21	2	56
Sazarka	43	38	1	52
Cape Artingal	44	08	0	06
Cape Pinas	44	04	0 Ea.	52
Lyons	43	49	2	06
St. Andrea	43	43	2	36
Bilbo	43	41	3	20
St. Abastian	43	40	4	19
Burdeux	45	10	5 Ea.	44
Bloy	45	28	5	19
Shorant	46	00	4	56
Rochel	46	17	4	54
Toppar	45	36	3	29
Mamosin	45	49	4	34
Olloron	45	58	4	30
St. Martins	46	16	4	29
Barges	46	30	3	54
Uss	46	44	3	20
Piller	47	04	3	22
Nants	47	45	4	15
Radon	47	55	3	33

The Coasts of Britanny.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Cardinals	47	27	2	24
Ballile	47	19	2	14
Groy	47	35	1	54
Glannats	47	33	1	34
Pennes, or Pennemark	47	35	1	10
Paiker	48	00	0 We.	01
Seames	48	04	0 Ea.	23
Camarita Bay	48	25	0	56
Brist	48	35	0	59
Conquer	48	45	0	19
Ushant	48	48	0	05
Island of Basse	49	01	1	27
Morlias	48	54	1	39
Satta Isles	49	7	2	02
St. Mallas	48	45	3	39
Chosol	49	5	3	44
Boffin	49	19	3	42
Jarze	49	30	3	24
Sark	49	37	3	09
Garnasse	49	43	2	49
Arme	49	48	3	05
Caskats	50	7	3	09
Arderny	50	2	3	37
Cape Hag.	50	4	3	52
Cape Barslaw	49	57	4	32
Rone	49	46	5	54
Saine Head	50	4	5	28
St. Vallari	50	8	5	29
Deip	50	15	6	39
Callis	51	13	7	16

The Sea-coast of England from the Lizard to Newcastle.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
The Lizard	50	10	00	00
Falmouth	50	22	00	12
Foy	50	35	00	34
Ramhead	50	34	00	49
Plymouth	50	36	00	51
The Edistone	50	22	00	44
The Start	50	27	1	19
Dartmouth	50	37	1	28
Torbay	50	42	1	36
The Bary	50	40	1	35
Absom Bar	50	47	1	37
Lime	50	55	2	10
Chiddock	50	57	2	14
Portland	50	50	2	36
Weymouth	51	3	2	44
Pool	51	4	3	34
Isle of Wight	50	58	4	08
Portsmouth	51	8	4	24
Shoram	51	7	4	57
Beache	50	58	5	15
Rye	51	13	6	09
Dongeness	51	9	6	15
Dover	51	25	6	32
Ripraps	51	13	6	49
The South Foreland	51	22	6	44
The Downs	51	25	6	45
Sandwich	51	27	6	33

North Foreland	51	28	6	44
Margaret	51	29	6	34
Quinborow	51	30	6	01
Rochester	51	28	5	54
London	51	30	5	24
Gravesend	51	35	5	44
Tilbury Hope	51	38	5	54
Colchester	52	04	6	02
Harwich	52	11	6	27
Ipswich	52	14	6	24
Orforduass	52	20	6	35
Alborow	52	24	6	39
Yarmouth	52	45	6	42
Winterton	52	52	6	46
Cromar	53	20	6	41
Blackness	53	4	6	19
Wells	53	7	6	02
Lin	52	58	5	33
Boston	53	9	5	02
Grimsbe	53	39	4	28
Hull	53	45	4	16
The Sporne	53	45	5	01
Burlington	54	00	4	28
Flamborough Head	54	8	4	35
Scarborough	54	20	4	21
Whitby	54	35	4	10
Hartlepool	54	37	3	29
Sinderland	54	42	3	26
Shelles	55	02	3	24
Newcastle	54	58	3	14

