found by Mid. Lat. or Mercator, by Infpection, which will be nearly as above.

A fhip from the Lizard, în lat. 49° 57′ N, and long. 5° 12′ W. is bound to Funchal in Madeira, in lat. 32° 38′ N. and long. 17° 5' W. fteers the following cou. S..S. W. 250 miles, W. 156, S. E. by S. 300, W. by N. 180, and S. 185 miles; required the lat. and long. fhe is in, and her direct cou. and dift, to the intended port?

By finding the diff. of long, for each cou. by calculation, the fhip is in lat. 39° 27' N. and long. 11° 15'W. by Mercator's Sailing; but by working by the whole diff. of lat. and dep. the long. will be 11° 19'W.

The cou. from the fhip to Funchal is S. 34° 19′ W. dist. 495,2 miles by Mercator's Sailing:

And S. 34°23′ W. dift. 495,3 miles, by Mid. Lat. Sailing.

A fhip from lat. 38° 14' N. and long. 25° 56′ W. runs the following courfes and diftances, viz. N. E. by N. & E. 56 miles, N. N. W. 38, N. W. by W. 45, S. S. E. 30, S. by W. 20, and N. E. by N. 60 miles; required the direct cou. and dift. made good, and the lat. and long. the is in?

The cou. is N. 14° E. dift. 108 miles, lat. in 39° 59′ N, long, in 25° 22' W.

Suppofe a fhip in lat. 67° 30' N. and long. 8° 46′ W. fails the following courfes, N. E. 64 miles, N. N. E. 50, N. W. by N. 58, W. N. W. 72, W. 48, S. S. W. 38, S by E. 45, and E. S. E. 40 miles; what lat. and long. is the in?

By working by the whole diff. of lat. and dep. the fhip is in lat. 68° 44' N. and long. 11° 4′ W. But

By finding the diff. of long. for each cou. and dift. fhe is in long. 11° 37 W. by Mid. Lat. Sailing, and 11° 44' W. by Mercator's Sailing.

Having gone through the neceffary Problems in Mercator's Sailing, we fhall now proceed to fhew how the true chart, commonly called Mercator's Chart, may be conftructed either for the whole, or any part of the Terraqueous Globe.

When a Chart is to commence from the Equator, or if the Equator is to run through it.

Having provided a fcale of convenient length, draw a line to reprefent the Equator, and, croffing that at right angles, another to reprefent the meridian of fome known pace, fuch as London, Paris, the Lizard, or any other place whofe longitude is known; the upper end of which will reprefent the north, and the lower the fouth.

From the scale take 60 in your compaffes, and with 1 foot upon the meridian, fet off that diftance on both fides of it upon the equator, if the chart is to contain eaft and weft longitude; but, if it is only to contain weft longitude, lay it off upon the left-hand fide of the meridian, but if easterly, on the right-hand fide, and that

02

will

will point out the degrees of longitude, which may be divided into halves, quarters, or minutes, if required.

Having fet off as many degrees of longitude as you intend the chart fhould contain, through the laft draw a line (or lines) parallel to the meridian, which will be the bounds of the chart eaft and weft.

Having divided the equator as above, proceed to fet off upon the two extreme meridians from the equator, the meridional parts (as found in the Table) belonging to each degree of latitude; that is, take from the fcale in your compaffes the miles answering to one degree in the Table, and, with one foot in the equator, fet off that distance on each fide of it upon the extreme meridians, if the chart is to contain north and fouth latitude; but if only north or fouth, upon one fide of the equator.

Again, take the meridional parts answering to 2 degrees and 3 degrees, &c. in your compaffes, and fet them off upon the meridian, from the equator, as before.

In like manner proceed to set off as many degrees as you intend the chart should contain; or, which will be the fame thing, take the meridional difference of latitude between any 2 parallels, and fet them off severally from the leaft latitude.

Lay a ruler on each of these divifions, and draw lines parallel to the equator, and they will be parallels of latitude, each of which will be enlarged towards the poles, in proportion as the degrees of longitude are.

