3. Lay 30 Minutes (on the Meridian) from A to D, and from D draw a Welt Line Parallel to AW, to cut the WŚW. Line in C.

4. Then Draw a Line from B to C, and it's done For the Angle ABC being measured on the Scale, fheweth the Current's Motion from SSW. and the Side BC being measured fheweth how much the Current fet the Ship.

By Plane Trigonometry, it's thus ;

1. In the Right Angle Triangle ADC, there is given the Leg AD 30 Minutes, Angle DAC fix Points, and Angle ACD two Points; to find the Hypothenufe AC, which is done by Axiom the first of Plane Trigonometry.

2. Then in the Oblique Triangle ABC, there is given the Side AB 49 Minutes, the Side AC found before, and the included Angle BAC 4 Points, equal to 45d. to find the Angle ABC, (the Current's Motion from SSW.) and the Side BC, its Motion how much, which is folved by Axiom the 3d, as was the last Problem. Let this fuffice for the First Part of Navigation, commonly called Plane-Sailing, though many more Problems might be invented. Wright's Sailing is next in order."

CHAPTER IV.

The Second Part of NAVIGATION, or the Doctrine of Plane Right-Angle-Triangles, applied in Problems of Mr. Wright's Sailing (commonly called) MERCATOR'S SAILING.

IT'
T's neceffary to defcribe Mr. Wright's Chart, and fhew the Ufes
thereof, before the Problems of Sailing by it, which, by this
Method, will be eafier understood.

Section I. The Defeription and Use of Mr. Wright's Chart. THIS Projection fuppofeth the Earth and Sea to make one. round Body or Globe: In order to the right understanding of which, obferve the following Definitions.

1. Upon this Earthly Globe are imagined two oppofite Points, one called the North Pole, the other the South Pole; as P and I, Plate 5. Fig. 1.

2. In the Middle between those two Poles, or equally diftant

tor; from which Latitude taketh its beginning, and in which Longitude is reckoned; as # A Q

3. Any Circle drawn through both Poles, is called a Meri- ̈ ́ dian, as PMI, PNI, &c. anfwerable thereunto is any North or South Line drawn in the Chart.

4. Those Circles which are parallel to the Equator, are called Parallels of Latitude; as alt, Zlt, &c. and are reprefented in the Chart by the East and West Lines.

5. Latitude of a Place, is the (neareft) Distance of any Parallel paffing over it from the Equator; from thence counted both Ways to each Pole, ending in 90 Degrees, the greatest Latitude.

6. North Latitude, is on that Side of the Equator towards the North Pole, and South Latitude on the other Side of the Equator, towards the South Pole.

7. Difference of Latitude, is the (nearest) Distance between any two Parallels, and fheweth how far one Place is to the Northward or Southward of another, it never exceeds 180 Degrees.

8. Longitude, is reckoned in the Equator, round which (by fome) it's counted increafing to the Eaffward, 'till it ends (where it firft began) in 360 Degrees, the greatest Longitude: Others (as Mr. Wakely, in his Mariner's Compass Rectified, and also now in the Mariner's New Calendar) reckon it from one Meridian, both Easterly and Wefterly, till both Accounts meet at 180 Degrees in the oppofite Meridian, as in both the aforefaid Books, Longitude with the English begins at the Meridian of London, and from thence is counted Eafterly, Eaft Longitude 180 Degrees; and Wefterly, Weft Longitude 180 Degrees, at which both Longitudes end.

9. Difference of Longitude, is that Distance or Portion of the Equator contained between the Meridians of any two Places, and fheweth (in the Equator) how far the Meridian of one Place is to the Eastward or Weftward of the Meridian of another, and never exceeds 180 Degrees.

From these Definitions, or Principles, there must neceffarily follow thefe Theorems.

1. The Distance of any two Meridians, in any Parallel of Latitude, is less than their Diftance in the Equator, because all Meridians on the Globe meet in the Poles.

2. The Degrees of Longitude diminifh towards cach Pole; and the nearer the Pole, the lefs they are, because the Meridians approach nearer to one another, the farther you fail from the Equator, towards either Pole.

F 2

3. The

3. The Degrees of Latitude are equal in all Places or Parts of the Globe.

4. The Plane Chart, which counteth the Degrees (as well of Longitude as of Latitude) in all Places, to be equal, is notoriously false.

5. Mr. Wright's Projection (commonly known by the Name of Mercator's Chart) wherein (though the Degrees of Longitude are equal, having the Meridians parallel to one another) the Degrees of Latitude are enlarged towards each Pole, in the fame Proportion as the Degrees of Longitude diminish on the Globe, will in all refpects agree with the Globe, and is a true Way of Sailing.