The Coast of Scotland.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Barwick	55	49	2	39
Leith	56	3	2	09
Dondee	56	26	2	17
Aberdeen	57	22	2	29
Bafom Nass	57	48	1	34
Cat Nass	58	37	1	38
Isles of Orkney	58	50	2	02
Fair Esle	59	30	3	19
Shetland	60	22	2	54
Fair Head	58	43	2 W.	21
Island Lewes	58	30	2	48
Skey Island	57	40	2	3

The Sea coast of Flanders and Holland from Callis to the Scaw.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Duynkirk	51	18	7	49
Ostend	51	30	8	29
Sluice	51	38	9	11
Zealand	51	48	9	05
The Brill	52	8	9	08
Antwerp	51	37	9	46
Rotterdam	52	5	9	48
Amsterdam	52	40	10	01
The Tassel	53	20	10	16
The Uly	53	30	10	12
Skelling	53	35	10	14
Amaland	53	40	10	16
Embden	53	44	11	06
Breme	53	50	12	26
Hambrough	54	4	13	26
Holikeland	54	30
Stonar	55	17	12	08
The Scaw	57	52	13	51

The Sea-coast from the Lizard to Holy-head.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Lands end	50	20	0	34
Gulfe	50	11	1	22
Scilly	50	7	1	21
7 Stones	50	18	1	16
Harty Point	51	10	0 E.	19
Londy	51	20	0 W.	3
Holmes	51	26	1 E.	44
Bristol	51	29	2	34
Glocester	52	3	2	39
Caldy	51	53	0	10
Milford	52	5	0 W.	6
Ramza	52	12	0	38
Studwalls	53	12	0	04
Barzs	53	13	0 W.	16
Westchester	53	37	01 E.	04
Holy-head	53	44	0	26
Isle of Man	54	25	0	36

The Sea-coast of Ireland.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Lamby	44	44	1	46
Dublin	53	32	1	56
Wexford	52	33	1	44
Waterford	52	30	2	24
Corke	52	01	2	56
Kingsail	51	52	3	08
Old Head	51	40	3	14
Mizand Head	51	28	5	21
Cow and Calf	51	42	5	42
Skillukes	52	00	6	06
Blaskos	52	15	6	11
Limbrick	53	04	4	51
Loopas Head	52	44	5	41
Gally Head	53	20	5	36
Galloway	43	40	5	16
Isles of Aion.	53	21	6	36
Slages	54	27	6	21
Isles of Are	55	18	5	36
Fore Head	55	38	4	56
Fair Foreland	55	35	2	36

The Sea-coast of Iseland-Island.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Mage Nass	61	32	2	51
Merchant Foreland	63	52	11	42
Horn	63	42	10	16
Silly	64	50	9	56
Bargafar Point	65	27	7	01
Long Nass	66	26	7	36
Grimsa	66	42	9	20
Marza	67	8	9	42
Rage Point	66	40	12	00
Fair Foreland	65	40	14	53
Snow Hill	65	11	14	50
Rook Point	64	00	14	09
West main Isles	63	17	12	53
Gammat Isles	63	48	15	06
Grimes Hole.	63	23	15	46