Parallel to the meridian, draw lines through the points, expreffing the degrees of longitude, to cut the parallels of latitude, which bound the chart north and fouth,

The parallels of latitude may alfo be divided into halves, quarters, or minutes, by taking the meridional parts for degrees and minutes, and fetting them off as before.

Draw double lines on the borders of the chart, and mark out the degrees of latitude and longitude; and, in fome convenient place, draw the compafs. In like manner may a chart be made that shall contain any number of degrees and minutes required. When the chart is not to commence from the equator, but is only to ferve from a certain diftance on the meridian, between two parallels on the fame fide of the equator, then the meridians are to be drawn as before, and for the parallels of latitude you are to proceed thus:

From the meridional parts answering to each point of latitude in your chart, fubtract the meridional parts anfwering to the leaft latitude, and fet off the difference feverally from the parallels of the leaft latitude upon the two extreine meridians, and the lines joining these points of the meridian will reprefent the feveral parallels upon the chart.

Let it be required to draw a chart that fhall ferve from the latitude of 14 degrees north, to 52 degrees north, and that fhall contain 25 degrees of longitude weft of the meridian of Greenwich. See the Chart, page 110.

Draw

Draw a line to represent the meridian of Greenwich, from which fet off towards the left hand 25 degrees of weft longitude, as before directed; through the two laft points draw lines parallel to the meridian of London, and thefe will be the extreme meridians, or east and west bounds of your chart.

Having drawn the two meridians on the lower edge of the paper, draw a line perpendicular to the meridians, to reprefent the parallel of 14 degrees north; then, from the meridional parts anfwering to 15 degrees 910, fubtract the meridional parts anfwering to 14 degrees 849, and take the difference, 61, in your compafles, and fet it off from the parallel on both the meridians from you, and that will represent the parallel of 15 degrees.

Again, take the meridional parts of 15 degrees 910, from the meridional parts of 16 degrees 973, and fet off the difference 63, upon the meridians from the point reprefenting the parallel of 15 degrees, and that will reprefent the parallel of 16 degrees. In like manner proceed to fet off the parallels upon the meridians.

Or, if the meridional parts of 14 degrees be fubtracted from the meridional parts of every fucceeding parallel, and the difference be fet off from the parallel of 14 degrees upon the meridians, theie points will reprefent the feveral enlarged parallels of latitude, the fame as before; and, if it be required that the meridians fhould be divided into degrees and minutes, the meridional parts for fuch must be taken from the Table, and fet off as above.

Having fet off as many parallels as you intend the chart should contain, through each point draw parallels; or if you think drawing lines through every degree will crowd your chart too much, you may divide the borders only into fingle degrees, &c. and draw lines through every 5 degrees of latitude and longitude, as in the

chart.

Take from the Table of Latitude and Longitude of Places, the latitude and longitude of each particular place contained within the bounds of the chart, and lay a ruler over its latitude, and another croffing that over its longitude; the points where thefe crofs will represent the propofed place upon the chart. In like manner may any place be readily marked. Hence the particular points of a feacoaft may be laid down as above, and lines properly drawn from point to point will form the outlines of the fea-coafts, islands, &c. to which may be annexed, the depths of water, fetting of currents, and whatever elfe may be thought convenient for the chart to con

tain.

This map or chart is not to be confidered as a juft or similar representation of the earth's furface, for in it the figures of illands and countries are diftorted near the poles.

For

Suppofe an ifland in the latitude 60° N. or S. where the breadth of a degree of longitude is juft half as large as a degree upon the equator. Now, as the degrees of latitude are enlarged in proportion as the degrees of longitude are expanded towards the poles, it is plain, that every point of that ifland or country, being laid down

in

in its proper latitude and longitude, will be reprefented twice as large as it really is.

Hence it follows, that as the degrees of latitude are every where increased, like thofe of longitude, it is plain the bearing between places will be the fame on this chart as on the globe; and the proportions between the latitude and longitude and nautical distances, will be the fame upon this chart as upon the globe.

