To find the Departure it will be, To find the Distance it will be, As co-sine cou. 39 cò. ar. 0.10950 As the co-si. cou. 39° co. ar. 0.10950' Is to the diff. of lat. 266 · 2.42488 Is to the diff. of lat. 266 2.42488 So is the sine cou: 39° 9.79887 | Sọ is rad. 90o

10.00000

2.5343S

To find the Longitude in.

Lizard's long,

5° 12′ W.

0,17225

Diff. of lon. 320 miles or

5' 20 W.

2.33325

10.00000 Long. in

10 32 W.

To the diff of tong: 320.3 2.50550

CASE V.

Both Latitudes and Distance given, to find the Course and Difference of Longitude.

Suppose a ship runs 300 miles N. westerly, from 37° N. lat. and long. 10° 25' W. until she be in lat. 41° N.; what is her cou, and long, in?

To find the Course it will be, To find the Diff. of Lon. it will be,

7.52288 As co-si. mid. lat. 39° co. ar. 0.10950

As the dist. 300 co. ar.

Is to rad. 90°

So is diff. of lat. 240

10.00000 Is to tang. cou. 36.52

2.38021 So is diff. of lat. 240

9.87 501

2.38021

To the co-sine cou. 36° 52′ 9.90309 To d. lon. 231.6=3° 52′ W. 2.36472

Longitude left

Longitude in

CASE VI.

10° 25' W.

14 17 W.

One Latitude, Course, and Departure given, to find the Distance, Difference of Latitude, and Difference of Longitude.

A ship sails E. S. E. from the latitude 50° 10' S. and longitude 100 16 E. until her departure from the meridian be 957 miles; I demand her distance sailed, and the latitude and longitude she is in?

One Latitude, Distance sailed, and Departure from the Meridian given, to find the Course, Difference of Latitude, and Difference of Longitude.

A ship in Latitude 49° 30′ N. and longitude 24° 40′ W. sails south eastward 645 miles, until her departure from the meridian be 500 miles I demand the course steered, and the latitude and longitude the ship is in.

As co-si, m. lat. 46°6'co. ar. 0.15901 Longitude left is
Is to the departure 500 2.69897 Diff. of long. 721, or
So is radius

To diff of long. 721.1 2.85798

10.00000

MERCATOR'S SAILING.

PLANE SAILING, as has been before observed, supposes the earth and sea to be in the form of a bowling-green, on which the meridians are parallel, and the degrees of latitude and longitude equal in all places; but the earth and sea compose a round body, or globe, on which the degrees of latitude are equal in all places, and the degrees of longitude decrease from the equator in proportion to the sine-complements of the latitude.

Though the meridians all meet at the poles, and the parallels to the equator continually decrease, and that in proportion to the cosines of their latitudes; yet in old sea-charts the meridians were drawn parallel to each other, and, consequently, the parallels of latitude made equal to the equator, and so a degree of longitude on any parallel, as large as a degree on the equator: also, in these charts, the degrees of latitude were still represented (as they are in themselves) equal to each other, and to those of the equator; by these means the degrees of longitude being increased beyond their just proportion, and the more so the nearer they approached the poles, the degrees of latitude at the same time remaining the same; it is evident places must be very crroneously marked down upon those charts, with respect to their latitude and longitude, and, consequently, their bearings from one another must be very false. To remedy this inconvenience, so as still to keep the meridians parallel, it is plain we must lengthen the degrees of latitude in the same proportion as those of longitude are, that so the proportion in easting or westing may be the same with that of northing or southing; and, consequently, the bearing of places

from each other to be the same upon the chart as upon the globe

itself.

The difficulty in constructing a true sea-chart consists in finding a proper manner of applying the surface of a globe to a plane; which Mr. WRIGHT, an Englishman, by an ingenious conception, happily accomplished.

He conceived the surface of this globe to swell like a bladder while it is blowing up from the equator towards the poles, proportionally in latitude as it does in longitude, until every part of its surface meet that of a concave cylinder impressed on it, whose diameter was equal to the globe's diameter. The equator being thus confined, the parts towards the poles must be extended, both in latitude and longitude, to fill up the cylinder, or figure in the form of a rolling-stone, and impress on its concave surface the lines drawn on the surface of the globe. This cylinder being cut on one of the meridians, from north to south, and laid open, would represent a true sea-chart, the parts of which bear the same proportion to one another as the corresponding parts of the globe do; and on which ail the lines will be right lines; having every parallel of latitude on the globe increased till it is equal to the equator; and so the distance of the meridians in these parallels will become equal to their distance at the equator; consequently, the meridians on the chart are expressed by parallel right lines.

Also the meridians being lengthened as the parallels are increased, every degree of latitude is lengthened in the same proportion as the degrees of longitude are increased; therefore, the distance of the parallels of latitude grows wider and wider as they approach the poles.

Mr. GERRARD MERCATOR, a Fleming, in 1556, published a similar chart; but in what manner it was constructed he did not show, neither were those degrees in their true proportion; whence called Mercator's Chart.

Mr. WRIGHT, in 1599, published the Principles of the True Sea-Chart, and how to construct it on the following principles:

viz.

That the distance between any two meridians at the equator is in proportion to their distance in any parallel of latitude, as the radius is to the co-sine of that latitude:

That any part of a parallel of latitude is to a like part of the meridian, as the radius is to the secant of that parallel:

And, that the distance of any parallel of latitude from the equator, is equal to the sum of the secants of all the arches between the equator and that parallel.

From these principles, Mr. Wright set about forming a Table, by the continual additions of secants, of all the parallels of latitude, beginning with one minute, which he made radius, and thereto adding the second parallel of 2 minutes, and to the sum of these two, the secant of 3 minutes, &c. The Table thus formed, is that which is commonly called the Table of Meridional Parts, by mea