The Sea-coast In the Sound.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
Lizol	57	35	14	9
Anall	57	8	14	41
Elsen-nore	56	40	15	21
Copenhaven	56	17	15	18
Mooan	55	41	15	29
Witmond	55	20	16	32
Ismond	55	20	16	44
Burnthom	56	00	17	40
Erthholm	56	10	17	38
Gathe sand	56	15	22	03
Farro Sound	58	48	21	53
Gotland	58	20	21	22
Heda	55	53	21	29
Dormamel	56	55	23	44
Dines Nass	58	22	23	55
Righa	57	50	26	25
Runen	58	38	25	14
Parun	58	52	26	54
Shorham	58	58	26	30
Wile	59	6	25	6
Ardenbro	59	5	24	6
Dagaratt	59	44	23	55
Ogsholm	59	58	24	32
Norgin	60	10	25	14
East Rand	60	12	28	41
Wibro	61	16	30	00
Wakato	61	16	29	42
Patting	61	00	28	45
Burga	61	2	27	14
Rostbrugh	61	3	25	04
Abbo	61	8	23	28
Bushoers	60	9	21	54
Stockholm	58	49	20	6
Frouenboro	58	48	18	16
Stickholm	58	23	18	24
Yaffro	58	10	18	58
Fuland	57	42	19	12
Chiping	56	53	18	27
Fastinboro	56	2	15	49
Scarlet Island	56	40	16	02
Elsinbro	56	46	16	00
Cape Cole	57	00	15	36
Nading	57	53	15	04
Holm Sound	59	8	13	44
Mordo	58	37	12	2
Walle Sound	58	25	11	40
Long Sound	59	7	12	54

From Naze of Norway to Archangel.

The Places Names.	North Latitud.	East Longit.
	D.	M.	D.	M.
The Naze of Norway	58	00	10	26
Stave Angor	58	57	9	44
Out Shers	59	7	8	30
Bomal	59	31	9	04
Harla Island	60	24	9	02
Katts Nass	61	54	8	06
Swin	62	40	9	10
Gallee	62	52	9	46
Gripo	63	40	11	26
Ross Illes	67	1	13	30
Werro	67	38	13	52
Lowfat	68	30	14	40
Zanham	70	28	18	32
Assumption	71	7	20	38
North Cape	71	22	22	6
Skitanboro	70	56	24	2
Island Kilding	68	54	26	16
Cape Race	65	49	29	28
Cape Gallant	67	11	28	56
Cape Crace	65	17	28	54
Fox Naze	64	12	26	31
Archangel	63	22	26	46

The Coast of Greenland.

The Places Names.	North Latitud.	East Longit
	D.	M.	D.	M.
Cherri Island.	74	34	20	32
Hope Island	76	13	23	16
Hopeless Isles	77	00	22	54
Nageo Point	77	10	23	38
Duckus Cone	77	45	22	54
Cape Blande	78	25	23	26
Helis Sound	79	27	24	19
Point Lookcut	76	25	20	18
Horn Sound	77	7	20	00
Ball Sound	77	34	20	3
Foe Sound	78	38	20	45
Beare Sound	79	15	19	55
Black Point	78	32	18	34
Cape Cold	79	00	17	56
Fair Foreland	79	15	19	29

The Coast of the North-West Discovery.

The Places Names.	North Latitud.	West Longit.
	D.	M.	D.	M.
Cape Farewell	59	00	41	50
Sir Thomas Smith's Bay	79	10	79	50
Botton's Isles	60	20	62	50
Belisle	51	2	48	44
Where the Table is be∣gun, on the Coast of Terra Nova.

By multiplying the Hours by 15, and dividing the Minutes of Hours, if there be any, by 4, so will the number of Degrees arise; and if there remain any Minutes after the Division, they must be multiplied again by 15, and so will the number of Minutes of Degrees arise, by which these Places are distant from each other, which Distance is called the Difference of Longitude of that Place for which the Tables were calculated, if the other Place be Eastward of the first; but if it be more Westward, it is to be substracted from the Longitude of the other.

And this is the way we have endeavoured to settle the Longitude, with as much neerness to the truth as possible we could. I have not only made use of my own Cal∣culation of the Difference of Meridians of Places, as I have often used at Barbadoes and Virginia, or any other Place, from the Meridian of the Lizard; but I have also ob∣tained them from the best Geographical Charts that are yet discovered, and the latest Tables made; and so by consulting with the able and skilful Mariners, that have used the East and West India; by the first we have informed our selves for the setling ehe Longitude of Places in the East India, with the best approved Authors: as in page 161 of Harmonicon Coeleste we find the Difference of Meridians betwixt Calicut in East-India and London to be 5 hours and 50 min. which being converted into Degrees and Minutes as before directed, is 37 deg. 30 min. the Difference of the Meridian of London and Calicut; and the Difference of the Meridian of London and the Lizard,

5 deg. 24 min. added to it, gives the Difference of the Meridian of Calicut and the Lizard, it makes 92 deg. 54 min. the Difference of Longitude to the Eastward of the Meridian of the Lizard.

