Problem XX. If a Ship fails S. by E. 36 Minutes in a Current, and then arrives at a Port which lieth from the Place fhe departed from SE. by S. Distance 54 Minutes: I demand the Current's Motion both in Quality and Quantity; that is, How it fetteth, and how fast?

Afwer. The Current fetteth South 57d 21m. East; or ESE. is the Drift of the Current as to Quality, and Minutes 24.9 Tenths is its Drift as to Quantity; and is demonftrated by the Plane Scale after this manner;

1. As before, having described a Circle, &c. Lay one Point from S towards E, and by it and A, draw a S. by E. Line 36 Minutes long, from A to B;

2. Lay three Points from S towards E, and by it and A, draw a SE. by S. Line 54 Minutes long, from A to C.

3. Then draw a Line from B to C, and it's done: For the Angle ACB measured (on the Scale) fheweth the Current's Motion as to its Quality, which Way from the SE. by S. and the Side BC measured (on the Scale) fheweth the Current's Motion, as to its Quantity, how much, or how faft.

But by Plane Trigonometry, 'tis thus,

In the Oblique Triangle ABC, there are given two Sides, and an included Angle; that is, the Side AC 54 Minutes, the Side AB 36 Minutes, and the Angle BAC two Points, equal to 22d. 30m. to find the Angles ABC, ACB, and the Side, BC; which is wrought by Axiom the third, and is like the third Problem of this Section.

Problem XXI. Suppose a Ship fails from a certain Cape, or Headland, and (by the Log) in 24 Hours, runneth SSW. 49 Minutes, in a Current fetting between the N. and the W. and then the Gape did bear ENE. from the Ship, and by Obfervation, the Difference of Latitude was 30 Minutes; I demand the Current's Motion; that is, upon what Point of the Compass, and how fast?

Anfw. The Current fets North 74d. 7m. Weft, or WNW. half W. neareft, and at the Rate of Minutes 2.325 an Hour, and is thus demonftrated by the Plane Scale.

1. After the Circle is defcribed, quartered, &c. lay two Points from S towards W, and by it and A draw a SSW. Line 49 Minutes long, from A to B.

2. Lay fix Points from S towards W, and by it and A, draw a WSW. and ENE, Line AC.

3. Lay 30 Minutes (on the Meridian) from A to 1), and from D draw a Weft Line Parallel to AW, to cut the WSW. 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 theweth 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 Hypotenufe AC, which is done by Axiom the firft 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.

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'S
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 the eafier understood.

Section I. The Defcription and Ufe of Mr. Wright's Chart. THIS Projection fuppofeth the Earth and Sea to make one round Body or Globe: In order to the right underflanding 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 thofe two Poles, or equally diftant from cach, is drawn a Circle round the Globe, called the Equator;

from which Latitude taketh its beginning, and in which Longitude is reckoned; as EA Q

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

4. Thofe Circles which are parallel to the Equator, are called Parallels of Latitude; as a lt, Zlt, &c. and are reprefented in the Chart by the Eaft and Weft 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 Eastward, 'till it end (where it first 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 begins at the Meridian of London, and from thence is counted Eafterly, Eaft Longitude 180 Degrees; and Wefterly, West Longitude 180 Degrees, at which both Longitudes end.

9. Difference of Longitude, is that Diftance or Portion of the Equator contained between the Meridians of any two Places, and theweth (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 diminish towards each 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.

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 Defcription 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 Use 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. r. Take the nearest Distance from the proposed 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 stood 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 Teneriff; 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 Eastward and Weftward, 180 Degrees.

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

This is done as before, in the Use 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 Diflance.

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 Distance.

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

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

Cafe 3. Two Places in ene Parallel (that is, differing only in Longitude) being given, to find their Diftamce.

The Rule. 1. Take the Distance between the given Places in the Compasses.

2. Lay that Diftance on the graduated Meridian, fo 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 Fect of the Compaffes, and 'tis the Distance réquired.

Example. I demand the Distance from the Lizard in England, to Pengwin Inland on the Coast of Newfoundland, both being nearly in the Latitude of 50d. oom. North.