And fince the meridians in this projection are right lines, it follows, that the rhumbs, which form equal angles with the meridians, will be ftraight lines, which render this projection of the earth's furface much more eafy and proper for the mariner's use than any other.

Gunter's Scales have drawn upon them two lines, one marked N M, fignifying the Nautical Meridian; and the other, directly under it, marked E P, fignifying Equal Parts, or degrees of longitude upon a Mercator's Chart.

Thofe are equal parts, or degrees of longitude, to which the degrees of the nautical meridian are fitted, by increafing them, in their true proportion; hence the limits or bounds of a Mercator's Chart by these lines are cafily made, by transferring the divifions correfponding to the degrees to be used from the scale to the paper the chart is to be drawn upon: but as the degrees drawn by thefe lines are too fmall for the feaman's ufe, it is much better to use a fcale of equal parts as before, and, confequently, the degrees may be made of any proposed length.

By the Latitude and Longitude in, to prick off the Ship on the Chart.

RULE. Lay the ruler across the chart in the latitude your ship is in, then look upon the equator, or line marked with the degrees of longitude, for the longitude your fhip is in by your reckoning, and.fetting one foot of your compaffes in that longitude, take the neareft diftance to fome north and fouth line, and from where that line croffes the edge of the ruler that lies in the given latitude, lay off that fame diftance along the edge in the ruler to the right hand, if the longitude you are in was to the right hand of the north and fouth line; or to the left hand, if it was to the left hand; where this fails will be the place of the fhip; but this will only do when the longitude marked on the chart, and your reckoning of longitude in, are both counted from the fame meridian. Therefore, for a general rule, take the following, viz.

By the Latitude in and Longitude made, to prick off the Ship's Place.

RULE. Set one foot of your compaffes in the place you take your departure from, and take the neareft diftance to fome north or fouth line, and from where that falls upon the equator, or the Jine marked with the degrees of longitude, fet off that diftance the fame way the place lies from it; that is, to the right hand, if the

place

place lies to the right hand of the north and fouth line, or to the left hand if it lies to the weft; and make a mark with a black lead pencil; this mark will ferve to prick off by, till you come to take a new departure; and then rub it out, and make a new one as before.

Then lay a ruler acrofs the chart in the latitude you are in, and taking fo many degrees in your compaffes from the line of longitude, as your longitude made comes to, fet them off from your black-lead mark along the edge of the ruler to the eastward; if the longitude made be ealt, or to the weftward if it be weft; where this falls will be the longitude the thip is in by the chart; from which take the nearest diftance to fome north and fouth line, and from where that line, &c. as in the first cafe.

The ship's place on the chart being found, as before taught, it remains in the next to fhew how to find the bearing and distance of any place from the fhip; and firft,

To find how any Place bears from the Ship.

RULE. Lay a ruler from the place of the ship to the place you would know the bearing of; then fet one foot of your compafles in the centre of fome compafs near the ruler, and take the nearest diftance to the edge of the ruler, then run one foot of your compaffes along by the edge of the ruler, and obferve what point of the compafs the other comes nearest to, which will be the bearing required.

CASE I.

To find the Distance of any Place from the Ship.

If the place be in the fame longitude that the fhip is in; that is, if it bears due north or fouth, then the difference of latitude between them, turned into miles or leagues, will be the distance.

CASE II.

If the place be in the fame latitude the fhip is in; that is, if it bears due eaft or due weft, then take half the diftance between the fhip and the place in your compaffes; and, fetting one foot on the line marked with the degrees of latitude, in the latitude the fhip is in, fee what latitudes the other foot will reach to, both above and below it; the difference between thefe two latitudes will be the diftance required.

CASE III.

When they are neither in the fame Latitude nor in the fame Longitude with the Ship.

RULE. Take the difference of latitude between both places in your compaffes from the equator, or graduated parallel; and lay. ing a ruler over both places, put one foot upon the fhip's place, and

flide