And Macao in the Kingdom of Pegu, whose Difference of Meridians with the City of London is 7 ho. 9 min. which is 107 deg. 15 min. the former Difference added makes Macao to the Eastward of the Lizard 112 deg. 39 min. The Difference betwixt the Tables before-going, and the Eclipses, in the Difference of Meridians of Calicut and London, is very small, the Tables 4 min. more; and the Difference between the Eclipses and the Tables is 22 min. more. Then the Observation of Macao and London, being so small, it may very well be born withal: And we have setled the Longitude of the West India, according to long and approved Experience of Voyages of my self and others, from the Lizard to Barbadoes, and to Cape Henry and Charles the Capes of Virginia.

The Latitude of a Place is the Distance of the Zenith, or the Vertical Point thereof from the Aequator, or the Height of the Pole elevated above the Horizon. You have been shewed several ways already, for the finding the Poles Elevation above the Hori∣zon. but this Rule will not be impertinent to this Place, being not named before, which is by the Stars thus.

You must observe some Fixed Star in the Heavens, which is neer the Pole, and that never sets in that Region: Thus, you must observe the least and also the greatest Alti∣tude of the said Star, when he doth come to the Meridian under the Pole, and also above the Pole; which done, you must add the least Altitude to the greatest, and so the half of the deg. and min. thus numbred together, will be the Elevation of the Role, or Latitude of the Place.

An Example whereof may be this. The first Star of the three in the Tail of the Great Bear, in his least Altitude, observed at Bristol, is about 10 deg. 59 min. and the greatest Altitude of the same, when he is above the Pole, is found to be neerest 91 deg. 59 min. both which Numbers being added together, do make 102 deg. 58 min. the half of that same is 51 deg. 29 min. the true Latitude or Elevation of the Pole.

You may take notice, I begin the Longitude at the Meridian of the most Southern Parts of England at the Lizard, and increases on each side of that Meridian, from 1 deg. to 180 deg. both Eastward and Westward,; therefore you must note, That by these Tables all Places, that lie to the Eastward of the Meridian of the Lizard, are called East Longitude; and all Places on the West side of the Meridian of the Lizard, is called West Longitude.

Therefore a Ship being in East Longitude, sailing to the Eastward, she increas∣eth her Longitude; but sailing to the Westward, it decreaseth. And likewise if a Ship be to the Westward of the Lizard, that is, in West Longitude, and saileth to the Westward, the Longitude increaseth; but sailing to the Eastward, the Longitude de∣creaseth.

You must note, the Sun riseth to the Eastward, therefore all the Stars, and are carried West; and that all Places that are to the Eastward of the Meridian of the Lizard, the Sun comes to their Meridian first, according the time it is to the East∣ward of the Meridian of the Lizard: As you may note what was before directed, That every 15 deg. is an Hour, and 4 min. a Degree: Therefore in the former Exam∣ple of Calicut, whose Difference of Meridians is 5 ho. 50 min. that is to say, the Sun is on the Meridian in the East India at Calicut at 10 min. past 6 a Clock in the morn∣ing here at the Lizard, that is, 5 ho. 50 m. sooner than he comes to the Meridian of the Lizard, to make here 12 a Clock at Noon. And so on the contrary, lesser to the West by every 15 deg. As for Example.

The Difference of Longitude betwixt the Meridian of the Lizard and Barbadoes is 52 deg. 58 min. that converted into Time is 3 hours 42 min. the time the Sun comes to the Meridian of the Lizard, before it comes to the Meridian of Barbadoes; that is to say, it is our 3 a Clock 42 min. past at the Lizard in the afternoon, before it is 12 at Noon in the Barbadoes.