Thefe Definitions and Theorems duly confidered, there needs no further Description of this Chart, it having only this Difference from the Plane Chart before described in Chap. 3. Sect. 2. Page 53, that the Equator is divided and numbered in Degrees, as the graduated Meridian is in the other; the Ufes are as follow.

Problem I. To find the Latitude of any Place in the Chart?

This was taught before (in the Ufe of the Plane Chart) in Page 54, and needs no further Rule or Example.

Problem II. To find the Longitude of any Place in the Chart?

The Rule. 1. Take the nearest Distance from the propofed Place, to any Meridian.

2. Move the Compaffes (being kept at that Distance with one Foot on the Meridian) 'till both Feet come to the Equator, and the Foot which ftood on the propofed Place fheweth its Longitude required?

Example. I demand the Longitude of the Lizard in England?

Anfw. 9d. 42m. according to the old Way of computing the Longitude from the Meridian of Pico Teneriffa; but 5d. 14m. Weft Longitude, counting Eaft and Weft Longitude from the Meridian of London, according to the Mariner's Compafs Rectified.

Note; Some Charts begin Longitude at the Lizard, counting from thence Eaftward and Weftward, 180 Degrees.

Problem III. To find the Courfe or Bearing of any two Places in the Chart.

This is done as before, in the Ufe of the Plane Chart, in Page 55, and needs no Example;

Problem IV. To find the Distance of any two Places in the Chart.

In this Problem are four. Cafes; the two Places may be fituated under one Meridian, under the Equator, or in one Parallel, or they may differ both in Latitude and Longitude.

Cafe 1. Two Places under one Meridian (that is, differing only in Latitude) being given, to find their Distance.

The Rule. Find the Difference of Latitude between the two given Places, and 'tis the Distance required.

How to find the Difference of Latitude between the two Places, has been taught in Chap. III. Sect. III. of Plane-Sailing, in Page 58.

Cafe 2. Two Places in the Equator given, to find their Diflance.

1

The Rule. Find the Difference of Longitude between them, and 'tis the Distance required.

How to find the Difference of Longitude, will be shewed in the next Section, in Page 89.

Cafe 3. Two Places in one Parallel (that is, differing only in Lon-' gitude) being given, to find their Distance.

The Rule. 1. Take the Diftance between the given Places in the Compaffes.

2. Lay that Distance on the graduated Meridian, so that one Foot may be as many Degrees above the Parallel of the given Places, as the other below it, there ftay the Compaffes.

3. Count the Degrees between the Feet of the Compasses, and 'tis the Distance required..

Example. I demand the Diflance from the Lizard in England, to Pengwin Island on the Coast of Newfoundland, both being nearly in the Latitude of 50d. com. North.

Here, The Distance from the Lizard to Pengwin Island applied to the Meridian as directed, will reach from 31d. 30m. to 62d. com. the latter being as much above 5od. oom. as the former is below it; and the Degrees intercepted are 30%, or 610 Leagues, which is the Distance required.

Take the Length of the Degree in the given Latitude, as here from 49d. 30m. to 50d. 30m. turn that over in a strait Line, from the Lizard to Pengwin Island, and it's 30 Times; which fhews the Distance 30d. 30m. as before.

Cafe 4. Two Places differing in Latitude and Longitude, being given, to find their Distance.

The Rule. 1. Take their Difference of Latitude from the Equator.

2. Lay a Ruler on both given Places, apply that Distance fo to the Ruler's Edge, that when one Foot is placed close to the Ruler, and the other turned about, it may juft touch fome East and Weft Line, croffed by the faid Ruler's Edge, there stay the Compaffes.

Then the Distance (by the Ruler's Edge) from the Place where the Compaffes refted, to that Place where the Ruler crolleth the aforefaid Eaft and Weft Line, measured on the Equator, giveth the Distance required.

Example.

1 demand the Distance from the Lizard, to the Island Barbadoes? The Lizard's Latitude is And Barbadoes Latitude is

49d.

12d. 53m.} by Problem 1.

Their Difference of Latitude 36d. 59m.

Then take their Difference of Latitude 36d. 59m. from the Equator, and laying a Ruler on both Places, apply one Foot of the Compaffes fo to the Ruler's Edge, that turning the other about, it may touch an Eaft and Weft Line, croffed by the Ruler; then the Distance (by the Ruler's Edge) from the Place where the Compaffes refted, to the Place where the Ruler crossed the aforefaid Eaft and Weft Line, measured on the Equator, is 57d. 45m. or 1155 Leagues, the Distance required.

And here obferve; the Meridian Line and Line of equal Parts next one to another on the Gunter's Scale, the first represents the Meridian Line, and Degrees of Latitude in a Mercator's Chart; the latter the Equator-Line, and the Degrees of Longitude.