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 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.

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.