You may take notice, I took my first Latitude and Longitude from the Northern parts of Newfound-land, to the Westward at Cape Homblanto, neer Bell-ile, and so have coasted all round the Bay of Mexico, and taken the West India Islands in the way,

and so round the Coast by Brazil, and through the Straights of Magellane to Nova Albion, where Sir Francis Drake was on the back side of New-England, in the South Sea; and from thence to the East India, first the Islands, and then the Main Land, and back by Cape Bon Esprance, and round the Coast of Guinney and Barbary down from Tangire, and upon the Christian Shore to Giblitore and Tocke in the Canary Islands and Westward Islands, and so along the Coast from Cales to Callis, and from the Lizard to Newcastle, and from thence along the Coast of Scotland to Skey Island, and along the Coast from Calis to the Scaw, and along the Coast from the Lizard to the Isle of Man, and round the Coast of Ireland to the Sea-coast of Iseland, and so from the Scaw round the Sound, by the Nase of Norway to Archangel, and about by the Sea-coast of Greenland by the North-west Discovery, to the Coast of New-found Land, where first I began; whereby you may see I have traced a Path, or coasted round to the most Chief Harbours, Head-lands, and Islands in the World, by the Tables. And so I shall conclude with these Verses in Mr. Philips's Preface.

When Drake and Candish Sail'd the World about, And many Heroes found new Countries out To Britains Glory, and their lasting Fame: Were we like-minded, we might do the same.

The End of the Fourth Book.

Notes

• * 1.1

  I found 11 degr. in a Field at S. George's and Bristol being four miles di∣stant; and I made five Observati∣ons, as in p. 330. and differed ¼ of a degr. only.
• * 1.2

  How we keep our Reckoning.
• * 1.3

  The Rule of keeping a perfect Sea-Reckoning is best set down in particular after the general true Sea-Chart, in Chap. 17. of Great Circle Sail∣ing.
• * 1.4

  Apr.
• * 1.5

  May
• * 1.6

  〈 math 〉〈 math 〉
• * 1.7

  deg.	min.
  51	22
  38	11
  13	11
  Latitude of Bar∣badoes.
• * 1.8

  But add the difference of Lati∣tude as you sail to the Northward
• * 1.9

  The Errors of the Plain Sea-Chart.
• * 1.10

  	mil.
  South	8
  Current	3
  Goes a head	58
• * 1.11

  	mil.
  Current	8
  Ships Way	3
  Falls a stern	5
• * 1.12

  〈 math 〉〈 math 〉
• * 1.13

  20

  10

  200

  200

  The Square 400
• * 1.14

  1 Course S. W. ½ W. 2 Course S. S. E. ½ E.
• * 1.15

  Radius 10000, to Secant 20000.
• * 1.16

  Longitude.
  	d.	m.
  Lundy	25	52
  	360	00
  	385	52
  Barbad.	332	57
  Differ.	52	55
  	20
  	1040
  	18 ⅓
  	1058
• * 1.17

  51 d.	22 m.
  13	10
  38	12 (4
  20	3
  760
  4
  764
• * 1.18

  As was shewed in the last Ex∣ample.
• * 1.19

  Then you must put down the Course and Di∣stance and Me∣ridian distance in the Head of your Journal.
• * 1.20

  12002

  9345

  2657
• * 1.21

  〈 math 〉〈 math 〉
• * 1.22

  〈 math 〉〈 math 〉
• * 1.23

  Divide the Dif∣ference 197:5 by 20, the Quo∣tient will shew you the number of Degrees of the Aequinocti∣al and min. that makes the length of the Meridian Line; as for 6 deg. from A to D, will be 9 d. 55 m. of the Aequator.
• * 1.24

  You may divide every 10 Mi∣nutes into two Equal parts; so is every Degree divided into 5 min. as AB & DC into 10 m.
• * 1.25

  From D.
• * 1.26

  Plain Sailing, Mercator's.
• * 1.27

  This Arch of a Great Circle over two Places in Latitude 40 d. 00 m. and Difference of Longitude 70 deg. is the Line PW in the Di∣agram of the 14. Chap. of part of the Globe in Pla∣no.
• * 1.28

  	Latitude.
  Landse.	50:15
  Ribedev.	43:30
  Distance	7:45
  	20
  	140
  	15
  Leagues	155
  Mult. by	3
  Miles	465
• * 1.29

  To draw a Great Circle from the Ama∣zones over Lun∣dy, put the Dif∣ference of Lon∣gitude on the West Side from AE to G; and draw the prickt Line NS, N for the North, and S for the South Pole: and through G draw the Azimuth Circle NGS, and draw the Parrallel of Latitude CZC; and through Z draw the Arch AEZRVQ, for the Circle which passeth from AE Amazones to Z Lundy.
• * 1.30

  Measure NR on the half Tan∣gents, and the Angle of Posi∣tion, and the Distance is all one as before.
• * 1.31

  60	14
  73	51
  134	05
• * 1.32

  Meridian Altitude.

  33 d. Compl. 57 deg.

  77 d. Compl. 13 deg.

  Sum 70

  ½ Sum 35

  Mid. Lat. 15

  Nor. Ship 50 lat.

  South Ship 20 lat.
• * 1.33

  1306 P.

  1157 M.

  1140 G.

  Leag. 17

  166
• * 1.34

  How to find the Centers of the Meridian-cir∣cles.
• * 1.35

  How to find the Centers of the Parallels of Latitude.
• * 1.36

  It serves for the same numb. of deg. in South Latitude.
• * 1.37

  You may mea∣sure the Distan∣ces thus. Take BL the Di∣stance of the two Places, and put it upon the Me∣ridian BZ of Barbadoes the second Place, & you will find the Parallels of Latitude to be 57 d. the true Distance, as be∣fore sound.
• * 1.38

  How by the La∣titude well ob∣served, and the Rhomb discreet∣ly rectified, to find the La∣titude, Rhomb, and Longitude, and Distance, having two of them known, by an Arithmetical Rule, and by them to prick the same down in a Blank Chart or Mercator's Plat.
• * 1.39

  How to make the Meridian-line by the for∣mer Geometri∣cal Projection.
• * 1.40

  A Scale of Leagues.
• * 1.41

  The Protracting Quadrant.
• * 1.42

  Not that I do affirm the Vari∣ation to be Ea∣sterly for I know it to be 1 d. 30 m. West; but being neer the truth or not, it serves to exemplifie the Rule, that being the end for which this Ex∣ample is made.
• * 1.43

  But if you sail all on one Course, the Rule is in the third Probl, of Mercator Sailing.
• * 1.44

  As Radius 90 deg. To Tang. Rhomb: So difference of Lat. in Merid. parts, To diffe∣rence of Longi∣tude in Leagues or Miles.
• * 1.45

  8 min. is

  2 7/10 Lea. neer

  1201 to 520

  so 27:) 27

  3640

  1040

  14040
• * 1.46

  〈 math 〉〈 math 〉
• * 1.47

  This is because I find my self to the Northward, that is, less to the Southward by 11 m. than by Dead Reckon∣ing, & therefore less to the West∣ward 1 50/100 Leag. or so much to the Eastward, by reason my Course is in the S. W. Quarter, it must be corre∣cted in the con∣trary Quarter.
• * 1.48

  In sailing East and West, you have a Rule in Probl. 7. of sail∣ing by Mercator or Mr. Wright's Chart.
• * 1.49

  I hope this way will find good acceptation with the ingenious Mariner or Artist.